Mitch is attending a 4-year college. As a freshman, he was approved for a 10-year, federal
unsubsidized student loan in the amount of $8,100 at an APR of 4.29%. Mitch decides to
make no payments during the 4.5-year deferment period. After interest is capitalized at the
end of the 4.5-year period, what will his new principal amount be?

Answer:

55, 23, x+y =78; x-y =32

Step-by-step explanation:

-the system of equation

x+y = 78

x-y = 32

-solve by elimination

x-y = 32, add y to both sides

x= y+32

x +y =78, substitute x= y+32

y+32+y = 78, subtract 32 from both sides

y+y = 78-32, combine like terms

2y = 46, divide both sides by 2

y = 23

x +y =78, substitute y = 23

x+ 23 =78, subtract 23 from both sides

x = 78-23, combine like terms

x = 55

Answer:

The equation:

x + y = 78

x - y = 32

The answers:

x= 55

y = 23

Step-by-step explanation:

Call the first number (x) and the second number (y). Take is as a given that (x) is larger than (y). One is given the following information:

"The sum of two numbers is 78"

"Their difference is 32"

Rewrite this in numerical terms:

x + y = 78

x - y = 32

The process of elimination is a way of solving a system of equations. First one manipulates one of the equations such that one variable has an inverse coefficient of its like term in the other equation. This step one does not need to be performed, as the coefficients of the term (y) are inverses in the equations. Next, one adds the equations. Then one uses inverse operations to solve for the remaining variable. Finally, one back solves for the value of the eliminated variable by substituting the value of the solved variable into one of the equations, and simplifying.

Add the equations,

x + y = 78

x - y = 32

____________

2x = 110

Inverse operations,

2x = 110

x = 55

Back solve,

x + y = 78

x = 55

55 + y = 78

y = 23

Answer:

By the time her daughter is 21 years old 300 EUR will have been deposited into the account.

Step-by-step explanation:

Since a woman deposits 100 EUR in her daughter's bank account on her first birthday, and on every subsequent birthday, she deposits 10 EUR more than she deposited the previous year, so on her second birthday, she deposits 110 EUR, and on her third birthday she deposits 120 EUR, to determine, by the time her daughter is 21 years old, how much money has been deposited in her account, the following calculation must be performed:

100 + (20 x 10) = X

100 + 200 = X

300 = X

Therefore, by the time her daughter is 21 years old 300 EUR will have been deposited into the account.

Answer:

Step-by-step explanation:

The first box is 'not closed'

Second is ' an element'

Third = 'closed' and last is 'an element'.

Answer:

96

Step-by-step explanation:

Let the gladiolas Mr Haas has be x

We know that Mrs Albert has 3 times as many gladiolas as Mr. Haas, so Mrs Albert has:

3x gladiolas

Together they have 128 gladiolas, so:

x + 3x = 128

4x = 128

x = 128/4

x = 32

Therefore Mr Haas has 32 gladiolas & if Mrs. Albert has 3 times more than him she has (32x3) = 96 gladiolas.

answered by g a u t h m a t h

Answer:

x ≈ 13.7

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos70° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{40}[/tex] ( multiply both sides by 40 )

40 × cos70° = x , then

x ≈ 13.7 ( to the nearest tenth )

Answer:

Tony

Step-by-step explanation:

Answer:

0.625

Step-by-step explanation:

Since there are 4 options each time the spinner is spun, there are a total of [tex]4\cdot 4=16[/tex] non-distinct sums possible when we spin it twice.

Out of these, the possible sums that meet the condition (less than 6) are 2, 3, 4, and 5 (since the smallest sum possible is 1+1=2).

Count how many ways there are to achieve each of these sums:

[tex]1+1=2\\\\1+2=3\\2+1=3\\\\2+2=4\\1+3=4\\3+1=4\\\\2+3=5\\3+2=5\\4+1=5\\1+4=5[/tex]

Totally there are 10 ways to achieve a sum less than 6. Therefore, the desired probability is [tex]\frac{10}{16}=\frac{5}{8}=\boxed{0.625}[/tex]

Answer:

y=-3x+5

Step-by-step explanation:

concepts: y=mx+b is slope intercept equation formula

m=slope

b= y intercept

Therefore we need to find the slope and y intercept

first find slope

m=[tex]\frac{y2-y1}{x2-x1}[/tex]

let y2 be 2

let y1 be -4

let x2 be 1

let x1 be 3

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

6/-2 = -3

m=-3

slope is -3

y= -3x+ b

we need find y intercept now

just plug in (1,2) into that equation

2=-3(1)+b

b=5

y=-3x+5

Answer:

x=1

x=-3

Step-by-step explanation:

(x-1)(x^3 + 3x^2 +x +3) = 0

(x-1)( x+3)(x^2 +1)=0

Answer: 13

Step-by-step explanation:

Take 7 to the other side and divide 91 by 7, the answer will be 13.

