Assume that a varies directly as b. What is the constant of proportionality if a = 8 when b = 2?
k = 16
k = 4
k=1/4
k=6

Answer:

p=1, q=5. (1, 5).

Step-by-step explanation:

8p+7q=43

2p-7=-q

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

q=-2p+7=7-2p

8p+7(7-2p)=43

8p+49-14p=43

8p-14p=43-49

-6p=-6

6p=6

p=6/6=1

2(1)-7=-q

2-7=-5=-q

q=5

[tex](f o g)(x) = 245x^2+6\\(g o f)(x) = 5x^2+42\\ f(g(-4)) = 3926\\g(f(5)) = 917[/tex]

Step-by-step explanation:

Given

[tex]f(x) = 5x^2+6\\g(x) = 7x[/tex]

So

[tex](f o g)(x) = 5(7x)^2+6\\= 5(49x^2)+6\\=245x^2+6\\(g o f)(x) = 7(5x^2+6)\\= 35x^2+42\\(fog(x))=245x^2+6f(g(-4)) = 245(-4)^2+6 \\=245(16)+6\\=3920+6\\=3926\\g(f(x)) = 35x^2+42\\g(f(5)) = 35(5)^2+42\\=35(25)+42\\=875+42\\=917[/tex]

Hence,

[tex](f o g)(x) = 245x^2+6\\(g o f)(x) = 5x^2+42\\ f(g(-4)) = 3926\\g(f(5)) = 917[/tex]

Keywords: functions, Function composition

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Answer:

6

Step-by-step explanation:

Split the numerator/ denominator into like factors, that is

= [tex]\frac{72}{12}[/tex] × [tex]\frac{x^2}{x^2}[/tex] ← cancel to give 1

= 6 × 1

= 6

Answer:

Explanation:

The figure attached represents the situation.

The triangle on the left and the triangle on the right are similar triangles because they are right triangles and the marked angles are congruent.

The distance between the mirror and the basketball goal is represented by the unknown x.

By similarity:

Solving:

Thus, the mirror is 20/3 of feet, which is about 6.7 feet, from the basketball goal.

Answer:

64 crates

Step-by-step explanation:

Smaller Cube Side Length = 2 1/2 feet, or, 2.5 feet

Larger Container (Cube) Side Length = 10 feet

We find volume of larger container and find volume of small crates. We divide the large volume by volume of each crate. This will give us number of crates we can fit.

Volume of Cube = x^3

Where x is the side length of the cube

Now,

Small Crate Volume = (2.5)^3 = 15.625 cubic feet

Large Container Volume = 10^3 = 1000 cubic feet

Number of crates that would fit = 1000/15.625 = 64

So, 64 crates will fit in the largest shipping container

64 crates will fit into the largest shipping container.

1. Calculate the volume of each crate:

  Volume [tex]\( V_{\text{crate}} \)[/tex] of a cube with side length s:

 [tex]\[ V_{\text{crate}} = s^3 = (2.5)^3 \] \[ V_{\text{crate}} = 2.5 \times 2.5 \times 2.5 \] \[ V_{\text{crate}} = 15.625 \text{ cubic feet} \][/tex]

2. Calculate the volume of the larger container:

  Volume [tex]\( V_{\text{container}} \)[/tex] of the larger cube-shaped container:

 [tex]\[ V_{\text{container}} = (10)^3 = 1000 \text{ cubic feet} \][/tex]

3. Determine the maximum number of crates that can fit:

  To find out how many crates can fit into the container, divide the volume of the container by the volume of one crate:

 [tex]\[ \text{Number of crates} = \frac{V_{\text{container}}}{V_{\text{crate}}} \] \[ \text{Number of crates} = \frac{1000}{15.625} \] \[ \text{Number of crates} \approx 64 \][/tex]

Answer:

Its isosceles, so the the 2 sides other than st are equal. 2x+6=3x-6

Moves to one side. 12=x

x=12

Step-by-step explanation:

x=12

Step-by-step explanation:

You know that angles T and S are equal, meaning the lengths of the lines TV and SV are also equal. That means 2x+6=3x-6. You transfer the xs and get 6=x-6. You undo the negative 6, receiving 12=x.

Answer:

B

Step-by-step explanation

Answer:

Option B. a = −5, b = −9, c = 12

Step-by-step explanation:

The general form of the quadratic equation is as following

ax² + bx + c = 0

Where a, b and c are constants.

