 ## Full Length CLEP College Algebra Practice Test

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### CLEP College Algebra for Beginners

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CLEP College Algebra
Practice Test 2
$$60$$ questions Total time for this section: $$90$$ Minutes You can use a scientific calculator on this test.

1- If $$f(x)= 3 \ x \ – \ 1$$ and $$g(x)=x^2 \ – \ x$$, then find $$(\frac{f}{g})(x)$$.
(A) $$\frac{3 \ x \ -\ 1}{x^2 \ - \ x}$$
(B) $$\frac{x \ - \ 1}{x^2 \ - \ x}$$
(C) $$\frac{x \ - \ 1}{x^2 \ - \ 1}$$
(D) $$\frac{3 \ x \ + \ 1}{x^2 \ + \ x}$$
(E) $$\frac{x^2 \ - \ x}{3 \ x \ - \ 1}$$
2- In the standard $$(x, \ y)$$ coordinate plane, which of the following lines contains the points $$(3, \ - 5)$$ and $$(8, \ 15)$$?
(A) $$y=4 \ x \ - \ 17$$
(B) $$y=\frac{1}{4} \ x \ + \ 13$$
(C) $$y=- \ 4 \ x \ + \ 7$$
(D) $$y=- \frac{1}{4} \ x \ + \ 17$$
(E) $$y= \ 2 \ x \ - \ 11$$
3- If $$\frac{x \ - \ 3}{5}=N$$ and $$N=6$$, what is the value of $$x$$?
(A) $$25$$
(B) $$28$$
(C) $$30$$
(D) $$33$$
(E) $$35$$
4- Which of the following is equal to $$b^\frac{3}{5}$$?
(A) $$\sqrt{b^{\frac{5}{3}}}$$
(B) $$b^\frac{5}{3}$$
(C) $$\sqrt{b^3}$$
(D) $$\sqrt{b^5}$$
(E) $$\sqrt{b^3}$$
5- If the interior angles of a quadrilateral are in the ratio $$1: \ 2: \ 3: \ 4$$, what is the measure of the largest angle?
(A) $$36^\circ$$
(B) $$72^\circ$$
(C) $$108^\circ$$
(D) $$144^\circ$$
(E) $$180^\circ$$
6- If the area of a circle is $$64$$ square meters, what is its diameter?
(A) $$8 \ π$$
(B) $$8\sqrt{π}$$
(C) $$\frac{8\sqrt{π}}{π}$$
(D) $$\frac{8}{π}$$
(E) $$64 \ π^2$$
7- For $$i=\sqrt{- \ 1}$$, which of the following is equivalent of  $$\frac{2 + \ 3 \ i}{5 \ - \ 2 \ i}$$?
(A) $$\frac{3\ + \ 2 \ i}{5}$$
(B) $$5 \ + \ 3 \ i$$
(C) $$\frac{4 \ + \ 19 \ i}{29}$$
(D) $$\frac{4 \ + \ 19 \ i}{20}$$
(E) $$\frac{4 \ + \ 21 \ i}{20}$$
8- If function is defined as $$f(x)=bx^2 \ + \ 15$$, and $$b$$ is a constant and $$f(2)=35$$. What is the value of $$f(3)$$?
(A) $$25$$
(B) $$35$$
(C) $$60$$
(D) $$65$$
(E) $$75$$
9- An angle is equal to one fifth of its supplement. What is the measure of that angle?
(A) $$20$$
(B) $$30$$
(C) $$45$$
(D) $$60$$
(E) $$90$$
10- What is the value of $$x$$ in the following system of equations?
$$2 \ x \ + \ 5 \ y =11$$
$$4 \ x \ - \ 2 \ y =- 14$$
(A) $$- \ 1$$
(B) $$1$$
(C) $$- \ 2$$
(D) $$4$$
(E) $$8$$
11- Calculate $$f(4)$$ for the function $$f(x)=3 \ x^2 \ - \ 4$$.
(A) $$44$$
(B) $$40$$
(C) $$38$$
(D) $$30$$
(E) $$25$$
12- What is the sum of all values of n that satisfies $$2 \ n^2 \ + \ 16 \ n \ + \ 24=0$$?
(A) $$8$$
(B) $$4$$
(C) $$- \ 4$$
(D) $$- \ 8$$
(E) $$- \ 10$$
13- In the standard $$(x, \ y)$$ coordinate system plane, what is the area of the circle with the following equation?
$$(x \ + \ 2)^2 \ + \ (y \ - \ 4)^2=16$$
(A) $$8 \ π$$
(B) $$16 \ π$$
(C) $$64 \ π$$
(D) $$64$$
(E) $$128$$
14- Convert $$670,000$$ to scientific notation.
(A) $$6.70 \ × \ 1000$$
(B) $$6.70 \ × \ 10^{-5}$$
(C) $$6.7 \ × \ 100$$
(D) $$6.7 \ × \ 10^5$$
(E) $$6.7 \ × \ 10^4$$
15- For $$i=\sqrt{- 1}$$, what is the value of  $$\frac{3 \ + \ 2 \ i}{5 \ + \ i}$$ ?
(A) $$i$$
(B) $$\frac{32 \ i}{5}$$
(C) $$\frac{17 \ - \ i}{5}$$
(D) $$\frac{17 \ + \ 7 \ i}{26}$$
(E) $$3 \ + \ i$$
16- The equation above represents a parabola in the $$x \ y \ -$$plane.
Which of the following equivalent forms of the equation displays the $$x \ -$$intercepts of the parabola as constants or coefficients?
$$y=x^2 \ - \ 7 \ x \ + \ 12$$
(A) $$y=x \ + \ 3$$
(B) $$y=x \ (x \ - \ 7)$$
(C) $$y=(x \ + \ 3) \ (x \ + \ 4)$$
(D) $$y=(x \ - \ 3) \ (x \ - \ 4)$$
(E) $$y=(x \ - \ 3) \ (x \ - \ 2)$$
17- The function $$g(x)$$ is defined by a polynomial.
Some values of $$x$$ and $$g(x)$$ are shown in the table below. Which of the following must be a factor of $$g(x)$$?
 $$x$$ $$g(x)$$ $$0$$ $$5$$ $$1$$ $$4$$ $$2$$ $$0$$
(A) $$x$$
(B) $$x \ - \ 1$$
(C) $$x \ - \ 2$$
(D) $$x \ + \ 1$$
(E) $$x \ + \ 3$$
18- What is the value of $$\frac{4 \ b}{c}$$ when $$\frac{c}{b}=2$$
(A) $$8$$
(B) $$4$$
(C) $$2$$
(D) $$1$$
(E) $$0$$
19- Which of the following is equivalent to  $$\frac{x \ + \ (4 \ x)^2 \ + \ (3 \ x)^3}{x}$$?