Answer:

The answer is B. y=-3x+4

Step-by-step explanation:

Have a great day :)

Answer:

Answer is down below.

Step-by-step explanation:

To find the answer, we will have to use basic Algebra in order to view the solution.

Let the first number be = x

Let the second number be = x+2

Let the third number be= x+4

Let the fourth number be= x+6

(We did the x+ part because consecutive means following continuously..)

Now let's put the equation:

x+x+2+x+4+x+6 = 1052

Let's add all the variables and numbers separately in order to simplify:

4x+12 = 1052

Subtract 12 on both sides.

4x = 1040

Divide 4 on both sides

x = 260

Now, we know the value of x. Let's put it in our numbers.

Let the first number be = x = 260

Let the second number be = x+2 = 262

Let the third number be= x+4 = 264

Let the fourth number be+ x+6 = 266

Now, let's double check to see if our answers are correct.

260+262+264+266 = 1052

Valla! They are.

Hope this Helps! Please Mark Brainliest!

9514 1404 393

Answer:

Step-by-step explanation:

I find it convenient to use a graphing calculator to graph the function.

The "start" is x=0, where the distance from the sprinkler head is 0 feet. The value of h(0) is 9.5, the height of the sprinkler head.

The graph shows the vertex of the curve is (5, 34.5), meaning that a height of 34.5 feet is reached 5 feet horizontally from the sprinkler.

The graph shows the x-intercept at about 10.9. That is where the height of the spray is 0 feet above the ground.

Answer:

I think the answer is B.12

If this not correct, Sorry.

Answer:

64 vs. 4 so 60 extra people

Step-by-step explanation:

Answer:

I think 60 more people

Step-by-step explanation:

You just plug in p for period 4 and period 2 then solve for N. Then it's asking for how many more in pd 4 then 2 which is 60, I think..

Answer:

C.

–5; –135; –10,935

Step-by-step explanation:

Answer:

C. -5; -135, -10,935

Step-by-step explanation:

...............................................................................................................................................

Answer: Third Choice. Thousandths

Step-by-step explanation:

Concept:

Here, we need to know the order and name of each place value.

Please refer to the attachment below for the specified names.

Solve:

STEP ONE: Orde and name each place

2 ⇒ One Thousands

4 ⇒ Hundreds

5 ⇒ Tens

6 ⇒ Ones

.

1 ⇒ Tenths

3 ⇒ Hundredths

8 ⇒ One Thousandths

7 ⇒ Ten Thousandths

STEP TWO: Find the number [8] in the number

As we can see from the list above, 8 is at the right of the decimal point, thus, the place value is Thousandths.

Hope this helps!! :)

Please let me know if you have any questions

Answer:

5.7

Step-by-step explanation:

9^2=x^2+7^2

Solving for x we get 81 - 49 which is 32.

The square root of 32 rounds to 5.7

Answer:

top to bottom, the answers are b, c, a

Step-by-step explanation:

One way to find the solution to a system of equations is to substitute values in. For the first one,

y=2x+3

y=2x+5,

we can substitute 2x+3 =y into the second equation to get

y=2x+5

2x+3 = 2x+5

subtract 2x from both sides

3 = 5

As 3 is not equal to 5, this is never equal and therefore has no solution

For the second one,

y= 2x+7

y = (-2/3)x + 10

We can plug y=2x+7 into the second equation to get

2x + 7 = y = (-2/3)x + 10

2x + 7 = (-2/3)x + 10

add (2/3)x to both sides to make all x values on one side

2x + (2/3)x + 7  = 10

subtract 7 from both sides to make only x values on one side and only constants on the other

2x + (2/3)x = 3

(6/3)x + (2/3)x = 3

(8/3)x = 3

multiply both sides by 3 to remove a denominator

8x = 9

divide both sides by 8 to isolate x

x=9/8

There is only one value for when the equations are equal, so this has one solution

For the third one

y = x-5

2y = 2x - 10

Plug x-5 = y into the second equation

2 * y= 2*(x-5)

2 * (x-5) = 2x - 10

2x-10 = 2x-10

add 10 to both sides

2x=2x

As 2x is always equal to 2x, no matter what x is, there are infinitely many solutions for this system

Answer:

4

Step-by-step explanation:

2/5*3000 = 1200 seniors

then

3000 - 1200 = 1800 students not seniors

therefore

4/5* 1200 = 960 do not like rock climbing

and

9/10** 1800 = 1620 also do not like it:

"how many students are in favor of this idea?"

subtract the "don't likes" from 3000

3000 - (960+1620) = 420 like rock climbing:

3x-x+2=4

Step-by-step explanation:

here's the answer to your question

Answer:

Y =-2.5X +3.5

Step-by-step explanation:

x1 y1  x2 y2

-1 6  3 -4

(Y2-Y1) (-4)-(6)=   -10  ΔY -10

(X2-X1) (3)-(-1)=    4  ΔX 4

slope= -2  1/2    

B= 3  1/2    

Y =-2.5X +3.5    

Answer:

32 because I Don't know please vote my answer please

Answer:

12 (10) cm 937 637 = hafe 2929888389292822

Answer:

a.is approximately normal because of the central limit theorem.

