The width of a rectangular prism is w centimeters. the height is 2 centimeters less than the width. the length is 4 centimeters more than the width. of the volume of the prism is 8 times the measure of the length, find the dimensions of the prism

Answers

Answer 1
w x (w-2) = 8
w^2 - 2w = 8
w^2 - 2w - 8 = 0
(w-4)(w+2) = 0

w = 4 Or w = -2

However w cannot be less than 0

So w must = 4

Width is 4, height is 2, length is 8
Total Volume =64 which is 8(8).

Related Questions

PLEASE HELP

Missi designed a stained glass window and made a scale drawing using centimeters as the unit of measurement. She originally planned for the length of the window to be 44 in. but decided to change it to 48 in. If the length of the window in her scale drawing is 4 cm, which statement about the change of scale is true?

A)One cm represented 11 in. in the first scale, but now 1 cm represents 12 in. in the second scale.
B)One cm represented 44 in. in the first scale, but now 1 cm represents 48 in. in the second scale.
C)One cm represented 1 in. in the first scale, but now 1 cm represents 1 in. in the second scale.
D)One cm represented 12 in. in the first scale, but now 1 cm represents 11 in. in the second scale.

Answers

One cm represented 11 in. in the first scale, but now 1 cm represents 12 in. in the second scale.

Answer:

The correct answer is option A,

One cm represented 11 in. in the first scale, but now 1 cm represents 12 in. in the second scale

Step-by-step explanation:

The earlier planned length was [tex]44 in\\[/tex]

So the scale of the map was

[tex]\frac{44}{4} \\= 11\\1 cm = 11 in\\[/tex]

The second planned length was [tex]48 in\\[/tex]

So the second scale of the map was

[tex]\frac{48}{4} \\= 12\\1 cm = 12 in\\[/tex]

Thus, option A is correct.

A rectangle has a a perimeter of 72 ft. The length and width are scaled by a factor 3.5.



What is the perimeter of the resulting rectangle?



Enter your answer in the box.

Answers

Formula for perimeter of rectangle:
P=2(L+w)
P=2L+2w
Here Perimeter, p= 72 ft
And scale factor of length and width=3.5 which means rectangle is enlarged.
So perimeter of rectangle= 3.5 x 72
P=252ft 

Answer: 252 ft

We know the perimeter of the original rectangle is 72ft.
We also know that the perimeter P of the rectangle is defined as:
P=2L+2W.
So P is directly proportional to L+W. This means that if L or W were to get bigger, P will get bigger, and if L or W were to get smaller P will get smaller.

The question also states that both L and W are scaled by the same factor of 3.5 .
This means the sum of the dimensions L+W is scaled by 3.5
It also means that the perimeter is upscaled by 3.5 as it is proportional to L+W.
P = 72 ft × 3.5 = 252 ft.

252 ft is the answer.

Please help me! I don't know the answer.
Lines L and M are parallel. GEOMETRY

Answers

The angle measure of ∠2 is equal to 38°.

m∠2 = 38°.

What are the corresponding angles?

When two parallel lines are crossed by another line, comparable angles are the angles that are created in matching corners or corresponding corners with the transversal (i.e. the transversal).

Given:

Lines L and M are parallel lines.

And the parallel lines are cut by a traversal line.

From the property of corresponding angles:

The angle measure of ∠2 is equal to 38°.

Therefore, m∠2 = 38°.

To learn more about the corresponding angles;

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Genghis Motors wants to build cars and motorbikes on a budget. The company plans to spend at most $75000 and use at least 320 workers to build cars and motorbikes.
8000C+5500M≤75000 represents the number of cars C and motorbikes M the company can build by spending at most $75000.
52C+38M≥320 represents the number of cars and motorbikes the company can build by using at least 320 workers.
Can the company meet both of its expectations by building 4 cars and 6 motorbikes?

Answers

Evaluate each of the expressions for the given values of the variables and see if the condition is met.

8000*4 +5500*6 = 65000 ≤ 75000 . . . true

52*4 +38*6 = 436 ≥ 320 . . . . . . . . . . . . . true

Yes, the company can meet both its expectations by building 4 cars and 6 motorbikes.

Of course, another way to work this is to draw the graph and see if the offered point is in the feasible region. It is.

