The volume of a rectangular prism is the product of the prism's dimension (i.e. length, width and height). The dimension of the rectangular prism are:
[tex]Length = 3x^2\\ Width = 2x - 1\\ Height = 3x + 4[/tex]
Given that:
[tex]Volume = (18x^4 + 15x^3 - 12x^2)[/tex]
First, we factor out [tex]3x^2[/tex]
[tex]Volume = 3x^2 \times (6x^2 + 5x - 4)[/tex]
Expand
[tex]Volume = 3x^2 \times (6x^2 + 8x-3x - 4)[/tex]
Factorize
[tex]Volume = 3x^2 \times (2x(3x + 4) -1(3x + 4))[/tex]
Factor out [tex]3x + 4[/tex]
[tex]Volume = 3x^2 \times ((2x -1) (3x + 4))[/tex]
Rewrite as:
[tex]Volume = 3x^2 \times (2x -1) \times (3x + 4)[/tex]
The volume of a rectangular prism is:
[tex]Volume = Length \times Width \times Height[/tex]
So; by comparison:
[tex]Length = 3x^2\\ Width = 2x - 1\\ Height = 3x + 4[/tex]
Read more about polynomials and volumes at:
https://brainly.com/question/2141804
1. Which of the following is an example of like
terms?
a. - 16 and - 16x
b. x and x2
C, 50y and y
d. 20a and 2
If (x + 4)^2 = 49 and x < 0. what is the value of x?
Answer:
x = -11
Step-by-step explanation:
To get to 49 by squaring, you need to square 7. Since x can only be negative, you need to get to -7.
-11 + 4 = -7
(-7)^2 = 49
Answer:
x = -11
Step-by-step explanation:
To get to 49 by squaring, you need to square 7. Since x can only be negative, you need to get to -7.
Is the set of real numbers closed under addition? Explain why or why not. If it is not closed, give an example
Answer: Yes, the set of real numbers is closed under addition.
Explanation:
Let x and y be two real numbers. Their sum x+y is some other real number. This is what it means when we say the set of real numbers is closed under addition. Taking any two numbers and adding them will get us some other real number.
There is no way to have x+y be nonreal while x,y are both real.
ɪ ɴᴇᴇᴅ ʜᴇʟᴘ ᴡɪᴛʜ ᴛʜɪꜱ !
ᴍᴀᴛʜ ᴇxᴘᴇʀᴛꜱ ᴏɴʟʏ
Joanne a total score for a round of darts was -42 she had thrown 6 darts and scored the same each throw How many points did Joanne score on each throw
Answer:
7
Step-by-step explanation:
Answer:
7
Step-by-step explanation:
Ok, so we know 42 is the number of points added up, and we know that she threw 6 darts all scoring the same. Now, all we have to do is figure out what number(for example x) multiplied by 6 equals 42. Or in the form of an equation:
6x = 42
Now, to finish the equation, all we have to do is divide:
6x/6 = 42/6
42/6 = 7
x = 7
A truck can be rented from Company A for $120 a day plus $0.20 per mile. Company B charges $60 a day plus $0.40 per mile to rent the same truck. Find the number of miles in a day at which the rentals cost for company A and company B are the same.
please help..
Answer:
12 miles in a day.
Step-by-step explanation:
Variable x = number of miles
Company A: 120 + 0.20x
Company B: 60 + 0.40x
Set up an equation:
120 + 0.20x = 60 + 0.40x
60 + 0.20x = 0.40x
60 = 0.20x
12 = x
I divide my favorite number by its reciprocal , the quotient is 10 times as large as my favorite number. My favorite number is..
A. 1/10
B. 1/5
C. 1/2
D. 10
Answer:
1/10
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
x is the favorite number
x÷[tex]\frac{1}{x}[/tex] = 10x (flip the fraction and multiply)
[tex]x^{2}[/tex]=10x (divide both sides by x)
x=10
If(2x,x+y)=(y,9)find x and y.
Answer:
the value of X is 3 and y is 6 .
Factor this polynomial expression.
x2 + 8x + 16
A. (x-8)(x - 2)
B. (x + 4)(x + 4)
C. (x+8)(x+2)
D. (x-4)(x - 4)
Answer:
I think (x+4) (x+4) is right answer.
