Question 1
Here is the base of a prism.
a. If the height of the prism is 5 cm, what is its surface area? What is its volume?
b. If the height of the prism is 10 cm, what is its surface area? What is its volume?
c. When the height doubled, what was the percent increase for the surface area? For the volume?
Answers
Answer:
a ) Surface Area ⇒ 222 cm^2, Volume ⇒ 180 cm^3
b ) Surface Area ⇒ 372 cm^2, Volume ⇒ 360 cm^3
c ) Surface Area Increase ⇒ ( About ) 67.56 %, Volume Increase ⇒ 100 %
Step-by-step explanation:
a ) Consider dividing the figure into parts, first solving for the area of the base, using the attachment below for guidance;
As you can see, in the picture I have made it so that the base is nested in a rectangle with dimensions 8 by 5. Calculating the area of this rectangle, subtracting the area of a square with dimensions 2 by 2 cm, we can derive the area of the base in a much quicker manner;
[tex]Area of Base - ( 8 cm * 5 cm ) - ( 2 cm* 2 cm ) = 40 square cm - 4 square cm = \\Solution; Base = 36 square cm[/tex]
Now let us imagine adding the another dimensions to this two dimensional base. That would make a 3 - d prism, with surface area equivalent to mini rectangles and squares with a common dimension being the length of the height; 5 cm
[tex]Area of 1 Square = 5 cm * 5 cm = 25 square cm,\\Area of 2 Square = 25 square cm,\\Area of 1 Rectangle = 3 cm * 5 cm = 15 square cm,\\Area of 2 Rectangle = 15 square cm,\\Area of 3 Rectangle = 2 cm * 5 cm = 10 square cm,\\Area of 4 Rectangle = 10 square cm,\\Area of 5 Rectangle = 10 square cm,\\Area of 6 Rectangle = 8 cm * 5 cm = 40 square cm\\Area of Base 2 = 36 square cm,\\\\Surface Area of Figure = 25 + 25 + 15 + 15 + 10 + 10 + 10 + 40 + 36 + 36 = 222 square cm\\Volume = 36 square cm * 5 cm = 180cubiccm[/tex]
b ) We have calculated the area of the base before, now let us solve for all the " mini shapes " given a new height of 10 cm;
[tex]Area of Rectangle 1 = 5 cm * 10 cm = 50 cm^2,\\Area of Rectangle 2 = 50 cm^2,\\Area of Rectangle 3 = 3 cm* 10 cm = 30 cm^2,\\Area of Rectangle 4 = 30 cm^2,\\Area of Rectangle 5 = 2 cm * 10 cm = 20 cm^2,\\Area of Rectangle 6 = 20 cm^2,\\Area of Rectangle 7 = 20 cm^2,\\Area of Rectangle 8 = 8 cm * 10 cm = 80 cm^2,\\\\Surface Area of Figure = 50 + 50 + 30 + 30 + 20 + 20 + 20 + 80 + 36 + 36 = 372 cm^2\\Volume of Figure = 36 cm^2 * 10 cm = 360 cubic cm[/tex]
c ) Solution; Increase of Surface Area ⇒ ( About ) 67.56 %, Increase of Volume ⇒ 100 %
Related Questions
Whats the greatest number of cross sections?
Answers
Ms. Weston bought a watermelon that weighed 32ounces. She also bought an orange that was 1/4 the weight of the watermelon.
How many total pounds of fruit did she buy?
A: 1/2
B: 2 1/2
C: 8
D:56
Answers
Answer:
B is the correct answer
Step-by-step explanation:
Dimensional Analysis
The bottom part of this block is a rectangular prism. The top part is a square pyramid. You want to cover the block entirely with paper. How much paper do you need?
Answers
Answer:
970.2
28x11x6.3
1,940.4/2
970.2
If someone can solve and show where it should be on the number line please do so
Answers
Answer:
The number line should have a filled in dot at -3 and should extend to the left where it is negative.
Step-by-step explanation:
If -3 is greater than or equal to c, then c has to be equal to -3 or smaller. So, the number line should include -3 with a filled in dot and should extend to the left of -3 where the more negative numbers are.
Answer:---> or o---> i think
Step-by-step explanation:
A model airplane has a scale of 2 in: 9 yards. If the wing span of the model airplane is 18 inches, how many yards is the actual wing span?
Answers
Answer:
81 yards
Step-by-step explanation:
Solve the system of equations.
x + 3y = −1
2x + 2y = 6
(−4, 1)
(2, −1)
(4, −1)
(5, −2)
Answers
Answer:
(5,-2)
Step-by-step explanation:
Multiplying the first equation by 2 we get
2x+6y=-2
Subtracting the second equation we get
4y=-8
y=-2
Plugging y as -2 into the equation we get x=5
Answer:
(5, -2)
Step-by-step explanation:
x + 3y = −1
2x + 2y = 6 ⇒ x+y=3
Subtract second equation from the first one:
x+3y=-1x+y=33y-y= -1 -32y= -4y= -2x= 3+2= 5Write an expression that gives the area of the shaded region in the figure.
Answers
Answer:
Area = 88 square units
Step-by-step explanation:
The length of the blue rectangle can be found by subtracting 15 and 4, which equals 11. The width of the blue rectangle can be found by subtracting 6 from 14, which equals 8.
area = length x width
area = 11 x 8
area = 88 square units
Read the following paragraph. How does sentence 4 develop the main idea of the paragraph?
Gertrude Belle Elion was born on Jan. 23, 1918, in New York City.
She graduated from Hunter College in New York City with a degree in biochemistry in 1937.
Unable to obtain a graduate research position because she was a woman, she took a series of jobs, including lab assistant, chemistry and physics teacher in New York City high schools, and research chemist.
During this time she also took classes at New York University, where she earned a master's degree in 1941.
Because she could not devote herself to full-time studies, Elion never received a doctorate.
This sentence tells readers where she went to school for her doctorate degree.
This sentence shows Elion's determination and commitment to learn.
This sentence shows that Elion had to try many schools to get accepted into one.
This sentence proves the idea that Elion had to learn biochemistry in unusual ways.
Answers
Answer:
This sentence shows Elion's determination and commitment to learn.
Step-by-step explanation:
During this time she also took classes at New York University, where she earned a master's degree in 1941.
The way in which sentence 4 assists in developing the key idea of the paragraph would be:
B). This sentence shows Elion's determination and commitment to learn.
The key idea that the given paragraph aims to convey is a brief biography of Belle Elion to the readers, especially, her early life.Sentence 4 in the given paragraph aims to advance this idea by displaying the strength, dedication, and determination that she put towards learning.This helps the readers understand her character sketch more clearly and effectively.Thus, option B is the correct answer.
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I need help with question 1, 2, 6, 7 and 8.
Answers
Answer:
Step-by-step explanation:
Q1) 15+15+15+15+15+15=90
Answer : 1 over 90 as a fraction
Q2) 2 over 2
Q6) 13 over 52
The segments shown below could form a triangle?
Answers
Answer:
Option B; False
Step-by-step explanation:
Consider a Triangle Inequality to prove that these segments could form a triangle;
[tex]| a - b | < c < a + b,\\| c - a | < b < a + c,\\| c - b | < a < b + c, Considering - a - segment AC ( 8 units ) - b - BC ( 7 units ), - c - BC ( 15 units )\\\\| 8 - 7 | < 15 < 8 + 7,\\1 < 15 < 15, Now 15 is not < 15, it is =, thus ;\\Solution ; False[/tex]
These segments could not form a triangle
HELP!!! 2(4x+3)=x+1 It's geometry!
Answers
Answer:
[tex]x=-\frac{5}{7}[/tex]
Step-by-step explanation:
[tex]2(4x+3)=x+1[/tex]
[tex]8x+6=x+1[/tex]
[tex]8x-x=1-6[/tex]
[tex]7x=-5[/tex]
[tex]x=\frac{-5}{7}[/tex]
Answer:
x = -5/7
Step-by-step explanation:
2(4x+3)=x+1
Distribute
8x +6 = x+1
Subtract x from each side
8x+6-x = x+1-x
7x+6 = 1
Subtract 6 from each side
7x+6-6 = 1-6
7x =-5
Divide each side by 7
7x/7 = -5/7
x = -5/7
Two waiters at a cafe each served 10 large fruit smoothies. The amount in each large smoothie is shown below. What is the mean amounts in Waiter A's Large Smoothies? Do not include units in your answer.
Answers
Answer:
answer is 5 my explanation is I took the quiz a.d bit but right
Somebody help ASAP please please please. I basically forgot all the steps to do this.
Answers
Answer:
m=50
Step-by-step explanation:
m=4a+2c
m= 4(10)+2(5)
m= 40+10
m=50
Factor 64 – x15. (4 – x3)(16 + 4x3 + x3) (4 – x3)(16 + 4x3 + x6) (4 – x5)(16 + 4x5 + x5) (4 – x5)(16 + 4x5 + x10)
Answers
Answer:
D :)
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
1) Find the length of point A(-3,1) and B(2,6). Leave your
answer in RADICAL FORM ONLY.
Answers
Answer: The length of point A(-3,1) and B(2,6) is [tex]5\sqrt{2}\text{ units}[/tex] .
Step-by-step explanation:
We know that the distance between the two points (a,b) and (c,d) is given by :-
[tex]d=\sqrt{(a-c)^2+(b-d)^2}[/tex]
Given points = A(-3,1) and B(2,6)
Therefore the distance between the points A(-3,1) and B(2,6) is given by :-
[tex]d=\sqrt{(-3-2)^2+(1-6)^2}\\\\\Rightarrow\ d=\sqrt{(-5)^2+(-5)^2}\\\\\Rightarrow\ d=\sqrt{25+25}\\\\\Rightarrow\ d=\sqrt{50}\\\\\Rightarrow\ d=\sqrt{25\times2}\\\\\Rightarrow\ d=\sqrt{5^2\times2}\\\\\Rightarrow\ d=5\sqrt{2}\text{ units}[/tex]
Hence, the length of point A(-3,1) and B(2,6) is [tex]5\sqrt{2}\text{ units}[/tex] .
BRAINLIEST ANSWER Twice the difference of a number and 4 is equal to three times the sum of the number and 4. Find the number.
Answers
Answer: -20
Step-by-step explanation:
We can set up an equations with the conditions we are given. Let's use x for the missing number.
2(x-4)=3(x+4)
2x-8=3x+12
-20=x
Answer:
see below
Step-by-step explanation:
2(x-4) =3(x+4)
sum is addition
difference is subtraction
2 is multiply by2
solve 2(x-4) =3(x+4) distribute on both sides
2x - 8 = 3x + 12 add 8 on both sides
2x = 3x + 20 subtract 3x on both sides
-x = 20 multiply by -1
x = -20
100pts: What is the slope of the following curve at x = n, for an arbitrarily chosen integer n?:
y = 3x^2 - 37x + 6
Answers
Answer:
6n -37
Step-by-step explanation:
The slope would be the derivative of the function
dy/dx = 6x - 37 evaluated at the point n
dy/dx = 6n -37
Answer:
6n - 37
Step-by-step explanation:
The derivative of the function f(x) gives the gradient (slope) of the tangent to the graph of y = f(x) at the point (x, y).
Given:
[tex]y=3x^2-37x+6[/tex]
Therefore, the gradient (slope) of the given curve at x is:
[tex]\implies \dfrac{dy}{dx}=2 \cdot 3x^{2-1}-37x^{1-1}+0[/tex]
[tex]\implies \dfrac{dy}{dx}=6x-37[/tex]
To find the slope, simply substitute x for n:
[tex]\implies 6n-37[/tex]
Which function has the greatest value? Select all that apply
Answers
The athlete drink 16 ounces of water every two hours starting at 7:30 AM and continuing for the next 14 hours. A) how many quarts did the athlete consume? B) how many pints of water did the athlete consume?
Answers
When the athlete drink 16 ounces of water every two hours for the next 14 hours,
(A) The athlete consumes 3.5 quartz of water.
(B) The athlete consumes 7 pints of water.
Conversions(1) Ounce to Pints16 ounces = 1 pint
(2) Quarts to Ounces1 quart = 32 ounces.
(A) Calculation for the water consumed by athlete in quarts:The total duration for which athlete consumes the water is 14 hours with a after every 2 hours.
The total number of times the water consumed by athlete is 14/2 = 7.
Covert the 16 ounces of water in quarts
= 16/ 32
=1/2
The total quantity of water consumed in quarts is
= 7×(1/2)
= 3.5 quarts
Thus, the amount of water consumed by athlete in entire 14 hours is 3.5 quarts.
(B) Calculation for the water consumed by athlete in pints:The total duration for which athlete consumes the water is 14 hours with a after every 2 hours.
The total number of times the water consumed by athlete is 14/2 = 7.
Convert 16 ounce of water into pint
= 16/16
= 1
The total quantity of water consumed in pints is
= 7×1
= 7
Thus, the amount of water consumed by athlete in entire 14 hours is 7 pints.
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Complete the statement: 0.6L =______mL.
A. 600
B. 0.06
Answers
Answer: Complete the statement: 0.6L =______mL.
A. 600
plz help ill mark u brainliest do em all
Answers
#2 : 238 inches ^2
Answers:
1. 90in^2 2. 238cm^2
Step-by-step explanation:
For the first one:
6•3=18
6•3=18
3•3=9
3•3=9
6•3=18
6•3=18
Now we add them all up:
18+18+9+9+18+18=90in^2
For the second one:
7•5=35
7•5=35
7•7=49
7•7=49
7•5=35
7•5=35
Now we add them all up:
35+35+49+49+35+35=238cm^2
192 € down by a quarter?
Answers
Answer:
144 €
Step-by-step explanation:
If you begin with 192 € and these funds decline (go down) by a quarter, you'll end up with
(1.00 - 0.25)(192 €) = 144 €
1_____=1.6_____ What
Answers
Answer:
1 mile is 1.6 km
Step-by-step explanation:
I don't know how to explain
ANSWERR ASAPP
the directions on a lawn mower manual call for a mixture of oil and gasoline that is 60% oil. the tank holds 12 gallons. how many gallons will be oil?
