The value of x is at most 450.
a
x 450
c
x ≤ 450

d
x ≥ 450

Answer:

Junior PSAT

Training Packet

2016-17

Math Department  

Answer Key

Section 3: Math Test — No Calculator

QUESTION 1.

Choice C is correct. Subtracting 6 from each side of 5x + 6 = 10 yields 5x = 4.

Dividing both sides of 5x = 4 by 5 yields x =

_4

5

. Te value of x can now be

substituted into the expression 10x + 3, giving 10 ( _4

5 ) + 3 = 11.

Alternatively, the expression 10x + 3 can be rewritten as 2(5x + 6) − 9, and

10 can be substituted for 5x + 6, giving 2(10) − 9 = 11.

Choices A, B, and D are incorrect. Each of these choices leads to 5x + 6 ≠ 10,

contradicting the given equation, 5x + 6 = 10. For example, choice A is

incorrect because if the value of 10x + 3 were 4, then it would follow that

x = 0.1, and the value of 5x + 6 would be 6.5, not 10.

QUESTION 2.

Choice B is correct. Multiplying each side of x + y = 0 by 2 gives 2x + 2y = 0.

Ten, adding the corresponding sides of 2x + 2y = 0 and 3x − 2y = 10 gives

5x = 10. Dividing each side of 5x = 10 by 5 gives x = 2. Finally, substituting

2 for x in x + y = 0 gives 2 + y = 0, or y = −2. Terefore, the solution to the

given system of equations is (2, −2).

Alternatively, the equation x + y = 0 can be rewritten as x = −y, and substituting x for −y in 3x − 2y = 10 gives 5x = 10, or x = 2. Te value of y can then

be found in the same way as before.

Choices A, C, and D are incorrect because when the given values of x and

y are substituted into x + y = 0 and 3x − 2y = 10, either one or both of the

equations are not true. Tese answers may result from sign errors or other

computational errors.

QUESTION 3.

Choice A is correct. Te price of the job, in dollars, is calculated using

the expression 60 + 12nh, where 60 is a fxed price and 12nh depends on the

number of landscapers, n, working the job and the number of hours, h, the job

takes those n landscapers. Since nh is the total number of hours of work done

when n landscapers work h hours, the cost of the job increases by $12 for each

hour a landscaper works. Terefore, of the choices given, the best interpretation

of the number 12 is that the company charges $12 per hour for each landscaper.

Choice B is incorrect because the number of landscapers that will work each

job is represented by n in the equation, not by the number 12. Choice C is

incorrect because the price of the job increases by 12n dollars each hour,

which will not be equal to 12 dollars unless n = 1. Choice D is incorrect

because the total number of hours each landscaper works is equal to h. Te

number of hours each landscaper works in a day is not provided.

QUESTION 4.

Choice A is correct. If a polynomial expression is in the form (x)2

+ 2(x)(y) +

(y)2

, then it is equivalent to (x + y)2

. Because 9a4

+ 12a2

b2

+ 4b4

= (3a2

)2

+

2(3a2

)(2b2

) + (2b2

)2

, it can be rewritten as (3a2

+ 2b2

)2

.

Choice B is incorrect. Te expression (3a + 2b)4

is equivalent to the product

(3a + 2b)(3a + 2b)(3a + 2b)(3a + 2b). Tis product will contain the term

4(3a)3

(2b) = 216a3

b. However, the given polynomial, 9a4

+ 12a2

b2

+ 4b4

,

does not contain the term 216a3

b. Terefore, 9a4

+ 12a2

b2

+ 4b4 ≠ (3a + 2b)4

.

Choice C is incorrect. Te expression (9a2

+ 4b2

)2

is equivalent to the

product (9a2

+ 4b2

)(9a2

+ 4b2

). Tis product will contain the term (9a2

)

(9a2

Answer:

that looks hard

Step-by-step explanation:

b

6. The rungs of a ladder are each perpendicular to one side of the ladder. What can you conclude about the rungs of the ladder? Justify your answer by stating the theorem you used. ​

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1/4d=1/5g(g+e)-h solve for d

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Can some please help me it’s due today I appreciate your help .

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Matter is in a liquid state when its temperature is between its melting point and its boiling point. Suppose that some substance has a melting point of negative 35.84 degrees Upper C and a boiling point of 310.69 degrees Upper C . What is the range of temperatures in degrees Fahrenheit for which this substance is not in a liquid​ state? (Hint: Upper C equals five ninths left parenthesis Upper F minus 32 right parenthesis ​) Express the range as an inequality. Let x represent the temperature in degrees Fahrenheit. What is the range of temperatures for which this substance is not in a liquid​ state? nothing ​(Type an inequality or a compound inequality. Simplify your answer. Use integers or decimals for any numbers in the expression. Round to three decimal places as​ needed.)

What is the value of 11,340 divided by 27​

What is (-22)(-8) = pls help me I’m so lost and i dont wanna fail

given the equation h(z)=2(z-4),find h(-2).

Please answer for math, thank you!

Can somebody plz answer all of these right thx!!!<3
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WILL MARK BRAINLIEST !

Find the term named in the problem.
-21, - 13, -5, 3, ...
Find a23

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True or False: When comparing and ordering scientific notation we look at the exponent first​

You are taking a road-trip with your friends! You are driving from Detroit to Tennessee which is a 533 mile trip. You stop for gas about 105 miles into the trip and you are hungry! Your plan is to wait to stop for food once you are halfway through the trip. How many more miles do you have left until you stop to eat

The difference in the x-coordinates of two points is 3, and the difference in the y-coordinates of the two points is 6. What
is the slope of the line that passes through the points?
O 2
O 3
06
09

Jacque needs to buy some pizzas for a party at her office. She's ordering from a restaurant that charges a \$7.50$7.50dollar sign, 7, point, 50 delivery fee and \$14$14dollar sign, 14 per pizza. She wants to buy as many pizzas as she can, and she also needs to keep the delivery fee plus the cost of the pizzas under \$60$60dollar sign, 60.

Each pizza is cut into 888 slices, and she wonders how many total slices she can afford.

Let PPP represent the number of pizzas that Jacque buys.

1) Which inequality describes this scenario?

p(x) = 3x + 4
q(X) = 2x^2
Find a(p(x))

Helpppp plz!!!! Bout to FINSH

The mapping diagram shows a functional relationship.
Complete the statement.
f(3) is
Domain
Range
0
3
Tomos
-1
9
9

What percent of $18 is $6?

Select all the equations where z=5z=5z, equals, 5 is a solution.

Choose 3 answers:

Choose 3 answers:


(Choice A)

A

8=z+38=z+38, equals, z, plus, 3


(Choice B)

B

z-1=6z−1=6z, minus, 1, equals, 6


(Choice C)

C

20=40\div{z}20=40÷z20, equals, 40, divided by, z


(Choice D)

D

12z=6012z=6012, z, equals, 60


(Choice E)

E

12+z=1712+z=17

Can you simplify i47 as much as possible

What type of number is -7.89? Select all that apply

Whole number
Integer
Rational
Irrational

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What is the ratio of Reese's to all candy?

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