unit 5 relationships in triangles homework 1 triangle midsegments

Unit 5 Relationships In Triangles Homework 1 Triangle Midsegments

Answers

Answer 1

Based on the definition of a parallel line and the Midsegment Theorem the following are the right answers:

1. a.) BD║AE

b.) BF ║CE

c.) DF║CA

2. a.) YZ║RT

b.) RS ║XZ

c.) XY║TS

3. a.) FH = 24

b.) JL = 74

c.) KJ = 60

d.) FJ = 30

4. a.) AE = 26

b.) AN = 58

c.) CT = 21.5

d.) Perimeter of ΔAEN = 127

5. x = 15

6. x = 6

What are Parallel lines?

Parallel lines coplanar straight lines that do not meet each other and are equal distance from each other.

The Triangle Midsegment TheoremA midsegment is a line that connects the midpoints of the two sides of a triangle together. Every triangle three midsegments.Based on the Midsegment Theorem of a triangle, the third side of a triangle is always parallel to the midsegment, and thus, the third side is twice the size of the midsegment. In order words, length of midsegment = ½(length of third side).

Applying the definition of a parallel line and the Midsegment Theorem the following can be solved as shown below:

1. The pairs of parallel lines in ΔAEC (i.e. the midsegment is parallel to the third side) are:

a.) BD║AE

b.) BF ║CE

c.) DF║CA

2. The segment parallel to the given segments are:

a.) YZ║RT

b.) RS ║XZ

c.) XY║TS

3. Given:

FG = 37; KL = 48; GH = 30

a.) FH = ½(KL)

Substitute

FH = ½(48)

FH = 24

b.) JL = 2(FG)

Substitute

JL = 2(37)

JL = 74

c.) KJ = 2(GH)

Substitute

KJ = 2(30)

KJ = 60

d.) FJ = ½(KJ)

Substitute

FJ = ½(60)

FJ = 30

4. Given:

PT = 13

EN = 43

CP = 29

a.) AE = 2(PT)

Substitute

AE = 2(13)

AE = 26

b.) AN = 2(CP)

Substitute

AN = 2(29)

AN = 58

c.) CT = ½(EN)

Substitute

CT = ½(43)

CT = 21.5

d.) Perimeter of ΔAEN = EN + AN + AE

Substitute

Perimeter of ΔAEN = 43 + 58 + 26

Perimeter of ΔAEN = 127

5. 10x + 44 = 2(8x - 23) (midsegment theorem)

10x + 44 = 16x - 46

Add like terms together

10x - 16x = -44 - 46

-6x = -90

Divide both sides by -6

x = 15

6. 19x - 28 = 2(6x + 7) (midsegment theorem)

19x - 28 = 12x + 14

Add like terms together

19x - 12x = 28 + 14

7x = 42

Divide both sides by 7

x = 6

Learn more about midsegment theorem on:

https://brainly.com/question/11482568


Related Questions

Can someone help me out

Answers

Answer:

75.7

Step-by-step explanation:

Area of the sector,

17²×π×30/360

= 289π/12

= 75.7 (rounded to the nearest tenth)

Answered by GAUTHMATH

Please help me solve this

Answers

Answer:

43

78

56

Step-by-step explanation:

What is the solution, if any, to the inequality |3x|20?
all real numbers
solution
no
x>0
x

Answers

Answer:

20×2=40bnmcsshjvghjpiutewqadgjlmbcz

Answer: all real numbers

Step-by-step explanation:

Find SP where MP=Rs875 and discount =Rs75

Answers

Answer:

SP is Rs 800.

Step-by-step explanation:

MP = Rs 875

Discount = Rs 75

so

SP = MP - discount

= Rs 875 - Rs 75

= Rs 800

Find the measure of the missing arc KN labeled on the graph. Show ll your work that leads the final answer. *

Answers

Answer:

Arc KN = 201°

Step-by-step explanation:

Recall: According to the tangent-secant exterior angle theorem, the measure of the vertex angle formed at an external point where a tangent and a secant meet outside a circle is ½ of the difference between the intercepted major and minor arcs.

Applying this to the problem given, we have:

m<L = ½(Arc KN - Arc KM)

m<L = 70° (given)

Arc KN = ?

