9-41. A. Describe the solid formed by the net below. What are its dimensions (length, width, and height)?B. On graph paper, carefully draw the net of a similar solid using your enlargement ratio. Then cut out your net and build the solid (so that the gridlines end up on the outside the solid) using scissors and tape. (1) 1 (2) 2 (3) 3 (4) 4 C. How does the volume change when a three-dimensional solid is enlarged or reduced to create a similar solid? For example, if a solid’s length, width, and depth are enlarged by a linear scale factor of 10, then how many times bigger does the volume get? What if the solid is enlarged by a linear scale factor of r? Explain.
Answers
Part A
The solid formed by the net has a bottom and a top face which are rectangles with a width of 3 and a length of 4.
Also, it has four lateral faces which are rectangles: two with a length of 4 and a width of 2, and the other two with a length of 3 and a width of 2.
Notice that the width of the lateral faces corresponds to the height of the solid.
Thus, the solid is a rectangular prism, with dimensions:
• length: 4
,• width: 3
• height: 2
Part B
A similar solid with an enlargement ratio of 2 changes the length, width, and height of the solid to: 8, 6, 4.
For an enlargement ratio of 1, the dimensions stay the same.
For an enlargement ratio of 3, each dimension is multiplied by three.
For an enlargement ratio of 4, each dimension is multiplied by four.
Part C
The volume of a rectangular prism is the product of its three dimensions. So, when we enlarge each of its dimensions by a linear scale factor of 10, the volume is changed as follows:
[tex]\begin{gathered} \text{new Volume}=10(length)\times10(w\imaginaryI dth)\times10(he\imaginaryI ght) \\ \\ \text{new Volume}=10(length)\times10(w\imaginaryI dth)\times10(he\imaginaryI ght) \\ \\ \text{new Volume}=10\times10\times10(length)\times(w\imaginaryI dth)\times(he\imaginaryI ght) \\ \\ \text{new Volume}=1000\text{ \lparen original Volume\rparen} \end{gathered}[/tex]Therefore, the volume increases 1000 times.
And if the solid is enlarged by a linear scale factor of r, we have:
[tex]\begin{gathered} \text{new Volume}=r(length)\times r(w\imaginaryI dth)\times r(he\imaginaryI ght) \\ \\ \text{new Volume}=r(length)\times r(w\imaginaryI dth)\times r(he\imaginaryI ght) \\ \\ \text{new Volume}=r\times r\times r(length)\times(w\imaginaryI dth)\times(he\imaginaryI ght) \\ \\ \text{new Volume}=r^3\text{ \lparen original Volume\rparen} \end{gathered}[/tex]Therefore, the volume increases by a factor of r³.
Related Questions
Devon is trying to find the unit price of a6-drink package on sale for $ 2.99. His sister saysthat at that price, each drink would cost just over $ 2.00.Is he right and how do you know? If not, how would Devon's sister find the right price?
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Devon is trying to find the unit price of a
6-drink package on sale for $ 2.99. His sister says
that at that price, each drink would cost just over $ 2.00.
Is he right and how do you know? If not, how would Devon's sister find the right price?
To find the unit price, divide the total cost by the number of drinks
so
2.99/6=$0.50 per drink
therefore
He is not right
Simplify the expression. Write your answer as a power. 1 5 T 1 3 The expression is
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19 cm Find the missing value. Round to the nearest tenths. 52.1 cm 37.90 52.1° 50.6 cm
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52.1º
1) As we have a right triangle, then we can make use of a trigonometric ratio sine and the arcsine:
[tex]\begin{gathered} \sin (\theta)=\frac{opposite\text{ leg}}{\text{hypotenuse}} \\ \sin (\theta)=\frac{15}{19} \\ \end{gathered}[/tex]2) Let's calculate the arcsine of 15/19 to get the angle measure:
[tex]\begin{gathered} \theta=\sin ^{-1}(\frac{15}{19}) \\ \theta\text{ =52.1363}\approx52.1 \end{gathered}[/tex]3) As the measure of the angle is given either in radians or degrees, then the answer is 52.1º
Use the information given to find the equation of the line using the point-slope formula (y-y_1)=m(x-x_1)). Then convert your answer to slope-intercept form (y=mx+b).Parallel to y=2x+5 and passes through the point (4,3)The point slope form is (y-Answer)=Answer(x-Answer)Converting it to slope intercept form gives us: y=Answerx+Answer
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point-slopeWe are required to get the equation of the line in the point-slope and slope-intercept forms.
