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3 years ago

What is the rate of change between (2,2) and (17,7)

Mathematics

1 answer:

ziro4ka [17]3 years ago

6 0

Answer:

$\frac{1}{3} = m$

Step-by-step explanation:

$\frac{-y_1 + y_2}{-x_1 + x_2} = m$

$\frac{-2 + 7}{-2 + 17} = \frac{5}{15} = \frac{1}{3}$

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Identify the vertex, the focus, and the directrix of the parabola with the given equation.

Elenna [48]

Vertex: (-4,-3)
Focus: (-4, -11/4)
Directrix: y= -13/4

7 0

3 years ago

Negative three over four times five over seven divided by negative one over two

LekaFEV [45]

Answer:

$1 \frac{1}{14}$

Step-by-step explanation:

$- \frac{3}{4} \times \frac{5}{7} \div - \frac{1}{2} = - \frac{15}{28} \times -2 = \frac{30}{28} = 1 \frac{2}{28} = 1 \frac{1}{14}$

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3 years ago

To avoid dehydration, a person should drink 8 ounces of water for every 15 minutes of exercise. How much water should Hahn drink

Lostsunrise [7]

Answer:

Step-by-step explanation:

1. Proportion:

8/15=x/135

2. Answer is 72

7 0

3 years ago

The fish tank has side lengths 20in, 10in and height 15in. The water level is two inches below the top of the tank. A glass sphe

Kitty [74]

Answer:

Part 1) The new distance from the water to the top of the tank is $1.979\ in$

Part 2) The maximum number of balls that can be put into the tank with the tank not overflowing is 95

Step-by-step explanation:

step 1

Find the total volume of the tank

$V=20*10*15=3,000\ in^{3}$

step 2

Find the volume of the tank if the water level is two inches below the top of the tank

$V=20*10*(15-2)=2,600\ in^{3}$

step 3

Find the volume of the glass sphere

The volume of the glass sphere is equal to

$V=\frac{4}{3}\pi r^{3}$

we have

$r=1\ in$

assume

$\pi=3.14$

substitute

$V=\frac{4}{3}(3.14)(1)^{3}$

$V=4.2\ in^{3}$

step 4

What is the new distance from the water to the top of the tank?

we know that

$2 in -----> represent (3,000-2,600)=400\ in^{3}$

using proportion

Find how many inches correspond a volume of $4.2\ in^{3}$

$\frac{2}{400}\frac{in}{in^{3}}=\frac{x}{4.2}\frac{in}{in^{3}}\\ \\x=4.2*2/400\\ \\x=0.021\ in$

The new distance from the water to the top of the tank is

$2-0.021=1.979\ in$

step 5

Find how many of these balls can be put into the tank with the tank not overflowing

we know that

The volume of one ball is equal to $4.2\ in^{3}$

using proportion

$\frac{1}{4.2}=\frac{x}{400}\\ \\x=400/4.2\\ \\x=95.23\ balls$

therefore

The maximum number of balls that can be put into the tank with the tank not overflowing is 95

4 0

3 years ago

The area of the entire rectangle to the right is x(x+4). Find another expression for this area by finding the sum of the areas o

Ainat [17]

Answer:

x² + 4x

Step-by-step explanation:

Divide the rectangle into a square with sides 'x' and a rectangle with sides 'x' and '4'

(x)(x) + (4)(x)

x² + 4x

3 0

3 years ago