In rectangle WXYZ, A is on side WX such that AX = 4, B is on side YZ such that BY = 18, and C is on side XY such that angle ACB= 90 degrees and CY = 2CX. Find AB.
Answers
Answer:2*sqrt(130)
Step-by-step explanation:[tex]From right triangle $AXC$, we have $\angle XAC = 90^\circ - \angle XCA$. We also must have $\angle YCB + \angle ACB + \angle XCA = 180^\circ$, so $\angle YCB = 180^\circ - 90^\circ - \angle XCA = 90^\circ - \angle XCA$, which means $\angle YCB = \angle XAC$. Combining this with $\angle X = \angle Y$, we have $\triangle XCA \sim \triangle YBC$ by AA Similarity, and\[\frac{CX}{AX} = \frac{BY}{CY},\]so\[\frac{CX}{4} = \frac{18}{2CX}.\]\\\\This gives us $2CX^2 = 72$, so $CX^2 =36$ and $CX=6$. \\\\\\\\[/tex][tex]Therefore, $CY = 12$.Applying the Pythagorean Theorem to right triangles $XCA$ and $CYB$ gives us\begin{align*}CA^2 &= XA^2 + XC^2 = 16 + 36 = 52,\\BC^2 &= CY^2 + BY^2 = 144 + 324 = 468.\end{align*}Applying the Pythagorean Theorem to right triangle $ABC$ gives\[AB = \sqrt{AC^2 + BC^2} = \sqrt{52 + 468} = \sqrt{520} = \boxed{2\sqrt{130}}.\](We can also compute $AB$ by dropping a perpendicular from $A$ to $\overline{YZ}$, which creates a right triangle.)[/tex]
The length of the side AB from the figure is approximately 22.8.
Given a rectangle WXYZ.
Consider triangles ΔACX and ΔBCY.
∠AXC = ∠BYC
Also, ∠CAX + ∠ACX = 180° - 90°
So, ∠CAX = 90° - ∠ACX [Equation 1]
Given that ∠ACB = 90°
Also, ∠ACX, ∠ACB, and ∠BCY form linear angles.
So, ∠ACX + ∠ACB + ∠BCY = 180°
So, ∠ACX + 90° + ∠BCY = 180°
∠ACX + ∠BCY = 90°
∠BCY = 90° - ∠ACX [Equation 2]
From [Equation 1] and [Equation 2], ∠CAX = ∠BCY
By AA similarity, triangles ΔACX and ΔBCY are similar.
So, the corresponding sides are proportional.
AX / CY = CX / BY
4 / 2CX = CX / 18
(CX)² = 36
CX = 6
Now, using the Pythagoras theorem:
AC = √(4² + 6²) = √52
BC = √(18² + 12²) = √468
So, AB = √(√52)² + (√468)²
= √520
≈ 22.8
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Related Questions
Please answer this question GEOMENTRY
Answers
Answer:
4 in
4√2 in
Step-by-step explanation:
Part A
Missing angle= 90°-45°=45°
Missing leg = 4 in as opposite angles are equal
Part B
According to Pythagorean theorem
Hypotenuse²= (4in)²+(4in)²= 32 in²
c=√32 in²= 4√2 in
which of the following is not a polynomial (a)x^2+ root2*x -3 (b)x^2+ root2x+6 (c)x^3+3x^2-3 (d)6x+4 Pls ans it fast....!!!!!
Answers
Answer:
the answer is B)
In a standard 52−card deck, half of the cards are red and half are black. The 52 cards are divided evenly into 4 suits: spades, hearts, diamonds, and clubs. Each suit has three face cards (jack, queen, king), and an ace. Each suit also has 9 cards numbered from 2 to 10.
Suppose a solitaire player has played 800 games. Predict how many times the player turned over a black card as the first card.
The player can expect to turn over a black card about
( answer ) times.
Answers
Answer:
the player can expect to turn over a black card about 400 times.
