Answers
Consider the attached diagram. Segment KO is an altitude of the triangle, so KO ⊥ LM. ∠L has measure 180° -105° -30° = 45°, so ΔKOL is an isosceles right triangle.
If we let segment LO have measure 1, then KO also has measure 1 and KL has measure √(1²+1²) = √2 by the Pythagorean theorem.
ΔKMO is half of an equilateral triangle, so KM has measure 2, and MO has measure √(2²-1²) = √3 by the Pythagorean theorem.
Then the ratio of KM to LM is 2:(1+√3) and the ratio of KL to LM is √2:(1+√3). That is, ...
... KL = LM×(√2)/(1+√3) = (20√3)(√2)/(1 +√3)
... KL = (20√6)/(√3 +1) = (20√6)(√3 -1)/(3 -1) . . . . . with denominator rationalized
... KL = 30√2 -10√6 ≈ 17.9315
and
... KM = LM×2/(1+√3) = KL×√2
... KM = (30√2 -10√6)√2
... KM = 60 -20√3 ≈ 25.3590
== == == == == ==
The Law of Sines tells you ...
... KL/sin(M) = KM/sin(L) = LM/sin(K)
Then ...
... KL = sin(M)·LM/sin(K) = sin(30°)·20√3/sin(105°) ≈ 17.9315
... KM = sin(L)·LM/sin(K) = sin(45°)·20√3/sin(105°) ≈ 25.3590
Answer:
≈ 12 unitsStep-by-step explanation:
Since m∠1 = m∠2, KF is angle bisector of ∠K
In the ΔKFM we have:
∠K = 34°/2 = 17°∠M = 15°∠F = 180° - (17° + 15°) = 148°KM = 24 unitsUsing low of sines:
sin F / KM = sin M / KFsin 148° / 24 = sin 15° / KFKF = 24*sin 15°/ sin 148°KF = 11.72 ≈ 12 unitsRelated Questions
Luke has 9/10 yard of colored ribbon. He plans to cut the ribbon into pieces. Each piece will be 1/6 yard long. How many whole pieces can luke make from the ribbon?
Answers
Answer:
He can make 5 ribbons and 2/5 yards is left over.
Step-by-step explanation:
It is given that,
Length of the colored ribbon = 9/10 yards
Luke plans to cut the ribbon into pieces.
Each piece will be 1/6 yard long.
We need to find the number of pieces that Luke can made from the ribbon. Let he can make x pieces.
[tex]x=\dfrac{\dfrac{9}{10}}{\dfrac{1}{6}}\\\\=\dfrac{9}{10}\times 6\\\\=5.4\\\\=5\dfrac{2}{5}[/tex]
It means he can make 5 ribbons and 2/5 yards is left over.
¿Por qué la luna no se sale de su órbita y siempre gira en torno a la tierra?
Answers
Answer:
El período de rotación de la luna no siempre era igual a su órbita alrededor del planeta. Al igual que la gravedad de la luna afecta las mareas del océano en la Tierra, la gravedad de la Tierra afecta a la luna. Pero debido a que la luna carece de un océano, la Tierra tira de su corteza, creando un maremoto en la línea que apunta hacia la Tierra.
Step-by-step explanation:
Answer:
Porque la gravidad de la tierra es mas fuerte que la gravidad the la luna.
Step-by-step explanation:
write and equation of the line below
Answers
Answer:
y = 1/4x + 0 or just y = 1/4x
Step-by-step explanation:
First I need the slope so I look at the dots and see how much boxes it goes up and then to the side. So it’s up 2 to the side 8. The slope would be 2/8 but you can simply it by 2 and you get 1/4. And the y intercept is given its zero.
What are exercises to strengthen the upper body?
Answers
Answer:
Banded Lat Stretch. The range of motion in the shoulders is directly connected to how well the muscles of the upper back allow them to move.
Banded Pull Aparts.
Banded Pass Through.
Pull Ups
Push Ups
Step-by-step explanation:
Some exercises to strengthen the upper body include:
1. Chest Press.
2. Bench Dip.
3. Bicep Curl.
4. Pull Ups.
5. Push Ups.
6. Arm Raise
I don’t get it , can somebody help me please don’t give me the wrong answer
Answers
Answer:
D) 132
Step-by-step explanation:
y + 3x = 180 {Co interior angles}
y = 180 - 3x ------------(I)
7x + 20 = y {Vertically opposite angles}
7x + 20 = 180 - 3x {From equation (I)}
7x + 3x +20 = 180
10x + 20 = 180
10x = 180 -20
10x = 160
x = 160/10
x = 16
Plug in x = 16 in equation (I)
y = 180 - 3x
= 180 - 3*16
= 180 - 48
y = 132
(IM GIVING 15 POINTS )A water cooler holds 15 liters of sports drink. Approximately how many gallons is this? (1 gallon = 3.785 liters)
3 gallons
4 gallons
11 gallons
18 gallons
Answers
Answer:
4 gallons
Step-by-step explanation:
divide 15 by 3.785
Answer:
4 gallons
Step-by-step explanation:
15 divided by 3.785 liters)
A map has a scale of 4 cm : 4 km. If
Union and Clayton are 8 km apart, then
they are how far apart on the map?
Answers
Answer:
If Union and Clayton are 8 km apart, it means they are 8 cm far apart on the map.
Step-by-step explanation:
Map scale = 4 cm : 4 km
Hence,
1 cm : 1 kmGiven that Union and Clayton are 8 km apart.
Since 1 km is scaled as 1 cm on the map.Therefore, if Union and Clayton are 8 km apart, it means they are 8 cm far apart on the map.
The money m (in £) Paul has to spend each week is his wage w (in £) subtract the tax t (in £) he pays on his income. Enter a formula for the money he can spend and enter how much he has to spend if he earns £160 a week and pays £38 in tax.
Answers
Answer:
m = £122
Step-by-step explanation:
m = w - t
Where,
m = money Paul had to spend each week (£)
w = Paul's wage (£)
t = tax paid on his income (£)
If w = £160 and t = £38
Find m
m = w - t
= £160 - £38
= £122
Paul has £122 to spend if he earns £160 a week and pays £38 in tax
Which is the following is a solution to the solution to the inequality 2x+y > 0
Answers
PLEASE HELP 20 points!!!6) Find the inverse function. Use f-1(x) to indicate the inverse function and 5 points
parenthesis for the numerator, if needed. Example: f-1(x)=(x+7)/5 *
f(x) = 4x - 2
Your answer
Answers
Answer:
Step-by-step explanation:
ANSWER: 16x+=92
What’s 2/3 divided by 5
Answers
Answer:
10/3
3.3reaping
3 1/3
Step-by-step explanation:
Which expression has the same value as 37.4 - 54.9?
Answers
Answer:
D
Step-by-step explanation:
In the original expression = 37.4 - 54.9 = -17.5
So, we have to solve all the equations but 1 of them has to equal to -17.5
A) -54.9 + (-37.4) = -92.3
Remove parentheses
= -54.9 - 37.4
Subtract the numbers
-92.3
B) 54.9 - 37.4 = 17.5
Since 54.9 is greater than 37.4 just subtract normally
4 14
5 4. 9 < ------- Line up the decimal points like this
- 3 7. 4 <--------- Subtract the decimals
-----------------
1 7 . 5 <---------- This is the final answer to B.
C) 37.4 - (- 54.9) = 92.3
Change the sign to addition
=37.4 + 54.9
Add the numbers normally
54.9
+ 37. 4
--------------
92.3
D) 37.4 + (-54.9) = -17.5
Change the sign to subtraction
= 37.4 - 54.9
Subtract them normally (but as you can see you are subtracting a smaller number from a larger number so heres a trick that you can use switch the equation by putting the larger number in first like this....)
54.9 - 37.4 = 17.5 (REMEMBER the answer is not 17.5 because the original equation of D is reversed 37.4 - 54.9 so in this case your answer should be
- 17.5)
37.4 - 54.9 = -17.5
Your final answer is D because it matches 37.4 - 54.9.
Hope this helps!
Answer: -54.9+(-37.4)
Step-by-step explanation:
Your final answer is D because it matches 37.4 - 54.9.
The price of a video game is $55.00. The Gamer Stop is offering a 50% discount on the
video game. What is the sale price of the game?
PLEASE HELP!!!! It would be greatly appreciated
Answers
Answer:
$27.50
Step-by-step explanation:
55*50%
=55*1/2
=55/2
=27.5
Answer:
27.5
Step-by-step explanation:
50 divided into 2 is 20.50
5 divided by 2 is 2.50
jamie is making chocolate cupcakes. the recipe calls for 2/3 cup of cocoa. she wants to make 1/2 of the recipe. how much cocoa will she need?
Answers
Answer:
I think its 1/3
Step-by-step explanation:
heights of adults women have a mean of 63.6 in and a standard deviation of 2.5 indies chebyshevs theorem say about the percentage of women with heights between 58.6 and 68.6in
Answers
Answer:
Chebyshev's Theorem (Tchebysheff's Theorem) suggests that this percentage would be greater than [tex]75\%[/tex].
Step-by-step explanation:
Let [tex]Y[/tex] be a random variable with a mean of [tex]\mu[/tex] and a (finite) variance of [tex]\sigma[/tex]. By Chebyshev's Theorem, for any constant [tex]k[/tex] where [tex]k > 0[/tex]:
[tex]\displaystyle P\left(\left|Y -\mu\right| \le k\, \sigma\right) \ge 1 - \frac{1}{k^2}[/tex].
In this question, let [tex]Y[/tex] denote height (in inches.) Accordingly, [tex]\mu = 63.6[/tex] whereas [tex]\sigma = 2.5[/tex].
Note, that the interval of interest [tex](58.6,\, 68.6)[/tex] is centered at [tex]\mu = 63.6[/tex]. Besides, the difference between [tex]\mu[/tex] and either endpoints of this interval is equal to [tex]5.0[/tex], which is the same as [tex]2\, \sigma[/tex].
Rewrite the interval [tex](58.6,\, 68.6)[/tex] as [tex](63.6 - 2\times 2.5,\, 63.6 + 2 \times 2.5)[/tex].
For the height [tex]Y[/tex] of one such individual, [tex]Y \in (58.6,\, 68.6)[/tex] is equivalent to [tex]\left|Y - 63.6\right| < 2 \times 2.5[/tex]. With [tex]\mu = 63.6[/tex] whereas [tex]\sigma = 2.5[/tex], that expression is equivalent to [tex]\left|Y - \mu \right| < 2\, \sigma[/tex].
The percentage of individuals with a height in the interval [tex](58.6,\, 68.6)[/tex] would be equal to the probability [tex]P(\left|Y - \mu \right| < 2\, \sigma)[/tex].
Compare this expression to Chebyshev's Theorem. Notice that [tex]k = 2[/tex]. Therefore:
[tex]\displaystyle P\left(\left|Y -\mu\right| \le 2\, \sigma\right) \ge 1 - \frac{1}{2^2} = 0.75[/tex].
In other words, at least [tex]75\%[/tex] of the heights would be between [tex]58.6[/tex] inches and [tex]68.6[/tex] inches.
А 65° B 45° 70°
answer this for me please
Answers
Answer:
"With the high level of interest in our 45-70
Step-by-step explanation:
HELP ASAP PLEASE & THANK U!!!!
Answers
Answer:
1. (1, -3.5)
2. (-9, 25) *note, there is a typo in the question, please ask your teacher about this
Step-by-step explanation:
Use the midpoint formula to calculate the midpoint.
Use the formula to find the end point, and double the distance between your endpoint and midpoint to find the other endpoint.
Since the distance between the x coordinate is 8 (from -1 to 7), then the other endpoint is 8 away from -1, or -9.
please give thanks :)
Select all expressions that are equivalent to 6x+1−1(3x−1) . a. 6x+1−3x−1a. 6 x plus 1 minus 3 x minus 1 b. 6x+(−3x)+1+1b. 6 x plus open paren negative 3 x close paren plus 1 plus 1 c. 3x+2c. 3 x plus 2 d. 6x−3x+1−1d. 6 x minus 3 x plus 1 minus 1 e. 6x+1+(−3x)−(−1)
Answers
Answer:
c. 3x + 2( 3 x plus 2 )
d. 6x − 3x+ 1 −1(6 x minus 3 x plus 1 minus 1)
Step-by-step explanation:
We are given the expression:
6x+1−1(3x−1) .
Solving this expression:
6x + 1 - 3x +1
Collect like terms
6x - 3x +1 +1
3x + 2
Hence, the expression that are equivalent to 3x + 2 are:
c. 3x+2( 3 x plus 2 )
d. 6x−3x+1−1(6 x minus 3 x plus 1 minus 1)
The graph shows the distance, y in miles, of a moving train froma station for a certain period of time, x, in hours:
Distanco vs. Time
$5
30C
256
from Station 20
Distance
(in mi )
10
2 nr)
5
Time
What is the speed (in miles per hour) of the train?
Answers
Answer:
50 miles per hour
Step-by-step explanation:
The speed can be found from a graph of distance versus time by looking at the slope of the graph. Here, the graph is a straight line, so the slope is constant. This means the speed is constant.
__
It can be convenient to determine the speed by looking at distance for times that are 1 time unit apart. Here, that could be the distances at t=0 and at t=1. We see in that hour, the train traveled from 100 miles to 150 miles away from the station. Its speed was 150 -100 = 50 miles per hour.
Answer:
50 miles per hour
Step-by-step explanation:
Hope this helps sorry if it doesn't
How many solutions does the system have?
You can use the interactive graph below to find the answer.
2x+3y=-6
3x-4y=-12
A: exactly one solution
B: no solutions
C: infinitely many solutions
Answers
Answer:
1 solution
Step-by-step explanation:
when you graph it, there is only one point in the line that you can see matches up
F∝a If F=48 when a=4 find, F when a=5
Answers
Step-by-step explanation:
48/4 = F/5
Therefore F is 60 when a is 5.
Val measures the perimeter of her rectangular garden as 80 ft. Use the perimeter of the garden and the appropriate formula. Solve the formula for the width of the garden. Use the equation to help explain how the width changes in relation to changes in the length. A. w = 40 − l; the width increases as the length decreases B. w = l − 40; the width increases as the length increases C. w = 40 − l; the width increases as the length increases D. w = l − 40; the width increases as the length decreases
Answers
Answer:
D. w = l − 40; the width increases as the length decreases
Step-by-step explanation:
The formula for the perimeter of a rectangle =
P = 2l + 2w
Where to find the Width, we make w the subject of the formula.
Hence:
P - 2l = 2w
w = P - 2l/2
From the question, P = 80
Hence,
w = 80 - 2l/2
w = 80/2 - 2l/2
w = 40 - l
The width of a rectangle is always the longer side ,hence:
D. w = l − 40; the width increases as the length decreases
Which of the following values could x represent in the bar diagram?
PLEASE HELP!!! Worth 27 points!!
Answers
Answer:
$48. is correct answer friend
Step-by-step explanation:
OK please follow me
Consider a geometric sequence who third term is 9 and whose sixth term is -8/3. What is the first term? QUICKLY PLEASE!
Answers
Answer:
81/4Step-by-step explanation:
GivenGeometric sequence with:
a₃ = 9a₆ = -8/3To findThe first term a₁SolutionFormula for nth term is:
aₙ = a₁rⁿ⁻¹For the given terms we have:
a₃ = a₁r² anda₆ = a₁r⁵Comparing the terms:
a₆/a₃ = r³Substituting values to find the value of r:
-8/3 : 9 = -8/27 = (-2/3)³ r³ = (-2/3)³r = -2/3Then finding a₁:
a₁(-2/3)² = 9a₁(4/9) = 9a₁ = 81/4Which of these units would be best to measure the length of our classroom?
1. meters
2. centimeters
3. liters
4. kilometers
5. millimeters
Answers
Answer:
1. meters
Step-by-step explanation:
The smallest unit given in the choice is millimeters. Then comes the centimeters, then meters, and the kilometers.
Liters is used to measure the volume of a liquid. For example we get 1 liters of milk but not 1 kilometers of milk.
The kilometers has a 1000 meters and
1m= 100 cm
1cm = 10mm
The kilometers is quite a large space and usually long distances such as length between 2 towns is measured in kilometers.
The area of the room or length is usually measured in feet but since feet is not given here.
1 feet = 0.3048 m
so the most suitable selection would be meters.
The millimeters is very small. 1 cm has 10 mm. A foot consists of 30.48 cm.
So meters is used.
Clancy has 423 cups of yogurt to share with his friends at a party. Each guest will receive 1 serving of yogurt which is 34 of a cup. How many people can Clancy invite to his party if he needs a serving of yogurt as well?
Answers
Answer:
564 people
Step-by-step explanation:
Total cups of yogurt to share = 423 cups
Each guests get = 3/4 of a cup per serving
How many people can Clancy invite to his party if he needs a serving of yogurt as well?
Number of people Clancy can invite to his party = Total cups of yogurt to share / servings per guests
= 423 cups ÷ 3/4 cups
= 423 × 4/3
= 141 × 4
= 564
Number of people Clancy can invite to his party = 564 people
48 ounces of liquid detergent
for $6.19
Find the unit rate
Answers
Answer:
Step-by-step explanation:
48/6.19=7.7544
Round that answer so it’s 7.75
Unit rate is $7.75 per ounce
NUMBER 14 PLEASE
i need this soon
Answers
Answer:
a=22.478
Step-by-step explanation:
Answer:
Angle DE = 11
Step-by-step explanation:
DE = DF
8x + 3 = 6x + 5
8x = 6x + 5 - 3
8x - 6x = 2
2x = 2
2x/2 = 2/2
x = 1
DE = 8x + 3
DE = 8(1) + 3
DE = 8 + 3
DE = 11
Hope this helps
Please answer am really failing my math and i need this answer asap
Answers
Answer:
[tex]9) \: y = - 1x - 6[/tex]
[tex]10) \: y = \frac{1}{6}x + 4[/tex]
|9+x|>19 absolute value
Answers
Answer:
x ∈ (-∞ , -19) ∪ (10 , ∞)Step-by-step explanation:
|9 + x| > 19
9 + x > 19 ∨ 9 + x < -19
x > 10 ∨ x < -19
x ∈ (-∞ , -19) ∪ (10 , ∞)