1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Usimov [2.4K]
2 years ago
10

LOTS OF POINTS GIVING BRAINLIEST I NEED HELP PLEASEE

Mathematics
1 answer:
Sidana [21]2 years ago
8 0

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 <u>parallel</u> 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><u>Segment BC:</u></h3>

The <u>y-intercept</u> 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 <u>slope-intercept form</u> (y = mx + b) to solve for the y-intercept, <em>b. </em>

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 <u><em>y-intercept</em></u> of segment BC is: <em>b</em> = 2.

Therefore, the linear equation in <u>slope-intercept form of segment BC</u> is:

⇒  y = -x + 2.

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

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

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 <u><em>y-intercept</em></u> of segment BC is: <em>b</em> = 8.

Therefore, the linear equation in <u>slope-intercept form of segment EF</u> is:

⇒  y = -x + 8.

You might be interested in
2/9 multiplied by 9/5
r-ruslan [8.4K]

Answer:

2/5

Step-by-step explanation:

simplify by cross multiplying

7 0
3 years ago
Read 2 more answers
Three times a number is subtracted from another number and the difference is 3.  The sum of  the two numbers is 31.  What is the
Brut [27]
Using the equations y-3x=3 and x+y=31 you can find that x=7 and y=24. There for x is the smaller of the two numbers.
5 0
3 years ago
What is the approximate area of the circle?
Sophie [7]

Answer:

B

Step-by-step explanation:

because it is

5 0
3 years ago
Read 2 more answers
Variable expression for 3x+7
evablogger [386]

Answer:

y=3x+7

Step-by-step explanation:

Where y is the dependent variable and x is the independent variable. When we change x , Y also changes.

3 0
3 years ago
What is the y-intercept of the function f(x)=4 – 5x?
schepotkina [342]
The slope-intercept form of a line is
y=mx+b
where m is the slope
b is the y-intercept

if you convert the function into an equation, then
y=4-5x

rearranging the equation
y=-5x +4
thus
m=-5 and b=4

the y-intercept of the function is 4
8 0
3 years ago
Read 2 more answers
Other questions:
  • The stem-and-leaf plot below shows the number of pages each student in the class read the previous evening. A stem and leaf plot
    9·2 answers
  • What's 4x² - 9y² factorised?
    13·1 answer
  • Find the quotient. 54÷ 1 1/12 =
    10·1 answer
  • The packaging process in a breakfast cereal company has been adjusted so that an average of 13.0 oz of cereal is placed in each
    7·1 answer
  • Vectors and scalars (are/arenot) the same
    12·2 answers
  • Ex 9-9 Straight-line depreciation ObJ. 2
    11·1 answer
  • Plz help, asap!!
    11·2 answers
  • A rocket is launched with an initial upward velocity of 320 feet per second from an initial height of 15 feet.
    14·1 answer
  • To the nearest tenth, what is the value of x?<br>A. 3.5<br>B. 4.8<br>C. 5.9<br> D. 7.3<br>E. 9.8 ​
    8·1 answer
  • Please help me !! Show work if possible
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!