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
Learn more about Pythagoras theorem here :
https://brainly.com/question/31658142
#SPJ2
Related Questions
Need help AsAp WIll give brainlist!!!
Answers
Answer:
-5
Step-by-step explanation:
Score in first round = +15
Scores lost in second round = -30
Score in third round = 10
Total points = 15+-30+10= -5
Exponential function f is represented by the table.
x 0 1 2 3 4
f(x) 15 7 3 1 0
Function g is an exponential function passing through the points (0,9) and (3,0).
Which statement correctly compares the two functions?
A.
Both functions are decreasing on [0, 3], and function g is decreasing at a faster rate.
B.
Only function g is decreasing on [0, 3], and only function f is positive on that interval.
C.
Only function f is decreasing on [0, 3], and both functions are positive on that interval.
D.
Both functions are decreasing on [0, 3], and function f is decreasing at a faster rate.
Answers
Considering the given exponential functions, it is found that the correct statement is:
D. Both functions are decreasing on [0, 3], and function f is decreasing at a faster rate.
What is the behavior of each exponential function?For function f, we have that it is decreasing, as it is greater at x = 0 than at x = 4, and it decreases by an average of 3.75 units when the input changes by 1.For function g, we also have that it is decreasing, as as it is greater at x = 0 than at x = 3, and it decreases by an average of 3 units when the input changes by 1.Hence option D is correct.
More can be learned about exponential functions at https://brainly.com/question/25537936
75% of_____ = 300
Please help me
Answers
Answer:
400
Step-by-step explanation:
75%=0.75
300/0.75 = 400
Answer:
400
Step-by-step explanation:
75/100 of x = 300
75x/100 = 300
Cross multiplying
75x = 30000
Dividing the both by 75
x = 400
Find the value of x please!!
Answers
Answer:
x = 9
Step-by-step explanation:
[tex]\frac{12}{8} = \frac{x}{6}[/tex]
x = [tex]\frac{12}{8}[/tex] x 6 = 9
Use the graph to determine the domain and range
of the piecewise defined function.
Domain:
-6
-6
1 <<6
2
Answers
Answer:
Domain = {-6 ≤ x ≤ 2, x ≠ 0}
Range = {1 < y ≤ 6}
Step-by-step explanation:
Answer:
Domain: -6[tex]\leq x<0 or 0<x\leq 2[/tex] Option A
Range: 1<y[tex]\leq 6[/tex]
Step-by-step explanation:
Joshua uses his thermometer and finds the boiling point of ethyl alcohol to be 75 degrees Celsius. He looks in a reference book and finds that the actual boiling point of ethyl alcohol is 80 degrees Celsius. What is his percent error?
Answers
Answer:
6.25%
Step-by-step explanation:
75 - 80 = -5
Absolute value of -5 is positive so -5 = 5
5 ÷ 80 = 0.0625 (1/16)
0.0625 × 100 = 6.25%
Joshua's percent error is 6.25%
Which statement best describes how to determine where f(x)=x^2-x+8 is an even function
Answers
Answer:ogros reconocer a negra denda como el me de una sumatoria que permite calcular ... Como vimos, entre más subdivisiones del intervalo tomemos, mejor será la ... que la aproximan y luego determinar a qué valor tiende el área cuando n ... n k=1 1 ( kYo 1 - — lí X +- o = + (Vé ejemplo 8. a-na-n X () 3 (véase e eje plo 8.)
Step-by-step explanation:
Sharon drops a rubber ball from a height of 48 feet. Every bounce sends the
ball half as high as it was before.
What is the total vertical (up and down) distance the ball has traveled, from
the moment it is dropped to the moment it hits the floor for the fourth time?
(Do not include units in your answer.)
Answers
Answer:
132
Step-by-step explanation:
48 first hit and rises 24
24 second and rises 12
12 third hit and rises 6
6 forth hit
48+24+24+12+12+6+6= 132
After the 4th hit the total distance up and down covered by the ball will be 90 feet.
Why the ball is bouncing back less and less distance upward after every drop ?
Some of the kinetic energy of the ball has been transferred by the ball to the ground after each drop also when it is in the process of going upwards force of gravity is working on the opposite direction which is downwards.
There are other factors too ask your physics teacher if you are more curious.
According to the given question
First time it has been dropped from a height of 48 feet as at every bounce it bounces back half of it's value it will go up to 24 feet repeating this process of bouncing back for the fourth time
It will be (48 + 24 + 12 + 6) = 90 feet
Learn more about Kinetic energy here :
https://brainly.com/question/15764612
#SPJ2
Please help me!!! :(
Answers
Answer:
Green Material: 129.6 in³
Brown Material: 194.4 in³
Step-by-step explanation:
The volume of the bin is 4×18×9 in³ or 648 in³
20% of 648 is 129.6 in³ (brown material)
30% of 648 is 194.4 in³ (green material)
A trader purchased 1,000 books at the rate of $5.40 per book and spent $200 towards transportation. If he wants to earn a profit of 12.5%, at what price should he sell each book?
( with explanation )
Answers
Answer:
$6.3
Step-by-step explanation:
Cost of one book = $5.40
cost of 1000 books = 1000* Cost of one book = $5.40*1000 = $5400
Transportation cost for all the books = $200
Thus, total cost for all the books = cost of 1000 books + Transportation cost for all the books = $5400 + $200 = $5600.
Given , trader wants to earn a profit of 12.5%
thus, we find 12.5 % of total cost incurred by trader
12.5 % of total cost incurred by trader = 12.5/100 * $5600. = $700
Thus, total profit for 1000 books will be $700
we know that
selling price = cost price + profit
therefore, in the given problem
selling price for 1000 books = total cost for 1000 books + total profit
substituting the value as calculated above
selling price for 1000 books = $5600 + $700 = $6300
To find selling price for one book, lets divide LHS and RHS by 1000
selling price for 1000/100 books = $6300/1000 = $6.3
Thus, trader should sell each book at $6.3 to earn a profit of 12.5%.
Which of the following best represents 43?
A number between ____ and ____.
A. 7 and 8
B. 8 and 9
C. 5 and 6
D. 6 and 7
Answers
Answer:
D
Step-by-step explanation:
If you mean the sqrt of 43, then
sqrt 36 is 6
sqrt 49 is 7,
since sqrt of 43 is between sqrt 36 and sqrt 49,
sqrt of 43 is between 6 and 7
Which situation could the equation -3*20=-60 represent?
Answers
Answer:
total temp of 20 winter days
Step-by-step explanation:
Which set of numbers could be the length of the sides of a right triangle?
A) {10,24,26}
B) {12,16,30}
C) {3,4,6}
D) {4,7,8}
***YOU DON'T HAVE TO SHOW WORK***
Answers
10^2 + 24^2 = 26^2
This is known as Pythagorean theorem
I know it's Negative Correlation buy I'm so confused on b....
Answers
Basically, the question is asking you if there’s any outliers. An outlier is a data point that seems to not follow the other data points. The outlier here is at about (8, 8000). This point does not follow the negative trend of the other points.
-4|x|=-12 solve the equation
Answers
Answer:
-4|x| = -12
|x| = 3
x = 3, x = -3
Answer:
x=3, x=-3
Step-by-step explanation:
-4|x|=-12
Divide each side by -4
-4/-4|x|=-12/-4
|x|=3
There are two solutions to an absolute value one positive and one negative
x=3, x=-3
Which one is greater -3 1/4 or 3 6/25
Answers
Answer:
3 6/25 is greater
Step-by-step explanation:
Because -3 1/4 is a negative number
it is 3 1/4coz to be equal the other one had to be 3 6/24
do complementary angles form straight angles?
Answers
Explanation: Complementary angles form a right angle (L shape) and have a sum of 90 degrees.
Will Give Brainilest If Correct:
True or False:
0 is neither positive or negative.
Answers
Answer:
true
Step-by-step explanation:
0 is one of the many things in life that make no sense.
// have a great day //
Answer:
True
Step-by-step explanation:
0 is like the barrier between positive and negative numbers.
So the answer is true.
I NEAD HELP ASAP The Lewis family dined at a restaurant. Their bill came to $52, and they plan on leaving a 19% gratuity. This means that the total amount they will pay is 119% of the bill. Which calculation results in the best estimate of the total amount they will pay in dollars? Assume there is no tax. (50) (110 percent) = (50) (100 percent + 10 percent) = (50) (100 percent) + (50) (10 percent) = (50) (1.0) + (50) (0.1) = 50 + 5 = 55 (50) (120 percent) = (50) (100 percent + 20 percent) = (50) (100 percent) + (50) (20 percent) = (50) (1.0) + (50) (0.2) = 50 + 10 = 60 (60) (110 percent) = (60) (100 percent + 10 percent) = (60) (100 percent) + (60) (10 percent) = (60) (1.0) + (60) (0.1) = 60 + 6 = 66 (60) (120 percent) = (60) (100 percent + 20 percent) = (60) (100 percent) + (60) (20 percent) = (60) (1.0) + (60) (0.2) = 60 + 12 = 72
Answers
Answer:
Step-by-step explanation:
multiply 52 times 90% +52
Answer:
Option B is the correct answer.
