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Cerrena [4.2K]
3 years ago
9

A bank loaned out $10,000, part of it at the rate of 6% per year and the rest at 16% per year. If the interest received in one y

ear totaled $1000, how much was loaned at 6%?
How much of the $10,000 did the bank loan out at 6%?
Mathematics
1 answer:
Oduvanchick [21]3 years ago
5 0

Answer:

  $6,000 was loaned at 6%

Step-by-step explanation:

Let 'a' represent the amount loaned at 6%. Then the amount of interest from the loans was ...

  a·6% + (10000 -a)·16% = 1000

  -0.10a +1600 = 1000 . . . . . simplify

  600 = 0.10a . . . . . . . . . . . . add 0.10a-1000

  6000 = a . . . . . . . . . . . . . . divide by 0.10

The bank loaned $6000 at 6%.

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Please I really need help
ohaa [14]

9514 1404 393

Answer:

  • scale factor: 3
  • rule: (x, y) ⇒ (3x +15, 3y -24)
  • center: (-7.5, 12)

Step-by-step explanation:

The scale factor can be found by comparing the length of CB to the length of RQ.

  B-C = (-2, 8) -(-4, 9) = (2, -1)

  Q-R = (9, 0) -(3, 3) = (6, -3)

The length of RQ is clearly 3 times the length of CB, so the scale factor (k) is ...

  ratio of corresponding differences = 6/2 = -3/-1 = 3 . . . . . scale factor

__

We know that for dilation about a point O, the distance from O is multiplied by the scale factor. For dilation of point B to point Q, this means ...

  k(B -O) = (Q -O)

Solving for Q, we get ...

  Q = kB -kO +O . . . . this is what our dilation rule will look like.

The quantity O-kO can be found by subtracting kB:

  Q -kB = O -kO = O(1 -k)

This is what we need for our dilation rule.

  Q -kB = (9, 0) -3(-2, 8) = (9+6, 0-24) = (15, -24)

So, our dilation rule is ...

  (x, y) ⇒ k(x, y) +(15, -24)

  (x, y) ⇒ (3x +15, 3y -24) . . . . . dilation rule

__

The center of dilation can be found from ...

  (Q -kB)/(1 -k) = O

  O = (15, -24)/(1 -3) = (-7.5, 12)

The center of dilation is (-7.5, 12).

_____

<em>Additional comments</em>

On the graph, the center of dilation can be found by drawing a line through a point and its image. (Points are always dilated along a line through the center of dilation.) The intersection of two such lines is the center of dilation.

On this graph, the center is just above the top edge of the chart, at point (-7.5, 12). You can see this if you carefully draw lines BQ and AP.

You usually have coordinates for two original points and two image points, so finding the scale factor the way we did is not difficult. If you just have one point on the original and the image, the scale factor is found by finding their distances from the center of dilation. Each image point is k times as far as each original point from that center.

7 0
3 years ago
Please help??!?!??? Bplease
amid [387]

Answer:

radical 7<14÷5

bcoz radical 7 is 2.645

and 14÷5 is 2.8

3 0
3 years ago
What's the present value of $9,500 discounted back 5 years if the appropriate interest rate is 4.5%, compounded semiannually?
nasty-shy [4]

Answer:

$427.50

Step-by-step explanation:

I think this is the answer because 4.5 percent of $9,500 is $427.50

4 0
3 years ago
The range of the function f(k) = k2 + 2k + 1 is {25, 64}. What is the function’s domain? {5, 8} {-5, -8} {3, 8} {4, 7} {4, 8}
Sergeu [11.5K]
I think the answer is {5,8}
4 0
3 years ago
An architect is designing a building each floor will be 12 ft tall. Write an expression for the number of floors the building ca
Svet_ta [14]

Answer:

\frac{h}{12}

Where "h" is the height of the building.

Step-by-step explanation:

For this exercise it is important to read and analize carefully the information provided.

According to the data given in the exercise, the height of each floor the arquitect is designing is 12 feet.

You want to know the number of floors of 12 feet tall that building can have for a given building height.

Then, you can let "h" represents the height of the building. This will be the variable in the expression.

In order to find the number of those floors that the building can have for "h", you need divide this height by the height of each floor.

Therefore, you can determine that the expression asked in the exercise is the following:

\frac{h}{12}

Where "h" is the height of the building.

8 0
4 years ago
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