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2 years ago

What is the equation of the line that passes through the point (−1,−5) and has a slope of −3?

Mathematics

1 answer:

Hitman42 [59]2 years ago

6 0

Answer:

$y=-3x-8$

Step-by-step explanation:

Linear equations are typically organized in slope-intercept form:

$y=mx+b$ where $m$ is the slope and $b$ is the y-intercept (the value of y when the line crosses the y-axis)

<u>1) Plug the slope (m) into the equation</u>

We're given that the slope is -3. Plug -3 into the equation

$y=-3x+b$

<u>2) Solve for the y-intercept (b)</u>

To solve for b, plug the given point (-1,-5) into the equation as (x,y).

$-5=-3(-1)+b\\-5=3+b$

Subtract 3 from both sides

$-5-3=3+b-3\\-8=b$

Therefore, the y-intercept is -8. Plug -8 back into our original equation as b

$y=-3x-8$

I hope this helps!

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(√3-√2) (√3+√2) simplify this question

cestrela7 [59]

Answer:

Step-by-step explanation:

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2 years ago

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PLEASE HHELP!!! Bring the fraction:

Anna35 [415]

Answer:

$\frac{b}{7a^2c} = \frac{5abc^2}{35a^3c^3}$

$\frac{a}{a - 4} = \frac{-a^2 - 4a}{16 -a^2}$

Step-by-step explanation:

Given

$\frac{b}{7a^2c}$

Express the denominator as $35a^3c^3$

To do this, we divide $35a^3c^3$ by the denominator

$\frac{35a^3c^3}{7a^2c} = 5ac^2$

So, the required fraction is:

$\frac{b}{7a^2c} * \frac{5ac^2}{5ac^2}$

$\frac{5abc^2}{35a^3c^3}$

Hence:

$\frac{b}{7a^2c} = \frac{5abc^2}{35a^3c^3}$

Given

$\frac{a}{a - 4}$

Express the denominator as $16 - a^2$

Multiply the fraction a+4/a+4

So, we have:

$\frac{a}{a - 4} * \frac{(a + 4)}{(a + 4)}$

Apply difference of two squares to the denominator

$\frac{a^2 + 4a}{a^2 - 16}$

Take the additive inverse of the numerator and denominator

$\frac{-(a^2 + 4a)}{-(a^2 - 16)}$

$\frac{-a^2 - 4a}{16 -a^2}$

Hence:

$\frac{a}{a - 4} = \frac{-a^2 - 4a}{16 -a^2}$

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2 years ago

A waiter earns $128 for six hours of work. The total included $86 in tips. How much does the waiter earn each hour??A waiter arm

Lady bird [3.3K]

Answer:

The waiter earns $7 per hour

Step-by-step explanation:

In this question, we are asked to calculate the amount a waiter earns per hour at work given the total he had earned including tips.

To solve this question, we can see that we have been given the total amount he has earned and also the amount he has also earned in tips.

Now, to get the standard amount he’s supposed to earn per hour, firstly, we have to subtract the amount he has earned in tips from the total. Mathematically that is 128-86 = $42

This means, by standard he has earned $42 in six hours. Now, we need to calculate the amount she earns by hour.

To do this, we simply divide the total amount earned by the number of hours.

Mathematically that is $42/6 hours = $7 per hour

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2 years ago

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Santiago wants the lateral surfaces of the ramp to be painted red. how many squares feet of the ramp will be painted red?

Annette [7]

Answer:

262 square feet

Step-by-step explanation:

The lateral surface is the side surfaces, except top and bottom.

There are 3 lateral surfaces.

The 2 sides are triangles with length 20 and height 8.5

And

The back is a rectangle with length 12 and height 8.5

We sum up all the 3 surface areas, that will give us the answer.

Area of triangle is (0.5) * length * height

So,

Area of 1 triangle = 0.5 * 20 * 8.5 = 80

Area of 2 triangles = 80 * 2 = 160

Area of rectangle = length * height

so,

Area of back rectangle = 12 * 8.5 = 102

Total Lateral Surface Area = 160 + 102 = 262 square feet

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2 years ago

Find the missing values of the variables. The diagram is not to scale.

____ [38]

Answer:

The answer is the option B

$x=91\°,y=75\°$

Step-by-step explanation:

we know that

The sum of the internal angles of the polygon is equal to

$S=(n-2)*180\°$

where n is the number of sides

In this problem

$n=2$

substitute

$S=(4-2)*180\°=360\°$

Step 1

Find the value of y

$105\°+y\°=180\°$ -------> by supplementary angles

Solve for y

$y=180\°-105\°=75\°$

Step 2

Find the value of x

The sum of the internal angles of the polygon is equal to $360\°$

$125\°+69\°+75\°+x=360\°$

Solve for x

$269\°+x=360\°$

$x=360\°-269\°=91\°$

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2 years ago

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