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3 years ago

Devin is collecting signatures for a petition to open a new park in her town. She needs to collect at least 1,000

Mathematics

1 answer:

Paraphin [41]3 years ago

3 0

Answer:

P = t - f

Step-by-step explanation:

First we need to find how many pages in total she needs so 1,000/80 - 12.5 so 13 pages. Then 380/80 4.75 of a page filled so subtract that from 12.5 to get 8 pages left to fill.

let p = pages left to fill

let T = total pages needed

let F = pages already filled

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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

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6 0

1 year ago

twice the sum of a number and 6 is equal to 3 times the difference of the number and 8. Find the number

Serhud [2]

In order to solve this problem, we must solve an equation.

First, we need to define our unknown.

Let's call our number "n".

So, the sum of the number and 6 is the same as saying n+6

Then we need to multiply it by 2 (since it's twice the sum)

2(n+6)

This whole thing is equal to three times of the difference of the number and 8

n-8 is equal to the difference between the number and 8, then we need to multiply it by three.

3(n-8)

now, we set both sides equal and solve

$2(n+6)=3(n-8)\\2n+12=3(n-8)\\2n+12=3n-24\\12=n-24\\36=n$

The number is 36

5 0

3 years ago

The khans car averages 22 miles per gallon of gas predict how far can thay travel on 5 gallons of gas

kodGreya [7K]

If the Khans car runs 22 miles per one gallon, then on 5 gallons of gas they can drive 110 miles.

1 gallon = 22 miles

5g x 22m = 110

I hope this helps! If I did something wrong, please correct me!

5 0

3 years ago

Are the graphs of 2x+7y=6 and 7y = 2x +6 parallel? Explain.

avanturin [10]

With questions like this (to see if theyre parallel), all you have to do is see if lines have a congruent slope. if yes (ex: 2 and 2), then they are parallel. if the slopes are opposites (ex: 4 and -1/4), then they are perpendicular. If they have no such relation (ex: -3 and 1/7), then they are neither.

with this problem, find the slope by separating the same variable in each equations, like this:

2x + 7y = 6
-2x -2x

7y = -2x + 6

(the second equation is already separated) so now we have

7y = -2x + 6 and 7y = 2x + 6

since -2 does NOT equal 2, these two graphs/lines are NOT parallel.
Hope this helped!

7 0

3 years ago

Forty students took a statistics exam having a maximum of 50 points. The distribution of score is given in the stem-and-leaf plo

Aneli [31]

Based on the fact that Tess's score was 25 in the statistics exam as shown by the stem-and-leaf plot, her Tess's percentile was 30th.

<h3>What was Tess's percentile?</h3>

Tess's percentile depends on the number of people whose scores she is above.

When looking at the stem-and-leaf plot, we see that Tess's score of 25 is the 13th score.

Her percentile is therefore:

= (13 - 1) / 40

= 12 / 40

= 30th percentile

Rest of the question is:

Tess’s score was 25. What was her percentile?

Find out more on percentile scores at brainly.com/question/24245405

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5 0

2 years ago