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mina [271]
3 years ago
7

Samantha took out two loans totaling $6000 to pay for her first year of college. She narrowed the maximum amount she could at 3.

5% simple annual interest and the remainder at 7% simple annual interest. At the end of the first year, she owed $259 in interest. How much was bolorrowed
Mathematics
1 answer:
Dovator [93]3 years ago
5 0

Our simple interest formula is I = prt, where I is the amount of interest, p is the amount of principal, r is the percentage written as a decimal, and t is the amount of time (in this case in years).  We will define our variable x as the amount borrowed at the lower percentage rate.  Our formula would then look like

.  (Remember that when we convert percentages to decimals, we divide by 100; 3.5/100 = 0.035.)

The remaining money borrowed was invested at 7% interest.  The expression to represent the remaining money would be 6000 - x, as it is what was left over to borrow.  The interest formula for this loan would be

. (Again, we must divide 7 by 100 to convert the percentage; 7/100=0.07.)

Using the distributive property we have:

(t in this case is 1, since it is 1 year.)

The total amount of interest for both loans for one year was $259, so we have:


Combine our like terms:


Cancel 420 by subtracting:


Cancel -0.035 by dividing:


This means she borrowed $4600 at the lower interest rate.  The remainder would be $6000-$4600=$1400 at the higher interest rate.




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Answer:

B because you multiply all the similar numbers together then at the end you add them all up.Step-by-step explanation:

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3 years ago
A grocer has two kinds of tea, one selling for 80 cents per pound and the other selling for 60 cents per pound. How many pounds
ruslelena [56]
X*80+y*60= 50*74
x      +y      =50            | * ( -60)

80x  + 60y= 50*74
-60x  - 60y=-50*60
---------------------------
20x= 50*(74-60)=50*14
x=50*14/20=35 pounds of 80 cents tea
y=50-35=15 pounds of 60 cents tea
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3 years ago
Given the graph below how many solutions would they have?
slava [35]

Answer: infinite

Step-by-step explanation:

the lines go on forever

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3 years ago
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What are the possible values of x if (4c-5)^2= 49?
kykrilka [37]

Answer:

c = 3                              c = -1/2

Step-by-step explanation:

(4c-5)^2= 49

Take the square root of each side

sqrt((4c-5)^2)= ±qrt(49)

4c-5 = ±7

Separate into two equations

4c-5 = 7           4c-5 = -7

Add 5 to each side

4c-5+5 = 7+5          4c-5+5 =-7+5

4c =12                         4c = -2

Divide by 4

4c/4 = 12/4                     4c/4 = -2/4

c = 3                              c = -1/2

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3 years ago
Read 2 more answers
A balloon rises at the rate of 10 ft/sec from a point on the ground 100 feet from an observer. Find the rate of change of the an
lubasha [3.4K]

The rate of change of the angle of elevation of the balloon from the observer when the balloon is 100 feet above the ground is  1/20 degree/sec.

<h3>What is angle of elevation?</h3>

It is described as a relationship between an oblique line from the observer's eye to an item above his eye and the horizontal plane. This angle eventually develops above the surface. The angle of elevation is made in such a way that it is above the observer's eye, as the name suggests.

Calculation for the rate of change of angle of elevation-

According to the question,

A balloon rises at the rate of 10 ft/sec from a point on the ground 100 feet from an observer.

The balloon is 100 feet above the ground.

Let the height of the balloon be 'h' ft.

Then tanØ = h/100

h = 100tanØ

Differentiate the above equation with respect to time.

dh/dt = 100 sec² Ø (dØ/dt)

We know dh/dt = 10 ft/sec.

when h = 100

tanØ = 100/100 = 1/1

tanØ = Perpendicular/Base

On comparing above two equations,

Perpendicular = 1; Base = 1.

By Pythagoras the hypotenuse is,

H² = P² + B²

    = 1² + 1²

    = 2

H = √2

Now, calculate the value of cosØ.

cosØ = B/H = 1/√2

Squaring both side

cos² Ø = 1/2

sec² Ø = 1/cos² Ø

sec² Ø = 2

The main equation was,

dh/dt = 100 sec² Ø (dØ/dt)

Substitute the values,

dØ/dt = (dh/dt )/100 sec² Ø

         = (10)/(100×2)

dØ/dt = 1/20 degree/sec.

Therefore, the rate of change of the angle of elevation of the balloon from the observer is  1/20 degree/sec.

To know more about the angle of elevation, here

brainly.com/question/9817377

#SPJ4

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