Which is equivalent to 2 to the fourth power

Answer:

Part a) [tex]\frac{AB}{A'B'}=\frac{BC}{B'C'} =\frac{AC}{A'C'}[/tex]

Part b) The dilation is an enlargement, because the sides of the image are larger than the sides of the original figure.(the scale factor is greater than 1)

Part c) The scale factor is [tex]3[/tex]

Step-by-step explanation:

Part a) Write the similarity statement

we know that

If two figures are similar, then the ratio of its corresponding sides is equal

so

[tex]\frac{AB}{A'B'}=\frac{BC}{B'C'} =\frac{AC}{A'C'}[/tex]

substitute the values

[tex]\frac{9}{27}=\frac{12}{36} =\frac{15}{45}[/tex]

[tex]\frac{1}{3}=\frac{1}{3} =\frac{1}{3}[/tex] ----> is true

therefore

the figures are similar

Part b) The dilation is an enlargement, because the sides of the image are larger than the sides of the original figure. (the scale factor is greater than 1)

Part c) we know that

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

Let

z------> the scale factor

x-----> corresponding side of the image

y------> corresponding side of the original figure

so

[tex]z=\frac{x}{y}[/tex]

we have

[tex]x=A'B'=27\ units[/tex]

[tex]y=AB=9\ units[/tex]

substitute

[tex]z=\frac{27}{9}=3[/tex]

The scale factor is greater than 1

therefore

Is an enlargement

It is a geometric sequence but not an arithmetic sequence. So the answer is B

Answer:

A

Step-by-step explanation:

B doesn't work because you can have people who are in a band and not in a band at the same time, which is showing in the first spot

Answer: Option 'a' is correct.

Step-by-step explanation:

Since we have given that

Number of students asked in a survey = 60

Number of students who play an instrument = 35

Number of students who are in band = 30

Number of students who are not in band = 30

So, the two way frequency table would be :

                                          Play instrument     Not play instrument    Total

In band                                       30                             0                           30

Not in band                                  5                             25                          30

Total                                          35                             25                           60

Hence, option 'a' is correct.

Answer:

10 carrots and 5 potatoes

Step-by-step explanation:

1) 15÷6=2.5

2)4 x 2.5=10

3)2 x 2.5=5

Answer:

Step-by-step explanation:

The first and the last of these functions are exponential functions.  Such functions can be recognized by the constant base and variable exponent found in each:  3^x, (5)^x, in this particular problem.

5x^2 is not an expo function because the base is not constant; this is called a power function.

the exponential function is f(x) = 3^x and 3(5)^x. Therefore, option a and d both are the correct answer.

The correct answers are f(x) = 3^x (choice A) and f(x) = 3(5) (choice D) for exponential functions, then it means you're considering a constant function (f(x) = 3(5)) as a simple form of an exponential function where the base is 3 and the exponent is 5.

This is a valid interpretation, but typically exponential functions are written as f(x) = a^x, where 'a' is a constant, and 'x' is the variable in the exponent.

In this case, if you're considering f(x) = 3(5) as an exponential function, it represents a specific case with a constant exponent.

So, both A and D can be considered as exponential functions depending on the context of the question.

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Answer:

(-x+7) (-2x+5) are the factor of 2x²-19x+35=0

Answer:

0.78

Step-by-step explanation:

"The probability that a family with 5 children will have at least 2 boys" is equivalent to the complement 1 - P(family will have 1 or 0 boys).

We can use a calculator with statistical functions built in to calculate this probability.  The function needed is for binomial probability:  binom(n, p, x).

P(family will have 1 or 0 boys) = binomcdf(5, 0.5, {0, 1} ) produces two results:  one the probab. of having 0 boys and one the probab. of having 1 boy:  0.03125 and 0.1875.  We add these together, obtaining 0.21875.

Then we subtract this result from 1 to obtain The probability that a family with 5 children will have at least 2 boys:  1 - 0.21875 = 0.78125, which may be reasonably rounded off to 0.78.

Answer:

81.3%.

Step-by-step explanation:

This is  Binomial probability.

Prob( Getting 1 boy) = 5C1 (1/2)^5

= 0.156

Prob ( Getting all girls = 5C5  (1/2)^5

= .031.

So Prob( at least 2 boys = 1 - (0.156 + 0.031)

= 0.813

= 81.3%.

Answer:

Step-by-step explanation:

H=7+30t-16t²

20=-16t²+30t+7

0=-16t²+30t-13

T=(-30±√(900-4(16)13))/-32

T=0.68 s or T=1.2 s

Answer:

Step-by-step explanation:

Answer:

[tex]\frac{x}{4}-\frac{111}{4}\\x=2y+7[/tex]

I'm pretty sure this is correct!

