Answer:
− (8b − x) (5b + x)
Step-by-step explanation:
Find the surface area and lateral area of the following three prisms. Be sure to show all of your work.
Problem 1
L = 10 = length
W = 5 = width
H = 4 = height
SA = surface area of a rectangular prism, aka block or box
SA = 2*(LW+LH+WH)
SA = 2*(10*5+10*4+5*4)
SA = 220
--------------------
LA = lateral area, aka wall area
LA = (perimeter of the base)*(height)
LA = (2L+2W)*H
LA = (2*10+2*5)*4
LA = 120
or
LA = SA - (floor area) - (ceiling area)
LA = SA - 2*(area of the floor)
LA = 220 - 2*(LW)
LA = 220 - 2*(10*5)
LA = 220 - 100
LA = 120
--------------------
Answers:
Surface Area = 220 square feet
Lateral Area = 120 square feet
==========================================================
Problem 2
Imagine rotating the object so that the triangular face is resting on the flat ground. This means the triangular faces are the floor and ceiling. The walls of any prism are always rectangles.
Focus on the right triangle with leg b = 4 and hypotenuse c = 5.
Use the pythagorean theorem to find that a = 3 is the missing leg length.
The triangle has base = 4 and height = 3, so its area is base*height/2 = 4*3/2 = 6 square inches. This is the area of the floor and ceiling each.
--------------------
This is the summary so far
base or floor area = 6 square inchesdepth of the prism = 8 inches(a,b,c) = (3,4,5) are the sides of the right triangleThose values are then plugged into the formulas below.
SA = surface area of a triangular prism
SA = 2*(base area) + depth*(a+b+c)
SA = 2*(6) + 8*(3+4+5)
SA = 108
LA = lateral area
LA = depth*(a+b+c)
LA = 8*(3+4+5)
LA = 96
or
LA = SA - 2*(floor area)
LA = 108 - 2*(6)
LA = 96
Note that a+b+c = perimeter of the triangular base.
--------------------
Answers:
Surface Area = 108 square inches
Lateral Area = 96 square inches
==========================================================
Problem 3
Imagine rotating the figure so that the octagon is resting on the flat ground.
Refer to the screenshot below to see the steps on computing the area of the regular octagon, aka the floor area.
The floor area is approximately 120.710678 square cm. The same goes with the ceiling because the floor and ceiling are congruent regular octagons that are parallel.
Each rectangular wall has an area of 5*22 = 110 square cm. Eight identical walls give a total lateral area of 8*110 = 880 square cm.
Add the floor and ceiling area to the wall area to get the total surface area
floor + ceiling + walls = 120.710678 + 120.710678 + 880 = 1121.421356
--------------------
Answers:
Surface Area = 1121.421356 square cm (approximate)
Lateral Area = 880 square cm
You must really like math to want to answer this ngl
Answer:
a) 2/10
b) 3/20
c) option 2
Step-by-step explanation:
{20, 25, 19, 18, 21, 24, 15, 25} What is the mean of the data set? Make sure to show ALL of your work
Answer:
20.875
Step-by-step explanation:
Mean is to add up the scores then divide by the number so 20 + 25 + 19 + 18 + 21 + 24 + 15 + 25 which is 167 then divide by 8 which is 20.875
Find the volume of the cylinder.
Answer:
120 i am sorry if i am wrong
Step-by-step explanation:
the volume of the cylinder is 120 cm
I have tried my hardest on studying this
question i am sorry if its wrong
Please help me....Use the Pythagorean identity
Using the Pythagorean identity, the value of the cosine ratio is [tex]\cos(\theta_1) = \frac{84}{85}[/tex]
How to determine the cosine ratio?The given parameter is:
[tex]\sin(\theta_1) = -\frac{13}{85}[/tex]
By the Pythagorean identity, we have:
[tex]\sin^2(\theta_1) + \cos^2(\theta_1) = 1[/tex]
So, we have:
[tex](-\frac{13}{85})^2 + \cos^2(\theta_1) = 1[/tex]
This gives
[tex]\cos^2(\theta_1) = 1 - (-\frac{13}{85})^2[/tex]
Evaluate
[tex]\cos^2(\theta_1) = 1 - \frac{169}{7225}[/tex]
Take LCM
[tex]\cos^2(\theta_1) = \frac{7225 -169}{7225}[/tex]
This gives
[tex]\cos^2(\theta_1) = \frac{7056}{7225}[/tex]
Take the square root of both sides
[tex]\cos(\theta_1) = \pm \frac{84}{85}[/tex]
Cosine is positive in the fourth quadrant.
So, we have:
[tex]\cos(\theta_1) = \frac{84}{85}[/tex]
Hence, the cosine value is [tex]\cos(\theta_1) = \frac{84}{85}[/tex]
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How many millimeters are in 27 centimeters? (2 points)
a
27 mm
Ob
270 mm
Ос
2,700 mm
Od
27,000 mm
What is -8.2 ÷ 4.32 = ?
