Answer:
length, width, and height are (b+2), (b-2), (b+3)
Step-by-step explanation:
Doing what the problem statement tells you to do, you get ...
(b^3 +3b^2) -(4b +12)
= b^2(b +3) -4(b +3) . . . factor each pair of terms
= (b^2 -4)(b +3) . . . write as a product
= (b -2)(b +2)(b +3) . . . use the factoring of the difference of squares
The three factors are (b-2) , (b+2) , and (b+3). We have no clue as to how to associate those with length, width, and height. We just know these are the dimensions of the box.
The possible dimensions of the prism are:
Length: 9x, 5x + 7, or x + 3
Width: 5x + 7, x + 3, or 9x
Height: x + 3, 9x, or 5x + 7
What is a prism?A prism is a three-dimensional object.
There are triangular prism and rectangular prism.
We have,
To find the possible dimensions of the prism, we need to factor the given volume expression into three factors, each representing the length, width, and height of the box.
We start by looking for common factors among the coefficients of the three terms:
45x³ + 198x² + 189x
= 9x (5x² + 22x + 21)
Now we can factor the quadratic expression inside the parentheses:
5x² + 22x + 21
= 5x² + 15x + 7x + 21
= 5x(x + 3) + 7(x + 3)
= (5x + 7) (x + 3)
The volume expression can be factored as:
45x³ + 198x² + 189x
= 9x (5x + 7) (x + 3)
Thus,
The possible dimensions of the prism are:
Length: 9x, 5x + 7, or x + 3
Width: 5x + 7, x + 3, or 9x
Height: x + 3, 9x, or 5x + 7
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The area of Tyrone's square bedroom is 144 square feet. He wants to paint the walls of his room. How much paint would he need to paint all four sides?
I'll give brainliest
Answer:
Each side is 12 feet.
What is the area, in square feet, of the trapezoid below?
Answer:
68.75
Step-by-step explanation:
Measure the length of the parallel sides and add them together. Then multiply this number by the height of the area. Then multiply by ½ or divide by two to find the square footage of the trapezoid.
13.6 + 5.9= 19.5
19.5 + 8 = 27.5
27.5 x 5 = 137.5
137.5 x 1/2 = 68.75
The variable Q varies inversely as the cube of V. FK is the constant of variation, which equation represents this situation?
A. qv^3=k
B. q^3v=k
C. q/v^3=k
D. q^3/v=k
Step-by-step explanation:
When 2 variables are inversely proportional to each other, their product is a constant.
Since Q and V³ are inversely proportional to one another, QV³ = k. (B)
What is the equation of a line that passes through the points (–3, 4) and (2, 8)?
Answer:
[tex] \frac{y - 4}{x - ( - 3)} = \frac{8 - 4}{2 - (- 3)} \\ \frac{y - 4}{x + 3} = \frac{4}{5} \\ 5(y - 4) = 4(x + 3) \\ 5y - 20 = 4x + 12 \\ \boxed{4x - 5y + 32 = 0}[/tex]
4x-5y+32=0 is the right answer.i need help on this question
Answer:
5
Step-by-step explanation:
9+6=15
15/3=5
Step-by-step explanation:
[tex] \frac{a + b}{c} = \frac{9 + 6}{3} = \frac{15}{3} = 5 \: ans[/tex]
Anyone know the answer ?
Answer:
74 is the answer
Step-by-step explanation:
64+42=106
180-106=74
hope this helped!
Answer: 74°
42+64=106
180-106=74
I hope this helps :
Хеллльпппппп please ......
Answer:
B
Step-by-step explanation:
The difference of two numbers is 18. Their sum is 66. What are the numbers? List the numbers from least to greatest.
can someone help simplify the following expression. 7t -3t + 4
A 4t + 4
B 7t - 1
D 10t + 4
C10 + 4
14a + 8
Factor the Algebraic Expression
Answer:
Step-by-step explanation:
2 is the largest shared factor. Thus, the given 14a + 8 = 2(7a + 4).
Which expression is equivalent to 5/6c + 76c, if c+ 0?
Answer:
0
Step-by-step explanation:
If c=0
that expression also equals 0
What is the answer to the problem 50 Х200=
Answer:
10000
Step-by-step explanation:
50 times 200
5 times 2 is 10
add three zeros: 10000
A restaurant keeps eggs in a rack that has 5 layers. Each layer has 5 rows, with 5 eggs in each row. How many eggs does each 5-layer rack hold?
Answer:
The answer is 125 eggs.
The total number of eggs required will be 125.
What is an expression?The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.
Given that a restaurant keeps eggs in a rack that has 5 layers. Each layer has 5 rows, with 5 eggs in each row. The number of eggs will be calculated as:-
Number of eggs = 5 x 5 x 5
Number of eggs = 125
Therefore, the total number of eggs required will be 125.
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2. Lorena is trying to choose between two different savings accounts at H-Town Bank. She will deposit $3,500 dollars and will leave the money in the account for 12 years. There will be no additional money deposited or withdrawn from the account.
Answer:
First of all, this question is not complete. So, we will be hypothetically create two accounts and try to choose the one with the greater profit.
