Answer:
A: Congruent
Step-by-step explanation:
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:
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A dog kennel board dogs for $8 a day. The kennel will also groom a dog for $12. Write an equation that gives the total cost of lodging a dog and having it groomed once before it comes home.
Can someone answer these two questions I submitted a photo of them it’s worth 50 points
Answer:
Step-by-step explanation:
1). Let the equation of the line is,
y = mx + b
Here, m = slope of the line
b = y-intercept
Slope of a line passing through two points,
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
We take two points from the table given (-3, -19) and (0, -1)
m = [tex]\frac{-19+1}{-3-0}[/tex]
m = 6
y - intercept 'b' = -1 [For x = 0]
Therefore, equation of the line will be,
y = 6x - 1
2). Equation of a line passing through a point (x', y') is,
y - y' = m(x - x')
Slope of the line passing through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is,
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
We take two points from the given table as (2, 12) and (3, 18).
Slope of the line passing through these points will be
m = [tex]\frac{18-12}{3-2}[/tex] = 6
Equation of the line passing through (2, 12) will be,
y - 12 = 6(x - 2)
y = 6x - 12 + 12
y = 6x
By using a graphing tool we can graph these lines representing the tables.
What is the slope indicated in the table below?
(x) 5, 10, 15, 20
(y) 7, 14, 21, 28
PLS EXPLAIN
Answer:
it goes up (x) goes by 5 and (y) by 7
Step-by-step explanation:
6x + 39 (if x = 10)..
Answer:
3(2x+13) or 99
Step-by-step explanation:
Factor 6x+39
6x+39
=3(2x+13)/ 99
Answer:
3(2x+13) or 99
Answer:
99
Step-by-step explanation:
x=10 we know that
so then we have 6 lots of 10s
that is 60
next step is 60+39
that equals to 99
Write an equation in slope intercept form of the line that passes through (-2,10) and (1,1).
Answer:
Step-by-step explanation:
1st use the two points to find the slope of the line that passes thru those two points
m = y2 - y1 / x2 - x1
where point1 = ( x1, y1 ) and point2 = (x2, y2 )
your are given P1 = ( -2,10) and P2 = (1,1)
find the slope
m = 1-(-2) / 1-10
m = 1+2 / -9
m = 3 / -9
m = - 1/3
then use the point-slope formula [y-y1 = m(x-x1)] with either of the two points, I'll use P2 b/c it seems easier (1,1) , you get the same results with either point and work the problem to the slope-intercept form [y = mx +b ]
y -y1 = m(x-x1)
y-1 = -1/3(x-1)
y-1 = -1/3x + 1/3
y = -1/3x + 1/3 + 1
y = -1/3x + 4/3
:) got it ?
I need help with this
Answer:
C
Step-by-step explanation:
You have to distribute the negative into the second set of parentheses first, and since 2x is positive, it will be negative, -3 is negative so it will be positive, and 18 is positive so it will be negative
what is the slope of the line?
Answer:
-2
Step-by-step explanation:
BTW, maybe this would help:
1. Pick two points on the line and determine their coordinates.
2. Determine the difference in y-coordinates of these two points (rise).
3. Determine the difference in x-coordinates for these two points (run).
4. Divide the difference in y-coordinates by the difference in x-coordinates (rise/run or slope).
Hope it helps! ;)
Which expression is equivalent to 1/3y?
1. 1/3 (y + 12) - 12
2. 1/6y+ 1/3 (y+3)
3.1/6y+ 1/6(y+12)-2
4. 1/3y +1/3(6-y)
Please hurry I’m in a meet :,(
Step-by-step explanation:
1/6y+ 1/6(y+12)-2
hope it helps !
please answer?!!!?!?
Find the percent of increase from 28 songs to 57 songs. Round to the nearest tenth of a percent if necessary.
Answer:
The answer is 50.8 but to the nearest tenth its 51% increase
Step-by-step explanation:
Can someone help!
What is 10% of 812?
Answer:
81.2
Step-by-step explanation:
DON'T ANSWER IF YOU DON'T KNOW THAT ANSWER I NEED ANSWERS PLEASE ASAP DUE TODAY ALL 5 QUESTIONS PLEASE AND WHAT YOU DID TO GET THAT ANSWER PLEASE PLEASE
The goalie on the Iceblades hockey team saves (blocks) 73% of the opponent's shots. With 10 minutes to go, the Iceblades are ahead by one goal, and they will win if the other team does not score. The other team takes 5 shots in the final 10 minutes. The Iceblades do not score any more goals.