Step-by-step explanation:
here,
x2+8x+16
=x2+(4+4)x+ 16
=x2+4x+4x+16
=x(x+4)+4(x+4)
=(x+4)(x+4) Ans
What is the length of AB?
Select the best answer from the choices provided.
A.3.5
B.3
C. 7
D.14
The perimeter of an equilateral triangle can be represented by 6x+36. Which of the following expressions represents the length of one of the sides of the triangle?
A. 3(2x+12)
B. 2x+12
C. 6x+33
D. 3x+18
Please help quick!!
Answer:
2x + 12
Step-by-step explanation:
6x + 36 / 3 =
(6x)/3 + (36)/3 = 2x + 12
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Line segment JM has endpoints with coordinates 0 and 25 on a number line. Points K and L are on segment JM. K has a coordinate of 5 and point L has a coordinate of 12. Find the probability that a point on JM is placed first on JL and a second point is not placed on KL.
Answer:
D. 216/625Step-by-step explanation:
The length of the segment JM is 25 units.The segment JL is between 0 and 12, so is 12 units.The segment KL is between 5 and 12, so is 7 units.The probabilities for each point:
P(point on JL) = 12/25P(point not on KL) = 1 - 7/25 = 18/25Required probability:
P = 12/25*18/25 = 216/625Correct choice is D
please help me with this and explain your answer
Answer:
B
Step-by-step explanation:
t=4x+c
Since we are looking for x,
t-c=4x
Divide through by the coefficient of x which is 4
4x/4=t-c/4
Therefore, x=t-c/4
0.6m=____mm . answer the question
Answer:
600
Step-by-step explanation:
since 1m=1000mm
Which names are other ways to name _1? Select each correct answer.
y
pfy
pyf
p
yfp
ypf
f
Answer:
your answer is F
I hope it's helps you
5. You want to have a pizza party this weekend for some friends and family. You have $48
budgeted for the pizza and plan on having 56 pieces available. A large pizza has 16 pieces and
costs $14. A medium pizza has 12 pieces and costs $10. How many large and medium pizzas do
you need to buy?
Solve 6x + ( 14x - 5 ) + ( 17 - 3x ) , - ( 2 - x ) -3 ( 6 + 8x ) -12, ( 4x - 9 ) + 8 ( 2x + 3 ) -7x
Answer:
Step-by-step explanation:
6x + ( 14x - 5 ) + ( 17 - 3x )
= 17x + 12
- ( 2 - x ) -3 ( 6 + 8x ) -12,
= -23x - 32
( 4x - 9 ) + 8 ( 2x + 3 ) -7x
= 13x +15
what is 3 feet + 14 inches
Answer:
3.14
Step-by-step explanation:
What is the sum of all the positive integers from √24 to √102
Answer:
[tex] \sqrt{24} = 4.9[/tex]
[tex] \sqrt{102} = 10.1[/tex]
positive integers = x
4.9 < x < 10.1
x = 5, 6, 7, 8, 9, 10
sum = 5 + 6 + 7 + 8 + 9 + 10
= 45
Which of the following equations has the same solution as: |3x + 2| = 4x + 5
Answer:
Step-by-step explanation:
simplify (a+1/a)^2-(a-1/a)^2
HELPPPPP PLSS- What is the area of this figure? 9 yd 5 yd 7 yd 3 yd 2 yd 6 yd square yards
Answer:
99
Step-by-step explanation:
9x5 + 7X6 + 3X4 + 2X6
If f(x) = 24 +5, then what is the remainder when f(x) is divided by 2 + 2?
Answer:
The question is incorrect as it lacks the "x" component. Function f(x) cannot be stated without the x, elseways it couldn't be called "f(x)"
What is the solution of the equation?
8-3t=t
-1/4
-4
2
1/2
Answer:
t = 2
Step-by-step explanation:
8-3t=t
add 3t to both sides
8=4t
then divide both sides by 4 leaving you with
t=2
The distance between two points on a map is 6.5 cm. The scale of the map is 1:1000. Find the actual distance between the two points in km.
I need the answer asap
Answer:
0.065km
Step-by-step explanation:
1:1000 in cm
so in km its
cm:km
1:0.01
6.5:X
so its 0.065 km
hope it helps and correct
keep loving maths
Helllllpppppppp!!!!!
