1. The tension t in a spring varies directly with the distance d the spring is stretched. If the tension is 46 pounds when the spring is stretched 4 inches, find the tension when the spring is stretched twice as far.

2. The time t it takes to fill a bucket varies directly with the volume g of the bucket. If it takes 2 minutes to fill a 8-gallon bucket, how long will it take to fill a 5-gallon bucket?

3. The power P in an electric circuit varies directly with the square of the current I. If P = 30 when I = 2, find P when I = 5.

4. The amount of money M a woman makes per week varies directly with the number of hours h she works per week. If she works 28 hours and earns $137, how much does she make if she works 42 hours?

5. The weight F of a body varies inversely with the square of the distance d between the body and the center of the Earth. If a man weighs 250 pounds 4,000 miles from the center of the Earth, how much will he weigh at a distance of 5,000 miles from the center of the Earth.

Answer:

430 dollars per year

Step-by-step explanation:

The formula to use is...

C=250+15x

C is the cost per year

250 is the flat fee

15 is the cost per month

x is the number of months

Answer:

8, 3 pointers =24 points 4, 2 pointers = 8points 24+8= 34 points

Step-by-step explanation:

Answer:

8 baskets worth 3 points each and 4 baskets worth 2 points each

Step-by-step explanation:

It is 8 baskets worth 3 points each and 4 baskets worth 2 points each because it says Juarez scored twice as many baskets worth 3 points than the baskets worth 2 points. 4 x 2 = 8

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6 baskets worth 3 points each and 7 baskets worth 2 points each : wrong because 7 x 2 = 14.

10 baskets worth 3 points each and 1 basket worth 2 points : wrong because 1 x 2 = 2.

4 baskets worth 3 points each and 10 baskets worth 2 points each: wrong because 10 x 2 = 40.

Please mark brainliest. I only need 3 more brainliest before I can level up.

Answer:

looks like it's 29.6 yards

Answer and Step-by-step explanation:

We are not given the function in question, but in order to explain, will form a function. Suppose f(x) = 3x + 2.

If f(x) = 17, then

3x + 2 = 17, to find the value of x, we have solve for x in the equation.

3x = 17 – 2

3x = 15

x = 5

This is the method that can be used to solve problems of this nature.

Answer:

4 and 7

Step-by-step explanation:

There are probably several ways to do this but this is how I did it:

First, I listed all the number combinations, that added together equaled 11.

This is what it looked like:

1, 10

2, 9

3, 8

4, 7

5, 6

6, 5

7, 4

I stopped here since the next step would be to double the first number and 8*2 would already be more than 15.

Then, I doubled the first number and added the second number to it, when I saw that didn't equal 15, I eliminated that possibility and moved on to the next set of numbers. When I reached 4, 7 I saw that 4*2 equaled 8 and 8 plus 7 equals 15 so I had the answer.

There are probably much more efficient ways to do this but this is how I did it.

Hope it helped!

The first number is 4 and second number is 7.

Let us consider that first number is x and second number is y.

            [tex]2x+y=15\\\\x+y=11[/tex]

Substitute [tex]y=11 - x[/tex]in equation [tex]2x+y=15[/tex]

        [tex]2x+11-x=15\\\\x=15-11=4[/tex]

So,   [tex]y=11-x=11-4=7[/tex]

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Answer:

21 1/2

Step-by-step explanation:

Answer:

The given system of equations is :

2x + 3y + 5z = 1 -> eq. (1)

3x + 2y + z = 5 -> eq. (2)

Multiplying eq. (1) with 3 and eq. (2) with 2, we get :

6x + 9y + 15z = 3 -> eq. (3)

and, 6x + 4y + 2z = 10 -> eq. (4)

respectively.

Subtracting eq. (4) from eq. (3) :

5y + 13z = -7 -> eq. (5)

Multiplying eq. (1) with 2 and eq. (2) with 3, we get :

4x + 6y + 10z = 2 -> eq. (6)

and, 9x + 6y + 3z = 15 -> eq. (7)

respectively.

Subtracting eq. (7) from eq. (6) :

-5x + 7z = -13 -> eq. (8)

Let z = t, where t is a parameter.

We can write eq. (5) and eq. (8) as :

5y + 13t = -7 & -5x + 7t = -13

i.e., 5y = -7 - 13t & 5x = 13 + 7t

y = -(7/5) - (13t/5) & x = (13/5) + (7t/5)

Therefore, the solution for the given system of equations is :

x = (13/5) + (7t/5)

y = -(7/5) - (13t/5)

z = t

where, t can take any value.

Step-by-step explanation:

Answer:

The correct answer is C

Step-by-step explanation:

Tbh I just guessed but I got a 100% on the test, so I hoped that helped

Answer:

yeah its c

Step-by-step explanation:

-17.6

Because

50 + 5/13 x -26

50+2.6 x -26

50 + -67.6

-17.6

Answer:

They intersect at an x value of 2

Step-by-step explanation:

Rewrite the equations into slope y-int form:

-2x + y = -6

y = 2x - 6

x + 2y = -2

2y = -2 - x

y = -1/2x - 1

Next, set the two equations as equal and solve for x:

2x - 6 = -1/2x - 1

2x + 1/2x = -1 + 6

4x + x = -2 + 12

5x = 10

x = 2

Problem 1

A = length times width

A = w(w + 0.6)

A = w^2 + 0.6w

Answer choice D.

Problem 2

16/9 = 42/x

9(42) = 16x

378 = 16x

378/16 = x

23.625 = x

Answer choice C.

