1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
son4ous [18]
3 years ago
13

A dog trainer is trying to find a triangular area behind his house that encloses 1800 square feet for his dog to run. He has the

first two fence posts at (6, 0) and at (0, 25). The final fence post is on the property line at x = 30. Find the point where the trainer can place the final fence post.
Mathematics
1 answer:
aliina [53]3 years ago
7 0

Answer:

C = (30,500)

Step-by-step explanation:

Given

Area = 1800ft^2

A = (6,0)

B = (0,25)

C(x,y) = (30,y)

Required

Determine the coordinates of C

The area of triangle is calculated as thus:

Area = \frac{|A_x(B_y - C_y) + B_x(C_y - A_y) + C_x(A_y - B_y)|}{2}

This gives:

1800= \frac{|6(25 - y) + 0(y - 0) + 30(0 - 25)|}{2}

1800= \frac{|6(25 - y) + 30(0- 25)|}{2}

1800= \frac{|6(25 - y) + 30(-25)|}{2}

1800= \frac{|150 - 6y -750 |}{2}

1800= \frac{|150  -750- 6y |}{2}

1800= \frac{|-600- 6y |}{2}

Multiply through by 2

2 * 1800= |-600- 6y|

3600= |-600- 6y|

3600= |-(600+ 6y)|

3600= 600+ 6y

Solve for 6y

6y = 3600 - 600

6y = 3000

Solve for y

y = 3000/6

y = 500

Hence:

The point is:

C = (30,500)

You might be interested in
Samantha went shopping for a new dress. Last week she saw it being sold for $75. When she returned to the store today, she saw t
lions [1.4K]

Answer:

Step-by-step explanation:

20%

3 0
3 years ago
Read 2 more answers
An entertainment firm offer serveral DJ choices and light shows that range in price based on the rental time period. The DJs cos
Fantom [35]

Answer:

378\le x\le 678.

Step-by-step explanation:

If you are booking both a DJ and a light show and the DJs cost between $219 and $369 per night and the light shows cost between $159 and $309 per night,  then the possible total amount you would pay x must be between $(219+159)=$378 (the least price) and $(369+309)=$678 (the greatest price).

A compound inequality will take look

378\le x\le 678.

3 0
2 years ago
Supposethat z is a normally distributed variable with variance 4. You collect a sample of size n for which you get a sample aver
Nikitich [7]

Answer:

The sample size is 4

Step-by-step explanation:

Null hypothesis: The mean is 2

Alternate hypothesis: The mean is less than 2

Mean = 3

sd = sqrt(variance) = sqrt(4) = 2

At 95% confidence level, t-value is 1.960

Assuming the lower bound of the mean is 1.04

Lower bound = mean - (t×sd/√n)

1.04 = 3 - (1.96×2/√n)

3.92/√n = 3 - 1.04

3.92/√n = 1.96

√n = 3.92/1.96

√n = 2

n = 2^2

n = 4

7 0
3 years ago
Help please<3 for all questions with solutions plz
antiseptic1488 [7]

Answer:

a) h = -\frac{7}{4}, b)  h = f\,\circ\,g (-5) = \frac{3}{2}, c) h = g\,\circ\,f (-2) = \frac{3}{8}

Step-by-step explanation:

We proceed to solve each exercise below:

a) f(-2) +3\cdot g(0)

h = \frac{2\cdot (-2)}{3\cdot (-2)+5}+3\cdot \left(\frac{3}{0+4} \right)

h = \frac{-4}{-6+5} +3\cdot \left(\frac{3}{4} \right)

h = -4+\frac{9}{4}

h = \frac{-16+9}{4}

h = -\frac{7}{4}

b) h = f\,\circ \,g (-5)

h = f\,\circ\,g (x)  = \frac{\frac{6}{x+4} }{\frac{9}{x+4}+5 }

h = f\,\circ\,g (x)= \frac{\frac{6}{x+4} }{\frac{9+5\cdot (x+4)}{x+4} }

h = f\,\circ\,g (x) = \frac{6}{29+5\cdot x}

h = f\,\circ\,g (-5) = \frac{6}{29+5\cdot (-5)}

h = f\,\circ\,g (-5) = \frac{3}{2}

c) h = g\,\circ\,f(-2)

h = g\,\circ \, f (x) = \frac{3}{\frac{2\cdot x}{3\cdot x + 5} + 4  }

h = g\,\circ\,f (x) = \frac{3}{\frac{2\cdot x +4\cdot (3\cdot x +5)}{3\cdot x +5 } }

h = g\,\circ \,f (x) = \frac{3\cdot (3\cdot x +5)}{2\cdot x +12\cdot x +20}

h = g\,\circ\,f(x) = \frac{9\cdot x +15}{14\cdot x +20}

h = g\,\circ\,f(-2) = \frac{9\cdot (-2)+15}{14\cdot (-2)+20}

h = g\,\circ\,f (-2) = \frac{-3}{-8}

h = g\,\circ\,f (-2) = \frac{3}{8}

6 0
3 years ago
Nigel, Gina, and Kamal each spend between $15 and $20 on dog supplies.
motikmotik

Answer:

456+56+54+4+4

Step-by-step explanation:

65+465+5+56

7 0
3 years ago
Read 2 more answers
Other questions:
  • A random sample of 4"4 fields" of barley has a mean yield of "49.6"49.6 bushels per acre and standard deviation of 7.997.99 bush
    9·1 answer
  • Can -62 be classified as a natural number
    12·1 answer
  • What is Slope and how is it determined from a graph?
    11·1 answer
  • HELP ME WITH MY LAST QUESTION PLEASE I FORGOT HOW TO FIND INTERVALS
    12·2 answers
  • What is the greatest common factor of 56 and 72
    15·2 answers
  • What is the surface area?
    6·1 answer
  • One angle of a triangle measures 95°. The other two angles are in a ratio of 4:13. What are the measures of those two angles?
    8·1 answer
  • The midpoint of (2,7) and (6,3)
    11·1 answer
  • Together Elizabeth and Norman have 45 postcards. Norman has 4 Times as many postcards as Elizabeth. How many postcards are in No
    9·1 answer
  • Find the value of x. Round the length to the nearest tenth.
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!