Which is the constant of proportionality for the data in the table?



A

18


B

2


C

6


D

12

Step-by-step explanation:

Look at the picture.

[tex]-5\leq x\leq4\to x\in[-5,\ 4][/tex]

[tex]-4\leq y\leq9\to y\in[4,\ 9][/tex]

To calculate Melanie's savings from paying off a 20-year loan early, we compare total payments over 20 years to total payments made if the loan is finished 6 years early, focusing on the saved interest.

Without the monthly payment, we can't provide the exact savings figure, but it certainly would be less interest paid over 14 years versus 20 years.

To calculate the savings from paying off a loan early, we need to compare the total amount paid under the original loan terms with the total amount paid if the loan is paid off early.

For Melanie's 20-year loan of $50,000 at an APR of 3.3% compounded monthly, we can use financial formulas or a calculator to determine the monthly payment and the total amount paid over the terms of the loan.

If the loan is paid off 6 years early, we would compare the interest paid over 14 years with the interest paid over 20 years.

However, without the exact formula being used or the provided calculator, we can't give an exact figure for the amount saved.

You will typically find that by paying off a loan early, you save money on interest that would have accrued over the remaining term of the loan.

To answer the question, Melanie would need to calculate or look up the monthly payment, multiply by the number of payments she would make in the two scenarios, and then subtract the smaller total from the larger one to determine her savings.

Answer:

US$ 1,084.80 were raised from the raffle tickets and US$ 1,035 are the profits after paying the prizes.

Step-by-step explanation:

1. Let's review the data given to us for solving the question:

Number of raffle tickets sold = 1,356

Cost of each raffle ticket = US$ 4/5

Number of prizes = 6

Cost of each prize = US$ 8 3/10

2. How much money was raised from the raffle tickets?

For easier calculation, let's convert the fraction numbers to decimal numbers:

Cost of each raffle ticket = US$ 4/5 = US$ 0.80

Cost of each prize = US$ 8 3/10 = US$ 8 + 0.30 = US$ 8.30

Now, we use this formula to calculate how much money was raised and the profits:

Profits = (Number of tickets sold * Cost of each ticket) - (Number of prizes * Cost of each prize)

Replacing with the real values, we have:

Profits = 1,356 * 0.80 - 6 * 8.30

Profits = 1,084.80 - 49.80

Profits = 1,035

US$ 1,084.80 were raised from the raffle tickets and US$ 1,035 are the profits after paying the prizes.

Final answer:

The total amount of money raised from the sale of 1,356 raffle tickets, priced at 4/5 dollars each, is $1,084.8.

Explanation:

To determine how much money was raised from the raffle tickets, we first need to calculate the total cost of each ticket and then multiply it by the total number of tickets sold. The question states that each raffle ticket is sold for 4/5 dollars. Since a total of 1,356 raffle tickets were sold, the total amount raised can be calculated as follows:

Total amount raised = Price per ticket × Total number of tickets

= (4/5) × 1,356

= 1,084.8 dollars

Therefore, the total amount of money raised from the raffle tickets is $1,084.8.

Answer:

The two equations would be

x+y=29       5x+2y=100

Step-by-step explanation:

Looking at the points, x and y add up to be 100

x is worth 5 hence 5x and y are worth 2, hence 2y.

there are 29 problems in total. meaning the x + the y add up to 29 problems

The length of NT in isosceles triangle RST is 7.

In an isosceles triangle, the base angles are congruent, and the sides opposite those angles are also congruent. Let's denote the length of RS (and RT) as r, and the length of MN as m  Since M and N are midpoints, MN is parallel to the base, and its length is half the length of the base. Therefore, [tex]\( m = \frac{r}{2} \).[/tex]

The perimeter of the triangle is the sum of the three sides, so [tex]\( 2r + r = 25 \) (as RS = RT).[/tex] Solving for r, we get [tex]\( r = \frac{25}{3} \).[/tex]

Now, we know that [tex]\( m = \frac{r}{2} \),[/tex] so [tex]\( m = \frac{25}{6} \)[/tex]. Finally, the length of NT is the difference between RT and MN, which is [tex]\( \frac{25}{3} - \frac{25}{6} = 7 \).[/tex]Therefore, the length of NT is 7 units.

QUESTION:Consider isosceles triangle RST, where RS = RT. Let M and N be the midpoints of sides RS and RT, respectively. A segment MN is drawn with a length of 3.5 units. The perimeter of triangle RST is given as 25 units. Determine and state the length of NT.

Please provide a comprehensive solution to this problem, including step-by-step calculations and explanations.

Final answer:

By applying properties of isosceles triangles and the given conditions, we calculate that the length of segment NT is 4.5 units.

Explanation:

The subject matter is a geometrical problem involving an isosceles triangle with given conditions. In isosceles triangle RST, RS and RT are equal in length, M and N are the midpoints of RS and RT respectively, and MN is drawn with a length of 3.5 units. Given that the perimeter of the triangle is 25 units, we need to find the length of segment NT.

To solve this, we first understand that in an isosceles triangle, the perpendicular from the vertex to the base bisects the base. Therefore, segment MN cuts the base ST equally in two, making each half 3.5 units, since MN = 3.5 units. Furthermore, because M and N are midpoints, segments MS and NT are equal. Finally, by knowing the perimeter, we can deduce that RS + ST + RT equals 25 units.

Thus, we can derive the lengths of RS and RT (which are equal) and then use that information to calculate the length of NT. If RS = RT and we call that length x, then 2x + 2(3.5) = 25. Solving for x gives us x = (25 - 7)/2 = 9. Thus, segment NT as the half of either RS or RT is 9/2 = 4.5 units.

Answer:

A.The large box contains twice as many ounces of strawberries as the small box.   TRUE

B.To get the maximum ounces for her money, Emma should buy 1 large and 1 small box of strawberries. TRUE

C.Emma spends a total of $11.00; therefore, she is purchasing 2 small boxes of strawberries.  FALSE

D.Emma purchases a small box and a medium box of strawberries. The total purchase is $11.75. FALSE

Step-by-step explanation:

Here, the amount Emma has to be spent = $12

According to the question:

Small box -- 8 ounces --$4.50

Medium box -- 12 ounces -- for $6.50

Large box -- 1 pound -- $7.25

Now, the given statements are:

A.The large box contains twice as many ounces of strawberries as the small box.

The amount of strawberry in large box  =  1 pound

Amount of strawberry in small box  = 8 ounce

Now, double of 8 ounce = 16 ounce = 1 pounds

So, the given statement is TRUE.

B.To get the maximum ounces for her money, Emma should buy 1 large and 1 small box of strawberries.

Total ounces in 1 large and 1 small box = 16 ounce + 8 = 22 ounces

The price total = $4.40 + $7.25 = $11.65

So, the given statement is TRUE.

C.Emma spends a total of $11.00; therefore, she is purchasing 2 small boxes of strawberries.

cost of 1 small box = $4.50

Cost of 2 small box =  2 x $4.50 = $9

The given statement is FALSE

D.Emma purchases a small box and a medium box of strawberries. The total purchase is $11.75.

cost of 1 small box = $4.50

Cost of 1 medium box =  $6.50

So, the total cost is  $4.50 + $6.50  = $11.00

So, the given statement is FALSE.

Answer:

Step-by-step explanation:

[tex]\bold{METHOD\ 1:}\\\\\text{Use}\ (a-b)^2=a^2-2ab+b^2\\\\(x-7)^2=x^2-2(x)(7)+7^2=x^2-14x+49\\\\\bold{METHOD\ 2:}\\\\\text{We know:}\ a^2=a\cdot a\\\\(x-7)^2=(x-7)(x-7)\\\\\text{Use FOIL:}\ (a+b)(c+d)=ac+ad+bc+bd\\\\=(x)(x)+(x)(-7)+(-7)(x)+(-7)(-7)\\\\=x^2-7x-7x+49\qquad\text{combine like terms}\\\\=x^2-14x+49[/tex]

Answer:

5850 miles

Step-by-step explanation:

150 X 39 = 5850

We multiple because it says Joanna ran 39 more TIMES than Jack.

Joanna ran 5850 miles.

Answer:

45%

Step-by-step explanation:

The formula to work out the decrease is:

Percentage Decrease= actual decrease / original amount X 100%

1) So firstly, we have to work out the decrease, to do this we have to do is do $750-$412.50= $337.50

2) We can now substitute this into our formula which will now be. (We will also add the original amount, which is $750.00)

Percentage Decrease= 337.50 / 750.00 X 100% = 45

The percentage decrease is 45%

What you want to do is plot each point on the graph according to both the x and y coordinate. Then, when you've drawn all four points in their appropriate place, draw a relatively straight line through all of them. You might need to use a ruler for that part.

The table shows the month and the the total number of people

The graph for the given table is attached below.

Given :

The table shows the number of people who attended her first, second, third, and fourth month of her career.

