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Ne4ueva [31]
2 years ago
8

How can we get Equation B from Equation A? A. 5 = -2 (x - 1) B. 5 = -2x + 2 How can we get Equation B from Equation A?

Mathematics
1 answer:
lesya [120]2 years ago
7 0

Answer:

Please check the explanation.

Step-by-step explanation:

<u>Determining equation B from Equation A</u>

Given the equation A

5\:=\:-2\:\left(x\:-\:1\right)

Apply distributive law a\left(b-c\right)=ab-ac

5= -2x+2    which is equation B

Hence, equation B can be obtained by implementing the distributive law operation on equation A.

<u>Determining equation A from Equation B</u>

Given the equation B

5 = -2x + 2

Factor out common term -2 on the right-hand side of the equation

5=-2\left(x-1\right)  which is the equation A

Hence, equation A can be obtained by factoring out the common term -2 on the right-hand side of equation B.

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Step-by-step explanation:

STEP 1

Calculate the slope from 2 points.

STEP 2

Substitute either point into the equation. You can use either (3,7) or (5,11)

STEP 3

Solve for b, which is the y-intercept of the line.

STEP 4

Substitute b, -1, into the equation from step 2.

6 0
3 years ago
By definition, a round character _____.
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3 years ago
The area of the yellow region is 112 cm^2. find the value of x​
mrs_skeptik [129]
<h3>Answer:   x = 7</h3>

===========================================================

Explanation:

The largest rectangle (composed of the green and yellow sections combined) has area of 11*12 = 132 cm^2.

The yellow region takes up 112 of those 132 sq cm. This must mean the green region takes up 132-112 = 20 cm^2.

The horizontal portion of the green rectangle is 12-x cm. The vertical portion is 11-x cm. We can form the area of the green rectangle as an algebraic expression like so

area = length*width

area = (11-x)*(12-x)

area = 132 - 11x - 12x + x^2 .... apply the FOIL rule

area = x^2 - 23x + 132

Set this equal to the 20 cm^2 we found earlier.

x^2 - 23x + 132 = 20

x^2 - 23x + 132-20 = 0

x^2 - 23x + 112 = 0

We could factor or we could use the quadratic formula. I'll go with the second option.

We'll plug in a = 1, b =  -23, c = 112

x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-23)\pm\sqrt{(-23)^2-4(1)(112)}}{2(1)}\\\\x = \frac{23\pm\sqrt{81}}{2}\\\\x = \frac{23\pm9}{2}\\\\x = \frac{23+9}{2}\ \text{ or } \ x = \frac{23-9}{2}\\\\x = \frac{32}{2}\ \text{ or } \ x = \frac{14}{2}\\\\x = 16\ \text{ or } \ x = 7\\\\

One of these solutions isn't feasible. Note how if x = 16, then this exceeds both the 11 cm and 12 cm sides. So this x value is not possible.

However, x = 7 is possible.

If x = 7, then the horizontal portion of the green rectangle is 12-x = 12-7 = 5 cm. Also, the vertical portion of the green rectangle would be 11-x = 11-7 = 4 cm. The area then is length*width = 5*4 = 20 cm^2 which matches up with what we got earlier. So the answer is confirmed.

7 0
3 years ago
Freddy poured 1.4 liters of soda pop from a full 2-liter container. How much soda pop was left in the container?
german

Answer:

0.6 liters left

Step-by-step explanation:

So we know that the container is filled with 2 liters.

We also know that he poured 1.4 liters out of the container.

This leads to the conclusion

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6 0
3 years ago
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What the example of constant and variable?​
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Examples of constant :

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2 years ago
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