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
Ng Order of Operations George has $15. He would like to know if he has enough money to see a movie ($9.00) and buy a pretzel ($2.65), a drink ($1.35), and two veggie cups ($1.74 each). George incorrectly used this numerical expression to decide if he had enough money. 15 - 9 + 2.65 + 1.35 + 2(1.74) Use the order of operations to simplify this expression.
Answers
Answer:
No, George does not have enough money to buy everything.
The correct expression is:
15 - 9 - 2.65 - 1.35 - 2(1.74)
Step-by-step explanation:
Given that:
Money present with George initially = $15
Money required to see the movie = $9
Money required to buy a pretzel = $2.65
Money required to buy a drink = $1.35
Money required to buy 2 veggie cups = $2(1.74)
To find:
Whether there is enough money with George to complete all the tasks.
Solution:
First of all, let us calculate all the money required and then we can subtract all the money from the initial amount to find whether there is enough money present with George.
If the result is in positive, there is enough money with George.
Total money required for all the activities = $9 + $2.65 + $1.35 + $2(1.74) = $16.48
Expression = $15 - $16.48 = -$1.48
The result is negative, therefore there is not enough money.
The correct expression is:
15 - 9 - 2.65 - 1.35 - 2(1.74)
The Mexican Hot Chocolate Recipe makes 2 cups of hot chocolate per batch. 1 serving is equal to 1 cup.
How many batches of the recipe will you need to make to have enough hot chocolate for 6 people
Answers
Answer:
3
Step-by-step explanation:
For one batch there is 2 cups so for one person it's one serving so you will need 3 batches for 6 people.
What best describes the expression 6 over y? (1 point)
A. 6 times some number
B. 6 divided by some number
C. 6 minus some number
D. 6 more than some number
Brainliest goes to the first answer, thank you!
Answers
PLZZZ Help with this!
Star A is about 3.4 X 10^18 miles from Earth. Star B is 6.8 X 10^16 miles from Earth. Star A is how many times as far from Earth as Star B?
Answers
Answer:
Concept: Numerical Analysis
Star A is 3.4 ×10 ^18Star B is 6.8 × 10^16Hence we want how much farther Star A is from Star B.Hence Star A/Star B = 50 times fartherRATE BRAINLISTAnswer:
1/50 as far
Step-by-step explanation:
6.8 x 10[tex]^{16}[/tex] ÷ 3.4 x 10[tex]^{18}[/tex]
Rules state that you divide numbers and subtract exponents
6.8/3.4 = 2
10[tex]^{16}[/tex] ÷ 10[tex]^{18}[/tex] = [tex]10^{-2}[/tex]
whenever exponent is negative, it gets turned into a fraction with 1 as the numerator and the exponent will become positive when placed in the denominator
10^-2 = 1/10^2 which is the same as 1/100
2 multiplied by 1/100 = 1/50
find the value of x
guys please give only right answer.....ᕦ⊙෴⊙ᕤ
Answers
Answer:
x=2
Step-by-step explanation:
25/625 is 1/25
1/25 = 1/5^x
1/5 =sqrt 1/25 and that is 2
so x=2.
Hope this helps plz hit the crown :D
If x < 3, the arrow points to the left.
True or false
Answers
Answer:
true
Step-by-step explanation:
A speed limit is 35 mph. A car is travelling 10 mph over the speed limit. I’d that a sum of 0
Answers
Answer:
The car is going 45 mph
Step-by-step explanation:
Since the speed limit is 35 mph and the car is 10 mph over the speed, we can add them to find out how fast the car is going. We can solve 35+10 which will give us 45. So it is not a sum of 0 but instead a sum of 45.
(hope this helped)
Answer:
35+10 =45
Step-by-step explanation:
add 10 to 35 then divide by 2
15 m/s in km/h plz help
Answers
Answer:
54 km/h
Step-by-step explanation:
Step one:
given data
We are required to perform unit from m/s km/h
from 15m/s to km/h
Step two:
1 meter= 1/1000 km,
1 seconds= 1/3600 hour
1m/s = 1/1000/1/3600= km/h= 3600/1000= 36/10= 18/5 km/h
so of 1m/s is equivalent to 18/5 km/h
then 15m/s is equivalent to x
cross multiply
x= 15*18/5
x= 3*18
x=54 km/h
Find the length of side x in the simplest radical form with a rational denominator.
Answers
The answer is 60 or 15 because you need to have 150 for a triangle
−2 4/5 ÷ (−7) i need this i will give brainiest
Answers
Answer:
0.4
Step-by-step explanation:
Pls mark me brainliest! :D
Answer:It is 0.4 or 2/5
Step-by-step explanation:
Hope this helps!!
Please help me with this problem!!
Answers
Hey peeps I need help pls! Roger says that 10% of a number will always be less than 25% of any other number.
