Explanation

Given equation: 2x + 5 = 13

Subtract 5 from both sides to isolate 2x:

2x = 13 - 5

2x = 8

Now, divide by 2 to solve for x:

x = 8 / 2

x = 4

Therefore, the solution to the equation 2x + 5 = 13 is x = 4.

Explanation

To find two consecutive even integers whose sum is 46, let's set up the equation:

Let the first integer be x. Then the next consecutive even integer is 

x+2.

The equation is:

x+(x+2)=46

Simplify and solve for 

2x+2=46

2x=44

x=22

So, the two consecutive even integers are 22 and 24.

Explanation

Given equation: 3x - 2y = 9

Substitute x = 5 into the equation:

3(5) - 2y = 9

15 - 2y = 9

Subtract 15 from both sides to isolate -2y:

-2y = 9 - 15

-2y = -6

Divide by -2 to solve for y:

y = -6 / -2

y = 3

Explanation

To determine the total number of fence poles used, we need to consider that each corner pole is counted twice when calculating the poles for each side.

Each side of the square plot has 27 poles.

Since the plot is square, it has 4 sides.

First, calculate the total number of poles if we didn't account for the corners:

27 poles/side×4 sides=108 poles

However, this calculation counts each corner pole twice.

A square has 4 corners, so we need to subtract the 4 extra poles that were counted twice:

108 poles−4 extra poles=104 poles

Explanation

To solve the equation sqrt(x + 3) = 2,

we need to isolate x by getting rid of the square root.

Given equation:

sqrt(x + 3) = 2

Square both sides to eliminate the square root:

(x + 3) = 2^2

x + 3 = 4

Subtract 3 from both sides to solve for x:

x = 4 - 3

x = 1

Explanation

To determine the solutions of the equation 2x + 4 = 3x + 1, we need to solve for x.

Given equation: 2x + 4 = 3x + 1

Subtract 2x from both sides to isolate x:

4 = x + 1

Subtract 1 from both sides to solve for x:

x = 3

After solving for x, we find that x = 3.

This means there is one solution to the equation.

Explanation

Explanation

To find the fraction of green marbles, we need to calculate the total number of marbles first.

Sara has:

- 5 red marbles

- 3 green marbles

- 2 blue marbles

Total marbles = 5 (red) + 3 (green) + 2 (blue) = 10 marbles

Next, we determine the fraction of green marbles out of the total marbles:

Fraction of green marbles = Number of green marbles / Total number of marbles

Fraction of green marbles = 3 / 10

Explanation

The recipe calls for 2 cups of sugar, but Sarah has only 1/2 cup.

To find out how much more sugar she needs, subtract the amount she has from the amount required:

2cups - 1/2 cup = 1/2 cups - 1/2 cup = 3/2 cups

So, Sarah needs 1 1/2 cups (or 3/2 cups) more sugar.

The correct answer is: 3/2 cup

Explanation

Given:

The total of their current ages is 80 years.

Three years ago, each of them was 3 years younger, so:

Amar's age three years ago = Amar's current age - 3

Akbar's age three years ago = Akbar's current age - 3

Ali's age three years ago = Ali's current age - 3

The total of their ages three years ago would be:

(Amar ′ s current age−3)+(Akbar ′ s current age−3)+(Ali ′ current age−3)

This simplifies to:

(Amar  ′ s current age+Akbar′ s current age+Ali' s current age)−9

Since the total of their current ages is 80 years:

80−9=71

Therefore, the total of their ages three years ago was 71 years