(A) $$16 \ x^2 \ + \ 27 \ x \ + \ 1$$
(B) $$27 \ x^2 \ + \ 16 \ x \ + \ 1$$
(C) $$16 \ x^2 \ + \ 27 \ x$$
(D) $$27 \ x^3 \ + \ 16 \ x^2 \ + \ 1$$
(E) $$27 \ x^2 \ + \ 16 \ x$$
20- If  $$\frac{a \ - \ b}{b}=\frac{10}{11}$$, then which of the following must be true?
(A) $$\frac{a}{b}=\frac{11}{10}$$
(B) $$\frac{a}{b}=\frac{21}{11}$$
(C) $$\frac{a}{b}=\frac{11}{21}$$
(D) $$\frac{a}{b}=\frac{21}{10}$$
(E) $$\frac{a}{b}=\frac{9}{11}$$
21- Which of the following lines is parallel to: $$6 \ y \ - \ 2 \ x =24$$
(A) $$y=\frac{1}{3} \ x \ + \ 2$$
(B) $$y=3 \ x \ + \ 5$$
(C) $$y=x \ - \ 2$$
(D) $$y=2 \ x \ - \ 1$$
(E) $$y=4 \ x \ - \ 1$$
22- construction company is building a wall.
The company can build $$30$$ cm of the wall per minute.
After $$40$$ minutes $$\frac{3}{4}$$ of the wall is completed. How many meters is the wall?
(A) $$6$$
(B) $$8$$
(C) $$14$$
(D) $$16$$
(E) $$20$$
23- What is the solution of the following inequality?
$$| \ x \ - \ 2 \ | \ ≥ \ 3$$
(A) $$x \ ≥ \ 5 \ ∪ \ x \ ≤ \ - \ 1$$
(B) $$- \ 1 \ ≤ \ x \ ≤ \ 5$$
(C) $$x \ ≥ \ 5$$
(D) $$x \ ≤ \ - \ 1$$
(E) Set of real numbers
24- When $$5$$ times the number $$x$$ is added to $$10$$, the result is $$35$$. What is the result when $$3$$ times $$x$$ is added to $$6$$?
(A) $$10$$
(B) $$15$$
(C) $$21$$
(D) $$25$$
(E) $$28$$
25- If $$3 \ h \ + \ g=8 \ h \ + \ 4$$, what is $$g$$ in terms of $$h$$?
(A) $$h=5 \ g \ - \ 4$$
(B) $$g=5 \ h \ + \ 4$$
(C) $$h=4 \ g$$
(D) $$g=h \ + \ 1$$
(E)  $$g=5 \ h \ + \ 1$$
26- If $$8 \ + \ 2 \ x$$  is $$16$$ more than $$20$$, what is the value of $$6 \ x$$?
(A)  $$40$$
(B)  $$55$$
(C)  $$62$$
(D)  $$84$$
(E)  $$88$$
27- If $$a \ - \ b \ > \ 10$$ and $$a \ + \ b \ < \ 14$$, which of the following pairs could not be the values of $$a$$ and $$b$$?
(A) $$(11, \ 0)$$
(B) $$(13, \ 2)$$
(C) $$(13, \ 0)$$
(D) $$(12, \ 1)$$
(E) $$(12, \ 2)$$
28- Simplify.
$$4 \ x^2 \ y^3 \ + \ 5 \ x^3 \ y^5 \ - \ (5 \ x^2 \ y^3 \ - \ 2 \ x^3 \ y^5)$$
(A) $$- \ x^2 \ y^3$$
(B) $$6 \ x^2 \ y^3 \ – \ x^3 \ y^5$$
(C) $$7 \ x^2 \ y^3$$
(D) $$7 \ x^3 \ y^5 \ - \ x^2 \ y^3$$
(E) $$6 \ x^5 \ y^8$$

### 5 CLEP College Algebra Practice Tests

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29- What are the zeroes of the function $$f(x)=x^3 \ + \ 5 \ x^2 \ + \ 6 \ x$$?
(A) $$0$$
(B) $$– \ 2, \ – \ 3$$
(C) $$0, \ 2, \ 3$$
(D) $$– \ 1, \ – \ 3$$
(E) $$0, \ – \ 2, \ – \ 3$$
30- If   $$x \ + \ sin^2 \ a \ + \ cos^2 \ a=3$$, then $$x =$$ ?
(A) $$1$$
(B) $$2$$
(C) $$3$$
(D) $$4$$
(E) $$5$$
31- If $$\sqrt{6 \ x}= \sqrt{y}$$, then $$x=$$
(A) $$6\ y$$
(B) $$\sqrt{\frac{y}{6}}$$
(C) $$\sqrt{6\ y}$$
(D) $$y^2$$
(E) $$\frac{y}{6}$$
32- The average weight of $$18$$ girls in a class is $$60$$ kg and the average weight of $$32$$ boys in the same class is $$62$$ kg.
What is the average weight of all the $$50$$ students in that class?
(A) $$60$$
(B) $$61.28$$
(C) $$61.68$$
(D) $$61.90$$
(E) $$62.20$$
33- If $$y=(- \ 3 \ x^3)^2$$, which of the following expressions is equal to $$y$$?
(A) $$- \ 6 \ x^5$$
(B) $$- \ 6 \ x^6$$
(C) $$6 \ x^5$$
(D) $$9 \ x^5$$
(E) $$9 \ x^6$$
34- What is the value of the expression $$5 \ (x \ - \ 2 \ y) \ + \ (2 \ - \ x)^2$$ when $$x=3$$ and $$= -\ 2$$ ?
(A) $$- \ 4$$
(B) $$20$$
(C) $$36$$
(D) $$50$$
(E) $$80$$
35- What is the value of $$x$$ in the following system of equations?
$$5 \ x \ + \ 2 \ y = 3$$
$$y = x$$
(A) $$x=\frac{3}{7}$$
(B) $$x=\frac{1}{3}$$
(C) $$x=\frac{2}{3}$$
(D) $$x=\frac{4}{3}$$
(E) $$x=\frac{5}{3}$$
36- In a hotel, there are $$5$$ floors and $$x$$ rooms on each floor.
If each room has exactly $$y$$ chairs, which of the following gives the total number of chairs in the hotel?
(A) $$5 \ x \ y$$
(B) $$2 \ x \ y$$
(C) $$x \ + \ y$$
(D) $$x \ + \ 5 \ y$$
(E) $$2 \ x \ + \ 5 \ y$$
37- If $$α=2 \ β$$ and $$β=3 \ γ$$, how many $$α$$ are equal to $$36 \ γ$$ ?
(A) $$12$$
(B) $$2$$
(C) $$6$$
(D) $$4$$
(E) $$1$$
38- Which of the following is one solution of this equation?
$$x^2 \ + \ 2 \ x \ - \ 5 =0$$
(A) $$\sqrt{6} \ - \ 1$$
(B) $$\sqrt{2} \ + \ 1$$
(C) $$\sqrt{6} \ + \ 1$$
(D) $$\sqrt{2} \ - \ 1$$
(E) $$\sqrt{12}$$
39- Simplify $$\frac{4 \ - \ 3 \ i}{-\ 4 \ i}$$ ?
(A) $$\frac{3}{4} \ + \ i$$
(B) $$\frac{3}{4} \ - \ i$$
(C) $$\frac{1}{4} \ - \ i$$
(D) $$\frac{1}{4} \ + \ i$$
(E) $$i$$
40- Which of the following is the sum of the two polynomials shown above?
$$4 \ x^2 \ + \ 6 \ x \ -\ 3$$ , $$3 \ x^2 \ - \ 5 \ x \ + \ 8$$
 $$x$$ $$1$$ $$2$$ $$3$$ $$g(x)$$ $$-\ 1$$ $$-\ 3$$ $$-\ 5$$
(A) $$5 \ x^2 \ + \ 3 \ x \ + \ 4$$
(B) $$4 \ x^2 \ - \ 6 \ x \ + \ 3$$
(C) $$7 \ x^2 \ + \ x \ + \ 5$$
(D) $$7 \ x^2 \ + \ 5 \ x \ + \ 1$$
(E) $$x^2 \ + \ 5 \ x \ + \ 4$$
41- The table above shows some values of linear function $$g(x)$$. Which of the following defines $$g(x)$$?
(A) $$g(x)=2 \ x \ + \ 1$$
(B) $$g(x)=2 \ x \ - \ 1$$
(C) $$g(x)=- \ 2 \ x \ + \ 1$$
(D) $$g(x)=x \ + \ 2$$
(E) $$g(x)=2 \ x \ + \ 2$$
42- Which of the following expressions is equal to $$\sqrt{\frac{x^2}{2} \ + \ \frac{x^2}{16}}$$ ?
(A) $$x$$
(B) $$\frac{3 \ x}{4}$$
(C) $$x\sqrt{x}$$
(D) $$\frac{x \sqrt{x}}{4}$$
(E) $$4 \ x$$
43- What is the $$y \ -$$intercept of the line with the equation $$x \ - \ 3 \ y=12$$ ?
(A) $$1$$
(B) $$- \ 2$$
(C) $$3$$
(D) $$- \ 4$$
(E) $$5$$
44- If $$4 \ a \ - \ 3 = 14$$ what is the value of $$6 \ a$$?
(A) $$5$$
(B) $$15$$
(C) $$30$$
(D) $$45$$
(E) $$50$$
45- If $$x \ ≠ \ 0$$ and $$x=x^{-6}$$, what is the value of $$x$$?
(A) $$- \ 2$$
(B) $$1$$
(C) $$2$$
(D) $$3$$
(E) $$4$$
46- Which of the following is equal to expression $$\frac{5}{x^2} \ + \ (\frac{7 \ x \ - \ 3}{x^3})$$?
(A) $$\frac{6 \ x \ + \ 1}{x^3}$$
(B) $$\frac{10 \ x \ + \ 6}{x^3}$$
(C) $$\frac{12 \ x \ + \ 1}{x^3}$$
(D) $$\frac{13 \ x \ + \ 2}{x^3}$$
(E) $$\frac{6 \ x \ + \ 4}{x^3}$$
47- Which of the following is the equation of a quadratic graph with a vertex $$(3, \ - 3)$$?
(A) $$y=3 \ x^2 \ - \ 3$$
(B) $$y=- \ 3 \ x^2 \ + \ 3$$
(C) $$y=x^2 \ + \ 3 \ x \ - \ 3$$
(D) $$y=4 \ (x \ - \ 3)^2 \ - \ 3$$
(E) $$y=4\ x^2 \ + \ 3 \ x \ - \ 3$$
48- What is the average of $$4 \ x \ + \ 2$$,$$- \ 6 \ x \ -5$$ and $$8 \ x \ + \ 2$$ ?
(A) $$3\ x\ +\ 2$$
(B) $$3\ x\ -\ 2$$
(C) $$2\ x\ +\ 1$$
(D) $$2\ x\ -\frac{1}{3}$$
(E) $$x\ -\frac{1}{3}$$
49- What is the slope of a line that is perpendicular to the line
$$4 \ x \ - \ 2 \ y=12$$ ?
(A) $$-\ 2$$
(B) $$-\frac{1}{2}$$
(C) $$4$$
(D) $$12$$
(E) $$14$$
50- In a coordinate plane, triangle ABChas coordinates: $$(−\ 1, \ 6)$$, $$(−\ 2, \ 5)$$, and $$(5, \ 8)$$.
If triangle ABC is reflected over the -axis, what are the coordinates of the new image?
(A) $$(−\ 1, \ − \ 6),\ (−\ 2, \ −\ 5),\ (−\ 5, \ − \ 8)$$
(B) $$(− \ 1, \ − \ 6),\ (−\ 2, \ − \ 5),\ (5, \ − \ 8)$$
(C) $$(1, \ 6),\ (2, \ 5),\ (5, \ 8)$$
(D) $$(−\ 1, \ 6),\ (−\ 2, \ 5),\ (5, \ 8)$$
(E) $$(1, \ 6),\ (2, \ 5),\ (−\ 5, \ 8)$$
51- What is the difference in area between a $$9$$ cm by $$4$$ cm rectangle and a circle with diameter of $$10$$ cm? $$(π \ =3)$$
(A) $$49$$
(B) $$39$$
(C) $$6$$
(D) $$4$$
(E) $$2$$
52- If $$f(x)=2 \ x^3 \ + \ 2$$ and $$(x)=\frac{1}{x}$$ , what is the value of $$f(g(x))$$?
(A) $$\frac{1}{2\ x^3\ +\ 2}$$
(B) $$\frac{2}{x^3}$$
(C) $$\frac{1}{2\ x}$$
(D) $$\frac{1}{2\ x\ +\ 2}$$
(E) $$\frac{2}{x^3 \ +\ 2}$$
53- What is the value of $$x$$ in the following equation?
$$6^x=1296$$
(A) $$3$$
(B) $$4$$
(C) $$5$$
(D) $$6$$
(E) $$7$$
54- A cruise line ship left Port A and traveled $$80$$ miles due west and then $$150$$ miles due north.
At this point, what is the shortest distance from the cruise to port A?
(A) $$70$$ miles
(B) $$80$$ miles
(C) $$150$$ miles
(D) $$170$$ miles
(E) $$230$$ miles
55- The length of a rectangle is $$3$$ meters greater than $$4$$ times its width. The perimeter of the rectangle is $$36$$ meters.
What is the area of the rectangle?
(A) $$12$$ m$$^2$$
(B) $$27$$ m$$^2$$
(C) $$36$$ m$$^2$$
(D) $$45$$ m$$^2$$
(E) $$90$$ m$$^2$$
56- Tickets to a movie cost $$12.50$$ for adults and $$7.50$$ for students. A group of $$12$$ friends purchased tickets for $$125$$.
How many student tickets did they buy?
(A) $$3$$
(B) $$5$$
(C) $$7$$
(D) $$8$$
(E) $$9$$
57- If the ratio of $$5 \ a$$ to $$2 \ b$$ is $$\frac{1}{10}$$, what is the ratio of $$a$$ to $$b$$?
