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3 years ago

(3,4) (3,5) (3,6) y as a function of x

Mathematics

1 answer:

Nezavi [6.7K]3 years ago

6 0

Answer:

Step-by-step explanation:

y is NOT a function of x because there is not a unique y for each x.

The vertical line through these three points is

x = 3

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Find the value of X and prove the following

natali 33 [55]

The value of the variable x can be determined using the circle theorem to

determine the angle formed by x.

The correct responses are;

(1) x = 30°

(2) x = 100°

(3) x = 60°

Reasons:

(1) From circle theorem, we have;

Equal chords subtends equal arcs and vice versa

Equal chords subtend equal angles at the center of a circle

Therefore;

Angle subtended by $\displaystyle \widehat {AB}$ at center = Angle subtended by $\widehat {BC}$ at the center;

Angle at the center = 2 × Angle at the circumference

Therefore;

Angle subtended by $\displaystyle \widehat {AB}$ at the circumference = Angle subtended by $\mathbf{\widehat {BC}}$ at the circumference

Which gives;

x = 30°

(2) $\displaystyle \widehat {AB} = \mathbf{\widehat {CD}}$ given

Angle subtended by arc $\widehat {CD}$ at the center = x

Equal arcs subtend equal angles at the center of a circle.

Therefore;

Angle subtended by arc $\mathbf{\widehat {AB}}$ at the center = x

Angle at center = 2 × angle at circumference

Therefore;

x = 2 × 50° = 100°

x = 100°

(3) $\displaystyle \widehat {AC} = \mathbf{ 3 \times \widehat {AB}}$ given

By definition, we have;

Angle subtended by $\widehat {AC}$ at the center = 3 × Angle subtended by $\widehat {AB}$ at the center

According to circle theorem, we have;

Angle at the center = 2 × Angle at the circumference

Let y represent the angle subtended at the circumference by $\widehat {AB}$ , we have;

y = 20°

$\widehat {AB}$ = 2·y

$\widehat {AC}$ = 3 × $\widehat {AB}$ = 3 × 2·y = 6·y

Therefore;

$\widehat {AC}$ = 6 × 20° = 120°

$\widehat {AC}$ = 120°

$\widehat {AC}$ = 2·x

Therefore;

2·x = 120°

$\displaystyle x = \frac{120^{\circ}}{2} = \mathbf{ 60^{\circ}}$

x = 60°

Learn more circle theorems here:

brainly.com/question/16879446

5 0

1 year ago

Read 2 more answers

naomis fish is 40 ml long her guinea pig is 25 cm long how much longer is her guinea pig than her fish

aliya0001 [1]

Answer:

the guinea pig is 21 cm longer

Step-by-step explanation:

fish = 40 mm

guinea pig 25 cm

convert the fish to cm

1 cm = 10 mm

40 mm * 1 cm/10 mm = 4 cm

guinea pig - fish

25 cm - 4 cm

21 cm

the guinea pig is 21 cm longer

3 0

3 years ago

NEED HELP FINDING SLOPE OF THE LINE

mamaluj [8]

Answer:

slope = - $\frac{2}{3}$

Step-by-step explanation:

calculate the slope m using the slope formula

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

with (x₁, y₁ ) = (- 4, 2) and (x₂, y₂ ) = (2, - 2) ← 2 points on the line

m = $\frac{-2-2}{2-(-4)}$ = $\frac{-4}{2+4}$ = $\frac{-4}{6}$ = - $\frac{2}{3}$

5 0

1 year ago

At RSM summer camp 100 students had enough food for a 30-days stay. After 2 days 40 new students joined the camp. After that 2 w

omeli [17]

Answer:

"no additional days of food need to be ordered."

Step-by-step explanation:

Suppose initial quantity of food is x units

Assuming each student eats 1 unit of food per day,

x = 30 * 100 = 3000 units of food

In 2 days, food eaten:

100 * 1 * 2 = 200 units

So food left after 2 days is 3000 - 200 = 2800 units

Now, there are 140 students. They stay 2 weeks (14 days) - 2 = 12 more days

So food eaten in 12 days:

140 * 1 * 12 = 1680 units

THus, after total 14 days gone, the amount of food left is:

2800 - 1680 = 1120 units

Half students left, so there are 70 students left for the last 16 days. How much food would they need?

70 * 1 * 16 = 1120 units

And there are exactly 1120 units left. So, no additional days of food need to be ordered.

6 0

2 years ago

Ms. White measured the number of the ounces of juice left behind by 3 students after breakfast. She plotted the data on the line

xxMikexx [17]

Answer: 7 3/4

Step-by-step explanation:

3 1/4 + 4 2/4 = 7 3/4

7 0

2 years ago