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2 years ago

m∠ABC=(6x+8)° and m∠DEF=(12x−8)°. If ∠ABC and ∠DEF are supplementary, what is the measure of each angle?

Mathematics

1 answer:

LUCKY_DIMON [66]2 years ago

3 0

<h3>★ Solution:</h3>

Since it is given that the two angles are supplementary their sum must be equal to 180 degree

6x + 8 + 12x - 8 = 180°

→ 18x = 180°

→ x = 10°

Now substitute the value of x in the given two measures of angles.

m∠ABC = 6x + 8 = 68°
m∠DEF = 12x - 8 = 112°

Therefore the 2 angles are 68° and 112°

Hope it helps you :)

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3 years ago

solve the below systems of equations using linear combination method. 2x + 3y =1. and y= -2x - 9. explain

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Answer:

Solving below systems of equations using linear combination method we get

x = -7

y = 5

Step-by-step explanation:

Linear combinations which is also commonly known as the addition method is used for solving the system of equations without graphs

Step 1: arrange the equation in standard form

2x + 3y = 1----------------------(1)

2x + y = -9--------------------(2)

Step 2: Set one of the coefficient to opposite sides

So lets multiply eq(2) with negative sign, so

2x + 3y = 1

-2x - y = 9

Step 3: Perform Addition

2x + 3y = 1

-2x - y = 9

-----------------------

0x +2y = 10

--------------------------

Step 4: Solve for y

2y =10

$y =\frac{10}{2}$

y = 5

Step 5: Substitute y value in equation(1)

2x + 3(5) = 1

2x + 15 =1

2x = 1-15

2x =-14

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x = -7

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A bowl contains 6 green grapes, 10 red grapes, and 8 black grapes. Which of the following is the correct

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<h3>What is a probability?</h3>

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, we have that there is a total of 6 + 10 + 8 = 24 grapes. For the first grape, 10 are red, hence the probability that the first grape is red is:

$pR = \frac{10}{24} = \frac{5}[12}$

For the second grape, considering that the first was red and was removed, there will be 23 grapes, out of which 6 will be green, hence the probability that the second grape is green is:

$pG = \frac{6}{23}$