Arc KM = 61°

Substitute

70° = ½(Arc KN - 61°)

2*70° = Arc KN - 61°

140° = Arc KN - 61°

140° + 61° = Arc KN

201° = Arc KN

Arc KN = 201°

Two walls of a canyon form the walls of a steady flowing river. From a point on the shorter wall, the angle of elevation to the top of the opposing wall is 20° and the angle of depression to the bottom of the opposing wall is 320 feet. Using the appropriate right triangle solving strategies, solve for the following: (Do not round intermediate calculated values. Only the final answer should be rounded to one decimal place.)

Answers

Answer:

x is approximately 226.3 feet

y is approximately 308.6 feet

z is approximately 226.3 feet

Step-by-step explanation:

The given parameters of the walls are;

The angle of elevation from the top of the shorter wall to the top of the opposing wall, θ₁ = 20°

From the diagram, the angle of depression from the top of the shorter wall to the bottom of the opposing wall, θ₂ = 45°

The distance from the bottom of the shorter wall to the base of the opposing wall, l = 320 feet

x = The height of the shorter wall = l × sin(θ₂)

∴ x = 320 feet × sin(45°) = 320 feet × (√2)/2 = 160·√2 feet ≈ 226.3 feet

∴ x ≈ 226.3 feet

By observation, we have;

y = x + z × tan(θ₁)

Where;

z = l × cos(θ₂)

∴ y = 160·√2 + 320 × cos(45°) × tan(20°) ≈ 308.6

y ≈ 308.6 feet

z =  l × cos(θ₂)

∴  z = 320 × cos(45°) = 160·√2 ≈ 226.3

z ≈ 226.3 feet.

If (x + 1) is a factor of 2x - kx²-8x + 5, find the value of k.
[ Using Factor Theorem ]​

Answers

Answer:

k = 11

Step-by-step explanation:

What the factor theorem is telling us is that if x + 1 is a factor of 2x - kx²-8x + 5 then when x = - 1 is put into the equation, the result will be 0. That's because x +1 = 0 when x  = - 1

f(-1) = 2(-1) - k(-1)^2 - 8(-1) + 5

f(-1) = -2 - k(1) + 8 + 5 = 0

-k*(1) + 11 = 0

-k = -11

k = 11

What is the translation from the preimage to the image in the graph?​

Answers

Answer:

(x, y ) → (x + 4, y - 1 )

Step-by-step explanation:

Consider the coordinates of K and K'

K (- 3, 5 ) , K' (1, 4 )

x- direction : - 3 → 1 is + 4 units to the right

y- direction : 5 → 4 is - 1 units down

translation rule is (x, y ) → (x + 4, y - 1 )

amy bill and cara each played a game . amy’s scored was ten times bill’s scored . cara’s down the ratio of amy’s scored to bill’s scored to cara’s score. give your answer in its simplest form

Answers

Answer:

10:1:5

Step-by-step explanation:

Given that,

A game was played by Amy, Bill, and Cara.

Let Amy's score be x. Then,

Bill's score would be x/10

Cara's score = x/2

Now,

The ratio of their scores;

x: x/10: x/2

= 1 : 1/10 : 1/2

To equalize the scores, multiply all of them by 10

= (1 * 10): (1/10 * 10) : (1/2 * 10)

= 10 : 1 : 5

Thus, the simplest ratio form would be 10:1:5

Answer:

Step-by-step explanation:

10:1:5

Two cars leave the park at the same time opposite directions one goes 3 times faster after 6 hours they travel 140miles how fast did theyg go

Answers

Answer:

Their speeds are;

5.83 mph and 17.49 mph

Step-by-step explanation:

We are told that they leave the park the same time.

Let the speed one car traveled be v

Since the other car is 3 times faster, then it means that, it's speed is 3v.

Now, after 6 hours they travel 140 miles.

We know that;

Speed = distance/time.

Thus;

(v + 3v) = 140/6

4v = 140/6

v = 140/24

v = 5.83 mph

Thus, second car's speed = 3v = 3 × 5.83 = 17.49 mph

Find the measure of each angle supplementary angles with measures 2X +3 and 3X +2

Answers

supplementary angles = the sum of those angles will equal to 180 degrees

so,

2x + 3 + 3x + 2 = 180

5x + 5 = 180

5x = 175

x = 35

angle 1 -> 2x + 3 = 70 + 3 = 73

angle 2 -> 3x + 2 = 105 + 2 = 107

if you want to check, 107 + 73 = 180

hope it helps :)

1 point
Andrea and Barry are sharing a bag of popcorn at the movies. By himself,
Barry can eat the whole bag of popcorn in 30 minutes. Andrea takes 20
minutes to eat the whole bag. If they both eat popcorn at their usual rates,
approximately how long will it take them to finish the bag of popcorn?