Step-by-step explanation:

The central limit theorem states that if we have a population with mean μ and standard deviation σ and we take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed.

For any distribution if the number of samples n ≥ 30, the sample distribution will be approximately normal.

Since in our question, the sample of observations is 50, n = 50.

Since 50 > 30, then our sample distribution will be approximately normal because of the central limit theorem.

So, a is the answer.

Answer:

a = 13/12

General Formulas and Concepts:

Pre-Algebra

Equality Properties

Step-by-step explanation:

Step 1: Define

Identify

a - 1/3 = 3/4

Step 2: Solve for a

Answer:

C. 7 units

Step-by-step explanation:

The given parameters are;

The length of the chord of the circle, [tex]\overline{AC}[/tex] = 14 units

The orientation of the radius and the chord = The radius is perpendicular to the chord

We have in ΔAOC, [tex]\overline{AO}[/tex] = [tex]\overline{OC}[/tex] = The radius of the circle

[tex]\overline{OB}[/tex] ≅ [tex]\overline{OB}[/tex]  by reflexive property

The angle at point B = 90° by angle formed by the radius which is perpendiclar to the chord [tex]\overline{AC}[/tex]

ΔAOB and ΔCOB are right triangles (triangles having one 90° angle)

[tex]\overline{AO}[/tex] and [tex]\overline{OC}[/tex] are hypotenuse sides of ΔAOB and ΔCOB respectively and [tex]\overline{OB}[/tex] is a leg to ΔAOB and ΔCOB

Therefore;

ΔAOB ≅ ΔCOB, by Hypotenuse Leg rule of congruency

Therefore;

[tex]\overline{AB}[/tex] ≅ [tex]\overline{BC}[/tex] by Congruent Parts of Congruent Triangles are Congruent, CPCTC

[tex]\overline{AB}[/tex] = [tex]\overline{BC}[/tex] by definition of congruency

[tex]\overline{AC}[/tex] = [tex]\overline{AB}[/tex] + [tex]\overline{BC}[/tex] by segment addition postulate

∴ [tex]\overline{AC}[/tex] = [tex]\overline{AB}[/tex] + [tex]\overline{BC}[/tex] =  [tex]\overline{AB}[/tex] + [tex]\overline{AB}[/tex] = 2 ×  [tex]\overline{AB}[/tex]

∴  [tex]\overline{AB}[/tex] = [tex]\overline{AC}[/tex]/2

[tex]\overline{AB}[/tex] = 14/2 = 7

[tex]\overline{AB}[/tex] = 7 units.

Answer:

7 units

Step-by-step explanation:

Answer:

Step-by-step explanation:

I think that you cut off the leading number in the BD segment 8cm appears to be truncated....

if that number was in the image....

BC would be sqrt(52.3 ^2 + ?.8^2)

if you  have BC then

sin(θ)/BC = sin(90)/18.6

Answer:

5

The correct answer is Y= - __

4

[tex] \Large \colorbox{red}{ \sf\color{white}{Aиswεr : }}[/tex]

Sudden uncontrollable fear or anxiety, often causing wildly unthinking behaviour.

Answer:

y = 0.45x

Step-by-step explanation:

After 2 secs can ring 2 × 0.45

After 3 secs can ring 3 × 0.45

After 4 secs can ring 4 × 0.45 , then

After x secs can ring y = x × 0.45 = 0.45x , that is

y = 0.45x

Answer:

CB = 7

Step-by-step explanation:

CB = CK

5x - 3 = 3x + 1

5x - 3x = 1 + 3

2x = 4

x = 4 / 2

x = 2

CB = 5x - 3

= 5 ( 2 ) - 3

= 10 - 3

CB = 7

Answer:

CB = 7

Step-by-step explanation:

since the 2 triangles are AAS (B, K, E, CE as shared side) proven congruent, CB and CK must have the same length.

5x - 3 = 3x + 1

2x = 4

x = 2

CB = 5x - 3 = 5×2 - 3 = 10 - 3 = 7

Answer:

24 hours

Step-by-step explanation:

The formula is

1/a + 1/b = 1/c  where a and b are the times alone and c is the times together

1/12 + 1/b = 1/8

Multiply by 24b to clear the fractions

24b(1/12 + 1/b = 1/8)

2b + 24 = 3b

Subtract 2b from each side

2b +24-2b = 3b-2b

24 = b