Given B(17,5), C(11, -3), D-1, 2), and
E(x, -6), find the value of x so that BC || DE.
Answers
Answer:
[tex]x=-7[/tex]
Step-by-step explanation:
Remember that:
Two lines are parallel if their slopes are the same.Two lines are perpendicular if their slopes are negative reciprocals.And two lines are neither (a.k.a intersecting) if they are neither parallel nor perpendicular.We want to find the value of x such that [tex]\overline{BC}\parallel\overline{DE}[/tex].
Therefore, the slopes of BC and DE must be equivalent.
So, let's find the slope of BC first.
BC)
We can use the slope formula:
[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Let B(17, 5) be (x₁, y₁) and let C(11, -3) be (x₂, y₂). Substitute:
[tex]\displaystyle m=\frac{-3-5}{11-17}[/tex]
Subtract:
[tex]m=-8/-6=4/3[/tex]
So, the slope of BC is 4/3.
DE)
Let D(-1, 2) be (x₁, y₁) and let E(x, -6) be (x, y₂). Substitute:
[tex]\displaystyle m=\frac{-6-2}{x-(-1)}[/tex]
We know that the two slopes must be equal. So, the slope of DE must also be 4/3. Substitute 4/3 for m:
[tex]\displaystyle \frac{4}{3}=\frac{-6-2}{x-(-1)}[/tex]
Solve for x. Simplify the right:
[tex]\displaystyle \frac{4}{3}=\frac{-8}{x+1}[/tex]
Cross multiply:
[tex]4(x+1)=-8(3)[/tex]
Multiply on the right:
[tex]4(x+1)=-24[/tex]
Divide both sides by 4:
[tex]x+1=-6[/tex]
Subtract 1 from both sides:
[tex]x=-7[/tex]
So, the value of x is -7.
And we're done!
Related Questions
use the slope to determine if lines AB and CD are parallel, perpendicular, or neither. (please help asap!!)
Answers
Answer:
It’s perpendicular
Step-by-step explanation:
If the slopes are the same and the y-intercepts are different, the lines are parallel. If the slopes are different, the lines are not parallel. Unlike parallel lines, perpendicular lines do intersect.
lines AB and CD are perpendicular to each other
This is all about getting the slope of a line between two coordinates.
The formula for the slope in this case is;
m = (y2 - y1)/(x2 - x1)
We are given coordinates of A and B as;
A(9, 2) and B(-1, 8)
Thus;
m = (8 - 2)/(-1 - 9)
m = 6/-10
m_ab = -6/10 = -3/5
For coordinates of C and D, we have;
C(-5, 16) and D(-8, 11)
Thus;
m_cd = (11 - 16)/(-8 - (-5))
m_cd = -5/-3 = 5/3
For the slopes to be parallel, they have to be equal but for the slopes to be perpendicular, one of them would have to be negative inverse of the other.
We see that; m_cd = 5/3 is same as -1/(m_ab) = -1/(-3/5) = 5/3
Thus, lines AB and CD are perpendicular to each other.
Read more at; brainly.com/question/4853862
A box of 200 baseball cards included 10 cards that featured the Los Angeles Dodgers.
1. What fraction of the cards featured the LA Dodgers. Use simplest form.
2. What is the amount as a decimal?
3. What percent of the cards featured the LA Dodgers?
Answers
Answer:
1. 1/20
2. 0.05
3. 5%
Step-by-step explanation:
Hope it helps :)
Have a good day/night
Brainliest pls?
A circle measures _____.
Answers
Answer:
360 degress
Step-by-step explanation:
the circumference of a circle is its perimeter or distance around it. it is denoted by c in math formulas and has units of distance, such as milimeters, centimeters, meters, or inches. the circumference of a circle is the easured total length around a circle, which when measured in degrees in equal to 360 degress.
I WILL GIVE YOU BRAINLIEST IF YOU CAN ANSWER PLEASE !?
Its propertys i have yo find which property it is please help?.
Answers
Answer:
Given
distributive property
Subtraction property of equality
Addition property of equality
Division property of equality
Solution
Step-by-step explanation:
The length of a rectangular field is 7 m less than 4 times the width. The perimeter is 136 m. Find the width and length
Answers
Answer:
Width: 15 Length: 53
Step-by-step explanation:
Please help!! Thanks
Answers
Answer:
the x-intercept is 3 and the y-intercept is -4
Step-by-step explanation:
Answer:
x-intercept: (3,0)
y-intercept: (0,-4)
Given the speeds of each runner below, determine who runs the fastest. Emily runs 15 feet per second. Noah runs 358 feet in 36 seconds. Liz runs 1 mile in 405 seconds. Zach runs 768 feet in 1 minute.
