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son4ous [18]
2 years ago
7

"The output is one-fourth of the input."

Mathematics
1 answer:
Alenkasestr [34]2 years ago
3 0

Step-by-step explanation:

Using functions, the input is x, the output is y.

<u>Break down the problem:</u>

The output (y) is (equals) one-fourth (1/4) of the input (x)

y equals 1/4 of x

y =  \frac{1}{4} x

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Can someone help me please? It’s like my 3rd time trying to get some answers for this question. Thanks. :)
mote1985 [20]

Answer:

both rates of change equal the slope of the line (3/4)

Step-by-step explanation:

Part a)

We calculate the rate of change using the formula:

\frac{y_2-y_1}{x_2-x_1}

for the first interval [0,6], we calculate the y-values at x=0 and x=6;

at x=0 : y=\frac{3}{2} (0)+2=2

at x=6 : y=\frac{3}{2} (6)+2=11

therefore, the rate of change in this interval is: \frac{y_2-y_1}{x_2-x_1}=\frac{11-2}{6-0}=\frac{9}{6} =\frac{3}{2}

For the second interval [-4,4], we calculate the y-values at x=-4 and x=4;

at x=-4 : y=\frac{3}{2} (-4)+2=-4

at x=4 : y=\frac{3}{2} (4)+2=8

therefore, the rate of change in this interval is: \frac{y_2-y_1}{x_2-x_1}=\frac{8-(-4)}{4-(-4)}=\frac{12}{8} =\frac{3}{2}

Part b):

Notice that both rates of change equal the value of the slope of the linear function (3/2)

4 0
3 years ago
2. Which equation in standard form has a graph that passes through the point (-5,8) and has a
atroni [7]

Answer:

a

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - \frac{1}{5}, thus

y = - \frac{1}{5} x + c ← is the partial equation

To find c substitute (- 5, 8) into the partial equation

8 = 1 + c ⇒ c = 8 - 1 = 7

y = - \frac{1}{5} x + 7 ← in slope- intercept form

Multiply through by 5

5y = - x + 35 ( add x to both sides )

x + 5y = 35 ← in standard form → a

3 0
3 years ago
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prohojiy [21]
M=49
h=65
g=115
k=131
5 0
3 years ago
Each cone of the hourglass has a height of 12 millimeters. The total height of the sand within the top portion of the hourglass
Ratling [72]

The solution would be like this for this specific problem:

Volume of a cylinder = pi * r^2 * h 

Volume of a cone = 1/3 * pi * r^2 * h 

Total Height = 47

Height of the cone = 12

Height of the cylinder = 35

If the top half is filled with sand, then:

volume (sand) = pi * 4^2 * 36

volume (cone) =  1/3 * pi * 4^2 * 12

Total volume = 1960.353816 cubic millimeters

353816 / (10 * pi) = 62.4 seconds.

It will take 62.4 seconds until all of the sand has dripped to the bottom of the hourglass.

8 0
3 years ago
Mark the angles and sides of each pair of triangles to indicate that they are congruent.
Sophie [7]
5 because I believe I think I believe it’s 5 I believe yea it’s 5 definitely
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3 years ago
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