Answer:
Answer C.12
Step-by-step explanation:
v/V=(h/H)^3
1/8=(h/24)^3
1/8=h^3/24^3
1/8=h^3/13824
8h^3=13824
H=1728√3
h= \sqrt[3]{1728}
h=12 cm
the height of the smaller pyramid is 12 inches.
What is a triangular pyramid?
A triangular pyramid is a 3D geometric shape in which all the three lateral faces are triangles with a common vertex. If all the three triangular faces are equilateral, then such a pyramid is called a tetrahedron.
For the given situation,
The ratio of the volumes of two geometrically similar pyramids = 1:8
The height of the larger pyramid = 24 inches.
Let the volume of smaller pyramid be v1 and larger pyramid be v2.
Let the height of smaller pyramid be h1 and larger pyramid be h2.
The relation between the volume of pyramid and height is given as
[tex]v=\frac{1}{3} (base area)(height)[/tex]
Let us consider the triangle to be equilateral triangle. So all the sides are equal.
We know that, Base area = [tex]a^{2}[/tex] and [tex]a=h[/tex]
The volume becomes [tex]v=\frac{1}{3} h^{3}[/tex]
The ratio becomes,
⇒ [tex]\frac{v1}{v2} =\frac{h1^{3} }{h2^{3}}[/tex]
⇒ [tex]\frac{1}{8} =\frac{h1^{3} }{24^{3}}[/tex]
⇒ [tex]h1^{3}=\frac{24^{3} }{8}[/tex]
⇒ [tex]h1^{3}=\frac{13824 }{8}[/tex]
⇒ [tex]h1^{3}=1728[/tex]
⇒ [tex]h1=\sqrt[3]{1728}[/tex]
⇒ [tex]h1=12[/tex]
Hence we can conclude that the height of the smaller pyramid is 12 inches.
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-12m-8m+5=-25m-20 solve equation
Answer:
m=-5
Step-by-step explanation:
Given: -12m-8m+5=-25m-20
Combine like terms on left side: -20m+5=-25m-20
Add 25m to both sides: 5m+5=-20
Subtract 5 on both sides: 5m=-25
Divide both sides by 5: m=-5
So m=-5
Answer:
m = -5
Step-by-step explanation:
-12m-8m+5=-25m-20
Combine like terms
-20m +5 = -25m -20
Add 25m to each side
-20m+25m+5=-25m+25m-20
5m +5 = -20
Subtract 5 from each side
5m+5-5=-20-5
5m = -25
5m/5 = -25/5
m = -5
If g(x ) = 3x + 1, evaluate g(-14). -5 -10 -41
Answer:
-41
Step-by-step explanation:
g(x) = 3x + 1
g(-14) = 3*(-14) + 1
= -42 + 1
= -41
He ran 220 meters farther than she ran she ran 2.4 kilometers.how many kilometers did he run
Answer:
He ran 2.62 km
Volume of a shape
Jacob’s dad gave him a soda can to use. He was able to cut off the top to have a full opening. The can is 5 inches tall and the opening has a diameter of 3 inches.
Jacob’s little sister ate her ice cream, but didn’t want to eat the cone. Jacob decided to use the cone to scoop sand and build his castle. The cone is 5 inches long and has an opening diameter of 3 inches
Answer:
The can's volume is 35.34 inches
the cone's volume is 11.78 inches
hope it helps you!!
The question asks for the volume of a cylinder and a cone, both with a height of 5 inches and a diameter of 3 inches. The volume of the cylinder is calculated as approximately 35.34 inches³, and the volume of the cone is about 11.78 inches³.
The question involves finding the volume of two different 3-dimensional shapes: a cylinder (soda can) and a cone (ice cream cone). To calculate the volume of the cylinder, we use the formula V = π r² h, where r is the radius of the circular base, and h is the height of the cylinder.
Since the diameter of the soda can is given as 3 inches, the radius (which is half of the diameter) would be 1.5 inches. For the cone, the formula for volume is V = {1}/{3} π r² h, using the same measurements for r and h as the soda can. The calculations then proceed as follows:
Cylinder: V = π (1.5)² × 5 = π × 2.25 × 5
Cone: V = {1}/{3} π (1.5)² × 5 = {1}/{3} π × 2.25 × 5
The volume of the cylinder would be approximately 35.34 inches³ and the volume of the cone would be about 11.78 inches³, assuming π is approximately 3.14159.
Which rule describes the translation?
O (x, y) = (x–8, y-3)
* (x, y) = (x-3, y + 3)
O (x, y) + (x+8, y-3)
O (x, y) + (x + 3, 7 + 8)
Answer:
c
Step-by-step explanation:
on ed 2020
Answer:
C) (x, y) → (x + 8, y – 3)
Step-by-step explanation:
9.5g of sugar is needed for every cake made. How much sugar is needed for 6 cakes?
Answer: 57
Step-by-step explanation:
Since you need 9.5 grams of sugar for each cake, and you need enough for 6 cakes, you need to multiply 9.5 to 6. Your final answer should be 57.
Answer:
39.2
Step-by-step explanation:
4 times 9.5 equals 39.2
y=7x + 10
y=-4x – 23
Answer:
x = -3
y = -11
Step-by-step explanation:
to solve this linear equation using substitution method
let us say that
y=7x + 10.........................................................equation 1
y= -4x – 23...................................................... equation2
substitute equation 1 into equation 2
7x + 10 = -4x - 23
collect the like terms
7x + 4x = -23 -10
11x = -33
divide both sides by the coefficient of x which is 11
11x/11 = -33/11
x = -3
put the value of x = -3 into equation 2
y= -4x – 23...................................................... equation2
y = -4(-3) - 23
y = 12 - 23
y = -11
therefore the value of x and y is -3 and -11 respectively
Solution is x=-3 , y=-11.
We set the ys equal.
[tex]7x+10=-4x-23\\7x+4x=-23-10\\11x=-33\\x=-3[/tex]
For x=-3,
[tex]y=7x+10\\y=7(-3)+10\\y=-21+10\\y=-11[/tex]
Solution is x=-3 , y=-11.
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Scientists are monitoring the populations of two insect species in a remote location in Alabama. They estimate that the
current population of insect A is 2.5 million. But it's declining at the rate of 4% per year because of habitat loss. The
estimated population of insect B is 1.2 million, and it's increasing at the rate of 200,000 per year. Let x represent the
population of each insect species in millions, and y represent the elapsed time in years. Which equation can be used to
determine how long it will take for the populations of the two species to be equal?
Answer:
2.5e^-0.04x = 1.2 + 0.2x
Step-by-step explanation:
Cole is studying employment trends.
He found that 20% of the social workers he surveyed, or 45 social workers,
work part time. How many social workers did Cole survey altogether?
Answer:
225
Step-by-step explanation:
So we know that 20% of the social workers he surveyed was 45 people. The easiest way to find all 100% of the social workers is to do 45 x 5 because 20% x 5 = 100%. So 45 x 5 = 225.
Hope this helped! :)
Help, I'm really stuck on this, has to be in by tomorrow! The question = Describe fully the single transformation that maps shape A onto shape B
Answer:
One thing for sure is that there is a reflection along the x-axis
Step-by-step explanation:
Answer:
reflection
Step-by-step explanation:
its a reflection across the X axis
reflection is to turn a shape across an axis
other transformations are:...
translation= to slide a shape up or down left or right when they give u the units
dilation= to make a shape bigger or smaller with they center of dilation that they give
rotation= turn a shape depending if its clockwise or counter clockwise and they will give u a degree
hope this helped
Please help me just the first two questions mark brainly
Answer:
the height is 16 and the volume is 476.24 i think
Step-by-step explanation:
For the diagram shown, x = 80 and y = 30. Determine the value of z. A) 20 B) 40 C) 50 D) 100
Answer:D
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
What do you want to do fo a career and how math is used in that career?
