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4 years ago

Find the values of a, b and c.

Mathematics

1 answer:

valina [46]4 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

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

2c - 1 = 45 |add 1 to both sides

2c = 46 |divide both sides by 2

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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

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Evaluate the function f(x) at the given numbers (correct to six decimal places). F(x) = x2 − 5x x2 − x − 20 , x = 5.5, 5.1, 5.05

exis [7]

we are given

$f(x)=\frac{x^2-5x}{x^2-x-20}$

Firstly, we will simplify it

$f(x)=\frac{x(x-5)}{(x-5)(x+4)}$

$f(x)=\frac{x}{(x+4)}$

At x=5.5:

we can plug x=5.5

$f(5.5)=\frac{5.5}{(5.5+4)}$

$f(5.5)=0.578947$

At x=5.1:

we can plug x=5.1

$f(5.1)=\frac{5.1}{(5.1+4)}$

$f(5.1)=0.56043956$

At x=5.05:

we can plug x=5.05

$f(5.05)=\frac{5.05}{(5.05+4)}$

$f(5.05)=0.558011$

At x=5.01:

we can plug x=5.01

$f(5.01)=\frac{5.01}{(5.01+4)}$

$f(5.01)=0.5560488$

At x=5.005:

we can plug x=5.005

$f(5.005)=\frac{5.005}{(5.005+4)}$

$f(5.005)=0.5558023$

At x=5.001:

we can plug x=5.001

$f(5.001)=\frac{5.001}{(5.001+4)}$

$f(5.001)=0.5556049$

At x=4.9:

we can plug x=4.9

$f(4.9)=\frac{4.9}{(4.9+4)}$

$f(4.9)=0.5505617$

At x=4.95:

we can plug x=4.95

$f(4.95)=\frac{4.95}{(4.95+4)}$

$f(4.95)=0.5530726$

At x=4.99:

we can plug x=4.99

$f(4.99)=\frac{4.99}{(4.99+4)}$

$f(4.99)=0.55506117$

At x=4.995:

we can plug x=4.995

$f(4.995)=\frac{4.995}{(4.995+4)}$

$f(4.995)=0.55503085$

At x=4.999:

we can plug x=4.999

$f(4.999)=\frac{4.999}{(4.999+4)}$

$f(4.999)=0.55550616$

7 0

4 years ago

An object is placed 21 cm from a concave lens of focal length 25 cm. what is the magnification?

wariber [46]

The magnification is 0.54

Given,

The distance between object and concave lens, u = -21 cm

Focal length of the concave lens, f = -25 cm

Let m be the magnification.

m = v/u

Here v is the position of image.

We have to find v first.

By using lens equation we can determine v.

That is,

1/f = 1/v – 1/u

So,

- (1/25) = 1/v – (-1/21)

- (1/25) = 1/v + 1/21

1/v = - (1/25) – 1/21

1/v = (-25 – 21) / (21 x 25)

1/v = - (46/525)

Therefore v = - (525/46)

v = -11.41 cm

Now we have to find magnification, m.

m = v/u

= (-11.41) / (-21)

= 0.54

Here magnification is 0.54

Learn more about concave lens here: brainly.com/question/12944945

#SPJ4

6 0

2 years ago

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vladimir1956 [14]

Answer:incomplete

Step-by-step explanation:

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3 years ago

-9 more than a number results in -20

Alona [7]

Answer:

-11

Step-by-step explanation:

-20-(-9)= -11

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3 years ago

What is a quartic function with only two real zeros atx x = 7 and x = 13

kramer

Answer:

1098765432

Step-by-step explanation:

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3 years ago