1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
irga5000 [103]
3 years ago
11

Tyler finds a rock in the shape of a triangular pyramid. The dimensions of the rock are shown. A triangular pyramid. The base ha

s a base of 8.5 inches and a height of 4 inches. The height of the pyramid is 12 inches. [Not drawn to scale] The formula for the volume of a triangular pyramid is V = one-third B h. Which expression can be used to find the volume of the rock in cubic inches? V = one-third (8.5) (12) V = one-third (4) (12) V = one-third (34) (12) V = one-third (17) (12)
Mathematics
1 answer:
creativ13 [48]3 years ago
4 0

Answer:

Volume of the rock=V=\frac{1}{3} (17)(12)

Step-by-step explanation:

Volume of triangular pyramid = \frac{1}{3} BH

Where B is the area of base

H is the height of pyramid

Length if base of base triangle = 8.5 inches

Height of base = 4 inches

Area of base triangle = \frac{1}{2} \times base \times height = \frac{1}{2} \times 8.5 \times 4=17 inches^2

Height of pyramid = 12 inches

Volume of triangular pyramid = \frac{1}{3} BH=\frac{1}{3} (17)(12)

So, option D is true

Volume of the rock=V=\frac{1}{3} (17)(12)

You might be interested in
1-determine whether the function / is one-to- one:
Nadusha1986 [10]

Answer:

f(t) is a function but not one-to-one.

Step-by-step explanation:

<em>Please refer to my Answer from this Question to know how to Determine whether a Relation is a Function or not: <u>brainly.com/question/2476082</u></em><em>9</em>

This is a function because time can only move forward and there can't be different numbers of people, f(t), at the same time, t. The only thing that is possible is we can have the same number of people, f(t), at the different times, t. So, this isn't one-to-one but many-to-one.

3 0
3 years ago
30 points!! Help please!! Will give Brainliest!!!
Leto [7]

Answer:

B

Step-by-step explanation:

Area of a trapezoid = (1/2)*(base1+base2)*height

Area = (1/2)*(15+7)*height

DC is 7 which means EF is also 7.

AB = 15

AB - EF = AE + FB = 8

And AE = FB we know that AE is 8/2 = 4

We were given AD = 5. We have a 3-4-5 right triangle and therefore DE is 4. The height of the trapezoid is 3 ft.

Area = 1/2 (15+7)*(3)

Area = (1/2)*22*3

Area = 11 * 3

Area = 33 ft^2

Your answer is B

3 0
3 years ago
For friends share three apples equally what fraction of an apple does each friend get
Semmy [17]
Each friend would get 3/4 of an apple.
6 0
3 years ago
CAN U PLZ HELP THANK YOU
Ulleksa [173]

Answer

second one

Step-by-step explanation:

3 0
3 years ago
I really need it to be sold in imaginary numbers
Yuliya22 [10]
Solving a 5th grade polynomial

We want to find the answer of the following polynomial:

x^5+3x^4+3x^3+19x^2-54x-72=0

We can see that the last term is -72

We want to find all the possible numbers that can divide it. Those are:

{±1, ±2, ±3, ±4, ±6, ±8, ±9, ±12, ±18, ±36, ±72}

We want to factor this polynomial in order to find all the possible x-values. In order to factor it we will have to find some binomials that can divide it using the set of divisors of -72.

We know that if

(x - z) is a divisor of this polynomial then z might be a divisor of the last term -72.

We will verify which is a divisor using synthetic division. If it is a divisor then we can factor using it:

Let's begin with

(x-z) = (x - 1)

We want to divide

\frac{(x^5+3x^4+3x^3+19x^2-54x-72)}{x-1}

Using synthetic division we have that if the remainder is 0 it will be a factor

We can find the remainder by replacing x = z in the polynomial, when it is divided by (x - z). It is to say, that if we want to know if (x -1) is a factor of the polynomial we just need to replace x by 1, and see the result:

If the result is 0 it is a factor

If it is different to 0 it is not a factor

Replacing x = 1

If we replace x = 1, we will have that:

\begin{gathered} x^5+3x^4+3x^3+19x^2-54x-72 \\ \downarrow \\ 1^5+3\cdot1^4+3\cdot1^3+19\cdot1^2-54\cdot1-72 \\ =1+3+3+19-54-72 \\ =-100 \end{gathered}

Then the remainder is not 0, then (x - 1) is not a factor.

Similarly we are going to apply this until we find factors:

(x - z) = (x + 1)

We replace x by -1:

\begin{gathered} x^5+3x^4+3x^3+19x^2-54x-72 \\ \downarrow \\ (-1)^5+3\cdot(-1)^4+3\cdot(-1)^3+19\cdot(-1)^2-54\cdot(-1)-72 \\ =-1+3-3+19+54-72 \\ =0 \end{gathered}

Then, (x + 1) is a factor.

