All categories

2 years ago

L 5.2.3 Quiz: Two-Variable Systems: Substitution

Mathematics

1 answer:

Misha Larkins [42]2 years ago

6 0

Answer:

We get x=3 and y=21

The ordered pair will be: (3,21)

Step-by-step explanation:

We need to use the substitution method to solve the system of equations.

$y = 10x-9\\y = x + 18$

For substitution method we substitute the value of x or y from one equation to other.

Let:

$y = 10x-9--eq(1)\\y = x + 18--eq(2)$

Putting value of y from equation 2 into equation 1

$y=10x-9\\Put\:y=x+18\\x+18=10x-9\\x-10x=-9-18\\-9x=-27\\x=\frac{-27}{-9}\\x=3$

So, we get value of x=3

Now, for finding value of y, We substitute the value of x

Find value of x from equation 2

$y=x+18\\x=y-18$

Now, putting value of x in equation 1

$y=10x-9\\Put\:x=y-18\\y=10(y-18)-9\\y=10y-180-9\\y-10y=-189\\-9y=-189\\y=\frac{-189}{-9}\\y=21$

So, we get value of y=21

So, We get x=3 and y=21

The ordered pair will be: (3,21)

You might be interested in

Whats the sum of -7x*y + 4x^2 - 2 and 4x'y + 1 - 8x^y?

matrenka [14]

Answer:

-7xy+4x^2-8 and y+1-8x^y

Step-by-step explanation:

8 0

2 years ago

The longest fingernails ever recorded were 8.650 meters. How long were the fingernails in a feet and inches?

Oksana_A [137]

Answer: 28 feet and 4.5 inches

8 meters = 26.24...

.650 meters = 25 inches.

25 inches = 2 feet 1 inch

28 and 4.5 inches is your answer.

4 0

3 years ago

The figure is a square. Find the length of side x in simplest radical form with a rational denominator.

nika2105 [10]

Answer:

$10\sqrt{2}$

Step-by-step explanation:

The diagonal of any square with side length $s$ is equal to $s\sqrt{2}$ . Since the side length of the square is 10, the diagonal must be $\boxed{10\sqrt{2}}$ .

To support and prove this:

The diagonal creates two 45-45-90 triangles, with the diagonal being the hypotenuse of both of these triangles. The Pythagorean Theorem states that in any triangle, the sum of the squares of both legs is equal to the square of the hypotenuse ( $a^2+b^2=c^2$ ).

Call the diagonal $d$ . In these two triangles, both legs are equal to 10 (the side lengths of the square), and the hypotenuse is the diagonal. Thus, we have:

$10^2+10^2=d^2,\\100+100=d^2,\\d^2=200,\\d=\sqrt{200}=\sqrt{100}\cdot \sqrt{2}=\boxed{10\sqrt{2}}$

4 0

3 years ago

Read 2 more answers

6. Find d.<br><br><br> Please help

Anvisha [2.4K]

Answer:

Step-by-step explanation:

The first thing we are going to do is to fill in the other angles that we need to solve this problem. You could find ALL of them but all of them isn't necessary. So looking at the obtuse angle next to the 35 degree angle...we know that those are supplementary so 180 - 35 = the obtuse angle in the small triangle. 180 - 35 = 145. Within the smaller triangle we have now the 145 and the 10, and since, by the Triangle Angle-Sum Theorem all the angles have to add up to equal 180, then 180 - (10 + 145) = the 3rd angle, so the third angle is 180 - 155 = 25. Now let's get to the problem. If I were you, I'd draw that out like I did to keep track of these angles cuz I'm going to name them by their degree. In order to find d, we need to first find the distance between d and the right angle. We'll call that x. The reference angle is 35, the side opposite that angle is 12 and the side we are looking for, x, is adjacent to that angle. So we will use the tan ratio to find x:

$tan(35)=\frac{12}{x}$ Isolating x:

$x=\frac{12}{tan(35)}$ so

x = 17.1377 m

Now we have everything we need to find d. We will use 25 degrees as our reference angle, and the side opposite it is 12 and the side adjacent to it is

d + 17.1377, so that is the tan ratio as well:

$tan(25)=\frac{12}{d+17.1377}$ and simplifying a bit: