Three neighbors plan to complete fencing projects this spring. As shown in the diagrams below, Neighbor A plans to fence in his rectangular backyard with a 6-foot tall wooden privacy fence. Neighbor B plans to construct a circular chain link fence around his pool. And, Neighbor C is putting a vinyl fence around three side of his front yard. Note: Diagrams are not drawn to scale. Intended fences are marked with a dashed line.

Wood fencing is sold in 8 foot sections for $111.50. Chain link fencing costs $9.75 per linear foot (in whole foot lengths). And, vinyl fencing can be purchased for $53.55 per linear yard (in whole yard lengths).

Which neighbor's fencing project will cost the most?
Which neighbor's fencing project will cost the least?

The answer is:

The rewritten expression is:

[tex]cos(2x)+sin(x)=(cos(x)+sin(x))*(cos(x)-sin(x))+sin(x)[/tex]

To solve this problem we need to use the trigonometric identity of the double angle for the cosine which states that:

[tex]cos(2\alpha)=cos^{2}(\alpha)-sin^{2}(\alpha)[/tex]

Also, if we want to rewrite only with terms of cos(x) and sin(x), we can apply the following property:

[tex](a^{2} -b^{2})=(a+b)(a-b)[/tex]

So, rewriting the trigonometric equation, we have:

[tex]cos^{2}(\alpha)-sin^{2}(\alpha)=(cos(x)+sin(x))*(cos(x)-sin(x))[/tex]

Then, we are given the expression:

[tex]cos(2x)+sin(x)[/tex]

Now, rewriting the given expression with only sin(x) and cos(x), we have:

[tex]cos(2x)+sin(x)=(cos(x)+sin(x))*(cos(x)-sin(x))+sin(x)[/tex]

Hence, the answer is:

[tex]cos(2x)+sin(x)=(cos(x)+sin(x))*(cos(x)-sin(x))+sin(x)[/tex]

Have a nice day!

Answer:

  A.  147 cubic units

Step-by-step explanation:

The area of the square base is ...

  B = (7 units)² = 49 units²

The volume is given by the formula ...

  V = (1/3)Bh = (1/3)(49 units²)(9 units) = 147 units³

ok well i forget how to find the area of a trapezoid but you can solve it by breaking it down into a rectangle and two triangles

so for the rectangle multiply 7 by 4 to get 28

for the triangle you have to subtract 7 from ten to get 3 this is the length of the base. then you multiply 4 by 3 by 0.5 to get 6

now you have two triangles so multiply 6 by 2 to get 12

now add it all up to get 28+12=40

ummmmmmmmmmmmmmmm so this isn't an answer choice

i looked up the trapezoid formula and it is [tex]A=\frac{a+b}{2} h[/tex]

so if you fill in the blanks A=((7+10)/2)4

so A=(17/2)4

A=8.5*4

A=34

so the actual answer is 34 feet

but i see how you got 40

Answer:

Option B.) $8,123.79

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=5\ years\\ P=\$7,000\\ r=0.03\\n=2[/tex]  

substitute in the formula above  

[tex]A=\$7,000(1+\frac{0.03}{2})^{2*5}[/tex]  

[tex]A=\$7,000(1.015)^{10}=\$8,123.79[/tex]  

The worth of the investment after 5 years at an interest of 3% is $8,123.79.

As the function for interest is already given to us, also,

The principal amount, P = $7,000

The rate of Interest, r = 3%

Time period, t =  5 years

Compounded semiannually, n = 2

Substitute the values,

[tex]A=P(1+\dfrac{r}{n})^{nt}[/tex]

   [tex]=7000(1+\dfrac{0.03}{2})^{2 \times 5}\\\\=\$ 8,123.79[/tex]

Hence, the worth of the investment after 5 years at an interest of 3% is $8,123.79.

Learn more about Compound Interest:

https://brainly.com/question/25857212

Answer:

[tex]14+3+c=14+8\quad :\quad c=5[/tex]

Hope this helps!!!