Choice 1 = X = Final Amount after 12 years = $5600
Choice 2 = Y = Final Amount after 12 years = $6285.50
Hence, Lorena should choose choice 2, as it gives more profit over than choice 1.
Step-by-step explanation:
First of all, this question is not complete. So, we will be hypothetically create two accounts and try to choose the one with the greater profit.
Initial Deposit Amount = $3500
Time period = 12 years
Let's Suppose Lorena has two X and Y choices of accounts at H-town Bank.
X = simple interest of 5% over the initial amount for 12 years.
Y = Compound interest 5% over the initial amount for 12 years.
Solution:
Let's calculate the profit for choice 1 = X
Simple interest = 5%
Initial amount = $3500
Time period = 12 years
Formula = A = P (1 + rt)
where, A = Final amount after 12 years
t = time period in years = 12
P = initial amount to be deposited = $3500
r = annual interest rate = 5%
Plug in the values to get the total amount.
A = 3500(1+0.05x12)
A = $5600 = final amount Lorena will get after 12 years.
Let's calculate the profit for choice 2 = Y
Compound interest = 5%
Initial amount = $3500
Time period = 12 years
Formula = A = P [tex](\frac{r}{n} + 1)^{nt}[/tex]
where,
A = Final amount after 12 years
t = time period in years = 12
P = initial amount to be deposited = $3500
r = annual interest rate = 5%
n = number of times interest rate is applied or compounded. = 12
Plug in the values to get the total amount.
A = P [tex](\frac{r}{n} + 1)^{nt}[/tex]
A = $6285.50
Hence, Lorena should choose choice 2, as it gives more profit over than choice 1.
Draw an ordered stem and leaf diagram to show this information.
245, 250, 251, 253, 258, 264, 267, 269, 273, 276
Key:
2415 means
Answer:
24|5
25|0;1;3;8
26|4;7;9
27|3;6
Step-by-step explanation:
key in the bottom right:
24|5means 245
Help plz ASAP !!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
-2
Step-by-step explanation:
Let's solve your equation step-by-step.
−(3v+1)+7(6v+6)=−37
Step 1: Simplify both sides of the equation.
−(3v+1)+7(6v+6)=−37
−3v+−1+(7)(6v)+(7)(6)=−37(Distribute)
−3v+−1+42v+42=−37
(−3v+42v)+(−1+42)=−37(Combine Like Terms)
39v+41=−37
39v+41=−37
Step 2: Subtract 41 from both sides.
39v+41−41=−37−41
39v=−78
Step 3: Divide both sides by 39.
39v
39
=
−78
39
v=−2
Answer:
v=−2
Answer:-2
Step-by-step explanation:
Casi drove 135 miles in 3 hours. Use a proportion to find how long it would take her to drive 360 miles at the same speed.
Answer:
8 hours
Step-by-step explanation:
We are given that
Casi traveled distance in 3 hours=135 miles
We have to find the time taken by Casi to drive 360 miles at the same speed using proportion .
Let time taken by Casi to drive 360 miles=x
We know that
Speed=[tex]\frac{Distance}{time}[/tex]
Using proportion
[tex]\frac{a}{b}=\frac{c}{d}[/tex]
[tex]\frac{135}{3}=\frac{36}{x}[/tex]
[tex]x=\frac{360\times 3}{135}[/tex]
[tex]x=8[/tex]
Hence, the time taken by Casi to drive 360 miles=8 hours
CAN SOMEONE HELP ME ??? This is areas and volumes of similar solids!!!!!! It’s urgent!!
Answer:
Step-by-step explanation:
let x be the unknown volume
5/7=50/x
x=70
Answer:
137.2 m³
Step-by-step explanation:
Given the ratio of sides a : b , then
ratio of volumes = a³ : b³
Here ratio of sides = 5 : 7 , then
ratio of volumes = 5³ : 7³ = 125 : 343
let x be the volume of the larger prism then by proportion
[tex]\frac{50}{125}[/tex] = [tex]\frac{x}{343}[/tex] ( cross- multiply )
125x = 17150 ( divide both sides by 125 )
x = 137.2
That is volume of larger prism is 137.2 m³
please help!
