Find the volume of the triangular prism shown in the diagram. The unlabeled point is F (0,0,1) . Outline your steps to explain the process you used.

Answers

Answer 1

Answer: Volume = (LWH)/2
Length = Difference between the two x values
Using A (4, 3, 1) an B (0, 3, 1) we can use these two x values to find the length of the triangular prism
4 - 0 = 4
Length = 4
Width = This is exactly the same process, however we use the y values
Using E (4, 0, 1) and A (4, 3, 1) we can use the two y values to find the width
3 - 0 = 3
Width = 3
Height = Again, the same but using the z values
Using E (4, 0, 1) and D (4, 0, 5) we can find the difference
5 - 1 = 4
Height = 4

Now we have all out values, we can put them in the formula to work out the volume.
(4 x 3 x 4)/2
48/2
24 (units)³

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Lisa has a certain amount of money. She spent 39 dollars and has 3/4th of the original amount left. How much money did she have originally

20 is what percent of 52?

Answers

20 is 38.46% of 52. Hope i helped

If 52 ------> =100% (=1)
Then 20----> x
(Rule of 3)
X=20/52 =38.46%

Jonas is jogging from the Park to the school. He has jogged 0.424 miles so far. He has 0.384 mile left to jog. How far is the park located away from the school?

Answers

Answer:the park is located 0.808 miles away from the school

Step-by-step explanation:

Jonas is jogging from the Park to the school. The total number of miles that Jonas has jogged so far is 0.424.

He has 0.384 mile left to jog. This means that the distance of the park from the school would be the sum of the distance that he has jogged so far and the distance that he has left to jog. It becomes

0.424 + 0.384 = 0.808 miles

abbie spent 5/8 of her money and saved the rest. if she spent 45,how much money did she have at first?

Answers

$72

Further explanation

Given:

Abbie spent ⁵/₈ of her money and saved the rest.

She spent $45.

Question:

How much money did she have at first?

The Process:

The meaning of "Abbie spent ⁵/₈ of her money" is that she has spent 5 of the 8 parts of the money she had at first.

Let us make a pattern of 8 units for the amount of money that Abbie had at first.

$\boxed{\cdot}\boxed{\cdot}\boxed{\cdot}\boxed{\cdot}\boxed{\cdot}\boxed{\cdot}\boxed{\cdot}\boxed{\cdot}$

Since Abbie spent ⁵/₈ of her money, then we create a pattern of 5 units containing $9 each. Recall that $\boxed{\$ 45 / 5 = \$ 9}$

$\boxed{\$ 9}\boxed{\$ 9}\boxed{\$ 9}\boxed{\$ 9}\boxed{\$ 9} = \$ 45$

From the pattern above, we can see that $\boxed{ \ 1 \ unit = \$ 9 \ }.$

Let us calculate how much money Abbie had at first.

$\boxed{ \ 1 \ unit = \$ 9 \ }$

$\boxed{ \ 8 \ unit = \ ? \ }$

$\boxed{ \ 8 * \$ 9 = \$ 72 \ }$

Thus, the money Abbie had at first is $72.

The complete pattern of Abbie's initial money is as follows:

$\boxed{\$ 9}\boxed{\$ 9}\boxed{\$ 9}\boxed{\$ 9}\boxed{\$ 9}\boxed{\$ 9}\boxed{\$ 9}\boxed{\$ 9} = \$ 72$

- - - - - - - - - -

Quick Steps:

Let M as Abbie's initial money.

$\boxed{ \ (5)/(8) * M = \$ 45 \ }$

Both sides are multiplied by ⁸/₅ so that M is the subject alone on the left side.

$\boxed{ \ M = (8)/(5) * \$ 45 \ }$

We crossed out 5 and 45.

$\boxed{ \ M = 8 * \$ 9 \ }$

$\boxed{ \ M = \$ 72 \ }$

Thus, the money Abbie had at first is $72.

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Keywords: Abbie, spent 5/8 of her money, saved the rest, $45, $72, how much money, she have at first, the pattern

Note that 5/8 is equivalent to $45

1/8 is equivalent to $45 ÷ 5 = 9

8/8 (aal) is equivalent to 8 x 9 = 72

She had $72

Some $1.50 per oz spice and some $2.50 per oz are mixed to produce 20 oz of a mixture worth 1.90 per oz. How many oz of each should be used

Answers

Answer:

3 ounces of the seed and 7 ounces of the dried fruit.

Step-by-step explanation:

solve quadratic formula
x-2x-15=0

the first x is squared

Answers

You said that x² - 2x - 15 = 0 .

You could factor the left side:

(x + 3) (x - 5) = 0

This equation is true if either of the factors is zero.

First factor:
x + 3 = 0
x = -3

Second factor:
x - 5 = 0
x = 5

$x^2-2x-15=0\n x^2-5x+3x-15=0\n x(x-5)+3(x-5)=0\n (x+3)(x-5)=0\n x=-3 \vee x=5$

The circumference of a circle is 19π in. What is the area, in square inches? Express your answer in terms of π.

Answers

Answer:

A = 90.25 pi in^2

Step-by-step explanation:

The circumference is given by

C = 2*pi*r

19pi = 2*pi*r

Divide each side by 2 pi

19pi / 2 pi = 2*pi*r/ 2pi

9.5 = r

The area is given by

A = pi r^2

A = pi ( 9.5)^2

A = 90.25 pi in^2

Answer:

The area of circle is 90.25 π inches².

Step-by-step explanation:

Given:-

Circumference of circle is 19 π in.

To Find :-

Area of circle

Solution :-

Firstly, we need to find radius of circle

Using formula

Circumference of circle = 2 π r

substitute the value

19 π inches = 2 π r

Divide each side by 2 π

19 π inches / 2 π = 2 π r / 2 π

9.5 inches = r

Now, Finding the area of circle

Using formula

Area of circle = π × r²

Where,

r, radius of circle = 9.5 inches

Substitute the values

Area of circle = π × ( 9.5 inches)²

Evaluate the exponent

Area of circle = π × 90.25 inches ²

multiply ,we get

Area of circle = 90.25 inches²

Hence, the area of circle is 90.25 π inches².

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