13. Marco took out an unsubsidized student loan for $20,000, which he will start paying in 4
years, after he graduates. If the interest rate is 4.2%, what is the amount he will owe once he
graduates?

Answer:

x=10

Step-by-step explanation:

The triangles are similar so we can use ratios to solve

6.5      (6.5+6.5)

------ = -----------------------

5              x

6.5      (13)

------ = -----------------------

5              x

Using cross products

6.5x = 65

Divide by 6.5

6.5x/6.5 = 65/6.5

x = 10

Answer:

Step 2: addition property of equality

Step 4: multiplication property of equality

Step-by-step explanation:

=>In step 2, from step 1, where you have [tex] -\frac{y}{2} - 6 = 15 [/tex] , to make -6 cross over to the other side of the equation, the addition property of equality was applied. That would ensure the equation remains balanced. Thus, 6 is added to both sides of the equation.

[tex] -\frac{y}{2} - 6 + 6 = 15 + 6 [/tex]

[tex] = -\frac{y}{2} = 21 [/tex]

=>In step 4, the multiplication property of equality was used as both sides of the equation were multiplied by -2, to balance the equation and also solve for y.

Answer:

Step 2 > addition

Step 4 > multiplication

Step-by-step explanation:

Answer:

9 ft

Step-by-step explanation:

a²+b²=c²

20²+b²=25²

400=b²=625

b²=625-400

b²=225

b=15 (the distance up the wall the ladder is to begin with)

20-13=7

7²+b²=25²

49+b²=625

b²=625-49

b²=576

b=24 (The distance up the wall the ladder is after moving it)

24-15=9

Answer:

5 pounds of miniature chocolate and 2 butterscotch hard candies

Step-by-step explanation:

5 x $1.80 =$9 for 5 pounds of candy

2 x $1.00 =$2 for 2 pounds of candy

2 + 5 =7 pounds

7 pounds of candy using $11.00

All three series converge, so the answer is D.

The common ratios for each sequence are (I) -1/9, (II) -1/10, and (III) -1/3.

Consider a geometric sequence with the first term a and common ratio |r| < 1. Then the n-th partial sum (the sum of the first n terms) of the sequence is

[tex]S_n=a+ar+ar^2+\cdots+ar^{n-2}+ar^{n-1}[/tex]

Multiply both sides by r :

[tex]rS_n=ar+ar^2+ar^3+\cdots+ar^{n-1}+ar^n[/tex]

Subtract the latter sum from the first, which eliminates all but the first and last terms:

[tex]S_n-rS_n=a-ar^n[/tex]

Solve for [tex]S_n[/tex]:

[tex](1-r)S_n=a(1-r^n)\implies S_n=\dfrac a{1-r}-\dfrac{ar^n}{1-r}[/tex]

Then as gets arbitrarily large, the term [tex]r^n[/tex] will converge to 0, leaving us with

[tex]S=\displaystyle\lim_{n\to\infty}S_n=\frac a{1-r}[/tex]

So the given series converge to

(I) -243/(1 + 1/9) = -2187/10

(II) -1.1/(1 + 1/10) = -1

(III) 27/(1 + 1/3) = 18

Answer: 32/345 wall per gallon

Step-by-step explanation:

Rate is defined as ratio between two quantities with different units.

Gallons of paint used by Martin = 8 5/8 gallons = 69/8 gallons

Portion of wall Martin wishes to pint = 4/5 wall

Rate at which Martin paints the wall:

= Portion of wall covered / paint used

=

4/5 / 69/8 = 32/345 wall per gallon

Answer:

Martin paints 0.093 walls per gallon of paint

Step-by-step explanation:

1. Let's review the information provided to us to answer the question correctly:

Amount of paint used by Martin = 8 5/8 of a gallon

Ratio of wall painted by Martin with 8 5/8 of a gallon = 4/5

2. What is the unit rate at which Martin paints in walls per gallon?

Let's convert the mixed fractions to decimals this way:

8 5/8 = 8 + 0.625 = 8.625

4/5 = 0.8

Now, let's use the Direct Rule of Three, this way:

Gallons                      Walls

8.625                          0.8

x                                   1

Solving for x :

0.8x = 8.625 * 1

x = 8.625/0.8

x = 10.78125

x = 10.8 (rounding to next tenth) gallons

For painting a wall, we will use 10.8 gallons of paint. Now, we can calculate the unit rate at which Martin paints in walls per gallon, this way:

Gallons                      Walls

10.8                               1

 1                                  x

Solving for x :

10.8x = 1

x = 1/10.8

x = 0.09259

x = 0.093 (rounding to the next hundredth) walls per gallon of paint

Answer:

Option 4

Step-by-step explanation:

=> [tex]\frac{4}{5} x^{-9}y^6z^8[/tex]

If there is any variable having a negative exponent, we should move it to its opposite side (Denominator to numerator and vice versa) So that it's exponent become positive.

=> [tex]\frac{4y^6z^8}{5x^9}[/tex]

Answer: D) [tex]\frac{4y^6z^8}{5x^9}[/tex]

Step-by-step explanation:

(4/5)x^-9y^6z^8 = [tex]\frac{4x^{-9}y^6z^8}{5}[/tex]

Any negative exponent can be taken to the other side of the fraction to be positive.  Thus,

[tex]\frac{4x^{-9}y^6z^8}{5}[/tex] = [tex]\frac{4y^6z^8}{5x^9}[/tex]

Hope it helps <3

Hello!

Answer:

12 cm, 12 cm, 10 cm.

Step-by-step explanation:

Given:

Perimeter, or P = 34 cm

Ratio of sides = 6 : 6 : 5

To find the length of each side, we can use a variable in the ratio to find the perimeter:

34 = 6x + 6x + 5x

Combine like terms:

34 = 17x

Solve for x:

34/17 = 17x/17; x = 2

Plug in this value of "x" into each expression for the side-lengths:

6(2) = 12 cm

6(2) = 12 cm

5(2) = 10 cm

Therefore, the lengths of each side of the triangle are 12 cm, 12 cm, 10 cm.

Hope this helped you! :)

Answer:

12, 12 and 10 cm.

Step-by-step explanation:

6 + 6 + 5 = 17

So one side = 6/17 * 34 = 12 cm

One other side is also 12 cm

The third side = 5/17 * 34 = 10 cm.

Answer:

x = ---------- = 1

Step-by-step explanation:

The formula for the axis of symmetry is x = -b/(2a).  In this case b = -4 and a = 2, and so the axis of symmetry is

        -(-4)

x = ---------- = 1

       2(2)

Answer:

x=1

Step-by-step explanation:

because I said so

Answer:

Step-by-step explanation:

Open box is in rectangular shape. cuboid that is open in the top

l = length = 30 - (2.5 + 2.5 ) = 30 - 5 = 25 cm

h = 2.5 cm

w = width = 30 - (2.5 + 2.5) = 30 - 5 = 25 cm

Surface Area = 2lh + 2wh + lw

                     = 2*25*2.5 + 2* 25*2.5 + 25*25

                    =125 + 125 + 625

                   = 875 square cm

Volume = lwh

             = 25*25*2.5

             = 1562.5 cubic cm

Answer:

A

Step-by-step explanation:

Answer:

80$

Step-by-step explanation:

total amount of needed=200

Total =Tef +Angelina+Jason

200=90+30+Angelina

Angelina=200-120

Angelina=80$

Answer: 5.34

Step-by-step explanation: 18 - 12.66 = 5.34

Answer:

Step-by-step explanation:I think the answer is 12?

Answer:

583.33 cm³

Step-by-step explanation:

From the image attached, the total height (H) of the pyramid is 30 cm, the height of the frustrum (h) = 15 cm, the Frustrum base = lower base = B = 10 cm . To find the length of the upper base (b), we use:

[tex]\frac{b}{H-h}=\frac{B}{H}\\ b=(H-h)\frac{B}{H}\\b=(30-15)\frac{10}{30}=5\\b=5\ cm[/tex]

The volume of the frustrum is given by:

[tex]V=\frac{1}{3}h(B_1+B_2+\sqrt{B_1B_2} )\\ Where\ B_1\ is \ the\ area \ of\ the\ upper\ base= 5cm*5cm=25cm^2\\B_1\ is \ the\ area \ of\ the\ lower\ base= 10cm*10cm=100cm^2\\V=\frac{1}{3}(10)(25+100+\sqrt{25*100} )=583.33\\V=583.33\ cm^3[/tex]

Answer:

Hey there!