Elevii clasei a IV-a se informeaza despre preturile unor obiecte:3 aparate foto de acelasi fel si un laptop costa 2700lei,iar 5 aparate foto si 2 laptopuri,de acelasi fel ca primele costa,4900lei.Cat costa un aparat foto?Dar un laptop?Prin metoda compaatiei va rog !!!!!!! URGENT !!!!!!

Answers

Laptops are 1200 each and cameras are 500 each.

Using elimination:
3c+l=2700
5c+2l=4900

We will make the coefficients of l the same by multiplying the top equation by 2:
2(3c+l=2700)
6c+2l=5400

Our system is now
6c+2l=5400
5c+2l=4900

Subtract the bottom equation:
6c+2l=5400
-(5c+2l=4900)

We have
1c=500
So each camera is 500.

Substitute that in our original first equation:
3(500)+l=2700
1500+l=2700
1500+l-1500=2700-1500
l=1200

Write -3r+3u in polar form PLEASE HELP

Answers

we have that
 -3r+3u

Step 1
Use the distance formula to find the radius
r = √(x^2 + y^2)
 (x,y)----------> (-3,3)
r= √(-3^2 + 3^2)=√18=3√2

Step 2
Use the tangent to find the angle  
θ = arctan(y/x)  
θ = arcTan(3/-3)= -45°-------> II Quadrant
then 
θ=180-45=135°

Step 3 
write in polar form
(x,y)------------> (r, θ)
so
(-3,3)----------> (3√2, 135°)

the answer is (3√2, 135°)

Find the surface area of the rectangular solid.

l=16 in, w=13 in, h=15in.

Surface area is in inches and to the 2nd power.

Answers

The surface area is the sum of the areas of each of the 6 rectangular surfaces. There are two surfaces that have the same area, so we can find the areas of the three different rectangles and double that total.
.. A = 2(LW +LH +WH)
.. = 2(LW +H(L +W))
.. = 2((16 in)(13 in) +(15 in)*(16 in +13 in))
.. = 2(208 in^2 +435 in^2)
.. = 1286 in^2

The surface area of the prism is 1286 in^2.

how do you solve FOIL problems for algebra 1

Answers

FOIL= first, outside, inside, last

These refer to the position of terms in the parentheses and the order they are multiplied.

Example:
(x+1)(x+2)
multiply first positions (far left)
(x*x)
then multiply the two outside
(x*2)
multiply inside terms
(1*x)
multiply last terms (far right)
(1*2)

Solution to example:
(x+1)(x+2)
(x*x)+(2*x)+(1*x)+(1*2)
combine terms
x^2+3x+2

Hope this helps! :)

Jackson currently has $35 in his bank account , he is saving $15 a week to eventually buy a new cell phone. He can represent the amount in his account with the equation y=15x+35.
I also need help answer the other questions to

Answers

X represents the number of weeks he has been saving Y is the total money in his account the slope is $15 and the Y intercept is $35 for the the starting balance in his account

Answer:

1. We have our function y = 15x + 35

a) Where the x represents the numbers of weeks since each week he is saving $15, which is the independent variable.

b) Where the y represents the total money he has, which is the dependent variable.

c) the slope is 15, as x increments, the slope goes up by 15.

d) The y-intercept is 35, because when x = 0, y = 35.

2. To create the table you have to find the value of y, knowing the values of x.

Using our function, when x = 0

y = 15(0) + 35

y = 0 + 35

y = 35

Using our function, when x = 1

y = 15(1) + 35

y = 15 + 35

y = 50

Using our function, when x = 2

y = 15(2) + 35

y = 30 + 35

y = 65

Using our function, when x = 3

y = 15(3) + 35

y = 45 + 35

y = 80

Using our function, when x = 4

y = 15(4) + 35

y = 60 + 35

y = 95

Using our function, when x = 5

y = 15(5) + 35

y = 75 + 35

y = 110

Yes, the table is proportional, because for each week, the value of his money is increasing by 15.

3. To create the graph, you can put the values of the table into the graph

And the graph is not proportional because to be proportional the relationship between “x” and “y” should be constant, meaning that, if “x” changes, “y” changes by the same percentage.

In this case our function has an intercept of 35 meaning that at week 0, he has $35 saved,

after a week: $50,

after two weeks: $65,

So, although is linear, is not proportional because when you double the weeks saved, you don't double the money saved.

