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lbvjy [14]
2 years ago
13

What is the first step in proving that the sum of the measures of triangle XYZ is 180 degrees?

Mathematics
1 answer:
mylen [45]2 years ago
6 0
In geometry, the definition of a triangle is a two-dimensional closed figure with three sides. Aside from this, it is proven that the sum of the angles of a triangle is 180°. This is a triangle's innate property. Therefore, any closed shape with three sides is a triangle and it follows that the sum of the three angles is equal to 180°.

It is logical therefore, that the first step in proving this is by using the definition of a triangle.
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Use this graph of velocity vs. time for two objects to answer the question.
Lynna [10]

Using derivatives, it is found that the correct option is:

A. Object C has an acceleration that is greater than the acceleration for D.

The acceleration is the <u>derivative of the velocity</u>, given by change in velocity divided by change in time, that is:

a = \frac{\Delta_v}{\Delta_t}

In this problem:

  • The change in time for objects C and T is the same.
  • The <u>change in velocity for object C is greater</u>, thus, it has a greater acceleration, and the correct option is:

A. Object C has an acceleration that is greater than the acceleration for D.

A similar problem is given at brainly.com/question/14516604

6 0
2 years ago
Read 2 more answers
The altitude of Death Valley California is 282 ft below sea level of hot air balloon is launched From The Bottom Of Death Valley
asambeis [7]

Answer:

177 ft below sea level.

Step-by-step explanation:

Initial altitude of the hot air balloon = 282 below sea level

Rate of rise of balloon = 10 ft / second

Time = 12 seconds

Total rise in 12 seconds = Rate of rise of balloon \times Time

\Rightarrow 10 \times 12 = 120 ft

Now, we will have to subtract to find the new altitude.

New altitude = 282 - 120 = 162 ft

Now, it is given that balloon Captain lowers the balloon 15 ft.

To find the final altitude, we will have to add it to the previous altitude.

Therefore, the final altitude = 162 + 15 = <em>177 ft below sea level </em>

6 0
2 years ago
You saved $20,000.00 and want to diversify your monies. You invest 45% in a Treasury bond for 3 years at 4.35% APR compounded an
Maru [420]

Compound Interest

A total of $20,000 is invested in different assets.

45% is invested in a Treasury bond for 3 years at 4.35 APR compounded annually.

For this investment, the principal is P = 0.45*$20,000 = $9,000.

The compounding period is yearly, thus the interest rate is:

i = 4.35 / 100 = 0.0435

The duration (in periods) is n = 3

Calculate the final value with the formula:

M=P_{}(1+i)^n

Substituting:

\begin{gathered} M=\$9,000_{}(1+0.0435)^3 \\ M=\$9,000\cdot1.136259062875 \\ M=\$10,226.33 \end{gathered}

The second investment is a CD at 3.75% APR for 3 years compounded annually. The parameters for the calculations are as follows:

P = 15% of $20,000 = $3,000

i = 3.75 / 100 = 0.0375

n = 3

Calculating:

\begin{gathered} M=\$3,000_{}(1+0.0375)^3 \\ M=\$3,000\cdot1.116771484375 \\ M=\$3,350.31 \end{gathered}

The third investment is in a stock plan. The initial value of the investment is

P = 20% of $20,000 = $4,000

By the end of the first year, the stock plan increased by 8%, thus its value is:

M1 = $4000 * 1.2 = $4,800

By the end of the second year, the stock plan decreased by 4$, thus the value is:

M2 = $4,800 * 0.96 = $4,608

Finally, the stock plan increases by 6%, resulting in a final balance of:

M3 = $4,608 * 1.06 = $4,884.48

Finally, the last investment is in a savings account at 2.90% APR compounded annually for 3 years (not mentioned, but assumed).

P = $20,000 - $9,000- $3,000 - $4,000 = $4,000

i = 2.90 / 100 = 0.029

n = 3

Calculating:

\begin{gathered} M=\$4,000_{}(1+0.029)^3 \\ M=\$4,000\cdot1.089547389 \\ M=\$4,358.19 \end{gathered}

To summarize, the final balances for each type of investment at the end of the third year are:

Investment 1; $10,226.33

Investment 2: $3,350.31

Investment 3: $4,884.48

Investment 4: $4,358.19

Total balance: $22,819.32

3 0
1 year ago
What is the base 5 representation of the number 465^8
andreev551 [17]

Answer  

Option C : 2214(5)

Solution


The given number is 465 in base 8. To convert this number to base 5,we need to convert this number to base 10, then only we can compute the number in base 5


Step1 : Convert 465 to the base 8 to base 10


4 x 82=256


6 x 81=48


5 x 80=5


Adding 256 + 48+ 5 = 309(10)


Step2 : Convert 309(10) to base 5  

5 | 309  

5 | 61 |4


5 | 12 | 1


5 | 2  | 2


5 | 0  | 2



Therefore Answer = 2214(5 )

4 0
3 years ago
Scenario: A new Swimming pool is opening up this summer in the Bronx. Students that are 13 - 18 years old can use the pool, gym
MA_775_DIABLO [31]
The answer to your question is 15(12)+40=?
15 being the per month fee, 12 being all 12 months, and 40 being the sign up fee. You can also put 15x12+40=?
3 0
3 years ago
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