Explain how you use prime factors to find the GCF of 45 and 75.
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Amie published her first book. She was given $20,000 and an additional $0.15 for each copy that sold. Her earnings,d, in dollars,from the publication of the book are given d=20,009 + 0.15n where n is the number of copies sold. During the first year, Amie earned $22,100 from the publication and the sale of her book. How many copies of her book were sold?
Which fraction is greater 6/6 or 6/8
Find the distance cd rounded to the nearest tenth. c=(8,-3) and D=(-9,-6)
For the school play, adult tickets cost $4 and children tickets cost $2. Natalie is working at the ticket counter and just sold $20 worth of tickets. What are all the possible ticket combinations for $20 worth of tickets?
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The length and width of the rectangle is 12 feet and 5.5 feet respectively given that the area of a rectangle is 66 feet², and the length of the rectangle is 1 feet more than twice the width. This can be obtained by finding algebraic expression for length by assuming width to be b and solving the quadratic equation formed after substituting it in the formula of area of rectangle.
What is the formula of area of a rectangle?
Area of a rectangle,
A= l × b, where A is the area, l is the length and b is the width.
Find algebraic expression for length:
Let us assume that width of the rectangle is b.
Given that, length of the rectangle is 1 feet more than twice the width
⇒ l = 2b+1 is the required expression.
Calculate the length and width:
Given that A= 66 feet²
In the formula, A= l × b we can substitute the expression for length.
66=(2b+1)b
2b²+b=66
⇒ 2b²+b-66=0
The quadratic equation can be solved using splitting the middle term,
2b²+12b-11b-66=0
2b(b+6)-11(b+6)=0
(2b-11)(b+6)=0
b=11/2 or b= - 6
Taking positive value of b, b=11/2⇒b=5.5 feet
Substitute for length, l = 2b+1 = 2(11/2)+1=11+1 =12 ⇒l = 12 feet
Hence the length and width of the rectangle is 12 feet and 5.5 feet respectively given that the area of a rectangle is 66 feet², and the length of the rectangle is 1 feet more than twice the width.
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w = n
l = 2n+1
w*l = 66
n(2n+1) = 66
2n^2 + n =66
2n^2 + n - 66 = 0
using quadratic equation
n = 11/2
width = 11/2 = 5.5
length = 11 + 1 = 12
(There are two questions)
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Answer:
1. 2x4=8
2x3=6
2. 3x4=12
3x3=9
Step-by-step explanation:
Hello :)
In this problem, you have to create an equation to figure out the length of each bar. The first bar has two sets of 3 blocks; you can see each set by a color change.
Therefore, this equation would be 2 times 3, since there are 2 sets of 3. This answer equates to 6.
The next one has two bars of four blocks. This means it is 2 times 4, because there are two sets of 4 blocks, and this would constitute as the answer 8.
The second question is a bit tricker. If we look at the first bar, we see that there are 3 blocks per set (noted by color change) and we have 3 of those. If we count all of those up, they have 9 blocks overall. After all, 3 times 3 is nine.
The other problem has 4 blocks a set, and there are three of those. 4 times 3 is 12.
13x-11y=-12
9x-7y=-7
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Answer:
The correct answer is A. 3y = 2
Step-by-step explanation:
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No, she is not correct because she has 5 options of seat covers to choose from.
We have to determine the number of options for seat covers
Here given that,
Color options for leather seats =3
Color options for cloth seats = 2
What is probability?
Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.
What is the formula for combinations?
The total number of combinations = nCr!/n!(n-r)!
Where n is the total number of choices available, and r stands for the number of choices to be made.
Here the number of leather seat options presented = 3
The number of options available for cloth seats =2
Total number of options = leather + cloth = 3 + 2 = 5
The number of options available to her
⇒ 5!/ 1!×(5-1)!
⇒ 5!/4!
⇒ 5×4!/4!
⇒ 5
She can only select one style of cover at a time, therefore she has five options for seat covers. The cover may be made of tan cloth, grey cloth, blue leather, black leather, or brown leather.
Hence, she has 5 options of seat covers to choose from.
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Answer:
Sample response: Adele is not correct. There are only 5 choices. Here, we are not able to use the fundamental counting principle because there are different choices for each material.
Step-by-step explanation: