Penny attended a four year state college. She took out a student loan to pay for her tuition and room & board for the four years she was attending the college. Her tuition fees were $6,970 per year, and the cost of her room and board was $11,320 per year. Now that she has graduated, she will have to start paying back her loan. Fortunately, Penny has a grace period of one year before she has to start paying back the loan. Her loan details are as follows: there is a fixed-rate interest of 4.5% and the interest compounds each month. During her one year grace period, interest will accrue on the loan, so that when she has to start paying the loan back she will owe more than what she owes now. Her goal is to be able to payoff the loan in 10 years.

Given all of this information, answer the following questions:

1. What is the original loan amount, i.e. how much were the total costs for tuition plus room & board for the four years that Penny attended the college?

2. What is the new loan amount after the one-year grace period (remember that interest will accrue on the loan during this initial 12-month period that she is not paying anything back on the loan)? This is the amount that she will be responsible for paying back. (Round your answer to the nearest whole dollar)

3. Given that she can pay back the loan in full after 10 years of payments, what is the total amount she will end up paying back (both principal and interest that has accrued over the 10 years)? And how much will her monthly payments on the loan be for those 10 years? (Round your answers to the nearest whole dollar)

Answer:

x = 5

Brainliest, please!

Step-by-step explanation:

90 + 39 + (7x + 16) = 180

7x + 145 = 180

7x = 180 - 145

7x = 35

x = 5

Answer:

x=5

Step-by-step explanation:

Sum of the angles in a triangle is 180.

7x +16 +39 +90= 180

7x + 125 = 180

7x = 180-145

7x=35

x=35/7

x=5

Answer:

∠ P ≈ 46.9°

Step-by-step explanation:

The area (A) of Δ PST is calculated as

A = [tex]\frac{1}{2}[/tex] × PS × PT × sinP

Here A = 71.24 , then

[tex]\frac{1}{2}[/tex] × 15 × 13 × sinP= 71.24 , that is

97.5 × sinP = 71.24 ( divide both sides by 97.5 )

sinP = [tex]\frac{71.24}{97.5}[/tex] , then

∠ P = [tex]sin^{-1}[/tex] ([tex]\frac{71.24}{97.5}[/tex] ) ≈ 46.9° ( to the nearest tenth )

Answer:

false it would be something like x root 2

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

1.5+2.5+2+4=10 b/c the figure is the half of the biger lines

The perimeter of the quadrilateral EFGH is 10 units.

Perimeter is the total length of the boundary of a closed shape. The perimeter of the polygon is measured as the sum of all the sides.

For the given situation,

The diagram shows the two quadrilaterals ABCD and EFGH.

The quadrilaterals are similar, ABCD ≅ EFGH. So their ratios are equal.

Here BC = 5.0, FG = 2.5

⇒ [tex]\frac{FG}{BC} =\frac{2.5}{5.0}[/tex]

⇒ [tex]\frac{1}{2}[/tex]

So the lengths of EFGH is half than that of ABCD.

Then the lengths of EFGH are 2.5, 2.0, 4.0, 1.5

Thus the perimeter of EFGH is

Perimeter = Sum of all sides

⇒ [tex]Perimeter = 2.5+2.0+4.0+1.5[/tex]

⇒ [tex]Perimeter = 10.0[/tex]

Hence we can conclude that the perimeter of the quadrilateral EFGH is 10 units.

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Answer: c

Step-by-step explanation:

c is the same and it is the correct answer

Answer:

Step-by-step explanation:

Using Pythagoreus Theorem

In the smaller rectangle

2²+4² = h²

20 = h²

h = √20

h = 2√5

Therefore two sides of the rectangle will 2√5

No using pythagoreus theorem in the bigger triangle

x² + (2√5)² = 9²

x² = 9² - (2√5)²

x² = 81 - 20

x = √61

x = 7.8102496759

When rounded off to nearest tenth the hundreth digit is in 0-5 range

x = 7.81

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Answer:

$84.60

Step-by-step explanation:

$84.60 is what david will earn in 9 hours becuz 9.40 times 9 is 84 dollars and 60 cents

Answer:

a. 1:3

Step-by-step explanation:

theres a pattern of x^2 but 1:3 is 1x3

( − 2 ) ( 3+ 2 2 − − 2 )

Hope this helps, have a great day!

