Mathematics High School

The cube root of a number x, written ex, is the number y whose cube is x. That is, y² = x. DO NOW: The Number That Cubes: A cube whose side lengths measure 1 unit has been dilated by several scale factors to make new cubes. 1. For what scale factor will the volume of the dilated cube be 27 cubic units? 2. For what scale factor will the volume of the dilated cube be 1,000 cubic units? Task #1 Suppose we have a solid with volume 10 cubic units. It's dilated, and the volume of the image is 40 cubic units. How can you find the scale factor that was used? Task #2 A superhero action figure has a volume of 1500 cm³. The figure is dilated to create a store display. The volume of the dilated figure is 45,000 cm³. What was the approximate scale factor of the dilation? *STUDENT REFLECTION: GIVE YOUR BEST EFFORT? COMPLETE ALL PARTS? UNDERSTAND? LEARNING OBJECTIVES: I WILL BE ABLE TO: 1) show relationships between volumes and scale factors. 2) find a scale factor by working backwards from a volume. PAGE 1 5.7 FOCUS: How do we analyze relationships between volumes and scale factors? PAGE 2 Lesson 7 Practice Problems 1. A solid with volume 8 cubic units is dilated by a scale factor of k to obtain a solid with volume V cubic units. Find the value of k which results in an image with each given volume. a. 216 cubic units b. 1 cubic unit c. 1,000 cubic units 2. A solid with surface area 8 square units is dilated by a scale factor of k to obtain a solid with surface area A square units. Find the value of k which leads to an image with each given surface area. a. 512 square units b. square unit C. 8 square units 3. A solid with volume 8 cubic units is dilated by a scale factor of k. Find the volume of the image for each given value of k. a. k = + b. k = 0.6 c. k = 1.5 4. Noah edits the school newspaper. He is printing a photograph of a flyer for the upcoming school play. The original flyer has an area of 576 square inches. The picture Noah prints will be a dilation of the flyer using a scale factor of. What will be the area of the picture of the flyer in the newspaper? 5. Angle S is 90 degrees and angle T' is 45 degrees. Side ST is 3 feet. How long is side SU? LEARNING OBJECTIVES: I WILL BE ABLE TO: 1) show relationships between volumes and scale factors.2) find a scale factor by working backwards from a volume.

Answers

Answer 1

In these tasks, we are exploring the relationship between volume, scale factor, and dilations. We are given different volumes of dilated objects and need to find the corresponding scale factor. Additionally, we encounter a problem involving surface area and another problem related to angles and side lengths. By applying the concept of dilations and their effects on volume, surface area, and side lengths, we can find the scale factors and solve the given problems.

In Task #1, we have a solid with an initial volume of 10 cubic units that is dilated to obtain a solid with a volume of 40 cubic units. To find the scale factor, we can divide the final volume by the initial volume: 40 / 10 = 4. Therefore, the scale factor used in the dilation is 4.
In Task #2, a superhero action figure has a volume of 1500 cm³, which is dilated to create a store display with a volume of 45,000 cm³. To find the scale factor, we divide the final volume by the initial volume: 45,000 / 1500 = 30. Therefore, the approximate scale factor of the dilation is 30.
For the practice problems listed, they involve finding scale factors, volumes, surface areas, and areas of dilated objects using given information and applying the relevant formulas and concepts. By understanding the relationships between volumes, scale factors, and dilations, we can solve these problems effectively.

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Related Questions

this year, donna watched 40 movies. She thought that 8 of them were good. Of the movies she watched, what percentage did she think were good?

Answers

Answer:

20%

Step-by-step explanation:

40 / 8 = 20

20 * 1 = 20

HOPE THIS HELPS

PLZ MARK BRAINLIEST

Answer:

20%

Step-by-step explanation:

[tex]\frac{Number. she .thought. was .good}{Total} =\frac{unknown.percent}{100} \\\frac{8}{40} =\frac{x}{100} \\800=40x\\ x=20\\[/tex]

I NEED HELP ASAP please!!!!

Answers

Answer:

A

Step-by-step explanation:

the equation doesn't use the Additive Inverse.

solve for x. 4(2-x)+13=2x+3

Answers

Answer:

x = 3

Step-by-step explanation:

4(2-x)+13=2x+3

distribute the 4.

8 - 4x + 13 = 2x + 3

combine like terms.

21 - 4x = 2x + 3

18 = 6x

divide by 6.

x = 3

check.

4(2 - 3) + 13 = 2(3) + 3

4(-1) + 13 = 6 + 3

-4 + 13 = 9

9 = 9

correct!

Evaluate the formula for the volume of a rectangular prism to solve the problem.



Volume = length times width times h. A swimming pool has a height of 3 meters, width of 25 meters, and length of 50 meters.

