A. What is the relationship between FEB and ABE?

Each line represents a proportional relationship. Write an equation for each line. Show your work.

tiny-mole [99]

Answer:

The equation of line a is y = x

The equation of line b is y = $\frac{2}{3}$ x

Step-by-step explanation:

The equation of the proportional is y = m x, where

m is the slope of the line (constant of proportionality)

The rule of the slope of a line is m = $\frac{y2-y1}{x2-x1}$ , where

(x1, y1) and (x2, y2) are two points on the line

∵ Line a passes through points (0, 0) and (3, 3)

∴ x1 = 0 and y1 = 0

∴ x2 = 3 and y2 = 3

→ Substitute them in the rule of the slope above

∵ m = $\frac{3-0}{3-0}=\frac{3}{3}$

∴ m = 1

→ Substitute in the form of the equation above

∴ y = (1)x

∴ y = x

∴ The equation of line a is y = x

∵ Line b passes through points (0, 0) and (3, 2)

∴ x1 = 0 and y1 = 0

∴ x2 = 3 and y2 = 2

→ Substitute them in the rule of the slope above

∵ m = $\frac{2-0}{3-0}=\frac{2}{3}$

∴ m = $\frac{2}{3}$

→ Substitute in the form of the equation above

∴ y = ( $\frac{2}{3}$ ) x

∴ y = $\frac{2}{3}$ x

∴ The equation of line b is y = $\frac{2}{3}$ x

7 0

3 years ago

Find the measure of the exterior angle in the following triangle. DUE SOON PLZ HELP WITH STEP BY STEP

PSYCHO15rus [73]

Answer:

The measure of an exterior angle = 125°

Hence, option A is correct.

Step-by-step explanation:

As the given triangle is a right-angled triangle ΔABC.

Given the angles

m∠A = 35°

m∠C = 90°

We know that the sum of angles in a triangle is 180°.

Thus,

m∠A + m∠B + m∠C = 180°

substituting m∠A = 35° and m∠C = 90° in the equation

35° + m∠B + 90° = 180°

125 + m∠B = 180°

subtract 125 from both sides

125 + m∠B - 125 = 180° - 125

m∠B = 55°

Thus, the measure of angle B is:

m∠B = 55°

As the exterior angle of the given triangle is adjacent to m∠B = 55°.

We know that the exterior angle of a triangle is equal to the sum of two opposite interior angles.

Here,

∠A and ∠C are two opposite interior angles of the exterior angle.

Thus,

The measure of an exterior angle is equal to the sum of two opposite interior angles.

as

m∠A = 35°

m∠C = 90°

so

Exterior angle = m∠A + m∠C

= 35° + 90°

= 125°

Thus, the measure of an exterior angle = 125°

Hence, option A is correct.

8 0

3 years ago

Select all the parallelograms that have an area of 16 square units

Georgia [21]

Answer:it's c and b

Step-by-step explanation:

It's c an b

3 0

3 years ago

-4x + 8x - 6x

valina [46]

Answer:

The answer are

$34 = - 2x \\ 35 = - \frac{1}{4} n \\ 36 = - \frac{13}{3} a \\ 37 = - \frac{1}{24} b$

3 0

3 years ago

A charter airline finds that on its Saturday flights from Philadelphia to London all 180 seats will be sold if the ticket price

Darina [25.2K]

Answer:

$S = -\dfrac{1}{3}P+\dfrac{740}{3}$

Step-by-step explanation:

Given that:

Number of seats sold is 180 with ticket price $200.

Number of seats decreases by one when the ticket price is increased by $3.

To find:

The formula for the number of seats sold (S) when the ticket price is P dollars.

Solution:

It is linear dependency of number of seats sold, S on ticket price, P.

$S\propto P$

It can be written as:

$S = kP+C$

Where $k$ is the constant of proportionality and

$C$ is a constant.

Now, putting the given values:

$180 = 200k +C ..... (1)$

$179 = 203k+C$ ...... (2)

Subtracting (1) from (2):

$3k = -1\\\Rightarrow k =-\dfrac{1}{3}$

Putting the value in (1):

$\Rightarrow C = 180+\dfrac{200}{3} = \dfrac{740}{3}$

Therefore the equation becomes:

$S = -\dfrac{1}{3}P+\dfrac{740}{3}$

4 0

3 years ago