Answer: The correct answer is C
Step-by-step explanation:The graph is horizontally stretched by a factor of 1/5 because you are literally multiplying x by 1/5. So, your answer is C. Hope it makes sense. mark me brainlest
a.) The median player salary for the New York Yankees was $1.5 million in 2007 and $1.7 million in 2013. Write a linear equation giving the median salary y in terms of the year x. (Let y be in millions of dollars and let
x = 7
represent 2007.)
b.) Use the equation to predict the median salary in 2048. (Round your answer to one decimal place.)
$ million
A general linear equation is given by:
[tex]y = a*x + b[/tex]
Where a is the slope and b is the y-intercept.
Here we will find that the linear equation that represents the situation is
[tex]y = 0.033*x + 1.269[/tex]
And we can expect that the median salary in 2048 is $2.853 million
If the line passes through the points (x₁, y₁) and (x₂, y₂) then the slope can be written as:
[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Here we know that:
in 2007 (x = 7) the median player salary was y = $1.5 million
in 2013 (x = 13) the median player salary was y = $1.7 million.
Then we have two points that we can write as:
(7, 1.5)
(13, 1.7)
Note that the y-value is in millions.
Then the slope of the linear equation will be:
[tex]a = \frac{1.7 - 1.5}{13 - 7} = 0.033[/tex]
So the linear equation is something like:
[tex]y = 0.033*x + b[/tex]
To find the value of b, remember the point (7, 1.5), this means that when we have x = 7, we also have y = 1.5, then we can replace these in the above equation:
[tex]1.5 = 0.033*7 + b\\\\1.5 - 0.033*7 = b = 1.269[/tex]
Then the linear equation is:
[tex]y = 0.033*x + 1.269[/tex]
b) Now we want to predict the median salary in 2048. For 2048 the x-value is x = 48
So we just need to evaluate this in the linear equation:
[tex]y = 0.033*48 + 1.269 = 2.853[/tex]
Then the median salary in 2048 will be $2.853 million
If you want to learn more, you can read:
https://brainly.com/question/1189779
find the radius of a circle that has an area of 803.84 cm squared
Answer:
Radius = 16
Step-by-step explanation:
Area = πr²
803.84 = 3.14(r²)
256 = r²
√256 = 16
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
With 4 weeks remaining in the season, Lisa has 31 more homeruns than Mark. If Mark is to hit more homeruns than Lisa, he must average at least how many more homeruns per week than Lisa?
Answer:
31/4
= 7.75
So Mark has to average more than 7.75 homeruns per week.
Step-by-step explanation:
Mark me as brainliest.
An object travels back and forth along a straight line. Its velocity, in centimeters per second, is given by the
function v(t)
= 13 sin(pi/(45)t), where t is time in seconds.
What is the maximum velocity of the object?
O 0 cm/s
O 13 cm/s
O 26 cm/s
O 90 cm/s
A function in mathematics is a relation between two sets such that each element of the first set is matched to exactly one of the second set element
The correct option for the maximum velocity of the object is the option;
13 cm/s
The reason for the selection is as follows:
The known parameters of the motion of the vehicle are:
The type motion of the vehicle = Repetitive back and forth
The path of the motion of the object = Along a straight line
The function that gives the velocity in centimeters per second (cm/s) is given as follows;
[tex]v(t) = \mathbf{13 \cdot sin \left(\dfrac{\pi}{45} \cdot t \right)}[/tex]
Where;
t = The time in seconds (a set of the input variables of the function)
v(t) = The velocity of the object (the output variables of the function)
The velocity of the object, v(t), depends (is given by) on the time t, therefore;
The maximum velocity is given at a particular value of t, which together with [tex]\dfrac{\pi}{45}[/tex] is operated by the sine function
The maximum output value of the sine function = 1, therefore;
[tex]\mathbf{Maximum \ value \ of \ sin \left(\dfrac{\pi}{45} \cdot t \right)_{max}} = 1[/tex]
[tex]The \ maximum \ velocity \ v(t)_{max}} = 13 \times sin \left(\dfrac{\pi}{45} \cdot t \right)_{max} = 13 \times 1 = \mathbf{ 13}[/tex]
The units of the of the function is cm/s
Therefore, the maximum velocity of the object is 13 cm/s
Learn more about functions here:
https://brainly.com/question/23999020
Answer: B. 13 cm/s
Step-by-step explanation:
