What is (−11)^4 when evaluated?

Answer:   [tex]3\sqrt{6}[/tex]

Step-by-step explanation:

[tex]\sqrt{9}[/tex] × [tex]\sqrt{3}[/tex] × [tex]\sqrt{2}[/tex] = [tex]\sqrt{54}[/tex]

                    = [tex]3\sqrt{6}[/tex]

The required product of two rational numbers is 8y² - 28y + 4) / (6y² - 21y + 9).

What is a rational number?

Any real number that can be represented in the form of p/q, where q is not equal to 0 is called a rational number. The decimal expansion of rational numbers is terminating and repeating.

Calculation of the product of two rational numbers

Given two rational numbers,

8y - 4 / 10y - 5 and 5y -15 / 3y - 9

We need to multiply both the numbers i.e.

= (8y - 4 / 10y - 5) × (5y -15 / 3y - 9)

= (8y -4) × (5y - 15) / (10y - 5) × (3y - 9)

= (40y² - 140y + 20) / (30y² - 105y + 45)

= (8y² - 28y + 4) / (6y² - 21y + 9)

= (8y² - 28y + 4) / (6y² - 21y + 9)

The restriction is that the denominator, 6y² - 21y + 9 should not be 0.

Hence, the required product of two rational numbers is 8y2 - 28y + 4) / (6y2 - 21y + 9).

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The time taken to travel the distance 70 Km/h is 11 hours.

Speed tells us how fast something or someone is travelling. You can find the average speed of an object if you know the distance travelled and the time it took.

The formula can be rearranged in three ways:

Given:

time = 9 hours

speed = 85 Km/h

Now, distance

=speed * time

=85 * 9

= 765 km

As, the speed is 70 km/h

time = distance/ speed

time = 765 / 70

time = 10.92

time= 11 hours

Hence, the time taken to travel the distance 70 Km/h is 11 hours.

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The translation of the question is:

A car takes 9 hours to travel a distance with a speed of 85km/h, how long will it take to travel the same distance at 70km/h?

If Heavy Hulk is cutting their sign-up fee in half for new members. If Brett signs up at a gym today, the number of months that the cost of the memberships be the same is: 23 months.

Let x represent the number of months

Hence,

Formulate

$34.04x+24= $34.29x+(36.50/2)

Collect like terms

($34.04x -34.29x)= 24-(36.50/2)

0.25x=24-18.25

0.25x=5.75

Divide both side by 0.25x

x=5.75/0.25

x=23 months

Therefore If Heavy Hulk is cutting their sign-up fee in half for new members. If Brett signs up at a gym today, the number of months that the cost of the memberships be the same is: 23 months.

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Answer:

Step-by-step explanation: 44.

f(x)=6x-4

x=8

f(8)=6(8)-4

f(8)= 48-4

f(8)=44

The best approximation for the solution to the system of equation is option C) (-2.2 , -3)

According to the question we have been given two system of linear equation which are:

         y = -3          (1)

and   y = x - 0.8        (2)

Now solving these two equation and find the value of x

Substituting the value of y from equation (1) to the equation (2) we get

               -3 = x - 0.8

                -3 + 0.8 = x

                   x = -2.2

Thus the best approximation for the solution to the system of equation is option C) (-2.2 , -3)

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After playing 100 times the player will loose $-16.67.

Given the outcomes and the probability is:

Outcome            Probability

-$10                       1 (cost to play)

$14 draw red          5/12

$12 draw yellow      4/12

therefore, expected probability = ∑x.p(x)

x is no of trials and

p(x) is probability of the results.

E(x) = (14)5/12 + (12)4/12 + (0)3/12 - 10

E(x) = -2/12

E(x) = -10.1667

For 100 games the expected value E(100x) =

E(100x) = E(x) × 100

E(100x) = -10.1667 × 100

E(100x) = -16.67 i.e loss after game.

Hence the player lose $-16.67 after 100 games.

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Answer:

23 times 10 is

230 so your answer is 2 times 10

Answer:

Evan, Liza, Tasha, Devon

Step-by-step explanation:

A customer should buy minimum 16 boxes of pavers.

In this question, a customer is ordering brick pavers to cover a rectangular walkway that is 3 feet by 15 feet and a square sitting area that is 6 feet on a side.

First we find the total area that will be covered by  pavers.

Area of rectangle = length × width

Area of rectangle = 15 × 3

Area of rectangle = 45

And the area of square = side²

             area of square =   6²

             area of square =  36

So, the total area would be,

Total area = area of rectangle + area of square

Total area = 45 + 36

Total area = 81

So, the total area is 81 square feet.

one box of pavers covers 5.28 square feet.

So using unitary method,

81 / 5.28

= 15.534

≈ 16 boxes

This means, approximately 16 boxes will require to cover the above area.

Therefore, the customer should buy minimum 16 boxes of pavers.

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An equivalent form of 5 / ( 2 + 2 i ) is ( 5 -5 i ) / 4 [ option I ]

Given,

5 / ( 2 + 2 i )

To find its equivalent form we need to simplify the term by using the concept of conjugates.

Conjugate of a term results in opposite power of the imaginary part.

The conjugate of 2 + 2 i = 2 - 2 i

Multiply and divide the term with the conjugate

=> 5 * ( 2 - 2 i ) / ( 2 + 2 i ) * ( 2 - 2 i )

=> 10 - 10 i / 2 ² - ( 2 i ) ²                [ ( a + b ) ( a - b ) = a ² - b ² ]

=> 10 - 10 i / 4 - (-4)                        [ i ² = - 1 ]

=> 10 - 10 i / 8

=> 5 - 5 i / 4

This matches with option I

Therefore, we get an equivalent form of 5 / ( 2 + 2 i ) as ( 5 -5 i ) / 4

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Answer:

AD

Step-by-step explanation:

It is the only segment that meets a side of triangle ABC at a right angle.

Answer: The answer is $1.13.

Step-by-step explanation:

There are 12 cups inside a 3-quart container.

The solution to the system where the system contains linear equations is (59/16, -65/32)

Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

A system of linear equations is a collection of at least two linear equations.

In this case, the system of equations is given as

2x + 12y = −17

3x + 2y = 7

Multiply through 3x + 2y = 7 by 6

So, we have

18x + 12y = 42

Subtract the equation 2x + 12y = −17 from 18x + 12y = 42

So, we have

18x - 2x + 12y - 12y = 42 + 17

Evaluate the like terms

So, we have

16x = 59

Divide both sides by 16

So, we have

x = 59/16

Substitute x = 59/16 in 3x + 2y = 7

3 x 59/16 + 2y = 7

This gives

177/16 + 2y = 7

So, we have

2y = 7 - 177/16

Evaluate the difference

2y = -65/16

Divide by 2

y = -65/32

Hence, the solution to the system where the system contains linear equations is (59/16, -65/32)

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Answer:

7

Step-by-step explanation:

You have to do the square root of: (5-(-2)) squared pluse (2-2) squared

Now you have the square root of 7 squared

7 squared is 49, so you have the square root of 49

that equals 7

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Answer:

more than 6 feet  for 20 feet horizontal

Step-by-step explanation:

Increasing the rise increases the pitch

The measure of the angle that complements m∠W is 17°. Option C

Complementary angles are defined as angles that sum up to 90 degrees.

They are also called angles at right angle.

Example:

If x and y are termed complementary angles, then

x + y = 90°

From the information given, we have that;

m∠W is complementary to another unknown angle x

This is represented as;

x + m∠W = 90°

But m∠W = 73°

Substitute the value into the equation

x + 73° = 90°

collect like terms

x = 90 - 73

x = 17°

Thus, the measure of the angle that complements m∠W is 17°. Option C

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The correct option is (c) 16 daisies

If the bouquet contains 24 flowers then total 16 daisies are in the bouquet.

In mathematics, polynomial function can be defined as the equation which consist of coefficient, variables and exponents. All the equations such as quadratic equation, cubic equation which has non  negative number as their powers are part of polynomial equation.

Some examples of polynomial equation are :

Now, for the given  question,

let d = number of daisies

     t = number of tulips

according to statement polynomial equation  is,

  d + t = 24    , say equation (i)

Twice as many daisies as tulips:

  d=2t

Put the value of d in equation (i)

  2t + t = 24

  3t = 24

  t = 8

As, number of daisies = 2 (number of tulips)

Therefore, d = 2t = 2 (8) = 16

Thus,  total 16 daisies are in the bouquet.

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Answer:

I think the first

Step-by-step explanation:

Step-by-step explanation:

4-digit number abcd

a >= 2

a×b = d

so, 2 <= b <= 4 to allow a single digit result of a×b, and if b would be 1 or 0, the result would be either a copy of a or of b violating the rule that no 2 digits are the same.

that means a >= 3, because with a = 2 and b <= 4 the number can't be larger than 2500.

and that again means 2 <= b <= 3 and 3 <= a <= 4 to allow a single digit result of a×b.

the sum of "my digit" ? I guess you mean the sum of all digits is 16.

a + b + c + d = 16

so, my first guess :

a = 3

b = 2

therefore

d = 3×2 = 6

that means we have already 11 as sum of the digits, that leaves 5 for c.

so, the number would be

3256

the only alternative would start with a = 4 and then b = 2.

but that would make d = a×b = 8. abd 8 + 4 + 2 = 14, and that leaves for c only 2 to sum up to 16, and that would duplicate b.

so, 3256 is the only solution.