Step-by-step explanation:
the way to solve a probability question is like this:
there are 52 total cards, out of those 52 cards, half of them are black cards.
that means 1/2 of 52 = black cards
if the plays 800 times, and half of the cards are black, the player can expect to have a 50% chance of flipping over a black card.
800/50 = 400.
therefore the player can expect to have flipped a black card 400 times.
what is the value of a in simplest form?
Answers
Answer:
[tex]x^4[/tex]
Step-by-step explanation:
[tex]\frac{x^{3} }{\sqrt[6]{x}}[/tex]
[tex]((\sqrt{x})^{2})(x^{3} )[/tex]
[tex](x)(x^3)\\x^4[/tex]
Find the number that makes the ratio equivalent to 2:3.
6: ___
Answers
Answer:
Step-by-step explanation:
2:3 = 6: ___
[tex]\frac{2*3}{3*3}=\frac{6}{9}[/tex]
2:3 = 6 :_9___
Answer:2:3=6:9
Step-by-step explanation:
2×3/3×3=6/9
2:3=6:9 !!!!!!!!
To create an image, Figure B is going to be rotated 90° around the point indicated in the figure, translated horizontally across the y-axis and reflected across the x-axis. What must be true about Figure B and its image?
Answers
Answer: D. They are both congruent
Step-by-step explanation:
The only difference in the two shapes is the locations. One shape is located in the 4th (-x, +y) quadrant, while the other shape is located in the 2nd quadrant (+x, -y)
They two shapes are the same size with the same area, so they are both congruent.
Answer:
The answer on Imagine Math is...
-They are congruent
Step-by-step explanation:
I got the answer right on Imagine Math. Hope my answer can help those who need it. God bless you all!!
Raj takes a taxi to the airport. He expects the taxi to travel at an average speed of 40 mph. The distance from Raj's house to the airport is 30 miles. If Raj's taxi actually travels at an average speed of 30 mph, how many more minutes does the journey take than expected?
Answers
Answer:
15 minutes more, as 60-45mins = 15 minutes
Step-by-step explanation:hope it helps
It will take 15 more minutes for the journey than the expected.
What is Speed?Speed is the unit rate in terms of distance travelled by an object and the time taken to travel the distance.
Speed is a scalar quantity as it only has magnitude and no direction.
Given that,
The distance from Raj's house to the airport is 30 miles.
He expects the taxi to travel at an average speed of 40 mph.
If he travels at a speed of 40 mph, let t be the time taken.
Speed = Distance / Time
40 = 30 / t
t = = 0.75 hours = 45 minutes
If Raj's taxi actually travels at an average speed of 30 mph, let t' be the time taken.
30 = 30 / t'
t' = 1 hour = 60 minutes.
t' - t = 60 - 45 = 15 minutes
Hence the journey takes 15 more minutes than expected.
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FAST ANSWER PLZ
Describe a way that you can remember the elements of the reflection matrices if you forget where the 1s, -1s, and 0s belong.
Answers
Answer:
Associate the numbers or coordinates with something in your life. Think of it from every possible aspect. For example, number 7. I just think of it as "7 is half of 14, there are 7 days in a week, 7 can be said as 70, which means 7 tea cups. See like that, now when you try and remember the numbers, you are able to pick up on these trail of thoughts are trace it back to its origin, which here is 7.
Answer:
Multiplying the vertex matrix with the matrix gives us a reflection matrix. The most common matrix reflections are seen as a reflection in the x-axis as well as reflection in the y-axis. It can also be reflected by 90 degrees or by 180 degrees. So, one way to remember the elements is by multiplying the given matrix by a unit matrix. And on the other hand, you can remember the elements remembering by what degree we are reflecting the matrix. This way makes it easier to remember the elements.
Step-by-step explanation:
100% on edge2020
What is the product of (-3s+2t) (4s-t)?
