Pyramid A has a triangular base where each side measures 4 units and a volume of 36 cubic units. Pyramid B has the same height, but each side of its base is 6 units long.
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:
ose baked 36 cookies. He wants to share them equally among 16 people. How many cookies will each person get?
Draw a line segment to connect the two whole numbers that the answer lies between.
Please help due in 5 min
Answer:
nobody can see the question(s)
Graham wants to determine which football team is the most popular at a game between the home team and the visiting team. Which of the following methods will give him the most accurate results?
a radioactive materal has a half- life of 60 months. How much of a 1000g sample would remain after 42 months?
Answer:
100
Step-by-step explanation:
100
A circle has a radius of 8. Find the area of a sector of this circle that is intercepted by central angle measuring pi over 7
Answer:
14.4 square units
Step-by-step explanation:
Keep in mind that the area here is a fraction of the area of a full circle of radius 8.
(area of sector) = (fraction)(pi)(8)^2
The fraction is the given central angle (pi over 7) divided by 2pi:
pi 1
--------- * ----------- = 1/14
7 2pi
Multiply the formula (fraction)(pi)(8)^2 found above by this fraction:
area of sector = (1/14)(pi)(8)^2 = 14.4 square units
please help!
A restaurant needs a block of ice that is exactly 480 cubic inches in volume.
The height of the ice block must be 10 inches.
Answer:
Step-by-step explanation:
Part A,
99% sure this is D
Part B
It's probably about 4 feet tall.
Part C,
4 in. x 12 in.
2 in. x 24 in.
8 in. x 6 in.
3 in. x 16 in.
Answer:
part A: all the above
partt B: 48
part C: 4 in. x 12 in.
2 in. x 24 in.
8 in. x 6 in.
3 in. x 16 in.
Step-by-step explanation:
If the loss incurred on selling an article is 7/20 of the cost price, then find the loss percentage.
Answer: The loss percentage = 65%
Step-by-step explanation:
Let x be the cost price.
As per given,
Selling price = [tex]\dfrac{7}{20}x[/tex]
Loss =Cost price - Selling price
[tex]=x-\dfrac{7}{20}x\\\\=\dfrac{20-7}{20}x\\\\=\dfrac{13}{20}x[/tex]
The loss percent = [tex]\dfrac{loss}{Cost\ price}\times100[/tex]
[tex]=\dfrac{\dfrac{13}{20}x}{x}\times100\\\\=\dfrac{13}{20}\times100\\\\=13\times5\%\\\\=65\%[/tex]
Hence, the loss percentage = 65%
Claudia was cooking breakfast for her entire family. She made double the amount of chocolate chip pancakes as she did with the regular pancakes. She only made half as many blueberry pancakes as the regular pancakes. Claudia also knows her family loves sausages, so she made triple the amount of sausage as blueberry pancakes.
How many of each breakfast item did Claudia make if she cooked 100 times in total?
Answer:
easy the answer is 0.0.0
Step-by-step explanation:
1x0=0.0.0
Find the value of x
5(x−7)=25
Answer:
x=12
Step-by-step explanation:
5(x−7)=25
Divide both sides by 5.
x−7=25/5
Divide 25 by 5 to get 5.
x−7=5
Add 7 to both sides.
x=5+7
Add 5 and 7 to get 12.
x=12
Answer:
x = 12
Step-by-step explanation:
5(x-7) = 25 (distribute)
5x-35 =25 (add 35 on both sides)
5x = 60 (divide)
x = 12
What's the perimeter?
Answer:
the line crossing the trapezoid, the one that helps you find the S. In this case the perimeter is 4 (;
Step-by-step explanation:
Answer:
24
Step-by-step explanation:
perimenopause is inside just count the inside of the trapezoid
hope this helps
can someone solve this by factoring? i need to show work but don't really understand what we're doing..
the problem is:
Answer:
The answer is x = -7 and x = -8
Step-by-step explanation:
Evaluate the function.
f(x)= -x^2
find f(3)
Answer:
f(3) = - 9
Step-by-step explanation:
To evaluate f(3) , substitute x = 3 into f(x) , that is
f(3) = - (3)² = - 9
What is the M? Will mark brainlist if correct
what is 8/16 as a whole number
Answer:
2 is the simplified fraction for 8/16. Simplify 8/16 to the simplest form.
Step-by-step explanation:
What is 8/16 Simplified? - 1/2 is the simplified fraction for 8/16. Simplify 8/16 to the simplest form. Online simplify fractions calculator to reduce 8/16 to the lowest terms quickly and easily.