Answer:
-8.2 / 4.32 is an infinite nummber but an aproximate is -1.9 or -2
Step-by-step explanation:
Coffee Tea
17
New York 43
Chicago 21 39
Did a larger percentage of people in New York or Chicago prefer coffee?
Answer:
A larger percentage of people in New York prefer coffee
Which expression represents the volume, in cubic units, of empty space in the cube? four-thirdsπ(4.53) – (4.5)3 (9)3 – four-thirdsπ(4.52) four-thirdsπ(4.53) – (9)3 (9)3 – four-thirdsπ(4.53)
The expression that represents the volume of the empty space is 9³ - 4 / 3 π(4.5)³ cubic units.
How to find the expression for volumes?
The volume of the empty space can be represented as follows
volume of the empty space = volume of cube - volume of sphere
Therefore,
volume of sphere = 4 / 3 πr³
where
r = radiusVolume of cube = L³
where
L = side lengthTherefore,
volume of cube = 9³
volume of sphere = 4 / 3 π(4.5)³
Hence,
volume of the empty space = 9³ - 4 / 3 π(4.5)³
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Answer:
D
Step-by-step explanation:
other dude typed too much lam
The sum of two integers is 9 and their product is 18. What are the integers?
Answer:
The integers are 2.
Step-by-step explanation:
Answer: 3 and 6
Step-by-step explanation:
3+6=9
3x6=18
help asap pls pls pls
Answer:
the answer is 13, all you had to do was substitute 5 for N, so all you had to do was 3 + 2(5) which is 13
Janette measures the heights in inches of some of the flowers in her garden to see which ones are growing more. the heights are listed below. which line plot represents the data correctly? 7 1 2 7 7 1 2 6 3 4 7 1 4 7 1 4 7 1 4 7 6 1 2 7 3 4 7 3 4 6 3 4 8 1 4 7 7 1 2 7 7 1 4 7 7 1 2 7 1 2 a. a line plot named b. a line plot named c. a line plot named d. a line plot named
The line plot that represents the height of the flowers in the garden is the line plot named a.
What is a line plot?A line plot is a diagram that is used to represent data. The line plot is made up of dots that are used to represents the frequency with which the number appears.
Please find attached the line plot that represents the answer. To learn more about line plots, please check: https://brainly.com/question/16321364
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Jasmin rakes leaves at two different houses. it takes her 2 1/3 hours to rake leaves at the first house. it takes her 1/2 of that time to rake leaves at the second house. how long does it take jasmin to rake leaves at the second house.
The Jasmine take 1 whole 1/6 seconds to rake leaves at the second house.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
We have:
Jasmin rakes leaves at two different houses. it takes her 2 1/3 hours to rake leaves at the first house. it takes her 1/2 of that time to rake leaves at the second house.
From the problem:
[tex]= \rm 2\dfrac{1}{3}\times \dfrac{1}{2}[/tex]
[tex]= \rm \dfrac{7}{3}\times \dfrac{1}{2}[/tex]
[tex]= \rm \dfrac{7}{6}[/tex]
[tex]= \rm 1\dfrac{1}{6}[/tex]
Thus, the Jasmine take 1 whole 1/6 seconds to rake leaves at the second house.
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A bus stops at a bus stop every 45 minutes. Once a person gets to the bus stio, what is the probability they will wait for no more than 20 minutes?
Answer:
≈ [tex]44.4%[/tex][tex]%[/tex]%
Step-by-step explanation:
The person will wait for no more than 20 minutes if they arrive when the bus is going to stop in 20 minutes, which means that they must arrive 25 minutes after the previous bus stops. So the probability that the person will not wait for more than 20 minutes will be [tex]\frac{20}{45}[/tex] which is about 44.4%.
substitution. y = x − 35 y=-4x
Answer:
(7, - 28 )
Step-by-step explanation:
y = x - 35 → (1)
y = - 4x → (2)
substitute y = x - 35 into (2)
x - 35 = - 4x ( add 4x to both sides )\
5x - 35 = 0 ( add 35 to both sides )
5x = 35 ( divide both sides by 5 )
x = 7
substitute x = 7 into either of the 2 equations
substituting into (1)
y = 7 - 35 = - 28
solution is (7, - 28 )
What is the area of a triangle with a base of 9 units and a height of 7 units?
Answer:
31.5 units.
Step-by-step explanation:
The area is the height times the base divided by 2.
9x7 = 63
63/2 = 31.5
Which is the graph of the circle (x−2)2+(y−1)2=25?
Answer: y=-x+31/2
Step-by-step explanation:
2x-4+2y-2=25
2y=-2x+31
y=-x+31/2
5. mr. and mrs. pinkerton have four boys. every time people notice this they comments to
the odds of this happening. the pinkertons decide to set up a simulation with 10 trids to
determine the probability,
The simulation that can best represent the chances of the Pinkertons having a boy or a girl is Flipping a coin.
What best shows the chances of having either a boy or girl?The question asks for the simulation that can represent the likelihood of having a boy or a girl.
Because there are two outcomes, they each have a 50% probability.
A good simulation to show this would therefore be flipping a coin because this has two outcomes as well which are heads or tails.
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The circumference of a circle is approximately 43.96 centimeters. what is the radius of the circle? use 3.14 for radius.
Answer:
7 cm
Step-by-step explanation:
The circumference of a circle is given in terms of its radius by the formula ...
C = 2πr . . . . where r represents the radius
__
Using the given values in the formula, we can find the radius to be ...
C/(2π) = r
43.96/(2×3.14) = r = 7 . . . . cm
The radius of the circle is 7 cm.
a girl exercises every day for half an hour how many minutes in total for over 5 days
Answer:
150 minutes
Step-by-step explanation:
30 × 5 = 150 minutes
Sofia works in a clothing store and earns $40 per day. She earns an extra $5 for each outfit she sells. If Sophia wants to earn at least $70 per day, which inequality shows the minimum number of outfits, n, that she should sell
Answer:
70= 5n+40
Step-by-step explanation:
(n=6 if you need it)
Hope this helps! ;-)
In order to find this answer, you will need to be able to make an inequality.
Step 1: Sophia makes $40 so start with that. 40
Step 2: Sophia also makes $5 per every outfit that she sells, so add that plus your variable (n). 40+5n
Step 3: Determine if Sophia wants to make more, equal to or more, less, or less than or equal to than what she wants to make per day. 40+5n *draw a greater than or equal to sign.
Step 4: Sophia wants to make more than or equal to what she makes per day. You will need to find what she wants to make more than. In this she wants to make more than or equal to $70.
Equation: 40+5n *greater than or equal to sign* $70
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Glass A contains 100 ml of water and glass B contains 100 ml of wine. A 10 ml spoonful of wine is taken from Glass B and mixed thoroughly with the water in Glass A. A 10 ml spoonful of the mixture from A is returned to B. Is there now more wine in the water or more water in the wine
Answer:
More wine in the water
Step-by-step explanation:
Hope this helped
Fine the length of the third side. If necessary, write in simplest radical form
Answer:
7.2
Step-by-step explanation:
(6)^2 + (4)^2
36 + 16
52
square root of 52 = 7.2
Austin uses a mold to make cone-shaped cupcakes. The diameter of the mold is 12 inches, and
the height of the mold is 10 inches. If one cubic inch is about 0.55 ounce, how many ounces will
2 cupcakes weigh? Use 3.14 for T. Round to the nearest tenth of an ounce. Only write the
number
Answer:
25.9
Step-by-step explanation:
So calculate volume of the mold, which is a cone: (pi) r2 (h/3) where r is radius and h is height
So diameter/2 = r which is 1.5 in
h = 2 in
V = (3.14)(1.52)(2/3) = 4.71 in3
If 1 in3 = 0.55 oz, and 1 mold = 4.71 in3, then one mold = 2.59 oz
2.59 oz * 10 cupcakes = 25.9 oz total
Step-by-step explanation:
the volume of a cone is
pi×r² × h/3
the radius is always half of the diameter, so, it is here
12/2 = 6 in.
h = 10 in.
so, we have here
pi×6²×10/3 = 3.14 × 36 × 10/3 = 3.14×120 = 376.8 in³.
2 cupcakes have then
376.8 × 2 = 753.6 in³
1 in³ = 0.55 ounces
so, the weight of 2 such cupcakes is
0.55 × 753.6 = 414.48 ounces ≈ 414.5 ounces
Solve for X
13=270 (0.5)^x/7
Answer:
Step-by-step explanation:
helpppppopppppoppppppp
A regular octagon has a radius of 6 ft and a side length of 4.6 ft.
Answer: the correct answer is.....101 ft sq.
Step-by-step explanation:
what is anwer ok ok ok
Answer:
3: equally likely
4: likely
Step-by-step explanation:
Question 3:
the spinner has 1, 2, 3, 4, 5, 6
2, 4, 6 are all even number which is 3 / 6 = 1 / 2
so half a chance can be odd or half even possibility of landing
Question 4:
- 13 yellow
- 4 green
- 3 blue
total marbles: 13 + 4 + 3 = 20
yellow / total = 13 / 20
which is more than half of the marbles are yellow
the answer equally
Step-by-step explanation:
equally
5 / 949 If they decide to drive 949 mi to Denver instead, how many miles will they drive each day?
the formula for converting degrees fahrenheit (f) to degrees kelvin (k) is:
solve for f, in terms of k
k=5/9(f+459.67)
Answer:
See below
Step-by-step explanation:
K = 5/9 (F + 459.67) Multiply both sides by 9/5
9/5 K = F + 459.67 Subtract 459.67 from both sides
9/5 K - 459.67 = F