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4 years ago

What is an equation of the line that passes through the points (-4,-1) and (2,8)?

Mathematics

1 answer:

lora16 [44]4 years ago

5 0

Answer:

y=3/2 x + 5

Step-by-step explanation:

$y = mx + c$

Firstly, find m (gradient).

m= (y1-y2)/(x1- x2)

m= 8-(-1)/ 2-(-4)

m= 9/ 6

m= 3/2

Please leave gradient in improper fraction if its value is not a whole number.

Now substitute m into the equation:

y= 3/2 x + c

Then substitute a coordinate to find c:

When y= 8, x= 2,

8= 3/2 (2) + c

8= 3 + c

c= 8 - 3 = 5

Thus, the equation of the line is y= 3/2 x + 5.

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A teacher wants to buy mini candy canes for her students. She wants each of her 32 students to have 8 mini candy canes. How many

Igoryamba

Answer:

11 packs

Step-by-step explanation:

32 x 8 = 256

256 / 24 = 10. 6666667

round up and you get 11

8 0

3 years ago

Can anyone help me solve this?

olya-2409 [2.1K]

Answery-(0,2.5)

X-(0,3.5):

Step-by-step explanation:

look where the lines intercept and look at the label for each line

4 0

4 years ago

Amos deposits an amount of R 1260 in an account that pays 8,5% interest per year, compounded quarterly. After six years the amou

Marysya12 [62]

FV = PV × (1+r)^n ; where FV = Future Value;
PV = Present Value;
r = annual interest rate;
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4 0

3 years ago

There are four cars entered into a pinewood derby race. in how many different orders can they cross the finish line, assuming th

artcher [175]

This is a problem of fundamental counting principle. In a sequence of events, the total possible number of ways all events can performed is the product of the possible number of ways each individual event can be performed. So here there is one car in each place so there 4 possible cars to get the 1st place, 3 possible car for the 2nd place, 2 possible cars for 3rd place and 1 for the 4th place. The 4x3x2x1 = 24 different order

4 0

3 years ago

Find the height of the triangle

Marianna [84]

Answer:

The height is 12 cm

Step-by-step explanation:

Hi there!

We are given a triangle with the 3 sides marked as 15, 20, and 25 and we want to find the height of it (marked as x in the problem).

This problem can seem a bit difficult, but let's see if the triangle is a right triangle first off.

One way to figure out if it is a right triangle is to apply the converse of the Pythagorean theorem.

Let's label the sides, where a is the shortest side, b is the second shortest side, and c is the longest side:

a=15

b=20

c=25

Now square a and b, then add the result together. If it's the same as c squared, then the triangle is a right triangle

15²+20²=25²

225+400=625

625=625

So we can safely say that the triangle is a right triangle

This makes the problem way easier, as there are 2 ways to find the area of a right triangle:

The first way is to multiply the legs (the sides that make up the right angle) together, then divide the result by 2

The other way is to multiply the height and the hypotenuse (the side OPPOSITE to the right angle) together, and then divide the result by 2

First, we need to figure out which sides are the legs, and which side is the hypotenuse

By the triangle inequality theorem, the hypotenuse of a right triangle is the longest side, which means that the 25 cm side is the hypotenuse, and that leaves 15 cm and the 20 cm sides as the legs

So let's find the area of the triangle using the legs

A= $\frac{15*20}{2}$ = $\frac{300}{2}$ =150

So the area of the triangle is 150 cm²

However, as mentioned above, we can also find the area of the triangle by multiplying the hypotenuse by the base, then dividing the result by 2

Which means that the area is also:

A= $\frac{25x}{2}$ cm²

As these both equal the area of the triangle, we can set them equal to each other. This is possible via a property known as transitivity (if a=b and b=c, then a=c)

$\frac{25x}{2}=150$

Multiply both sides by 2

25x=300

Divide both sides by 25

x=12 cm

So the height of the triangle is 12 cm

Hope this helps!

4 0

3 years ago