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2 years ago

Write the equation that represents the line that goes through the point (5, -7) and has slope m=-3

Mathematics

1 answer:

RUDIKE [14]2 years ago

4 0

Answer:

y = -3x + 8

Step-by-step explanation:

Given :-

Point on line = (5, -7)

Slope (m) = -3

To find :-

Equation of line

Solving :-

Using point-slope form of equation,

y - y₁ = m(x - x₁)

y + 7 = -3(x - 5)

y + 7 = -3x + 15

Solution :-

y = -3x + 8

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A ball is tossed between three friends. The first toss is 8.6 feet, the second is 5.8 feet, and the third toss is 7.5 feet, whic

Rainbow [258]

angles formed by these tosses are $79.45, 59.02$ and $41.53$ degrees to the nearest hundredth.

Step-by-step explanation:

Here , We have a triangle with sides of length 8.6 feet, 5.8 feet and 7.5 feet.

The Law of Cosines (also called the Cosine Rule) says:

$c^2 = a^2 + b^2 - 2ab (cosx)$

Using the Cosine Rule to find the measure of the angle opposite the side of length 8.6 feet:

⇒ $c^2 = a^2 + b^2 - 2ab (cosx)$

⇒ $c^2 -a^2 - b^2 = -2ab (cosx)$

⇒ $(cosx) =\frac{ c^2 -a^2 - b^2}{ -2ab}$

⇒ $(cosx) =\frac{(8.6^2 - 5.8^2 - 7.5^2)}{ ( -2(5.8)7.5)}$

⇒ $(cosx) =0.18310$

⇒ $cos^{-1}(cosx) = cos^{-1}(0.18310)$

⇒ $x = 79.45$

The Law of Sines (or Sine Rule) is very useful for solving triangles:

$\frac{a}{sin A} = \frac{ b}{sin B} = \frac{c}{sin C}$

We can now find another angle using the sine rule:

⇒ $\frac{ 8.6 }{ sin 79.45} = \frac{7.5}{ sin Y}$

⇒ $sin Y = \frac{(7.5 (sin 79.45))}{ 8.6}$

⇒ $Y = 59.02 degrees$

So, the third angle = $180 - 79.45 - 59.02 = 41.53 degrees.$

Therefore, angles formed by these tosses are $79.45, 59.02$ and $41.53$ degrees to the nearest hundredth.

4 0

4 years ago

The authors of a paper titled "Age and Violent Content Labels Make Video Games Forbidden Fruits for Youth" carried out an experi

o-na [289]

Answer:

T = 290

Step-by-step explanation:

We can find the sum of all observations multiplying sample size (n) by sample mean (x).

Sum of all observations in the data set is,

$T=n_{1} x_{1}+n_{2}x_{2}+n_{3}x_{3}+n_{4}x_{4}\\T=10(5.3)+10(7)+10(8.5)+10(8.2)\\T=53+70+85+82\\T=290$

Hope this helps!

7 0

3 years ago

(28 and 29) I really need help

scoundrel [369]

Answer:

28 is 11/60

29 is 7/30

Step-by-step explanation:

5 0

3 years ago

Х If 5.3 = 12, what is the value of x? 8 0 ООО 18 o 24

gladu [14]

Answer:18

Step-by-step explanation:

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3 years ago

Opposite sides of a rectangle must be parallel true or false

shtirl [24]

Yes it does have to be parallel or else it would not be a rectangle.So it is true.

Hope this helped! :)

6 0

4 years ago