A composite function exists as a function that depends on another function. A composite function exists formed when one function exists substituted into another function.

The value of f(g(x)) = (2x-6)/2 and g(f(x)) =  x - 6.

In mathematics, function composition exists as an operation ∘ that takes two functions f and g, and has a function h = g ∘ f such that h(x) = g. In this operation, the function g exists used to the result of applying the function f to x.

Function composition is a mathematical procedure where two functions, f, and g, are taken and a function, h = g ∘ f, is produced such that h(x) = g(f(x)). The function g exists used in this operation on the outcome of applying the function f to x.

Let the given functions be f(x) = x-3/2 and g(x) = 2x - 3

f(g(x)) = f(2x-3)

simplifying the above equation, we get

f(g(x)) = f(2x-3) = ((2x-3) - 3)/2

f(g(x)) = f(2x-3) = (2x-6)/2

f(g(x)) = (2x-6)/2

g(f(x)) =  g(x-3/2)

simplifying the above equation, we get

g(f(x)) =  g(x-3/2) = 2((x-3)/2) - 3

g(f(x)) =  g(x-3/2) = x - 6

g(f(x)) =  x - 6

Therefore, the value of f(g(x)) = (2x-6)/2 and g(f(x)) =  x - 6.

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Answer:

The correct answer is 4(x-7)²-(x-7)+3.

Step-by-step explanation:

When we have captured (t*s)(x), that is as equivalent as t(s(x)). To solve this, we take the important role of s(x), x-7, and call in an alternative for it in for every x in t(x). Instead of 4x², we have 4(x-7)²; instead of -x, we have -(x-7). This gives us 4(x-7)²-(x-7)+3.

If BD = 3, then it means that CD is also equal to 3 by definition of Isosceles triangle.

We are given a triangle with the condition that BA ≅ CA. This means that side BA has a length equal to that of side CA.

Now, an Isosceles triangle is defined as a triangle that has at least two sides of equal length. This means that the given triangle ABC is an Isosceles triangle.

Now, since Triangle ABC is an Isosceles triangle, it means that when we draw a perpendicular line through the point joining the two equal sides, it bisects the third side of the triangle.

Thus, it means that BD is congruent to CD.

If BD = 3, then it means that CD is also equal to 3 by definition of Isosceles triangle.

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Answer:

Step-by-step explanation:

h

Answer: Corresponding Angles

Step-by-step explanation:

Answer:

4:1, 20:5

Step-by-step explanation:

You can determine if a ratio is equivalent by dividing each term with the respective term in the other ratio. If you come out with 1, the ratios are equivalent.

Answer:

4:1 & 20:5

Step-by-step explanation:

These two ratios are equal and true to 12:3!

Hopefully this helps have a great day! :D

Answer:

No

Step-by-step explanation:

Without any side lengths, the most three angles can determine is similarity, not congruency. This means you can determine the ratio of the lengths of the sides, but not any of the sides individually.

After 4 stops both buses will have the same amount of riders that is 27.

So, Bus A: 15 people ( +3 at every stop)

Bus B: 35 people ( -2 at every stop)

Then,

Therefore, after 4 stops both buses will have the same amount of riders that is 27.

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The function f₁(x) can be either vertical stretch or vertical compress: TRUE

Here are a few examples of logarithmic functions:

So,

Given function:

Then,

Now, Put bˣ=f(x):

We discovered that:

So, depending on the values of b and h, c can be greater than or less than one.

Therefore, the statement "the function f₁(x) can be either vertical stretch or vertical compress" is TRUE.

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Answer:

x≤−9/2 or x>7/4

Step-by-step explanation:

The correct order from best to worst of the sample groups is b→ a→ c.

The study conducted by the City Council of USA incorporates the reviewing for the funding for local sports-related activities.

There are 3 sample groups selected from the population of Anytown residents with an active interest in sports. They are:

a. High-school students at three different schools.

b. People randomly approached at a softball tournament, a swim meet, an athletic supply store, and a sports bar.

c. People randomly approached at a department store and at a shopping mall

All these groups are selected randomly.

But for (b), the people are obviously interested in sports activities, as they are selected from softball tournament, a swim meet, an athletic supply store, and a sports bar.

Next would be (a), because the students being younger is probably more interested in sports than elder ones.

The last would be the (c), people selected from the department store since they would be less aware of local- sports related activities.

So the order of samples from best to worst is b→ a→ c.

The question is incomplete. Find the complete question below:

The city council of Anytown, U.S.A., is reviewing the funding for local sports-related activities. To be better informed, it commissions a study. Order the sample groups, best to worst, based on how well they would represent the population of Anytown residents with an active interest in sports.

a. high-school students at three different schools

b. people randomly approached at a softball tournament, a swim meet, an athletic supply store, and a sports bar

c. people randomly approached at a department store and at a shopping mall

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