Answer:
The volume of pyramid B is 81 cubic units
Step-by-step explanation:
Given
Pyramid A
[tex]s = 4[/tex] -- base sides
[tex]V = 36[/tex] -- Volume
Pyramid B
[tex]s = 6[/tex] --- base sides
Required
Determine the volume of pyramid B [Missing from the question]
From the question, we understand that both pyramids are equilateral triangular pyramids.
The volume is calculated as:
[tex]V = \frac{1}{3} * B * h[/tex]
Where B represents the area of the base equilateral triangle, and it is calculated as:
[tex]B = \frac{1}{2} * s^2 * sin(60)[/tex]
Where s represents the side lengths
First, we calculate the height of pyramid A
For Pyramid A, the base area is:
[tex]B = \frac{1}{2} * s^2 * sin(60)[/tex]
[tex]B = \frac{1}{2} * 4^2 * \frac{\sqrt 3}{2}[/tex]
[tex]B = \frac{1}{2} * 16 * \frac{\sqrt 3}{2}[/tex]
[tex]B = 4\sqrt 3[/tex]
The height is calculated from:
[tex]V = \frac{1}{3} * B * h[/tex]
This gives:
[tex]36 = \frac{1}{3} * 4\sqrt 3 * h[/tex]
Make h the subject
[tex]h = \frac{3 * 36}{4\sqrt 3}[/tex]
[tex]h = \frac{3 * 9}{\sqrt 3}[/tex]
[tex]h = \frac{27}{\sqrt 3}[/tex]
To calculate the volume of pyramid B, we make use of:
[tex]V = \frac{1}{3} * B * h[/tex]
Since the heights of both pyramids are the same, we can make use of:
[tex]h = \frac{27}{\sqrt 3}[/tex]
The base area B, is then calculated as:
[tex]B = \frac{1}{2} * s^2 * sin(60)[/tex]
Where
[tex]s = 6[/tex]
So:
[tex]B = \frac{1}{2} * 6^2 * sin(60)[/tex]
[tex]B = \frac{1}{2} * 36 * \frac{\sqrt 3}{2}[/tex]
[tex]B = 9\sqrt 3[/tex]
So:
[tex]V = \frac{1}{3} * B * h[/tex]
Where
[tex]B = 9\sqrt 3[/tex] and [tex]h = \frac{27}{\sqrt 3}[/tex]
[tex]V = \frac{1}{3} * 9\sqrt 3 * \frac{27}{\sqrt 3}[/tex]
[tex]V = \frac{1}{3} * 9 * 27[/tex]
[tex]V = 81[/tex]
Answer:
81
Step-by-step explanation:
2(3v - 8)
please help xxxxxxxxxxxxxxxxxxxxxxxxxx
Answer: 6 v − 16
Step-by-step explanation:
Can someone help me please?
Answer:
2. 216cm3
3. 748.75
Step-by-step explanation:
Cube v=Bh
To get Base area 9cm x 4cm=36cm2
36cm2 x 6cm=216cm3
what is 22% of 64.82
Answer:
14.2604
Step-by-step explanation:
this is because 22% as a decimal would be 0.22, and since this is out of 64.82, you have to multiply 0.22 by 68.82
\\
Hope this helps <33
Answer:
14.2604
Step-by-step explanation:
[tex]64.82*.22=14.2604[/tex]
What is the answer for, A metal bar 8.15 ounces 93% of the bar is sliver. How many ounces of silver are in the bar? ( round to the nearest thousandth)?
Answer:
7.580 ounces
Step-by-step explanation:
The question is asking how many ounces of silver are in the bar. We know that 93% of the bar is silver. The bar is 8.15 ounces. This means we need to find 93% of 8.15. Let's set up an equation.
93% of 8.15
93/100 • 8.15
0.93 • 8.15
= 7.5795
Round to the nearest thousandth.
7.580 ounces
Hope this helps!
A line with a slope of 5 passes through the point (1,9). What is its equation in slope-intercept form? Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
y = 5x + 4
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = 5, then
y = 5x + c ← is the partial equation
To find c substitute (1, 9) into the partial equation
9 = 5 + c ⇒ c = 9 - 5 = 4
y = 5x + 4 ← equation of line
what is the number of distinguishable permutations of the letters in the word, POTATO
Answer:
720
Step-by-step explanation:
Potato has 6 letters
6!/2!×2!
6×5×4×3×2/2×2
If a point is randomly selected from the area under the curve, what is the probability that it will be in the black region?
A) 0.5
B) 1.0
C) 1.5
D) 2.0
Answer:
A) 0.5
Step-by-step explanation:
The probability between 0 and 3 is 0.49865
The probability of 0 or less (≤ 0) is 0.50000
Took the test on USA Test prep
A storage shed with a flat roof is 12 feet long by 9 feet wide by 4 1/2 feet tall.
How many cubic feet of storage space does the shed enclose?
Answer:
To get the volume of the shed in yards, multiply 4*3*2.5=30
since one cubic yard is equal to 27 cubic feets, multiply 27 with 30 to get the volume in cubic feets 27*30=810
Step-by-step explanation:
find the area of the composite shape
Answer:
96 m²
Step-by-step explanation:
To calculate the area of a composite shape, you must divide the shape into rectangles, triangles, or other shapes.
A = l × w
L = length
W = width
Find the area and then add the areas back together.
12m × 8m
= 96 m²
The area of the composite shape is 96 m²
Given that f(x) = x2 - 6x – 16 and g(x) = x + 2, find (f=g)(x) and express
the result in standard form.
