Simplify each rational expression. State any restrictions on the variables.
x²+8 x+16 / x²-2 x-24

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.

Know more about Logarithmic Function here:

https://brainly.com/question/13473114

#SPJ4

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.

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.

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.

Know more about mathematical operations here:

brainly.com/question/20628271

#SPJ9

De acuerdo a la información se puede inferir que su hijo nació en el año 22 antes de Cristo.

Una recta numérica es una herramienta gráfica de las matemáticas que nos sirve para ubicar números positivos y negativos en un gráfico con el objetivo de organizarlos con respecto al número cero.

Las líneas de tiempo con fechas Antes y Después de Cristo se pueden asociar a una recta numérica debido a que los años Antes de Cristo se ubican en la parte negativa de la gráfica (a la izquierda del cero) y los número Después de Cristo se ubican en la parte positiva (a la derecha del cero).

Para identificar el año de nacimiento del hijo debemos tener en cuenta que las fechas que se ubican en la zona negativa de la recta numérica aumentan de forma invertida, es decir que si su hijo nació 28 años después de ella se debe restar este número a su fecha de nacimiento como se muestra a continuación:

50 - 28 = 22

Entonces, el año de nacimiento de su hijo sería el año 22 Antes de Cristo.

Aprenda más sobre rectas numéricas en: https://brainly.com/question/17447899

#SPJ1

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

Learn more about Conjugate of Complex Numbers here:

https://brainly.com/question/18392150?referrer=searchResults

#SPJ9

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:

AD

Step-by-step explanation:

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

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)

Read more about linear equations at

https://brainly.com/question/14323743

#SPJ1

Considering the definition of an equation and the way to solve it, the correct answer is the third option: Cadence baked 21 cupcakes on Monday.

An equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns.

The members of an equation are each of the expressions that appear on both sides of the equal sign.

The solution of a equation means determining the value that satisfies it. To solve an equation, keep in mind:

Being "x" the number of cupcakes baked by Cadence on Monday, and knowing that:

the equation in this case is:

3 + 2x= 45

Solving:

2x= 45 -3

2x= 42

x= 42 ÷ 2

x= 21

Finally, the correct answer is the third option: Cadence baked 21 cupcakes on Monday.

Learn more about equations:

brainly.com/question/4983716

brainly.com/question/13314678

#SPJ1

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.

Answer: The problem asks to solve for x. Equation B gives you the value of y, y = 2, so you can substitute 2 into Equation A for y.

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

Learn more about sample groups at https://brainly.com/question/24466382

#SPJ4

Answer:

The weight of the popcorn is off but the potato chips are safe. Simply determine whether each value is within the limit of deviation from eachother.

Answer: The answer is $1.13.

Step-by-step explanation:

There are 12 cups inside a 3-quart container.

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 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

Learn more about complementary angles here:

https://brainly.com/question/16281260

#SPJ1

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.

Learn more about speed- distance here:

https://brainly.com/question/25422529

#SPJ1

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?

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.

To know more about polynomial functions, visit:

brainly.com/question/17822016

#SPJ4

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.

Learn more about number of months here:https://brainly.com/question/1292807

#SPJ1

The correct option is (b) square root 112 units

By using Pythagoras theorem,

where a & b = legs of triangle and c = hypotenuse

Hence:

Answer:

Evan, Liza, Tasha, Devon

Step-by-step explanation:

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

*Don't forget to mark brainliest

Answer:

Step-by-step explanation:

h

Answer: Corresponding Angles

Step-by-step explanation:

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.

Read more about Length of triangle at; https://brainly.com/question/2217700

#SPJ1

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.

Learn more about Expected value here:

brainly.com/question/24855677

#SPJ9

Answer:

more than 6 feet  for 20 feet horizontal

Step-by-step explanation:

Increasing the rise increases the pitch

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)

Learn more about solution to equation here : https://brainly.com/question/13729904

#SPJ9

Answer:

23 times 10 is

230 so your answer is 2 times 10

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).

To learn more about rational numbers, visit here:

https://brainly.com/question/12088221

#SPJ4