Original Equation

-5x-4y=-8

Multiply by -1

5x+4y=8

Subtract 4y

5x=8-4y

Divide by 5

x=(8-4y)/5

Let me know if this helps :)

Answer:

x = -4/5y + 8/5

Step-by-step explanation:

So to single out x we use the communicative property,

its the moving of numbers and variables to each side of the equation.

So we have,

-5x - 4y = -8

+4y

-5x = 4y - 8

Divide -5 by both sides,

x = -4/5y + 8/5

Thus,

the equation rearanged is x = -4/5y + 8/5.

Hope this helps :)

Answer:

7/8 of the game is left. The game lasts for 592 minutes.

Step-by-step explanation:

It is halfway through the first quarter so it is 1/8. So that's 7/8 part of the game left. if 74 minutes of playing time has past, then you do 74*8 so that's 592 minutes.

Answer:

4) 1/8

3)74x8=592

6)592-74= 518

Step-by-step explanation:

Answer:

The speed of plane = 40 m/s

The speed of the wind = 300 m/s

Step-by-step explanation:

Let the speed of the plane = Y

And the speed of the wind = X

If the plane then travel 340 miles per hour with the wind, that means the plane and the wind are moving in the same direction. Therefore,

X + Y = 340 ..... ( 1 )

Also, 260 miles per hour against the wind. That is, the plane is moving opposite to the direction of the wind. Therefore,

X - Y = 260 ..... ( 2 )

Solve the two equations simultaneously by addition. That will eliminate Y

X + Y = 340

X - Y = 260

2X = 600

X = 600/2

X = 300 m/s

Substitutes X in equation (1)

300 + Y = 340

Make Y the subject of formula by collecting the like terms

Y = 340 - 300

Y = 40 m/s

Therefore, the speed of the plane is 40 m/s. While the speed of the wind is 300 m/s.

Answer:

C. [tex](5-\frac{1}{2})^6[/tex]

Step-by-step explanation:

Given

[tex]15(5)^2(-\frac{1}{2})^4[/tex]

Required

Determine which binomial expansion it came from

The first step is to add the powers of he expression in brackets;

[tex]Sum = 2 + 4[/tex]

[tex]Sum = 6[/tex]

Each term of a binomial expansion are always of the form:

[tex](a+b)^n = ......+ ^nC_ra^{n-r}b^r+.......[/tex]

Where n = the sum above

[tex]n = 6[/tex]

Compare [tex]15(5)^2(-\frac{1}{2})^4[/tex] to the above general form of binomial expansion

[tex](a+b)^n = ......+15(5)^2(-\frac{1}{2})^4+.......[/tex]

Substitute 6 for n

[tex](a+b)^6 = ......+15(5)^2(-\frac{1}{2})^4+.......[/tex]

[Next is to solve for a and b]

From the above expression, the power of (5) is 2

Express 2 as 6 - 4

[tex](a+b)^6 = ......+15(5)^{6-4}(-\frac{1}{2})^4+.......[/tex]

By direct comparison of

[tex](a+b)^n = ......+ ^nC_ra^{n-r}b^r+.......[/tex]

and

[tex](a+b)^6 = ......+15(5)^{6-4}(-\frac{1}{2})^4+.......[/tex]

We have;

[tex]^nC_ra^{n-r}b^r= 15(5)^{6-4}(-\frac{1}{2})^4[/tex]

Further comparison gives

[tex]^nC_r = 15[/tex]

[tex]a^{n-r} =(5)^{6-4}[/tex]

[tex]b^r= (-\frac{1}{2})^4[/tex]

[Solving for a]

By direct comparison of [tex]a^{n-r} =(5)^{6-4}[/tex]

[tex]a = 5[/tex]

[tex]n = 6[/tex]

[tex]r = 4[/tex]

[Solving for b]

By direct comparison of [tex]b^r= (-\frac{1}{2})^4[/tex]

[tex]r = 4[/tex]

[tex]b = \frac{-1}{2}[/tex]

Substitute values for a, b, n and r in

[tex](a+b)^n = ......+ ^nC_ra^{n-r}b^r+.......[/tex]