Answer:
Step-by-step explanation:
To find the x-intercept, substitute in
0
for
y
and solve for
x
. To find the y-intercept, substitute in
0
for
x
and solve for
y
.
x-intercept(s):
(
2
,
0
)
,
(
−
8
,
0
)
y-intercept(s):
(
0
,
−
16
What is the correct ordering on a number line from left to right of these four numbers: - 2/3, 5/8, -3/5, -1/2
Answer:
From least to greatest: -1/2,-2/3,-3/5,5/8
Step-by-step explanation:
-1/2 is the smallest
-2/3 is the second smallest
-3/5 is the second largest
5/8 is the largest
i messed up ignore thisisisids
Dan bought 35 pieces of candy. He gave 4 pieces to each of his friends. He only has 3 pieces left. Which equation, when solved for
X, gives the number of friends?
Answer:
35 - 4x = 3
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
35−4x=3
35+−4x=3
−4x+35=3
Step 2: Subtract 35 from both sides.
−4x+35−35=3−35
−4x=−32
Step 3: Divide both sides by -4.
-4x/−4 = −32/ −4
x=8
Answer:
8 friends
Step-by-step explanation:
4 doesn't go evenly to 9 ppl so it would be 8 friends and 3 extra pieces
Lucy's dog lost 6 pound How much weight does her dog need to gain in order to a net change of 0 pounds? _pounds?
Answer:
I think 6 pound. Beacuse 6-6=0
Look at this diagram:
Answer:
∠ GHE = 40°
Step-by-step explanation:
∠ IHE and ∠ GHE are adjacent angles and are supplementary, then
∠ GHE + ∠ IHE = 180°
∠ GHE + 140° = 180° ( subtract 140° from both sides )
∠ GHE = 40°
Help me plz !!!!! ):$$:):!:!!::
Answer:
9x - 13 = y
Step-by-step explanation:
big brain
Factor out the Greatest Common Factor (GCF): 36y - 16 ?
Answer: 4(9y-4)
Step-by-step explanation:
36y - 16
4 x 9 is 36
4(9 is just like 36y.
Find the output y when the input x is -5
y=?
Answer: y=7
Step-by-step explanation: looking at the graph when x is -5 y= 7
What is the sum of 5.6 + 2.89?
Answer:
The sum is 8.49
Step-by-step explanation:
All you have to do is add the tenths place together but keep the hundredths the same. Hope this helps.
PLS HELP
A jewelry company purchases a necklace for $24. If they mark it up 36% to sell it at their store, what is the selling price of the necklace? (If necessary, round to the hundredths)
Answer:
I believe the answer would be 32.64
Step-by-step explanation:
$24 x 36% = 8.64
8.64 + 24 = $32.64
The ratio of dogs to cats in the neighborhood was 3 to 7. If a total of 210 dogs and cats were in the neighborhood, how many cats were there? Complete the statement by providing the correct response in number form.
Answer:
147 cats
Step-by-step explanation
There are 3 dogs/ 7 cats
3x + 7x = 210
10x = 210
210 ÷ 10 = 21
Therefore,
x = 21.
dogs would be 3x (3 x 21) = 63
cats would be 7x (7 x 21) = 147
Can someone help?????
Answer:
i can Lol if you will help me after i help you
Step-by-step explanation:
put -6.5 in between -6 and -7. put -8.5 between -8 and -9. -6.5 is > than -8.5. hope this helped and i hope im right.
3 1/7 + 4 3/14 = ?
plz help me
please i really need help. dont spam i just really need help
Answer:
440 square miles would be the answer :)
Step-by-step explanation:
NEED ASAP Which line is parallel to the line y=4x-2?
Answer:
y = 4x + 1
Step-by-step explanation:
Given the equation y = 4x - 2, we need to find the equation parallel to this line. Note that for two equations to be parallel to each other, the must have the same slope
Standard form of an equation is y = mx + b
Compare;
mx = 4x
m = 4
Since the slope of the given equation is 4, the required equation must also have a slope of 4
Since we are not given an option, we can assume any equation with a slope of 4
y = 4x + 1 will be parallel to the given equation since they both have the same slope
Note that the equation can be different so far they have the slope of 4
Sophia babysits for $15 per hour. She mows lawns for $12 per hour.
This weekend, Sophia babysits 4 more hours than she mows lawns.
She earns a total of $195. Write a system of equations that can be used
to find how many hours she worked at each job.
Let b be hours babysitting. Let m be hours mowing.
b=m+ 4
hours worked
15b + 12m = 195 total money earned (please help me with both parts)
Answer:
0
Step-by-step explanation:
Esther uses 9.4 pints of blue paint and white paint to paint her bedroom walls. 3 5 of this amount is blue paint, and the rest is white paint. How many pints of white paint did she use to paint her bedroom walls?
Answer:
3.76
Step-by-step explanation:
Esther uses 9.4 pints of blur paint and white pant for her bedroom
3/5 of this amount is blue paint while the rest is white paint
3/5
= 0.6×100
= 60
Therefore the amount of white paint can be calculated as follows
40/100 × 9.4
= 0.4×9.4
= 3.76
PLEASE HELP ASAP!!
What is the value of x?
Enter your answer in the box.
Answer:
5
Step-by-step explanation:
[tex]x^{2} +12^{2} = 13^{2} \\ x^{2} =13^{2} -12^{2} \\ x^{2} =169-144\\ x^{2} =25\\ \sqrt{x^{2} } =\sqrt{25} \\ x=5[/tex]
Please please help this is algebra:(
please please help me
(the number in the photo is 20 and then the letter is x)
(also if you can pls go to my profile and answer the question underneath this one)
Answer:
20°
Step-by-step explanation:
for alternate angles
Answer:
angle x= 20°
I hope it's helps you
Maggie has exactly 20$ to buy decorations for the dance. Streamers cost 2$ per roll and balloons are 1.50$ per package. Which set of purchases is closest to her budget??
Answer:
675esa espuesatr
Step-by-step explanation:
