Barry’s Burger Barn opened 25 franchises in its first year of operation. The second year, they opened 30 additional franchises. They opened 35 more in the third year and 40 more in the fourth year. If this pattern holds for all future years, perform the following: a. Determine how many franchises Barry’s will open each year in year 5, year 14, and year 26. Explain how you did this. b. Determine how many total franchises Barry’s will have in operation in year 10, year 22, and in year 50. Explain how you did this. c. How did you determine your answers? (Relate the relevant information in the story problem above to your calculations.)

The domain of the linear function is a real number, and the range of the linear function is also a real number.

The domain means all the possible values of x and the range means all the possible values of y.

The table is given below.

  x               y

 -4              5

 -2              3

  0              1

  2             -1

  4             -3

Then the linear function will be

y – 1 = [(5 – 1) / (- 4 – 0)] (x – 0)

y – 1 = -x

x + y = 1

Then the domain of the linear function is a real number and the range of the linear function is also a real number.

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The expression 1/7 – 3(3/7n – 2/7) is equivalent to the expression 1 – 9/7n.

The equivalent is the expressions that are in different forms but are equal to the same value.

The expression is given below.

⇒ 1/7 – 3(3/7n – 2/7)

On simplifying the expression, we have

⇒ 1/7 – 9/7n + 6/7)

⇒ 1 – 9/7n

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Answer:

-9/7 n + 1

Step-by-step explanation:

On khan

Answer: 360

Step-by-step explanation: 6 times 6 times 10 = 360

3) [tex]3(2x-6)=\boxed{6x-18}[/tex]

4) [tex]2x(5x+11)=10x^{2}+22x[/tex]

Answer:

y = -x +1

Step-by-step explanation:

p1 (-3,4)

p2 ( 3, -2)

line equation y = mx + b

The slope m equals

[tex] \frac{y2 - 21}{x2 - x1} [/tex]

[tex] \frac{ - 2 - 4}{3 - - 3} = \frac{ - 6}{6} = - 1[/tex]

y = - x + b

from any point

-2 = -3 + b

b = 1

line equation = y = -x +1

Answer:

Answer:

(3*6) - (6/2) = 15

Step-by-step explanation:

3 and 6 are being multiplied by them selves, and then subtracted by the answer of 6/2.

The answer of the equation is 15.

To find the zeros of a rational function, we must identify values of x that make the numerator equal to 0. We can do this by factoring and by keeping in mind the zero-product property.

The zero-product property states that if the product of two terms is 0, then one of the terms must be equal to 0.

We're given:

[tex]f(x)=\dfrac{4x^2-36x}{x-9}[/tex]

First, factor 4x out of the numerator:

[tex]f(x)=\dfrac{4x(x-9)}{x-9}[/tex]

Let f(x) = 0:

[tex]0=\dfrac{4x(x-9)}{x-9}[/tex]

In this case, either x or (x-9) is equal to zero, as they are the two terms being multiplied in the numerator to get 0 as a product.

This makes the x-intercepts of this function 0 and 9.

However, the denominator in this function is x - 9. If x = 9, then it would make the denominator 0, which is not allowed. Therefore, x cannot equal 9, and the only x-intercept is 0.

x = 0

Answer:

23

Step-by-step explanation:

area of a trapezoid = 1/2 × (a + b) × h

so, we have

96 = 1/2 × ((4x - 1) + (x + 3)) × 6 = (5x + 2) × 3

32 = 5x + 2

30 = 5x

x = 6

a = 4x - 1 = 4×6 - 1 = 24 - 1 = 23

The greatest common factor for the numerical part will be 2.

The greatest common factor, as the name implies, is the greatest among all common factors among the quantities given.

We can factorize the quantities in the smallest relative factors possible (one level of factors over which all quantities can form themselves), and collect as many common factors as we could.

Those will together compose GCF(The greatest common factor).

Given;

[tex]6x^2-8+22[/tex]

Since the expression contains both numbers and a variable part.

For numerical parts 6, -8, 22

The factors are

6 = -6, -3. -2, -1,1, 2, 3 , 6

8 = -8, -4, -2, -1,1, 2, 4, 8

22 = -22, -11, -2, -1,1, 2, 11, 22

The greatest common factor for the numerical part will be 2.

The number part does not contain any common variable factor.

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Therefore, the incorrect statement is option B, which states that 28 pounds is equal to 44 dollars. The correct value should be 42 dollars.

To determine which statement is incorrect, we can use the given conversion rate of 2 pounds being equal to 3 dollars and evaluate each option accordingly:

A. 11 pounds is 16.50 dollars:

To check this, we can multiply 11 pounds by the conversion rate:

11 pounds * (3 dollars / 2 pounds) = 16.50 dollars

This statement is correct.

B. 28 pounds is 44 dollars:

Using the same calculation:

28 pounds * (3 dollars / 2 pounds) = 42 dollars

This statement is incorrect because 28 pounds would actually be equal to 42 dollars, not 44 dollars.

C. 10 pounds is 15 dollars:

Again, applying the conversion rate:

10 pounds * (3 dollars / 2 pounds) = 15 dollars

This statement is correct.

D. 23 pounds is 34.50 dollars:

Using the conversion rate:

23 pounds * (3 dollars / 2 pounds) = 34.50 dollars

This statement is correct.

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Answer:

B and D

Step-by-step explanation:

A is not a intersecting angles they are like doodles, B makes intersecting lines, C doesnt intersect properly its only like a Y with and extra angle and D is absolutely perfect. So, thats why its B and D

The slope- intercept is y> (1-4x) / 5 and y< 2x + 6

A  statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

Given:

4x – 5y < 1  and 1/2y – x < 3

Solving

4x – 5y < 1

-5y < 1- 4x

-y < (1-4x) / 5

y> (1-4x) / 5

Now, the second inequality,

1/2y – x < 3

1/2y< 3+x

y< 2x + 6

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Answer:

t = 2

Step-by-step explanation:

Look at the fraction on the left, 1/3.

Notice that the denominator is 3 times the numerator.

Since the fractions are equal, for the second fraction, you also need the denominator to be 3 times the numerator. Since the denominator is 6, the numerator must be 2 since 6 is 3 times 2.

Answer: t = 2

Of course, since you have two fractions that are equal, and fractions are also ratios, you have a proportion.

You can solve the problem as a proportion.

1/3 = t/6

Cross multiply:

3t = 1 × 6

3t = 6

t = 6/3

t = 2

Either way, you get t = 2.

The correct option is an open circle at 5 and a bold line starts at 5 and is pointing to the right.

The given inequality is -3(2x-5)<5(2-x).

Inequality is a declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to.

At first simplify each side

LHS of inequality -3(2x - 5) = -3(2x) + -3(-5) [∵(-)(-) = (+)]

⇒ -3(2x - 5) = - 6x + 15

Now, RHS of the inequality 5(2 - x) = 5(2) + 5(-x) [∵(+)(-) = (-)]

⇒ 5(2 - x) = 10 - 5x

Now, - 6x + 15 < 10 - 5x

Subtract 15 from both sides

That is, - 6x < -5 - 5x

Add 5x to both sides

That is, - x < - 5

Remember the coefficient of x is negative, and then when you divide both sides by it you must reverse the sign of inequality.

Now, the coefficient of x is -1

So, divide both sides by -1

Then, x > 5.

Hence, the correct option is an open circle at 5 and a bold line starts at 5 and is pointing to the right.

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Let that angle be x

Linear pairs are supplementary

So

Answer:

Each student ticket costs $10, and each adult ticket costs $17.

Step-by-step explanation:

Let s represent the cost of a student ticket and a represent the cost of an adult ticket.

31s + 32a = 854

31s + 31a = 837

----------------------

a = 17

31s + 31(17) = 837

31s + 527 = 837

31s = 310, so s = 10

Answer:

x=10

Step-by-step explanation:

Using proportions, it is found that the value of the total sum that was shared was of $45.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Considering the rates, Anne's and Kerisha's proportions, out of the total value N, are given by:

The difference is of $15, hence:

[tex]A - K = 15[/tex]

[tex]\frac{7N}{12} - \frac{3N}{12} = 15[/tex]

[tex]\frac{4N}{12} = 15[/tex]

[tex]\frac{N}{3} = 15[/tex]

N = 15 x 3 = 45

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An equation is formed when two equal expressions. The value of k that makes the equation true is 4.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The value of k that will make the equation true is,

[tex]5a^2b^3(6a^kb)=30a^6b^4\\\\30\ a^{(2+k)}\ b^{(3+1)} = 30\ a^6\ b^4\\\\30\ a^{(2+k)} \ b^4 = 30\ a^6\ b^4\\\\a^{(2+k)} =a^6\\\\2+k = 6 \\\\ k = 4[/tex]

Hence, The value of k that makes the equation true is 4.

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Answer:

A

Step-by-step explanation:

she worked a total of 34 hours , then

x + y = 34

earnings are $10 per hour babysitting , that is 10x for x hours

$15 per hour for yardwork, that is 15y for y hours

she made a total of $410 , then

10x + 15y = 410

system of equations is

x + y = 34

10x + 15y = 410

Answer:

1. m∠R > 90°

2. m∠S + m∠T < 90°

4. m∠R > m∠T

5. m∠R > m∠S

Step-by-step explanation:

Helpful fact:  Recall that the Triangle Sum Theorem states that m∠R + m∠S + m∠T = 180°.