(A) $$10$$
(B) $$25$$
(C) $$\frac{1}{25}$$
(D) $$\frac{1}{20}$$
(E) $$\frac{1}{10}$$
58- If $$x \ =9$$, what is the value of $$y$$ in the following equation?
$$2 \ y = \frac{2 \ x^2}{3} \ + \ 6$$
(A) $$30$$
(B) $$45$$
(C) $$60$$
(D) $$120$$
(E) $$180$$
59- Sara orders a box of pen for $$3$$ per box.
A tax of $$8.5\%$$ is added to the cost of the pens before a flat shipping fee of $$6$$ closest out the transaction.
Which of the following represents total cost of boxes of pens in dollars?
(A) $$1.085\ (3\ p)\ +\ 6$$
(B) $$6\ p\ +\ 3$$
(C) $$1.085\ (6\ p)\ +\ 3$$
(D) $$3\ p\ +\ 6$$
(E) $$p\ +\ 6$$
60- A plant grows at a linear rate. After five weeks, the plant is $$40$$ cm tall.
Which of the following functions represents the relationship between
the height $$(y)$$ of the plant and number of weeks of growth $$(x)$$?
(A) $$y(x)=40\ x\ +\ 8$$
(B) $$y(x)=8\ x\ +\ 40$$
(C) $$y(x)=40\ x$$
(D) $$y(x)=8\ x$$
(E) $$y(x)=4\ x$$
 1- Choice A is correct The correct answer is $$\frac{3 \ x \ -\ 1}{x^2 \ - \ x}$$$$(\frac{f}{g})(x)=$$ $$\frac{f(x)}{g(x)}$$$$=$$$$\frac{3 \ x \ – \ 1}{x^2 \ - \ x}$$ 2- Choice A is correct The correct answer is $$y=4 \ x \ - \ 17$$The equation of a line is: $$y=m \ x \ + \ b$$, where $$m$$ is the slope and $$b$$ is the $$y \ -$$intercept.First find the slope:$$m=\frac{y_2 \ - \ y_1}{x_2 \ - \ x_1 }=\frac{15 \ - \ (- \ 5)}{8 \ - \ 3}=\frac{20}{5}=4$$. Then, we have: $$y=4 \ x \ + \ b$$Choose one point and plug in the values of $$x$$ and y in the equation to solve for $$b$$.Let’s choose the point $$(3, \ -5)$$. $$y=4 \ x \ + \ b → - \ 5=4 \ (3) \ + \ b → - \ 5=12 \ + \ b → b=- \ 17$$The equation of the line is: $$y=4 \ x \ - \ 17$$ 3- Choice D is correct The correct answer is $$33$$Since $$N=6$$, substitute $$6$$ for $$N$$ in the equation $$\frac{x \ - \ 3}{5}=N$$, which gives $$\frac{x \ - \ 3}{5}=6$$.Multiplying both sides of $$\frac{x\ -\ 3}{5}=6$$ by $$5$$ gives $$x \ - \ 3=30$$ and then adding $$3$$ to both sides of $$x \ - \ 3=30$$ then, $$x=33$$. 4- Choice C is correct The correct answer is $$\sqrt{b^3}$$$$b^{\frac{m}{n}}$$$$=\sqrt[n]b^m$$ For any positive integers $$m$$ and $$n$$. Thus, $$b^{\frac{3}{5}}=\sqrtb^3$$. 5- Choice D is correct The corrcet answer is $$144^\circ$$The sum of all angles in a quadrilateral is $$360$$ degrees. Let $$x$$ be the smallest angle in the quadrilateral. Then the angles are: $$x, \ 2 \ x, \ 3 \ x, \ 4 \ x$$$$x \ + \ 2 \ x \ + \ 3 \ x \ + \ 4 \ x=360 → 10 \ x=360 → x=36$$The angles in the quadrilateral are: $$36^\circ, \ 72^\circ, \ 108^\circ$$, and $$144^\circ$$ 6- Choice C is correct The corrcet answer is $$\frac{8\sqrt{π}}{π}$$Formula for the area of a circle is: $$A=π \ r^2$$. Using $$64$$ for the area of the circle we have: $$64=π \ r^2$$. Let’s solve for the radius $$(r)$$.$$\frac{64}{π}=r^2 → r=\sqrt{\frac{64}{π}}=\frac{8}{\sqrtπ}=\frac{8}{\sqrt{π}} \ × \frac{\sqrt{π}}{\sqrt{π}}=\frac{8 \sqrt{π}}{π}$$ 7- Choice C is correct The corrcet answer is $$\frac{4 \ + \ 19 \ i}{29}$$To rewrite $$\frac{2 \ + \ 3 \ i}{5 \ - \ 2 \ i}$$ in the standard form a$$+$$bi, multiply the numerator and denominator of $$\frac{2 \ + \ 3 \ i}{5 \ - \ 2 \ i}$$ by the conjugate, $$5 \ + \ 2 \ i$$. This gives $$(\frac{2 \ + \ 3 \ i}{5 \ - \ 2 \ i}) (\frac{5 \ + \ 2 \ i}{5 \ + \ 2 \ i})=\frac{10 \ + \ 4 \ i \ + \ 15 \ i \ + \ 6 \ i^2}{5^2 \ - \ (2 \ i)^2}$$ . Since $$i^2=- \ 1$$, this last fraction can be rewritten as  $$\frac{10 \ + \ 4 \ i \ + \ 15 \ i \ + \ 6 \ (- \ 1)}{25 \ - \ 4 \ (- \ 1)}=\frac{4 \ + \ 19 \ i}{29}$$. 8- Choice C is correct The corrcet answer is $$60$$First find the value of $$b$$, and then find $$f(3)$$. Since $$f(2)=35$$, substuting $$2$$ for $$x$$ and $$35$$ for $$f(x)$$ gives $$35=b \ (2)^2 \ + \ 15=4 \ b \ + \ 15$$. Solving this equation gives $$b=5$$. Thus $$f(x)=5 \ x^2 \ + \ 15$$, $$f(3)=5 \ (3)^2 \ + \ 15 → f(3)=45 \ + \ 15$$, $$f(3)=60$$ 9- Choice B is correct The corrcet answer is $$30$$The sum of supplement angles is $$180$$. Let $$x$$ be that angle. Therefore, $$x \ + \ 5 \ x=180$$$$6 \ x=180$$, divide both sides by $$6$$: $$x=30$$ 10- Choice C is correct The correct answer is $$- \ 2$$Solving Systems of Equations by EliminationMultiply the first equation by $$(–\ 2)$$, then add it to the second equation.\cfrac{\begin{align}-\ 2\ (2\ x\ +\ 5\ y\ ) = 11\\ 4\ x\ -\ 2\ y\ = -\ 14\end{align}}{}$$\\ -\ 4\ x\ -\ 10\ y= -\ 22\\ 4\ x\ -\ 2\ y=-\ 14⇒ -\ 12\ y= -\ 36 ⇒ y= 3$$Plug in the value of $$y$$ into one of the equations and solve for $$x$$.