Answers
Step-by-step explanation:
Since the first is already given in terms of rate (10 feet per second), we need to find the other rates. Remember, to convert to feet/sec rates.
Noah:
10 ft/sec
Brooke:
489 feet in 36 seconds means:
489/36 = 13.58 ft/sec
Stephanie:
1 mile is 5280 feet, so we can say:
5280 feet is 557 seconds, so rate is:
5280/557 = 9.48 ft/sec
Liz:
732 feet in 1 minutes. We know 1 minute is 60 seconds, so we can say:
732 feet in 60 seconds, so rate is:
732/60 = 12.2 ft/sec
Comparing all the rates (in ft/sec), we can say that "Brooke" is the fastest.
Which names the longest segment in the figure?
В
Answers
Answer:
PQ
Step-by-step explanation:
Answer: PQ would be the longest segment
Step-by-step explanation:
PQ extend 2 units versus 1
A snail traveled 2 feet in 90. How far will it travel in 6 hours?
Answers
Answer:
it will travel 8 minutes
Step-by-step explanation:
Answer:
[tex]\frac{2}{15}[/tex] feet
Step-by-step explanation:
Set up a proportion: [tex]\frac{2}{90} = \frac{x}{6}[/tex] Cross multiply, then divide: 2 × 6 = 12, 12 ÷ 90 = [tex]\frac{2}{15}[/tex]I hope this helps!
The diagram shows TUV. Which term describes point W?
Answers
Answer:
centroid
Step-by-step explanation:
a centroid is the point of intersection of it's medians (center of the sides and the vortexes)
1
Amber ran 1
miles over a period of
1
of an hour. How fast in miles per hour is Amber running?
Answers
Answer: 1mph
Step-by-step explanation:
She s running 1 mile per hour because that's what it says in the problem.
Solve for t in the scientific formula C =Wtc1,000.
Answers
Mddffffvcfffff ggbtevtrvyrvyr eg rh rhbrybryvr th tu rybry th th ht
Answers
Answer:
Yup, same.
Step-by-step explanation:
Answer:
(keyboard spam, nice)
help me !!!!!!!!!!!!!!
Answers
Answer:
Step-by-step explanation:
The MAD is 2.
Find the distance between the points (5, 8) and (-1, 3). Round to the nearest tenth.
Answers
Answer:
7.81
Step-by-step explanation:
Like I said I’m horrible at math so I’m just gonna keep posting these.
Answers
Answer:
slope is -2/1
Step-by-step explanation:
when you find slope of a line, its rise over run
so when ever the line hits a point, it goes 2 down and 1 right (if you explain this simply)
Answer:
m= -2
Step-by-step explanation:
The two points are 0,2 and 1,0 and the equation used between them spits out -2
Are the triangles similar?
Answers
a cookie recipe uses 5/6 cups of sugar lindsey is making 1 1/2 times what the recipe calls for how much sugar is she using
Answers
Answer:
1 1/4 cups of sugar
Step-by-step explanation:
5/6 x 1 1/2 = 1 1/4
Answer:
5/4 cup of sugar.
Step-by-step explanation:
The recipe calls for 5/6 of a cup of sugar, so if you're making 1.5 times what the recipe calls for, you multiply 5/6 by 3/2 (or 1.5 if you prefer decimals) which would give you 15/12. Then simplify down to get 5/4 (or 1.25) cups of sugar.
Note: 5/4 also equals 1 1/4, they are both correct, it just depends on which way you choose to write it, or how your teacher wants you to write it.
Kk someone explain this i feel so dumb thanks
Answers
Answer:
Yes
Step-by-step explanation:
The reason is all u do is 12 +1=13 aka 1pm then 30 +50=80 making the time 2:20
Lines LaTeX: CEC E and LaTeX: ADA D intersect at LaTeX: BB. Lines C E and A D intersect at the point B. Angle A B C is labeled 37 degrees. Select all the true statements. Group of answer choices The measure of angle LaTeX: CBA C B A is equal to the measure of angle LaTeX: DBE D B E . The sum of the measures of angles LaTeX: CBA C B A and LaTeX: DBE D B E is 180 degrees. The measure of angle LaTeX: CBD C B D is equal to the measure of angle LaTeX: ABE A B E . The sum of the measures of angles LaTeX: CBD C B D and LaTeX: CBA C B A is 180 degrees. The sum of the measures of angles LaTeX: CBA C B A and LaTeX: DBE D B E is 90 degrees.
Answers
*see attachment below for the figure referred to
Answer:
*The measure of angle <CBA is equal to the measure of angle <DBE.
*The measure of angle CBD is equal to the measure of angle ABE.
*The sum of the measures of angles CBD and CBA is 180 degrees.
