the volume of a box is 45x^3 + 198x^2 + 189x. find expressions for the possible dimensions of the prism
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
Learn more about prism here:
https://brainly.com/question/12649592
#SPJ2
I need help on 9 10 and 13 plzzz
Answer:
its 35
Step-by-step explanation:
please help me find the slope im begging
Answer1)-1 2) 5/2:
Step-by-step explanation:
square root of 479/90
a question that is hard for me. I dont have my calculator
Answer:
the answer is 0.24317854031 hope this helps have a nice day please give me brainliest:))
Step-by-step explanation:
Answer:
0.24317854031
Step-by-step explanation:
1. Open your browser
3. Search up: square root of 479/90
4. Copy paste answer
5. Need I say more?
Algebra 2
Factoring Polynomials
Factor the polynomial completely.
1. x3 - 2x2 – 24x
Please help I don’t know how to answer !!!
Alex has saved $30 and he earns $12 per hour. He wants to have at least $150 in his savings account. How many hours can he work?
Answer: 10
Step-by-step explanation: 120 divided by 12 = 10
which expression represents purely real numbers and which expression represents non-real complex number?
Incomplete question. However, I provided some explanation about non-real complex numbers.
Explanation:
In Mathematics, the term complex numbers (non-real complex numbers) in simple terms refers to numbers that containing an imaginary addition to it.
For example, the numbers 3i, 3 + 5i, 3i/4 are non-real numbers because of the addition of an imaginary part which is denoted by 'i'.
While real numbers, on the other hand, are numbers that do not include an imaginary part; they stand on their own, such as whole numbers 0, 1, 2, 3, etc, rational numbers like 3/4, etc.
The expression
10
,
000
(
1.20
)
t
10,000(1.20)
t
represents the population of a town t years after 2000.
Select the value from each drop-down menu that best completes the sentence.
The population of the town
by
each year.
Answer:
According yo my calculations v=-92 that makes it so that 34×6÷39=124
Answer:
I Think it decreases by 10% each year.
Sorry if im wrong.
y = 3 2 x A 2-column table with 4 rows. Column 1 is labeled Days x with entries 1, 2, 3, 4. Column 2 is labeled Hours y with entries 1 and one-half, 3, 4 and one-half, 6. On a coordinate plane, a line goes through points (1, 1.5) and (2, 3). The models all represent a real-world problem. How would you match the models to a problem? Find a problem with the same variables and the same relationship between the quantities. Find a problem that has the same numbers. Find a problem that has the same variables. Find a problem that has the same x-values.
sorry about the girl who stole points anways on edg its A
Answer:
aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
Step-by-step explanation:
−8 (1 + x) + 7x PLEASE HELP
Answer:
-8-x or -x-8 or x=-8
Step-by-step explanation:
Distribute the -8 to the (1+x)
-8-8x+7x
then add the -8x+7x
-8-x or -x-8
and if you want to solve for x
x=-8
What is the area, in square inches, of the shaded part of the shape?
A.110 square inches
B.48 square inches
C.140 square inches
D.80 square inches
CAN SOMEONE DO MY KHAN ACADEMY FOR ME AND HELP ME WITH THIS QUESTION?
Answer:
The answer is C
Step-by-step explanation:
Answer:
most likely to me is a best option
Step-by-step explanation:
1/4 multiply 20 like a fraction like this 20/1 then multiply numerator and denominator or (top and bottem) which then gives you 20 /5
simplify it you get 4
A __________________ sample has characteristics similar to those of the entire population and, therefore, can be used to draw a conclusion about the (general) population.
Answer:
Representative.
Step-by-step explanation:
In Statistics, sampling can be defined as a process used to collect or select data (objects, observations, or individuals) from a larger statistical population using specific procedures.
A representative sample has characteristics similar to those of the entire population and, therefore, can be used to draw a conclusion about the (general) population. Thus, it is considered typically to be a subset of population and can be used to accurately make conclusions and reflect the characteristics of the larger sample (population).
A cyclist rides her bike at a speed of 18 kilometers per hour. What is the sped in kilometers per minute? How many kilometers will the cyclist travel in 10 minutes? Do not round around your answer.
