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3 years ago

Ten less than three times the sum of a number and five is equal to twenty-nine. What is the number ?

1 answer:

3 0

Hello!
So the following would be your equation.
3(x+5)-10= 29
Your first step would be to use the Distributive Property based upon PEMDAS (Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction). Since we have Parenthesis, we distribute first.
3(x+5)-10=29
^ ^
——————
So, your new equation would be—
3x+15-10=29
Now, you need to combine like terms—
15-10=29
3x+5=29
——————
Therefore your new equation is—
3x+5=29.
Now you need to move the constants (5,29) to one side of the equal sign. To do this, you would use the Subtraction Property of Equality and rid the 5–
3x+5=29
-5 -5
——————
Your equation is now—
3x=24.
Finally, you need to remove the 3 from x. This means you must use the Division Property of Equality, and rid the 3.
3x=24
— —
3 3
Your solved equation is—
X=8

Hope this helped!
~KayEmQue

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A movie theatre marks up the price of popcorn 12 3/4 times the original cost. express 12 3/4 as a percent and decimal.

horrorfan [7]

Answer:

Answer: F. 1,275% and 12.75.

Step-by-step explanation:

Ratios

Ratios are usually expressed as decimals, fractions, colon notation, and percentages.

For example, if the ratio of two quantities is 2, it can be expressed as:

2, 2/1, 2:1, 200%

To obtain the percentage expression, just multiply by 100%.

The price of the popcorn sold at a movie theatre was marked up as 12 3/4 times the original cost.

The mixed fraction can be converted to a decimal by just adding their parts as follows:

12 + 3/4 = 12.75

Now to express it as a percentage, multiply by 100%:

12.75 * 100% = 1,275%

Answer: F. 1,275% and 12.75.

4 0

3 years ago

The height of one solid limestone square pyramid is 21 m. A similar solid limestone square pyramid has a height of 30 m. The vol

Elina [12.6K]

Answer:

Part a) The scale factor of the smaller pyramid to the larger pyramid in simplest form is $\frac{7}{10}$

Part b) The ratio of the volume of the smaller pyramid to the larger pyramid is $\frac{343}{1,000}$

Part c) The volume of the smaller pyramid is $4,116\ m^{3}$

Step-by-step explanation:

Part a) The scale factor of the smaller pyramid to the larger pyramid in simplest form

we know that

If two figures are similar, then the ratio of its corresponding sides is equal and this ratio is called the scale factor

Let

z----> the scale factor

x----> the height of the smaller pyramid

y----> the height of the larger pyramid

$z=\frac{x}{y}$

substitute the values

$z=\frac{21}{30}$

Simplify

$z=\frac{7}{10}$ -----> scale factor in simplest form

Part b) Ratio of the volume of the smaller pyramid to the larger pyramid

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

Let

z----> the scale factor

x----> the volume of the smaller pyramid

y----> the volume of the larger pyramid

$z^{3}=\frac{x}{y}$

we have

$z=\frac{7}{10}$

substitute

$\frac{7}{10}^{3}=\frac{x}{y}$

Rewrite

$\frac{x}{y}=\frac{343}{1,000}$ -----> ratio of the volume of the smaller pyramid to the larger pyramid

Part c) The volume of the smaller pyramid

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

Let

z----> the scale factor

x----> the volume of the smaller pyramid

y----> the volume of the larger pyramid

$z^{3}=\frac{x}{y}$

we have

$z=\frac{7}{10}$

$y=12,000\ m^{3}$

substitute the values and solve for x

$(\frac{7}{10})^{3}=\frac{x}{12,000}$

$x=\frac{343}{1,000}(12,000)=4,116\ m^{3}$

8 0

3 years ago

Which answer choice shows that the commutative property does not hold for matrix multiplication?

Bess [88]

Given:

The matrix statements in the options.

To find:

The answer choice that show the commutative property does not hold for matrix multiplication.

Solution:

We known that matrix multiplication is not commutative. if A and B are two non-zero matrices, then

$AB\neq BA$

Let us assume,

$A=\begin{bmatrix}-1&-8\\-3&-5\end{bmatrix}\text{ and }B=\begin{bmatrix}1&3\\8&5\end{bmatrix}$

According to the above property of the matrix, we get

$\begin{bmatrix}-1&-8\\-3&-5\end{bmatrix}\begin{bmatrix}1&3\\8&5\end{bmatrix}\neq \begin{bmatrix}1&3\\8&5\end{bmatrix}\begin{bmatrix}-1&-8\\-3&-5\end{bmatrix}$

Therefore, the correct option is B.

3 0

3 years ago

7(2a+1) -4 (8a+3) plz help

maksim [4K]

Answer:

.7(2a +1) - 4(8a +3)

14a + 7 - 32a + 3

14a - 32a +7+3

= -18a + 10

Step-by-step explanation:

hello

hope that will help you

4 0

4 years ago

How do I solve this problem?

timofeeve [1]

Cross multiply

4n = 3 x 20

4n = 60

n = 15

8 0

3 years ago