A line given in the form: y = mx + b is given in the slope-intercept form where m and b are the slope and intercept on the vertical axis respectively.
A pair of parallel lines have the same gradient and we will leverage this fact to get the equation of the line that passes through the point (4,3).
The point-slope slope form of a line is:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \text{Where:} \\ x_1,y_1\text{ are the coordinates of the point} \end{gathered}[/tex]We therefore have:
[tex]\begin{gathered} y-3=2(x-4) \\ as\text{ our }point\text{ slope form} \end{gathered}[/tex]Converting to slope-intercept form:
[tex]\begin{gathered} y-3=2(x-4) \\ \text{Add 3 to both sides to get:} \\ y=2(x-4)+3 \\ y=2x-8+3 \\ y=2x-5 \end{gathered}[/tex]What is the slope of the line whose equation is x + 2y = 6?
Answers
Answer:
-1/2
Explanation:
The standard form of writng the equation of a line is expressed as y = mx+b
m is the slope
Given the equation x + 2y = 6
First we need to rewrite in standard form by making y the subject of the formula;
x + 2y = 6
2y = -x+6
y = -1/2 x + 6/2
y = -1/2 x + 3
Compare with y = mx+b
mx = -1/2 x
cancel out x from both sides to have;
m = -1/2
Hence the slope of the line whose equation is x+2y = 6 is -1/2
Question 410What is the length of line segment DK to the nearest tenth of an inch?
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The Solution:
Given the figure below:
We are required to find the length of DK to the nearest tenth of an inch.
By the Trigonometrical Ratio, we have that:
[tex]\sin 43^o=\frac{\text{opp}}{\text{hyp}}=\frac{16}{DK}[/tex][tex]\sin 43^o=\frac{16}{DK}[/tex]Cross multiplying, we get
[tex]DK\sin 43^o=16[/tex]Dividing both sides by sin43, we get
[tex]DK=\frac{16}{\sin 43^o}=23.4605\approx23.5^o[/tex]Therefore, the correct answer is 23.5 degrees.
Find the slop and the y-intercept of line there are 2 correct answer for this question
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Let's begin by listing out the information given to us:
[tex]\begin{gathered} (x_1,y_1)=(-3,4) \\ (x_2,y_2)=(0,2) \end{gathered}[/tex]The slope is calculated thus:
[tex]\begin{gathered} m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}=\frac{2-4}{0--3}=\frac{-2}{3}=-\frac{2}{3} \\ m=-\frac{2}{3} \end{gathered}[/tex]The y-intercept of the graph is given by the point where the straight line touches the y-axis which is 2.
[tex]b=2[/tex]The first and second options are the correct answer
Find the missing angle m21 m/2=m23=3287157°12
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To find angle 2 we need to remember that the addition of the interior angles of any triangle is equal to 180°, then we have:
[tex]\begin{gathered} m\angle2+71+57=180 \\ m\angle2=180-71-57 \\ m\angle2=52 \end{gathered}[/tex]Then m<2=52°.
Now, to find the angle 1 we need to notice that this is the supplementary angle of the 57° shown, then:
[tex]\begin{gathered} m\angle1+57=180 \\ m\angle1=180-57 \\ m\angle1=123 \end{gathered}[/tex]Then m<1=123°.
Finally to find angle 3 we use the same approach as we did for angle 2, in this case we have:
[tex]\begin{gathered} m\angle3+28+123=180 \\ m\angle3=180-123-28 \\ m\angle3=29 \end{gathered}[/tex]Then m<3=29°.
A rocket is launched from a tower. The height of the rocket, y in feet, isrelated to the time after launch, x in seconds, by the given equation. Usingthis equation, find the time that the rocket will hit the ground, to the nearest100th of second.y = -16x^2+157x + 124
Answers
When x = 0, y = 124ft, which is the height of the tower.
They ground is y= 0. So, we have to solve the quadratic equation
-16x^2+157x + 124 = 0
Using Bhaskara:
Delta = 157² - 4(-16)(124)
Delta = 24649 + 7936
Delta = 32585
Solving the equation:
x1 = (-b +sqrt 32585)/2(-16)
x1 = (-157 + 180,513)/ -32
x1 = 23,513 / -32
x1 = -0,734 (there's no such thing as negative time)
x2= (-b -sqrt 32585)/2(-16)
x2 = (-157 - 180,513) -32
x2 = 10,547
Answer rounded to nearest 10th: x2 = 10,55s
Complete this table so it shows a relation that is not a function
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For this question, we just need to know that for a function, each x-value has just one single y corresponding value. That means we just need to complete the missing value of the table repeating one of the x values because, if there is more the one y corresponding value for the same x value, it means the table does not represent a function So a final answer can be:
NOTE: that is important to remember f(x) represent the y values.