Speed:
Distance traveled in 10 minutes:
Answer:
speed: .3 kilometers a minute. Distance traveled in 10 minutes: 3 kilometers
Find the value of x in the triangle.
67 113
293
7
Answer:
x = 67°Step-by-step explanation:
The sum of measures of angles in triangle is allways 180°
So:
x + 53° + 60° = 180° {subtract 113° from both sides}
x = 67°
what is 69*773 I just need some help getting the answer?
Answer:
53,337
Step-by-step explanation:
Answer:
53337
Step-by-step explanation:
There ya go.
Two-Way Frequency Tables Please Help.
Answer:
17%
Step-by-step explanation:
Percentage of full time employees who ride bus to and fro from work?
Since the table as been arranged as a two way frequency table., we only need to find the value at the intersection of the two Given conditions ;
Horizontally, the type of ride = bus
Vertically, the type of employee = full-time
Hence, full time employees who take bus to and fro = 0.17
As a percentage =, (0.17 * 100) = 17%
The Benton family uses up a 1/2 gallon jug of milk every 3 days. At what rate do they drink milk?
Answer:
1/6
Step-by-step explanation: in a rate you need to make it a one so you double the 1/2 gallon to make it one gallon then since you doubled that you have to double the days to 6. So they drink 1 gallon per 6 days.
A store gives 20th customer a 20$ gift certificate.Every 75th customer gets a 75$gift certificate .Which customer will be the first to receive both types of gift certificates?
Solve for x, 3-5x=18
Answer:
X = 3
Step-by-step explanation:
18 - 3 = 15
5x = 15
divide both sides by 5
X = 3
Answer:
[tex]3 - 5x = 18 \\ - 5x = 18 - 3 \\ - 5x = 15 \\ x = \frac{15}{ - 5} \\ \boxed{x = - 3}✓[/tex]
x=-3 is the right answer.On a map of a fair, the Ferris wheel is located at (3, 2). The carousel is located 5 units south of the Ferris wheel. What ordered pair represents the location of the carousel?
Answer:
(3,-3)
Step-by-step explanation:
It is located 5 units south, which means it is on the y-axis line. So, you would subtract 5 from 2 (2-5) and that gives you -3.
What is 30% of 70? A:9
B:12 C:19 D:21
Answer:
Step-by-step explanation:
21
Find the discriminant of the equation and give the number and type of solutions of the equation 4x^2+2x-5=0
Please help fast!!
Answer:
The answer is 84.
Step-by-step explanation:
The given equation is
4x*2 + 2x -5 = 0
Here a= 4, b= 2, c= -5
Since Discriminant= b*2 -4ac
Putting values
Discriminant= (2)*2 - 4(4)(-5)
= 4 + 80
= 84
Since our Discriminant(84) is >0 and is not a perfect square so the roots of the given equation are unequal and irrational(real).
What’s the slope of the line? Please hurry please
Answer:
-3/1 or just -3
Step-by-step explanation:
If using the method of completing the square to solve the quadratic equation
2? + 4x + 3 = 0, which number would have to be added to "complete the square"?
Step 1 Divide all terms by a (the coefficient of x2). Step 2 Move the number term (c/a) to the right side of the equation. Step 3 Complete the square on the left side of the equation and balance this by adding the same value to the right side of the equation.
Answer:
to solve quadratic equations you need to first figure out how many terms you have and if you have more than 3, your in luck but the AZB formula will not include the terms 1 2 or 3
Step-by-step explanation:
what is the square root of 31
Answer:
5.567764363 or rounded off to two decimal places 5.57
Step-by-step explanation:
Calculator
make
x
the subject of the formula
p
+
x
=
t
Answer:
x = t - p
Step-by-step explanation:
p + x = t
subtract p from both sides.
x = t - p
solve for x round your answer to the nearest tenth
How many potential phone numbers can be created from the last seven digits (XXX – XXXX) if each digit can be any number 0-9?
100,000
1,000,000
10,000,000
10,000
Answer:
10,000,000
Step-by-step explanation: