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3 years ago

What is the solution to the system of equations?

Mathematics

1 answer:

s344n2d4d5 [400]3 years ago

5 0

Answer:

(3,2)

Step-by-step explanation:

Here's your given:

y = 4x - 10

y = 2

Because they both equal y, that means they equal each other:

2 = 4x - 10

Add 10 on both sides:

12 = 4x

Then, divide 4 on both sides:

3 = x

This represents the x coordinate.

Normally you would put this value into one of the equations to figure out y, but they already gave us that in the beginning:

y = 2

This represents the y coordinate.

Put the two values together to get: (3,2)

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3 years ago

Segment BD is an altitude of triangle ABC. Find the area of the triangle.

Sever21 [200]

Answer: The correct option is A, i.e., 7.5.

Explanation:

It is given that ABC is a triangle and BD is an altitude.

Since BD is an altitude, therefore the height of the triangle is BD and the base of the triangle is AC.

The distance formula to find the distance between two points is,

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

First, we find BD, where B(-1,4) and D(2,4).

$BD=\sqrt{(2+1)^2+(4-4)^2}=\sqrt{9} =3$

So, the height of the triangle is 3.

Now, we find the value of AC, where A(2,1) and C(2,6).

$AC=\sqrt{(6-1)^2+(2-2)^2}=\sqrt{25} =5$

So, the base of the triangle is 5.

The formula to find the area of a triangle is,

$A=\frac{1}{2}\times {\text{base}}\times {\text{height}}$

$A=\frac{1}{2}\times 5\times 3=\frac{15}{2}=7.5$

Therefore, the area of the triangle is 7.5 unit square and the correct option is A.

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3 years ago

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