Which measure describes how all of the values of a data set vary with a single number?
A) mean
B) median
C) mode
D) range

Answers

B) median


hope this helps<3

Answer:

The answer is d. range.

The lowest common denominator for the fractions 8/64 and 8/32 is ?

Answers

Final answer:

The lowest common denominator for the fractions 8/64 and 8/32 is 32. This is found by identifying 32 as the least common multiple of the denominators 64 and 32, allowing both fractions to be expressed with the same denominator.

Explanation:

Finding the Lowest Common Denominator

To find the lowest common denominator (LCD) for the fractions 8/64 and 8/32, you must identify the smallest number that both denominators can divide into without leaving a remainder. Both 64 and 32 can be divided by 32, so the LCD for these fractions is 32. It's important to understand that finding an LCD involves looking for the least common multiple (LCM) of the denominators. In this case, since 32 is a multiple of 64 (32x2=64), it serves as the LCM of 32 and 64, and consequently, the LCD of the fractions.

To further clarify, each fraction can be expressed with a denominator of 32. For 8/64, when we divide both the numerator and denominator by 8, we get 1/8. This fraction can then be converted to have a denominator of 32 through multiplication by 4 (1/8 * 4/4 = 4/32). Similarly, the fraction 8/32 is already expressed with the desired denominator.

By finding the LCD, it is easier to perform addition, subtraction, or comparison of fractions, as they will share the same denominator.

The lowest common denominator for the fractions [tex]\( \frac{8}{64} \) and \( \frac{8}{32} \) is \( \boxed{64} \).[/tex]

To find the lowest common denominator (LCD) for the fractions [tex]\( \frac{8}{64} \) and \( \frac{8}{32} \)[/tex], we need to determine the least common multiple (LCM) of the denominators 64 and 32.

Step 1: Find the prime factorization of each denominator:

[tex]- \( 64 = 2^6 \)[/tex]

[tex]- \( 32 = 2^5 \)[/tex]

Step 2: Determine the LCM by taking the highest power of each prime that appears in any factorization:

[tex]\[ \text{LCM} = 2^{\max(6, 5)} = 2^6 = 64 \][/tex]

Therefore, the LCD of the fractions [tex]\( \frac{8}{64} \) and \( \frac{8}{32} \) is \( 64 \).[/tex]

Step 3: Verify that ( 64 ) is indeed the LCD:

[tex]- \( \frac{8}{64} = \frac{1}{8} \)[/tex]

[tex]- \( \frac{8}{32} = \frac{1}{4} \)[/tex]

Both fractions can be rewritten with a denominator of ( 64 ):

[tex]- \( \frac{1}{8} = \frac{8}{64} \)[/tex]

[tex]- \( \frac{1}{4} = \frac{16}{64} \)[/tex]

Therefore, ( 64 ) is the lowest common denominator for[tex]\( \frac{8}{64} \) and \( \frac{8}{32} \).[/tex]

Thus, the lowest common denominator for the fractions [tex]\( \frac{8}{64} \) and \( \frac{8}{32} \) is \( \boxed{64} \).[/tex]

A woman walks 100 yards east along a straight shoreline and then swims 30 yards south into the ocean on a line that is perpendicular to the shoreline. Using her starting point as the pole and the east direction as the polar axis, give her current position polar coordinates. Round the coordinates to the nearest hundredth. Express θ in degrees. (11.40, –88.28°) (104.40, –88.28°) (11.40, –16.70°) (104.40, –16.70°)

Answers

Using trigonometric ratio tangent
Tan θ = 30/100
       θ =  16.70, but since it is in an anticlockwise direction it will be -16.7
using Pythagoras theorem
a²+b²=c²
thus, c²=100²+30²
         c = √(100²+30²)
           =  104.40.
Therefore,the current position coordinates will be
(104.40, -16.70°)

3. what is a popular sunday activity for families in mexico city ? ( 1point )

A. vista the beach

b. visit the prado museum

c. stroll by the roman aqueduct

d. go to the chapultepec park

Answers

The answer is D, Go to Chapultepec Park.
d. go to the Chapultepec park. Mexico city is the capital of Mexico. It is a densely populated place. So people like to go the Chapulepec park on the sunday. It is the biggest park in the Western hemisphere. It is also known as Bosque de Chapultepec. It is constructed on a rock formation with different sections. It extends to about 1695 acres.