And the given equation is −5x2 − 9x + 12 = 0

Comparing the given equation to the general form

  ax² + bx + c = 0

−5x2 − 9x + 12 = 0

So, a = -5  , b = -9  and   c = 12

Identifying the values a, b, and c is the first step in using the Quadratic Formula to find solution(s) to a quadratic equation.

So, the answer is option B: a = −5, b = −9, c = 12

Answer:

-4

Step-by-step explanation:

You can tell because every time the slope decreases by 5.

Answer:

-4

Step-by-step explanation:

Take the first two sets of points (-4,-2) and (-2,-10)

Then use the formula  Y2 - Y1 / X2 - X1  to find the slope

-10 + 2 / -2 + 4 = -8/2 which can be reduced to -4

Answer:

8 and 23

Step-by-step explanation:

let the 1st equation be i and 2nd be ii

now putting the value of x in eqn ii, we get

12x -4×(3x-1) = 12

12x-12x+4=12

x=12-4

x=8

again,

y=3×8-1

y=23

Initially I had 48 tokens initially

Given that , For every 8 tokens you have your friend has 3

Then, let us assume that, we have 8n tokens. Then our friend will have 3n tokens

After you give half of your tokens to your friend Your friend now has 18 more tokens than you.  

We have to find how many tokens did you start with

Now, after giving away half of tokens we will have 8n/2 = 4n tokens

And our friend will have 4n + 3n = 7n tokens.

And according to given information

Friends tokens – my tokens = 18 tokens

7n – 4n = 18  

3n = 18  

n = 6

Then, I will have initially 8n = 8 x 6 = 48 tokens.

Hence, I had 48 tokens initially

Answer:

gl hf

Step-by-step explanation:

Answer:

B. 1/2n - 3

Step-by-step explanation:

One way to get half a number is to multiply it by 1/2.

The phrase "a number less than an other number" often indicates subtraction.

[tex]\frac{1}{2}n-3[/tex]

Answer:1/2n-3

Step-by-step explanation:

because three less than half of a number means half minus three

Answer:

The quantity of Type A coffee were used is 32 pounds .

Step-by-step explanation:

Given as :

The cost of type A coffee = $ 5.50 per pound

The cost of type b coffee = $ 4.25 per pound

The total cost of coffee = $ 448.00

The quantity of coffee of type B is twice than type A

Let The quantity of type A coffee = x pound

So, The quantity of type B coffee = 2 × x   pound

Now, According to question

x × $ 5.50 + 2 x × $ 4.25 = $ 448

Or,  x × $ 5.50 + x × $ 8.5 = $ 448

Or, 14 x = 448

∴ x = [tex]\frac{448}{14}[/tex]

I.e x = 32

∴ The quantity of type A coffee = 32 pound

And, The quantity of type B coffee = 2 × 32 = 64   pound

Hence The quantity of Type A coffee were used is 32 pounds . Answer

Final answer:

By setting up an equation based on the costs per pound and the relationship between quantities of coffee types A and B, we find that Kaitlin used 32 pounds of type A coffee for her blend.

Explanation:

We need to determine how many pounds of type A coffee were used in the blend, given that twice as many pounds of type B were used and that the total cost was $448.00. Let x be the pounds of type A coffee. Then, 2x will represent the pounds of type B coffee since twice as much type B is used compared to type A.

The cost equation can be represented as:

5.50x + 4.25(2x) = 448

Solving for x:

5.50x + 8.50x = 448

14x = 448

x = 448 / 14

x = 32

Therefore, Kaitlin used 32 pounds of type A coffee for her blend.

The probability that the next marble Kerry selects will be white is; D: 63%

The results of Kerry randomly selecting one marble from the bag out of 65 selections are;

Now, these numbers of marbles represents the amount of times the respective colors are gotten for every 65 selections. Thus;

P(next marble that Kerry selects will be white) = 41/65 * 100

P(next marble that Kerry selects will be white) ≈ 63%

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Answer:

1; solution is not extraneous

Step-by-step explanation:

the value 3=3 is true, meaning its not extraneous and also I got it correct on the test

The value of x is 1, and the solution is not extraneous.

Given that,

Equation; [tex]\sqrt{3x+6 } = 3[/tex]

We have to determine,

The value of x and identify if it is an extraneous solution.

According to the question,

Equation; [tex]\sqrt{3x+6 } = 3[/tex]

To find the value of the x following all the steps given below.

