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2 years ago

Which of the following is a solution of the system x – 2y < 4 and y > – 2x – °5?

Mathematics

1 answer:

Nutka1998 [239]2 years ago

8 0

Answer: B

Step-by-step explanation:

Given the two systems of inequality to be:

x – 2y < 4

Rearrange the equation,

X - 2y < 4

-2y < 4 - x

The sign will change as we divide both sides by -2

Y > -2 + x/2

Y > x/2 - 2 ...... (1)

and

y > – 2x – 5 ..... (2)

Multiply (1) by 2 and (2) by 1/2

2y > x - 4

y/2 > -x - 5/2

Since the inequality sign of the two are the same, you can eliminate x by addition.

2 1/2 y > - 4 5/2

Change mixed fraction to improper fraction.

5y/2 > -13/2

Cross multiply

10y > -26

y > -26/10

y > - 2.6

Base on the value got for y, the correct answer is B ( -8, 2 ) because only option B and D has negative value for x and y is not equal to zero.

You confirm by plugging in the value in the two inequality equations.

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3 years ago

The center of a hyperbola is (−4,3) , and one vertex is (−4,7) . The slope of one of the asymptotes is 2.

Monica [59]

Answer:

The answer to your question is below

Step-by-step explanation:

C (-4, 3)

V (-4, 7)

asymptotes = 2 = $\frac{b}{a}$

- This is a vertical hyperbola, the equation is

$\frac{(y - k)^{2} }{a^{2} } + \frac{(x - h)^{2} }{b^{2} } = 1$

slope = 2

a is the distance from the center to the vertex = 4

b = 2(4) = 8

$\frac{(y - 3)^{2} }{4^{2} } + \frac{(x + 4)^{2} }{8^{2} } = 1$

$\frac{(y - 3)^{2} }{16} + \frac{(x + 4)^{2} }{64} = 1$

7 0

3 years ago

Read 2 more answers

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3 years ago

N-7=sqrt(n+5) Solve the following equation for all the values of y.

Ray Of Light [21]

Step-by-step explanation:

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3 years ago

1. Two thousand dollars is invested at 5.5 percent interest compounded

Dafna11 [192]

Two thousand dollars is invested at 5.5 percent interest compounded

quarterly for 2 years. Then the amount is $ 2230.88

Solution:

Given that Two thousand dollars is invested at 5.5 percent interest compounded quarterly for 2 years

The formula for amount using compounded quarterly is given as:

$\text { Amount }=P\left(1+\frac{R / 4}{100}\right)^{4 T}$

Where, "p" is the principal sum

"R" is the rate of interest

"T" is the number of years

Here in this problem,

P = 2000 ; R = 5.5 ; T = 2 years

Plugging in values in formula we get,

$\text {Amount}=2000\left(1+\frac{\frac{5.5}{4}}{100}\right)^{4 \times 2}$

$=2000\left(1+\frac{1.375}{100}\right)^{8}$

On solving we get,

$=2000(1+0.01375)^{8}=2000(1.11544)=2230.88$

Hence the amount is $ 2230.88

4 0

3 years ago