Caroline borrowed 300,000 from the bank in order to buy a house. If the simple interest RATE that the bank charged her was 3.5%, and she ended up paying the bank back a total of $615,000 (principal and interest total), how long (in years) did it take her to pay back the loan?

The cosine of angle ∠B will be 3 / 5. Then the correct option is C.

The connection between the lengths and angles of a triangular shape is the subject of trigonometry.

The cosine of the angle θ is the ratio of the side adjacent to the angle and the longest length of the triangle which is the hypotenuse.

cos θ = base / hypotenuse

Triangle ABC is shown below. The side BC is base which is equal to 3. And the side AB is hypotenuse which is equal to 5.

Then the cosine of the angle ∠B will be given as,

cos θ = base / hypotenuse

cos B = 3 / 5

The cosine of angle ∠B will be 3 / 5. Then the correct option is C.

More about the trigonometry link is given below.

https://brainly.com/question/22698523

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Answer:

Hope it help

Mark me as brainliest

Step-by-step explanation:

Answer:

cholesterol in egg= 273 mg

cholesterol in cupcake = 18 mg

cholesterol in slice of pizza = 9 mg

Step-by-step explanation:

Given data:

1 egg , 1 cupcake , 1 slice of pizza  = 300mg

3 cupcakes , 4 slices of pizza = 90mg

2 eggs , 1 cupcake = 564mg

Let egg be x , let cupcake be y and let pizza be y

x + y + z = 300 (equation 1)

0x + 3y + 4z = 90 (equation 2)

2x + y + 0z = 564 (equation 3)

Using equation 1 and equation 2

x + y + z = 300 (Multiply equation by 3)

0x + 3y + 4z = 90

3x + 3y +3z =900

0x +3y +4z = 90  (Subtracting the equations)

3x - z = 810  (equation 4)

Using equation 2 and equation 3

0x + 3y + 4z = 90

2x + y + 0z = 564 (Multiply equation by 3)

0x + 3y + 4z = 90

6x +3y + 0z = 1692 (Subtracting the equations)

-6x +4z =-1602  (equation 5)

Solving equation 4 and equation 5

3x - z = 810  therefore z =3x -810

Substituting z into equation 5

-6x +4(3x - 810) =-1602  

-6x + 12x - 3240 = -1602

6x = -1602+3240

6x = 1638

x = 273

Substituting x into z = 3x - 810

z = 3(273) - 810

z = 819-810

z = 9

Using equation 1 to find y

x + y + z = 300

273 + y + 9 = 300

282 + y = 300

y = 300-282

y = 18

Answer:

[tex]Time = 11\frac{2}{3}\ min[/tex]

Step-by-step explanation:

Given

[tex]Security\ A = 2\ mins, 20\ secs[/tex]

[tex]Security\ B = 1\ mins, 40\ secs[/tex]

Required

After how many minutes, will they round together

First, convert the given time to minutes

[tex]Security\ A = 2\ mins, 20\ secs[/tex]

[tex]Security\ A = 2\ mins+ 20\ secs[/tex]

[tex]Security\ A = 2\ mins+ \frac{20}{60}\ min[/tex]

[tex]Security\ A = 2\ mins+ \frac{1}{3}\ min[/tex]

[tex]Security\ A = 2\frac{1}{3}\ min[/tex]

[tex]Security\ B = 1\ mins, 40\ secs[/tex]

[tex]Security\ B = 1\ mins+ 40\ secs[/tex]

[tex]Security\ B = 1\ mins+ \frac{40}{60}\ min[/tex]

[tex]Security\ B = 1\frac{2}{3}\ min[/tex]

So, we have:

[tex]Security\ A = 2\frac{1}{3}\ min[/tex]

[tex]Security\ B = 1\frac{2}{3}\ min[/tex]

List out the multiples of the time of both security personnel take round.

