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3 years ago

Find an equation for the perpendicular bisector of the line segment whose endpoints are (7,1)(7,1) and (-9,9)(−9,9)

1 answer:

3 0

First we are going to find the slope of these two endpoints.

Slope = $\frac{Y2-Y1}{X2-X1}$

Slope = $\frac{9-1}{-9-7}$
Slope = $\frac{8}{-16}$
Slope = $- \frac{1}{2}$

Because we need the perpendicular bisector, we do the opposite reciprocal of the slope. This is positive two.

Your perpendicular equation begins as y = 2x + b

To find where it will bisect, we need to find the midpoint of the two endpoints.

Midpoint = $( \frac{X1+X2}{2} , \frac{Y1+Y2}{2} )$

Mdpt = $( \frac{7+(-9)}{2} , \frac{1+9}{2} )$
Mdpt = $( \frac{-2}{2} , \frac{10}{2} )$
Mdpt = (- 1, 5)

We plug this into our incomplete equation to solve for b.

5 = 2(- 1) + b
5 = - 2 + b
7 = b

Your perpendicular bisector equation is y = 2x + 7

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If angle adc=134 and adb=5x+4 and bdc=7x-2 what does angle bdc measure

ruslelena [56]

As I've shown on picture that I attached:
∠ADC=∠ADB+∠BDC⇒134=5x+4+7x-2
12x+2=134
12x=132⇒x=132/12
x=11
Angle BDC measure 7x-2=7*11-2⇒∠BDC=75.

8 0

3 years ago

"isotherms are drawn at regular intervals; on this map, the interval between successive isotherms is ______ fahrenheit degrees."

Marizza181 [45]

An isotherm on a geographic map is a type of equal temperature at a given date or time. And if we talk about thermodynamics, it is a curve on a Pressure – Volume diagram at a constant temperature.

Basing from the graph, we can actually see that the interval is:

10 Fahrenheit degrees

6 0

3 years ago

Help 16-18 thank you

saw5 [17]

Answer:

16. (80)(60) = 4800

17. (500)(600) = 300000

18. (700)(800) = 560000 a). high

Step-by-step explanation:

5 0

3 years ago

1. If a scale factor is applied to a figure and all dimensions are changed proportionally, what is the effect on the perimeter o

scZoUnD [109]

Answer:

Part 1) The perimeter of the new figure must be equal to the perimeter of the original figure multiplied by the scale factor (see the explanation)

Part 2) The area of the new figure must be equal to the area of the original figure multiplied by the scale factor squared

Part 3) The new figure and the original figure are not similar figures (see the explanation)

Step-by-step explanation:

Part 1) If a scale factor is applied to a figure and all dimensions are changed proportionally, what is the effect on the perimeter of the figure?

we know that

If all dimensions are changed proportionally, then the new figure and the original figure are similar

When two figures are similar, the ratio of its perimeters is equal to the scale factor

The perimeter of the new figure must be equal to the perimeter of the original figure multiplied by the scale factor

Part 2) If a scale factor is applied to a figure and all dimensions are changed proportionally, what is the effect on the area of the figure?

we know that

If all dimensions are changed proportionally, then the new figure and the original figure are similar

When two figures are similar, the ratio of its areas is equal to the scale factor squared

The area of the new figure must be equal to the area of the original figure multiplied by the scale factor squared

Part 3) What would happen to the perimeter and area of a figure if the dimensions were changed NON-proportionally? For example, if the length of a rectangle was tripled, but the width did not change? Or if the length was tripled and the width was decreased by a factor of 1/4?

we know that

If the dimensions were changed NON-proportionally, then the ratio of the corresponding sides of the new figure and the original figure are not proportional

That means

The new figure and the original figure are not similar figures

therefore

Corresponding sides are not proportional and corresponding angles are not congruent

A) If the length of a rectangle was tripled, but the width did not change?

Perimeter

The original perimeter is P=2L+2W

The new perimeter would be P=2(3L)+2W ----> P=6L+2W

The perimeter of the new figure is greater than the perimeter of the original figure but are not proportionals

Area

The original area is A=LW

The new area would be A=(3L)(W) ----> A=3LW

The area of the new figure is three times the area of the original figure but its ratio is not equal to the scale factor squared, because there is no single scale factor

B) If the length was tripled and the width was decreased by a factor of 1/4?

Perimeter

The original perimeter is P=2L+2W

The new perimeter would be P=2(3L)+2(W/4) ----> P=6L+W/2

The perimeter of the new figure and the perimeter of the original figure are not proportionals

Area

The original area is A=LW

The new area would be A=(3L)(W/4) ----> A=(3/4)LW

The area of the new figure is three-fourth times the area of the original figure but its ratio is not equal to the scale factor squared, because there is no single scale factor

4 0

3 years ago

f(x) = 500(1.05)x What was the average rate of change of the value of Sophia's investment from the second year to the fourth yea

hjlf

$\bf slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ f(x_2)}}-{{ f(x_1)}}}{{{ x_2}}-{{ x_1}}}\impliedby 
\begin{array}{llll}
average\ rate\\
of\ change
\end{array}\\\\
-------------------------------\\\\
f(x)=500(1.05)^x \qquad 
\begin{cases}
x_1=2\\
x_2=4
\end{cases}\implies \cfrac{f(4)-f(2)}{4-2}
\\\\\\
\cfrac{[500(1.05)^4]~-~[500(1.05)^2]}{4-2}\implies \cfrac{56.503125}{2}\implies 28.2515625$

6 0

3 years ago