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1 year ago

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Type the correct answer in the box. If necessary, use / for the fraction bar. A shaded triangular pyramid and an inverted shaded

triangular pyramid has their bases on the bottom and the top sides of a rectangular prism. Both pyramids in the figure have the same base area as the prism. The ratio of the combined volume of the pyramids to the volume of the prism, expressed as a fraction in simplest form, is . Reset Next

1 answer:

Lapatulllka [165]1 year ago

7 0

The ratio of the combined volume of these pyramids to the volume of the prism as a fraction is equal to 1/3.

<h3>How to calculate the volume of a pyramid?</h3>

Mathematically, the volume of a pyramid can be calculated by using this formula:

Volume = 1/3 × b × h

<u>Where:</u>

h is the height.

b is the base area.

Since both pyramids have the same base area as the prism, their combined volume is given by:

Combined volume = (1/3 × b × h) + (1/3 × b × h)

Combined volume = 2/3 × b × h

Also, the volume of this prism = 1/2 × b × h

Thus, the ratio is given by:

Ratio = (2/3 × b × h)/(1/2 × b × h)

Ratio = 2/3 × 1/2

Ratio = 1/3.

Read more on pyramid here: brainly.com/question/16315790

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Solve for x by completing square x^2-18x=65

Nastasia [14]

Answer:

See Image below:)

Step-by-step explanation:

You can use the app photo math, you just take a picture of the question and it shows you the steps.

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2 years ago

Alla [95]

90° is equal to $\frac{\pi}{2}$ or 1.5707 radians.

Step-by-step explanation:

Step 1:

If an angle is represented in degrees, it will be of the form x°.

If an angle is represented in radians, it will be of the form $\frac{\pi}{x}$ radians.

To convert degrees to radians, we multiply the degree measure by $\frac{\pi}{180}$ .

For the conversion of degrees to radians,

the degrees in radians = (given value in degrees)( $\frac{\pi}{180}$ ).

Step 2:

To convert 90°,

$90 (\frac{\pi}{180} ) = \frac{\pi}{2}.$

$0.5 \pi = 1.5707$ radians.

So 90° is equal to $\frac{\pi}{2}$ or 1.5707 radians.

3 0

3 years ago

Question 1 (Essay Worth 10 points) (01.02 MC) Part A: If (26)x = 1, what is the value of x? Explain your answer. (5 points) Part

katen-ka-za [31]

Answer:

See Explanation

Step-by-step explanation:

The question is not clear. However, I will treat the question as:

$(26)x = 1$

$(50)x = 1$

and:

$(2^6)^x = 1$

$(5^0)^x = 1$

Solving: $(26)x = 1$ and $(50)x = 1$

$(26)x = 1$

Divide both sides by 26

$x = \frac{1}{26}$

$(50)x = 1$

Divide both sides by 50

$x = \frac{1}{50}$

Solving $(2^6)^x = 1$ and $(5^0)^x = 1$

$(2^6)^x = 1$

Express 1 as 2^0

$(2^6)^x = 2^0$

Remove bracket

$2^{6x} = 2^0$

Cancel out 2

$6x = 0$

Divide both sides by 6

$x = \frac{0}{6}$

$x = 0$

$(5^0)^x = 1$

Express 1 as 5^0

$(5^0)^x = 5^0$

Cancel out 5^0

$x = 1$

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2 years ago

Ann [662]

1) The accumulated amount after six years and the total interest that Trevor will receive if the interest rate is 4.5% per annum simple interest after 6 years are <u>R25,400</u> and <u>R5,400</u> respectively.

2) The accumulated amount after six years and the total interest that Trevor will receive if the interest rate is 4.5% per annum compound interest after 6 years are<u> R26,045.20</u> and <u>R6,045.20</u> respectively.

<h3>Data and Calculations:</h3><h3>Simple Interest:</h3>

Principal = R20,000

Investment period = 6 years

Interest rate = 4.5%

Simple interest for 6 years = R5,400 ($20,000 x 6 x 4.5%)

Principal + Interest = R25,400 (R20,000 + R5,400)

<h3>Compound Interest:</h3>

Principal = R20,000

Investment period = 6 years

Interest rate = 4.5%

N (# of periods) = 6 years

I/Y (Interest per year) = 4.5%

PV (Present Value) = R20,000

PMT (Periodic Payment) = R0

<u>Results</u>:

FV = R26,045.20

Total Interest = R6,045.2

Learn more about simple and compound interests at brainly.com/question/3575751

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1 year ago

Is it possible for a system to have more than one solution? Explain your answer

Anastasy [175]

A linear system can have infinite solutions if both systems represent the same line. if a linear system down not represent the same line then it can only have one or no solutions. No solution is if the system is representing parallel lines and one solution represents an intersection of the two lines. in a nonlinear system you can have infinite or up to a maximum of intersections as the highest degree of the systems.

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2 years ago