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3 years ago

Write an equation of a line with the given slope and y-intercept. slope: - 13 y-intercept: –1

Mathematics

1 answer:

Naddik [55]3 years ago

8 0

Answer:

y = -13x - 1

General Formulas and Concepts:

Algebra I

Slope-Intercept Form: y = mx + b

m - slope
b - y-intercept

Step-by-step explanation:

Step 1: Define

Identify variables

Slope m = -13

y-intercept b = -1

Step 2: Find Equation

Substitute in variables [Slope-Intercept Form]: y = -13x + -1
Simplify: y = -13x - 1

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Find the measures of the angles of the triangle whose vertices are A = (-3,0) , B = (1,3) , and C = (1,-3).A.) The measure of ∠A

alekssr [168]

Answer:

$\theta_{CAB}=128.316$

$\theta_{ABC}=25.842$

$\theta_{BCA}=25.842$

Step-by-step explanation:

A = (-3,0) , B = (1,3) , and C = (1,-3)

We're going to use the distance formula to find the length of the sides:

$r= \sqrt{(x_1-x_2)^2+(y_1-y_2)^2+(z_1-z_2)^2}$

$AB= \sqrt{(-3-1)^2+(0-3)^2}=5$

$BC= \sqrt{(1-1)^2+(3-(-3))^2}=9$

$CA= \sqrt{(1-(-3))^2+(-3-0)^2}=5$

we can use the cosine law to find the angle:

it is to be noted that:

the angle CAB is opposite to the BC.

the angle ABC is opposite to the AC.

the angle BCA is opposite to the AB.

to find the CAB, we'll use:

$BC^2 = AB^2+CA^2-(AB)(CA)\cos{\theta_{CAB}}$

$\dfrac{BC^2-(AB^2+CA^2)}{-2(AB)(CA)} =\cos{\theta_{CAB}}$

$\cos{\theta_{CAB}}=\dfrac{9^2-(5^2+5^2)}{-2(5)(5)}$

$\theta_{CAB}=\arccos{-\dfrac{0.62}}$

$\theta_{CAB}=128.316$

Although we can use the same cosine law to find the other angles. but we can use sine law now too since we have one angle!

To find the angle ABC

$\dfrac{\sin{\theta_{ABC}}}{AC}=\dfrac{\sin{CAB}}{BC}$

$\sin{\theta_{ABC}}=AC\left(\dfrac{\sin{CAB}}{BC}\right)$

$\sin{\theta_{ABC}}=5\left(\dfrac{\sin{128.316}}{9}\right)$

$\theta_{ABC}=\arcsin{0.4359}\right)$

$\theta_{ABC}=25.842$

finally, we've seen that the triangle has two equal sides, AB = CA, this is an isosceles triangle. hence the angles ABC and BCA would also be the same.

$\theta_{BCA}=25.842$

this can also be checked using the fact the sum of all angles inside a triangle is 180

$\theta_{ABC}+\theta_{BCA}+\theta_{CAB}=180$

$25.842+128.316+25.842$

$180$

6 0

3 years ago

Read 2 more answers

Identify rational numbers and intergers from the following

Nina [5.8K]

Answer:

Rational: all

Integers: 4, -36, -6

Step-by-step explanation:

A rational number is a number that can be written as a fraction of integers.

All numbers shown are rational numbers.

The integers are all positive and negative whole numbers and zero.

The integers are: 4, -36, -6

6 0

3 years ago

Protractors cost 16p each how much would 26 protractors cost

AveGali [126]

Answer:

The answer is £4.16

Step-by-step explanation:

26 x 16 = 416 = £4.16

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3 years ago

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Solve the equation -6a(-5-2a)=0

Anuta_ua [19.1K]

Answer:

A=0,-2 1/2

Step-by-step explanation:

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3 years ago

Morgan is playing a board game that requires three standard dice to be thrown at one time. Each die has six sides, with one of t

PIT_PIT [208]

The probability of having a 17 is the number of ways of having 17 divided by the number of different possible outcomes.

Ways of having 17:

Die 1 Die 2 Die 3 sum
6    6    5 6+6+5 = 17
6    5    6     6+5+6 = 17
5    6    6     5+6+6 = 17

Those are the only 3 possibilities of having 17 (you can only loose 1 point).

The total number of outcomes are 6*6*6 = 216

So the chances (probability) to win is 3 / 216 = 1/72 = 0.0139

8 0

3 years ago