Option 1.  m∠R > 90°

Start with m∠R > m∠S + m∠T.

Adding m∠R to both sides of the inequality...

m∠R + m∠R > m∠R + m∠S + m∠T

There are two things to note here:

2* m∠R > 180°

Dividing both sides of the inequality by 2...

m∠R > 90°

So, the first option must be true.

Option 2.  m∠S + m∠T < 90°

Start with m∠R > m∠S + m∠T.

Adding (m∠S + m∠T) to both sides of the inequality...

m∠R + (m∠S + m∠T) >  m∠S + m∠T + (m∠S + m∠T)

There are two things to note here:

Substituting

180° > 2* (m∠S+m∠T)

Dividing both sides of the inequality by 2...

90° > m∠S+m∠T

So, the second option must be true.

Option 3.  m∠S = m∠T

Not necessarily.  While m∠S could equal m∠T, it doesn't have to.  

Example 1:  m∠S = m∠T = 10°;  By the triangle sum Theorem, m∠R = 160°, and the angles satisfy the original inequality.

Example 2:  m∠S = 15°, and m∠T = 10°;  By the triangle sum Theorem, m∠R = 155°, and the angles still satisfy the original inequality.

So, option 3 does NOT have to be true.

Option 4.  m∠R > m∠T

Start with the fact that ∠S is an angle of a triangle, so m∠S cannot be zero or negative, and thus m∠S > 0.

Add m∠T to both sides.

(m∠S) + m∠T > (0) + m∠T

m∠S + m∠T > m∠T

Recall that m∠R > m∠S + m∠T.

By the transitive property of inequalities, m∠R > m∠T.

So, option 4 must be true.

Option 5.  m∠R > m∠S

Start with the fact that ∠T is an angle of a triangle, so m∠T cannot be zero or negative, and thus m∠T > 0.

Add m∠S to both sides.

m∠S + (m∠T) > m∠S + (0)

m∠S + m∠T > m∠S

Recall that m∠R > m∠S + m∠T.

By the transitive property of inequalities, m∠R > m∠S.

So, option 5 must be true.

Option 6.  m∠S > m∠T

Not necessarily.  While m∠S could be greater than m∠T, it doesn't have to be.  (See examples 1 and 2 from option 3.)

So, option 6 does NOT have to be true.

Answer: Option 1, 2, 4, & 5  or  

A. m∠R > 90°;  B. m∠S + m∠T < 90°;  D. m∠R > m∠T;  & E. m∠R > m∠S

Step-by-step explanation:   Trust Me!  

If you are working on Edge the answer is correct. The proof is down below. I hope someone finds this helpful.

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Answer:

374795-57770

Step-by-step explanation:

Abby uses

The Correct Question is ......

Question :

Choose the simplified form of  the fifth term of  ⁶C₄ (2x)² (-y²)⁴

Answer: D. 60x²y⁸ is the simplified form of the fifth term of the

expansion ⁶C₄ (2x)² (-y²)⁴.

An expression is a sentence with a minimum of two numbers or variables and at least one math operation.

This math operation can be addition, subtraction, multiplication, or division.

According to the Given Expression,

⁶C₄ (2x)² (-y²)⁴

The value of the combination can be written as,

[tex]= [\frac{6!}{4!(6-4)!} ] (2x)^{2} (-y^{2})^{4}[/tex]

= 15 (4x²)  (-y²)⁴

The value of y can be written as,

= 15 (4x²)  y⁸

= 60 x²y⁸

Therefore,

The value of the expression ⁶C₄ (2x)² (-y²)⁴ is 60x²y⁸.

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Answer:

B

Step-by-step explanation:

There is 2 options, win and lose, no tie so 3 and 4 get cancelled. there are only 2 roots so 1 gets cancelled leaving 2 (B)

Graphically, we will see that the solutions of the system are (−4,2) and (2,−1)

To solve the system of equations graphically, we need to graph both of the equations and see in which points the graphs intercept.

The graph of the system can be seen below, there you can see that the intercepts are at:

(-4, 2) and (2, -1)

So these are the two solutions of the system of equations.

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Answer:

x- intercept = - 1 , y- intercept = 2

Step-by-step explanation:

the x- intercept is the value of the x- coordinate where the curve crosses the x- axis , that is

x- intercept = - 1

the y- intercept is the value of the y- coordinate where the curve crosses the y- axis , that is

y- intercept = 2

Answer:

(9, 3 )

Step-by-step explanation:

under a reflection in the y- axis

a point (x, y ) → (- x, y ) , then

(- 9, 3 ) → (9, 3 )