Complete one inequality to support Roger's claim and one to show that he is incorrect.
PLSSSSSSSSS HELp
Answers
Answer: [tex]0.1x-0.25y<0[/tex]
Step-by-step explanation:
Let the two numbers be x and y
10% of the first number will be;
10% of x
[tex]=\frac{10}{100} of x[/tex]
[tex]=0.1x[/tex]
25% of the other number will be ;
25% of y
[tex]0.25y[/tex]
If 10% of the first number is less than 25% of the other number, this is expressed as;
[tex]0.1x<0.25y[/tex]
[tex]0.1x-0.25y<0[/tex]
Hence the required inequality is [tex]0.1x-0.25y<0[/tex]
PLEASE MARK ME AS BRAINLIEST
What is 0.7439 rounded to the nearest hundredth need help
Answers
Answer:
0.74
Step-by-step explanation:
0.7439 = 0.74
7th grade help me please :))
Answers
Answer:
Terms: -8, -4c, 7, -c, -12c, -2
Variables: c
Coefficients: -4, -1, -12
Constants: -8, 7, -2
Step-by-step explanation:
Terms are anything in between a plus or minus.
Variables are anything that is not a real number, such as c.
Coefficients are the number directly before a variable, such as -4 in -4c.
Constants are any real numbers without a variable, such as -8.
Geometry:
What is the volume of the cone?
A. 2876.7 yd
B. 4625.36 yd
C. 4258.44 yd
D. 2787 64 yd
Answers
Answer:
D. 2787.64 yd^3
Step-by-step explanation:
This is the formula for the volume of a cone:
[tex]V=\frac{1}{3} \pi r^2h[/tex]
The height of the cone is 22 yd. The radius of the base of the cone is not given but we can use the diameter to calculate it since the radius is equal to half of the diameter.
[tex]r=\frac{1}{2}d\\r=\frac{1}{2}(22)\\r=11yd[/tex]
Therefore, the radius of the base of the cone is 11 yd.
Now, we plug our values into the formula and solve.
[tex]V=\frac{1}{3} \pi r^2h\\V=\frac{1}{3} \pi (11^2)(22)\\V=\frac{1}{3} \pi (121)(22)\\V=\frac{1}{3} \pi (2662)\\V=\frac{1}{3} \pi (2662)\\V=2787.64 yd^3[/tex]
Therefore, the volume of the cone is equal to 2787.64 yd^3.
I hope this helps!
Is this a square root graph?
Is this graph a reflection of its parent graph?
this graph shifted _
The equation to this graph would transform the parent function f(x) to _
Answers
Answer:
Thus, [tex]y=-\sqrt{x+3}[/tex] represents the transformed graph on the attached figure, which is a translated square root graph i.e. vertically reflected across the y-axis and also horizontally translated or shifted 3 units to the left.
Step-by-step explanation:
Consider the function
y = f(x)
The rule of horizontal translation
y = f(x-h)
When 'h' is positive, the function is shifted to the right.
When 'h' is negative, the function is shifted to the left.
The rule of implying vertical reflection across the x-axis
y = -f(x)
Applying the rule:
We know that the square root function is
[tex]y=\sqrt{x}[/tex]
We know that if the graph would be reflected across the x-axis, then
[tex]y=-\sqrt{x}[/tex]
We know that is horizontally translated or shifted 3 units to the left, it implies +
3 inside the radical implies. Then the transformed function becomes .
Please check the attached diagram. From the diagram,
The blue graph shows the parent function [tex]y=\sqrt{x}[/tex].The red graph shows the transformed function i.e. vertically reflected across the y-axis and also horizontally translated or shifted 3 units to the left.Thus, [tex]y=-\sqrt{x+3}[/tex] represents the transformed graph on the attached figure, which is a translated square root graph i.e. vertically reflected across the y-axis and also horizontally translated or shifted 3 units to the left.
What is the value of a if a is equal to a×a×a=a+a+a
Answers
Answer:
a = ±sqrt(3)
Step-by-step explanation:
a×a×a=a+a+a
Simplifying each side
a^3 = 3a
Divide each side by a
a^3 /a = 3a/a
a^2 = 3
Take the square root of each side
sqrt(a^2) = ±sqrt(3)
a = ±sqrt(3)
Answer:
nope its not equal
a×a×a=a³, but a+a+a=3a
so, a³≠3a
Step-by-step explanation:
i hope this helps....can i have brainliest
MERRY CHRISTMAS!!!......ENJOY UR HOLIDAY!!!
Good Night Bewtiful peeps!
What is 2097÷4?
Answers
Answer: 2097÷4 = 524.25
Answer:
524.25
Step-by-step explanation:
Good bewtiful to u too
Please help The sum of two numbers is 36 and the difference is 6. What are the numbers?