Which is a possible number of distinct real roots for a cubic function? Select all that apply.
0
1
2
3
4

Answers

3

I don't know how to explain, but 3

Answer: The answer is  1 and 3.

Step-by-step explanation:  We are to select the correct options about the number of real roots of a cubic function.

We know that there are three roots of a cubic function, out of which one must be real because the least number of real roots of an odd degree function is 1.

Also, if the second root is real, then the third one must also be real because the complex roots of a function occur in pairs.

Therefore, there is one real root or three real roots for a cubic function.

Thus, the answer is 1 and 3.

What Is 7 minutes after 1? And what is 23 minutes after 4?

Answers

1:07 and 4:23 if it is time you are asking about... If it's not time then I am not quite sure of what you are asking.

Answer: 7 minutes after 1 is 1:07 and 23 minutes after 4 is 4:23

Step-by-step explanation: Please mark me brainliest ✨

Good luck on whatever you’re working on!

banananana help me i need you

Answers

The first question should be a Pentagon as it has 5 sides, but it should also be a regular shape.
Pentagon; Regular
----------------------------
The second question shows something that obviously is not a square nor rectangle, so by process of elimination Parallelogram is your answer.
Parallelogram

Answer:

Banananana. How do you know that person?  

Step-by-step explanation:

WILL GIVE BRAINLIEST!!! 12 POINTS!!!!!!

The table below represents the height of a shot basketball, f(x), based on its horizontal position in relation to the basket, x.

x f(x)
-24 7
-20 12
-16 15
-12 16
-8 15
-4 12
0 7

If all quantities are in feet, what is the height of the basketball as it passes the hoop?

Answer: _____ feet

Answers

Answer:  " 7 (seven) " [feet] .
_________________________________________________
Note:  This is the value of "f(x)"  when "x = 0" .
_________________________________________________

Which best describes the function on the graph?

Answers

The answer is going to be B
I believe its A because Its rise over run so the rise would be -2 and the run would be one so its not B or D which leaves the options A and C and its Direct variation because its passing through the origin. Hope i helped :)

In oder to join a yoga club there is a $100 annual fee and a $5 fee for each class ytouattend. Write an equation in slope-intercept form that models this situation.

Answers

y=5x+100
___
5 being the daily fee, and x being each day you attend. Multiply these. 

Compare the domains of the logarithmic function f(x) and the square root function g(x).
Graph of f(x):
https://homelifetn.ignitiaschools.com/media/g_alg02_ccss_2016/9/al2_9_20a_media02.gif
https://homelifetn.ignitiaschools.com/media/g_alg02_ccss_2016/9/img_alg02u09c03q25d_02.gif
In two or more complete sentences, explain whether or not the domains of the two functions are the same.

Answers

We have that the logarithmic function has a domain from 0 (without including 0) to plus infinity. That is because of the property that e=2.71 raised to any power is positive. We also have that the square root function is defined only from 0 to plus infinity, since every square of a number is positve or 0. The answer is that the domains differ; they are almost equal, except for the fact that the domain of the square root function additionally contains 0.

Factor completely. a2+3a−28 Enter your answer in the box.

Answers

By a2, I assume you mean a squared. If so, then the answer is (x+7)*(x-4).

Imari went on a hike and recorded the number of each type of bird he saw. The circle graph shows the results of his count. Imari saw 42 sparrows. How many birds did he count in all? Enter your answer in the box. A pie chart depicting a count for bird species. Cardinals are at 13 percent, Sparrows are at 35 percent, Chickadees are at 23 percent, Blue Jays are at 8 percent, Woodpeckers are at 4 percent, and Robins are at 17 percent.Imari went on a hike and recorded the number of each type of bird he saw. The circle graph shows the results of his count. Imari saw 42 sparrows. How many birds did he count in all?

Answers

the answer is 120 for sure

Answer: 120


Hope This Helps ^_^


Help please got to finish khan academy I’m really confused

Answers

= 64^(t^3)*64^(-t/2)
= 64^(t^3)*(64^(-1/2))^t . . . . change the sum of exponents to a product
= 64^(t^3)*(1/√64)^t . . . . . . negative exponent signifies inverse, 1/2 power is sqrt
= 64^(t^3)/8^t . . . . . . . . . . . simplify
= (4^3)^(t^3)/8^t . . . . . . . . . .replace 64 with 4^3
= 4^(3t^3)/8^t . . . . matches the first selection only

5.11 find the probability of a couple having a baby girl when their third child is​ born, given that the first two children were both girls. assume boys and girls are equally likely. is the result the same as the probability of getting all girls among three ​children?

