What’s the missing factors for these questions?

LOTS OF POINTS GIVING BRAINLIEST I NEED HELP PLEASEE

Sidana [21]

Answer:

Segment EF: y = -x + 8

Segment BC: y = -x + 2

Step-by-step explanation:

Given the two similar right triangles, ΔABC and ΔDEF, for which we must determine the slope-intercept form of the side of ΔDEF that is parallel to segment BC.

Upon observing the given diagram, we can infer the following corresponding sides:

$\displaystyle\mathsf{\overline{BC}\:\: and\:\:\overline{EF}}$

$\displaystyle\mathsf{\overline{BA}\:\: and\:\:\overline{ED}}$

$\displaystyle\mathsf{\overline{AC}\:\: and\:\:\overline{DF}}$

We must determine the slope of segment BC from ΔABC, which corresponds to segment EF from ΔDEF.

<h2>Slope of Segment BC:</h2>

In order to solve for the slope of segment BC, we can use the following slope formula:

$\displaystyle\mathsf{Slope\:(m)\:=\:\frac{y_2 \:-\:y_1}{x_2 \:-\:x_1}} }$

Use the following coordinates from the given diagram:

Point B: (x₁, y₁) = (-2, 4)

Point C: (x₂, y₂) = ( 1, 1 )

Substitute these values into the slope formula:

$\displaystyle\mathsf{Slope\:(m)\:=\:\frac{y_2 \:-\:y_1}{x_2 \:-\:x_1}}\:=\:\frac{1\:-\:4}{1\:-\:(-2)}\:=\:\frac{-3}{1\:+\:2}\:=\:\frac{-3}{3}\:=\:-1}$

<h2>Slope of Segment EF:</h2>

Similar to how we determined the slope of segment BC, we will use the coordinates of points E and F from ΔDEF to find its slope:

Point E: (x₁, y₁) = (4, 4)

Point F: (x₂, y₂) = (6, 2)

Substitute these values into the slope formula:

$\displaystyle\mathsf{Slope\:(m)\:=\:\frac{y_2 \:-\:y_1}{x_2 \:-\:x_1}}\:=\:\frac{2\:-\:4}{6\:-\:4}\:=\:\frac{-2}{2}\:=\:-1}$

Our calculations show that segment BC and EF have the same slope of -1. In geometry, we know that two nonvertical lines are parallel if and only if they have the same slope.

Since segments BC and EF have the same slope, then it means that $\displaystyle\mathsf{\overline{BC}\:\: | |\:\:\overline{EF}}$ .

<h2>Slope-intercept form:</h2><h3>Segment BC:</h3>

The y-intercept is the point on the graph where it crosses the y-axis. Thus, it is the value of "y" when x = 0.

Using the slope of segment BC, m = -1, and the coordinates of point C, (1, 1), substitute these values into the slope-intercept form (y = mx + b) to solve for the y-intercept, b.

y = mx + b

1 = -1( 1 ) + b

1 = -1 + b

Add 1 to both sides to isolate b:

1 + 1 = -1 + 1 + b

2 = b

Hence, the y-intercept of segment BC is: b = 2.

Therefore, the linear equation in slope-intercept form of segment BC is:

⇒ y = -x + 2.

<h3></h3><h3>Segment EF:</h3>

Using the slope of segment EF, m = -1, and the coordinates of point E, (4, 4), substitute these values into the slope-intercept form to solve for the y-intercept, b.

y = mx + b

4 = -1( 4 ) + b

4 = -4 + b

Add 4 to both sides to isolate b:

4 + 4 = -4 + 4 + b

8 = b

Hence, the y-intercept of segment BC is: b = 8.

Therefore, the linear equation in slope-intercept form of segment EF is:

⇒ y = -x + 8.

8 0

2 years ago

How to do splitting method of x square- 2x -8

Leni [432]

Answer:

Hey mate

kindly see attached picture:)

hope it helped you ☺️

3 0

3 years ago

Read 2 more answers

HELP FAST!!! Find 78% of 380. Round to the nearest tenth if necessary.

bonufazy [111]

78% = 78 / 100 = 0.78

What is 78% of 380

= 78% * 380

= 0.78 * 380

= 296.4

U said I should round it up IF NECESSARY so yeah....

5 0

3 years ago

Read 2 more answers

What is the ratio for sin B?

Y_Kistochka [10]

Answer: 22.6°

Approximately: 23°

Step-by-step explanation:

Sin B = Opp/Hyp

Sin B = 5/13

Sin B = 0.3846

Inverse of Sin B

B = 22.6°

Approximately: 23°

3 0

3 years ago

Find the indicated area under the curve of the standard normal distribution; then convert it to a percentage and fill in the bl

galben [10]

Answer:

95%

Step-by-step explanation:

About 95% of the area is within two standard deviation in standard normal distribution. This can be explained by finding the probability within 2 standard deviation using standard normal distribution.

P(z1<Z<z2)=P(-2<Z<2)

P(-2<Z<2)=P(-2<Z<0)+P(0<Z<2)

P(-2<Z<2)=0.4772+0.4772

P(-2<Z<2)=0.9544

Thus, About 95% of the area is between z2 and z2

4 0

3 years ago