"The subject of this question is Mathematics." The student asked to solve two equations, one of which is already true and the other involves finding the value of a variable. By simplifying the equation, we can find that c is equal to 5.

The subject of this question is Mathematics.

In the equation 14 = 14, both sides are equal to each other, so the equation is true by the reflexive property of equality.

In the equation 14 + 3 + c = 14 + 8, we can simplify both sides of the equation. Starting with the left side, 14 + 3 + c becomes 17 + c. On the right side, 14 + 8 becomes 22. So, the equation can be rewritten as 17 + c = 22.

To solve for c, we subtract 17 from both sides of the equation. This gives us c = 22 - 17, which simplifies to c = 5.

https://brainly.com/question/27235369

#SPJ12

Two possible values for the length of the third side of a right angle triangle are 6 and [tex]\sqrt{164}[/tex].

" Right angle triangle is a triangle whose one of the interior angle is of 90°."

Formula used

Pythagoras theorem,

(Hypotenuse)² = (Opposite side)² + (adjacent side)²

According to the question,

Two sides of a right triangle measure 10 m and 8 m

Here it is not mentioned 10m and 8m representing which side , that's why this is not enough information to be sure of the length of the third side.

Two possibilities

If Hypotenuse = 10m

Length of one of the side of the right triangle  = 8m

Measure of other side  'x' equals to

[tex](10)^{2} = 8^{2} + x^{2}[/tex]

⇒[tex]x^{2} = 100 -64[/tex]

⇒[tex]x^{2} =36[/tex]

⇒[tex]x=6[/tex]

If Hypotenuse is not given then,

(Hypotenuse)² = [tex]10^{2} +8^{2}[/tex]

⇒(Hypotenuse)² = [tex]100 + 64[/tex]

⇒ Hypotenuse = [tex]\sqrt{164}[/tex]

Hence, two possible values for the length of the third side of a right angle triangle are 6 and [tex]\sqrt{164}[/tex].

Learn more about right angle triangle here

https://brainly.com/question/3770177

#SPJ2

Final answer:

Without knowing which of the two given sides is the hypotenuse in a right triangle, we cannot definitively calculate the length of the third side. It could be greater or less than 10.3 m depending on whether the 10 m side is the hypotenuse or one of the legs.

Explanation:

If two sides of a right triangle measure 10 m and 8 m, it is not enough information to be sure of the length of the third side. The reason is that without knowing which of the sides is the hypotenuse, or whether the given sides are the two legs or one leg and the hypotenuse, we cannot use the Pythagorean Theorem to find the exact length of the third side.

If the 10 m side is the hypotenuse, the other side (of length 8 m) would be a leg, and we could find the length of the remaining leg using the equation a² + b² = c², where c is the hypotenuse and a and b are the other two sides. Thus, the length of the third side would be less than 10.3 m.

However, if the side that measures 10 m is not the hypotenuse, then the remaining side would have to be longer than 10 m to satisfy the Pythagorean Theorem. The length of the third side would be greater than 10.3 m in this case.

Without additional information, we cannot commit to a single value for the third side and must acknowledge that both possibilities exist.

Answer:

Zero

Step-by-step explanation:

A letter C or Z is not in the word Bulldog.

First, see how many she had in all(before she gave some to her brother):

54 + 10 = 64

Then, divide to get how many were in each package:

64/8 = 8

There were 8 markers in each package.

Answer:

[tex]\large\boxed{8n^{18}}[/tex]

Step-by-step explanation:

The formula of an area of a square:

[tex]A=s^2[/tex]

s - side length

We have

[tex]A=64n^{36}[/tex]

Method 1:

Substitute:

[tex]s^2=64n^{36}[/tex]

[tex]s^2=8^2n^{18\cdot2}[/tex]            use [tex](a^n)^m=a^{nm}[/tex]

[tex]s^2=8^2(n^{18})^2[/tex]         use [tex](ab)^n=a^nb^n[/tex]

[tex]s^2=(8n^{18})^2\to s=8n^{18}[/tex]

Method 2:

Substitute:

[tex]s^2=64n^{36}\to s=\sqrt{64n^{36}}[/tex]   use [tex]\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}[/tex]

[tex]s=\sqrt{64}\cdot\sqrt{n^{36}}[/tex]

[tex]s=8\sqrt{n^{(18)(2)}[/tex]     use [tex](a^n)^m=a^{nm}[/tex]

[tex]s=8\sqrt{(n^{18})^2}[/tex]      use [tex]\sqrt{a^2}=a[/tex] for [tex]a\geq0[/tex]

[tex]s=8n^{18}[/tex]

Answer:

[tex]\large\boxed{A(r(C))=\dfrac{C^2}{4\pi}}[/tex]

Step-by-step explanation:

[tex]A(r)=\pi r^2\\\\r(C)=\dfrac{C}{2\pi}\\\\A(r(C))\to\text{put}\ r=\dfrac{C}{2\pi}\ \text{to}\ A(r):\\\\A(r(C))=\pi\left(\dfrac{C}{2\pi}\right)^2\qquad\text{use}\ \left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}\ \text{and}\ (ab)^n=a^nb^n\\\\A(r(C))=\pi\cdot\dfrac{C^2}{2^2\pi^2}\qquad\text{cancel one}\ \pi\\\\A(r(C))=\dfrac{C^2}{4\pi}[/tex]

Answer:

There is no solution to the given problem [tex]|x|=-2[/tex].

Step-by-step explanation:

Given equation is [tex]|x|=-2[/tex].

Now we need to determine if there is solution to this equation or not.

We know that [tex]|x|[/tex] represents absolute value function.

By definition of absolute value function, we know  that output of [tex]|x|[/tex] must always be positive.

But in given equation [tex]|x|=-2[/tex], we have output -2 which is negative.

That is not possible.

Hence there is no solution to the given problem [tex]|x|=-2[/tex].

Please add more to the question.

Answer:

Simplifying

3.2 = 2y

Solving

3.2 = 2y

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-2y' to each side of the equation.

3.2 + -2y = 2y + -2y

Combine like terms: 2y + -2y = 0

3.2 + -2y = 0

Add '-3.2' to each side of the equation.

3.2 + -3.2 + -2y = 0 + -3.2

Combine like terms: 3.2 + -3.2 = 0.0

0.0 + -2y = 0 + -3.2

-2y = 0 + -3.2

Combine like terms: 0 + -3.2 = -3.2

-2y = -3.2

Divide each side by '-2'.

y = 1.6

Simplifying

y = 1.6

Step-by-step explanation:

The equivalent expressions are

3x + 5x and 8x

3(x + 4) and 3x + 12

a + b + a and 2a + b

What are equivalent expressions?

Equaivelnt expressions are expressions that the terms are equal. That is to say rearranging the terms will result to the term to be compared with it.

In this case the expressions are said to be equaivalent

Examining the expressions we can see that

3x + 5x = 8x

3(x + 4) = 3x + 12

a + b + a = 2a + b

The number of students with white shirts on is 19.

The answer is 19 because you do 50 times 38 and get 1900 and divide it by a 100 and get 19.

Convert the whole number 4 into a fraction using 4 as the denominator:

4/1 × 4/4 = 16/4

Hope this helps :D

Answer:ignore sorry

Step-by-step explanation:

Answer:

Function represents decay.

[tex]V(t)=3000(0.70)^t[/tex]

Step-by-step explanation:

Given that the value of a $3000 computer decreases about 30% each year. Now we need to write a function for the computers value V(t). then determine if the function represent growth or decay.

It clearly says that value decreases so that means function represents decay.