Answers

Answer:

12 minutes

Step-by-step explanation:

We can use the formula

1/a+ 1/b = 1/c  where a and b are the times alone and c is the time together

1/20 + 1/30 = 1/c

Multiply by the common denominator to clear the fractions

60c(1/20 + 1/30 = 1/c)

3c +2c = 60)

5c = 60

Divide by 5

5c/5 = 60/5

c = 12

12 minutes

Answer: 12 minutes

Step-by-step explanation: To solve this kind of a problem, which is called a work problem, it's important to understand the following idea:

Since Barry can eat a bag of popcorn in 30 minutes, we know that in 1 minute, Barry can eat 1/30 of the bag of popcorn and in 2 minutes, Barry can eat 2/30 of the bag of popcorn. Therefore, in t minutes, Barry can eat t/30 of the bag of popcorn. The same thing applies for Andrea. In t minutes, Andrea can eat t/20 of the bag of popcorn.

Now to solve the problem, we use the following formula:

Part of Job done by Barry + Part of Job done by Andrea = 1 job done

The part of job done by Barry is t/30 and the part

of the job done by Andrea is t/20.

So we have t/30 + t/20 = 1.

To solve for t, multiply both sides by the common denominator of 60.

So we get 2t + 3t = 60 or 5t = 60 so t = 12.

So Barry and Andrea can eat 1 bag together in 12 minutes.

A national caterer determined that 37% of the people who sampled their food said that it was delicious. If the 144 people at the Valley Ridge Nursing Home are given the same food, and asked by tables what the deliciousness of the food, what is the mean of the sampling distribution of p-hat (the population proportion)

Answers

Answer:

Hence the mean of the sampling distribution of proportion is,  

[tex]\mu\hat p = p = 0.37[/tex].

Step-by-step explanation:

Here the given details are,  

p = 0.37  

1 - p = 1 - 0.37 = 0.63  

n = 144  

The mean of the sampling distribution of proportion is,  

[tex]\mu\hat p = p = 0.37[/tex]

Find the interior angle sum for the following polygon

Answers

140 is ur answer…
Im not really sure but I think this is it
Really hope this helps

a) (x3 – 7x + 3 – x2) : (x – 3);

b) (2x4 – 3x3 – 3x2 – 2 + 6x) : (x2 – 2)

Answers

Answer:

Step-by-step explanation:

X^2+2x-1

2X^2-3x+1

9) Assume that the random variable X is normally distributed, with mean = 90 and standard deviation o = 12. Compute the probability P(57 < X < 105).
A) 0.7888 B) 0.8944 C) 0.8914 D) 0.8819​

Answers

Answer:

Step-by-step explanation:

The mean, [tex]\bar{x}[/tex], is 90 and the standard deviation, [tex]\sigma[/tex], is 12.  We are looking for the probability that the variable X will fall between 57 and 105. We use the z-score table for this, AFTER we find the z scores. The formula to find the z-scores for us is:

[tex]P(\frac{57-\bar{x}}{\sigma}\leq z\leq \frac{105-\bar{x}}{\sigma})[/tex] and we fill in accordingly:

[tex]P(\frac{57-90}{12}\leq z\leq \frac{105-90}{12})[/tex] which simplifies to

[tex]P(-2.75\leq z\leq 1.25)[/tex] and we will break them up into 2 different sets as follows:

P(-2.75 ≤ z ≤ 0) + P(0 ≤ z ≤ 1.25)

and based on the fact that z scores are given from 0 on up, we are going to convert the first one by using the logic that if z is greater than -2.75 but less than 0, by symmetry, z is greater than 0 but less than 2.75:

P(0 ≤ z ≤ 2.75) + P(0 ≤ z ≤ 1.25) and we go to the z-score table.

