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Kazeer [188]
3 years ago
10

The equation of the function h is h... PLEASE HELP MATH

Mathematics
1 answer:
Oduvanchick [21]3 years ago
4 0

Answer:

Part A) h(4) -m(16)=-4

Part B) The distance between the y-intercepts is equal to 4 units

Part C) The value of h(x) will always be greater than the value of m(x) for any value of x

Step-by-step explanation:

Part A) What is the value of h(4) -m(16)

we have

h(x)=\frac{1}{2}(x-2)^2

For x=4

h(4)=\frac{1}{2}(4-2)^2=2

Find the equation of the line m(x)

Find the slope

take the points

(8,2) and (12,4)

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}

substitute

m=\frac{4-2}{12-8}

m=\frac{2}{4}

m=\frac{1}{2}

Find the equation of the line in slope intercept form

y=mx+b

we have

m=\frac{1}{2}

point\ (8,2)

substitute

2=\frac{1}{2}(8)+b

solve for b

b=-2

y=\frac{1}{2}x-2

therefore

m(x)=\frac{1}{2}x-2

Find m(16)

m(16)=\frac{1}{2}(16)-2=6

so

h(4) -m(16)=2-6=-4

Part B) we know that

The y-intercept is the value of y when the value of x is equal to zero

Find the y-intercept of h(x)

For x=0

h(0)=\frac{1}{2}(0-2)^2=2

Find the y-intercept of m(x)

For x=0

m(0)=\frac{1}{2}(0)-2=-2

therefore

The distance between the y-intercepts is equal to 2-(-2)=4 units

Part C)

Graph both equations

h(x)=\frac{1}{2}(x-2)^2

m(x)=\frac{1}{2}x-2

using a graphing tool

see the attached figure

The value of h(x) will always be greater than the value of m(x) for any value of x

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What is the distance between point C and point D?
e-lub [12.9K]

Answer:

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Step-by-step explanation:

let

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The measures of two complementary angles have a ratio of 3 : 2. What is the measure of the larger angle?
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<em>Question:</em>

The measures of two complementary angles have a ratio of 3 : 2. What is the measure of the larger angle?

—————

<em>Solution:</em>

Call those two angles  x  and  y, where  x  is the larger one.

If they are complementary, then their sum equals  90°:

x + y = 90°      (i)


Also, the ratio between  x  and  y  is  3 : 2, so

  x           3
——  =  ——
  y           2


Product of the extremes = product of the means:

2x = 3y

2x – 3y = 0        (ii)


Now, just solve this system of equations:

  x  +  y = 90°         (i)
2x – 3y =   0          (ii)


Solve it with elimination. Since you want to know the value of the larger angle, which is  x, then eliminate the variable  y  by doing the following:

Multiply the equation  (i)  by  3,

3x + 3y = 270°        (iii)
2x – 3y =     0          (ii)


then add both equations, so you cancel out the variable  y:

3x + 2x + 3y – 3y = 270° + 0

3x + 2x = 270°

5x = 270°

         270°
x  =  ———
           5

x = 54°    <———  this is the measure of the larger angle.


I hope this helps. =)


Tags:  <span><em>system of linear equations elimination method solve complementary angles algebra geometry</em>
</span>
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