Answer:

(- 97, - 52)

Step-by-step explanation:

given the 2 equations

x - 4y = 111 → (1)

2y - x = - 7 → (2)

Rearrange (1) expressing x in terms of y by adding 4y to both sides

x = 111 + 4y → (3)

Substitute x = 111 + 4y into (2)

2y - (111 + 4y ) = - 7 ← distribute and simplify left side

2y - 111 - 4y = - 7

- 2y - 111 = - 7 ( add 111 to both sides )

- 2y = 104 ( divide both sides by - 2 )

y = - 52

Substitute y = - 52 into (3) for corresponding value of x

x = 111 + 4(- 52) = 111 - 208 = -97

Solution is ( - 97, - 52 )

Answer:

2(x-4) = 5

Step-by-step explanation:

2(x-4) = 5 since the difference of a number and 4 translates to x-4 and twice the difference translates to 2(x-4).

The required equation is, 2(x-4) = 5

It is a mathematical statement which contains two algebraic expressions on both sides of an ' = ' sign.

Equation shows the equality between the expressions in left hand and right hand side.

According to the problem, the variable for the unknown number = x

Now we have to establish the equation.

Difference between x & 4 = (x-4)

Twice the difference between x & 4 = 2(x-4)

Twice the difference between x & 4 is equals to 5.

∴ The equation is, 2(x-4) = 5

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Find the ratio of the known sides.

6/4 = 1.5

The larger triangle is 1.5 times larger than the smaller one.

Area is in square units, so to find the area of the larger triangle square the ratio and multiply that by the area of the known triangle.

1.5^2 x 40 = 90 square cm.

Answer:  The correct answer is -2,5/2 which is the last answer.

Step-by-step explanation:

* Hopefully the work below helps:)Mark me the brainliest:)!!

Answer:   [tex]\bold{\{-2, \dfrac{5}{2}\}}[/tex]

Step-by-step explanation:

2x² - x - 10 = 0

Replace -x with 4x - 5x and factor using Grouping Method:

2x² + 4x  -5x - 10   = 0

2x(x + 2)  -5(x + 2) = 0

(2x - 5) (x + 2) = 0

2x - 5 = 0   and    x + 2 = 0

2x = 5         and    x = -2

x = 5/2

Answer:

C. b = -5/3

Step-by-step explanation:

9b2 + 30b + 25 =0

(3b)^2 + 30b +(5)^2  = 0  <---perfect square

(3b + 5)^2 = 0

(3b + 5) = 0

3b = -5

 b = -5/3

Answer

C. b = -5/3

Answer:

C. b = -5/3

Step-by-step explanation:

9b² + 30b + 25 = 0

We can factor: two numbers that add up to 30 and its' product is 225: 15 & 15.

So we have 9b² + 15b + 15b + 25 = 0.

We can change this to (3b + 5) (3b + 5), or (3b + 5)².

This means there is only one solution: 3b + 5 = 0.

This can be turned into 3b = -5 -> b = -5/3.

Answer:

x=1

Step-by-step explanation:

you would substitute the first equation in for the y in the second equation

x + 2x+3 =6

then you would combine the x's

3x +3 = 6

Then you would move the 3 to the other side with the six

3x =6-3       3x = 3

Then finally you would divide the three

3x/3 = 3/3   x=1

Hey there!

When x=12 the equation would look like this: 3 + 5 * 12

Therefore, the answer is 63

Hope this helps you!

God bless ❤️

xXxGolferGirlxXx

a yard = 3 feet, a foot =12 in, so 3 yardsx3 feet would be 9 feet, plus the 2 other feet, would be 11, times 12 inches, would be 132 inches.

Answer:

The correct answer is 3 yards 2 feet = 132 inches

Step-by-step explanation:

Points to remember

1 Yard = 3 foot

1 foot = 12 inches

It is given that,  3 yards 2 feet we have to convert it into inches.

To convert into inches

3 yards to feet

we have, 1 Yard = 3 foot

3 yards = 3 * 3 = 9 feet

3 yards 2 feet = 9 feet + 2 feet = 11 feet

11 feet to inches

1 foot = 12 inches

11 feet = 11 * 12 = 132 inches

Answer:

11*w=x

Step-by-step explanation:

x= the amount of money he will have after w weeks

so, 11 times the amount of weeks will give you the amount he has after any number of weeks

Answer:

A. 7

Step-by-step explanation:

count the squares

Answer:

The answer is A

Step-by-step explanation:

Each square on the grid is 1 unit, and the distance from A to B is 7 squares which is 7 units

Answer:

33.61 ft

Step-by-step explanation:

First you find the product of 3ft and 8%

3.0(0.8)=2.4

Then you find the product of 2.4 and 14years

2.4(14)=33.61

Using the formula for exponential growth, a tree that is initially 3 feet tall and grows at a rate of 8% per year would be approximately 5.23 feet tall at the end of 14 years.

To solve this problem, we can use the formula for exponential growth: Final amount = Initial amount * (1 + Growth rate) ^ Number of periods.

The initial height of the tree is given as 3 feet. This is our initial amount. The growth rate is 8% per year, so we represent this as 0.08 in our formula. The number of periods is 14 years.

So, we have:

Final height = 3 * (1 + 0.08) ^ 14

To find the final height, we multiply 3 by 1.08 raised to the power of 14. Doing the math, the tree would be approximately 5.23 feet tall at the end of 14 years, rounded to the nearest hundredth.

