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Galina-37 [17]
3 years ago
10

Gary won $70,000 in the lottery after all tax deductions. He invested part of the money at 11% and deposited the remainder in ta

x-free bonds at 12%. His total annual income from the investments was $7900. Find the amount invested at 11%. Find the amount invested at 12%.
Mathematics
1 answer:
Tju [1.3M]3 years ago
4 0
X - invested for the money at 11%
70 000 - x - deposited at 12%

0.11x + 0.12(70000-x)=7900
0.11x + 8400 - 0.12x = 7900
8400- 7900 = 0.01x
500 = 0.01x
x=50 000 invested at 11%
rest (20K) invested at 12%

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Decompose the rectangle along the diagonal and recompose the two pieces to make a different shape, then five different ways are shown.

<h3>Further explanation </h3>

Area is the number of squares inside a two-dimensional shape.

Here are two important principles for finding area:

  • If two figures can be placed one on top of the other, then they have the same area so that they match up exactly.
  • We can decompose a figure (break a figure into pieces) and rearrange the pieces (move the pieces around) to find its area.

A rectangle has two diagonals. Each one is a line segment drawn between the opposite vertices (corners) of the rectangle. For rectangle, shapes can be decomposed and rearranged back to rectangles to find the area.  When decomposing and rearranging shapes the area of the polygon does not change.

The rectangle is shown in the picture below. After decompose the rectangle along the diagonal, we can varied the pieces to make various different shape. Picture below also shown the five different ways pieces from the rectangle.

<h3>Learn more</h3>
  1. Learn more about rectangle brainly.com/question/2810576
  2. Learn more about Decomposing and Rearranging brainly.com/question/3026941
  3. Learn more about Area and Surface Area brainly.com/question/9265968

<h3>Answer details</h3>

Grade:  9

Subject:  Mathematics

Chapter:  Area and Surface Area

Keywords: Area, Surface Area, Decomposing, Rearranging, rectangle

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The tires on Pablo's bicycle have a radius of 10 inches. Use the appropriate formula model to find the circumference. What is th
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Answer:

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USPshnik [31]

Answer:

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Step-by-step explanation:

Applicable relations are ...

  C = 2πr . . . . . . . r = radius, C = circumference

  LA = 1/2·Ch . . . . h = slant height, LA = lateral area

  SA = πr² +LA . . . SA = total surface area

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1. Given r and SA, we can find the other measures as ...

  LA = SA -πr² = 50 ft² -π(3 ft)² ≈ 21.7 ft²

  C = 2πr = 2π(3 ft) ≈ 18.8 ft

  h = 2·LA/C ≈ 2·21.7 ft²/(18.8 ft) ≈ 2.3 ft

(Please note that for calculations using intermediate results, we used the full-precision values of those results, not the rounded ones. Rounding is always the last operation. Please note, too, that we have used a value for π sufficient to ensure accuracy in all the digits shown here.)

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2. Given C and LA, we can find the other measures as ...

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  r = C/(2π) = (44 in)/(2π) ≈ 7.0 in

  SA = LA +πr² = LA +rC/2 ≈ 176 in² +(7.0 in)(44 in)/2 ≈ 330.1 in²

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