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2 years ago

What is the slope of a line of best fit if its equation is y = −2x + 3?

Mathematics

1 answer:

EastWind [94]2 years ago

8 0

If given a line in the slope-intercept form

y=mx+b

m is the slope and b is they y-intercept

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How to solve this question

erica [24]

Multiplication property; distribution property of an exponent. Multiply exponents together, then distribute the ¨( )¨

3 0

2 years ago

Find exact values for sin θ, cos θ and tan θ if csc θ = 3/2 and cos θ < 0.

kumpel [21]

Answer:

Part 1) $sin(\theta)=\frac{2}{3}$

Par 2) $cos(\theta)=-\frac{\sqrt{5}}{3}$

Part 3) $tan(\theta)=-\frac{2\sqrt{5}}{5}$

Step-by-step explanation:

step 1

Find the $sin(\theta)$

we have

$csc(\theta)=\frac{3}{2}$

Remember that

$csc(\theta)=\frac{1}{sin(\theta)}$

therefore

$sin(\theta)=\frac{2}{3}$

step 2

Find the $cos(\theta)$

we know that

$sin^{2}(\theta) +cos^{2}(\theta)=1$

we have

$sin(\theta)=\frac{2}{3}$

substitute

$(\frac{2}{3})^{2} +cos^{2}(\theta)=1$

$\frac{4}{9} +cos^{2}(\theta)=1$

$cos^{2}(\theta)=1-\frac{4}{9}$

$cos^{2}(\theta)=\frac{5}{9}$

square root both sides

$cos(\theta)=\pm\frac{\sqrt{5}}{3}$

we have that

$cos(\theta) < 0$ ---> given problem

$cos(\theta)=-\frac{\sqrt{5}}{3}$

step 3

Find the $tan(\theta)$

we know that

$tan(\theta)=\frac{sin(\theta)}{cos(\theta)}$

we have

$sin(\theta)=\frac{2}{3}$

$cos(\theta)=-\frac{\sqrt{5}}{3}$

substitute

$tan(\theta)=\frac{2}{3}:-\frac{\sqrt{5}}{3}=-\frac{2}{\sqrt{5}}$

Simplify

$tan(\theta)=-\frac{2\sqrt{5}}{5}$

6 0

2 years ago

Which equation best describes the same line as y - 6 = -4(x+1)

Kobotan [32]

Answer:

y - 6 = -4(x+1) is equivalent to equation C: y = -4x + 2

Step-by-step explanation:

Solve the given y - 6 = -4(x+1) for y and remove the parentheses shown:

y - 6 = -4(x+1) becomes

y = -4(x + 1) + 6, or

y = -4x - 4 + 6, or

y = -4x + 2 This is equivalent to equation C.

7 0

3 years ago

Enter an algebraic expression that represents the sum of fifty-seven and x cubed.

tresset_1 [31]

Jdnsjaiajiajsiiaiaia ajjakskskks

8 0

2 years ago

A pharmacist has a 12% solution and a 20% solution of boric acid. How much of each should she use to make 80 grams of a 15% solu

nlexa [21]

Step-by-step explanation:

If x = the amount of 12% and y = the amount of 20%, then x + y = 80

Since we need 80 grams of 15%, 80(.15) = 12.

We are given that .12x + .20y = 12.

We can solve the first equation for x or y. Let's do x.

x = 80 - y

.12(80 - y) + .20y = 12

9.6 - .12y + .20y = 12

.08y = 2.4

y = 30

x = 80 - 30 = 50

5 0

3 years ago

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