From the given table the month represents x  and number of people represents y

Lets make 4 coordinates  from the given table

Plot all the 4 points on the graph

(1, 124), (2,201)  (3,390)

(4,700)

For (1,124) , we take x=1  and y = 124 on graph

Look at the point where x=1  and y=125 intersects. That point is (1,124)

All the data are shown in the graph attached below

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1/3 off means it is selling for 2/3 the original price.

Multiply the price by 2/3:

450 x 2/3 = (450 x 2) /3 = 900/3 = 300

The sale price is $300

Answer:

$300

Step-by-step explanation:

The TV's regular price is 450 dollars, and we are looking for the sale price after a third of it gets marked off.

We first need to find 1/3 of 450.

[tex]\frac{1}{3}* 450 = \frac{450}{3}=150[/tex]

One third of the original price is $150.

Now, we need to subtract 150 from 450.

[tex]450-150=300[/tex]

So, the sales price of the TV would be $300.

Hope this helps!

Answer:

From a starting position of 13,500 feet above the ground, she is descending at 32 feet per second.

Step-by-step explanation:

The equation is in slope intercept form. [tex]y=mx+b[/tex]

The slope (m) is -32. This can be used as a unit rate: -32 ft per second.

The y-intercept (b) is 13,500. It would make most sense if she started at 13,500 ft in height.

From a starting position of 13,500 feet above the ground, Pam is descending at 32 feet per second.

Answer:

The answer is B) From a starting position of 13,500 feet above the ground, she is descending at 32 feet per second.

Step-by-step explanation:

D does not make since because if you start at 32ft you can't fall 13,500ft. There is nowhere for you to go.

A and C don't make since because you can't fall upward.

Answer:

n +(-8)=14

Step-by-step explanation:

a number is 'n'

is adding negative of 8

i. e. -8

is eaual to 14

then n=14+8

or; n =22

therefore the number is 22.

Answer:

45 degrees

Step-by-step explanation:

As all of the angles in a triangle add up to 180 and we already know that one angle is 90, that means that the sum of the other two angles is 90. So, you can do 90/2=45.

Answer:

The ratio  of Jay's age to Kiaria's age to Martha's age​ is 1: 2 : 4.

Step-by-step explanation:

Here, let us assume the age of jay = u years

So, the age of Kiaria = Age of Jay + 7   =   u + 7

And, the age of Martha  = 2 x ( age of Kiaria) = 2 ( u + 7)

Now, the sum of the ages  = 7 u

⇒ (u) + (u + 7)  + 2 ( u + 7)  = 7 u

or,  u + u + 7 + 2 u + 14 = 7 u

or, 4 u +  21 =  7 u

⇒ 3  u = 21  or u = 21/3 =  7

⇒ u  = 7 years

Hence, the age of Jay =  m = 7 years

Age of Kiaria = m + 7 = 7 + 7 = 14 years

Age of Martha  =2 (  m+7) = 2 ( 7 +7) = 28 years

So, the ratio of Jay's age to Kiaria's age to Martha's age​

is 7: 14: 28 = 1: 2 : 4

Hence, the final ratio of the ages is 1: 2 : 4.

Answer:

After t weeks, the balance in the expense account and fundraising account is

f(t)= 400 -40t +150+32t

f(t)= 550 -8t

After 12 weeks,

f(12) = 550- 8(12) = 454

Answer:

Step-by-step explanation:

After t weeks, the balance in the expense account and fundraising account is

f(t)= 400 -40t +150+32t

f(t)= 550 -8t

After 12 weeks,

f(12) = 550- 8(12) = 454

Answer:

-5.1, -14/3, -4

brainlist accepted!;)

Answer:

Step-by-step explanation:

[tex]\bold{METHOD\ 1:}\\\\\begin{array}{ccc}126\ mi&-&3h\\\\x\ mi&-&4h\end{array}\qquad\text{cross multiply}\\\\3x=(126)(4)\\3x=504\qquad\text{divide both sides by 3}\\x=168\ mi[/tex]

[tex]\bold{METHOD\ 2:}\\\\126\ mi\ \text{in}\ 3\ h,\ \text{then}\ \dfrac{126\ mi}{3}=42\ mi\ \text{in}\ 1\ h.\\\\\text{If}\ 42\ mi\ \text{in}\ 1\ h,\ \text{then}\ (42\ mi)(4)=168\ mi\ \text{in}\ 4h.[/tex]

Answer:I don’t know

I thought you won’t grieve me he answer straight up

Step-by-step explanation:

y = 12x represents the gallons of paint used in x hours.

