Math help please! - ( 3/5 )

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

Answer:

false

Step-by-step explanation:

Answer:

false you will need more info

Step-by-step explanation:

Y-3=1/5(x+2) is the answer.

Answer:

2 1/3 > 2 1/6

Step-by-step explanation:

2.33 > 2.17 True

How do you know if it is inequality or not w/ fraction?

An equation or an inequality that contains at least one variable is called an open sentence. When you substitute a number for the variable in an open sentence, the resulting statement is either true or false. If the statement is true, the number is a solution to the equation or inequality.

To solve an inequality using the following steps:

1) Eliminate fractions by multiplying all terms by the least common denominator of all fractions.

2) Simplify by combining like terms on each side of the inequality.

3) Add or subtract quantities to obtain the unknown on one side and the numbers on the other.

Answer:

B

Step-by-step explanation:

I did the quiz

Answer:

2.26 hours

Step-by-step explanation:

Given that:

Stock 1:

Initial price = 13.17

Rate of increase = $0.11 per hour

13.17 + 0.11h - - - (1)

Stock 2 :

Initial price = 13.69

Rate of decrease = 0.12 per hour

13.69 - 0.12h - - (2)

13.17 + 0.11h = 13.69 - 0.12h

0.11h + 0.12h = 13.69 - 13.17

0.23h = 0.52

h = 0.52 / 0.13

h = 2.26 hours

Answer:

to evaluate a function, substitute the input

Step-by-step explanation:

(the given number or expression) for the function variable (place holder, x) replace the x with the number or expression. 1. given function f (x)=3x -5 finf (f) 4.

Answer:

x  = - y-12/5+4k

Step-by-step explanation:

Solve 12-5x-4kx=y for x

12-5x-4kx  =  y for x

substract 12 from both side

   -5x-4kx  =  y-12

Factor of -5x-4kx = -x(5+4k)

   -x(5+4k) =  y-12

Solve for x

             -x =  y-12/(5+4k)

Therefore x = - y-12/5+4k

Answer:

Table C, Table D, Table E

Step-by-step explanation:

See attachment for tables

Given

[tex]p = 3.25b[/tex]

Required

Which of the tables is more expensive than the given function

To answer this question, we simply determine the equation of each table and then compare the equation with [tex]p = 3.25b[/tex]

Table A:

Consider two corresponding points in the table, we have:

[tex](b_1,p_1) = (1,2.75)[/tex]

[tex](b_2,p_2) = (4,11)[/tex]

Determine the slope

[tex]m = \frac{p_2 - p_1}{b_2 - b_1}[/tex]

[tex]m = \frac{11 - 2.75}{4 - 1}[/tex]

[tex]m = \frac{8.25}{3}[/tex]

[tex]m = 2.75[/tex]

The equation is determined as follows:

[tex]p - p_1 = m(b-b_1)[/tex]

[tex]p - 2.75 = 2.75(b-1)[/tex]

[tex]p - 2.75 = 2.75b-2.75[/tex]

[tex]p = 2.75b[/tex]

Comparing this equation to [tex]p = 3.25b[/tex], we have that:

[tex]2.75 < 3.25[/tex]

Hence:

This equation is less expensive than [tex]p = 3.25b[/tex]

Table B:

Consider two corresponding points in the table, we have:

[tex](b_1,p_1) = (1.5,3.75)[/tex]

[tex](b_2,p_2) = (6,15)[/tex]

Determine the slope

[tex]m = \frac{p_2 - p_1}{b_2 - b_1}[/tex]

[tex]m = \frac{15 - 3.75}{6 - 1.5}[/tex]

[tex]m = \frac{11.25}{4.5}[/tex]

[tex]m = 2.5[/tex]

The equation is determined as follows:

[tex]p - p_1 = m(b-b_1)[/tex]

[tex]p - 3.75 = 2.5(b-1.5)[/tex]

[tex]p - 3.75 = 2.5b- 3.75[/tex]

[tex]p = 2.5b[/tex]

Comparing this equation to [tex]p = 3.25b[/tex], we have that:

[tex]2.5 < 3.25[/tex]

Hence:

This equation is also less expensive than [tex]p = 3.25b[/tex]

Table C:

Consider two corresponding points in the table, we have:

[tex](b_1,p_1) = (2,7)[/tex]

[tex](b_2,p_2) = (4,14)[/tex]

Determine the slope

[tex]m = \frac{p_2 - p_1}{b_2 - b_1}[/tex]

[tex]m = \frac{14 - 7}{4 - 2}[/tex]

[tex]m = \frac{7}{2}[/tex]

[tex]m = 3.5[/tex]

The equation is determined as follows:

[tex]p - p_1 = m(b-b_1)[/tex]

[tex]p - 7 = 3.5(b - 2)[/tex]

[tex]p - 7 = 3.5b - 7[/tex]

[tex]p = 3.5b[/tex]