$$2\ x\ +\ 5\ (3)= 11 ⇒ 2\ x\ +\ 15= 11 ⇒ 2\ x= -\ 4 ⇒ x= -\ 2$$ 11- Choice A is correct The correcte answer is $$44$$Identify the input value. Since the function is in the form $$f(x)$$ and the question asks to calculate $$f(4)$$, the input value is four.$$f(4) → \ x=4$$, Using the function, input the desired $$x$$ value.Now substitute $$4$$ in for every $$x$$ in the function.$$f(x)=3 \ x^2 \ - \ 4$$, $$f(4)=3 \ (4)^2 \ - \ 4$$, $$f(4)=48 \ - \ 4$$, $$f(4)=44$$ 12- Choice D is correct The correct answer is $$- \ 8$$The problem asks for the sum of the roots of the quadratic equation $$2 \ n^2 \ + \ 16 \ n \ + \ 24=0$$. Dividing each side of the equation by $$2$$ gives $$n^2 \ + \ 8 \ n \ + \ 12=0$$. If the roots of $$n^2 \ + \ 8 \ n \ + \ 12=0$$ are $$n_1$$ and $$n_2$$, then the equation can be factored as $$n^2 \ + \ 8 \ n \ + \ 12=(n \ - \ n_1)\ (n \ - \ n_2 )=0$$. Looking at the coefficient of $$n$$ on each side of $$n^2 \ + \ 8 \ n \ + \ 12=(n \ + \ 6)\ (n \ + \ 2)$$ gives $$n=- \ 6$$ or $$n=- \ 2$$ , then, $$- \ 6 \ + \ (- \ 2)=- \ 8$$ 13- Choice B is correct The correct answer is $$16 \ π$$The equation of a circle in standard form is: $$(x \ - \ h)^2 \ + \ (y \ - \ k)^2=r^2$$, where $$r$$ is the radius of the circle. In this circle the radius is $$4$$. $$r^2=16 → r=4$$. $$(x \ + \ 2)^2 \ + \ (y \ - \ 4)^2=16$$Area of a circle: $$A=π \ r^2=π \ (4)^2=16 \ π$$ 14- Choice D is correct The correct answer is $$6.7 \ × \ 10^5$$$$670000=6.7 \ × \ 10^5$$ 15- Choice D is correct The correct answer is $$\frac{17 \ + \ 7 \ i}{26}$$ To perform the division  $$\frac{3 \ + \ 2 \ i}{5 \ + \ i}$$, multiply the numerator and denominator of $$\frac{3 \ + \ 2 \ i}{5 \ + \ 1 \ i}$$ by the conjugate of the denominator, $$5 \ - \ i$$. This gives $$\frac{(3 \ + \ 2 \ i)\ (5 \ - \ i)}{(5 \ + \ 1 \ i)\ (5 \ - \ i)}$$=$$\frac{15 \ - \ 3 \ i \ + \ 10 \ i \ - \ 2i^2}{5^2 \ - \ i^2}$$. Since $$i^2=- \ 1$$, this can be simplified to $$\frac{15 \ - \ 3 \ i \ + \ 10 \ i \ + \ 2}{25 \ + \ 1}=\frac{17 \ + \ 7 \ i}{26}$$ 16- Choice D is correct The correct answer is $$y=(x \ - \ 3) \ (x \ - \ 4)$$The $$x \ -$$intercepts of the parabola represented $$by y=x^2 \ - \ 7 \ x \ + \ 12$$ in the $$x \ y \ -$$plane are the values of $$x$$ for which $$y$$ is equal to $$0$$.The factored form of the equation, $$y=(x \ - \ 3) \ (x \ - \ 4)$$, shows that $$y$$ equals $$0$$ if and only if$$x=3$$ or $$x=4$$. Thus, the factored form $$y=(x \ - \ 3) \ (x \ - \ 4)$$, displays the $$x \ -$$intercepts of the parabola as the constants $$3$$ and $$4$$. 17- Choice C is correct The correct answer is $$x \ - \ 2$$If $$x \ - \ a$$ is a factor of $$g(x)$$, then $$g(a)$$ must equal $$0$$. Based on the table $$g(2)=0$$.Therefore, $$x \ - \ 2$$ must be a factor of $$g(x)$$. 18- Choice C is correct The correct answer is $$2$$To solve this problem first solve the equation for $$c$$. $$\frac{c}{b}=2$$. Multiply by $$b$$ on both sides. Then: $$b \ × \frac{c}{b}=2 \ × \ b → c=2 \ b$$ . Now to calculate $$\frac{4 \ b}{c}$$, substitute the value for $$c$$ into the denominator and simplify. $$\frac{4 \ b}{c}=\frac{4 \ b}{2 \ b}=\frac{4}{2}=\frac{2}{1}=2$$ 19- Choice B is correct The correct answer is $$27 \ x^2 \ + \ 16 \ x \ + \ 1$$Simplify the numerator. $$\frac{x \ + \ (4 \ x)^2 \ + \ (3 \ x)^3}{x}=\frac{x \ + \ 4^2 \ x^2 \ + \ 3^3 \ x^3}{x}=\frac{x \ + \ 16 \ x^2 \ + \ 27 \ x^3}{x}$$.Pull an x out of each term in the numerator. $$\frac{x \ (1 \ + \ 16 \ x \ + \ 27 \ x^2)}{x}$$. The $$x$$ in the numerator and the $$x$$ in the denominator cancel: $$1 \ + \ 16 \ x \ + \ 27 \ x^2=27 \ x^2 \ + \ 16 \ x \ + \ 1$$ 20- Choice B is correct The correct answer is $$\frac{a}{b}=\frac{21}{11}$$The equation $$\frac{a \ - \ b}{b}=\frac{10}{11}$$ can be rewritten as $$\frac{a}{b} \ - \frac{b}{b}=\frac{10}{11}$$, from which it follows that $$\frac{a}{b} \ - \ 1=\frac{10}{11}$$, or  $$\frac{a}{b}=\frac{10}{11} \ + \ 1=\frac{21}{11}$$. 21- Choice A is correct The correct answer is $$y=\frac{1}{3} \ x \ + \ 2$$First write the equation in slope intercept form. Add $$2 \ x$$ to both sides to get $$6 \ y=2 \ x \ + \ 24$$. Now divide both sides by $$6$$ to get $$y=\frac{1}{3} \ x \ + \ 4$$. The slope of this line is  $$\frac{1}{3}$$, so any line that also has a slope of $$\frac{1}{3}$$ would be parallel to it.Only choice  A has a slope of $$\frac{1}{3}$$. 