Step-by-step explanation:

CJ uses 3 gallons of paint in 15 minutes,

15 minutes = 3 gallons

1 minutes = [tex]\frac{3}{15} = \frac{1}{5} \ gallons\\[/tex]

1 hour = 60 minutes

Gallons of paint used in 1 hour;

1 hour = [tex]\frac{1}{5}*60=12\ gallons[/tex]

CJ uses 12 gallons of paint in 1 hour.

For x hours = 12*x = 12x

Gallons of paints used = y

y = 12x represents the gallons of paint used in x hours.

Keywords: linear equation, multiplication

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Answer:

x= 16/7

Step-by-step explanation:

Answer:

the functions have the same domains

Step-by-step explanation:

because since the functions f(x) and g(x) have the same (x)

The only value that is in the domains of both functions is 0.

and the range of g(x) is all values less than or equal to 0 are correct.

A relation is a function if it has only One y-value for each x-value.

The original function is f(x)=√x

As this is condition for √x function, x≥ 0

Domain= [0, infinity)

Range= [0, infinity)

After the reflection across x-axis and y-axis, we get a function,

g(x)=-√-x

-x≥ 0 means x≤ 0,

So,

Domain= (-infinity, 0]

Range= (-infinity, 0]

From this you can see that the only value that is in the domains of both functions is 0.

The range of g(x) is all values less than or equal to 0.

Hence,  the only value that is in the domains of both functions is 0.

and the range of g(x) is all values less than or equal to 0 are correct.

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The graph of f(x) =sqrt of x is reflected across the x-axis and then across the y-axis to create the graph of function g(x). Which statements about the functions f(x) and g(x) are true? Check all that apply. The functions have the same range. The functions have the same domains. The only value that is in the domains of both functions is 0. There are no values that are in the ranges of both functions. The domain of g(x) is all values greater than or equal to 0. The range of g(x) is all values less than or equal to 0.

Answer:

The correct answer would be option C.

Step-by-step explanation:

Since he gives the dog 3 liters of water and 500 grams of food a day we know that on the fifth day the dog will have gotten 15 liters of water and 2,500 grams of food.

The required coordinate will be (15, 2,500)

Hence the required coordinate will be (15, 2,500) which is interpreted as the fifth day, Julie gave Banjo 15 liters of water and 2,500 grams of food.

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Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}-5a+b=8&\text{add}\ 5a\ \text{to both sides}\\7a+9b=-32\end{array}\right\\\\\left\{\begin{array}{ccc}b=5a+8&(1)\\7a+9b=-32&(2)\end{array}\right\\\\\text{Substitute (1) to (2):}\\\\7a+9(5a+8)=-32\qquad\text{use the distributive property}\\\\7a+(9)(5a)+(9)(8)=-32\\\\7a+45a+72=-32\qquad\text{subtract 72 from both sides}\\\\52a=-104\qquad\text{divide both sides by 52}\\\\\boxed{a=-2}\\\\\text{Put the value of}\ a\ \text{to (1):}\\\\b=5(-2)+8\\\\b=-10+8\\\\\boxed{b=-2}[/tex]

Answer:

x 4 −4 5 −5

y 2 2 3 3

Step-by-step explanation:

This is the obvious answer, since there are no repetitive x-coordinates.

I am joyous to assist you anytime.

The table which represents the function is:

x    4    −4       5      −5

y    2     2        3         3

A function is a mathematical relationship where each input (x-value) corresponds to exactly one output (y-value).

To determine which table represents a function, we need to check if there are any repeated x-values with different y-values.

x    4    −4       5      −5

y    2     2        3         3

This table  represent a function.

Each x-value corresponds to a unique y-value, and there are no repeated x-values with different y-values.

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Answer:

600

Step-by-step explanation:

20%=0.2

120/0.2=600

Answer:

12 hours

Step-by-step explanation:

Let the cruise ship travel x hours before the container ship caught up and the container ship starts y hour after the cruise ship starts.

So, the distance traveled by the cruise ship in x hours = distance traveled by the container ship in (x - y) hours.

So, x - y = 10 ........ (1) (Given)

And 5x = 6(x - y)

⇒ x = 6y .......... (2)

Now, solving equations (1) and (2, we get 5y = 10, ⇒ y = 2 hours.

And x = 6y = 12 hours.

So, the cruise ship travels for 12 hours before the container ship caught up. (Answer)