Answers
Answer:
15 and 21
Step-by-step explanation:
Answer:
15 and 21
Step-by-step explanation:
select the correct answer for x, each answer is rounded to the nearest tenth.
Answers
Answer:
x ≈ 27.2
Step-by-step explanation:
Using the sine ratio in the right triangle
sin54° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{22}{x}[/tex] ( multiply both sides by x )
x × sin54° = 22 ( divide both sides by sin54° )
x = [tex]\frac{22}{sin54}[/tex] ≈ 27.2 ( to the nearest tenth )
A spherical balloon is inflated with gas at a rate of 500 cubic centimeters per minute. (a) How fast is the radius of the balloon changing at the instant the radius is 40 centimeters
Answers
Answer:
[tex]\mathbf{ \dfrac{dr}{dt} = 0.03730 \ cm/min}[/tex]
Step-by-step explanation:
The rate of the inflation of the balloon with time can be denoted as:
[tex]\dfrac{dv}{dt} = 500 \ cm^3/m[/tex]
To determine; how fast does the radius change with time.
i.e.
[tex]\dfrac{dr}{dt}=???[/tex]
where r = 40 cm and the volume of sphere = [tex]\dfrac{4}{3} \pi r^2[/tex]
∴
[tex]\dfrac{dv}{dt}= \dfrac{4}{3} \pi 2(r^3) \dfrac{dr}{dt}[/tex]
[tex]500= \dfrac{4}{3} \pi \times 2(40^2) \dfrac{dr}{dt}[/tex]
[tex]500= 13404.13 \dfrac{dr}{dt}[/tex]
[tex]\dfrac{500}{13404.13} = \dfrac{dr}{dt}[/tex]
[tex]\mathbf{ \dfrac{dr}{dt} = 0.03730 \ cm/min}[/tex]
A 14-ounce bottle of Nesquik chocolate milk cost $1.89. What is the cost per ounce?
Answers
Answer:
Step-by-step explanation:
1.89/14= .135
estimating to the nearest cent would be .14
If a projectile is fired straight upward from the ground with an initial speed of 64 feet per
h(t) = - 16t? + 64t. Find the maximum height of the projectile.
The maximum height of the projectile is
(Simplify your answer.)
Answers
Answer:
h = 64 feet
Step-by-step explanation:
If you graph the function you see that 64 feet is the maximum of the parabola so this is the max height that the projectile reaches.
Question 4 please help me
Answers
Answer:
Step-by-step explanation:
I don't know what you were supposed to do with 3 but 4 looks much easier.
It's telling you to increase the side lengths by a factor of 3y
4x(3y) + 4x(3y) = 3y * 3y
12xy + 12xy = 9y^2
Perimeter = 24xy + 9y^2
I can't see anything else to do with this question. If you think I've misread it or there is more to it, leave me a note.
solve tje equation for t. Round the answer off to two places after the decimal point.
Answers
if you round it, the answer is 1.7
PLEASE HELP VERY URGENT!!!!!!!!!!!!!!!
Simplify (5 ^1/3)^3
A. 5
B. 5^9
C. 1/5
D. 5^3
Answers
Answer:
A) 5
Step-by-step explanation:
(5^(1/3))^3=5^(1/3*3)=5^(3/3)=5^1=5
yall I need help QUICK
Write an equation of a line that passes through the x-intercept 4 with slope -3
PLEASE HELP
Answers
Answer:
y=-3x-12
Step-by-step explanation:
:)
Solve for u .
-3 (-6u+6) - u = 2 (u-6) - 1
Answers
Answer: U = 18
Step-by-step explanation:
U in (-oo:+oo)
U/(-6)+2 = -1 // + 1
U/(-6)+1+2 = 0
3-1/6*U = 0 // - 3
-1/6*U = -3 // : -1/6
U = -3/(-1/6)
U = 18
U = 18
Answer:
-3 (-6u+6) - u = 2 (u-6) - 1
18u -18 -u = 2u -12 -1
18u-u-2u=-12-1+18
15u= 5
u =5/15 = 1/3
Step-by-step explanation:
Find the value of each variable that makes the equation true.
1. 89 = 1
2. 94.9-6 = 96
3. 5-3.2-3 = 100
Answers
PLEASE HELP...
A car is bought at the price of $20,000. The value decreases at the rate of .20 every year (t). The exponential expression 20,000(0.80)t describes this situation. Find the price of the car after 3 years.
Question 2 options:
A)
$10,240
B)
$11,874
C)
$5,892
D)
$9,399
Answers
Answer:
$10,240
Step-by-step explanation:
y = 20,000 (.80)^t
y = 20,000 (0.80)^3
0.8^3 = 0.512
0.512 x 20,000 = 10240
Your answer would be A. $10,240.
