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3 years ago

Points (3,1) and (1,4) lie on line k. What is the slope of the line that is perpendicular to k?

1 answer:

6 0

First we need to find the slope of line k. Using the slope formula, we fill in accordingly: $m= \frac{4-1}{1-3}$ . The slope is -3/2. The slope of a line that is perpendicular to line k will have the opposite sign (so, positive) and will be the reciprocal of the line k's slope (so, 2/3). You could also say, more "mathematically legal", that the product of the slopes of perpendicular lines is -1, but it's easier to just say that they are opposite reciprocals. The slope you're looking for is 2/3. Choice 3 above.

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Select the correct answer.

Ilya [14]

Answer:

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Write this ratio as a fraction in the simplest form without any units. 8 yards to 15 feet. full anwser.

KATRIN_1 [288]

Answer:

8/3

Step-by-step explanation:

15 feet = 3 yards

8 yards to 3 yards

Your welcome!

Kayden Kohl

8th Grade Student

4 0

3 years ago

A rectangular parcel of land has an area of 6,000 ft2. A diagonal between opposite corners is measured to be 10 ft longer than o

Drupady [299]

Answer:

50ft by 120ft

Step-by-step explanation:

Area of a rectangle = L × W

6000ft² = L × W

L = 6000/W

When a diagonal line divides a rectangle into 2 right angled triangles, the diagonal line = Hypotenuse of either of the triangle and it is the longest side.

The formula for a right angle triangle =

a² + b² = c²( c = hypotenuse)

We are told in the question that:

A diagonal between opposite corners is measured to be 10 ft longer than one side of the parcel

Let us assume the side that the hypotenuse is longer than = Width

Hence, the Diagonal = (W + 10)²

Therefore

L² + W² = (W + 10)²

Since L = 6000/W

W² + (6000/W)² = (W + 10)²

W² + (6000/W)² = (W + 10) (W + 10)

W² + (6000/W)² = W² + 10W + 10W + 100

W² + (6000/W)² = W² + 20W + 100

W² - W² + (6000/W)² = 20W+ 100

6000²/W² = 20W + 100

6000² = W²( 20W + 100)

6000² = 20W³ + 100W²

20W³ + 100W² - 6000² = 0

20W³ + 100W² - 36000000 = 0

20(W³ + 5W² - 1800000) = 0

Factorising the quadratic equation,

20(W − 120)(W² + 125W + 15000) = 0

W - 120 = 0

W = 120

Therefore,

W(Width) = 120feet

Since the Width = 120 feet

We can find the length

6000ft² = L × W

L = 6000/W

L = 6000/120

L = 50 feet

The dimensions of the land, correct to the nearest foot is 50ft by 120ft

3 0

3 years ago

HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Gre4nikov [31]

Answer:

93° (to the nearest degree)

Step-by-step explanation:

sum of the interior angles of a triangle = 180°

Find angle C first, then subtract angle C and angle B from 180° to find angle A.

Use the sine rule $\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}$ to find angle C:

Therefore,

$\frac{sinB}{b}=\frac{sinC}{c}$

$\frac{sin38}{9}=\frac{sinC}{11}$

angle C = 48.80523914...°

Angle A = 180 - 38 - 48.80523914...°

= 93.19476086..°

= 93° (to the nearest degree)

7 0

2 years ago

If f(x)=x+7 and g(x)=<br><img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7Bx%20-%2013%7D%20" id="TexFormula1" title=" \frac{

Sergio [31]

Hi,

$f(x)=x+7\\

g(x)= \dfrac{1}{x-13} \\

(fog)(x)=f(g(x))=f(\dfrac{1}{x-13})=\dfrac{1}{x-13}+7\\


$
Domain of (fog)(x) is R \ {13} =(-oo 13[ U ]13 +oo)

8 0

3 years ago