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HACTEHA [7]
3 years ago
8

Using the image below, identify the angles that are vertical angles, list the angles that are linear pairs, and then solve for ,

, and .

Mathematics
1 answer:
34kurt3 years ago
6 0

Answer:

Step-by-step explanation:

y and 76 are vertically opposite angles

x and z are vertically opposite angles

Linear pairs.

If sum of two adjacent angles are 180, then they are linear pair.

x & 76 are linear pairs

y & z are linear pairs

z & 76 are linear pairs

x and y are linear pairs

Solutions:

y = 76   { vertically opposite angles are equal}

x + 76 = 180  { linear pair}

x = 180 - 76

x = 104

z = x  {Vertically opposite angles are equal}

z = 104

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When it is perpendicular, the slope is the negative reciprocal so it would equal -3/2x. Plug in the points to the equation so you can find the intercept. -8=-3/2(4)+b
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Add 6: -2=b
The equation would be f(x)=-3/2x-2
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The graph would be a compressed inside down U shape

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Adrian is going on holiday.
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The radius r of a sphere is increasing at a constant rate of 0.04 centimeters per second. (Note: The volume of a sphere with rad
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Answer:

The rate of the volume increase will be \frac{dV}{dt}=50.27 cm^{3}/s

Step-by-step explanation:

Let's take the derivative with respect to time on each side of the volume equation.

\frac{dV}{dt}=4\pi R^{2}\frac{dR}{dt}

Now, we just need to put all the values on the rate equation.

We know that:

dR/dt is 0.04 cm/s  

And we need to know what is dV/dt when R = 10 cm.

Therefore using the equation of the volume rate:

\frac{dV}{dt}=4\pi 10^{2}0.04

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I hope it helps you!

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2 years ago
For the piecewise function, find the values h( - 6), h(0), h(5), and h(9).- 5x – 13, for x < -3h(x) = { 5, for - 35x<5for
sleet_krkn [62]

Given the piecewise function h(x):

h(x)=\begin{cases}-5x-13,x

-When x is less than "-3", h(x)=-5x-13

-When x is between -3 and 5, h(x)=5

-When x is greater than or equal to 5, h(x)=x+1

1) For h(-6), this notation indicates that you have to determine the value of h(x) when x=-6

-6 is less than -3, which means that for this value of x, the function has the following shape

h(x)=-5x-13

Replace the expression with x=-6 and calculate the corresponding value of x:

\begin{gathered} h(-6)=-5(-6)-13 \\ h(-6)=30-13 \\ h(-6)=17 \end{gathered}

2) For h(0), you have to determine the value of h(x) when x=0. Zero is between -3 and 5, for this value of x, the function h(x) has the following shape:

h(x)=5

This equation represents a horizontal line, which means that for every value within the interval of definition -3≤x<5, the function always has the same value h(x)=5

We can conclude that:

h(0)=5

3) For h(5), you have to determine the value of h(x) for x=5, for values of x greater than or equal to 5, h(x) has the following shape:

h(x)=x+1

Replace the expression with x=5 and calculate the corresponding value of h(x):

\begin{gathered} h(5)=5+1 \\ h(5)=6 \end{gathered}

4) For h(9), you have to determine the value of h(x) when x=9, 9 is greater than 5, for this value of x, the function has the following shape:

h(x)=x+1

Replace the expression with x=9, and calculate the corresponding value of h(x):

\begin{gathered} h(9)=9+1 \\ h(9)=10 \end{gathered}

So, to sum up:

undefined

5 0
1 year ago
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