A: -12s^2 -2t^2
B: -12s^2 + 2t^2
C: -12s^2 + 8st - 2t^2
D: -12s^2 + 11st -2t
Answers
Answer:
c
Step-by-step explanation:
(-3s+2t)(4s+t)=-12s^2-3st+8st+2t^2 = [tex]-12s^2+8st-2t^2[/tex]
The diagram shows two sets of vectors that result in a single vector. What are the first two steps for finding the magnitude of the resultant vector?
A. Find the square of the first horizontal vector and the square root of the first vertical vector
B. Find the square root of the first horizontal vector and the square root of the second horizontal vector
C. Find the sum of the two horizontal vectors in the summer for two vertical vectors
D. Find the difference between the two horizontal vectors and the difference between the two vertical vectors
Answers
C. Find the sum of the two horizontal in the summer for two vertical vectors.
Answer:
Can confirm C is right i got 100 on the unit test
Step-by-step explanation:
Which value of b will cause the quadratic equation x2 + bx + 5 = 0 to have two real number solutions? –5 –3 3 4
Answers
Answer:
-5
Step-by-step explanation:
For a quadratic equation to have two real number solutions, the discriminant must be positive. The discriminant of a quadratic equation is:
[tex]b^2-4ac[/tex]
This means that b^2 must be larger than 4ac. Since in this case 4ac is 4(1)(5)=20, b must be -5 out of the answer choices given. Hope this helps!
Answer:
A. -5
Step-by-step explanation:
Cindy dissolves 19 1 /4 grams of drink mix in 1 3 /4 ounces of water. What is the unit rate in grams of drink mix per ounce of water?
A) 11
B) 15 4/5
C) 17 1/2
D) 21
Answers
Answer:
Unit rate in grams of drink mix per ounce of water = 11 gram / ounces
Step-by-step explanation:
Given:
Amount of drink mix = 19 (1 /4) gram = 19.25 gram
Amount of water = 1 (3 /4) ounces = 1.75 ounces
Find:
Unit rate in grams of drink mix per ounce of water = ?
Computation:
⇒ Unit rate in grams of drink mix per ounce of water = Amount of drink mix / Amount of water
⇒ Unit rate in grams of drink mix per ounce of water = 19.25 / 1.75
⇒ Unit rate in grams of drink mix per ounce of water = 11 gram / ounces
find the missing angle
Answers
Answer:
56.44
Step-by-step explanation:
The sine of an angle is the length of the opposite side divided by the length of the hypotenuse, which in this case is 40/48=5/6. Therefore, that angle is the arcsin of this, or approximately 56.44 degrees, or answer choice C. Hope this helps!
A group of 9 friends went bowling. Each person pays the same amount to bowl several games and a $3 fee to rent shoes. The total cost for the friends to bowl and rent shoes is $162. How much does it cost each friend to bowl ( not counting the shoe rental fee)?
Answers
Answer:
Each friend payed $15
Step-by-step explanation:
( 9 x 3 - 162 ) divide that answer by 9 to get the amount of how much each friend payed.
Help!!!
An employee at a factory is paid $9.25 per hour plus an $8.00 bonus for every 20 transformers assembled. Last week an employee worked 36 hours and assembled 380 transformers. How much money did the factory employee actually earn per hour last week rounded to the nearest cent?
Answers
Answer: $13.47 per hour.
Step-by-step explanation:
Hi, to answer this question we have to write an equation:
Total earnings = 9.25 (h) + 8 (t/20)
Where h is the number of hours and t is the number of transformers.
Since he worked for 36 hours and assembled 380 transformers:
Total earnings = 9.25 (36) + 8 (380/20)
Total earnings = 333+152 = $485
Finally, to find how much he earned per hours, we simply have to divide the result by the number of hours worked (36):
485/36 = $13.47 per hour.
please help! i need this asap
Answers
ordered data: 3o(oranges), 3g(green), 6y, 8r, 13b(black, 15b(blue
mean: 8 mode: 3 range: 12
Two similar cylinder have radii 3 cm and 4 cm. If the first cylinder has a volume of 270cm³ , find the volume of the second cylinder.