Problem 3

f(-5) = 4(-5) + 3

f(-5) = -20 + 3

f(-5) = -17

Answer choice B.

Answer:

slope = 2

y int = -4

Step-by-step explanation:

4x - 2y > 8

8 <  4x - 2y

/-2

-4 < -2x + y

2x - 4 < y

slope = 2

y int = -4

(I'm not sure if it is right sorry! hope this helps!)

Answer:

10

Step-by-step explanation:

Set it up algebraically first. Let x be that unknown number

5x - 9 = 4x + 1

5x = 4x + 10

x = 10

So the number is 10

Answer:

3. obtuse

4.acute

Step-by-step explanation:

Answer:

6.2%

Step-by-step explanation:

Credit rating is an evaluation of the credit risk of a borrower, that how often a person is going to repay their debt, by credit rating it predicts the ability of the debtor to payback.

Mike has credit rating = 720

Tyler has credit rating = 560

Both are approved for loan. Mike's Credit score is higher, which means he is a much safer debtor as compared to Tyler. Mike will be able to pay back much easily than Tyler. Therefore Mike interest rate is 3.2%

Interest rate of Tyler is higher as he is not that trusted and has low Credit rating. Tyler is approved for a loan that charged 3 percentage points higher because of his inferior credit rating so it interest on the loan will be

Interest = 3.2%+3% = 6.2%

Answer: 45

Step-by-step explanation:

Answer:

The Answer is 56

Step-by-step explanation:

[tex] \sqrt{98} \times \sqrt{32} = 56[/tex]

the square root of 98 is 9.89 continuous

the square root of 32 is 5.65 continuous so when you put it into calculations you should get 56

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here's your solution ~

[tex]\qquad \sf  \dashrightarrow \: \sqrt{98} \times \sqrt{32} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sqrt{2 \times {7}^{2} } \times \sqrt{2 {}^{5} } [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sqrt{2 {}^{6} \times {7}^{2} } [/tex]

[tex]\qquad \sf  \dashrightarrow \: {2}^{3} \times 7[/tex]

[tex]\qquad \sf  \dashrightarrow \: 8 \times 7[/tex]

[tex]\qquad \sf  \dashrightarrow \: 56[/tex]

Answer:

Alright! First you'd have to subtract the flat fee of the mug which is $8.95, then you'd have to divide by the rate which is $1.50. Your equation would be:

(26.95 - 8.95) ÷ 1.50 = r

Then you solve using your head.. lol.

(26.95 - 8.95) = 18.

(18 ÷ 1.50) = 12.

R = 12.

Answer:

12

Step-by-step explanation:

Answer:

64 inches

Step-by-step explanation:

162.56 / 2.54

Answer:

162.56/2.54=64

Answer:

C. $14.20

Step-by-step explanation:

I got this answer because $8.95 plus $5.25 equals $14.20.

Please mark brainliest

Answer:

39

Step-by-step explanation:

The answer is = 39

1 to the pwer of 1 = 1

3 to the power of 3 = 27

The amounts for the other three partners are $25000, $100000, and $200000.

The amount that the other people will share will be:

= $400000 - $50000

= $350000

Therefore this will be divided as follows:

A = 2/(2+4+8) × $350000

= 2/14 × $350000

= $25000

B = 4/14 × $350000

= $100000

C = 8/14 × $350000

= $200000

Therefore, the amounts for the other three partners are $25000, $100000, and $200000.

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Answer:C

Step-by-step explanation:

c amount made in hour (9) times the number of hours workd (t) equals m
9t=m   for example you work 5 hours 9(5)=45 so the answer is c m=9t

Answer:

The answer is below

Step-by-step explanation:

Which equation in slope-intercept form represents a line that passes through the point (2,3) and is perpendicular to the line y−9=23(x+7)

Solution:

The equation of a line in slope intercept form is given as y = mx + b, where m is the slope and b is the y intercept.

Given a line y−9=23(x+7)

y - 9 = 23x + 161

y = 23x  + 170. The slope of this line comparing with y = mx + b gives m = 23

Two lines are perpendicular if the product of their slope gives -1.

Let [tex]m_1[/tex] be the slope of the perpendicular line, hence:

[tex]m_1(23)=-1\\\\m_1=\frac{-1}{23}[/tex]

Since the perpendicular line passes through (2, 3), we can get its equation using:

[tex]y-y_1=m_1(x_x_1)\\\\y-3=\frac{-1}{23}(x-2)\\\\y= \frac{-1}{23}x+\frac{2}{23}+3\\\\ y= \frac{-1}{23}x+\frac{71}{23}[/tex]

Answer:

y=−2/5x−6/5

Step-by-step explanation:

The required rate of the level of change of water in the swimming pool is 1 / 3 level per hour.

Given that,
The swimming pool is being filled with a hose.
The pool's water level rises 4 inches in hours.
To determine the rate per hour of the water level change.

Here,
Let 1 level of pool = 1 feet = 12 inches
The pool's water level rises 4 inches in hours. So, ti will rises 12 inches in 3 hours, which implies level change after 3 hours
Now the rate of level change of water = 1 / 3 level per hour

Thus, the required rate of the level of change of water in the swimming pool is 1 / 3 level per hour.

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Answer:

1/8 half-gallon or 1/16 full gallon

Step-by-step explanation:

Emma and her 3 friends= Four people

Four people shared 1/2 gallon= 1/2 divided by 4

1/2 divided by 4= 1/8

Each person got 1/8 of the half gallon.

This would mean that out of a FULL gallon, they would get 1/16

Answer:

The area is 1,725 ft²