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Alenkasestr [34]
3 years ago
11

Find a, b and c giving reasons for each answer.

Mathematics
1 answer:
kap26 [50]3 years ago
6 0

Answer/Step-by-step explanation:

1.

✔️a = 180 - 110 (consecutive angles are supplementary)

a = 70°

✔️b = a (corresponding angles are congruent)

b = 70°

✔️c = 110° (alternate interior angles are congruent)

2.

✔️a = 180 - 120 (linear pair)

a = 60°

✔️b = a (corresponding angles are congruent)

b = 60°

✔️c = a (alternate interior angles are congruent)

c = 60°

3.

✔️a = 55° (corresponding angles are congruent)

✔️b = 55° (Vertical angles are congruent)

✔️c = 180 - 55 = 125° (linear pair)

4.

✔️a = 115° (corresponding angles are congruent)

✔️b = 180 - a (linear pair)

b = 180 - 115

b = 65°

✔️c = b (vertical angles are congruent)

c = 65°

5.

✔️a = 180 - 25 = 155° (supplementary angles)

✔️b = 25° (corresponding angles)

✔️c = 25° (vertical angles)

6.

✔️a = 180 - 10 = 170° (linear pair)

✔️b = a (corresponding angles are congruent)

b = 170°

✔️c = 10° (corresponding angles are congruent)

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Step-by-step explanation:

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A new bank customer with ​$4 comma 500 wants to open a money market account. The bank is offering a simple interest rate of 1.5​
Jet001 [13]

a) Simple interest earned by customer in 10 years is $ 675

b) Account balance after 10 ​years is $ 5175

<em><u>Solution:</u></em>

<em><u>The simple interest is given by formula:</u></em>

Simple\ Interest = \frac{p \times n \times r}{100}

Where,

"p" is the principal

"r" is the rate of interest

"n" is the number of years

<em><u>a. How much interest will the customer earn in 10 ​years?</u></em>

From given,

Principal = p = $ 4500

Simple interest rate = r =1.5 %

n = 10

Substituting the values in formula,

Simple\ Interest = \frac{4500 \times 10 \times 1.5}{100}\\\\Simple\ Interest = 450 \times 1.5\\\\Simple\ Interest = 675

Thus simple interest earned by customer in 10 years is $ 675

<em><u>b. What will the account balance be after 10 ​years ?</u></em>

Account balance = principal + simple interest

Account balance = 4500 + 675 = 5175

Thus account balance after 10 ​years is $ 5175

8 0
3 years ago
The local park has a circular pond with a radius of 9 feet. What is the pond's circumference?
sergiy2304 [10]

Answer:

Using 3.14 as pi, the answer would be 56.52, and using just pi (as in the input on a calculator) would be 56.54867.

Step-by-step explanation:

The equation for circumference of a circle is C = πd, C representing the circumference and d representing the diameter. Since the equation shows the radius, the equation can also be C = 2πr, since the radius is half of the diameter. Multiply nine by two to get eighteen. 18 times 3.14 = 56.52.

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Answer:

1) C

2)C

3)B

4)A

Step-by-step explanation:

1) Circle

Solve for area

A≈28.27cm²

d=Diameter 6cm

Using the formulas

A=πr2

d=2r

Solving for A

A=1

4πd2=1

4·π·62≈28.27433cm²

2)

To calculate 5% of a number, simply divide 10% of the number by 2. For example, 5% of 230 is 23 divided by 2, or 11.5.

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