Julio's normal hourly rate (r) is equal to $11.8 per hour.

Translating the word problem into an algebraic expression, we have;

[tex]30r[/tex] ......equation 1

[tex](35 - 30)[/tex] × [tex]1.4r[/tex] [tex]= 5[/tex] × [tex]1.4r[/tex]

[tex]5[/tex] × [tex]1.4r = 7r[/tex]  .....equation 2

Next, we would equate the expressions to the total amount of money earned by adding eqn 1 and eqn 2.

[tex]30r + 7r = 436.60\\\\37r = 436.60\\\\r = \frac{436.60}{37}[/tex]

Julio's normal hourly rate, r = $11.8 per hour.

Therefore, Julio's normal hourly rate (r) is equal to $11.8 per hour.

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Answer:

answer of this question is 55.844

Step-by-step explanation:

may this answer is helpful for you

Answer:

About 13 weeks

Step-by-step explanation:

Answer:

b. never

Explanation:

A fraction is always in the form p/q, where q is not 0; or can be converted in that form (in case of mixed fraction).

A number is said to be irrational, if it cannot be expressed in the form p/q, where q is not 0.

[tex]\\ \sf\longmapsto m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\\ \sf\longmapsto m=\dfrac{1-3}{-4-3}[/tex]

[tex]\\ \sf\longmapsto m=\dfrac{-2}{-7}[/tex]

[tex]\\ \sf\longmapsto m=\dfrac{2}{7}[/tex]

Points are (-7,6),(11,-4)

[tex]\boxed{\sf slope(m)=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

[tex]\\ \sf\longmapsto m=\dfrac{-4-6}{11+7}[/tex]

[tex]\\ \sf\longmapsto m=\dfrac{-10}{18}[/tex]

[tex]\\ \sf\longmapsto m=-\dfrac{5}{9}[/tex]

Answer:

Step-by-step explanation:

Slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

9) Mark any two point on the line

(x₁ , y₁) = (3 , 3)   ;   (x₂, y₂) = (-4 ,1)

[tex]Slope =\frac{1-3}{-4-3}\\\\=\frac{-2}{-7}\\\\=\frac{2}{7}[/tex]

10) (x₁ , y₁) = ( -7 , 6)   ;   (x₂, y₂) = (11 ,-4)

[tex]Slope =\frac{-4-6}{11-[-7]}\\\\ =\frac{-4-6}{11+7}\\\\=\frac{-10}{18}\\\\=\frac{-5}{9}[/tex]

Step-by-step explanation:

Algebra is a topic that covers linear equations, system of equations, sequences, exponential functions, polynomials, quadratic, exponents, radicals, functions, and more. I'm going to give use algebraic formulas and not all the topics.

Like Terms Rule: If two terms that share the same variable are separated by a binary operation, we can combine them.

For example, look at

[tex]6 + 7x + 9x[/tex]

We can combine 7x and 9x.

[tex]7x + ( + 9x) = 16x[/tex]

Add the coeffceint and keep the variable.

16x+6

Solving Algebraic Equations:

Alot questions in Algebra asks you to isolate a variable. For example,

[tex] \frac{x}{2} + 6 = 9[/tex]

First step, is to get the x variable by itself. To do this subtract 6 by both sides. Why? Because Subtraction is a inverse operation off addition. Remeber the Golden Rule of Algebra,

WHAT WE DO TO ONE SIDE. WE DO TO THE OTHER.

[tex] \frac{x}{2 } = 3[/tex]

Now, we multiply both sides by 2 because multiplying is the inverse operation of division and vice versa.

[tex]x = 6[/tex]

If we plug this in, it is indeed true.

[tex] \frac{6}{2} + 6 =[/tex]

[tex]3 + 6 = 9[/tex]

Some other rules are

If we multiply a term by a one term, we only affect the term that is being multiplied, for example

[tex]2x \times 3[/tex]

2 and 3 are both real numbers so we just multiply 2 and 3. and put x behind the answer.

