Calculate a X
\( (9+17x)\times(6+1)=420 \)
Calculate a X
\( (a+3a)\times(5+2)=112 \)
Calculate a a
\( (7x+3)\times(10+4)=238 \)
Calculate the area of the rectangle below in terms of a and b.
Express the area of the rectangle below in terms of y and z.
Calculate a X
We begin by solving the addition exercise in the right parenthesis:
We then multiply each of the terms inside the parentheses by 7:
We continue by solving each of the exercises inside of the parentheses:
Following this we rearrange the sections whilst maintaining the appropriate sign:
Finally we divide the two parts by 119:
3
Calculate a a
We begin by solving the two exercises inside of the parentheses:
We then divide each of the sections by 4:
In the fraction on the left side we simplify by 4 and in the fraction on the right side we divide by 4:
Remember that:
Lastly we divide both sections by 7:
4
We begin by solving the addition exercise in the right parenthesis:
We then multiply each of the terms inside of the parentheses by 14:
Following this we solve each of the exercises inside of the parentheses:
We move the sections whilst retaining the appropriate sign:
Finally we divide the two parts by 98:
2
Calculate the area of the rectangle below in terms of a and b.
Let us begin by reminding ourselves of the formula to calculate the area of a rectangle: width X length
When:
S = area
w = width
h = height
We take data from the sides of the rectangle in the figure.
We then substitute the above data into the formula in order to calculate the area of the rectangle:
We use the formula of the extended distributive property:
We substitute once more and solve the problem as follows:
Therefore, the correct answer is option B: ab+8a+3b+24.
Keep in mind that, since there are only addition operations, the order of the terms in the expression can be changed and, therefore,
ab + 8a + 3b + 24
Express the area of the rectangle below in terms of y and z.
Let us begin by reminding ourselves of the formula to calculate the area of a rectangle: width X height
Where:
S = area
w = width
h = height
We must first extract the data from the sides of the rectangle shown in the figure.
We then insert the known data into the formula in order to calculate the area of the rectangle:
We use the distributive property formula:
We substitute all known data and solve as follows:
Keep in mind that because there is a multiplication operation, the order of the terms in the expression can be changed, hence:
Therefore, the correct answer is option D:
A building is 21 meters high, 15 meters long, and 14+30X meters wide.
Express its volume in terms of X.
Given the rectangular area 78 cm².
Find X
Calculate the area of the rectangle
Look at the rectangle in the figure.
What is its area?
Which expressions represent the area of the rectangle in the drawing?
\( 56x \)
\( 9(3x^2+5x) \)
\( x(3x+5)+9(3x+5) \)
\( 32x+x^2 \)
\( 3x^2+45 \)
\( 3x^2+32x+45 \)
A building is 21 meters high, 15 meters long, and 14+30X meters wide.
Express its volume in terms of X.
We use a formula to calculate the volume: height times width times length.
We rewrite the exercise using the existing data:
We use the distributive property to simplify the parentheses.
We multiply 21 by each of the terms in parentheses:
We solve the multiplication exercise in parentheses:
We use the distributive property again.
We multiply 15 by each of the terms in parentheses:
We solve each of the exercises in parentheses to find the volume:
Given the rectangular area 78 cm².
Find X
We know that the area of a rectangle is equal to its length multiplied by its width.
We begin by writing an equation with the available data.
We then use the distributive property to solve the equation.
That is, we multiply each of the terms inside of the parentheses by 3:
We move 21 to the other side and use the appropriate sign:
Lastly we divide both sides by 3:
Calculate the area of the rectangle
Let's begin by reminding ourselves of the formula to calculate the area of a rectangle: width X length
Where:
S = area
w = width
h = height
We extract the data from the sides of the rectangle in the figure.
We then substitute the above data into the formula in order to calculate the area of the rectangle:
We use the formula of the extended distributive property:
We once again substitute and solve the problem as follows:
Therefore, the correct answer is option C: xy+2x+5y+10.
Look at the rectangle in the figure.
What is its area?
We know that the area of a rectangle is equal to its length multiplied by its width.
We begin by writing an equation with the available data.
Next we use the distributive property to solve the equation.
We then solve each of the exercises within the parentheses:
Finally we add up all the coefficients of X squared and all the coefficients of X cubed and we obtain the following:
Which expressions represent the area of the rectangle in the drawing?
3, 6
Gerard plans to paint a fence 7X meters high and 30X+4 meters long.
Gerardo paints at a rate of 7 m² per half an hour.
Choose the expression that represents the time it takes for Gerardo to paint one side of the fence.
Gerard plans to paint a fence 7X meters high and 30X+4 meters long.
Gerardo paints at a rate of 7 m² per half an hour.
Choose the expression that represents the time it takes for Gerardo to paint one side of the fence.
hours