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2 years ago

Find the equation of the line described.

Mathematics

1 answer:

tino4ka555 [31]2 years ago

4 0

Answer:

y = - $\frac{1}{3}$ x + $\frac{19}{3}$

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 )

y = 3x + 6 ← is in slope- intercept form

with slope m = 3

Given a line with slope m then the slope of a line perpendicular to it is

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{3}$ , thus

y = - $\frac{1}{3}$ x + c ← is the partial equation

To find c , substitute (4, 5) into the partial equation

5 = - $\frac{4}{3}$ + c ⇒ c = 5 + $\frac{4}{3}$ = $\frac{19}{3}$

y = - $\frac{1}{3}$ x + $\frac{19}{3}$ ← equation of perpendicular line

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What is the slope of the line passing through the points (0, 4) and (-8, -1)?

Bas_tet [7]

Answer:

0.625

Step-by-step explanation:

Given the points :

(0, 4) and (-8, -1)

x1 = 0 ; y1 = 4

x2 = - 8 ; y2 = - 1

Slope, m = rise / run

Rise = y2 - y1 = - 1 - 4 = - 5

Rise = x2 - x1 = - 8 - 0 = - 8

The slope, m = - 5 / - 8

Slope, m = 0.625

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3 years ago

Find the perimeter of each polygon created by the coordinates.

maks197457 [2]

I believe the answer is c

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3 years ago

Here are the vertices of rectangle FROG: (-2,5),(-2,1),(6,5),(6,1). Find the perimeter of this rectangle. If you get stuck, try

ryzh [129]

Answer:

Part 1) The perimeter of rectangle is equal to 24 units

Part 2) The area of rectangle is equal to 32 square units

Step-by-step explanation:

Part 1) Find the perimeter of rectangle

we know that

The perimeter of rectangle is equal to

$P=2(L+W)$

where

L is the length of rectangle

W is the width of rectangle

we have

$F(-2,5),R(-2,1),O(6,1),G(6,5)$

Plot the figure to better understand the problem

using a graphing tool

see the attached figure

Remember that in a rectangle opposite sides are congruent and the measure of each interior angle is equal to 90 degrees

$FG=RO=L\\RF=OG=W$

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

step 1

Find the distance FG

$F(-2,5),G(6,5)$

substitute the values

$d=\sqrt{(5-5)^{2}+(6+2)^{2}}$

$d=\sqrt{(0)^{2}+(8)^{2}}$

$FG=8\ units$

step 2

Find the distance RF

$R(-2,1),F(-2,5)$

substitute the values

$d=\sqrt{(5-1)^{2}+(-2+2)^{2}}$

$d=\sqrt{(4)^{2}+(0)^{2}}$

$RF=4\ units$

step 3

Find the perimeter

$P=2(L+W)$

we have

$FG=RO=L=8\ units\\RF=OG=W=4\ units$

substitute

$P=2(8+4)=24\ units$

Part 2) Find the area of rectangle FROG

we know that

The area of rectangle is equal to

$A=LW$

we have

$FG=RO=L=8\ units\\RF=OG=W=4\ units$

substitute

$A=(8)(4)=32\ units^2$

8 0

3 years ago

Use the standard normal distribution or the t-distribution to construct a 99% confidence interval for the population mean. Jus

vichka [17]

Answer:

(25.732,30.868)

Step-by-step explanation:

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Since only sample std deviation is known we can use only t distribution

Std error = $\frac{s}{\sqrt{n} } =\frac{6.09}{\sqrt{42} } \\=0.9397$

$df = 42-1 =41$

t critical for 99% two tailed $= 2.733$

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Confidence interval lower bound = $28.3-2.568=25.732$

Upper bound = $28.3+2.568=30.868$

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3 years ago

The square below has an area of 16 +82 + square meters.

svlad2 [7]

Answer:

120 meters

Step-by-step explanation:

16 + 82 = 98

98 + 22 = 120

3 0

3 years ago

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