[tex]2 \times 3 = 6(x)[/tex]

[tex]2x \times 3 = 6x[/tex]

When we multiply 2 variables, we put the variable near each other. For example,

[tex]x \times y = xy[/tex]

When we add term, we add the coeffcient parts

[tex]y + y = 1y + 1y = 2y[/tex]

Know that

[tex]y = 1y[/tex]

When we multiply same term variables, we get

[tex]x \times x = {x}^{2} [/tex]

There is more formulas for Algebra. But these are the basicis.

Answer:

6m

Step-by-step explanation:

The ratio of the length and the breadth of rectangle=2:1

Let length be 2x, then breadth = x

Now,

Length(l)=12 m

or,2x=12m

or,x=6m

x=breadth=6m

Answer:

76.50

Step-by-step explanation:

We are given the fact that you bought an object for 90 dollars, and in which you sold said object for a loss of 15%, we are then asked how much would that object be sold for.

To find the answer, we need to subtract the original amount by the percent loss, so :

90 - 15%

15% of 90 is 13.5, therefore :

90 - 13.5

76.5

Answer: 21

Step-by-step explanation:

Step-by-step explanation:

tbh I have no idea

doing this for points

so yeah

225125₆/101₆ = 2225₆

One way to arrive at this is to convert both given numbers to base 10, compute the quotient in base 10, then convert back to base 6.

101₆ = 1×6² + 0×6¹ + 1×6⁰ = 37

225125₆ = 2×6⁵ + 2×6⁴ + 5×6³ + 1×6² + 2×6¹ + 5×6⁰ = 19,277

So we have

225125₆/101₆ = 19,277/37 = 521

Next,

521 = 2×216 + 89 = 2×6³ + 89

89 = 2×36 + 17 = 2×6² + 17

17 = 2×12 + 5 = 2×6¹ + 5×6⁰

and so

521 = 2×6³ + 2×6² + 2×6¹ + 5×6⁰ = 2225₆

Or you can use the long division algorithm. Division in base 6 is the same as in base 10, except numerals range from 0 to 5 instead of 0 to 9. See if you can follow this diagram (replaced with an attachment)

Answer:

(2 + 1)^2 + 2 = 10 - 6  

Falso

Step-by-step explanation:

The left side  

11

does not equal to the right side  

4

, which means that the given statement is false.

False

Answer:

4/9

Step-by-step explanation:

(2/3)^2

(2/3) * (2/3)

4/9

Answer:

Aroun 203 knots.

Step-by-step explanation:

we look at the x axis and find 937 kPa. Since it's in between 930 and 940 we find a estimate for it. we then move up until we reach the line that was graphed. we check what the y coordinate is, which is around the 203 mark

Answer:

1) 19200- for Aarati 2) 17280- for Aakriti

Step-by-step explanation:

1. 16000/100*20=3200- THE MONEY WHICH ARE THE PROFIT,

2. 16000+3200=19200- THE PRICE for Aarati

3. 100-10=90 PERCENTS - the price for AAkriti contains from the price from Aarati

4. 19200*(90/100)= 17280- the price for Aakriti

Answer:

20.66 cm^2

Step-by-step explanation:

area =1/2 AxB sine C

=1/2 x11x8 x sine 152

=11x4x0.46947156279

20.65674876258 cm^2

=20.6567cm^2

rounding it to the nearest hundredth we get,

20.66 cm^2

Answer:

the awnser is d 1000 pediatricians

Answer:

(0.5, 0.5)

Step-by-step explanation:

Use the midpoint formula: [tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

The points are:

[tex](\frac{-2+3}{2},\frac{4-3}{2})\\\\(\frac{1}{2},\frac{1}{2})[/tex]

Therefore, the midpoint between A and C is located at (0.5, 0.5).

9.4 × [tex]10^{2}[/tex]

1) Move the decimal point 2 times to left in the number so that number, 940 so it's between 1-10: 9.4 or 9.40

2) After we moved our decimal point to the left, the decimal count would be 12 and that we moved 2 places to the left

3) We know that the notation is a x [tex]10^{b}[/tex]

a=9.4 and 6=2

9.4 × [tex]10^{2}[/tex]=a x [tex]10^{b}[/tex]

I hope I've helped!