West junior High needs to fill its swimming pool with water. Determine the amount of water it needs by finding the volume of the pool. Use the drop-down menus to complete the statements.

Answers

Answer:

B, A, C, and D

Step-by-step explanation:

Did the assignment

Answer:

First, write the  

✔ formula: V = lwh

.

Next, use parentheses when you substitute  

✔ 50, 25, and 3

for l,w, and h.

Now, simplify by  

✔ multiplying

50, 25, and 3.

The volume of the pool is  

✔ 3,750

m3.

I WILL GIVE BRAINLIEST!!!! HELP PLEASE!!!!!!!!!!!!!!!! BRAINLIEST!!!!!!!!!!!!! PLEASE HELP ME!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!BRAINLIEST!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
(please note I can only give brainliest after 2 people have answered.) thanks!

The following description appeared on a news Web site after the world's largest passenger plane was introduced. "That airline will see the A380 transporting some 555 passengers, 139 more than a similarly set-up 747." How many passengers will a similarly set-up 747 transport?

Answers

Answer:

416 passengers

Step-by-step explanation:

Dont stress out, it’s just simple subtraction,

so A380 can transport 555 which is 139 more then 747

so subtract 555-139 which will give you 416 passengers.

Answer:

What up I’m the alt

the answers 416

Step-by-step explanation:

555-139=416

-1/5n + 7 = 2 n = ?
what does n equal ?

Answers

n= 35/11

hope it helps

Solve the literal equation for A
2A+x=-8
and then Evaluate for X=-4 and after simplify
PLZ HELP ITS DUE TODAY

Answers

Answer:

a=[tex]\frac{-1}{2}[/tex]x−4

Step-by-step explanation:

Step 1: Add -x to both sides.

2a+x+−x=−8+−x

2a=−x−8

Step 2: Divide both sides by 2.

[tex]\frac{2a}{2}[/tex]=[tex]\frac{-x-8}{2}[/tex]

Ninety-three percent of a town’s population owns cars. If the number of cars owned is 5,208, what is the population of the town?
You have 2 attempts left to earn the full credit for this problem.

Answers

Answer:

  5600

Step-by-step explanation:

Let p represent the number of people in the town. If we assume that each car owner owns only one car, then we have ...

  0.93p = 5208

  p = 5208/0.93 = 5600

The population of the town is 5600.

A rectangular box is 8 inches long, 10 inches wide, and 6 inches tall.

What is the approximate length of its longest diagonal?



a. 4.9 inches


b. 14.1 inches


c. 10 inches


d. 24 inches

Answers

C I think is correct

What is the value of x in the figure below?
A. 22.5°
B. 45°
C. 55°
D. 57.5°​

Answers

Answer:

sorry i cant see the pic

Step-by-step explanation:

Explain why a +b= d.​

Answers

Answer:

see explanation

Step-by-step explanation:

a + b + c = 180 ( sum of angles in a triangle )

c + d = 180 ( adjacent angles are supplementary ), thus

a + b + c = c + d ( subtract c from both sides )

a + b = d

The reason for the value of a+b being equal to d is because adjacent angles are supplementary.

First and foremost, it should be noted that a triangle has three sides and the sum of the angles in the triangle will be equal to 180°.

Therefore, based on the information given in the question, the solution will go thus:

a + b + c = 180°

Note that c + d = 180° since adjacent angles are supplementary.

Therefore, a + b + c = c + d

Collect like terms

a + b + c - c = d

a + b = d

Therefore, the equation has been proven and showed that a + b = d.

Read related link on:

https://brainly.com/question/10585424

Which unit abbreviation is a measurement of force?
A.
m/s
B.
m/s2
C.
N
D.
N/s Could anyone help?

Answers

Answer: C. N

N stands for Newtons

In terms of SI units, 1 newton = 1 kg m/s^2

It's based off the equation F = ma, which is Newton's second law.

------------

Extra info:

Choice A is velocityChoice B is accelerationChoice D is some unit I don't really recognize, so I'm not sure if its nonsense or it may have some use. Though I'm sure that N/s isn't a measurement of force.

Answer:

C.  N

Step-by-step explanation:

4x + 7 = 5 solve for x​

Answers

Answer:

-1/2

Step-by-step explanation:

4x + 7 = 5

4x=5-7

4x=-2

x=-2/4

x=-1/2

hope this helps u!

Answer:

0.5

4x+7=5

4x=5-7

4×=-2

4\=/4

answer is -0.5

I need help Asap!!!!!!!!!

Answers

-8 and 3 ...... I think

What is the slope of the line through (-10,1) and (0,-4)

Answers

Answer:

y=3/10x+4 thats why i got

Step-by-step explanation:

Donna worked for 13 hours each day for 6 days. Then the next day she worked 7 hours. How many hours did Donna work in all?

