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PilotLPTM [1.2K]
3 years ago
12

? What is the solution of a system defined by 5x + 2y = 30 and -5x + 4y = 0? 0 (0, 30) O (6, 15) O (4,5) 0 (6,0)​

Mathematics
1 answer:
Pepsi [2]3 years ago
3 0

Answer:

(4,5)

Step-by-step explanation:

Hi there!

We are given the system of equations:

5x+2y=30

-5x+4y=0

and we need to find the solution

there are 3 ways to solve a system of equations, but let's use the elimination method, where we will add the systems together to clear one variable out, solve for the other variable, and use the value of the solved variable to find the other variable

When we clear a variable, the coefficients need to be opposites (ex. 2 and -2). In this case, the coefficients in front of x are 5 and -5 in the first and second equation respectively

5x+2y=30

-5x+4y=0

add the equations together

6y=30

divide both sides by 6

y=5

we found the value of y

now we need to find the value of x

substitute 5 as y into either one of the equations (ex. the first one) to solve for x

5x+2(5)=30

multiply

5x+10=30

subtract 10 from both sides

5x=20

divide both sides by 5

x=4

so the answer is x=4, y=5; as a point, it's <u> (4,5)</u>

Hope this helps! :)

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Consider the first four terms of the sequence below. -3, -12, -48, -192, . . . What is the 8th term of this sequence? A. -49,152
kolbaska11 [484]

Answer:

A

Step-by-step explanation:

there is a common ratio between consecutive terms , that is

- 12 ÷ - 3 = - 48 ÷ - 12 = - 192 ÷ - 48 = 4

this indicates the sequence is geometric with nth term

a_{n} = a₁ r^{n-1}

where a₁ is the first term and r the common ratio

here a₁ = - 3 and r = 4 , then

a₈ = - 3 × 4^{7} = - 3 × 16,384 = - 49,152

7 0
1 year ago
Two angles form a linear pair. The measure of one angle is twice the measure of the other angle. Find the measure of each angle.
Flauer [41]

Answer:

The smaller angle measures = 60º

The larger angle measures = 120º

Step-by-step explanation:

The sum of angles in linear pair is 180

The measure of one angle is twice the measure of the other angle.

x + 2x = 180

Combine like terms

3x = 180

Divide both sides by 3

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3 years ago
Find a solution to the linear equation −2x−2y=8 by filling in the boxes with a valid value of x and y.Provide your answer below:
inna [77]

Given

-2x-2y=8

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\begin{gathered} -2x+2x-2y=8+2x \\ -2y=2x+8 \end{gathered}

-Divide both sides by -2:

\begin{gathered} \frac{-2y}{-2}=\frac{2x}{-2}+\frac{8}{-2} \\ y=-x-4 \end{gathered}

Once you have expressed the equation of the line in slope-intercept form, replace it with any value for x and calculate the corresponding value of y, for example, x=2

\begin{gathered} y=-(2)-4 \\ y=-2-4 \\ y=-6 \end{gathered}

One solution for the linear equation is x=2 and y=-6, you can check the solution by replacing the values on the original equation, with both values the result should be 8:

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As you can see the values are a valid solution for the linear equation.

So the solution is:

-2(2)-2(-6)=8

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1 year ago
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hjhkhhuh

Step-by-step explanation:

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Answer:

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the square root of 20 is 4.472135955, rounded to the nearest hundreth is 4.47

7 0
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