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JulsSmile [24]
2 years ago
8

A painter made the table below to show the amount of paint it takes to cover a certain amount of square feet. The amount of pain

t varies directly with the area of each wall.

Mathematics
2 answers:
Sliva [168]2 years ago
4 0

Answer:

Option A.

Step-by-step explanation:

The table made by the painter shows the amount of paint required to cover a certain amount of area of the wall.

Amount of paint is directly proportional to the area covered

In other words Amount of paint (y) ∝ Area covered (x)

y ∝ x

As we know when proportionality sign is removed, a constant known as proportionality constant is multiplied with the variable.

So y = k(x) where k is the proportionality constant

Now from the table to cover the area of 64 square feet, 4 pints of paint is required.

Now from the formula

4 = 64x

x = \frac{4}{64}=\frac{1}{16}

Now we have to calculate the amount of paint required to cover the area of 256 square feet.

y = \frac{1}{16}\times 256

y = 16 pints

Therefore, 16 pints of the paint will be required to cover 256 square feet.

Option A is correct.

Minchanka [31]2 years ago
3 0

Answer:

Just Pick 16 Pints

Step-by-step explanation:

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Simplify (write without absolute value sign): |x+3|, if x>2
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Step-by-step explanation:

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Identify the ordered pair that represents the vector from a(-9,9) to b(7,3) and the magnitude of ab.
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Answer:

Answers below

Step-by-step explanation:

1. Order pair method

[(x2-x1) , (y2-y1)] = b-a = [(7--9) , (3-9)] = (16,-6)

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7 0
3 years ago
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10 points, doing this one again because I got a wrong answer last time but regardless thank you for trying to help​
Alik [6]

Hey ! there

Answer:

  • Value of missing side i.e. TE is <u>1</u><u>2</u><u> </u><u>feet</u>

Step-by-step explanation:

In this question we are provided with a <u>right</u><u> </u><u>angle </u><u>triangle</u> having <u>TS </u><u>-</u><u> </u><u>35</u><u> </u><u>ft </u><u>and</u><u> </u><u>SE </u><u>-</u><u> </u><u>37</u><u> </u><u>ft </u>. And we are asked to find the missing side that is <u>TE </u>using Pythagorean Theorem .

<u>Pythagorean Theorem :</u> -

According to Pythagorean Theorem sum of squares of perpendicular and base is equal to square of hypotenuse in a right angle triangle i.e.

  • H² = P² + B²

<u>Where </u><u>,</u>

  • H refers to <u>Hypotenuse</u>

  • P refers to <u>Perpendicular</u>

  • B refers to <u>Base</u>

<u>Solution</u><u> </u><u>:</u><u> </u><u>-</u>

In the given triangle ,

  • Base = <u>TE </u>

  • Perpendicular = <u>TS </u><u>(</u><u> </u><u>35</u><u> </u><u>feet </u><u>)</u>

  • Hypotenuse = <u>SE </u><u>(</u><u> </u><u>37</u><u> </u><u>feet </u><u>)</u>

Now applying Pythagorean Theorem :

\quad \longmapsto \qquad \:SE {}^{2}  = TS {}^{2}  + TE {}^{2}

Substituting values :

\quad \longmapsto \qquad \:37 {}^{2}  = 35 {}^{2}  + TE {}^{2}

Simplifying it ,

\quad \longmapsto \qquad \:1369 = 1225  + TE {}^{2}

Subtracting 1225 on both sides :

\quad \longmapsto \qquad \:1369 - 1225  = \cancel{1225}  + TE {}^{2}  -  \cancel{1225}

We get ,

\quad \longmapsto \qquad \:144 = TE {}^{2}

Applying square root to both sides :

\quad \longmapsto \qquad \ \sqrt{ 144} =  \sqrt{TE {}^{2}}

We get ,

\quad \longmapsto \qquad \:     \red{\underline{\boxed{\frak{TE  = 12 \: feet}}}} \quad \bigstar

  • <u>Henceforth</u><u> </u><u>,</u><u> </u><u>value </u><u>of </u><u>missing </u><u>side </u><u>is </u><em><u>1</u></em><em><u>2</u></em><em><u> </u></em><em><u>feet </u></em><em><u>.</u></em>

<u>Verifying</u><u> </u><u>:</u><u> </u><u>-</u>

Now we are verifying our answer using Pythagorean Theorem . We know that according to Pythagorean Theorem ,

  • SE² = TS² + TE²

Substituting value of SE , TS and TE :

  • 37² = 35² + <u>1</u><u>2</u><u>²</u>

  • 1369 = 1225 + 144

  • 1369 = 1369

  • L.H.S = R.H.S

  • Hence , Verified .

<u>Therefore</u><u> </u><u>,</u><u> </u><u>our</u><u> answer</u><u> is</u><u> correct</u><u> </u><u>.</u>

<h2><u>#</u><u>K</u><u>e</u><u>e</u><u>p</u><u> </u><u>Learning</u></h2>
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2 years ago
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