For decay we use formula:

[tex]A=P(1-r)^t[/tex]

where P=initial value = $3000,

r= rate of decrease =30% = 0.30

t= number of years

A=V(t) = future value

so the required function is [tex]V(t)=3000(1-0.30)^t[/tex]

or [tex]V(t)=3000(0.70)^t[/tex]

Answer:

2.02

Step-by-step explanation:

2.02

The final answer is 3+9i

Answer:

3+9i

Step-by-step explanation:

The given expression is

(4 + 2i) - (1 - 7i)

Expand the parenthesis to obtain;

4 + 2i-1 + 7i

Group the imaginary parts and the real number parts separately to obtain;

4 -1+ 2i+ 7i

Combine the similar terms to get;

3+ 9i

Answer:

(A. 16.25 in^2

The area of triangle with base of the triangle be 10 in and the height be 9 in, 45 in²

Area is the amount of space occupied by a two dimensional shape or object.

The area of triangle = (1/2) * base * height

Let the base of the triangle be 10 in and the height be 9 in, hence:

The area of triangle = (1/2) * 10 * 9 = 45 in²

Find out more on area at: https://brainly.com/question/25292087

Answer:

90 degrees

Step-by-step explanation:

FIGURE IT OUT

x=15 and y=25.98 or 26

Answer:18

Step-by-step explanation:

Answer:

i think the answer is 18

Step-by-step explanation:

Answer:

In mathematics, the Pythagorean theorem, also known as Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. The theorem can be written as an equation relating the lengths of the sides a, b and c, often called the "Pythagorean equation":[1]

Step-by-step explanation:

Answer:

C. is the answer

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = 4, thus

y = 4x + c ← is the partial equation

To find c substitute (- 4, - 5) into the partial equation

- 5 = - 16 + c ⇒ c = - 5 + 16 = 11

y = 4x + 11 → C

Answer:

(x+8)^2 - 67

Step-by-step explanation:

1) Rearrange the quadratic into the standard format: ax^2 + bx + c

In this case you rearrange it to x^2 + 16x - 3

2) Write out the initial bracket: (x + b/2)^2    -    Just divide the value of b (which in this case is 16) by 2 (which in this case gives you 8)

3) Multiply out the brackets and compare to the original to find what you need to add or subtract to complete the square

In this case you do (x+8)^2 which gives you x^2 + 16x +64

You compare this to the original: x^2 + 16x - 3

4) Add or Subtract the adjusting number to make it match the original

In this case you need to subtract 67 from x^2 + 16x +64 (which is the same as (x+8)^2) in order to make it match the original x^2 + 16x - 3

64 - 67 = -3

Answer:

D. 1/6.

Step-by-step explanation:

These are all of the steps to completely get the correct answer to this question.

Hope this help!!!

Kyle.

I believe the answer is D

For this case we must solve the following inequality, finding the values for the variable "t":

[tex]t + 18 <43[/tex]

We subtract 18 from both sides of the inequality:

[tex]t + 18-18 <43-18\\t <25[/tex]

Thus, the variable "t" is defined for all strict lower values than 25.

Answer:

[tex]t <25[/tex]

Option A

Answer:

C 3/14

Step-by-step explanation:

There are a total of 8 checkers

P (black) = black/total

               = 2/8 = 1/4

Then we keep the checker, so there are only 7 checkers in the bag, 6 red and 1 black

P ( red) = red/total

           = 6/7

P (black, red) = 1/4 * 6/7

                      = 6/28 = 3/14

Answer:

8

Step-by-step explanation:

Find the point on the x-axis where x = 3 and look at the height of the line there.

Hello! :)

All angles in triangles must equal 180* degrees. So there is the 90 degrees at the meter Q and you add: 43+90=133* degrees. Remember, to make 180 so you do 180-133=47* degrees. I didn’t get any answer choices but if there are, choose the closest one to 47* degrees.

Hope this helped and I hope I answered in time!

Good luck!

~ Destiny ^_^

Answer:

The value of x = 47°

Step-by-step explanation:

From the figure we can see that a circle with center O.

PQ is a tangent to the circle fro point P.

m<P = 43°

Therefore <Q = 90°

To find the value of x

From the given triangle we can write,

x + m<Q + m<P = 180

x = 180 - (m<Q + m<P)

 = 180 - (90 + 43)

 = 180 - 133 = 47°

Therefore the value of x = 47°