[tex]Security\ A = 2\frac{1}{3}min,\ 4\frac{2}{3}min,\ 7min,\ 9\frac{1}{3}min,\ 11\frac{2}{3}min...[/tex]

[tex]Security\ B = 1\frac{2}{3}min,\ 3\frac{1}{3}min,\ 5min,\ 6\frac{2}{3}min,\ 8\frac{1}{3}min,\ 10min\ ,11\frac{2}{3}min,...[/tex]

In the above lists, the common time is:

[tex]Time = 11\frac{2}{3}\ min[/tex]

This implies that they go on round after [tex]11\frac{2}{3}\ min[/tex]

Answer:

More

Step-by-step explanation:

If we divide 30 by .25 we will get 120

Answer:

8-3i

Step-by-step explanation:

additive inverse of a+bi is -(a+bi)

so -(-8+3i) -- distribute negative through ()

8-3i

Answer:

First and last

Step-by-step explanation:

(4x - 7) (x + 3)

FOIL

4x^2 + 5x - 21

Answer:

He would have 2.75 gallons left after 5 hours.

Step-by-step explanation:

Answer:

Your answer will be (2,4) :)

Answer:

a) 24[tex]ft^2[/tex]

b) 52ft

Step-by-step explanation:

a)

This question asks to find the capacity of the container. This is essentially asking what the volume of the container is. This can be done by multiplying the length by the width by the height.

4 * 2 * 3

= 24

b)

This question is asking how much material was used to make the prism. This is essentially asking what the surface area of the prism is. This can be found by finding the area of all the sides of the prism and then adding it up. Since it is a rectangular prism, opposite faces are congruent, hence one only has to find the area of three faces, add it up, then multiply it by two to find the answer.

2 ( 4 * 2 ) + 2 ( 3 * 4 ) + 2 ( 2 * 3 )

= 2(8) + 2(12) + 2(6)

= 16 + 24 + 12

= 52

Answer:

Max p = 28x + 41y

Subject to

59x + 58y ≤ 3660

21x + 34y ≤ 4020

x  ≥  0, y ≥ 0

Step-by-step explanation:

As given ,

                                       Windbreakers          Rain breakers              Total

Finishing time                         59 min                     58 min                   61 hr

Packaging time                        21 min                      34 min                   68 hr

Profit                                          28                                41

Let

The number of windbreaker jackets they should produce = x

The number of rain breaker jackets they should produce = y

As given,

The company wants to maximize profit.

⇒ Maximum Profit , p = 28x + 41 y

Now,

As 1 hour = 60 min

⇒61 hours = 61×60 = 3660 min

and 67 hours = 67×60 = 4020 min

∴ we get

The equations become

59x + 58y ≤ 3660

21x + 34y ≤ 4020

x  ≥  0, y ≥ 0

So, the Linear Programming Problem (LPP) for this problem is -

Max p = 28x + 41y

Subject to

59x + 58y ≤ 3660

21x + 34y ≤ 4020

x  ≥  0, y ≥ 0

Answer:

sa taas nito ay 50 square meter kung pagbabasihan mo sa ibaba 55 square meter malaki rin sa baba kaya ang tawag dyaan ay centementer

I hope I can help you and give me a star even if I am only 5 or 4 stars and please put a heart for many

Answer:

Step-by-step explanation:

I think that you want to know how many total pounds of beans do you have.

Well, to find this, simply find the LCM of 6 and 4. That is 12.

So convert the fractions to have a denominator of 12.

10/12, 9/12

Now add:

(10+9)/12 = 19/12 = 1 7/12

Answer:

Your answer is A

Step-by-step explanation:

I hope I helped :)

Answer:

The order of large fries costs $ 2.10, while each hamburger costs $ 3.25.