22- Choice D is correct The correct answer is $$16$$The rate of construction company$$=\frac{30\ cm}{1\ min}=30$$ cm/minHeight of the wall after $$40$$ minutes $$=\frac{30 \ cm}{1 \ min} \ × \ 40$$ min$$=1200$$ cm Let $$x$$ be the height of wall, then $$\frac{3}{4} \ x=1200$$ cm$$→ \ x=\frac{4 \ × \ 1200}{3} → x=1600$$ cm$$=16$$ m 23- Choice A is correct The correct answer is $$x \ ≥ \ 5 \ ∪ \ x \ ≤ \ - \ 1$$$$x \ - \ 2 \ ≥ \ 3 → x \ ≥ \ 3 \ + \ 2 → x \ ≥ \ 5$$ Or $$x \ - \ 2 \ ≤ - \ 3 → x \ ≤ \ - \ 3 \ + \ 2 → \ x \ ≤ \ - \ 1$$Then, solution is: $$x \ ≥ \ 5 \ ∪ \ x \ ≤ \ - \ 1$$ 24- Choice C is correct The correct answer is $$21$$When 5 times the number $$x$$ is added to $$10$$, the result is $$10 \ + \ 5 \ x$$. Since this result is equal to $$35$$, the equation $$10 \ + \ 5 \ x \ = 35$$ is true. Subtracting $$10$$ from each side of $$10 \ + \ 5 \ x = 35$$ gives $$5 \ x=25$$, and then dividing both sides by $$5$$ gives $$x=5$$.Therefore, $$3$$ times $$x$$ added to $$6$$, or $$6 \ + \ 3 \ x$$, is equal to $$6 \ + \ 3 \ (5)=21$$ 25- Choice B is correct The correct answer is $$g=5 \ h \ + \ 4$$Fining g in term of $$h$$, simply means “solve the equation for $$g$$”. To solve for $$g$$, isolate it on one side of the equation. Since $$g$$ is on the left-hand side, just keep it there.Subtract both sides by $$3 \ h$$. $$3 \ h \ + \ g \ - \ 3 \ h=8 \ h \ + \ 4 \ - \ 3 \ h$$And simplifying makes the equation $$g=5 \ h \ + \ 4$$, which happens to be the answer. 26- Choice D is correct The correct answer is $$84$$The description $$8 \ + \ 2 \ x$$ is $$16$$ more than $$20$$ can be written as the equation $$8 \ + \ 2 \ x=16 \ + \ 20$$, which is equivalent to $$8 \ + \ 2 \ x=36$$. Subtracting $$8$$ from each side of $$8 \ + \ 2 \ x \ =36$$ gives $$2 \ x=28$$. Since $$6 \ x$$ is $$3$$ times $$2 \ x$$, multiplying both sides of $$2 \ x=28$$ by $$3$$ gives $$6 \ x=84$$ 27- Choice B is correct The correct answer is $$(13, \ 2)$$From the choices provided, plugin the values of $$a$$ and $$b$$ into both inequalities and check. A. $$(11, \ 0) → a \ - \ b=11 \ - \ 0=11 \ > \ 10$$ and $$a \ + \ b=11 \ + \ 0=11 \ < \ 14$$B. $$(13, \ 2) → a \ - \ b=13 \ - \ 2=11 \ > \ 10$$ and $$a \ + \ b=13 \ + \ 2=15 \ > \ 14$$C. $$(13, \ 0) → a \ - \ b=13 \ - \ 0=13 \ > \ 10$$ and $$a \ + \ b=13 \ + \ 0=13 \ < \ 14$$D. $$(12, \ 1) → a \ - \ b=12 \ - \ 1=11 \ > \ 10$$ and $$a \ + \ b=12 \ + \ 1=13 \ < \ 14$$E. $$(12, \ 2) → a \ - \ b=12 \ - \ 2=10=10$$ and $$a \ + \ b=12 \ + \ 2=14 \ < \ 14$$For choice $$B, \ 15$$ is not less than $$14$$. Therefore, choice B does not provide the correct values of $$a$$ and $$b$$. 28- Choice D is correct The correct answer is $$7 \ x^3 \ y^5 \ - \ x^2 \ y^3$$$$4 \ x^2 \ y^3 \ + \ 5 \ x^3\ y^5 \ – \ (5 \ x^2\ y^3 \ – \ 2 \ x^3 \ y^5 )=4 \ x^2 \ y^3 \ - \ 5 \ x^2 \ y^3 \ + \ 5 \ x^3 \ y^5 \ + \ 2 \ x^3 \ y^5=7 \ x^3 \ y^5 \ - \ x^2 \ y^3$$ 29- Choice E is correct The correct answer is $$0, \ – \ 2, \ – \ 3$$Frist factor the function: $$f(x)=x^3 \ + \ 5 \ x^2 \ + \ 6 \ x=x (x \ + \ 2)\ (x \ + \ 3)$$To find the zeros, $$f(x)$$ should be zero. $$f(x)=x \ (x \ + \ 2)\ (x \ + \ 3)=0$$Therefore, the zeros are: $$x=0$$, $$(x \ + \ 2)=0 ⇒ x=- \ 2$$, $$(x \ + \ 3)=0 ⇒ x=- \ 3$$ 30- Choice B is correct The correct answer is $$2$$$$sin^2 \ a \ +$$ cos$$^2\ a=1$$, then: $$x\ +\ 1=3$$, $$x=2$$ 31- Choice E is correct The correct answer is $$\frac{y}{6}$$Solve for $$x$$ $$\sqrt{6\ x}=\sqrt{y}$$. Square both sides of the equation: $$(\sqrt{6 \ x})^2=(\sqrt{y})^2 → 6 \ x=y → x=\frac{y}{6}$$ 32- Choice B is correct The correct answer is $$61.28$$average $$=\frac{sum \ of \ terms}{number \ of \ terms}$$. The sum of the weight of all girls is: $$18\ ×\ 60 = 1080$$  kgThe sum of the weight of all boys is: $$32\ ×\ 62=1984$$ kg. The sum of the weight of all students is: $$1080\ +\ 1984 = 3064$$ kg. average $$=\frac{3064}{50} = 61.28$$ 33- Choice E is correct The correct answer is $$9 \ x^6$$$$y=(- \ 3 \ x^3)^2=(- \ 3)^2 (x^3)^2=9 \ x^6$$ 34- Choice C is correct The correct answer is $$36$$Plug in the value of $$x$$ and $$y$$. $$x=3$$ and $$y=- \ 2$$$$5 \ (x \ - \ 2 \ y) \ + \ (2 \ - \ x)^2=5 \ (3 \ - \ 2 \ (- \ 2)) \ + \ (2 \ - \ 3)^2=5 \ (3 \ + \ 4) \ + \ (- \ 1)^2 = 35 \ + \ 1=36$$ 35- Choice A is correct The correct answer is $$x=\frac{3}{7}$$Substituting $$x$$ for $$y$$ in first equation. $$5 \ x \ + \ 2 \ y=3$$, $$5 \ x \ + \ 2 \ (x)=3$$, $$7 \ x \ =3$$Divide both side of $$7 \ x=3$$ by $$3$$ gives $$x=\frac{3}{7}$$ 36- Choice A is correct The correct answer is $$5 \ x \ y$$There are $$5$$ floors, $$x$$ rooms in each floor, and $$y$$ chairs per room. If you multiply $$5$$ floors by $$x$$, there are $$5 \ x$$ rooms in the hotel. To get the number of chairs in the hotel, multiply $$5 \ x$$ by $$y$$. $$5 \ x \ y$$ is the number of chairs in the hotel. 