How many solutions does the equation 2(2x – 10) - 8 = -2014 - 3x) have?
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Given the equation :
[tex]undefined[/tex]Find the sales tax on an appliance costing $272.26 if the tax rate is 5.2%.The sales tax is $_(Round to the nearest cent.)
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To determine the sales tax, we have to compute the 5.2% of 272.26. To determine the x% of y, we use the following expression:
[tex]y*\frac{x}{100}.[/tex]Therefore, the 5.2% of 272.26 is:
[tex]272.26*\frac{5.2}{100}.[/tex]Simplifying the above result, we get:
[tex]sales\text{ tax}\approx14.16.[/tex]Answer: $14.16Consider the circle below what is the length of the radius
Answers
Given:
Here AE=4 and AM=9 is given and angle A is right angle means 90
Required:
We have to find the value of r means radius
Explanation:
If the radius is r than AG=r-4
now use the Pythagoras theorem for A is right angle
[tex]r^2=9^2+(r-4)^2[/tex][tex]r^2=81+r^2-8r+16[/tex][tex]8r=97[/tex][tex]r=12.125[/tex]Final answer:
The length of radius is 12.1 as option a
Question 5 of 10 If f(x) = 2x +4, which of the following is the inverse of f(x)? , x) 7 7 O A. F-1(x) = 2(x-4) 22x O B. f-1(x) = 2(x+4) 7 O C. f-'(x) = 7(x+4) (4 2 O D. f-'(x) = 7(x-4) 2 SUBMIT 1
Answers
y = 2x/7 +4
To find the inverse, exchange x and y and solve for t
x = 2y/7 +4
Subtract 4 from each side
x-4 = 2y/7 +4 -4
x-4 = 2y/7
Multiply each side by 7
7(x-4) = 2y/7 *7
7(x-4) = 2y
Divide each side by 2
7/2 (x-4) = 2y/2
7(x-4) /2 = y
The inverse
f^-1 (x) = 7( x-4)
---------
2
How do I divide complex numbers?[tex] \frac{(6 - i)}{(5 + 4i)} [/tex]
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Convert 3 1/3 miles to feet?
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1 mile = 5280 ft
So:
3 1/3 x 5280 = 17,600 ft
Midpoint is (-19,-19), endpoint (-18,-11) what is the other endpoint?!
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Given: Midpoint is (-19,-19), endpoint (-18,-11)
so, as shown C is the midpoint of AB
C = ( -19 , -19)
Let one of the endpoint like B = (-18 , -11)
So, it is required to find A
We should know that:
[tex]\begin{gathered} C=\frac{A+B}{2} \\ A+B=2C \\ A=2C-B \\ A=2\cdot(-19,-19)-(-18,-11) \\ A=(-38,-38)-(-18,-11) \\ A=(-38,-38)+(18,11) \\ A=(-20,-27) \end{gathered}[/tex]so, the other end point is (-20, -27)
Math Question 11 Assignment from math book If a seed is planted, it has a 80% chance of growing into a healthy plant.If 10 seeds are planted, what is the probability that exactly 3 don't grow? Round your answer to three decimal places.A good calculator is found at: Stattrek Binomial Calculator ________.
Answers
Given:
If a seed is planted, it has a 80% chance of growing into a healthy plant.
10 seeds are planted.
Required:
To find the probability that exactly 3 don't grow.
Explanation:
[tex]\begin{gathered} p=80\% \\ \\ =0.8 \\ \\ 1-p=1-0.8 \\ \\ =0.2 \end{gathered}[/tex][tex]\begin{gathered} N=10 \\ k=3 \end{gathered}[/tex]Seven success in 10 trails, therefore
[tex]\begin{gathered} =(10\text{ choose 7\rparen}\times(0.8)^7\times(0.2)^3 \\ \\ =\frac{(10\times9\times8)}{(3\times2)}\times(0.8)^7\times(0.2)^3 \\ \\ =(5\times3\times8)\times0.2097\times0.008 \end{gathered}[/tex][tex]=0.2013[/tex]Therefore 20% that exactly 3 don't grow.
