How many solutions are there for the system of equations shown on the graph?

A. No solution
B. One solution
C. Two solutions
D. Infinitely many solutions

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:

62.6

Step-by-step explanation:

Answer:

3 + x

Step-by-step explanation:

Sum means to add, so you would just add 3 and x (since they haven't given an actual number and only a variable).

The sum of the number 3 and the variable x will be (x + 3).

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

In the linear expression, the degree of the variable is one.

The sum of 3 and a number x.

Then the expression will be

⇒ 3 + x

The number 3 is a constant number and the term x is a variable.

The expression (x + 3) is a linear expression because the degree of the expression is one.

The number of the variable is one, then the expression is linear expression of one variable.

Thus, the sum of the number 3 and the variable x will be (x + 3).

More about the Algebra link is given below.

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Answer:

1. (-6,1)

2. (-1.5,4)

Step-by-step explanation:

1. (-6,3) and (-6,-1)

Midpoint = [tex](\frac{-6+ -6}{2} , \frac{3 + -1}{2}) = (-6, 1)[/tex]

2. (-3,-1) and (0,9)

Midpoint = [tex](\frac{-3 + 0}{2} , \frac{-1 + 9}{2} ) = (-1.5,4)[/tex]

Answer:

4 weeks

Step-by-step explanation:

5,600/200 = 28

28/7 = 4

Answer:

4 weeks

Step-by-step explanation:

200x7=1400

5600/1400=4

Answer:

17 feet

Step-by-step explanation:

Given

Downward Movements: 12 feet; 9 feet; 6 feet

Upward Movement: 10 feet

Required

Determine the position at which the swimmer got the fish

First, we need to add up the downward movements;

[tex]Downward = 12ft + 9ft + 6ft[/tex]

[tex]Downward = 27ft[/tex]

Then subtract the upward movement

[tex]Position = Downward - Upward[/tex]

[tex]Position = 27ft - 10ft[/tex]

[tex]Position = 17ft[/tex]

Answer:

55 < 2x-15 < 105

Step-by-step explanation:

Just set the equation less than and greater than the variables given

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:

You get 17.80 cents back

Step-by-step explanation:

4.5 times 0.49 is 2.20 cents

20 minus 2.20 is 17.80 dollars

11. 654,321

12. 56.99

Answer:

11. Standard form: 654,321

12. Standard form: 56.99

Word Form:

11. Six hundred fifty four thousand, three hundred twenty one

12. Fifty six point ninety nine

I hope this helps!

Answer:

the answer is 0

Step-by-step explanation:

I hope this answer is correct

Answer:

560 students

Step-by-step explanation:

1400*.40=560 students in 6th grade

Answer:

Step-by-step explanation:

Ok so the question say if A is a half

(a+b)h

You'll get 1/2+b x h which is the answer but I can't find h because you haven't stayed what h would be.

Adiosss

Answer:

the first answer is correct Edge 2020

Step-by-step explanation:

Answer:

Step-by-step explanation:

-6

Answer:

answer = -1

.-(-2)^2 +3 = -4 +3 = -1

Answer:

21/16

Step-by-step explanation:

Answer:

danny makes 250 per month

Step-by-step explanation:

Answer:

Darryl earned $250.00 in a month.

Step-by-step explanation:

Answer:

3 times

Step-by-step explanation:

She would have to weigh the fake coins and another bag of real coins to spot a difference, and then she would need to check another bag to see which was correct. Maybe thats right.

Answer: aproximently d

Step-by-step explanation:

Answer:

9^3

Step-by-step explanation:

Since you are given 9^2 already and have to multiply that result by yet another nine, then your problem is 9^3

Hope this helps!

Answer:

63 :)

Step-by-step explanation:

Answer:

Step-by-step explanations:

10x - 2x

8x

10x - 2x in fewer terms is 8x.

Subtraction can be done for any numbers or algebraic expressions. It is the process of taking out certain value from a given amount of number.

The process of subtraction can also be termed as finding difference.

Given is an expression 10x - 2x.

We have to find the difference of these two expressions.

We can add or subtract only the like terms.

Like terms are terms which consist of same kind of variables.

Here 10x and 2x have same variable x.

So they can be subtracted.

10x - 2x = x(10 - 2) = 8x

Hence the difference of 10x and 2x is 8x.

To learn more about Subtraction, click on the link given below :

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Answer:

1) The frequency of the light is approximately 4.283 × 10¹⁴ Hz

2) The color of the light is red

Step-by-step explanation:

1) The given parameter;

The wavelength of the line contained in the Neon spectrum, λ = 700 nm = 0.0000007 m = 7.0 × 10⁻⁷ m

The speed of light, v = 299,792,000 m/s

v = f × λ

The frequency, f of the light = v/λ = 299,792,000/(7.0 × 10⁻⁷) ≈ 4.283 × 10¹⁴ Hz

The frequency of the light ≈ 4.283 × 10¹⁴ Hz

2) Given that light with wavelength between 620 - 750 nm constitute red light, we have that the given light with a wavelength of 700 nm is a red light source.

Answer:

Let's simplify step-by-step.

3−3/4x−1/4x−7

=3+ −3/4x+ −1/4x+ −7

Combine Like Terms:

=3+ −3/4x+ −1/4x+ −7

=(−3/4x+ −1/4x)+(3+ −7)

=−x+ −4

Answer:=−x−4

Step-by-step explanation:

answer:-4

Answer:

C

Step-by-step explanation:

Morgages is spelled mortgages

Answer:

After 2 hours the Red Cross raises $250 and after 6 hours it raised a total of $785. What's the average rate of change in terms of dollars per hour? Add answer. Log in to add ... If we start with 5 cells, and each cell divides in two every 15 minutes, how many total after 1 hour? if you what 3x +2/w is than you ...

Step-by-step explanation:

Answer:

Actually it is 4 mph.

Step-by-step explanation:

I know because I had it on a test I just took.

Her fastest speed was 4 miles per hour.

Given that,

Elena goes for a long walk.

This graph shows her time and distance traveled throughout the walk.

We have to find,

What was her fastest speed, in miles per hour?

According to the question,

The graph shows the time and distance traveled throughout the walk.

The distance traveled in every hour is given as follows.

Therefore, Her fastest speed was 4 miles per hour.

For more details refer to the link given below.

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