37- Choice C is correct The correct answer is $$6$$If $$β=3\ γ$$, then multiplying both sides by $$12$$ gives $$12 \ β=36 \ γ$$.$$α=2 \ β$$, thus $$α=6 \ γ$$. Multiply both sides of the equation by $$6$$ gives $$6 \ α=36 \ γ$$. 38- Choice A is correct The correct answer is $$\sqrt{6} \ - \ 1$$$$x_{1,2} =\frac{- \ b\ ± \sqrt{b^2 \ - \ 4 \ a\ c}}{2\ a}$$ $$a\ x^2\ +\ b \ x\ +\ c=0$$ $$\ x ^2 \ + \ 2 \ x \ – \ 5=0$$ ⇒ then: $$a=1, \ b=2$$ and $$c= –\ 5$$ $$x =\frac{- \ 2 \ + \sqrt{2^2 \ - \ 4.1 .- \ 5}}{2.1}=\sqrt{6}- \ 1$$ $$x =\frac{- \ 2 - \sqrt{2^2 \ - \ 4 .1 . \ - \ 5}}{2.1} =- \ 1 \ -\sqrt{6}$$ 39- Choice A is correct The correct answer is $$\frac{3}{4} \ + \ i$$$$\frac{4 \ - \ 3 \ i}{- \ 4 \ i}× \frac{i}{i}=\frac{4 \ i \ - \ 3 \ i^2}{- \ 4 \ i^2}$$. $$i^2 \ - \ 1$$, Then: $$\frac{4 \ i \ - \ 3 \ i^2}{- \ 4 \ i^2}=\frac{4 \ i \ -3 \ (- \ 1)}{- \ 4\ (- \ 1)}=\frac{4 \ i \ + \ 3}{4}=\frac{4 \ i}{4} \ + \frac{3}{4}=i \ + \frac{3}{4}$$ 40- Choice C is correct The correct answer is $$7 \ x^2 \ + \ x \ + \ 5$$The sum of the two polynomials is $$(4 \ x^2 \ + \ 6 \ x \ - \ 3) \ + \ (3 \ x^2 \ - \ 5 \ x \ + \ 8)$$This can be rewritten by combining like terms: $$(4 \ x^2 \ + \ 6 \ x \ - \ 3) \ + \ (3 \ x^2 \ - \ 5 \ x \ + \ 8)=(4 \ x^2 \ + \ 3 \ x^2 ) \ + \ (6 \ x \ - \ 5 \ x) \ + \ (- \ 3 \ + \ 8)=7 \ x^2 \ + \ x \ + \ 5$$ 41- Choice C is correct The correct answer is $$g(x)=- \ 2 \ x \ + \ 1$$For $$(1, \ - \ 1)$$ check the options provided:A. $$g(x)=2 \ x \ + \ 1 → - \ 1=2 \ (1) \ + \ 1 → - \ 1=3$$ This is NOT true.B. $$g(x)=2 \ x \ - \ 1 → - \ 1=2 \ (1) \ - \ 1=1$$ This is NOT true.C. $$g(x)=- \ 2 \ x \ +\ 1 → - \ 1=2 \ (- \ 1) \ + \ 1 → - \ 1=- \ 1$$ This is true.D. $$g(x)=x \ +\ 2 → - \ 1=1 \ + \ 2 → - \ 1=3$$ This is NOT true.E. $$g(x)=2 \ x \ + \ 2 → - \ 1=2 \ (1) \ + \ 2=1$$ This is NOT true.From the choices provided, only choice C is correct. 42- Choice B is correct The correct answer is $$\frac{3 \ x}{4}$$Simplify the expression. $$\sqrt{\frac{x^2}{2} \ + \frac{x^2}{16}}$$$$=\sqrt{\frac{8 \ x^2}{16} \ + \frac{x^2}{16}}=$$$$\sqrt{\frac{9 \ x^2}{16}}=$$$$\sqrt{\frac{9}{16} \ x^2}$$=$$\sqrt{\frac{9}{16}}×\sqrt{x^2}=\frac{3}{4} \ × \ x=\frac{3 \ x}{4}$$ 43- Choice D is correct The correct answer is $$- \ 4$$To find the $$y \ -$$intercept of a line from its equation, put the equation in slope-intercept form:$$x \ - \ 3 \ y=12$$, $$- \ 3 \ y=- \ x \ + \ 12$$, $$3 \ y=x \ - \ 12$$, $$y=\frac{1}{3} x \ - \ 4$$The $$y \ -$$intercept is what comes after the $$x$$. Thus, the $$y \ -$$intercept of the line is $$- \ 4$$. 44- Choice C is correct The correct answer is $$30$$Adding both side of $$4 \ a \ - \ 3=17$$ by $$3$$ gives $$4 \ a=20$$Divide both side of $$4 \ a=20$$ by $$4$$ gives $$a=5$$, then $$6 \ a=6 \ (5)=30$$ 45- Choice B is correct The correct answer is $$1$$The easiest way to solve this one is to plug the answers into the equation.When you do this, you will see the only time $$x=x^{(- \ 6)}$$ is when $$x=1$$ or $$x=0$$. Only $$x=1$$ is provided in the choices. 46- Choice C is correct The correct answer is $$\frac{12 \ x \ + \ 1}{x^3}$$First find a common denominator for both of the fractions in the expression $$\frac{5}{x^2} + \frac{7 \ x \ - \ 3}{x^3}$$.of $$x^3$$, we can combine like terms into a single numerator over the denominator:$$\frac{5 \ x \ + \ 4}{x^3} \ + \frac{7 \ x \ -\ 3}{x^3} =\frac{(5 \ x \ + \ 4) \ + \ (7 \ x \ - \ 3)}{x^3} =\frac{12 \ x \ + \ 1}{x^3}$$ 47- Choice D is correct The correct answer is $$y=4 \ (x \ - \ 3)^2 \ - \ 3$$Let’s find the vertex of each choice provided:A. $$y=3 \ x^2 \ - \ 3$$ The vertex is: $$(0, \ - \ 3)$$B. $$y=- \ 3 \ x^2 \ + \ 3$$ The vertex is: $$(0, \ 3)$$C. $$y=x^2 \ + \ 3 \ x \ - \ 3$$ The value of $$x$$ of the vertex in the equation of $$a$$ quadratic in standard form is: $$x=\frac{- \ b}{2 \ a}=\frac{- \ 3}{2}$$(The standard equation of a quadratic is: $$a \ x^2 \ + \ b \ x \ + \ c=0)$$The value of $$x$$ in the vertex is $$3$$ not $$\frac{- \ 3}{2}$$. D. $$y=4 \ (x \ - \ 3)^2 \ - \ 3$$Vertex form of $$a$$ parabola equation is in form of $$y=a \ (x \ - \ h)^2 \ + \ k$$ , where $$(h, \ k)$$ is the vertex. Then $$h=3$$ and $$k=- \ 3$$. (This is the answer)E. $$y=4 \ x^2 \ + \ 3 \ x \ - \ 3$$. $$x=\frac{- \ b}{2 \ a}=\frac{- \ 3}{2 \ × \ 8}=\frac{- \ 3}{16}$$. The value of $$x$$ in the vertex is $$3$$ not $$\frac{- \ 3}{16}$$. 