Locate 2.7 down along the left side and move over til you're under the .05; that gives us the z-score for 2.75 which is .4970. Do the same for 1.25 to get a z-score of .3944. Add them together to get a final z-score that covers the range of values for X:

.4970 + .3944 = 0.8914

a two digit number divided by another two digit number,we get 3.675 what are the numbers?​

Answers

Answer:

Step-by-step explanation:

I can't get the exact answer you've given, but I can tell you some things about it. The largest number in the denominator is 30 or 31. That's because 31 * 3 is 93 exactly. However the fraction is a problem and will likely push you over 100.

3.675 * 31 = 113 something. So 31 is too big.

The closes I came was 98 / 26 which is 3.769


Show working please

Answers

Answer:

Step-by-step explanation:

       1.159 R (remainder) 42

     | ------------------------

73  | 84.649

      -73

       116 (brought 6 down)

       -73

         434 (brought 4 down)

         -365

          699 (brought 9 down)

         -657

             42 is the remainder

↪[tex] \: \: \: \: \: \: \: \: \: \: \huge \rm{answer:} \boxed{ \purple{42}}[/tex]

[tex] \huge \red {\boxed{\sf{armed \: account}}}[/tex]

[tex] \huge\frac{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \rm1159r42}{ \: 73) \: \:84649} \\ \huge \frac{ - 73}{ \: \: \: \: \: \: 116} \\ \huge \frac{ \: \: \: \: - 73}{ \: \: \: \: \: \: \: \: \: 434} \\ \huge \frac{ \: \: \: \: \: \: - 365}{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: 699} \\ \huge\frac{ \: \: \: \: \: \: \: \: \: \: - 657}{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \red{42} }[/tex]

➖➖➖➖➖➖➖➖➖➖➖➖➖➖

And that's it! Hope it wasn't too hard to understand✏

➖➖➖➖➖➖➖➖➖➖➖➖➖➖

Step-by-step explanation:

[tex] \huge \rm{Hope \: this \: helps}[/tex]

The skateboard Rita would like to buy costs $ 6 less than 3 times the amount she saved. The skateboard costs $ 69. How much money has Rita saved? Choose the steps that show how to solve this problem using arithmetic

Answers

Given:

The skateboard Rita would like to buy costs $ 6 less than 3 times the amount she saved.

The skateboard costs $69.

To find:

The saved amount.

Solution:

Let x be the saved amount.

The skateboard Rita would like to buy costs $ 6 less than 3 times the amount she saved. So, the cost of the skateboard is [tex]3x-6[/tex].

The skateboard costs $69.

[tex]3x-6=69[/tex]

[tex]3x=69+6[/tex]

[tex]3x=75[/tex]

Divide both sides by 3.

[tex]x=\dfrac{75}{3}[/tex]

[tex]x=25[/tex]

Therefore, Rita saved $25.

help please I'll give brainliest

Answers

Answer:

35

Step-by-step explanation:

6:5

 We need to get the first number to 43

6*7 = 42

Multiply each term by 7

6*7 : 5*7

42  : 35

2.1: Solve the one step equation

9. 70 = -5x
10. x4 = 36
11. 7x = -54

Answers

Answer:

-14, 9 and - 54/7

Step-by-step explanation:

70=-5x, x=-144x=36, x=97x=-54, x=-54/7

3.3 Is it possible that a vehicle could travel so fast that the trip could be done in no time at all? Give a reason for your answer.​

Answers

Answer:

No.

Step-by-step explanation:

No matter how fast something is going it still takes a moment in time, even if it's only 1/10000 of a second.

A car travels 32 km due north and then 46 km in a direction 40° west of north. Find the direction of the car's resultant vector. [?] Round to the nearest hundredth.

Answers

Answer:

Step-by-step explanation:

This requires some serious work before we even begin. First off, we will convert the km to meters:

32 km = .032 m

46 km = .046 m

And then we have to deal with the angle given as 40 degrees west of north. An angle 40 degrees west of north "starts" at the north end of the compass and moves towards the west (towards the left in a counterclockwise manner) 40 degrees. That means that the angle that is made with the negative x axis is a 50 degree angle. BUT the way angles are measured in standard form are from the positive x-axis, therefore:

40 degrees west of north = 50 degrees with the negative x axis = 130 degrees with the positive x axis. 130 is the angle measure we use. Phew! Now we're ready to start. Adding vectors requires us to use the x and y components of vectors in order to add them.

[tex]A_x=.032cos90.0[/tex] so

[tex]A_x=0[/tex] (the 90 degrees comes from "due north")

[tex]B_x=.046cos130[/tex] so

[tex]B_x=-.030[/tex] and if we add those to get the x component of the resultant vector, C:

[tex]C_x=-.030[/tex]   And onto the y components:

[tex]A_y=.032sin90.0[/tex] so

[tex]A_y=.032[/tex]

[tex]B_y=.046sin130[/tex] so

[tex]B_y=.035[/tex] and if we add those together to get the y component of the resultant vector, C:

[tex]C_y=.067[/tex]  Note that since [tex]C_x[/tex] is negative and [tex]C_y[/tex] is positive, the resultant angle (the direction) will put us into QII.

We find the magnitude of C:

[tex]C_{mag}=\sqrt{(-.030)^2+(.067)^2}[/tex]

We will round this after we take the square root to the thousandths place.

[tex]C_{mag}=.073m[/tex] and now for the angle:

[tex]\theta=tan^{-1}(\frac{.067}{-.030})[/tex] which gives us an angle measure of -67, but since we are in QII, we add 180 to that to get that, in sum:

The magnitude of the resultant vector is .073 m at 113°

Mar-Vell Studios' blockbuster movie Gray Widow: It's About Time She Got a Movie premiered last weekend simultaneously in theaters and on streaming video. On opening weekend, the total revenue from the movie was $127,265,468, with the movie making 75% more revenue in theaters than it did via streaming video. How much money did Gray Widow make in theaters on opening weekend

Answers

Answer:

Gray Widow made $111,357,284.5 in theaters on opening weekend.

Step-by-step explanation:

75% more revenue in theaters than it did via streaming video.

The sum of the revenues is 100%.

So the theaters were responsible for the following percentage:

[tex]P = 50 + \frac{75}{2} = 50 + 37.5 = 87.5[/tex]

How much money did Gray Widow make in theaters on opening weekend?

87.5% of the total revenue, that is, 0.875 out of $127,265,468.

0.875*127,265,468 = $111,357,284.5

Gray Widow made $111,357,284.5 in theaters on opening weekend.

SOMEONE PLEASE HELP ME
Sandra is choosing an Internet service provider.
• Smart Dot Company costs $12 per month plus $0.50 for each hour of Internet used.
• Communication Plus costs $2.50 for every hour of Internet used.
a. Create an equation to represent the cost of using the internet with each company. (2 marks) Let C represent the cost of using internet in any month.
Let t represent the number of hours used

Answers

Smart Dot, multiply the cost per hour by number of hours (t) and add to the monthly fee:

C = 0.50t + 12

Communication plus: Multiply the cost per hour by number of hours (t)

C = 2.50t

If the city bus through Austin travels at 40 miles per hour, how many miles
will it travel in 4.5 hours.

Answers

It will travel 180 miles

4.5 • 40= 180

Can someone please help marking brainliest

Answers

Answer:

down below!

Step-by-step explanation:

a) width: 2,3,4,5  length:9,8,7,6

all you need if for those numbers to add up to 11 together because the perimeter itself is 22 so you always want to be able to add those two numbers and be able to double it to the perimeter if that makes sense.

b) the greatest area there will be would be width: 5 and length: 6 because 5x6 equals 30 and multiplying the others would be less than that. hence 2x9=18, 3x8=24, and 4x7=28  

please let me know if this helps if not I can try to explain another way!

HELP ME pleaseeee help help

Answers

Step-by-step explanation:

a. x+10.

b. (5)(x)(x+10)=V

c. 5×8×18=720

d. 5,8,18

e. Yes, the dimensions all stay the same so the volume should be the same.

Decide whether the graphs of the two equations are parallel. y=3x+8 and y/3-3=x

Answers

Answer:

Equation #1:

[tex]y = 3x + 8[/tex]

Equation #2:

[tex]\frac{y}{3} -3=x\\\\\frac{y}{3}=x+3\\\\y=3(x+3)\\\\y=3x+9[/tex]

Parallel equations have the same slope. Since both share the same slope of 3, they're parallel.

In a right triangle ∠A = 32° with an adjacent side of 44 what is the length of the opposite side, x?

Answers

Answer: About 27.49

Step-by-step explanation:

You use the laws of tangent within a triangle to find x:

[tex]tan(32)=\frac{opposite}{adjacent}= \frac{x}{44}\\ \\x=44*tan(32)=27.49425...[/tex]

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