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3 years ago

Write an equation of the line passing through each of the following pairs of points. a (−10, 4), (2, −5)

Mathematics

1 answer:

rusak2 [61]3 years ago

8 0

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 10, 4) and (x₂, y₂ ) = (2, - 5)

m = $\frac{-5-4}{2+10}$ = $\frac{-9}{12}$ = - $\frac{3}{4}$ , thus

y = - $\frac{3}{4}$ x + c ← is the partial equation of the line

To find c substitute either of the 2 given points into the partial equation

Using (2, - 5), then

- 5 = - $\frac{3}{2}$ + c ⇒ c = - 5 + $\frac{3}{2}$ = - $\frac{7}{2}$

y = - $\frac{3}{4}$ x - $\frac{7}{2}$ ← equation of line

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The pizza parlor is running a special on 3-toppings pizzas. The topping choices include pepperoni, sausage, bacon mushrooms, oni

choli [55]

Answer:

Well there are 6 toppings. For one person to select sausage, it is \frac{1}{6} . For two people, multiply them together and the probability is \frac{1}{36}

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3 years ago

Two adjacent angles form a complementary relationship. One angle is twelve more than twice the other angle. Draw a picture to re

Anon25 [30]

Answer:

The angles are 26 and 64

Step-by-step explanation:

When two angles are complementary, what this means is that the add up to 90 degrees

Now, let’s say one of the angles is x, the other angle is 12 more than twice it; mathematically that would be 2x + 12

Since they add up to be 90, we have

x + 2x + 12 = 90

3x + 12 = 90

3x = 90-12

3x = 78

x = 78/3

x = 26

The other angle is 2x + 12 = 2(26) + 12 = 52 + 12 = 64

7 0

3 years ago

4x^2 + 3 ( 3 - 3x^2)

AnnyKZ [126]

-5x^2(small two at top ) +9

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3 years ago

Bir kırtasiyeci aldığı kalemlerin tanesini

andrew11 [14]

Answer: Option B: 120.

Step-by-step explanation:

I will answer in English

This problem can be translated to:

A man bought N pens, (at a cost C) if he sells each pen at 2 lira, he will have a profit of 40 lira.

If he sells each pen at 1.5 lira, he will loss a total of 20 lira.

We want to find N, the number of pens that he bought.

if he sells the N pens at 2 lira each, the revenue is:

N*2 lira

And the profit is the difference between the revenue and the cost, then the profit (40 lira in this case) is:

N*2 lira - C = 40 lira.

When he sells each pen at 1.5 lira the equation is:

N*(1.5 lira) - C = -20 lira.

Then we have two equations:

N*2 lira - C = 40 lira.

N*(1.5 lira) - C = -20 lira.

To solve this we need to isolate the variable C in one of the equations, i will isolate C in the second equation:

N*(1.5 lira) + 20 lira = C.

Now we can replace this in the first equation to get:

N*(2 lira) - (N*(1.5 lira) + 20 lira) = 40 lira.

We can solve this for N.

N*(2 lira) - N*(1.5 lira) - 20 lira = 40 lira

N*(2 lira - 1.5 lira) = 60 lira

N*(0.5 lira) = 60 lira

N = (60lira/0.5lira) = 120

N = 120

This means that he bought 120 pens.

The correct option is B.

3 0

3 years ago

A prism is filled with 48 cubes with a side length of 1/2 unit. What is the volume of the prism in cubic units? Please I need he

Aleksandr [31]

Answer:

The volume of the prism is 6 unit³

Step-by-step explanation:

In order to calculate the volume of the prism we first need to calculate the volume of each cube. The volume of a cube is given by the formula below:

volume cube = a³

Where a is the length of the side of the cube. So each cube has a volume of:

volume cube = (1/2)³ = 1/8 unit³

Since the cubes are filling the prism, the volume of the prism is the sum of the volume of all the cubes, in this case 48. Since all the cubes are equal, we can multiply the number of cubes by the volume of one cube in order to calculate the volume of the prism. We have:

volume prism = 48*volume cube

volume prism = 48*(1/8) = 6 unit³

5 0

3 years ago