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Furkat [3]
4 years ago
5

Please help me with this!!

Mathematics
1 answer:
Art [367]4 years ago
4 0
Answer: Choice C) 115 degrees

--------------------------------

Explanation:

The three angles are 42, 73 and 65 degrees. Let's call them x,y, and z respectively
x = 42
y = 73
z = 65

To find an exterior angle for x, we subtract the given angle x from 180
180-x = 180-42 = 138
The exterior angle adjacent to angle x is 138 degrees. This isn't listed so we move on

Do the same for y
180-y = 180-73 = 107
This isn't listed either. So we move on

Repeat for angle z
180-z = 180-65 = 115
This is listed as choice C. That's why choice C is the answer

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Office equipment was purchased for $20,000 and is assumed to have a scrap value of $2,000 after 10 years. If its value is deprec
boyakko [2]

According to the information given in the exercise:

- The office equipment was purchased for $20,000.

- The scrap value is assumed to be $2,000 after 10 years.

- -It's depreciated linearly from $20,000 to $2,000.

(a) The Slope-Intercept Form of the equation of a line is:

y=mx+b

Where "m" is the slope of the line and "b" is the y-intercept.

Let be "V" the value (in dollars) and "t" the time (in years).

Analyzing the information given in the exercise, you can set up that the equation will have this form:

V=mt+b

Where "m" is the slope and "b" is the y-intercept.

Notice that you have these two points:

\begin{gathered} (0,20000) \\ (10,2000) \end{gathered}

Then, you can apply the formula for calculating the slope:

m=\frac{y_2-y_1}{x_2-x_1_{}}

You can say that:

\begin{gathered} y_2=2000 \\ y_1=20000 \\ x_2=10 \\ x_1=0 \end{gathered}

Substituting and evaluating, you get:

m=\frac{2000-20000}{10-0}=\frac{-18000}{10}=-1800

To find "b", you need to remember that the value of "x" is zero when the line intersects the y-axis. Therefore, knowing that one of the points is:

(0,20000)

You can determine that:

b=20000

Hence, the equation is:

V=-1800t+20000

(b) To find the value of the equipment after 6 years, you need to set up that:

t=6

Then, substituting this value into the equation and evaluating, you get:

\begin{gathered} V=-1800(6)+20000 \\ V=9200 \end{gathered}

Therefore, the answers are:

(a)

V=-1800t+20000

(b) $9,200

6 0
1 year ago
Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false:
kondaur [170]
\text{Proof by induction:}
\text{Test that the statement holds or n = 1}

LHS = (3 - 2)^{2} = 1
RHS = \frac{6 - 4}{2} = \frac{2}{2} = 1 = LHS
\text{Thus, the statement holds for the base case.}

\text{Assume the statement holds for some arbitrary term, n= k}
1^{2} + 4^{2} + 7^{2} + ... + (3k - 2)^{2} = \frac{k(6k^{2} - 3k - 1)}{2}

\text{Prove it is true for n = k + 1}
RTP: 1^{2} + 4^{2} + 7^{2} + ... + [3(k + 1) - 2]^{2} = \frac{(k + 1)[6(k + 1)^{2} - 3(k + 1) - 1]}{2} = \frac{(k + 1)[6k^{2} + 9k + 2]}{2}

LHS = \underbrace{1^{2} + 4^{2} + 7^{2} + ... + (3k - 2)^{2}}_{\frac{k(6k^{2} - 3k - 1)}{2}} + [3(k + 1) - 2]^{2}
= \frac{k(6k^{2} - 3k - 1)}{2} + [3(k + 1) - 2]^{2}
= \frac{k(6k^{2} - 3k - 1) + 2[3(k + 1) - 2]^{2}}{2}
= \frac{k(6k^{2} - 3k - 1) + 2(3k + 1)^{2}}{2}
= \frac{k(6k^{2} - 3k - 1) + 18k^{2} + 12k + 2}{2}
= \frac{k(6k^{2} - 3k - 1 + 18k + 12) + 2}{2}
= \frac{k(6k^{2} + 15k + 11) + 2}{}
= \frac{(k + 1)[6k^{2} + 9k + 2]}{2}
= \frac{(k + 1)[6(k + 1)^{2} - 3(k + 1) - 1]}{2}
= RHS

Since it is true for n = 1, n = k, and n = k + 1, by the principles of mathematical induction, it is true for all positive values of n.
3 0
3 years ago
Find the slope of the line: y+5 = -3/4x
Stella [2.4K]

Answer:

y = -3/4x - 5

Slope: -3/4

y-intercept: -5

8 0
3 years ago
xander walks 389 steps from his house to the toy store .it is 149 steps to elm street.. it is 52 steps from elm street to maple
aalyn [17]

Answer:

the answer is 590 steps

Step-by-step explanation:

389+ 149+ 52= 590

6 0
3 years ago
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3 years ago
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