what is 2/7 x 1/3
Answer:2/21
Step-by-step explanation:
2 x 1 2
——- =. -
7 x 3. 21
please help me answer this question its urgent
Answer:
Step-by-step explanation:
1). [tex]\frac{2}{3}n-\frac{3}{4}n+\frac{1}{6}n+2\frac{2}{9}n[/tex]
= [tex]\frac{2}{3}n-\frac{3}{4}n+\frac{1}{6}n+(2+\frac{2}{9})n[/tex]
= [tex](\frac{2}{3}-\frac{3}{4}+\frac{1}{6})n+(2+\frac{2}{9})n[/tex]
= [tex](\frac{8}{12}-\frac{9}{12}+\frac{2}{12})n+(2+\frac{2}{9})n[/tex]
= [tex]\frac{(8-9+2)}{12}n+(2+\frac{2}{9})n[/tex]
= [tex]\frac{1}{12}n+(2+\frac{2}{9})n[/tex]
= [tex](\frac{1}{12}+2+\frac{2}{9})n[/tex]
= [tex](\frac{3}{36}+\frac{72}{36}+\frac{8}{36})n[/tex]
= [tex]\frac{83}{36}n[/tex]
= [tex]2\frac{11}{36}n[/tex]
2). [tex]\frac{2}{5}g-\frac{1}{6}-g+\frac{3}{10}g-\frac{4}{5}[/tex]
= [tex](\frac{2}{5}-1+\frac{3}{10})g-(\frac{1}{6}+\frac{4}{5})[/tex]
= [tex](\frac{4}{10}-\frac{10}{10}+\frac{3}{10})g-(\frac{5}{30}+ \frac{24}{30})[/tex]
= [tex](\frac{4-10+3}{10})g-(\frac{5+24}{30})[/tex]
= [tex]\frac{-3}{10}g-\frac{29}{30}[/tex]
= [tex]-\frac{3}{10}g-\frac{29}{30}[/tex]
3). [tex]i+6i-\frac{3}{7}i+\frac{1}{3}h+\frac{1}{2}i-h+\frac{1}{4}h[/tex]
= [tex]7i-\frac{3}{7}i+\frac{1}{2}i+\frac{1}{3}h-h+\frac{1}{4}h[/tex]
= [tex](7-\frac{3}{7}+\frac{1}{2})i+(\frac{1}{3}-1+\frac{1}{4})h[/tex]
= [tex](\frac{98}{14} -\frac{6}{14}+\frac{7}{14})i+(\frac{4}{12}-\frac{12}{12}+\frac{3}{12})h[/tex]
= [tex](\frac{98-6+7}{14})i+(\frac{4-12+3}{12})h[/tex]
= [tex]\frac{99}{14}i-\frac{5}{12}h[/tex]
Please help
Regroup and write your answer in simplest form
3/5 pint of juice is poured equally into 6 glasses. How much juice is in each glass? Answer in a complete sentence.
Answer:
3/30
Step-by-step explanation:
Answer:
1/10
Step-by-step explanation:
you divide by 3/5 by 6
A stack of books is 5 feet 5 inches high. How high is it in inches?
Well first, you have to know that there are 12 inches in a foot so, that's 12 / 3 = 4, so that means that for every foot, there are 4 books. The books are 5 feet tall so 4 x 5 = 20. Your answer is: 20 books are in a stack.
Answer:
Step-by-step explanation: I would do 5x12 because there are 12 inches in one foot so 5x12 is 60 so there is 60 inches
Teresa is going with her family to watch
professional barrel racers. Her family
buys 6 tickets. They have a coupon for
$1.50 off each ticket. They pay $52.50
altogether for their tickets. Write an
equation that you could use to represent
the situation. What is the price of a ticket
before using the coupon?
Answer:
6 * (x - 1.50) = 52.50 ; 10.25
Step-by-step explanation:
Given that :
Number of tickets purchased = 6
Coupon off per ticket = 1.50
Total Amount paid for tickets = $52.50
Let x = initial price of ticket :
Number of tickets purchased * (Initial ticket price - coupon) = total amount paid
6 * (x - 1.50) = 52.50
6x - 9 = 52.50
6x = 52.50 + 9
6x = 61.50
x = 61.50 / 6
x = 10.25
Hence, initial price of ticket = $10.25
5. The point (-7, 4) is reflected over the line x = -3. Then,
the resulting point is reflected over the line y = x. Where
is the point located after both reflections?
A. (-10,-7)
B. (1,4)
C. (4, -7)
D. (4,1)
Answer:
(4,1)
Step-by-step explanation:
Reflected over x = -3, new point : (1,4)
Reflected over y=x, new point = (4,1)
Please PLEASE HELPPP!!!!!!
Answer:
5/2
Step-by-step explanation:
10 multiplied by 5/2 gives us 25, so the scale factor is 5/2.
Due in 15 minutes helppppp
Answer:
13,5,12 inches hope this helps
Step-by-step explanation:
The function can be used to determine the milligrams D of a certain drug in a patient's bloodstream h hours after the drug has been given. How many milligrams (to two decimals) will be present after
Answer: 0.09 mg
Step-by-step explanation:
To find out the milligrams in the blood after 10 hours you just need to replace the 'h' in the equation to 10.
= 5e⁻⁰°⁴ˣ¹⁰
= 5e⁻⁴
= 0.09157819444
= 0.09 mg
hii I really need help!!
sorry if it’s kinda long lol.
question:
Sonia has two packages of hamburger meat. The first package weighs 1.76 pounds and the second package weighs 2.29 pounds. She mixed the two packages together and forms hamburgers that weigh 0.25 pounds each. What is the greatest number of 0.25-pound hamburgers Sonia can make using the hamburger meat she has?
Answer:
16
Step-by-step explanation:
2.29+1.76=4.05
4.05/0.25=16.2
round down to 16
you would have a little extra but you would only be able to make 16 .25 pound ones
What is the value of X?
The answer is x = 11/36
lt is 100% right