Please help me , i need help.
Answers
Answer: 480 cu. cm
Step-by-step explanation:
Height of first cylinder: h = V/pi r^
= 9.55 cm
Volume of second cylinder = pi r^2 h
= 480
Answer:
360
Step-by-step explanation:
Find the relativeness: If 3 is to 270 then 4 is to ?
270/3 = 90
90 times 4 = 360
Therefore if
3 is to 270
then
4 is to 360
giving brainliest to first answer!!
Determine the area of the composite figure to the nearest whole number.
A) 9 ft2
B) 11 ft2
C) 13 ft2
D) 17 ft2
Answers
Answer:
C
Step-by-step explanation:
3/4 * 4pi = 3pi
3pi + 4 =. 13
Could someone help what is the variable in “8y3”?
Answers
Answer:
y
Step-by-step explanation:
The variable in 8y^3 is y because a variable is a number that we don't know yet, and that is the only one.
Manuel's bank charges a $2 internal fee for using an ATM from another bank. Manuel withdraws $60 from an ATM owned by another bank that charges a $3 usage fee. What is the decrease in Manuel's account from this transaction? Enter your answer as a whole number, such as 5.
Answers
2+3+60=65
total is $ 65 ONLY IF U COUNTING THE WITHDRAWL MONEY TOO.
$5 is the answer IF U AINT COUNTING TE WITHDRAWL MONEY
hope this help ya
Answer:$65
Step-by-step explanation: It decreases by $65 because the the fees from his bank and the other bank equal 5 plus the original 60 he was taking out
How many years will Matt need to invest $4200 to earn $200 interest, if the simple interest rate is 2.5% p.a.? Round the answer to the nearest year
Answers
Answer: 2 years
Step-by-step explanation:
SI = prt / 100
200 = ( 4200 x 2.5 x t) / 100
200 = 105 t
t = 200/105 = 1.9
What’s the factor for x2 - 1.44
Answers
Answer:
Step-by-step explanation:
(5x + 6) • (5x - 6)
—————————
25
Find the domain and range of the relation. {(−7,−18),(−23,21),(4,13),(−17,22),(2,−10)}
Answers
Answer: Domain = all x values and Range = all y values
Step-by-step explanation:
The domain of a function is all the allowed x values that make the function true. Luckily you were already given the domain. Its all the x values.
The range of a function is pretty much all the allowed y values of a function. Or, what y values the function can be equal to. So that's just all the y values
When listing the domain and range, you generally want to do it from least to greatest and you do not want to repeat any values
Answer:
D:{ -23,-17,-7,2,4}
R:{-18,-10,13,21,22}
Step-by-step explanation:
The domain is the input
D:{ -7,-23,4,-17,2}
We normally put them in numerical order
D:{ -23,-17,-7,2,4}
The range is the output
R:{-18,21,13,22,-10}
We normally put them in numerical order
R:{-18,-10,13,21,22}
The probability of rain for the day of the race is 62%.
(a) What is the probability that it does not rain on the day
of the race?
Runners who complete the race in 2 hours 15 minutes or less
get a gold medal.
Bradley completed the race in 2 hours 13 minutes 22 seconds.
(b) Work out the difference between 2 hours 15 minutes,
and 2 hours 13 minutes 22 seconds.
Answers
a) 100%-62%=38%
b) 2h 15m- 2h 13m 22s= 15m- 13m 22s= (14m- 13m)+ (1m- 22s)= 1m+ 38s= 1m 38s
Write the quadratic function f(x) = 3(x + 1)(x – 7) in standard form.