48- Choice D is correct The correct answer is $$2\ x\ -\frac{1}{3}$$To find the average of three numbers even if they’re algebraic expressions, add them up and divide by $$3$$. Thus, the average equals: $$\frac{(4\ x\ +\ 2) \ + \ (-\ 6\ x\ -\ 5) \ + \ (8\ x\ +\ 2)}{3}=\frac{6\ x\ -\ 1}{3}=2\ x\ -\frac{1}{3}$$ 49- Choice B is correct The correct answer is $$-\frac{1}{2}$$The equation of a line in slope intercept form is: $$y=m\ x\ +\ b$$. Solve for $$y$$. $$4\ x\ -\ 2\ y=12 ⇒ -\ 2\ y=12\ -\ 4\ x ⇒ y=(12\ -\ 4\ x) \ ÷ \ (-\ 2) ⇒ y=2\ x\ -\ 6$$. The slope is $$2$$. The slope of the line perpendicular to this line is: $$m_1\ × m_2=-\ 1 ⇒ 2\ × m_2 = -\ 1 ⇒ m_2=-\frac{1}{2}$$ 50- Choice E is correct The correct answer is $$(1, \ 6), (2, \ 5), (−\ 5, \ 8)$$Since the triangle ABC is reflected over the $$y\ -$$axis, then all values of $$y$$’s of the points don’t change and the sign of all $$x$$’s change. (remember that when a point is reflected over the $$y\ -\ a$$ xis, the value of $$y$$ does not change and when a point is reflected over the $$x\ -\ a$$xis,the value of $$x$$ does not change). Therefore: $$(−\ 1, \ 6)$$ changes to $$(1, \ 6)$$. $$(−\ 2, \ 5)$$ changes to $$(2, \ 5$$). $$(5, \ 8)$$ changes to $$(−\ 5, \ 8)$$ 51- Choice B is correct The correct answer is $$39$$The area of rectangle is:$$9\ ×\ 4=36$$ cm$$^2$$. The area of circle is: $$π\ r^2=π\ ×(\frac{10}{2})^2=3\ ×\ 25=75$$ cm$$^2$$. Difference of areas is: $$75\ -\ 36=39$$ 52- Choice E is correct The correct answer is $$\frac{2}{x^3 \ +\ 2}$$$$f(g(x))=2\ ×$$$$(\frac{1}{x})^3\ +\ 2=\frac{2}{x^3}+2$$ 53- Choice B is correct The correct answer is $$4$$$$1269=6^4 →6^x=6^4 → x=4$$ 54- Choice D is correct The correct answer is $$170$$ milesUse the information provided in the question to draw the shape.Use Pythagorean Theorem: $$a^ 2\ +\ b^2 = c^2$$$$80^2\ +\ 150^2=c^2 ⇒ 6400\ +\ 22500 = c^2 ⇒ 28900 = c^2 ⇒ c =170$$ 55- Choice D is correct The correct answer is $$45$$ m$$^2$$Let $$L$$ be the length of the rectangular and $$W$$ be the with of the rectangular. Then, $$L=4\ W\ +\ 3$$The perimeter of the rectangle is $$36$$ meters. Therefore: $$2\ L\ +\ 2\ W=36$$ $$L\ +\ W=18$$Replace the value of L from the first equation into the second equation and solve for $$W$$:$$(4\ W\ +\ 3)\ +\ W=18 → 5\ W\ +\ 3=18 → 5\ W=15 → W=3$$The width of the rectangle is $$3$$ meters and its length is: $$L=4\ W\ +\ 3=4\ (3)\ +\ 3=15$$The area of the rectangle is: length $$×$$ width $$= 3\ ×\ 15 = 45$$ 56- Choice B is correct The correct answer is $$5$$Let $$x$$ be the number of adult tickets and $$y$$ be the number of student tickets. Then:$$x\ +\ y=12$$, $$12.50\ x\ +\ 7.50 \ y=125$$Use elimination method to solve this system of equation. Multiply the first equation by $$-\ 7.5$$ and add it to the second equation. $$-\ 7.5\ (x\ +\ y=12)$$, $$-\ 7.5\ x\ -\ 7.5\ y=-\ 90$$, $$12.50\ x\ +\ 7.50\ y=125$$. $$5\ x=35$$, $$x=7$$ There are $$7$$ adult tickets and $$5$$ student tickets. 57- Choice C is correct The correct answer is $$\frac{1}{25}$$Write the ratio of $$5\ a$$ to $$2\ b$$. $$\frac{5\ a}{2\ b}=\frac{1}{10}$$Use cross multiplication and then simplify. $$5\ a\ ×\ 10=2\ b\ ×\ 1 → 50\ a=2 \ b → a=\frac{2b}{50}=\frac{b}{25}$$Now, find the ratio of $$a$$ to $$b$$. $$\frac{a}{b}=\frac{\frac{b}{25}}{b}$$$$→\frac{b}{25}\ ÷\ b=\frac{b}{25}\ ×\frac{1}{b}=\frac{b}{25\ b}=\frac{1}{25}$$ 58- Choice A is correct The correct answer is $$30$$Plug in the value of $$x$$ in the equation and solve for $$y$$.$$2\ y=\frac{2\ x^2}{3}\ +\ 6 → 2\ y$$ =$$\frac{2\ (9)^2}{3}\ +\ 6 → 2\ y=$$ $$\frac{2\ (81)}{3}\ +\ 6 → 2\ y= 54\ +\ 6=60$$$$2\ y = 60 → y=30$$ 59- Choice A is correct The correct answer is $$1.085\ (3\ p)\ +\ 6$$Since a box of pen costs $$3$$, then $$3\ p$$ Represents the cost of $$p$$ boxes of pen. Multiplying this number times $$1.085$$ will increase the cost by the $$8.5%$$ for tax.Then add the $$6$$ shipping fee for the total: $$1.085\ (3\ p)\ +\ 6$$ 60- Choice D is correct The correct answer is $$y(x)=8\ x$$Rate of change (growth or $$x$$) is $$8$$ per week. $$40\ ÷\ 5=8$$Since the plant grows at a linear rate, then the relationship between the height $$(y)$$ of the plant and number of weeks of growth $$(x)$$ can be written as: $$y(x)=8\ x$$

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