Answers

The chance of having a girl is 50%. Having two other girls doesn't change the odds. However, having three girls in a row is a 12.5% chance.

PLS PLS PLS help I am rly confused

Answers

jjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjj

What is the value of x? Enter your answer in the box. x = . Triangle G E H with segment E D such that D is on segment G H, between G and H. Angle G E D is congruent to angle D E H. E G equals 99.2 feet, G D equals 62 feet, D H equals left parenthesis x plus 2 right parenthesis feet, and E H equals 112 feet.

Answers

Corresponding sides on either side of ED are proprotional, so
.. (x+2)/112 = 62/99.2
.. x +2 = 112*62/99.2 = 70

x = 68 . . . . feet

Answer:

The value of x is 68 ft.

Step-by-step explanation:

Given information: [tex]\angle GED\cong \angle DEH[/tex]

Bisector of an angle of a triangle theorem states that an angle bisector of a triangle divides the opposite side into segments that are proportional to the adjacent sides.

In triangle FEH, ED is an angle bisector

[tex]\frac{EH}{EG}=\frac{DH}{GD}[/tex]

[tex]\frac{112}{99.2}\times 62=x+2[/tex]

[tex]70=x+2[/tex]

[tex]70-2=x[/tex]

[tex]68=x[/tex]

Therefore the value of x is 68 ft.

:)If Dani has 5,054 of a certain item and she needs to collect 6,000 of it, how much more does she need to reach her goal? :) Just for fun lol

Answers

Take 6,000-5,054= 946
6,000-5,054=946......

Perform the indicated operation.
(w 3 + 64) ÷ (4 + w)

w² - 4w - 16
w² + 4w - 16
w² - 4w + 16

THE ANSWER IS:
w^2 - 4w + 16

The reason I included the correct answer in the question is that this question was not yet asked and I felt that some people might need to know this. Feel free to answer the question and get the points! :)

Answers

w^2 - 4w + 16

Thanks for the points :)

w^2 - 4w + 16


tytytytytyty


Need help with this too, all connected

Answers

#5 C. 5/12

#6 B. 6:2

#7 C. 25%

#8 If the veterinarian treats 50 dogs in a week, they would treat 10 reptiles in the same amount of time.

The sum of the square of a positive number and the square of 3 more than the number is 45. what is the​ number?

Answers

x= a number

sum= add
more than= add
is= equal sign
square of= multiply the # by itself

x^2 + (x+3)^2= 45
x^2 + (x+3)(x+3)= 45

x^2 + x^2 + 3x + 3x + 9 = 45
combine like terms

2x^2 + 6x + 9= 45
subtract 9 from both sides

2x^2 + 6x= 36
reduce by dividing everything by 2

x^2 + 3x= 18
subtract 18 from both sides

x^2 + 3x - 18= 0
factor
(x+6)(x-3)= 0

x+6= 0
x= -6

x-3=0
x= 3

The question asks for the POSITIVE integer, so...

ANSWER: x= 3

Hope this helped! :)

The positive integer is [tex]3[/tex]

Let the number be [tex]a[/tex]

square of [tex]a = a^{2}[/tex]

Square of [tex]3[/tex] more than [tex]a[/tex] = [tex](3+a)^{2}[/tex]

[tex](3 + a)^{2} = (3+a)(3+a) = 9 + 3a + 3a + a^{2} = a^{2} + 6a + 9[/tex]

[tex]a^{2} + a^{2} + 9a + 9 = 45[/tex]

[tex]2a^{2} + 6a + 9 = 45[/tex]

Subtract 9 from both sides :

[tex]2a^{2} + 6a = 45 - 9[/tex]

[tex]2a^{2} + 6a = 36[/tex]

Divide through by 2

[tex]a^{2} + 3a = 18\\a^{2} + 3a - 18 = 0[/tex]

Factorize :

[tex]a^{2} + 6a - 3a - 18 = 0\\a(a + 6) - 3(a + 6) = 0\\a + 6 = 0\\or\\a - 3 = 0[/tex]

[tex]a = 3 ;\\or\\a = - 6[/tex]

since, a is a positive integer, then [tex]a = 3[/tex]



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