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coldgirl [10]
3 years ago
12

Find the values of a, b and c.

Mathematics
1 answer:
valina [46]3 years ago
7 0

Look at the picture.

Corresponding Angles are equal.

Alternate Angles are equal.

Consecutive Angles add up to 180°.

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

3a and 45 are Consecutive Angles. Therefore

3a + 45 = 180    |subtract 45 from both sides

3a = 135      |divide both sides by 3

<h3>a = 45.</h3>

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

(2c - 1) and 45 are Corresponding Angles. Therefore

2c - 1 = 45     |add 1 to both sides

2c = 46     |divide both sides by 2

<h3>c = 23.</h3>

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

3a and (12b + 3) are Alternate Angles. Therefore

3(45) = 12b + 3

135 = 12b + 3     |subtract 3 from both sides

132 = 12b      |divide both sides by 12

<h3>b = 11.</h3>
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Find the modulus of the complex number 6-2i
Papessa [141]

Answer:

The modulus of the complex number 6-2i is:

|z|\:=2\sqrt{10}

Step-by-step explanation:

Given the number

6-2i

We know that

z = x + iy

where x and y are real and \sqrt{-1}=i

The modulus or absolute value of z is:

|z|\:=\sqrt{x^2+y^2}

Therefore, the modulus of 6-2i  will be:

z=6-2i

z=6+(-2)i

|z|\:=\sqrt{x^2+y^2}

|z|\:=\sqrt{6^2+\left(-2\right)^2}

    =\sqrt{6^2+2^2}

    =\sqrt{36+4}

    =\sqrt{40}

    =\sqrt{2^2}\sqrt{2\cdot \:5}

    =2\sqrt{2\cdot \:5}

   =2\sqrt{10}

Therefore, the modulus of the complex number 6-2i is:

|z|\:=2\sqrt{10}

3 0
3 years ago
Renata and her family go through an average of more than 15 cans of sparkling water each day. They buy cases of 24 cans at $3.50
DENIUS [597]

Answer:

The inequality required to express the above condition is   x     ≥    18.75

Step-by-step explanation:

Renata and her family go through an average of more than 15 cans of sparkling water each day.

The number of cases of 24 cans of sparkling water.

We can take the number of cases to be x.

Each case is said to cost $3.50.

An inequality for the number of cases that Renata's family go through in 24 days can be written as

       x ≥ \frac{15 \times 30}{24}           ⇒     x    ≥   \frac{450}{24}         ⇒   x ≥     18.75

Therefore the inequality required to express the above condition is

x     ≥    18.75

3 0
3 years ago
An airplane covers 94 miles in 6 of an hour.<br> The plane can cover<br> miles in 6 hours.
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Answer:

in 6 hours it will be 3384

7 0
3 years ago
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Directions: Simplify the following expressions using the imaginary number.
drek231 [11]

Answer:

1  i(sqrt5)

2  7i

3  -9i

4  -64i

5  -5i(sqrt2)

6  -4i(sqrt3)

7  10i(sqrt3)

8  2i(sqrt2)

9  3i(sqrt7)

10  -30i(sqrt2)

Step-by-step explanation:

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5 0
1 year ago
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