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3 years ago

What is the volume of the following triangular prism?

Mathematics

1 answer:

Eva8 [605]3 years ago

4 0

Answer:

$V=150cm^3$

Step-by-step explanation:

First we need to find area of the triangle with a base of 4 cm and a height of 5cm, and then multiply that by the length of the prism of 15cm.

The area of the triangle is given by the formula:

$A_T=\frac{bh}{2}$

where b is the base: $b=4cm$ and h is the height: $h=5cm$

thus, in this case we have:

$A_T=\frac{(4cm)(5cm)}{2}\\ \\A_T=\frac{20cm^2}{2} \\\\A_T=10cm^2$

And now, the volume will be the area of the triangle multiplied by the length $l=15cm$ of the prism:

$V=A_T*l$

Substituting the known values:

$V=10cm^2*15cm\\V=150cm^3$

The volume in cubic centimeters is 150.

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I honestly don't even know where to start //// on his last 4 tests , Danilo scored 55% 78% 84% and 93%. What score should he get

skelet666 [1.2K]

Answer:

The answer to your question is He must get 80%

Step-by-step explanation:

Data

Scores 55%, 78%, 84%, 93% and X

Average 80%

Process

1.- Write a equation to solve this problem

- There are five scores

Score 1 = S1 = 55

Score 2 = S2 = 78

Score 3 = S3 = 84

Score 4 = S4 = 93

Score 5 = S5 = X

Equation

Average = (S1 + S2 + S3 + S4 + S5) / 5

- Solve for S5

5 Average = S1 + S2 + S3 + S4 + S5

S5 = 5 Average - S1 - S2 - S3 - S4

- Substitution

S5 = 5(80) - 55 - 78 - 84 - 93

- Simplification

S5 = 400 - 310

- Result

S5 = 90

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3 years ago

Write 460,053 in expanded form

Marianna [84]

400,000 60,000
0,000
000
50
3

6 0

3 years ago

Read 2 more answers

When the polynomial x3 − 7x2 + ax + 3 is divided by x − 3, the remainder is –18. Using synthetic division, determine the value o

KiRa [710]

Correct answer of a is 5

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3 years ago

Determine if the following statement is true or false. (Enter TRUE if the statement is true, enter a counterexample if the state

ehidna [41]

Answer:

The answer is: the satement is FALSE.

Step-by-step explanation:

The first step is to transform the propositons in the statement into symbols:

A: m is any positive integer

B: n is any positive integer

C: mn is a a perfect square

D: m is a perfect square

E: n is a perfect square

After that we replace the symbols into the statement:

If A and B and C, then D and E

Logical connectives on the satement are:

p⇒q conditional (if ...,then...). For this connective the only case when is FALSE is when the antecedent is true and the consequent is false.
p ∧ q conjunction (p and q). For this connective the only case when is TRUE is when the two propositions are true at the same time.

So now, we are going to replace the logical connectives on the statement:

((A ∧ B) ∧ C) ⇒ (D ∧ E)

There is a hierarchy in logical connectives, first we evaluate those inside brackets. The principal connective is evaluated at the end. In this particular case, the principal connective is the conditional.

As we have five different propositions, the combinations are given by the following rule:

2^n= 2^5=32

32 different combinations

In figure 1, added bellow, it shows the construction of truth table.

In figure 2, added bellow, it shows the development of the truth table. In the development, we don't have as a result a tautology, therefore the statement is FALSE.

Download pdf

8 0

3 years ago

To the nearest tenth, what is the area of the figure shown in the image? Segment BF is a line of symmetry of the pentagon ABCDE.

Sidana [21]

Answer:

C, 39.3 in²

Step-by-step explanation:

Lets first find the area of the rectangle part of the house.

To find the area of a rectangle its base × height.

So its 6×4=24 in².

Now lets find the area of the top triangle.

Area for a triangle is (base × height)/2.

The height is 3 inches, because its 7-4. While the base is 6 inches.

(6×3)/2=9 in².

To find the area of the half circle the formula, (piR²)/2.

The radius of the circle is 2 because its half of the diamter which is 4.

(pi2²)/2=6.283 in².

Now we just need to add up the area of every part,

24+9+6.283=39.283in²

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3 years ago