Answers

Answer:

85 hours

Step-by-step explanation:

Multiply 13 by 6 to know how much she worked in those 6 days and then add 7 more hours to that and you should get 85 hours in total.

Answer: 85 hours

Step-by-step explanation:

Donna worked for 13 hours every day for 6 days:

This means that she worked 13 hours each day so what we have to do is this:

13·6 = 78   <------- That is the amount of hours she worked for 6 days

Now we have to figure the last day:

Donna worked 7 hours.

This part is simple, all we have to do is add 78 from our previous equation and add it to 7 hours which gives us a total of 85 hours!

Hope this helps :)

Make sure to mark brainliest!

how do you do this one? :/

Answers

Answer:

x = -2 , x = - 4

Step-by-step explanation:

since the function has been factored, you can just set the factors to zero and solve

Need a answer for p help me out please

Answers

Answer:

p = 13

Step-by-step explanation:

Answer:

p = 13

Step-by-step explanation:

find the value of a²-b² when a-b=3 and a+b=4​

Answers

Answer:

12

[tex] {x}^{2} - {y}^{2} = (x - y) \times (x + y) = 3 \times 4 = 12 [/tex]

A density curve is shown below.
If a point within the density curve is chosen at random,
what is the probability that the value lies between 2.25
and 4.75?

Answers

Answer:

.417

Step-by-step explanation:

What compound inequality represents the phrase? Graph the solutions.

all real numbers w that are less than –7 or greater than 14

Answers

w < -7 OR w >14 Since this is an "or" problem, you must use one to separate the two inequality phrases.  

HOPE IT HELPS (◕‿◕✿)

Find the coordinate of the midpoint of the segment with the given endpoints.
- 9 and 0
The midpoint is
(Simplify your answer.)

Answers

Answer:

4.5

Step-by-step explanation:

-4.5+-4.5=-9

Find m2V.
S
T
(9x – 19)°
U
111°
((7x + 3)
X
(5x + 8)
128°
W

Answers

Answer:

103

Step-by-step explanation:

6 sides

(6-2)180 =720

720 = S×T+U+V+W+X

S=90

720 = 90 + (9X-19) + (111) + (5X+8) + (128) + (7X+3)

COMBINE LIKE TERMS

720= (90-19+111+8+128+3) + (9X+5X+7X)

720 = 321 + 21X

720-321 = 321-321 + 21X

399 = 21X

19 = X

mV = 5X + 8

mV = 5(19) + 8

mV = 95 + 8

mV = 103

I pushed the button for Classic Coke and received a bottle of Classic Coke.
My friend Cory decided to be different and pushed the other button for Classic Coke. He also received a bottle of Classic Coke.
Each of us asked five friends to push one of the two Coke buttons and the ALL got a bottle of Classic Coke.
Is the machine functioning consistently? Why or why not?

Answers

Answer:

yes

Step-by-step explanation:

because you all asked the machine for classic coke

Please someone help with my homework​

Answers

Answer:

x is bigger than or equal to -3

Step-by-step explanation:

Answer:

Sould be x ≥ −3

Step-by-step explanation

You flip the eqation, subtract 8 from both sides, and divide both by 4.

Does anybody know this? ill give brainliest to anyone to answers it correctly

Answers

Answer:

25/3

Step-by-step explanation:

not confident if you know please make me correct

Answer:

[tex]25/3.[/tex]

Step-by-step explanation:

[tex]if \: x = 5\\ if \: y = 3 \\ then \to \\ {9x}^{2} y {}^{ - 3} = \frac{ {9x}^{2} }{y{}^{3} } = \frac{9 \times {5}^{2} }{ {3}^{3} } \to \\ \\ {9x}^{2} y {}^{ - 3} = {5}^{2}3{}^{ - 1} \\ {9x}^{2} y {}^{ - 3} = \boxed{25/3} \to \: if \: x \: = 5 \: and \: y = 3.[/tex]

♨Rage♨

Select the two expression equivalent to the given expression. Let x,y and z by numbers​

Answers

Answer:

ponits

Step-by-step explanation:

What is x if 6x-7=13x+8

Answers

Answer:

6x-7=13x+8

6x-13x=8+7

-7x=15

x=-15/7

Solve the following equation for y. 4x - 6y - 8 = 0

Answers

Answer:

y = 2/3x + -4/3

Step-by-step explanation:

4x - 6y - 8 = 0 (Add -4x to both sides)

-6y - 8 = 4x (Add 8 to both sides)

-6y = 4x + 8 (Divide -6 from both sides)

y = 2/3x + -4/3

Determine the type and degree of each of the following polynomial expressions
9x^4 y^9




x^4-3x^2+7x^5



19a^6b^2 + 8ab^3c -27a^7

Answers

Step-by-step explanation:

i hope i have been useful buddy.

good luck

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