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3 years ago

Solve each equation for y. 1. 2y + 4x = 8; x = -2, 1, 3

Mathematics

1 answer:

prohojiy [21]3 years ago

7 0

Answers:

IF: x = -2, THEN: y = 8

IF: x = 1, THEN: y = 2

IF: x = 3, THEN: y = -2

Isolate the variable, y. Note the equal sign, what you do to one side, you do to the other. When isolating, do the opposite of PEMDAS. When solving, follow PEMDAS.

If: x = -2

Plug in -2 for x in the equation.

2y + 4 (-2) = 8

First, multiply. Note that when you multiply a negative and a positive number, your answer will be negative:

2y + (4 * -2) = 8

2y - 8 = 8

Isolate the variable, y. First, add 8 to both sides:

2y - 8 (+8) = 8 (+8)

2y = 8 + 8

2y = 16

Next, divide 2 from both sides of the equation:

(2y)/2 = (16)/2

y = 16/2

y = 8

IF x = -2, then y = 8.

If: x = 1

Plug in 1 for x in the equation.

2y + 4(1) = 8

First, multiply:

2y + (4 * 1) = 8

2y + 4 = 8

Next, isolate the variable, y. Note the equal sign; do the opposite of PEMDAS.

First, subtract 4 from both sides:

2y + 4 (-4) = 8 (-4)

2y = 8 - 4

2y = 4

Next, divide 2 from both sides to isolate y:

(2y)/2 = (4)/2

y = 4/2

y = 2

If: x = 1, then y = 2.

If: x = 3

Plug in 3 for x in the equation:

2y + 4(3) = 8

First, multiply:

2y + (4 * 3) = 8

2y + 12 = 8

Next, isolate the variable, y. Note the equal sign; do the opposite of PEMDAS.

First, subtract 12 from both sides of the equation:

2y + 12 (-12) = 8 (-12)

2y = 8 - 12

2y = -4

Next, divide 2 from both sides of the equation:

(2y)/2 = (-4)/2

y = -4/2

y = -2

If: x = 3, then y = -2.

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A rectangle is constructed with its base on the diameter of a semicircle with radius 2 and with its two other vertices on the se

stealth61 [152]

Answer:

L = 2*√2

w = √2

Step-by-step explanation:

Given:

A rectangle is constructed with its base on the diameter of a semicircle with radius 2 and with its two other vertices on the semicircle.

Find:

What are the dimensions of the rectangle with maximum area?

Solution:

- Let the length and width of the rectangle be L and w respectively.

- We know that Length L lie on the diameter base. So , L < 4 and the width w is less than 2 . w < 2.

- Using the Pythagorean Theorem, we relate the L with w using the radius r = 2 of the semicircle.

r^2 = (L/2)^2 + (w)^2

sqrt (4 - w^2 ) = L / 2

L = 2*sqrt (4 - w^2 ) L < 4 , w < 2

- The relation derived above is the constraint equation and the function is Area A which is function of both L and w as follows:

A ( L , w ) = L*w

- We substitute the constraint into our function A:

A ( w ) = 2*w*sqrt (4 - w^2 )

- Now we will find the critical points for width w for which A'(w) = 0

A'(w) = 2*sqrt (4 - w^2 ) - 2*w^2 / sqrt (4 - w^2 )

0 = [2*sqrt (4 - w^2 )*sqrt (4 - w^2 ) - 2*w^2] / sqrt (4 - w^2 )

0 = 2*(4 - w^2 ) - 2*w^2

0 = -4*w^2 + 8

8/4 = w^2

w = + sqrt ( 2 ) ..... 0 < w < 2

- From constraint equation we have:

L = 2*sqrt (4 - 2 )

L = 2*sqrt(2)

7 0

4 years ago

-4x-3(-44-23)=13 please show the work, i’ll mark brainliest

pychu [463]

Answer:

Step-by-step explanation:

Let's solve your equation step-by-step.

−4x−3(−44−23)=13

Step 1: Simplify both sides of the equation.

−4x+201=13

Step 2: Subtract 201 from both sides.

−4x+201−201=13−201

−4x=−188

Step 3: Divide both sides by -4.

−4x

−4

−188

−4

x=47

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3 years ago

Kim rolls a six-sided number cube labeled from 1 to 6.

boyakko [2]

The answer is A) 2/3....

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3 years ago

Read 2 more answers

Using the frequency table given, find the mean, median, and mode.

aalyn [17]

Answer:

$Mean = 69$

$Mode = 66$

$Median = 69$

Step-by-step explanation:

Given

The frequency table

Required

Determine the mean, median and mode

Calculating Mean

$Mean = \frac{\sum fx}{\sum f}$

Where

fx = product of frequency and inches

f = frequency

So;

$Mean = \frac{63 * 2 + 65 * 1 + 66 * 4 + 67 * 3 + 68 * 1 + 69 * 2 + 70 * 2 + 71 * 1 + 72 * 3 + 74 * 2 + 75 * 2}{2 + 1 + 4 + 3 + 1 + 2 + 2 + 1 + 3 + 2 + 2}$