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4 years ago

What is the volume of the prism

Mathematics

1 answer:

frosja888 [35]4 years ago

5 0

The area of the triangular base is
A = (1/2)bh
A = (1/2)(5 units)(12 units)
A = 30 units²

The "height" of the prism is 6 units, so the volume is
V = (area of base)×(height)
V = (30 units²)×(6 units)
V = 180 units³

The appropriate choice is
A. 180 units³

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Evaluate the expressions. 8!-6!, 7!-5!, and 12!/8! BRAINLIST 5 min left plz hurry

nordsb [41]

Answer:

The evaluated expressions are $8!-6!=39600$ , $7!-5!=4920$ and $\frac{12!}{8!}=11880$

Step-by-step explanation:

The factorial of a positive integer n is the product of all positive integers less than or equal to n:

$n!=n\times (n-1)\times (n-2)\times (n-3)\times ...\times 3\times 2\times 1$

The factorial of n is denoted by n!

Now to find the expressions 8!-6!, 7!-5!, and 12!/8! :

Given expression is 8!-6!:

$8!-6!=[8\times (8-1)\times (8-2)\times (8-3)\times (8-4)\times (8-5)\times (8-6)\times (8-7)]- [6\times (6-1)\times (6-2)\times (6-3)\times (6-4)\times (6-5)]$ (By using factorial of n formula)

$=[8\times 7\times 6\times 5\times 4\times 3\times 2\times 1]- [6\times 5\times 4\times 3\times 2\times 1]$

$=[6\times 5\times 4\times 3\times 2\times 1][(8\times 7)-1]$

$=[720][56-1]$

$=[720][55]$

$=39600$

Therefore $8!-6!=39600$

Given expression is 7!-5! :

$7!-5!=[7\times (7-1)\times (7-2)\times (7-3)\times (7-4)\times (7-5)\times (7-6)]-[5\times (5-1)\times (5-2)\times (5-3)\times (5-4)]$ (By using factorial of n formula)

$=[7\times 6\times 5\times 4\times 3\times 2\times 1]- [5\times 4\times 3\times 2\times 1]$

$=[5\times 4\times 3\times 2\times 1][(7\times 6)-1]$

$=[120][42-1]$

$=[120][41]$

$=4920$

Therefore $7!-5!=4920$

Given expression is $\frac{12!}{8!}$

$\frac{12!}{8!}=\frac{12\times (12-1)\times (12-2)\times (12-3)\times (12-4)\times (12-5)\times (12-6)\times(12-7)\times (12-8)\times (12-9)\times (12-10) \times(12-11)}{8\times (8-1)\times (8-2)\times (8-3)\times (8-4)\times(8-5)\times (8-6)\times (8-7)}$ (By using factorial of n formula)

$=\frac{12\times 11\times 10\times 9\times 8\times 7\times 6\times 5\times4\times 3\times 2\times 1}{8\times 7\times 6\times 5\times4\times 3\times 2\times 1}$

$=12\times 11\times 10\times 9$

$=11880$

Therefore $\frac{12!}{8!}=11880$

4 0

3 years ago

You can earn money by tutoring for $8 per hour and by walking dogs for $7.50 per hour. If you are scheduled to tutor for 10 hour

hoa [83]

Answer:

28 hours

Step-by-step explanation:

Let the number of hours required to:

Tutor = x

Walk the dog = y

If you are scheduled to tutor for 10 hours during the week

x = 10........ Equation 1

You can earn money by tutoring for $8 per hour and by walking dogs for $7.50 per hour. Create and solve an inequality that represents the number of hours you can walk dogs during the week in order to earn at least $290 for the week

$8 × x + $7.50 × y ≥ $290

8x + 7.50y ≥ 290..... Equation 2

We substitute 10 for x in Equation 2

8(10 ) + 7.50y ≥ 290

80 +7.50y ≥ 290

7.50y ≥ 290 - 80

7.50y ≥ 210

y ≥ 210/7.50

y ≥ 28 hours

The number of hours you can walk dogs during the week in order to earn at least $290 for the week is 28 hours

3 0

3 years ago

If m∠A = m∠B and m∠A + m∠C = ∠D, then

umka2103 [35]

Answer:

Substitution Property

Step-by-step explanation:

The change from the first equation to the final equation is m∠A has been replaced by m∠B. In other words, m∠B was substituted for m∠A.

7 0

3 years ago

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Question 8 of 10

Papessa [141]

Answer:

I'm pretty sure it's C

7 0

3 years ago

PLEASE ANSWER FAST IM FAILING MATH!!!

posledela

Answer:

Step-by-step explanation:

From the figure attached,

Point B has been dilated to form point B'.

B(3, 1) → B'(6, 2)

→ B'[(2 × 3), (2 × 1)]

Since rule for the dilation of a point (x, y) by a factor of k is,

B(x, y) → B'(kx, ky)

By comparing the coordinates k = 2 is the scale factor by which the point B has been dilated about the origin.

Therefore, other vertices of the quadrilateral will be,

A(-2, 3) → A'(-4, 6)

C(1, -1) → C'(2, -2)

D(-3, -2) → D'(-6, -4)

4 0

3 years ago