[tex](5+\frac{-1}{2})^6 = ......+ ^6C_4(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]

[tex](5-\frac{1}{2})^6 = ......+ ^6C_4(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]

Solve for [tex]^6C_4[/tex]

[tex](5-\frac{1}{2})^6 = ......+ \frac{6!}{(6-4)!4!)}*(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]

[tex](5-\frac{1}{2})^6 = ......+ \frac{6!}{2!!4!}*(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]

[tex](5-\frac{1}{2})^6 = ......+ \frac{6*5*4!}{2*1*!4!}*(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]

[tex](5-\frac{1}{2})^6 = ......+ \frac{6*5}{2*1}*(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]

[tex](5-\frac{1}{2})^6 = ......+ \frac{30}{2}*(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]

[tex](5-\frac{1}{2})^6 = ......+15*(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]

[tex](5-\frac{1}{2})^6 = ......+15(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]

[tex](5-\frac{1}{2})^6 = ......+15(5)^2(\frac{-1}{2})^4+.......[/tex]

Check the list of options for the expression on the left hand side

The correct answer is [tex](5-\frac{1}{2})^6[/tex]

Answer:

9 cm

Step-by-step explanation:

Pythagorean's Theorem: a^2+b^2=c^2

x^2+6^2=117 (the square root of 117, squared)

X^2+36=117

x^2=117-36

x^2=81

x=9

Answer:

x = 9 cm

Step-by-step explanation:

Use the Pythagorean Theorem to find the length of the missing side.

a² + b² = c²

a² + (6)² = (√117)²

a² + 36 = 117

a² = 81

a = √81

a = 9

X is equal to 9 cm.

Hope this helps.

Answer:

7.06

Step-by-step explanation:

17/8 = 15/DF

DF = 7.06

Answer:

Ok so im in 7thgrade so ima try to help answer is x= 8x9

Answer:

Domain: (-5,-4,-3,-2,-1,0,1,2,3,4,5)

Range: (0,1,2,3,4, -1, -2)

Step-by-step explanation:

Domain means all of the x-axis values on the graph, so for example in (-2,0), -2 would be part of the domain and 0 part of the range. Therefor, what you would do would be take all of the plots and put all x values as the domain and all y values as the range. Hope this helped!

Answer:

x = (3 +/- sqrt(17) / 4.

Step-by-step explanation:

x = [-(-3) +/- sqrt((-3)^2 - 4*2*-1)] / 4

x = (3 +/- sqrt(17) / 4.

Answer: 240

Step-by-step explanation:

5/6x=200

(6/5)5/6x=200(6/5)

1x=40(6/1)

x=40(6)

x=240

Answer:

Step-by-step explanation:

Hello,

a. The area of region P is the area of the rectangle 1 * e minus the

[tex]\displaystyle \int\limits^0_1 {e^x} \, dx=[e^x]^{1}_{0}=e-1[/tex]

So this is e - (e-1) = e - e + 1 = 1

b. The area of region P is the area of the rectangle 1 * e minus P and minus the

[tex]\displaystyle \int\limits^0_1 {e^{-x}} \, dx=[-e^{-x}]^{1}_{0}=-e^{-1}+1[/tex]

So this is

[tex]e - 1 - (-e^{-1}+1) = e-1+e^{-1}-1=e+e^{-1}-2[/tex]

This is around 1.08616127...

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

rational (I think

Step-by-step explanation:

Answer:

158m^3

Step-by-step explanation:

First, let's figure out the total amount of water in the tank.

It measures 4.5m by 6m by 8m. The volume of a rectangular prism is V=lwh.

Therefore, the volume is:

[tex]V=(4.5)(6)(8)=216 m^3[/tex]

We are told is it filled to the brim, so we can conclude that there are 216 cubic meters of water in the tank.

We used 58 cubic meters of water, so we simply need to subtract that from 216:

[tex]216m^3-58m^3=158m^3[/tex]

There is still 158 cubic meters of water left in the tank.

Answer:

158 m^3

Step-by-step explanation:

Volume of the tank

= 4.5 * 6 * 8

= 216 m^3.

So amount left in the tank

= 216 - 58

= 158 m^3.