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Answer:

$3,450

Step-by-step explanation:

As Maria earns 15% commission, a car sale of $23,000 would lead to a $3,450 commission. This can be achieved by multiplying .15 (15% translated into a decimal) to the total car sale of $23,000.

x = commission

x = 23,000 * (.15) = 3,450

Final answer:

Maria would earn a commission of $3,450 on a sale of a car priced at $23,000, calculated by multiplying the sale amount by her 15% commission rate.

Explanation:

Maria earns a 15% commission on her car sales. If she sells a car for $23,000, her commission is calculated by multiplying the total sale amount by the commission rate. To find the commission, use the following formula:

Commission = Sale Amount × Commission Rate

Commission = $23,000 × 0.15

Commission = $3,450

Therefore, Maria would earn a commission of $3,450 on a sale of $23,000.

Answer: 11x+ 8

Step-by-step explanation:

Answer:

Option C. The cost of transporting an automobile for a charge of $1.00 per mile with a pick-up fee of $100

Step-by-step explanation:

we know that          

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

verify each case

case A) The cost of purchasing candy bars at a price of $1.25 per candy bar.      

Let

y------> the cost

x----> the number of candy bars

The linear equation that represent the situation is

y=1.25x -------> represent a proportional relationship

case B) The number of cookies produced in a factory at a rate of 1,000 cookies per hour

Let

y------> the number of cookies

x----> the number of hours

The linear equation that represent the situation is

y=1,000x -------> represent a proportional relationship

case C) The cost of transporting an automobile for a charge of $1.00 per mile with a pick-up fee of $100

Let

y------> the cost

x----> the number of miles

The linear equation that represent the situation is

y=x+100 -------> not represent a proportional relationship

case D) The cost of a field trip to a museum for a group of high school students at a cost of $10.00 per student

Let

y------> the cost

x----> the number of students

The linear equation that represent the situation is

y=10x -------> represent a proportional relationship

Answer: The answer is B.

For this case we must evaluate the following expression:

[tex]\sqrt [4] {16}[/tex]

We have by definition of properties of powers and roots that:

[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]

On the other hand, we can rewrite the 16 as:

[tex]16 = 2 * 2 * 2 * 2 = 2 ^ 4[/tex]

So:

[tex]\sqrt [4] {16} = \sqrt [4] {2 ^ 4} = 2 ^ {\frac {4} {4}} = 2 ^ 1 = 2[/tex]

ANswer:

Option D

Answer:

468

Step-by-step explanation:

The volume of a cube is V = s³. Fin the volume of each cube separately and add together for the volume all together.

The small cube has side length 5 so V = 5³ = 125.

The large cube has side length 7 since 12 - 5 = 7. So V = 7³ = 343.

Together the volume is 125 + 343 = 468

Answer:

468

Step-by-step explanation:

Since OC is perpendicular to AB, the line AB gets split evenly. So

[tex]ab = 2ac[/tex]

So AB=2*6.7=13.4

Ans: Option B, 13.4 units

Length of ab is B. 13.4 units

According to the problem,

∴ OC should bisect AB

∴ Length of AB = 13.4 units.

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[tex] \frac{2x}{y} \: x = - 28 \: y = - 7[/tex]

[tex]2( - 28) \div ( - 7)[/tex]

[tex] \frac{ - 56}{ - 7} [/tex]

[tex] = 8[/tex]

The simplification of the given expression for x= -28 and y =-7 is 8.

Usually, simplification involves proceeding with the pending operations in the expression.

Simplification usually involves making the expression simple and easy to use later.

The given expression is 2x/y.

Substiute the given values;

x= -28 and y =-7

Then, 2x / y = 2(-28) / -7

= -56 / -7

= 8

Hence, the simplification of the given expression for x= -28 and y =-7 is 8.

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Answer:

140 ft²

Step-by-step explanation:

The figure is composed of a rectangle and a triangle

note triangle has a base = 16 - 12 = 4 ft

Area = area of rectangle + area of triangle

        = (16 × 8) + ([tex]\frac{1}{2}[/tex] × 4 × 6)

        = 128 + 12

        = 140 ft²

Answer:

- 77x + 42

Step-by-step explanation:

note that (f ○ g)(x) = f(g(x)

Substitute x = g(x) into f(x)

f(g(x))

= f(7x - 4)

= - 11(7x - 4) - 2

= - 77x + 44 - 2

= - 77x + 42

Answer:

1. B

2. 2 and 1/8 cups

Step-by-step explanation:

You just had to make common denominators and then your would subtract

Answer:

1) B

2) 2 1/8 cups

Step-by-step explanation:

1) make the denominator the same so it is 5 4/12 minus 2 9/12. You get 2 7/12 which is greater than 2 1/2 (2 6/12) and smaller th an 3

2) 8 7/8 minus 6 3/4 is equivalent to 8 7/8 minus 6 6/8 which is 2 1/8

All done mentally.