Trinity is going to the movies with some friends and will pay for her own ticket plus her own and her friends' small popcorns. Her total cost is given by the following expression: 8.5 + 6x What does the 6x represent?

A. The total cost of the small popcorns
B. The amount of small popcorns she is buying
C. The total cost
D. The cost of the ticket

Answer:

all work is shown and pictured

Answer:

see explanation

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

To obtain this firm use the method of completing the square

Factor out - 1 from each term

y = - (x² - 9x + 12)[tex]\frac{33}{4}[/tex]

To complete the square

add/subtract (half the coefficient of the x- term )² to x² - 9x

y = - (x² + 2( - [tex]\frac{9}{2}[/tex])x + [tex]\frac{81}{4}[/tex] - [tex]\frac{81}{4}[/tex] + 12 )

  = - ( (x - [tex]\frac{9}{2}[/tex])² - [tex]\frac{33}{4}[/tex] )

y = - (x - [tex]\frac{9}{2}[/tex] )² + [tex]\frac{33}{4}[/tex] ← in vertex form

Answer:

q = 3.636363636 repeating

Step-by-step explanation:

  - 4q + 9 = 7q - 31

   + 4q      + 4q

     9 = 11q - 31

  + 31         + 31

      40 = 11q

      [tex]\frac{40}{11} = \frac{11q}{11}[/tex]

Answer:

[tex]\large\boxed{q=\dfrac{40}{11}}[/tex]

Step-by-step explanation:

[tex]-4q+9=7q-31\qquad\text{subtract 9 from both sides}\\\\-4q+9-9=7q-31-9\\\\-4q=7q-40\qquad\text{subtract }\ 7q\ \text{from both sides}\\\\-4q-7q=7q-7q-40\\\\-11q=-40\qquad\text{divide both sides by -11}\\\\\dfrac{-11q}{-11}=\dfrac{-40}{-11}\\\\q=\dfrac{40}{11}[/tex]

Adam is carrying a total of 15.4 pounds of books to the classroom, calculated by multiplying the weight of one book (3.85 pounds) by the number of books (4).

The subject of this question is Mathematics, and it is appropriate for a middle school grade level. The student has asked about the total weight Adam is carrying when he transports four books to the classroom, with each book weighing 3.85 pounds.

To find the total weight of the books Adam is carrying, we multiply the weight of one book by the number of books:

Therefore, Adam is carrying approximately 15.4 pounds of books to the classroom.

Answer:

7

Step-by-step explanation:

12+9=21

21 divided by 3 is 7

Answer: May you please have answer choices. Please forgive me if I am being rude but I am not.

Answer:

Yes, the total price is proportional to the pounds of oranges she purchased.

Step-by-step explanation:

The price of oranges is $0.78 per pound.

So, the price $0.78 corresponds to one pound, in a way, that is called direct proportionality.

This means that the price will increase or decrease in a constant ratio, depending on the amount of pounds purchased.

For example:

If she buys 1 pound of oranges she will pay $0.78. Ratio is 0.78 (0.78/1)

If she buys 2 pounds of oranges she will pay $1.56. Ratio is 0.78 (1.56/2)

If she buys 2.5 pounds of oranges she will pay $1.95. Ratio is 0.78 (1.95/2.5)

If she buys 3 pounds of oranges she will pay $2.34. Ratio is 0.78(2.34/3)

We can see that ratio is constant, then we can say that the total price she pays is proportional to the pounds of oranged purchased.

Answer:

they are multiplicative inverses because to find the inverse of a number you change it from positive to negative or vice versa, and you have to change it to it's inverse. to do this you have to put it in fraction form if it isn't already (so 5 would be 5/1) and flip it (5/1 flipped would be 1/5)

Step-by-step explanation:

They are reciprocals, that is why they are multiplicative inverse.

If we have a number, then reciprocal of that number is called multiplicative inverse of the number.

Example : If m be a number then 1/m is its multiplicative number.

Here the number be -5.

Reciprocal of this number is -1/5

We know that reciprocal of a number is called multiplicative inverse.

So, -5 & -1/5 are multiplicative inverse of each other.

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Answer:

g(3)=9-7=2

f(2)=5×2-4=10-4=6

Answer:

Step-by-step explanation:

f(x)=5x-4 g(x)=3x-7

g(3) = 3(3)-7=2

f(g(3))=f(2) =5(2)-4 = 6

Answer: 0.667feet

Step-by-step explanation:

You divide 8in by 12

Answer:

Part 1) The equation is [tex]h=42y[/tex]

Part 2) The number of hats Paula can knit is 42 per yard of yarn

Part 3) see the procedure

Part 4) For 378 yards of yarn Paula can knit 9 hats

Step-by-step explanation:

Let

h -----> the number of hats

y ----> the amount of yarn in yards  

k ---> constant of proportionality

Part 1) Write an equation to represent the relationship between the numbers of yards of yarn Paula has and the number of hats she can knit

we know that

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

we have

[tex]k=42[/tex]

substitute

[tex]h=42y[/tex]

Part 2) What does the constant if proportionality 42, represent in this problem?

The constant of proportionality represent the slope of the linear equation

The value of the slope is [tex]42\ \frac{hats}{yd}[/tex]

That means that the number of hats Paula can knit is 42 per yard of yarn

Part 3) Complete the table showing the yards of yarn and the number of hats Paula can knit

we have

[tex]h=42y[/tex]

Part a) For y=0 yd Find the value of h

substitute in the linear equation the value of y and solve for h

[tex]h=42(0)=0\ hats[/tex]

Part b) For h=3 hats Find the value of y

substitute in the linear equation the value of h and solve for y

[tex]3=42y[/tex]

[tex]y=3/42\ yd[/tex]  ----> [tex]y=1/14\ yd[/tex]

Part c) For y=210 yd Find the value of h

substitute in the linear equation the value of y and solve for h

[tex]h=42(210)=8,820\ hats[/tex]

Part d) For y=378 yd Find the value of h

substitute in the linear equation the value of y and solve for h

[tex]h=42(378)=15,876\ hats[/tex]

Part 3) For h=11 hats Find the value of y

substitute in the linear equation the value of h and solve for y

[tex]11=42y[/tex]

[tex]y=11/42\ yd[/tex]  

Part 4) Interpret the meaning of the point (378,9)

we have that

y=378 yd

h=9 hats

That means -----> For 378 yards of yarn Paula can knit 9 hats

Answer:

yes

Step-by-step explanation:

yes thank you this is helping me a lot

Answer:

470

Step-by-step explanation:

1000 x 0.53 = 530

1000 - 530 = 470

Answer:

x=17

Step-by-step explanation:

we know that

The sum of the internal angles of a triangle must be equal to 180 degrees

so

In the triangle ABC

m∠A+m∠B+m∠C=180°

substitute the values and solve for m∠C

4x+49°+m∠C=180°

m∠C=180°-49°-4x

m∠C=131°-4x

In the triangle EDC

m∠E+m∠D+m∠C=180°

we have

m∠E=x

m∠D=100°

m∠C=131°-4x -----> by vertical angles

substitute the values

[tex]x+100\°+(131\°-4x)=180\°\\-3x+231\°=180\°\\3x=231\°-180\°\\3x=51\°\\x=17[/tex]

The value of x for the given geometric problem is determined to be 17 by using the concept that the sum of the internal angles of a triangle is equal to 180 degrees.

We are looking to find the value of x where two triangles are involved.

First, according to the laws of geometry, the sum of the internal angles of a triangle must be equal to 180 degrees.

So, in triangle ABC, m∠A+m∠B+m∠C=180°.

If we have m∠A = 4x and m∠B = 49°, then by substituting these values, m∠C becomes 180° - (49° + 4x) i.e 131° - 4x.

In the triangle EDC, the summation m∠E + m∠D + m∠C also equals 180°.

If m∠E=x, m∠D=100°, and m∠C=131°-4x, we can form an equation of x + 100 + 131 - 4x = 180 which simplifies to 231 - 3x = 180. Solving this equation gives x = 17.

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To find out the total cost after using a coupon, you first add the prices of the items - $1.29 for chips and $0.89 for a drink, totalling $2.18. Then subtract the value of the coupon, $0.75, from this amount. The final cost would be $1.43.

The first step in solving this problem is to add the prices of the bag of chips and the drink. According to the prices given, the chips cost $1.29 and the drink costs $0.89.

By adding these together, you will get the total cost before using the coupon. The sum of $1.29 and $0.89 equals $2.18. This is the total cost without any discounts.

Next, you need to take into account the coupon for $0.75 off the total price. Subtracting this from the initial cost, we get: $2.18 - $0.75 = $1.43.

So, the final cost of the bag of chips and the drink after using the 75 cents coupon would be $1.43.

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Bi weekly is a check every 2 weeks, so she would get 26 checks per year.

Monthly would be 12 checks per year.

When she gets paid monthly her pay increased by $2,800 each check.

Let x be one bi-weekly paycheck.

12(x+2800) = 26x

12x +33600 = 26x

Subtract 12x from both sides

33600 = 14x

Divide both sides by 14:

x = 33600/14

x = 2400

Her pay increased by 2800 each period:

2400 + 2800 = 5200 per check.

5200 x 12 months = 62400

Her annual salary is $62,400

Final answer:

Michelle's annual salary is $179,200, calculated by first understanding the pay period change from bi-weekly to monthly and then multiplying the additional $2,800 monthly increase by 12 to add to her bi-weekly annual salary.

Explanation:

Michelle Hong's gross pay per period increased by $2,800 when her employer switched from a bi-weekly pay plan to a monthly pay plan. To find Michelle's annual salary, we need to understand the terms of her payment cycle changes. On a bi-weekly plan, there are 26 pay periods per year since there are 52 weeks in a year. Under a monthly plan, there are 12 pay periods per year.

First, we calculate the pay for two bi-weekly periods: $2,800 x 2 = $5,600. This is because a bi-weekly pay period should be roughly half of the monthly pay since there are two bi-weekly periods in a standard month. Next, we will calculate the annual salary: $5,600 x 26 = $145,600. This is Michelle's annual salary on a bi-weekly pay plan.

For the monthly pay plan, we would simply take the increased pay of $2,800 and multiply by 12 months to find the annual salary: $2,800 x 12 = $33,600. This is the additional amount she earns by switching to the monthly plan. To find her total annual salary, we add this to her original annual bi-weekly salary: $145,600 + $33,600 = $179,200.

Therefore, Michelle's annual salary on the monthly pay plan is $179,200.

Answer:

Step-by-step explanation:

Yes, they have a proportional relationship.

The table shows sequences, where x-values increase +3, and y-values increase +5, that is, while x increases 3 unites, y increases 5 units, this ratio between variables can be described as the slope:

[tex]m=\frac{13-(-2)}{12-3} =\frac{15}{9}=\frac{5}{3}[/tex]

This fraction or ratio is referring to what we said in words, while y increases 5 units, x increases 3 units. We observe that is a positive ration, this means that magnitudes are both increasing.

Therefore, the right answer is the first one A.

Answer:

[tex] \sqrt{72} = \sqrt{36 \times 2} = 6 \sqrt{2} [/tex]

the simplified form

Answer: 6√2

Step-by-step explanation: The easiest way to do this problem is to factor 72 as 2 · 36 then recognize 36 as a perfect square, 6 · 6.

There is no need to factor further because the 6's pair up.

So a 6 comes out of the radical leaving a 2 inside.

Since the 2 doesn't pair up, it becomes the radicand.

When simplifying radicals using the factor tree,

always be on the lookout for perfect squares.

Answer:

x

Step-by-step explanation:

7x+18−6(x+1)−12

start out with distributive property

7x+18+(-6x)+(-6)+(-12)

then add the common things together

x+0

answer is just x, or infine answers, you could put in anything for x

Answer:

The answer is 23/y

Step-by-step explanation:

This is because the question is asking 23 divided into y. So, your answer is 23/y. I hope tis helps, I am sorry if it is wrong.

The expression for 23 divided into y is written as y / 23, which signifies dividing y by 23 into equal parts.

The expression for 23 divided into y is y / 23. This represents a division operation where y is being divided by 23. To explain this concept further, imagine you have y amount of something, and you want to divide it into 23 equal parts; the amount in each part is represented by the expression y / 23. This operation is fundamental in algebra and helps understand how to express the division of variables and constants.

An example to illustrate this could be if y is equal to 46, then 46 divided by 23 would give us 2. This means each of the 23 parts has a value of 2.

Answer:

a.  13xyz + 9 + 2xyz + 3

13xyz+2xyz+ 9+3 ( combine like terms)

15xyz+12

b. 6ab + (–2ab) + 4 + 6

6ab-2ab+4+6

4ab+10

Answer:

a. 13xyz + 9 + 2xyz + 3

Combine the coefficents of the like monomials.

(13 + 2 = 15)

15xyz + 9 + 3

Add the constants (9 + 3 = 12).

Answer: 15xyz + 12

b. 6ab + (–2ab) + 4 + 6

Combine the coefficents of the like monomials.

[6 + (–2) = 4]

4ab + 4 + 6

Add the constants (4 + 6 = 10).

Answer: 4ab + 10

Step-by-step explanation:

straight from Penn

Answer:

14.14

Step-by-step explanation:

10[tex]10^{2} +10^{2} =x^{2}[/tex]

Simplifying gives you:

10\sqrt{2} ≈ 14.14213562...

The length of the path through Chi's flower garden is approximately 14.14 feet, rounded to two decimal places.

We have,

To find the length of the path through the flower garden, you can use the Pythagorean theorem since the path forms a right-angled triangle inside the square garden.

The garden is a square with a side length of 10 feet.

The path goes from one corner of the square to the opposite corner, forming the hypotenuse of a right-angled triangle.

The other two sides of the triangle are the sides of the square, which are also 10 feet each.

Using the Pythagorean theorem, you can find the length of the hypotenuse (the path):

[tex]c^2 = a^2 + b^2[/tex]

where c is the length of the hypotenuse (the path), and a and b are the lengths of the other two sides (which are both 10 feet in this case).

[tex]c^2 = 10^2 + 10^2[/tex]

c² = 100 + 100

c² = 200

Now, take the square root of both sides to find the length of the path (c):

c = √200 ≈ 14.14 feet

Thus,

The length of the path through Chi's flower garden is approximately 14.14 feet, rounded to two decimal places.

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Answer:

a

Step-by-step explanation:

a. x=4, y=2

plug it in:

4+20=6 true

b. x=3, y=3

3+3=6

3=3+2

3=5 not equal

c. x=2,y=4

2+4=6

2=4+2

2=6 not true

d. x=6, y=4

6+4=6 not true

6=4+2

Answer:

8 hours

Step-by-step explanation:

81 - 17 = 64

64/8 = 8

A: 8 hours

A function assigns the value of each element of one set to the other specific element of another set. The number of hours for which Emily rents the bike is 8.

A function assigns the value of each element of one set to the other specific element of another set.

A function from a set X to a set Y allocates precisely one element of Y to each element of X. The set X is known as the function's domain, while the set Y is known as the function's codomain.

Given that Molly's Bikes rents bikes for $17 plus $8 per hour. Therefore, for x number of hours the function to calculate the total rent can be written as,

Total rent, f(x) = $17 + $8(x)

Now, if Emily paid $81 to rent a bike. The number of hours can be calculated as,

f(x) = $17 + $8(x)

$81 = $17 + $8(x)

$81 - $17 = $8(x)

$64 = $8(x)

x = $64 / 8x

x = 8

Hence, the number of hours for which Emily rents the bike is 8.

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Answer:Prime factorization of 46 is 2 * 23

Step-by-step explanation:

Answer:

I think the answer is j > 1

Answer:

mean = 5

Step-by-step explanation:

"mean" is another term for "average"

to find the mean, you have to add all the integers up, and divide by the number of integers there are.

So you have to combine all the numbers together

-26 +39 -10 -16 +12 +31 = 30

Now you have to divide by 6, since there are 6 integers that you combined to get 30

30/6 = 5

the mean = 5

Hope this helps!

If you have any questions, feel free to ask :)

The correct answer is B

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Under a clockwise rotation about the origin of 90°

a point (x, y ) → (y, - x ), thus

C(1, 2 ) → C'(2, - 1 ) → D

The image after the rotation is C' (2, -1), the correct option is D.

Here we have the point (1, 2), and we have a rotation of 90° clockwise.

Notice that our point is on the first quadrant, then a rotation of 90° will leave us in the fourth quadrant.

The change that we will have is a permutation of the values, and the y-value must become negative, then the transformation gives:

(1, 2) ---> (2, -1)

The correct option is D.

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Answer:

the last one

Step-by-step explanation:

Answer:

Step-by-step explanation:

the last one