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2 years ago

The following table shows the amount of water leaking from an inflatable pool as a function of time:

Mathematics

2 answers:

iris [78.8K]2 years ago

5 0

Answer:

Step-by-step explanation:

You are given the table

$\begin{array}{cc}\text{Time}&\text{Water}\\x&f(x)\\0&35\\1&30\\2&25\\3&20\\4&15\end{array}$

This table represents a linear relationship between time and water leaked, because

$\dfrac{30-35}{1-0}=\dfrac{25-30}{2-1}=\dfrac{20-25}{3-2}=\dfrac{15-20}{4-3}$

The linear function has the equation

$f(x)=mx+b$

Find m and b:

$f(0)=35\Rightarrow 35=m\cdot 0+b,\ b=35\\ \\f(1)=30\Rightarrow 30=m\cdot 1+b,\ 30=m+35,\ m=-5$

So,

$f(x)=-5x+35$

Find the x-intercept:

$f(x)=0\Rightarrow -5x+35=0\\ \\5x=35\\ \\x=7$

Hence, point (7,0) is x-intercept with the meaning x=7 is the time it takes to empty the water in the pool

Rufina [12.5K]2 years ago

5 0

Answer:

(7, 0); the time it takes to empty the water in the pool

Step-by-step explanation:

Took test

(Please give me brainiest)

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A) Two angles are adjacent if their measures add up to 90°.

slavikrds [6]

Answer:

A) False

B) False

Step-by-step explanation:

A. Two angles whose measures add up to 90° are said to be complementary, while two angles are adjacent when formed beside each other. So, adjacent angles might be complementary or supplementary. Thus, the answer to the first part of the question is false.

B. When two angles share a side, they are said to be adjacent to each other. But supplementary angles add up to $180^{o}$ . Since adjacent angles might be complementary or supplementary, then the answer to the second part of the question is false.

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2 years ago

Express the following repeating decimal as a fraction in simplest form.

Ivenika [448]

Answer:

$0.\overline{369} = \frac{41}{111}$

Step-by-step explanation:

x = 0.369369369...

10x = 3.69369369...

100x = 36.9369369...

1000x = 369.369369...

1000x - x = 369

999x = 369

$x = \frac{369}{999} \\\\x = \frac{123}{333}\\\\x = \frac{41}{111}$

4 0

3 years ago

Show your work please.

Kruka [31]

Answer:

Tauren has 78 keychains

James has 34 keychains

Marcus has 68 keychains

Yahya has 74 keychains

Step-by-step explanation:

I got this answer by doing this:

If Tauren has 78 keychains then its gonna be left like that.

If everybody else has an average of 68 keychains then divide 68 by 2 to get half of what marcus has which equals 34.

Then add the amount of James and marcus keychains which is 68 plus 34 which equals 102, the subtract the 28 because it says Yayha has 28 fewer keychains and that equals 74.

3 0

3 years ago

A triangle with vertices at A(0, 0), B(0, 4), and C(6, 0) is dilated to yield a triangle with vertices at A′(0, 0), B′(0, 10), a

sineoko [7]

ANSWER

The scale factor is
$2.5$

EXPLANATION

The given triangle has vertices,

$A(0,0),B(0,4),\:and\:C(6, 0)$ .

The vertices of the image triangle is,

$A'(0,0),B'(0,10),\:and\:C'(15, 0)$ .

The scale factor is given by

$k = \frac{image \: length}{object \: length}$

So we can use any of the corresponding sides to determine the scale factor,

$k = \frac{|A'B'|}{ |AB|}$

$k = \frac{ |10 - 0| }{ |4 - 0|}$

$k = \frac{ |10| }{ |4 |} = \frac{10}{4} = 2.5$

Or

$k = \frac{|A'C'|}{ |AC|}$

$k = \frac{ |15 - 0| }{ |6 - 0|}$

$k = \frac{ |15| }{ |6|} = \frac{15}{6} = 2.5$

Or

$k=\frac{|B'C'|}{|BC|}$

$k = \frac{\sqrt{(15 - 0)^2+(0-10)^2 }}{\sqrt{(6 - 0)^2+(0-4)^2}}$

$k = \frac{ 5\sqrt{13}}{2\sqrt{13}} = \frac{5}{2} = 2.5$

The correct answer is C

3 0

2 years ago

How far will a ball roll if it travels 12m/s<br> for 3 seconds?

GuDViN [60]

If it takes a ball to roll 12 meters per sec, and asks how far it will roll for 3 seconds you would multiply 12 and 3 getting 36.

The ball will roll 36 meters for 3 seconds

5 0

2 years ago

Read 2 more answers