Using synthetic division we have that:

Then:

x^5+3x^4+3x^3+19x^2-54x-72=(x+1)(x^4+2x^3+x^2+18x-72)

Now, we want to factor the 4th grade polynomial.

Let's remember our possibilities:

{±1, ±2, ±3, ±4, ±6, ±8, ±9, ±12, ±18, ±36, ±72}

Since we verified ±1, let's try with ±2 as we did before.

(x - z) = (x - 2)

We want to divide:

\frac{x^4+2x^3+x^2+18x-72}{x-2}

We replace x by z = 2:

\begin{gathered} x^4+2x^3+x^2+18x-72 \\ \downarrow \\ 2^4+2\cdot2^3+2^2+18\cdot2-72 \\ =16+16+4+36-72 \\ =0 \end{gathered}

Then (x - 2) is a factor. Let's do the synthetic division:

Then,

x^4+2x^3+x^2+18x-72=(x-2)(x^3+4x^2+9x+36)

Then, our original polynomial is:

\begin{gathered} x^5+3x^4+3x^3+19x^2-54x-72 \\ =\mleft(x+1\mright)\mleft(x^4+2x^3+x^2+18x-72\mright) \\ =(x-1)(x-2)(x^3+4x^2+9x+36) \end{gathered}

Now, let's prove if (x +2) is a factor, using the new 3th grade polynomial.

(x - z) = (x + 2)

We replace x by z = -2:

\begin{gathered} x^3+4x^2+9x+36 \\ \downarrow \\ (-2)^3+4(-2)^2+9(-2)+36 \\ =-8+16-18+36 \\ =26 \end{gathered}

Since the remainder is not 0, (x +2) is not a factor.

All the possible cases are:

{±1, ±2, ±3, ±4, ±6, ±8, ±9, ±12, ±18, ±36, ±72}

let's prove with +4

(x - z) = (x + 4)

We want to divide:

\frac{x^3+4x^2+9x+36}{x+4}

Let's replace x by z = -4 in order to find the remainder:

\begin{gathered} x^3+4x^2+9x+36 \\ \downarrow \\ (-4)^3+4(-4)^2+9(-4)+36 \\ =-64+64-36+36 \\ =0 \end{gathered}

Then (x + 4) is a factor. Let's do the synthetic division:

Then,

x^3+4x^2+9x+36=(x+4)(x^2+9)

Since

x² + 9 cannot be factor, we have completed our factoring:

\begin{gathered} x^5+3x^4+3x^3+19x^2-54x-72 \\ =(x-1)(x-2)(x^3+4x^2+9x+36) \\ =(x-1)(x-2)(x+4)(x^2+9) \end{gathered}

Now, we have the following expression:

(x-1)(x-2)(x+4)(x^2+9)=0

Then, we have five posibilities:

(x - 1) = 0

or (x - 2) = 0

or (x + 4) = 0

or (x² + 9) = 0

Then, we have five solutions;

x - 1 = 0 → x₁ = 1

x - 2 = 0 → x₂ = 2

x + 4 = 0 → x₃ = -4

x² + 9 = 0 → x² = -9 → x = ±√-9 = ±√9√-1 = ±3i

→ x₄ = 3i

→ x₅ = -3i

<h2><em>Answer- the solutions of the polynomial are: x₁ = 1, x₂ = 2, x₃ = -4, x₄ = 3i and x₅ = -3i</em></h2>

7 0
1 year ago
Other questions:
  • Classify the shape as precisely as possible based on its markings. Question 18 options: A) Square B) Quadrilateral C) Parallelog
    6·2 answers
  • based on what you know about emily dickinson, which of these did she write? a. a few fell at once, shot in the temple or heart,
    8·1 answer
  • What is the average rate of change for h(x)=x^2+x-6
    14·1 answer
  • a carton can hold 1000 unit cubes that measure 1 inch by 1 inch by 1 inch. Describe the dimensions of the carton using unit cube
    11·1 answer
  • Which sentence in this excerpt from Common Sense by Thomas Paine supports the claim that the American colonies could thrive inde
    10·1 answer
  • HELP PLEASE.. I WILL GIVE BRIANLIEST TYSM
    11·2 answers
  • Find the area of the regular figure
    15·1 answer
  • Ramon scored 16 points at the volleyball game. That was 8 times as many as David scored. How many points did David score? (Hint:
    15·1 answer
  • PLEASE HELP 30 POINTS
    11·1 answer
  • Hi , anyone can help?​
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!