MATHEMATICS MIDDLE SCHOOL

Consider solving the equation for x.3(3x + 4) - 5 = ax + b
Which statements are true about the solution to the equation when substituting values for a and b as specified?
Select all that apply.

A. If a=−3 and b=4 , then there is exactly one solution to the equation.
B. If a=−9 and b=13 , then there is no solution to the equation.
C. If a=9 and b=−2 , then there is no solution to the equation.
D. If a=−3 and b=−5 , then there are infinitely many solutions to the equation.
E. If a=9 and b=7 , then there is exactly one solution to the equation.

Answers

Answer 1

Answer:

Answer:

A. If a=−3 and b=4 , then there is exactly one solution to the equation.

C. If a=9 and b=−2 , then there is no solution to the equation.

Step-by-step explanation:

The given equation is

$3(3x+4)-5=ax+b$

To solve for $x$ , we need to use the distributive property

$3(3x+4)-5=ax+b\n9x+12-5=ax+b\n9x-ax=b-7\nx(9-a)=b-7$

To find the right statement, we need to the given values.

For a=-3 and b=4,

$x(9-a)=b-7\nx(9-(-3))=4-7\nx(9+3)=-3\n12x=-3\nx=(-3)/(12) =-(1)/(4)$

So, choice A is true, because there's one solution to the equation.

For a=-9 and b=13,

$x(9-a)=b-7\nx(9-(-9))=13-7\n18x=6\nx=(6)/(18)=(1)/(3)$

The choice B is false.

For a=9 and b=-2

$x(9-a)=b-7\nx(9-9)=-2-7\n0x=-9\n0=-9$

Choice C is correct, because there's no solution, because zero is not equal to -9.

For a=-3 and b=-5

$x(9-a)=b-7\nx(9-(-3))=-5-7\n12x=-12\nx=(-12)/(12)=-1$

Choice D is false, becuase there's only one solution.

For a=9 and b=7

$x(9-a)=b-7\nx(9-9)=7-7\n0x=0\n0=0$

Choice E is false, because there are infinite solutions in ths case.

Therefore, the right choices are A and C.

Answer 2

Answer: So let's simplify the equation first.

9x + 12 - 5 = ax + b
9x + 7 = ax + b
9x - ax - b = 7

Alright now plug in the numbers for each option.
I don't feel like doing all of them but I did A (one solution) and B (no solution because the two 9x's cancel out).

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What is 1/2 × s for s = 3/10

Answers

1/2 * s
1/2 * 3/10 = 3/20
3/20

Answer: s = 3/20

What is 1/5 of 40???????????

Answers

Answer:
8

Explanation:
To get a fraction of a number, we will simply multiply this fraction by the number.

In the given we want to find $(1)/(5)$ of 40.

This can be computed as follows:
$(1)/(5)$ of 40 = $(1)/(5)$ * 40

= $(40*1)/(5)$

= $(40)/(5)$

= 8

Hope this helps :)

After calculating the fraction (one-fifth) of 40, the answer is 8.

What is the fraction (one-fifth) of 40?

To calculate one-fifth of 40, we divide 40 by 5. When we divide 40 by 5, we get the result 8. Therefore, the fraction (one-fifth) of 40 is equal to 8.

Let's break it down further to understand the process.

One-fifth represents dividing a whole into five equal parts. When we divide 40 by 5, we are essentially splitting 40 into five equal parts. Each part will be the same size.

To divide 40 by 5, we start with the number 40 and divide it by 5.

40 ÷ 5 = 8

The result, 8, represents one-fifth of 40. This means that if you take 40 and divide it into five equal parts, each part will be 8.

Therefore, 1/5 of 40 is equal to 8.

Read more about fraction here: brainly.com/question/78672

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I need o fine the length and the width of the rectangle that haves the area 9in and the perimeter

Answers

The perimeter = (2 lengths) + (2 widths) = 12

(1 length) + (1 width) = 6

Area = (length) x (width)

So you need two numbers that add to 6 and multiply to 9 .

How about 3 and 3 ?

Area = 3 x 3 = 9
Perimeter = 3 + 3 + 3 + 3 = 12

It works, and your rectangle is actually a square !

June will spin the arrow on the spinner 5 times. What is the probability that the arrow will stop on A, then B, then C, then D, then A?

Answers

Ok so assuming the board only has 4 spaces to land on (A,B,C,D) all we need to do is weight the probability,

1/4 x 1/4 x 1/4 x 1/4 x 1/4 = 1/1024

To solve I put the number of favorable outcomes over the number of total outcomes, in this case we had 1 favorable outcome each time and a constant of 4 possible outcomes.

Tommy takes 4 hours to drive to NC which is 232 miles away. How fast is tommy driving?

Answers

Answer: 58 miles per hour (mph)

Explanation/Calculation:
You are asking for the rate. To find the rate, divide the 232 (miles) by the 4 (hours) to get 58. Then convert 58 into 58 MILES PER HOUR.

Hope this helped! :)

He is driving at the rate of 58 miles per an hour.

Which expression represents the polynomial −2x2−4x4+8x+x5−2x3 rewritten in descending order? A- −2x2−4x4+8x+x5−2x3
B- −4x4−2x2+8x+x5−2x3
C- −4x4−2x3−2x2+8x+x5
D- x5−4x4−2x3−2x2+8x
E- 8x+x5−2x2−2x3−4x4