A)
f(x) = x2 – 18x – 21
B)
f(x) = 3x2 – 18x – 21
C)
f(x) = x2 – 6x – 7
D)
f(x) = 3x2 – 6x – 7
Answers
Answer:
B
Step-by-step explanation:
Given
f(x) = 3(x + 1)(x - 7) ← expand the factors using FOIL
= 3(x² - 6x - 7) ← distribute the parenthesis
= 3x² - 18x - 21 → B
Find the radius round your answer to the nearest tenth
Answers
Answer:
r = 3m
Step-by-step explanation:
Formula for the volume of a sphere: V = [tex]\frac{4}{3}[/tex][tex]\pi[/tex][tex]r^{3}[/tex]
We want to find the radius so we use algebra to rearrange the equation to make the radius (r) the subject of the equation
Divide both sides by [tex]\frac{4}{3}[/tex]
[tex]\frac{3V}{4}[/tex] = [tex]\pi[/tex][tex]r^{3}[/tex]
Divide both sides by [tex]\pi[/tex]
[tex]\frac{3V}{4\pi }[/tex] = [tex]r^{3}[/tex]
Take the cube root of both sides
[tex]\sqrt[3]{\frac{3V}{4\pi } }[/tex]= r
Substitute V = 36[tex]\pi[/tex] into the equation
r = [tex]\sqrt[3]{\frac{3(36\pi) }{4\pi } }[/tex]
Expand the bracket
r = [tex]\sqrt[3]{\frac{108\pi }{4\pi } }[/tex]
Divide 108[tex]\pi[/tex] by 4[tex]\pi[/tex] (For this, the two [tex]\pi[/tex] in the numerator and denominator cancel each other out, and you only need to divide 108/4)
r = [tex]\sqrt[3]{27}[/tex]
The cube root of 27 is 3, because [tex]3^{3}[/tex] = 3 x 3 x 3 = 27
r = 3
Sara is moving into a new apartment. The Resort complex charges a $600 security
deposit and costs $950 a month for rent. The Uptown Suites Duplex charges a $300
security deposit and costs $1100 a month for rent. After how many months would the
apartments cost the same amount? Which apartment would you recommend Sara move
to if she plans on staying for 6 months? Please show work!
Answers
Answer:
1) 2 months
Step-by-step explanation:
y = 950x + 600
y = 1100x + 300
950x + 600 = 1100x + 300
-950x -950x
____________________ subtract slope from both sides
600 = 150x + 300 ( doesn't matter which one)
-300 - 300
____________________ subtract
300 = 150x
_________ Divide each # with the slope
150 = 150
2 = x
____________Answer 2_____________
Answer:
The Resort Complex would save you 300.
step-by-step solution:
you have to do is plug in the number of months.
then multiply
then subtract both Complexes
and compare
The Resort Complex. : y = 950(6) + 600 - 6300
The uptown suite duplex : y = 1100(6) + 300 - 6900
HOPE THIS HELPS!
5x2+3=0. find a=, b=, c=. thank you:)
Answers
Answer:
a=5 b=0 c=3
Step-by-step explanation:
The quadratic equation is written as
ax^2 + bx+c =0
5x^2 +3 =0
5x^2 +0x +3 =0
a=5 b=0 c=3
Thomas has two kittens. He records the
mass of one kitten as 2.2 kilograms and
the mass of the other kitten as 1,890 grams.
What is the total mass of the two kittens
in kilograms? (1 kilogram 1,000 grams)
Answers
Answer:
4.09
Step-by-step explanation:
Answer:
4.09
Step-by-step explanation:
change 1890 to kilograms
1890/1000= 1.89
add both weight = 1.89+2.2
4.09
Solve d = rt if r = 46 and t = 5
Answers
Hey!!
r=46
t=5
now,
D=RT
= 46*5
=230
the value of d is 230
hope it helps..
Answer:
230 is the answer
Step-by-step explanation:
Since r and t are given in the question as
r=46 and t=5
Substitute the value of r and t which is given in the polynomial
So it'll be,
d=rt
d = 46 x 5
= 230
Therefore d is 230 units
Hope this helps!