Comparing this equation to [tex]p = 3.25b[/tex], we have that:

[tex]3.5 > 3.25[/tex]

Hence:

This equation is more expensive than [tex]p = 3.25b[/tex]

Table D:

Consider two corresponding points in the table, we have:

[tex](b_1,p_1) = (2.5,10)[/tex]

[tex](b_2,p_2) = (5,20)[/tex]

Determine the slope

[tex]m = \frac{p_2 - p_1}{b_2 - b_1}[/tex]

[tex]m = \frac{20 - 10}{5 - 2.5}[/tex]

[tex]m = \frac{10}{2.5}[/tex]

[tex]m = 4[/tex]

The equation is determined as follows:

[tex]p - p_1 = m(b-b_1)[/tex]

[tex]p - 10 = 4(b - 2.5)[/tex]

[tex]p - 10 = 4b - 10[/tex]

[tex]p = 4b[/tex]

Comparing this equation to [tex]p = 3.25b[/tex], we have that:

[tex]4 > 3.25[/tex]

Hence:

This equation is more expensive than [tex]p = 3.25b[/tex]

Table E:

Consider two corresponding points in the table, we have:

[tex](b_1,p_1) = (6, 22.5)[/tex]

[tex](b_2,p_2) = (12,45)[/tex]

Determine the slope

[tex]m = \frac{p_2 - p_1}{b_2 - b_1}[/tex]

[tex]m = \frac{45 - 22.5}{12 - 6}[/tex]

[tex]m = \frac{22.5}{6}[/tex]

[tex]m = 3.75[/tex]

The equation is determined as follows:

[tex]p - p_1 = m(b-b_1)[/tex]

[tex]p - 22.5 = 3.75(b - 6)[/tex]

[tex]p - 22.5 = 3.75b - 22.5[/tex]

[tex]p = 3.75b[/tex]

Comparing this equation to [tex]p = 3.25b[/tex], we have that:

[tex]3.75>3.25[/tex]

Hence:

This equation is more expensive than [tex]p = 3.25b[/tex]

Table F:

Consider two corresponding points in the table, we have:

[tex](b_1,p_1) = (7, 21)[/tex]

[tex](b_2,p_2) = (14,42)[/tex]

Determine the slope

[tex]m = \frac{p_2 - p_1}{b_2 - b_1}[/tex]

[tex]m = \frac{42 - 21}{14 - 7}[/tex]

[tex]m = \frac{21}{7}[/tex]

[tex]m = 3[/tex]

The equation is determined as follows:

[tex]p - p_1 = m(b-b_1)[/tex]

[tex]p -21 =3(b -7)[/tex]

[tex]p -21 =3b -21[/tex]

[tex]p = 3b[/tex]

Comparing this equation to [tex]p = 3.25b[/tex], we have that:

[tex]3 < 3.25[/tex]

Hence:

This equation is less expensive than [tex]p = 3.25b[/tex]

Answer:

399.84

Step-by-step explanation:

408.00 x .98 (2% reduction from 100) = 399.84

Answer:

it represents the following

read in my explanation

Step-by-step explanation:

A bar chart is a graph with rectangular bars. The graph usually compares different categories. Although the graphs can be plotted vertically (bars standing up) or horizontally (bars laying flat from left to right), the most usual type of bar graph is vertical.

The horizontal (x) axis represents the categories; The vertical (y) axis represents a value for those categories. In the graph below, the values are percentages.

Answer:

The unit price in this situation is the approximate cost per pound of clementines. So, the x-axis should represent the number of pounds. The y-axis should represent the cost.

Step-by-step explanation:

Plato correct answer word for word

Answer: 1/2

Step-by-step explanation: got it right

The slope of the line that passes through the points (8,7) and (4, 5) is 1/2.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The formula to find the slope of a line is slope = (y₂-y₁)/(x₂-x₁).

The given coordinate points are (8, 7) and (4, 5).

Substitute (x₁, y₁)= (8, 7) and (x₂, y₂)= (4, 5) in slope formula, we get

Slope = (5-7)/(4-8

= -2/(-4)

= 1/2

Therefore, the slope of the line that passes through the points (8,7) and (4, 5) is 1/2.

To learn more about the slope of a line visit:

https://brainly.com/question/14511992.

#SPJ6

Answer:

The problem to get 358² is solved by adding 357 twice and then add 1 to the value of 357²

Step-by-step explanation:

The given information are;

The square of 356 = 126,736

The square of 357 = 127,449

We note that 357² = (356 + 1)² = 356² + 2×356 + 1 = 126,763 + 712 + 1 = 127,449

We can write the above equation as follows;

357² = (356 + 1)² = 356² + 356 + 356 + 1 = 126,763 + 712 + 1 = 127,449

357² = 127,449

Similarly, we have;

358² = (357 + 1)² = 357² + 357 + 357 + 1 = 128,164

358² =  128,164

We can also look at the question as forming squares with tiles

To form the square tile with 358 units per side, we add an extra row and column of 357 tiles each. Completing the figure with an extra tile at the top right or left corner

Therefore, the area of the 358 unit per side square = The area of the 357 unit per side + 357 + 357 + 1 =  128,164

Answer:

Pythagoras believed that numbers were not only the way to truth, but truth itself. Through mathematics, one could attain harmony and live an easier life. He is said to have proposed a number of mathematical theorems to this end but, of all these, only the famous Pythagorean Theorem remains.

Step-by-step explanation:

Answer:

68.1407 us the answer

Step-by-step explanation:

Just add

Answer:

c

Step-by-step explanation:

Answer:

7425

Step-by-step explanation:

First let's make the last two fractions improper.

-4  1/2 = -9/2    -2  1/5 = -11/5

Now we have to find the least common denominator.

[tex]\frac{5}{6} *\frac{-9}{2}*\frac{-11}{5}[/tex]

The least common denominator is 30 because all the denominators can be multiplied by something to get 30.

[tex](\frac{5}{5})*\frac{5}{6}* (\frac{15}{15})*\frac{-9}{2}* (\frac{6}{6})*\frac{-11}{5}[/tex] Simplify

[tex]\frac{25}{30}*\frac{-135}{30}*\frac{-66}{30}[/tex] simply

[tex]\frac{-3375}{30}*\frac{-66}{30}[/tex]

[tex]\frac{222750}{30}[/tex] simply

7425

Answer:   x = -3 + √3     or     x = -3 - √3

Step-by-step explanation:

X²+6x+6

now breaking 6x into 2x and 3x we get ,

X²+3x+2x+6

taking x common and 2 common we get ,

x(x+3)+2(x+3)

taking (x+3) common

(x+3) (x+2)

so comparing with zero to get values of x ,

either

x+3=0

x=-3

or x+2=0

x=-2

Answer:

[tex]x^3-5x^2+4x-20=(x-5)(x+2\mathbf{i})(x-2\mathbf{i})[/tex]

Step-by-step explanation:

Factorization of polynomials

Factor:

[tex]f(x)=x^3-5x^2+4x-20[/tex]

There are several techniques to factor polynomials. We'll use algebraic manipulation and common factor:

Separate in groups:

[tex](x^3-5x^2)+(4x-20)[/tex]

Factor out 4 from 4x-20:

[tex]=(x^3-5x^2)+4(x-5)[/tex]

Factor out [tex]x^2[/tex] from [tex]x^3-5x^2[/tex]

[tex]=x^2(x-5)+4(x-5)[/tex]

Factor out x-5:

[tex]=(x-5)(x^2+4)[/tex]

The roots of

[tex]x^2+4=0[/tex]

Are two complex numbers:

[tex]x=2\mathbf{i}, x=-2\mathbf{i}[/tex]

The complete factorization is:

[tex]\boxed{x^3-5x^2+4x-20=(x-5)(x+2\mathbf{i})(x-2\mathbf{i})}[/tex]

0.75 cups and 144 teaspoons

Step-by-step explanation:

I'm 99.99% sure I got it right

Answer:

(1,4)

Step-by-step explanation:

Use the midpoint formula to find the midpoint of the line segment.

Answer:

The answer is 12

Step-by-step explanation:

Answer:

27

Step-by-step explanation:

Answer:

1/36

Step-by-step explanation:

A dice have 6 faces, each face have 1/6 chance to land on, so the chance of landing on 3 two times in a row is 1/6 x 1/6 = 1/36

Answer:

Revised statement balance=$ 864.52

Yes Rona's is account reconcile

Step-by-step explanation:

Calculation to Find Rona's revised statement balance

Using this formula

Revised statement balance=Ending balance+Deposits-Checks Outstanding

Let plug in the formula

Revised statement balance=$ 725.71+$610.00-$ 471.19

Revised statement balance=$ 864.52

Based on the above calculation the Revised statement balance of the amount of $ 864.52 is equal to the balance from checkbook which simply means that Rona's ACCOUNT is RECONCILE

Answer:

-3n-7

Step-by-step explanation:

n-7-4n

and then u combine like terms and u get

-3n-7

Answer:

-3n-7

Step-by-step explanation:

n also means 1n

Answer:

x = 2

y = -3

Step-by-step explanation:

The given equation is,

22(x + yi) + (28 + 4i) = 72 - 62i

By solving this equation further,

22x + 22yi + 28 + 4i = 72 - 62i

(22x + 28) + (22y + 4)i = 72 - 62i

Now both the sides of the equation is in the form of complex number,

By comparing real and imaginary parts given on both the sides,

22x + 28 = 72

22x = 72 - 28

22x = 44

x = 2

22y + 4 = -62

22y = -62 - 4

22y = -66

y = -3

Therefore, x = 2 and y = -3 are the values for which the given equation is true.