The table shows pairs of random digits. The pairs in each group simulate the 5 shots taken by the opponent.
Answer the questions to estimate the probability that the Iceblades will win the game.
1. The paired digits 00 to 99 represent 100 shots.
Let 00 to 72 = a shot that is saved. Which digits represent a goal scored? Explain.
2. Each group represents the 5 shots taken by the other team. To win the game, the Iceblades cannot let the other team score any goals.
For a group to be a success, how many of the 5 shots does the goalie need to save?
3. Group 1 is a success. Explain why.
4. In this simulation, which groups are successes? How many successes are there in the 10 groups?
5. Estimate the probability the Iceblades will win the game. Give your answer as a percent.
Answer:
5 goals
Step-by-step explanation:
Answer:
I only know number 1 and 2, but number 1 was already answered.
Step-by-step explanation:
I'll see if i can come back with all of the answers, but number 2 is 3.
A cell phone normally sells for $500, but it is marked down 30% and you have a coupon for an additional 15% off. How much would it cost you to purchase the cell phone?
Answer:
$275
Step-by-step explanation:
30% + 15%=45%
45% of 500 is 225, because 500 x 0.45=225. Then subtract the discount from the total, 500 - 225, and you get 275
Will give 100 points and Brainliest for this question
Answer:
I think it is B
Step-by-step explanation:
hope this helps please give brainliest
Answer:
ty
Step-by-step explanation:
Find the product of 5,604 and 81
A453, 924
Step-by-step explanation:
Answer:
5,604•81= 453,924
Step-by-step explanation:
Which expression is equivalent to √147
write the in independent variable and the dependent and an equation pls help I will cash app you 20$
1) To fix a car, Fix-it Auto charges a base fee of $20 plus $40 per hour.
2) The cost of a banquet at Jean’s Banquet Hall is $450 for the rental of the hall and $15 per guest.
3) An author earns a royalty of $1.25 for each book sold.
4) Marie has $500 in her bank account. Each week she plans to deposit $20.
5) Paul has $1500 in his bank account. Each week he withdraws $100.
6) The cost to cut a lawn is a flat fee of $5 plus $6.50 per hour.
7) The charge to walk a dog is $10/hour.
8) Hans Building supplies sells sand for $19/ton plus $25 for delivery.
Answer:
12345678910
Step-by-step explanat
Does anyone know the answer for this?
Answer:
Up 2, right 5
Step-by-step explanation:
Which expression represents the correct form of the partial fraction decomposition of 19x + 20 answer asap
Answer:
B
Step-by-step explanation:
got it right on edge
Which of the following could be the measure of a pair of consecutive angles in a parallelogram?
Select the best answer from the choices provided.
A.
120° and 80°
B.
140° and 40°
C.
30° and 60°
D.
156° and 34°
Answer:b
Step-by-step explanation:it equals out to 180°
Andrew has $800 saved in his bank account, and he adds $50/month from his
allowance.
Answer:
So if you want an equation its
800+50x=?
So x could be the amount of months
anyone know this answer?
Answer:
The answer is invalid . R Is not remotley equilvent to T. If you try rooting it you will get runied
Step-by-step explanation:
The price of a laptop changed from $350.00 to $550.00. What is the percent change in the cost of the laptop? 200% increase 200% decrease 57.14% increase 57.14% decrease
Answer:
57.14% increase
Step-by-step explanation:
$350÷$200(amount of increase) = 0.5714
0.5714×100= 57.14%
5 feet a width of 2 feet and a height of 3 feet. What is the volume of the fish tank
Answer:
30.
Step-by-step explanation:
Multiply length, width, and height.
What is the value of the exponential expression5^0
Kathy is going to buy a book at the bookstore for $9.45. The tax rate is 10%. What is the total cost Kathy would have to pay?
Franz used 1/12
of his new shelf space for novels and 1/3
for textbooks.
i) What fraction of his shelf space did he use?
ii) What fraction of shelf space is left for his other books?
Answer:
1/12+1/3=5/12
1-5/12=7/12
Step-by-step explanation:
add fractions used
remaining space ,subtract used fraction from the total
CAN SOMEONE PLEASE HELP ME SOLVE THIS
What is the scale factor of the dilation shown?
A. 32
B. 2
C. 3
D. 23
Answer:
D
Step-by-step explanation:
Hope I helped good wap
