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AysviL [449]
2 years ago
10

The point P = (x, - 2/7) lies on the unit circle shown below. What is the value of x in simplest form?

Mathematics
1 answer:
miskamm [114]2 years ago
3 0

Answer: x = \frac{3\sqrt{5}}{7}\\\\

Explanation:

The equation of the unit circle is x^2+y^2 = 1\\\\

Plug in y = -2/7 and solve for x

x^2+y^2 = 1\\\\x^2+\left(-\frac{2}{7}\right) = 1\\\\x^2+\frac{4}{49} = 1\\\\x^2 = 1-\frac{4}{49}\\\\x^2 = \frac{49}{49}-\frac{4}{49}\\\\x^2 = \frac{45}{49}\\\\x = \sqrt{\frac{45}{49}} \ \ \text{ ... x is positive}\\\\x = \frac{\sqrt{45}}{\sqrt{49}}\\\\x = \frac{\sqrt{9*5}}{7}\\\\x = \frac{\sqrt{9}*\sqrt{5}}{7}\\\\x = \frac{3\sqrt{5}}{7}\\\\

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6 0
3 years ago
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Answer:

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3 years ago
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exis [7]

A. The coordinates of the midpoint of CD in terms of p and q is [(4 + p) / 2 , (5 + q) / 2]

B. The coordinates of D, Given that the midpoint of CD is (7, 1) is (10 , -3)

<h3>A. How to determine the mid point</h3>
  • Coordinate of C = (4, 5)
  • Coordinate of D = (p, q)
  • Mid point =?

Mid point = (X , Y)

X = (x₁ + x₂) / 2

X = (4 + p) / 2

Y = (y₁ + y₂) / 2

Y = (5 + q) / 2

Thus,

Mid point = (X , Y)

Mid point = [(4 + p) / 2 , (5 + q) / 2]

<h3>B. How to determine the coordinates of D</h3>
  • Mid point = (7, 1)
  • Coordinates of D =?

Mid point = (7, 1) = (X , Y)

X = (4 + p) / 2

7 = (4 + p) / 2

Cross multiply

7 × 2 = 4 + p

14 = 4 + p

Collect like terms

p = 14 - 4

p = 10

Y = (5 + q) / 2

1 = (5 + q) / 2

Cross multiply

1 × 2 = 5 + q

2 = 5 + q

Collect like terms

q = 2 - 5

q = -3

Coordinates of D = (p, q)

Coordinates of D = (10 , -3)

Learn more about coordinate geometry:

brainly.com/question/4976351

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5 0
2 years ago
Dawn has been using two bank accounts to save money for a car. the difference between account 1 and account 2 is $100. if she us
asambeis [7]
1) name the variables:

 - amount in account 1 "a"
 - amount in account 2 "b"

2) trtanslate the statements into equations:

<span>- the difference between account 1 and account 2 is $100.

=> a - b = 100

-  if she uses 3/8 of account 1 and 7/8 of account 2, Dawn will have a down payment of $2,000.

=> (3/8)a + (7/8)b = 2000

3) solve the system of equations

(1) a - b = 100
(2) (3/8)a + (7/8b) = 2000

Steps:

- multiply equation (1) by 7 and equaton (2) by 8

=>

(1) 7a - 7b = 700
(2) 3a + 7b = 16,000

- add the two equations

=>

7a + 3a - 7b + 7b = 700 + 16,000

- combine like terms:

10a = 16,700

- divide by 10:

a = 16,700 / 10 = 1670

- use equation (1) to find b:

a - b = 100 => b = a - 100 = 1670 - 100 = 1570

Answer: Dawn has $ 1670 in account 1 and $ 1570 in account 2. </span>
8 0
3 years ago
Read 2 more answers
Carol's starting pay for her summer job is $10.25 per hour. Carol earns exactly 3 raises this summer.
zlopas [31]
We know that
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</span><span>
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10.25+0.50=10.75
</span>Carol earn per hour=$10.75 per hour

3) <span>For the second rise, she receives a 10% raise per hour
10.75*1.10=11.825
</span>Carol earn per hour=$11.825 per hour

4) <span>For the third rise, she receives another 50 cent-per-hour raise
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</span>Carol earn per hour=$12.325 per hour

5) At the start of next summer. She will be given a 5% raise per hour based on her pay at the end of this summer. <span>
12.325*1.05=12.94125
</span>Carol will earn per hour=$12.94 per hour

the answer is
$12.94 per hour
4 0
3 years ago
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