Squaring both the sides to solve the equation,

[tex]\sqrt{3x+6 } = 3\\\\(\sqrt{3x + 6 })^2= 3^2\\\\3x + 6 = 9\\\\3x = 9-6\\\\3x = 3\\\\x = \dfrac{1}{1}\\\\x = 1[/tex]

An extraneous solution is a root of a transformed equation that is not a root of the original equation.

Therefore, The solution is not extraneous.

Hence, The value of x is 1, and the solution is not extraneous.

To know more about Function click the link given below.

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Answer:

(0,2)

Step-by-step explanation:

y-intercept: when x = 0

-3(0) + 12y = 24

12y = 24

y = 2

Answer:

Step-by-step explanation:

The answer is 18

Answer: The LCM of 6 and 9 is 18.

Step-by-step explanation: Using your basic multiplication facts, you know that 6 and 9 are both multiples of 18. Check to make sure 18 is the LCM.

Answer:

The ratio of consonants to is 4:3. 4 consonants and 3 wolves.

Answer:

Step-by-step explanation:

1) 15%=15/100=3/20

2) 36%=36/100=9/25

3) 44%=44/100=11/25

4) 45%=45/100=9/20

5) 8%=8/100=2/25

6) 60%=60/100=6/10=3/5

Answer:

ab² - b = b(ab -1)

Step-by-step explanation:

The variable b is common to both terms here.  Thus,

ab² - b = b(ab -1)

Answer:

Step-by-step explanation:

this  is  an solution

Answer:

The monthly fee for cable and internet is 200.

Step-by-step explanation:

Given:

Amount spend on one year for cable and internet service is 2440.90.

Now, to get the monthly fee for same amount spend on a year, by dividing the amount spend on a year with 12. As in one year there are 12 months.

So, [tex]2440.90\div 12[/tex]

    =[tex]203.41[/tex]

By estimating the amount we get 200. As estimating means to round off the number to the nearest of whole number.

Therefore, the monthly fee for cable and internet is 200.

Total amount of funds is $44.26 million.

Step-by-step explanation:

Given,

Donation received = $23.9 million

As it represents 54% of charity.

Let,

Total amount = x

Therefore,

54% of x = 23.9 million

[tex]\frac{54}{100}*x=23.9\\0.54x=23.9[/tex]

Dividing both sides by 0.54

[tex]\frac{0.54x}{0.54}=\frac{23.9}{0.54}\\x=\$44.26\ millions[/tex]

Total amount of funds is $44.26 million.

Keywords: percentage, division

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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:

Nancy needs to order 5 boxes of travoprost and 9 boxes of latanoprost for her pharmacy.

Step-by-step explanation:

Nancy counts 10 boxes of travoprost and the pharmacy needs 15 boxes to maintain a minimal level in the stock.

So, there is a need to order (15 - 10) = 5 boxes of travoprost.

Again, Nancy counts 3 boxes of latanoprost and the pharmacy needs to 12 boxes.  

So, there is a need to order (12 - 3) = 9 boxes of latanoprost.

Therefore, Nancy needs to order 5 boxes of travoprost and 9 boxes of latanoprost for her pharmacy. (Answer)

Final answer:

Nancy needs to order 5 boxes of travoprost and 9 boxes of latanoprost to fulfill the pharmacy's minimal stock requirement.

Explanation:

Nancy needs to order more boxes of eye medication to meet the pharmacy's minimal stock levels. For travoprost, the pharmacy requires 15 boxes but currently has only 10 boxes. So, Nancy needs to order:

15 boxes (required amount) - 10 boxes (current amount) = 5 boxes of travoprost.

For latanoprost, the pharmacy needs 12 boxes, but only has 3 boxes in stock, meaning Nancy needs to order:

12 boxes (required amount) - 3 boxes (current amount) = 9 boxes of latanoprost.

Answer:

4.775

Step-by-step explanation:

Answer:

4.775

Step-by-step explanation:

Add

0.975

3.800 =

4.775

x = 1240-y can be used to model the situation where x is the amount earned in second week.

Step-by-step explanation:

Given,

Total amount earned = D =  $1240

Amount earned in first week = y = $480

Let,

x be the amount earned in second week.

Therefore,

Total amount earned = Amount earned in 1st week + 2nd week amount

D = x + y

1240 = x + y

Solving for x;

[tex]x= 1240- y [/tex]

x = 1240-y can be used to model the situation where x is the amount earned in second week.

Keywords: linear equation, subtraction

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