A number plus 1/4 of the number can be expressed as

What is 4x-4y/2=x+2 in slope intercept form?

Alla [95]

Answer:

The equation would be y = 3/2x - 1

Step-by-step explanation:

To find the answer in slope-intercept form, simply solve for y.

4x-4y/2=x+2 ----> Subtract 4x from both sides

-4y/2=-3x+2 ----> Multiply both sides by 2

-4y = -6x + 4 -----> Divide by -4

y = 3/2x - 1

3 0

2 years ago

Laura owes $18,000 on her student loans. The interest rate on the bank loan is 2.5% and the interest rate on the federal loan is

Llana [10]

Answer:

The principal of the bank loan is $4,000

The principal of the federal lone is $14,000

Step-by-step explanation:

* Lets explain how to solve the problem

- Laura owes $18,000 on her student loans

- The interest rate on the bank loan is 2.5%

- The interest rate on the federal loan is 6.9%

- The total amount of interest she paid last year was $1,066

* Assume that the principle of the bank loan is $x and The principal of

the federal loan is $y

∵ Her loan is 18,000

∴ x + y = 18,000 ⇒ (1)

- The interest is I = PRT, where P is the principal, R is the rate of interest

in decimal ant is the time

# The bank lone

∵ P = $x

∵ R = 2.5/100 = 0.025

∵ T = 1

∴ The interest of the bank lone = x(0.025)(1) = 0.025 x

# The federal lone

∵ P = $y

∵ R = 6.9/100 = 0.069

∵ T = 1

∴ The interest of the federal lone = 9(0.069)(1) = 0.069 y

- The total interest is the sum of the interest of the bank lone and the

interest of the federal loan

∵ The total interest is $1,066

∴ 0.025 x + 0.069 y = 1,066 ⇒ (2)

* We have system of equations

- Multiply equation (1) by -0.025 to eliminate x

∴ -0.025 x - 0.025 y = -450 ⇒ (3)

- Add equations (2) and (3)

∴ 0.044 y = 616

- Divide both sides by 0.044

∴ y = 14,000

- Substitute value of y in equation (1) to find x

∴ x + 14000 = 18000

- Subtract 18000 from both sides

∴ x = 4000

∵ x represents the principal of the bake loan and y represents the

principal of the federal lone

* The principal of the bank loan is $4,000

* The principal of the federal lone is $14,000

3 0

2 years ago

The balanced scale represents the equation: 3x + 1 = x + 3

Afina-wow [57]

Given:

The given balanced scale is represented by the equation

$3x+1=x+3$ ----- (1)

We need to determine the process that balance the scale.

Process to balance the scale:

Given that the if one x block is subtracted from the right side and three numbered blocks are subtracted from the left side.

Thus, the equation (1) becomes

$(3x+1)-3=(x+3)-x$

$3x-2=3$ ----- (2)

Now, to balance the scale, let us subtract one block x from the left side and subtract three numbered blocks from the right side.

Thus, the equation (2) becomes,

$(3x-2)-x=3-3$

$2x-2=0$ ------ (3)

Thus, the equation (3) is the same as the equation (1).

Hence, the process required to balance the scale is to subtract one x block from the left side and subtract three numbered blocks from the right side.

Therefore, Option B is the correct answer.

6 0

2 years ago

Nick starts with 20 milligrams of a radioactive substance. The amount of the substance decreases by 12 each week for a number of

Gre4nikov [31]

Answer:

what the answer

Step-by-step explanation:

6 0

2 years ago

Rubi tosses a quarter off the Main Street bridge into the St. John’s River. The distance, in feet, the quarter is above the wate

Masja [62]

Answer: a. 112 feet, b= 3 seconds, c= 256 feet, d = 6 seconds

Step-by-step explanation:

Here is the complete question:

Rubi tosses a quarter off the Main Street bridge into the St. John’s River. The distance, in feet, the quarter is above the water is modeled by the equation d(t) = −16t2+96t + 112, where t represents time in seconds.

Find the actual value(s) now to each question. Use the solution from the previous question to assist you with what you are actual solving for.

(a) From what height was the quarter tossed?

The quarter was tossed at 112 feet.

(b) How long does it take the quarter to reach its maximum height?

It will take ________ seconds for the quarter to reach its maximum height.

(c) What is the maximum height of the quarter?

The maximum height of the quarter is ________ feet.

(d) How much time does it take for the quarter to hit the water?

It will take ______ seconds for the quarter to hit the water.

a. Since the function is

d(t) = −16t² + 96t + 112,

The coin is tossed at 112 feet. This is because it is the the initial value of the function. It is the constant term and does not depend on any other variable.

b. To calculate the maximum height, we have to find vertex of the function, that has coordinates of h,k and,

h = -b/2a and k = f(h).

From the question, we are aware that,

a = -16, b = 96, c = 112

Using the values, the vertex will be:

h = -b/2a

= -96/(2 × -16)

= -96/-32

= 3

k = f(3)

= 16t² + 96t + 112

= -16(3)² + 96(3) + 112

= -144 + 288 + 112

= 256

The maximum height is therefore 256 feet, and time needed to reach the height will be 3 seconds.

c. The maximum height has been calculated and it is 256 feet.

d. The time it take for the quarter to hit the water will be:

= 3 seconds × 2 = 6 seconds

Since the maximum height took 3 seconds, it would take another 3 seconds to hit the water. This makes it 6 seconds

4 0

2 years ago