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
Gwar [14]
3 years ago
10

Two streets bounding your triangular lot make an angle of 74∘. The lengths of the two sides of the lot on these streets are 126

feet and 110 feet. You want to build a fence on the third side, but have only 150 feet of fencing on hand. a. Do you have enough fencing? Justify your answer. b. What are the measures of the other two angles of the lot? c. The city has zoned the property so that any residence must have a square footage at least one-third the area of the lot itself. You plan to build a 2300ft2 home. Will the city approve your plans? Why or why not?
Mathematics
1 answer:
ycow [4]3 years ago
7 0

Answer: a) Yes, there is enough fance

b) 58.1° and 47.9°

c) The city will not approve, because 1/3 of the area is just 2220.5ft²

Step-by-step explanation:

a) using law of cosines: x is the side we do not know.

x² = 126² + 110² - 2.126.110.cos74°

x² = 20335.3

x = 142.6 ft

So 150 > 142.6, there is enough fance

b) using law of sine:

sin 74/ 142.6 = sinα/126 = sinβ/110

sin 74/ 142.6 = sinα/126

0.006741 = sinα/126

sinα = 0.849

α = sin⁻¹(0.849)

α = 58.1°

sin 74/ 142.6 = sinβ/110

sin 74/ 142.6 = sinβ/110

0.006741 = sinβ/110

sinβ = 0.741

β = sin⁻¹(0.741)

β = 47.9°

Checking: 74+58.1+47.9 = 180° ok

c) Using Heron A² = p(p-a)(p-b)(p-c)

p = a+b+c/2

p=126+110+142.6/2

p=189.3

A² = 189.3(189.3-126)(189.3-110)(189.3-142.6)

A = 6661.5 ft²

1/3 A = 2220.5

So 2300 >  2220.5. The area you want to build is bigger than the area available.

The city will not approve

You might be interested in
Find the domain of the function f(x) = 7x2 + 8x - 15.
amm1812

Answer:

Domain is all real numbers or (negative infinity, positive infinity)

Step-by-step explanation:

Domain is all values of <em>x</em> (inputs) that will work with the function. Since a parabola has no limits for <em>x</em>, and all numbers work for <em>x</em>, then the domain can be any number. That leaves us with All Real Numbers as our answer.

5 0
3 years ago
For the graph shown, the slope is changed to 1/5, but the y-intercept remains the same. What is the resulting equation for the n
Varvara68 [4.7K]

Answer: C. y=1/5x+1

Step-by-step explanation:

8 0
3 years ago
Name the three-dimensional figure that is formed by folding the net.
Ivanshal [37]
A triangular Prism I would say but it does have rectangles
3 0
3 years ago
Read 2 more answers
How many complex roots does the polynomial equation have? −3x4−7x+17=0
zimovet [89]

1) There are two complex roots. A is correct.

2) The function has three real zeros. The graph of the function intersects the x-axis at exactly three locations. D is correct

3) There are four complex roots. B is correct.

4) C is correct.

5)

Step-by-step explanation:

1) Number of complex root.

We can not factor it completely. Because it's prime equation. We will make the graph of  and then see the x-intercept of the graph.

Because number x-intercepts are the zeros of polynomial. Please see the attachment for graph. In graph we can see it cuts only two points but their highest degree is 4. Maximum possible roots are 4 but only 2 are real and 2 are complex.  

Thus, There are two complex roots.

2) This is cubic polynomial function.

Maximum number of zeros should be 3.

Please see the graph with attachment.

Zeros is a value of x where graph cuts x-axis. In graph we can see graph cuts x-axis at three points.

Thus, The function has three real zeros. The graph of the function intersects the x-axis at exactly three locations.

3) This is 4th degree polynomial.

Maximum number of zeros should be 4.

Please see the graph of polynomial.

Zeros is a value of x where graph cuts x-axis. In graph we can see doesn't cut x-axis at any points.

Thus, The function has four complex zeros. The graph of the function does not intersects the x-axis at any point.

4) We are given 3 degree polynomial. We need to factor it. First we split middle term and then factor it.

Now we factor quadratic part using quadratic formula

Complete factor of f(x)

Thus,

5) This is cubic polynomial. We need to factor it.

First we make two group and then factor it

Thus, complete factor of f(x) is (x+3)(x+4i)(x-4i)

8 0
3 years ago
Jimmy bought a sandwich. The price is $5 when he got the receipt he needed to pay 6% taxes, and he left a 10% tip how much did h
MA_775_DIABLO [31]
5.83............................
3 0
3 years ago
Read 2 more answers
Other questions:
  • A long distance runner starts a race at 1 m/s. he increases his speed to 3 m/s during the middle of the race and slows down to 2
    6·1 answer
  • A boat takes 5 hours to go upstream. It can go 50 miles downstream in the same time. Find the rate of the current in the rate of
    10·1 answer
  • 1. Find the Product of 8.02 and 6.1 and correct your answer to the highest whole number. 2. How many pieces of ribbon each 6cm l
    7·2 answers
  • HELP ME PLZZZ ITS PRECALC
    7·1 answer
  • A square has an area of 64 m². What is the length of each side?
    7·1 answer
  • What is x? The angle x
    10·2 answers
  • Find the missing length indicated.<br> 18<br> ?<br> 4<br> 8<br> A) 21<br> C) 9<br> B) 3<br> D) 25
    14·1 answer
  • If m is 2 times n minus 7 and y is the square of m, then write y as a function of n.
    14·1 answer
  • HI PLS HELP ASAP ILL GIVE BRAINLIEST
    6·2 answers
  • Write the equation of the line in fully simplified slope-intercept form.
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!