Step-by-step explanation:

Given that the cost of a hamburger is $ 1.15 more than an order of large fries, and Bill bought two hamburgers and an order of fries for a total of $ 8.60, to determine what is the price of each item, the following calculation must be performed:

X + X + 1.15 + X + 1.15 = 8.60

3X + 2.30 = 8.60

3X = 8.60 - 2.30

X = 6.30 / 3

X = 2.10

Thus, each order of large fries costs $ 2.10, while each hamburger costs $ 3.25.

Answer:

8

Step-by-step explanation:

Jeremiah bought x toy sets for $20 each and then a video game for $60. Jeremiah spent a total of $220. How may toy sets did he buy?

To find our answer, we can solve the equation:

20x + 60 = 220

        -60    -60

20x = 160

/20    /20

x = 8

Jeremiah bought 8 toy sets!

I hope this helps :)

Answer:

Total cost of the grill installment plan = 2290

Step-by-step explanation:

370 + 1920 = 2290

Answer:

Step-by-step explanation:

Using first equation in the second gives you

x-3(-2x+1)=11

x+6x-3=11

7x-3=11

7x=14

x=2, making y=-2x+1 become

y=-2(2)+1

y=-4+1

y=-3 so the solution is the point

(2,-3)

Answer:

English?

Step-by-step explanation:

Answer:

Step-by-step explanation:

a₁ = -3 = (-1)¹×3

a₂ = 6 = (-1)²×2×3

a₃ = -28 = (-1)³×2²×7

a₄ = 72 = (-1)⁴×2³×3²

a₅ = -360 = (-1)⁵×2³×3²×5

a₆ = 2160 = (-1)⁶×2⁴×3³×5

That's as far as I got. I can predict that a₇ is a multiple of -32 and a₈ is a multiple of 64, but I don't see the pattern with the other factors.

Answer:

(x+1)(x-6)

thats the ans :)

Answer:

750 cubic feet

Step-by-step explanation:

Answer:

Net Mass = 520 g

Step-by-step explanation:

Given:

Waste = 240 g

Gross mass = 760 g

Find:

Net Mass

Computation:

Net Mass = Gross mass - Waste

Net Mass = 760 g - 240 g

Net Mass = 520 g

Answer:

1

5

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If a+b=8, b+c=10 and c+a=12, what is the value of a+b+c?

Answer

12

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Patrick Ivers, former mathematics & English instructor

Answered June 26, 2018

If a+b=8, b+c=10 and c+a=12, what is the value of a+b+c?

The puzzle is solved by defining each variable in terms of another variable & a number & then making substitutions. Begin by taking each sum to define one of the variables in terms of the other. (Different combinations are available, but I’ll follow the a,b,c order.)

a+b=8 becomes a=8-b

b+c=10 becomes b=10-c

c+a=12 becomes c=12-a

Now subtract two of the equations that contain the same variable. I’ll pick two that contain an a: c+a =12 & a+b=8. Subtracting the latter from the former eliminates the “a”s, leaving c-b=4. Adding b to both sides to isolate c gives c=b+4. From above we can take b=10-c to substitute for b in c=b+4, giving us c=(10-c) + 4). Simplify the right side to c=14-c, add c to both sides, giving 2c=14, & then divide both sides by 2 to obtain c=7.

Replace the c in b=10-c with 7 to

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Related Answer

Paul K. Young, Former PhD candidate in Mathematics

Answered September 28, 2016

If A = B and B = C, does A = C?

In mathematics = is assumed to be a transitive relationship. Transitivity means precisely what you stated: A = B and B = C implies A = C.

While it’s possible to use = to represent a non-transitive relationship this would be considered an abuse of notation. A ~ B or R(A, B) would be a better way to express the relation in this case.

Similar assumptions are made about operators like + and *. + is generally assumed to be commutative, whereas * can be used for noncommutative operations like matrix multiplication. E.g. A * B != B * A.

Equality in programming is another story entirely.

In many languages = is the assignment operator and == is the equality operator. Assignment is not transitive - it’s not even a relation.There are cases where the equality operator doesn’t define a transitive relation.