Use the inequality to help you complete the statements.
j < –0.65
Answer:
the variable is j, in equality symbol is < , constant is -0.65,
Step-by-step explanation:
:D Took asignment got it right
Answer:
A table titled inequality symbols contains the symbols for less-than and greater-than.
Use the inequality to help you complete the statements.
j < –0.65
The variable in the inequality is
✔ j
.
The inequality symbol is
✔ <
.
The constant in the inequality is
✔ -0.65
.
Step-by-step explanation:
solve 5(3)x + 3 - 2 = 38 using logarithmic properties. Round your answer to three decimal places.
Answer:341/135
Step-by-step explanation:
Answer:
-1.107
Step-by-step explanation:
What is the arc measure of BDC in degrees?
if sin(x) = 0 and cos(x) = 1, what is cot(x)?
Answer:
undefined
Step-by-step explanation:
Sin(x) = 0 where x = 0
Cos(x) = 1 where x = 0
Cot(0) is undefined
Undefined.
Trigonometry:The study of correlations between triangles' side lengths and angles is known as trigonometry. The field was created in the Hellenistic era in the third century BC as a result of the use of geometry in astronomical research.Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (cosec).Given -
[tex]sin(x)=0\\cos(x)=1[/tex]
So [tex]cot(x)=-[/tex].
Therefore, [tex]cot(x)[/tex] is undefined.
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what is the coefficient of y2
Answer: A coefficient is simply a variable that has a number with it. For example 2y has a coefficient. The coefficient is 2 because you will multiply 2 by y.
A coefficient is a numerical or constant quantity placed before and multiplying the variable in an algebraic expression
To own and operate a home printer, it costs $100 for the printer and an additional $0.05 per page for ink. To print out pages at an office store, it costs $0.25 per page. Let p represent number of pages.
(1) For the costs to be the same, how many pages do you need to print?
(2) How much does it cost to print that many pages?
Answer:
1.) 500 pages
2.) $125
Step-by-step explanation:
Given that the printer cost $100. To operate at home will cost
100 + 0.05P
To print out pages at an office store, it will cost 0.25P
1.) For the costs to be the same, then
100 + 0.05P = 0.25P
0.25P - 0.05P = 100
0.20P = 100
P = 100/0.2
P = 500 pages
500 pages need to be printed
2.) How much does it cost to print that many pages?
Cost = 0.25P
= 0.25 × 500
= 125 dollars
Answer: (1) You would need to print 500 pages
(2) To print 500 pages from home would cost $125
Step-by-step explanation: The cost of printing at home has been given as a fixed cost of 100 plus an additional variable cost of 0.05 per page for ink, that is, Cost = 100 + 0.05p. Also, to print at the office, the cost has been given as 0.25 per page, that is, Cost = 0.25p.
Therefore for the costs to be the same, we need to equate both cost functions (that is, C = C) as follows;
100 + 0.05p = 0.25p
Collect like terms and we now have,
100 = 0.25p - 0.05p
100 = 0.20p
Divide both sides of the equation by 0.2
500 = p
To print 500 pages at home therefore would cost,
C = 100 + 0.05p
C = 100 + 0.05(500)
C = 100 + 25
C = 125
Therefore to print 500 pages from home would cost $125
The figure is made up of a semicircle and a triangle. Find the perimeter. Round your answer to the nearest hundredth.
Perimeter of figure = π*r * sum of all three sides
Step-by-step explanation:
Perimeter of a figure with semicircle and triangle .-
Perimeter of semicircle is = π*r
Perimeter of triangle = sum of all three sides
Perimeter of figure = π*r * sum of all three sides
we can't round up here as no value is given in question .
