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topjm [15]
4 years ago
14

The sum of two even consecutive integers is 114. What is the smallest integer?

Mathematics
1 answer:
Ainat [17]4 years ago
8 0

Answer:

56

Step-by-step explanation:

The sum of two <em>even</em> consecutive integers is 114.

Let's let the first even integer be 2n, where n is <em>some</em> integer: it doesn't matter what n is, but if we multiply n by 2, we are certainly getting an even number. This is because any integer multiplied by 2 is even.

So, this means that the second number is 2n+2.

Their sum is 114. In other words:

(2n)+(2n+2)=114

Solve for n.

Combine like terms:

4n+2=114

Subtract 2 from both sides:

4n=112

Divide both sides by 4:

n=28

So, n is 28.

This means that the first number is 28(2) or 56.

And the second number is 58.

So, the smallest integer is 56.

And we're done!

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Ben is three times as old as Kate. Kate is 6 years older than Jill. Jill is J years old. What is the combined age of the three p
harkovskaia [24]

Answer:

the combined age of the three people  is

5 J + 24

Step-by-step explanation:

Jill (J)

Kate (J+6)

Ben 3(J+6)

J + (J+6) + 3(J+6)

J+J + 6 +3 J +18

5 J + 24

8 0
3 years ago
Write the equation of the line slope 2, through (3,1)
Arisa [49]

answer:

y = 2x - 5

work:

to write equations, we use the format y = mx + b.

m stands for the slope, and b stands for the y intercept.

this means that you should be able to enter the values for y and x and get a valid equation as a result.

in this equation, we are not given a y intercept value, but we do have a slope and x and y values, so we have to solve by substituting.

so, let's substitute in the values of y and x and the slope,

and solve for b, the y intercept.

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

1 = 6 + b (subtract 6 from both sides)

- 5 = b

b has a value of -5. let's place this into the equation.

y = 2x - 5.

the slope is 2, and the y intercept is -5, let's plug in our y and x values to verify that this is true.

1 = 2(3) - 5

1 = 6 - 5

1 = 1

so, this equation is correct. hope this helps and have a great day!

6 0
3 years ago
Read 2 more answers
Make a list of two possible pairs of numbers that have a GCF of 5
Pie
Two possible numbers that might have a GCF common factor of 5 are 10 and 15, as well as 25. 5 is also the greatest common factor of itself.

So your numbers are : 5, 10, 15, and 25.
7 0
4 years ago
Which points are a distance of 5 units from (2, 3) if d = square root (x2 - x1)2 + (y2 - y1)?
qwelly [4]

Answer:

Step-by-step explanation:

hello :

note :

note : distance between A(X1,Y1) an B (X2,Y2) is :  

AB= √((X2 - X1)² + (Y2 - Y1)²)    (given point  B(2 , 3)

in this exercice : X1 = 2     X2 = ?      Y1 = 3      Y2 = ?   d=AB=5

d² = (X2 - 2)² + (Y2 - 3)² =25

the points are a distance of 5 units from B (2, 3) if d = 5 :

the points are located on a circle with center B and radius 5

8 0
3 years ago
Subtracting linear expressions (6x+2)-(9x+3)
UkoKoshka [18]

Answer:

-3x - 1

Step-by-step explanation:

(6x + 2)-(9x + 3)

We Begin by opening the brackets.

6x + 2 -9x - 3

Please note the change in the signs.

6x - 9x + 2 - 3

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4 0
3 years ago
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