Final Answer:
[tex]20\%[/tex]Lasso SelectInsert SpaceEditUnit 1 - Part 1 - Test ReviewWriting and Modeling with Equations1) A store sells ice cream with assorted toppings. They charge $3.00 for an ice cream, plus 50cents per ounce of toppings.a) Write an equation the represent the total cost (C) of an ice cream base on the ounce oftoppings (t).......b) Use the equation to determine how much Evan's ice cream would cost with 3 ouncesof toppings.
Answers
1
(a) The total cost, C, is given by:
[tex]C(t)=3+0.5t[/tex]b) With 3 ounces of toppings, we have
[tex]t=3[/tex][tex]C(3)=3+0.5(3)=3+1.5=4.5[/tex]Hence Evan's ice cream would cost $4.50
Find a real number, k, such that the line 12x + ky + 20 = 0 has y-intercept -9. K = ______
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Okay, here we have this:
Considering the provided information, we are going to find the requested number "k", so we obtain the following:
Since the y-intercept is the value of y when x equals zero then we get:
12x + ky + 20 = 0
12(0)+k(-9)+20=0
-9k+20=0
-9k=-20
k=-20/-9
k=20/9
Finally we obtain that k is equal to 20/9.
explain how you can use proportional reasoning to determine the whole if you know what 21 is 60% of the whole
Answers
The whole of the number is 35.
It is given in the question that 21 is 60 % of the whole of the number.
We have to find the whole of the number.
Let the whole of the number be x.
Hence, according to the data given in the question, we can write,
60 % of x = 21
Here, we can use the unitary method to find the whole of the number.
(60/100)*x = 21
(3/5)*x = 21
Dividing the equation by (3/5), we get,
x = 21/(3/5)
x = 21*(5/3)
x = 105/3
x = 35.
Hence, the whole of the number is 35.
To learn more about unitary method, here:-
https://brainly.com/question/22056199
#SPJ1
g(x) =19.60+1.74x. what is the value of g(x)=28.3. the answers is 6,5,0,8
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Answer:
5
Explanation:
Given the function
g(x) =19.60+1.74x
We are to find the value of x if g(x) = 28.3
Subctitute;
28.3 = 19.60+1.74x
Subtract 19.60 from both sides
28.3 - 19.60 = 19.60 + 1.74x - 19.60
Rearrange
28.3 - 19.60 = 19.60 - 19.60 + 1.74x
8.7 = 1.74x
x = 8.7/1.74
x = 5
Hence the value of x is 5
please explain to me how to get the answer as well as the answer.
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Solution
Step 1
The y-intercept is the point where the line crosses the y-axis.
Final answer
y-int = 2
z varies directly with x and inversely with y.When x = 6 and y = 2, z = 15What is the value of z when x = 4 and y = 9?
Answers
It is given that z varies directly with x and inversely with y.
[tex]z=\frac{kx}{y}[/tex]Where k is the constant of proportionality.
First, let us find the value of constant (k).
Substitute x = 6, y = 2, and z = 15
[tex]\begin{gathered} 15=\frac{k\cdot6}{2} \\ k\cdot6=2\cdot15 \\ k\cdot6=30 \\ k=\frac{30}{6} \\ k=5 \end{gathered}[/tex]So, the value of k is 5
[tex]z=\frac{5\cdot x}{y}[/tex]Finally, let us find the value of z when x = 4 and y = 9
[tex]\begin{gathered} z=\frac{5\cdot4}{9} \\ z=\frac{20}{9} \end{gathered}[/tex]Therefore, the value of z is 20/9
A number squared subtracted from 3 times the number is equal to negative 70. Set up and solve a quadratic equation, then solve by factoring.
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We will have the following:
From the problem we construct the expression:
[tex]3x-x^2=-70[/tex]Now, we solve for x:
[tex]\begin{gathered} \Rightarrow-x^2+3x+70=0\Rightarrow-(x^2-3x-70)=0 \\ \\ \Rightarrow-(x+7)(x-10)=0 \\ \\ x=-7 \\ x=10 \end{gathered}[/tex]The number can be either -7 or 10.
