Evaluate the expression.

Answer:

9y

Step-by-step explanation:

[tex]\bullet\; \tt{(3y)^2} = 3^2y^2 = 9y^2}[/tex]

[tex]\bullet\; \tt y^{-1} = \dfrac{1}{y}\\\\\bullet\;(3y)^2 \times y^{-1} = 9y^2 \times \dfrac{1}{y } = \dfrac{9y^2}{y}\\\\\\bullet \tt \dfrac{y^2}{y} = y\\\\\tt \bullet \dfrac{9y^2}{y} = 9y[/tex]

Model is same shape as original with scale factor 2:9.

Ratio of

a. Surface area of model and original is 4:81.

b. Height of model and original is 2:9.

c. Volume of model and original is 8:243.

As given,

Scale factor (a: b)=2:9

Ratio of model and original for

a. Surface area =a²: b²

                         =4:81

b. Height=a :b

              =2:9

c. Volume=a³ :b³

                =8:243

Therefore, model is same shape as original with scale factor 2:9.

Ratio of model and original for

a. Surface area is 4:81.

b. Height  is 2:9.

c. Volume is 8:243.

The complete question is :

A designer builds a model of a canoe. the finished model is exactly the same shape as the original, but smaller. the scale factor is 2:9.

(a) find the ratio of the surface area of the model to the surface area of the original. (b) find the ratio of the height of the model to the height of the original. (c) find the ratio of the volume of the model to the volume of the original.

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Answer:

810

Step-by-step explanation:

382.50-180= 202.5

202.5 / 0.25= 810

Hope this helps!

Answer:

810 miles

Step-by-step explanation:

$180 a week is the fixed cost so we subtract this first.

($382.50 - $180 = $202.50)

The number left is the amount of dollars charged per mile.

So if we divide this number by $0.25, we get how many miles travelled.

($202.50 ÷ $0.25 = 810 miles)

Answer:

169

Step-by-step explanation:

Answer:

Assume x to be the number of snow globe kits that come in each box.

Then the equation that describes the given situation is

13x - 10 = 172

13x = 182

x = 14

So, the number of snow globe kits that come in each box is 14.

Use a decimal number to fill in the blank. a 16 input mux has 4  select lines.

What is a decimal number?

How do you write decimal numbers?

To write a decimal in word form, follow these steps:

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Answer:

Step-by-step explanation:

Ans:

−

0.6

Alexandra could make 24 scarves if she spent the whole time knitting, by unitary method.

A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary method.

Now,

Refer to the image attached for the values and information.

Hence, Alexandra could make 24 scarves if she spent the whole time knitting, by unitary method.

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Answer:

34-5=29

Step-by-step explanation:

Answer:

29

Step-by-step explanation:

hope it helps and have a nice day! :)

Answer:

-5+12=7

Step-by-step explanation:

7-12=-5

Answer:

-5

Step-by-step explanation:

x + 12 = 7

x + 12 - 12 = 7 - 12

x = -5

Answer: 13 pieces

Step-by-step explanation:

4 m * 100 cm/1 m=

4 * 100/1=

4*100=400 cm.

400/30=

(10+390)/30=

10/30 + 390/30=

1/3 + 13 ==> 13 pieces

Work Shown:

1 meter = 100 cm

4 meters = 400 cm

400/30 = 13.33 approximately

That rounds down to 13

You'll have 400-13*30 = 400-390 = 10 cm of ribbon leftover.

The inverse function of f(x) = (x + 2)/(x - 3) is given as follows:

[tex]f^{-1}(x) = \frac{3x + 2}{x - 1}[/tex]

The function in this problem is defined as follows:

f(x) = (x + 2)/(x - 3).

Using the notation y = f(x), it is given as follows:

y = (x + 2)/(x - 3).

To obtain the inverse, the first step is exchanging the variables x and y, as follows:

x = (y + 2)/(y - 3).

Now the variable y must be isolated to obtain the inverse function, as follows:

xy - 3x = y + 2

xy - y = 3x + 2

y(x - 1) = 3x + 2

y = (3x + 2)/(x - 1).

Hence the inverse function is given by:

[tex]f^{-1}(x) = \frac{3x + 2}{x - 1}[/tex]

Meaning that the fourth option is correct.

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Based on the triangle sum theorem:

20° + (y - 10)° + 4y° = 180

y = 34

The triangle sum theorem states that if we add up all the three interior angles in a triangle, the sum we would get would be equal to 180 degrees.

Given the following are interior angles of a triangle:

Based on the triangle sum theorem, we have the following equation:

20° + (y - 10)° + 4y° = 180

Solve for y

20 + y - 10 + 4y = 180

10 + 5y = 180

5y = 180 - 10

5y = 170

5y/5 = 170/5

y = 34

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Answer:

Graph the solution to this inequality on the number line.

0.3(x − 4) > -0.3

Step-by-step explanation:

Her change in account is x - 75 dollars.

She makes 3 withdrawals of $25.

Her change in account can be calculated as follows:

Therefore, let's find her change in her account,

Let us say she had x dollars in her account.

She withdraws 25 dollars on three occasions.

Therefore,

total withdrawer = 25 × 3

total withdrawer = 75 dollars

Therefore,

Her change in account = x - 75

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Answer:

Step-by-step explanation:

1. 25x3

2.75

Tau is correct, the sum between -(1 ³/₄) and (2 ¹/₂) is equal to the difference between (2 ¹/₂) and (1 ³/₄)

Remember that the sum between a number A and a negative number -B is written as:

A + (-B)

And that is equal to the difference between A and B.

