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Arada [10]
2 years ago
7

Ignacio and Kirsten want to find out if the triangle formed by connecting (-1,-1). (-3,2), and (2, 1) is a right triangle Ignaci

o's plan: . Use the distance formula to find the lengths of the sides. • Then see if the side lengths satisfy the equation a2 + b2 = c2 to see if it is a right triangle Kirsten's plan: • Find the slopes of the three sides. • See if any two slopes are negative reciprocals of each other Which student's plan will work?​

Mathematics
1 answer:
navik [9.2K]2 years ago
8 0

Answer:

Both plans are correct

Step-by-step explanation:

I already did it

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2. Carl needs 15 hours longer than Jennifer to paint a room. If they work together, they can complete the job in 4 hours. Explai
nasty-shy [4]

Answer:

Jennifer would complete the job on her own in 5 hours.

Step-by-step explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

ax^{2} + bx + c, a\neq0.

This polynomial has roots x_{1}, x_{2} such that ax^{2} + bx + c = a(x - x_{1})*(x - x_{2}), given by the following formulas:

x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}

x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}

\Delta = b^{2} - 4ac

Rates

The together rate is the sum of their separates rate.

We have that:

Jennifer takes x hours to complete the job on her own, so her rate is 1/x.

Carl needs 15 hours longer than Jennifer, that is, 15 + x hours, so his rate is 1/(15+x).

The together rate is 1/4. So

\frac{1}{4} = \frac{1}{x} + \frac{1}{15+x}

\frac{1}{4} = \frac{15 + x + x}{x(15+x)}

\frac{1}{4} = \frac{15 + 2x}{x(15+x)}

Applying cross multiplication.

x^2 + 15x = 4(15 + 2x)

x^2 + 15x = 60 + 8x

x^2 + 7x - 60 = 0

Quadratic equation with a = 1, b = 7, c = -60. So

\Delta = 7^{2} - 4*1*60 = 289

x_{1} = \frac{-7 + \sqrt{289}}{2} = 5

x_{2} = \frac{-7 - \sqrt{289}}{2} = -12

Since the time to complete the job has to be a positive value.

Jennifer would complete the job on her own in 5 hours.

4 0
2 years ago
What is the circumference of a circle with a diameter of 7 inches? (use for pi)
Marrrta [24]

Answer:

21.9

Step-by-step explanation:

circumference = pi x diameter

3.14 x 7 = 21.9

3 0
3 years ago
Read 2 more answers
estamos construyendo una carretera que enlace los puntos a = 12 ,21 y b =(17,23) otro punto se encuentra en c =(3,9) es posible
Nadusha1986 [10]

Answer:

is not possible

Step-by-step explanation:

<u><em>The question in English is</em></u>

we are building a road that links the points a = (12 ,21) and b =(17,23) another point is in c =(3,9) it is possible that a single road allows to join these three points?

we know that

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}

step 1

Find the slope ab

we have

a = (12 ,21) and b =(17,23)

substitute

m=\frac{23-21}{17-12}

m=\frac{2}{5}

step 2

Find the slope ac

we have

a = (12 ,21) and c =(3,9)

substitute

m=\frac{9-21}{3-12}

m=\frac{-12}{-9}

simplify

m=\frac{4}{3}

step 3

Compare slopes ab and ac

The slopes are different

That means ----> is not possible that a single road allows to join these three points

7 0
3 years ago
Nick has an album that holds 700 compact discs. Each page of the album holds 7 compact discs. If 69​% of the album is​ empty, ho
mel-nik [20]

Answer:

41

Step-by-step explanation:

each page holds 7 discs. the alb holds 700 discs. that means there are 100 pages. 69% of the pages are empty so therefore 41 pages are filled.

4 0
3 years ago
What is the equation of the line that passes through the point (-8,1) and has a slope of -3/4
ioda

Answer:

y=-3/4-5

Step-by-step explanation:

plug in ordered pair  1= -3/4(-8)+b

solve for b. b= -5

plug in to y=mx+b

3 0
3 years ago
Read 2 more answers
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