Step-by-step explanation:
Since lines CE and AD bisects at D, they form two pairs of vertical angles that are congruent to each other. The vertical angle pairs formed are:
<CBD and <ABE;
<CBA and <DBE
Thus:
m<CBD = m<ABE;
m<CBA = <DBE = 37°
Also, m<CBA + m<CBD = 180° (supplementary linear pair)
m<ABE + m<DBE = 180° (supplementary linear pair)
Therefore, the following statements are TRUE:
*The measure of angle <CBA is equal to the measure of angle <DBE.
*The measure of angle CBD is equal to the measure of angle ABE.
*The sum of the measures of angles CBD and CBA is 180 degrees.
Find the value of f(-5).
Answers
Answer:
-5f
Step-by-step explanation:
move -5 to the left of f
Two angles form a linear pair. The measure of one angle is 1/3 of the other angle. Find the measure if each angle
Answers
Answer:
The measure of the angles is 45° and 135°
Step-by-step explanation:
When two lines intersect, a linear pair of angles is formed. Two angles are said to be linear if they are adjacent, so a linear pair of angles must add up to 180 degrees.
Let's call x and y the two required angles. Knowing they form a linear pair:
x+y=180
We also know one angle is 1/3 of the other angle, thus:
x=y/3
Or, equivalently:
3x=y
Substituting y into the first equation:
x+3x=180
Simplifying:
4x=180
Solving:
x=180/4=45
The other angle is:
y=3x=3\cdot 45=135
Thus the measure of the angles is 45° and 135°
Solve for x2:
y2 − y1 = m(x2 − x1)
this is literal equations btw
Answers
Answer:
x2 = y2/m - y1/m + x1
Step-by-step explanation:
Expand
y2 - y1 = mx2 - mx1
Rearrange
y2 - y1 + mx1 = mx2
Divide both sides by m to make x2 on its own
y2/m - y1/m + x1 (m's cancel out) = x2
Hence:
x2 = y2/m - y1/m + x1
Answer:
x2 = x1 + (y2 - y1)/mStep-by-step explanation:
Given equation
y2 − y1 = m(x2 − x1)Solving for x2
y2 − y1 = m(x2 − x1) ⇒ divide both sides by m(y2 - y1)/m = x2 - x1 ⇒ add x1 to both sidesx2 = x1 + (y2 - y1)/mor
x2 = x1 + y2/m - y1/mThe original amount borrowed is called the
A.principal
B.Time
C.interest
D.rate
Answers
Work out the size of angle x
Answers
Answer:
angle X will be 180-47=133---------------------------------------------
Your answer would be 133.
I’m doing a review but I forgot how to do this can someone help?
Answers
Answer:
-3x+10=5x-8
so basically its like grouping.
so answer is
8x=18?
Step-by-step explanation:
sorry if incorrect
Answer:
x=2.25
Step-by-step explanation:
three -x make -3x and 10 +1s make +10 and 5 xs make 5x and 8 -1s make -8
which makes
-3x+10=5x-8
just solve
18=8x
2.25=x
Here’s an algebra problem given 20 points and brainliest if correct
Answers
Answer:
12/7
Step-by-step explanation:
Hello,
C is the point (0,0)
D is the point (7,12)
So
[tex]\text{slope} =\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{12-0}{7-0}=\dfrac{12}{7}[/tex]
thanks
Answer:
12/7 possibly.
Step-by-step explanation:
Point C is (0,0) and point D is (7,12). Using the formula given, You should have something that looks like this:
[tex]\frac{(12-0)}{(7-0)}[/tex]
Then you solve:
[tex]\frac{12}{7}[/tex]
That would be your answer I believe.
I hope it helps.
At Wal Mart a 32 ounce gatorade cost $ 1.99 and at Target a 24 ounce gatorade costs $1.09. Which store has the better buy?
Answers
I believe target has the better deal.
A glass is 1/4
full. Then 70cm3 of orange juice is poured in.
The glass is now 3/5
full. What is the total volume of the glass?
Can you please tell me how to do it as well. Thanks
Answers
Paul's car is 16 feet long. He is making a model of his car that is 1/8 the actual size. What is the length of the model?
Answers
The length of the model car is 2 feet
Paul's car is 16 feet long. To create a model of his car that is 1/8 the actual size, we need to determine the length of the scaled-down model.
To find the length of the model, we multiply the length of the actual car by the scaling factor of 1/8.
Length of the model = Length of the actual car * Scaling factor
Length of the model = 16 feet * (1/8)
Length of the model = 16 feet * 1/8
Length of the model = 16/8 feet
Length of the model = 2 feet
Therefore, the length of the model car is 2 feet. The model car is 1/8 the size of the actual car, so it measures 2 feet in length.
This scaled-down model allows Paul to create a representation of his car that is much smaller and more manageable while maintaining the same proportions as the original car.
For more questions on length :
https://brainly.com/question/28322552
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