A - B

In this case, Tau says that the sum between:

-(1 ³/₄) and (2 ¹/₂)

Is written as:

(2 ¹/₂) + (-(1 ³/₄) )

(2 ¹/₂)  - (1 ³/₄)

And, using the above property, we conclude that this is equal to the difference between (2 ¹/₂) and  (1 ³/₄)

So Tau is correct.

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The simplified equation of the X/3 ≥-33 is will be X ≥ -99.

Solving a math problem is another way of saying simplifying an expression. When you simplify an expression, you are attempting to write it in the most straightforward manner feasible. Finally, no more adding, subtracting, multiplying, or dividing should be required.

To make anything simpler or simpler to reduce it to the fundamentals. to reduce in scope or complexity: to streamline management procedures.

Given  = X/3>-33

This can be written as:

X/3 ≥-33

X ≥ -33 * 3

X ≥ -99

The simplified equation of the X/3 ≥-33 is will be X ≥ -99.

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Answer:135

Step-by-step explanation:6075/45=135 hope this helps

Answer:

135

Step-by-step explanation:

Let x be the number of sessions.

Create an equation.

45x=6075

Divide 45 from both sides.

x=135

135 practice sessions.

Hope this helps! :)

The quotient of the equation (-y5 - 9y) = y

The term "quotient" is used frequently in mathematics, and it may also refer to a fraction or a ratio as well as the integer portion of a division (in the case of Euclidean division)[2] (in the case of proper division). In the Euclidean division sense, and in the proper division sense, the quotient is "6 with a remainder of 2" when 20 (the dividend) is divided by 3 (the divisor). A quotient in the second meaning is only the proportion of a dividend to its divisor.

According to the given value,

-y*5-9y=y

Mutiply

-5y-9y=y

Combine like terms

-14y=y

Rearrange the terms

-14y -y= O

Combine the terms

-15y =O

divide on both sides

y=o

Hence , the Quotient is 0.

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Answer:

72

Step-by-step explanation:

This is clearly multiplication so all you have to do is multiply 24 x 3 and your answer is There are 72 subscribers in week 24

The result of the operation is -27 < -18 and the result is true

The inequality expression is given as:

-15 < -6

The operation on the inequality expression is given as:

Subtract 12 from both sides of the inequality.

So, we start by subtracting 12 from both sides of the above inequality

This is represented as

-15 - 12 < -6 - 12

Evaluate the difference

So, we have

-27 < -18

The above inequality is true because -27 is less than -18

Hence, the result of the operation is -27 < -18 and the result is true

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The truck driver drive 36.61 miles per hour .

It is given that a truck driver drove 119 miles in 3 1/4 hours .

On simplifying the time , we get

[tex]3\frac{1}{4} =\frac{3\times4+1}{4}\\\\ 3\frac{1}{4} =\frac{13}{4}[/tex]

which means that truck driver drove 119 miles in [tex]\frac{13}{4}[/tex] hours .

Using unitary method , we get

[tex]\frac{13}{4}[/tex] hours is taken by driver to complete = 119 miles

1 hour is taken by driver to complete [tex]=\frac{119\times4}{13} \\[/tex]

                                                                [tex]=36.61 \ miles[/tex]

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Answer: 16

Step-by-step explanation:

Let's say x=Geometric mean.

4*64=x*x

x*x=256    

x^2=256

x=16

The difference between depths in January and July is equal to: D. 16 feet.

An absolute value function can be defined as a type of function that consist of an algebraic expression, which placed within absolute value symbols

In order to determine the difference between depths, we would calculate the magnitude of the depth for each of the month.

For January, we have:

January depth = 20 - 6

January depth = 14 feet.

For July, we have:

July depth = 20 - 22

July depth = -2 feet.

Now, we can calculate the difference between depths in January and July:

Difference = 14 - (-2)

Difference = 14 + 2

Difference = 16 feet.

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Answer:

[tex]15 \frac{1}{6}=15.167\:\:\sf(nearest\:thousandth)[/tex]

Step-by-step explanation:

[tex]15 \frac{1}{6}=15+\dfrac{1}{6}[/tex]

Convert ¹/₆ into a decimal by using long division:

[tex]\large \begin{array}{r}0.1\:6\:6\phantom{..}\\6{\overline{\smash{\big)}\,1. 0 \:0\: 0\: \phantom{.}}}\\{-~\phantom{(}\underline{0.6\:0\phantom{-)}}\\0.4\:0\:\:\phantom{))}\\-~\phantom{()}\underline{0.3\:6\:\:\phantom{))}}\\0.0\:4\:0\:\:\phantom{}\\-~\phantom{()}\underline{0.0\:3\:6\:\:\phantom{}}\\0.0\:0\:4\:\:\phantom{}\\\end{array}[/tex]

Therefore, ¹/₆ = 0.166666.....

[tex]\begin{aligned}\implies 15 \frac{1}{6} & =15+\dfrac{1}{6}\\\\& = 15 + 0.166666...\\\\& = 15.166666...\\\\& = 15.167\:\:\sf(nearest\:thousandth)\end{aligned}[/tex]

Answer:

15

Step-by-step explanation:

30 ÷ 2 = 15

to check, 15 × 2 = 30

Answer: D

Step-by-step explanation: 2.50xb=80 b= 32 boxes

The new balance in her account will be $150.

We have Alessa.

We have to find the new balance of her account after receiving four $-25 charges.

Account is referred here as a bank account used for the purpose of saving money by the people.

According to the question -

Initial money in Alessa's account = $50

Total money received = $25 x 4 = $100

Therefore, the new balance in her account will be -

$50 + $25 x 4 = $150

Hence, the new balance in her account will be $150.

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Answer:

B

Step-by-step explanation:

9+(−2)^3

=9+ −8

=1

Answer:

b is your answer