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ANEK [815]
3 years ago
9

Question

Mathematics
1 answer:
Juliette [100K]3 years ago
8 0

Given:

The compound inequality is

9

To find:

The solution for the given compound inequality in interval notation.

Solution:

We have,

9

Subtracting 6 from each side, we get

9-6

3

Divide each side by 3.

\dfrac{3}{3}

1

Here, 1 is not included in the solution set and 3 is included in the solution set.

Therefore, the solution in interval notation is (1,3].

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Find the area of the shaded region.
MariettaO [177]

Answer:

Area of  shaded region = 134.13 square feet

Step-by-step explanation:

Area of the shaded region = Area of square - Area of circle

                                         = ( 25 \times 25) - ( \pi 12.5^2)\\= 625 - 490.87\\= 134.13 ft^2

8 0
2 years ago
If you invest $4,500 in an account paying 2% compounded continuously, how much money will be in the account at the end of 4 year
saveliy_v [14]
Total = Principal * e^(rate*years)
Total = 4,500 * 2.718281828459^(.02*4)
Total = 4,500 * 2.718281828459^(.08)
Total = 4,500 * <span> <span> </span></span> <span> <span> <span> 1.0832870677 </span> </span> </span>
Total = <span> <span> <span> 4,874.79 </span> </span> </span>
calculator for checking the answer:
http://www.1728.org/compint.htm



7 0
3 years ago
Find the missing length ‘x’
givi [52]

Answer:

x = 13

Step-by-step explanation:

The area (A) of a trapezium is calculated as

A = \frac{1}{2} h (b₁ + b₂ )

where h is the perpendicular height and b₁, b₂ the parallel bases

Here A = 55, h = 5. b₁ = x, b₂ = 9, then

\frac{1}{2} × 5 × (x + 9) = 55

2.5(x + 9) = 55 ( divide both sides by 2.5 )

x + 9 = 22 ( subtract 9 from both sides )

x = 13

7 0
3 years ago
Parabolas y=−2x^2 and y=2x^2 +k intersect at points A and B that are in the third and the fourth quadrants respectively. Find k
OverLord2011 [107]

Answer:

-25  

Step-by-step explanation:

(1)   y = -2x²

(2) y =   2x² + k     Subtract (1) from (2)

    0 =  4x² + k      Subtract 4x² from each side

    k = -4x²

The parabolas are <em>symmetrical about the y-axis.</em>

Segment AB = 5, so x = +2.5 and x = +2.5.

k = -4(±2.5)² = -4 × 6.25 = -25

8 0
3 years ago
Jim owns stock in Gamma Vision Inc. That company announces that it will split its stock with three new shares per two old shares
ruslelena [56]

Answer:

<u>The correct answer is C. 600 shares worth $16.67 each </u>

Step-by-step explanation:

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

Number of old shares Jim owns in Gamma Vision Inc = 400

Value of each share = $ 25

Ratio of new shares : old shares after the split = 3:2

2. How many shares will he have after the split and how much will each be worth? Select the best answer from the choices provided.

A. Let's use the ratio provided to calculate the number of new shares Jim will own, this way:

New shares = 400 * 3/2 = 1,200/2 = 600

B. Let's calculate the price of the new share, this way:

The total value of the new shares should be the same than the total value of the old shares, then:

400 * 25 = 600 * x

10,000 = 600x

x = 10,000/600 = 16.67

<u>The correct answer is C. 600 shares worth $16.67 each </u>

3 0
3 years ago
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