A. 7.2 gallons
b. 5.8 gallons
c. 6.8 gallons
d. 5 gallons
Answers
In the diagram below, DE is parallel to XY. What is the value of x?
.
X
105
A. 75
B. 125
C. 105
D. 95
Answers
Answer:
105 degrees
Step-by-step explanation:
Corresponding angles
Answer:
x = 105⁰( corresponding angles)
Isabel invested $200 in a fund for 6 years and was paid simple interest. The total interest that she received on the investment was $48. As a percentage, what was the annual interest rate of her investment.
Answers
Can someone check my answers?
The amount of money in Alexander’s account is, = 4000 − 70, where is the amount in dollars and is the time in weeks.
a) Which variable is independent and which is dependent?
Answer: Dependent is -70x and independent is 4000
b) In which week will there be $1701 in the account?
Answer:
y=4000-70(x)
1701=4000-70(x)
-70x=1701-4000
-70x= -2299
x=-2299/-70
x=2299/70
x=32.843
x=33
c) How much will the amount in Alexander’s account change if the time increases by 15 weeks?
Answer:
y=4000-70(x)
y=4000-70(15)
y=2950
Answers
Answer:
yes you are correct
Step-by-step explanation:
The answers are a) y is the dependent variable, x is the independent value. b) 33 weeks and c) $2950
What are dependent and independent variables?The independent variable is the cause. Its value is independent of other variables in your study. The dependent variable is the effect. Its value depends on changes in the independent variable.
Given that, The amount of money in Alexander’s account is, y = 4000 − 70x, where y is the amount in dollars and x is the time in weeks.
a) Here, y is the dependent variable as it depends on the value of x, and x is the independent value.
b) We have, total amount = $1701
Therefore, put y = $1701
$1701 = 4000 − 70x
70x = 2999
x = 32.84 ≈ 33 weeks
c) In 15 weeks the amount will be =
y = 4000 - 70(15)
= $2950
Hence, the answers are a) y is the dependent variable, x is the independent value. b) 33 weeks and c) $2950
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(SAT Prep) In the figure, what is the ratio of the area of square KLMN to the area of △LOK?
Answers
Answer:
D. 2:1
Step-by-step explanation:
Imagine a line that is parallel to the top of the square that passes thru point O
that would make two more triangles. The two in the top would be equal and the two in the bottom would be equal.
Therefore, the area of square KLMN is two times the area of triangle LOK
Answer:
D. 2:1
Step-by-step explanation:
Area of square KLMN = LM*LKArea of triangle LOK= 1/2*LM*LKratio of areas:
LM*LK : 1/2 LM*LK= 2:1Answer: 2:1 option D
Zack needs $299.99 to buy the new bike he wants. He has saved $150 so far toward the new bike. From this week on, he will save $12.50 per week toward the new bike. Ten weeks from now, how much more money will he still need to save to buy the bike?
$24.99
$29.99
$127.49
$137.49
Answers
Answer:
The answer is $24.99
The solution is Option A.
The equation of line is y = 12.5x + 150 , where x is the number of weeks
The amount Zack needs after 10 weeks to buy the bike is $ 24.99
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
The price of the bike Zack needs to buy = $ 299.99
The initial amount with Zack = $ 150
The amount Zack saves in a week = $ 12.50
The number of weeks = x
The amount Zack saves in x weeks = 12.5x
So , the total amount with Zack after x week is given by the equation ,
Total amount with Zack after x week y = amount Zack saves in x weeks + initial amount with Zack
Substituting the values in the equation , we get
Total amount with Zack after x week y = 12.5x + 150
Now , after 10 weeks , the amount with Zack is
Substitute the value of x as 10 in the equation , we get
y = 12.5x + 150
y = 12.5 ( 10 ) + 150
y = 125 + 150
y = $ 275
Now , the amount left to buy the bike = price of the bike Zack needs to buy - amount with Zack after 10 weeks
Substituting the values in the equation , we get
Amount left to buy the bike A = $ 299.99 - $ 275
Amount left to buy the bike A = $ 24.99
Therefore , the value of A is $ 24.99
Hence , the amount Zack needs is $ 24.99
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Josh paid for four books with three $20 bills he received $12 in change each book was the same price how much did each book cost
Answers
Three $20 bills is a total of $60
$60 - $12 = $48
He spent a total of $48 on the books
Divide the total spent by the number of books:
48 / 3 = 16
Each book cost $16
Answer:$12 per book
Step-by-step explanation: $20 x 3= $60
If you have $12 change you minus that from the $60
Now that is $48 for 4 books.
To work out one book you do $48/4 which is $12 per book.