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tekilochka [14]
2 years ago
15

A jar is full of 100 coins. All of the coins are either nickels or dimes.

Mathematics
1 answer:
Elza [17]2 years ago
5 0

Answer:

73 nickels, 27 dimes

Step-by-step explanation:

x+y=100

5x+10y=635

x=100-y

5(100-y)+10y=635

500-5y+10y=635

500+5y=635

5y=135

y=27

5x+10(27)=635

5x+270=635

5x=365

73

73+27=100

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3 years ago
What is the product?<br><br> One-eighth times three-elevenths
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3/88

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2 years ago
2. Consider the circle x² + y2 = 1, given in figure. Let OP makes an angle 30° with the x axis.
PolarNik [594]

The equation of the tangent line to the circle passing through the point P is; y = (1/√3)x ± 2/√3

<h3>How to find the equation of the tangent?</h3>

I) We are given the equation of the circle as;

x² + y² = 1

Since angle of inclination is 30°, then slope is;

m = tan 30 = 1/√3

Then equation of the tangent will be;

y = (1/√3)x + c

Put  (√3)x + c into the given circle equation to get;

x² + ((1/√3)x + c)² = 1

x² + ¹/₃x² +  (2/√3)cx + c² = 1

⁴/₃x² +  (2/√3)x + (c² - 1) = 0

Since we need to find value of c for equation to become tangent, then the above quadratic equation must have real and equal roots.

Thus;

((2/√3)c)² - 4(⁴/₃)(c² - 1) = 0

⁴/₃c² - ¹⁶/₃(c² - 1) = 0

⁴/₃c² - ¹⁶/₃c² + ¹⁶/₃ = 0

4c² = ¹⁶/₃

c² = ⁴/₃

c = √⁴/₃

c = ±²/√3

Thus, equation of tangent is;

y = (1/√3)x ± 2/√3

II) Radius from the given equation is 1. Thus, we will use trigonometric ratio to find the x and y intercept;

x-intercept is at y = 0;

0 = (1/√3)x ± 2/√3

-(1/√3)x = ±2/√3

Intercept is positive. Thus;

x = (2/√3)/(1/√3)

x = 1

y - intercept is positive at x = 0;

y = (1/√3)0 ± 2/√3

y = 2/√3

Read more about Equation of tangent at; brainly.com/question/17040970

#SPJ1

6 0
1 year ago
Jessica makes overtime pay when she works more than 40 hours in a week. So far this week she has worked 29 hours. She will conti
Ray Of Light [21]

Answer:11 more hours

Step-by-step explanation:

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3 years ago
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lyudmila [28]

Answer:

Incorrect

Step-by-step explanation:

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