Answer:
0.5 or 1/2
Step-by-step explanation:
nothing can futher be simplified
Which data are represented by this dot plot a 2 4 0 2 4 6 3 0 7 1 2 7 8 1 1 b 0 1 2 3 4 5 6 7 8 0 1 2
Answer:
Mean (Average) 4.0384615384615
Median 2.5
Range 24
Mode 1, appeared 5 times
Geometric Mean 0
Largest 24
Smallest 0
Sum 105
Count 26
Step-by-step explanation:
also you put 'b' in the list so i removed that
Is it, a solution or, NOT a solution?
Answer:
Perosnally i think it is not a solution but let me check that for you!
Step-by-step explanation:
Answer:Answer x=15 and the answer for x=6 will be false!
Step-by-step explanation:X=6 is not a solution but the correct answer is 15 .First we know that 5+5=10,then if we add 10+5 that will give us 15.
find the angle sum of polygon which had 9 sides
Answer:
1260°
Step-by-step explanation:
Number of sides was given as 9, hence ( n= 9)
Sum of interior angle of a polygon can be determined using the expression below
[(2n-4)90°]
Substitute n=9
[((2×9) -4)) ×90]
= [(18-4)×90]
(14×90)=1260°
Hence, angle sum of polygon which had 9 sides is 1260°
Can someone please help me ⚠️
Triangle ABC has vertices with coordinates -1,-1 , 4,0 and 0,4 Prove that ABC is an isosceles triangle but not a right triangle.
I need help im doing IXL right now (BB.3 Complete a function table: quadratic functions)
i just need help with this final question (posted with a picture)
Answer:
0, 2, 4
Step-by-step explanation:-2 + 2 = 0 + 2= 2 + 2 = 4
The function table is solved and the quadratic equation is f ( x ) = -3x²
What is Quadratic Equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
where ( b² - 4ac ) is the discriminant
when ( b² - 4ac ) is positive, we get two real solutions
when discriminant is zero we get just one real solution (both answers are the same)
when discriminant is negative we get a pair of complex solutions
Given data ,
Let the quadratic equation be represented as A
Now , the value of A is
f ( x ) = -3x²
when x = -2
f ( -2 ) = -3 ( -2 )²
f ( -2 ) = -12
And , when x = 0
f ( 0 ) = 0
when x = 2
f ( 2 ) = -12
when x = 4
f ( 4 ) = -48
Hence , the function table is f ( x ) = { -12 , 0 , -12 , -48 }
To learn more about quadratic equations click :
https://brainly.com/question/25652857
#SPJ2
Which describes a number that cannot be irrational?
a number that can be used to solve an algebraic equation
a number that represents the ratio of the circumference to the diameter of a circle
a number that represents the length of the diagonal of a square
a number that can be written as the ratio of two integers
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Can you find the missing measure
Answer:
for which one
Step-by-step explanation:
Car Survey: In a survey of 2,400 people who owned a certain type of car, 1,680 said they would buy that type of car again. What percent of the people surveyed were satisfied with the car?
Answer:
70 percent
Step-by-step explanation:
convert pounds to ounces complete the following table Its due tomorrow
Answer:
64, 80, 96, and 112.
Step-by-step explanation:
Well, one pound equals 16 onces so you can multiply the number of pounds by 16 to get the answer. I hope this helps! Have a great rest of your day!
FREE! PLEASE ANSWER THE QUESTION TO WIN BRAINLIEST! (NO LINKS)
(Posting till I am out)
Question: Where should a line be drawn to make the below equation accurate?
Equation: 5 + 5 + 5 + 5 = 555
This one made me say "OHHHH-"
Answer:
In a plus sign
Step-by-step explanation:
Step-by-step explanation:
the line should be thought the (=) sign (≠)- like this
that means that it does not equal each other because I mean if you solve it, it made it 20=555 and 20 does not equal 555
What’s a possible answer for this question?
Answer:
x-4
Step-by-step explanation:
you get the value of h(x) by dividing f(x)/g(x), so you only put they values for divide.
for what value of x does the function have an output of 9, given that f(x)=2x+5
x= 2
2(2) + 5 = 9
Hope this helps!
HELPPP ASAP 10 POINTS
Answer:
43 degrees
Step-by-step explanation:
The two angles are supplementry because they form a 90 degree angle so you would subtract 47 from 90 to get 43 degrees.
Answer: 43
Step-by-step explanation: 47+ 43 = 90. since x is a vertical angle it is 43.
Simply the following expression: 12x + 5x - 8x