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3 years ago

Find the volume of the following. Please round your answer to the nearest tenth. Please do not put units.

Mathematics

1 answer:

Mars2501 [29]3 years ago

4 0

Answer:

The volume of the given figure is 150 mm³

Step-by-step explanation:

The formula of the volume of the triangular pyramid is V = $\frac{1}{3}$ AH, where

A is the area of its base

H is its height

The formula of the area of a triangle is A = $\frac{1}{2}$ bh, where

b is the length of its base

h is the length of its height

In the given figure

∵ The pyramid has a triangular base

∵ The triangle has a base of 12 mm and a height of 7.5 mm

∴ b = 12 mm and h = 7.5 mm

→ By using the 2nd formula above, find the area of the base

∴ A = $\frac{1}{2}$ (12)(7.5)

∴ A = 45 mm²

∵ The height of the pyramid is 10 mm

∴ H = 10 mm

∵ A = 45 mm²

→ Substitute them in the first formula above to find the volume

∴ V = $\frac{1}{3}$ (45)(10)

∴ V = 150 mm³

∴ The volume of the given figure is 150 mm³

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If f(x)=4x^5+5x^4+1, then what is the remainder when f(x) is divided by x-2

monitta

Answer:

Remainder 209

Step-by-step explanation:

f(x)= 4x⁵+5x⁴+1

x-2=0⇒x=2

Putting x=2 in the above equation

f(x)= 4(2)⁵ +5(2)⁴+1

f(x)= 4(32) +5(16) +1

f(x)= 128 +80+1

f(x)= 209

4 0

3 years ago

What is the equation of a line with a slope of 3 and a point

seraphim [82]

Answer: y = 3x-8

------------------------------------------------
------------------------------------------------

Explanation:

The slope is 3, so m = 3

The given point is (3,1) meaning x = 3 and y = 1. The x coordinate is always listed first in an ordered pair. The general format is (x,y)

We'll use m = 3, x = 3 and y = 1 to find the y intercept

y = mx+b
y = m*x+b
1 = 3*3+b ... plug in m = 3, x = 3 and y = 1
1 = 9+b
1-9 = 9+b-9 ... subtract 9 from both sides
-8 = b
b = -8

----------------

So we're given m = 3 as the slope and we just found that b = -8 is the y intercept

So y = mx+b updates to y = 3x-8. This is the final answer.

----------------

Side Notes:
* The slope of 3 means rise/run = 3/1 indicating each time we go up 3, we move to the right 1
* The y intercept -8 is the location on the vertical y axis numberline where the graph crosses. The point (0,-8) is on this line.

8 0

3 years ago

What was gabriel error

Pavlova-9 [17]

The change is given by the difference between how much you paid and how much you actually had to pay. For example, if you pay with a $50 bill and you had to pay $13, your change will be $50-13 = 37$ dollars.

In this case, we have

$30 - (2.5x+2y-2) = 30-2.5x-2y+2 = 32-2.5x-2y$

So, Gabriel's mistake was to leave the negative sign to the "-2" at the end of the expression, instead of flipping it to positive "+2" when subtracting it.

7 0

2 years ago

Anybody have the answer?

Mariulka [41]

80 inches squared, I would assume based off of the other one.

6 0

3 years ago

Read 2 more answers

If the Math Olympiad Club consists of 11 students, how many different teams of 3 students can be formed for competitions?

vivado [14]

Answer:

165 different teams of 3 students can be formed for competitions

Step-by-step explanation:

Combinations of m elements taken from n in n (m≥n) are called all possible groupings that can be made with the m elements so that:

Not all items fit
No matter the order
Elements are not repeated

That is, a combination is an arrangement of elements where the place or position they occupy within the arrangement does not matter. In a combination it is interesting to form groups and their content.

To calculate the number of combinations, the following expression is applied:

$C=\frac{m!}{n!*(m-n)!}$

It indicates the combinations of m objects taken from among n objects, where the term "n!" is called "factorial of n" and is the multiplication of all the numbers that go from "n" to 1.

In this case:

n: 3
m: 11

Replacing:

$C=\frac{11!}{3!*(11-3)!}$

Solving:

$C=\frac{11!}{3!*8!}$

being:

3!=3*2*1=6
8!=8*7*6*5*4*3*2*1=40,320
11!=39,916,800

So:

$C=\frac{39,916,800}{6*40,320}$

C= 165

<u><em>165 different teams of 3 students can be formed for competitions</em></u>

3 0

3 years ago