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laila [671]
2 years ago
10

What is the largest of 3 consecutive integers such that the sum of the first and third is equal to three times the second.

Mathematics
1 answer:
Norma-Jean [14]2 years ago
4 0

Answer:

1

Step-by-step explanation:

What is the largest of 3 consecutive integers such that the sum of the first and third is equal to three times the second?

3 consecutive angles

= x, x + 1, x + 2

We are told in the question that:

the sum of the first and third is equal to three times the second

a + c = 3b

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

2x + 2 = 3x + 3

3x - 2x = 2 - 3

x = -1

The largest of the three numbers is the third number

= x + 2

x = -1

x + 2 = -1 + 2

The third and largest number is 1

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Donna is running around a track.It takes her 3 1/2 minutes to run 1/4 of a lap.If she keeps running at the same speed,how long w
meriva

Answer:

70 minutes

Step-by-step explanation:

3 1/2 ÷1/4= 14 ×5= 70

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If ∆BCD ~ ∆GEF, find the value of x.
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It’s late work and I’ve forgotten how to do it
Veseljchak [2.6K]
You want to eliminate one of the terms (x or y) in one of the equations so you can solve for the other variable.  You have to multiply by the opposite number of the coefficient to be able to eliminate the term in the other equation.  If the x coefficient is 2, then you have to multiply the entire other equation by -2.  If the y coefficient is -5, then you have to multiply the entire other equation by 5.


10)
-4x + 9y= 9
x - 3y= -6

STEP 1:
multiply the bottom equation by 4
4(x- 3y)= 4(-6)
4x - 12y= -24

STEP 2:
add the top equation and the equation from step 2

-4x + 9y= 9
4x - 12y= -24
the x term cancels out

-3y= 15
divide both sides by -3

y= -5

STEP 2:
substitute the y value in either original equation to solve for x

x - 3y= -6
x - 3(-5)= -6

x + 15= -6
subtract 15 from both sides

x= -21

ANSWER: x= -21; y= -5
____________________

12)
-7x + y= -19
-2x + 3y= -19

STEP 1:
multiply the top equation by -3 to eliminate the y term and to solve for x

-3(-7x + y)= -3(-19)
21x - 3y= 57

STEP 2:
add the bottom equation and the equation from step 2 to solve for x

-2x + 3y= -19
21x - 3y= 57
the y term cancels out

19x= 38
divide both sides by 19

x= 2

STEP 3:
substitute the x value in step 2 to solve for y; you can use either original equation

-7x + y= -19
-7(2) + y= -19

-14 + y= -19
add 14 to both sides

y= -5

ANSWER: x= 2; y=-5

Hope this helps!  :)

4 0
3 years ago
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