How many solutions does the system have?
y = -7x + 8
y = -7x - 8
Choose 1 answer:
Answer:
No solutions
Step-by-step explanation:
If we try to solve this system for y at x = 1, we get an impossible situation:
[tex]y=-7(1)+8=-7+8=1\\y=-7(1)-8=-7-8=-15\\1=-15[/tex]
Clearly, 1 ≠ -15, and we'll see that any value of x that we pick gives us two contradictory values for y, so this system has no solutions.
Which of the following is most likely the next step in the series?
Answer:
the answer is C
Answer with A B C D. Correct answer gets brainlest.
Answer:
B
Step-by-step explanation:
Answer: B
Step-by-step explanation:
Would the value of{2+ [(15 – 3) – 61} = 2 change if the braces were removed? Explain.
HURRY TIME LIMIT
y + 2 = negative 2 (x minus 5)
What is the equation in slope-intercept form?
Answer:
[tex]y = -2x + 8[/tex]
Step-by-step explanation:
Step 1: Solve
[tex]y + 2 = -2(x - 5)[/tex]
[tex]y + 2 - 2 = -2x + 10 - 2[/tex]
[tex]y = -2x + 8[/tex]
Answer: [tex]y = -2x + 8[/tex]
Answer:
y= -2x + 12
Step-by-step explanation:
y +2 = -2 ( x - 5 )
y+2 = -2x + 10
-2 -2
y= -2x + 12
Solve for the missing measurement.
5. The area of the base of a rectangular prism is 225 units square If the volume is 1800 cubic
units, what is the height of the prism?
6. The volume of a rectangular prism is 216 cubic cm. If the height of the prism is 8 cm, what
is the area of its base? (Round to the nearest tenth)
Answer:
1) The height of the prism is 8 units.
2) The area of its base is 27 square cm.
Step-by-step explanation:
The formula of a rectangular prism is
[tex]\text{Volume}=\text{Area of base}\times \text{Height}[/tex]
1) Given : The area of the base of a rectangular prism is 225 units square If the volume is 1800 cubic units.
To find : What is the height of the prism?
Solution :
Volume = 1800 cubic units
Area of base = 225 units square
Substitute the value,
[tex]1800=225\times \text{Height}[/tex]
[tex]\text{Height}=\frac{1800}{225}[/tex]
[tex]\text{Height}=8[/tex]
The height of the prism is 8 units.
2) Given : The volume of a rectangular prism is 216 cubic cm. If the height of the prism is 8 cm.
To find : What is the area of its base?
Solution :
Volume = 216 cubic cm
Height = 8 cm
Substitute the value,
[tex]216=\text{Area of base}\times 8[/tex]
[tex]\text{Area of base}=\frac{216}{8}[/tex]
[tex]\text{Area of base}=27[/tex]
The area of its base is 27 square cm.
Graph the line x=-3
A 2-pack of notebooks costs $3.00. What is the unit price? per notebook
Answer:
$1.50
Step-by-step explanation:$3.00/2 is $1.50 hope this helps god bless
Answer:
The unit price is 1.50, you just needed to divide by two to see how much one note book costs.
Hope this helps <3
On a scale drawing with a scale of 1cm:4.5 m, the height of a tree is 2.4 cm. how tall is the actual tree?
Answer:
10.80
Step-by-step explanation:
1cm:4.5 meters
So if one cm is 4.5 meters, just multiply 2.4 by 4.5.
2.4*4.5=10.8
What is the probability of rolling at least one 5 or 6 when rolling the dice three times?
Answer:
19/27
Step-by-step explanation:
Each time that you roll a dice, there is a 1/3 chance you get a 5/6(assuming you have a fair dice). The probability of rolling that atleast once is the inverse of the probability of rolling a 1-4 each time. There is a [tex]\frac{2}{3}[/tex] chance each time you roll the dice. Thus raising this to the third power results in [tex]\frac{8}{27}[/tex]. Since we are looking for the inverse probability, we can do:
[tex]1-\frac{8}{27}[/tex] In order to get our final answer.