Michelle made a bead necklace with a length of 12 inches. The length of the necklace, in inches, is equal to 2 added to the quotient of the number of beads, b, and 7.
b ÷ 7 + 2 = 12
How many beads did she use?
A. 700
B. 46
C. 35
D. 70
To find out how many beads she used, we need to solve for b in the given equation:
b ÷ 7 + 2 = 12
b ÷ 7 = 10
b = 70
Therefore, Michelle used 70 beads. The answer is D. 70.
Solve the following equation for x.
x/5 - 9 = 2
To solve for x, we need to isolate x on one side of the equation. Here's how:
x/5 - 9 = 2
Add 9 to both sides:
x/5 = 11
Multiply both sides by 5 to get rid of the fraction:
x = 55
Therefore, the solution to the equation is x = 55.
Maggie is having the flooring replaced in her kitchen, living room, and master bedroom.
The kitchen is getting slate tile. The tile cost $1.73 per-square-foot plus an installation fee per-square-foot. The area of the kitchen is 120 square feet, and the total cost for the flooring with installation comes to $740.40.
The living room is getting hand-scraped hardwood flooring. The hardwood cost $4.98 per-square-foot plus an installation fee per-square-foot. The area of the living room is 200 square feet, and the total cost for the flooring with installation comes to $1,688.00.
The master bedroom is getting berber carpet. The carpet cost $2.48 per-square-foot plus an installation fee per-square-foot. The area of the master bedroom is 180 square feet, and the total cost for the flooring with installation comes to $928.80.
Place the flooring type in order from the least to greatest installation fee per-square-foot.
tile, hardwood flooring, carpet
_______, ________,________
( 1/ 9-2 )^2 = ?
To solve the given expression, we will follow the order of operations (PEMDAS/BODMAS) which stands for Parentheses/Brackets, Exponents/Orders (ie. Powers and Square Roots, etc.), Multiplication and Division (left-to-right) and Addition and Subtraction (left-to-right).
Given expression: (1/9 - 2)^2
First, we can compute the subtraction in the parentheses:
1/9 - 2 = 1/9 - 18/9 = -17/9
Next, square this result:
(-17/9)^2 = (-17/9) * (-17/9) = 289/81
Therefore, (1/9 - 2)^2 = 289/81.
9 + 7N = 23
Which of the following sentences represents the equation above?
The given equation is:
9 + 7N = 23
To represent this equation in a sentence, we can say:
"Nine added to seven times a number is equal to twenty-three."
So, the sentence representing the equation is:
"Nine added to seven times a number is equal to twenty-three."
Which value for x makes the sentence true?
10x - 4
A. -60
B. -6
C. - 34/5
D. -12
To find the value for x that makes the sentence true, we need to substitute the given values into the expression and see which one satisfies the equation.
Given expression: 10x - 4
Let's evaluate the expression for each of the answer choices:
A. -60:
10(-60) - 4 = -600 - 4 = -604
B. -6:
10(-6) - 4 = -60 - 4 = -64
C. -34/5:
10(-34/5) - 4 = -68 - 4 = -72
D. -12:
10(-12) - 4 = -120 - 4 = -124
From the calculations, we see that the expression equals -64 when x = -6.
Therefore, the value that makes the sentence true is x = -6, and the correct answer is B. -6.
To find the order of the flooring types from least to greatest installation fee per-square-foot, we need to divide the total cost of each type of flooring by the area to get the total cost per square foot, and then subtract the cost of the materials to get the installation fee per square foot.
For the slate tile:
Total cost = $740.40
Area = 120 square feet
Cost per square foot = $740.40 / 120 = $6.17 per square foot
Cost of materials = $1.73
Installation fee per square foot = $6.17 - $1.73 = $4.44
For the hardwood flooring:
Total cost = $1,688.00
Area = 200 square feet
Cost per square foot = $1,688.00 / 200 = $8.44 per square foot
Cost of materials = $4.98
Installation fee per square foot = $8.44 - $4.98 = $3.46
For the berber carpet:
Total cost = $928.80
Area = 180 square feet
Cost per square foot = $928.80 / 180 = $5.16 per square foot
Cost of materials = $2.48
Installation fee per square foot = $5.16 - $2.48 = $2.68
From least to greatest installation fee per-square-foot:
Carpet ($2.68), Tile ($4.44), Hardwood flooring ($3.46)
So, the order is:
Carpet, Tile, Hardwood flooring