Answer:

9.4x10^8

Step-by-step explanation:

940 million looks like

940,000,000. in scientific notation you would move the decimal left 8 spaces

Answer:

f⁻¹(-2) = 3 and f⁻¹(1) = 0.

Step-by-step explanation:

By the definition of inverse functions:

[tex]\displaystyle \text{If } f(a) = b\text{, then } f^{-1}(b) = a[/tex]

From the table, note that f(3) = -2.

Then by definition, f⁻¹(-2) = 3.

Likewise, f(0) = 1.

Then by definition, f⁻¹(1) = 0.

A midpoint is a point that divides a given line into two equal halves.The answers to the questions are:

1. BC = 89

b. AB = 45

c. AC = 44

2. The coordinate of I is 2.5

3. J = 19

4. MQ = 32

5. NO = 13

6. NO = 23

b. MN = 25

A line segment can be divided into different fractions. Where the point that divides the line segment into equal parts is the midpoint. however, number line is a system that shows the location or positions of all directed numbers.

The given questions can be solved as follows:

1. Given that point A is between BC and AB = 4x -3, BC = 7x + 5, AC = 5x - 16

But,

BC = AB + AC

7x + 5 = (4x -3) + (5x - 16)

          = 9x - 19

7x + 5 = 9x - 19

19 + 5 = 9x - 7x

24 = 2x

x = [tex]\frac{24}{2}[/tex]

x = 12

So that;

a. BC = 7x + 5

         = 7(12) + 5

BC = 89

The value of BC is 89.

b. AB = 4x -3

         = 4(12) - 3

AB = 45

Thus AB has a value of 45.

c.  AC = 5x - 16

          = 5(12) -16

 AC = 44

The value of AC is 44.

2. Given that H is the mid point of GI, and G = 8, I = -3.

Then;

I = 2.5

The coordinate of I is 2.5

3. A midpoint is a point that divides a line segment in to two equal halves. Given that J is the midpoint of KL. KL = 38

J = [tex]\frac{KL}{2}[/tex]

  = [tex]\frac{38}{2}[/tex]

J = 19

The value of the midpoint J is 19.

4. It can be deduced from the conditions given in the question that:

  MQ = MN + NO + OP + PQ

          = 8 + 8 + 16      (NB: OP + PQ = 16)

MQ = 32

Thus, value of MQ is 32.

5. Since P is the mid point of NQ, and OP = 11, OQ = 35

 Then;

PQ  = OQ - OP

      = 35 - 11

PQ = 24

Since, PQ = NP =24

Then;

NO = NP - OP

      = 24 - 11

NO = 13

NO has a length of 13.

6. NO = 2y + 11, OP = 3y - 2, NP = 6y + 3 and MP = 64.

But,

NO + OP = NP

(2y + 11) + (3y - 2) = 6y + 3

5y + 9 = 6y + 3

9 - 3 = 6y - 5y

y = 6

So that;

a. NO = 2y + 11

          = 2(6) + 11

NO = 23

Here, the value of NO is 23.

b. MN = MP - NP

But,

NP = 6y + 3

     = 6(6) + 3

NP = 39

Then;

MN = 64 - 39

MN = 25

So that MN has a value of 25.

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Answer:

4.44

Step-by-step explanation:

The tangent of B is the relation of the opposite cathetus to the lying cathetus

tg B= AC/CB= 40/9= 4.44

The value of the tangent of angle B is 4.4.

In trigonometry, the tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.

In other words, it is the ratio of sine and cosine function of an acute angle such that the value of cosine function should not equal to zero.

Given that, a right triangle Δ ABC, the measure of ∠C = 90°, AC = 40, BA = 41, and CB = 9. We need to find the value of the tangent of ∠B,

So, here,

The opposite side = AC and the adjacent side = CB

So, tan B = AC / CB = 40/9 = 4.4

Hence, the value of the tangent of angle B is 4.4.

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