1-37. On many graphing calculators, equations must be entered in y=form. Rewrite eachequation in y= form. Then use the Desmos tool to confirm that your equations are correct.1-37 HW e Tool (Desmos). Homework HelpIa. x=3y+6b. x=5y-10C. x=y2d. x=2y2-4e. x=(y-5)2
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Answer:
a) y = (x-6)/3
b) y = (x + 10)/5
c)
[tex]y=\sqrt{x}[/tex]d)
[tex]y=\sqrt{\frac{x+4}{2}}[/tex]e)
[tex]y=\sqrt{x}+5[/tex]Step-by-step explanation:
In each case, first we place everything with y on the left side and everything without y on the right side. Then we apply the operation needed to isolate y.
a. x=3y+6
3y + 6 = x
3y = x - 6
y = (x-6)/3
b. x=5y-10
5y - 10 = x
5y = x + 10
y = (x + 10)/5
C. x=y2
y² = x
To simplify the square, we apply the square root to both sides. So
[tex]\sqrt{y^2}=\sqrt{x}[/tex][tex]y=\sqrt{x}[/tex]d. x=2y2-4
2y2-4 = x
2y² = x + 4
y² = (x+4)/2
Again, to simplify the square, we apply the root to both sides.
[tex]\sqrt{y^2}=\sqrt{\frac{x+4}{2}}[/tex][tex]y=\sqrt{\frac{x+4}{2}}[/tex]e. x=(y-5)2
(y-5)² = x
[tex]\sqrt{(y-5)^2}=\sqrt{x}[/tex][tex]y-5=\sqrt{x}[/tex][tex]y=\sqrt{x}+5[/tex]
I need help solving this math problem Find the equation of the line in its form y = mx + b
Answers
ANSWER:
[tex]y=2[/tex]STEP-BY-STEP EXPLANATION:
The equation must be in its slope-intercept form, which is as follows:
[tex]\begin{gathered} y=mx+b \\ \text{where m is the slope and b is the y-intercept} \end{gathered}[/tex]We calculate the slope as follows:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \text{ Replacing the points:} \\ m=\frac{2-2}{7-(-1)}=\frac{0}{7+1}=\frac{0}{8}=0 \end{gathered}[/tex]Now, we calculate the value of b, like this:
[tex]\begin{gathered} 2=0\cdot7+b \\ b=2 \end{gathered}[/tex]Therefore, the equation is the following:
[tex]\begin{gathered} y=0x+2 \\ y=2 \end{gathered}[/tex]write the equation of a line with the slope, -1/4 which passes through the point (-4,1).Write the answer In slope-intercept form.
Answers
Given:
The slope is, m = - 1/4.
The points are, (x, y) = (-4, 1)
The general slope intercept form is given by,
[tex]y=mx+b[/tex]Here, b is the y intercept. b can be calculated by substituting the values of x and y in the slope intercept form,
[tex]\begin{gathered} 1=-\frac{1}{4}\times-4+b \\ 1=1+b \\ b=0 \end{gathered}[/tex]Thus, the equation is,
[tex]y=-\frac{1}{4}x[/tex]The playing surfaces of two foosball tables are similar. The ratio of the corresponding sidelengths is 10:7. If the perimeter of the smaller is 42, what is the perimeter of the larger table?
Answers
Given:
Ratio of corresponding sides = 10 : 7
Perimeter of smaller table = 42
Total ratio = 10 + 7 = 17
Let's find the perimeter of the larger table.
Given that both tables are similar, it means the corresponding sides are proportional.
To find the ratio of the larger table, let's first find the total perimeter of the both tables:
[tex]\frac{\text{smaller ratio}}{total\text{ ratio}}\times T=perimeter\text{ of smaller table}[/tex]Where T represents the total ratio.
Thus, we have:
[tex]\begin{gathered} \frac{7}{17}\times T=42 \\ \\ \text{Multiply both sides by 17:} \\ \frac{7}{17}\times17\times T=42\times17 \\ \\ 7T=714 \end{gathered}[/tex]Divide both sides by 7:
[tex]\begin{gathered} \frac{7T}{7}=\frac{714}{7} \\ \\ T=102 \end{gathered}[/tex]The total perimeter is 102.
To find the permeter of the larger table, we have:
Perimeter of larger table = Total perimeter - perimeter of smaller table.
Perimeter of larger table = 102 - 42
Perimeter of larger table = 60
Therefore, the perimeter of the larger table is 60.
ANSWER:
60
Tom needs to rent tables for his family reunion. There will be 105 people attending. Each table seats 8 people. how many tables does Tom need to rent?
Answers
Tom needs to rent 14 tables
Explanation:Number of people attending the reunion = 105
Number of people on a single table = 8
Number of tables that Tom needs to rent =
(Number of people attending the reunion)/(Number of people on a table)
Number of tables that Tom needs to rent = 105/8
Number of tables that Tom needs to rent = 13.125
Since the number of tables has to be a whole number. If he rents 13 tables, it will not be eniugh for the people attending the reunion. Therefore, Tom needs to rent 14 tables