Explanation:
The image below is the correct answer.
A planet has a circular orbit around a star. It is a distance of 59,000,000 km from the centre of the star. It orbits at an average speed of 41,000 km/h. How many Earth days does it take the planet to orbit the star? Give your answer to 2 sf.
Answers
Answer:
380 days
Step-by-step explanation:
Problem in post:
The radius of the orbit of the planet is 59,000,000 km.
The orbit is circular, so the length of the orbit is the circumference of a circle with radius 59,000,000 km.
distance = circumference of orbit = 2(pi)r = 2 * 3.14159 * 59,000,000 km = 370,707,933 km
speed = 41,000 km/h
speed = distance/time
time * speed = distance
time = distance/speed
time = (370,707,933 km)/(41,000 km/h) = 9,042 hours
Now we convert hours into earth days.
1 earth day = 24 hours
9,042 hours * (1 day)/(24 hours) = 376.73 days
Answer: 380 days
Problem in comments:
Nina and Jo both ran an 8 km race.
Nina took 45 minutes to run the whole race.
Jo started the race 4 minutes later than Nina but caught up when they had both travelled 5 km.
If Nina and Jo both ran at constant speeds, what is Jo's speed to 2 dp?
Solution:
They met at 5 km. Let's find out how long it took Nina to run 5 km.
We can use a proportion.
(8 km)/(45 min) = (5 km)/(x)
x * 8 km = 45 min * 5 km
x = [(45 * 5)/8] min
x = 28.125 min
They met after Nina was running for 28.125 minutes.
Jo started 4 minutes after Nina, so Jo ran for 4 minutes less than Nina. Jo ran 5 km in 24.125 minutes.
speed = distance/time
speed = (5 km)/(24.125 min) * (60 min)/(1 hr)
speed = 12.43523 km/h
Answer: Jo's speed is 12.44 km/h
what is the discriminant of f(x)=-x^2-x+5?
a.-21
b.0
c.2
d.21
Answers
Answer: d. 21
Step-by-step explanation:
The formula to find a discriminant is b^2-4ac.
ax^2+bx+c is the quadratic equation. In your equation, -1 is a, -1 is b, and 5 is c. Now we can plug in the numbers into the discriminant formula b^2-4ac!
(-1)^2-4(-1)(5)=
1-4(-5)
1+20
21
The discriminant is 21.
Hope this helps!
James is 5'10", Emily is 5'7", Ruby is 6'0", Chad is 6'0", Russell is 5'10", and Ariel is 5'9". What is the median height of the people? A. 5'10 B. 5'9 C. 6'0 D. 5'10 and 6'10
Answers
Answer:
A 5'10
Step-by-step explanation:
You have to put the heights in order from least to greatest
5'7, 5'9, 5'10, 5'10, 6'0, 6'0
The middle number is your median. Since there is and even amount of numbers you add the two that are in the middle the divide the sum by two
5'10 + 5'10 = 11'8
11'8 ÷ 2 = 5'10
Fully explain the solution set to the equation below.
1x = -1
Answers
Answer:
The answer for x should equal: -1.
Step-by-step explanation:
To find x, we would divide, our final value, by 1 to get x. In other words, you would divide: -1 ÷ 1 to get -1 as our unknown number.
There are 13 plates and 9 cups on a shelf in a cabinet. what is the ratio of the number of plates to the number of cups
Answers
Answer:
[tex]13 \: \: \: \: : \: \: \: \: 9[/tex]
Step-by-step explanation:
[tex]plates = 13 \\ cups = 9[/tex]
So the ratio of the number of plates to the number of cups.
[tex]plates \: \: \: \: \: : \: cups \\ \: \: \: \: \: \: \: \: 13 \: \: \: \: \: \: \: \: : \: \: 9[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
I need help again brainiest who ever get this right
Answers
Answer:
Step-by-step explanation:
26x25x24x23x22x21x10x9=30,891,577,600
=Thirty billion, eight hundred ninety-one million, five hundred seventy-seven thousand, six hundred.
the answer was kind of in the question btw :)
I need help with this last question
Answers
the statement (l4x-2l = -6) is false (no solution) for any value of x because the absolute value function is always positive or 0
A toy store marks down every toy by 15% in June. How much does a toy cost during June?
Answers
Answer:
since the toy is marked down 15%,
you do p*.85
to find the remaining cost
Step-by-step explanation:
PLS HELP!! IT"S DUE SOON! An iron bar that weighs 2 1/4 lb. is cut into smaller bars that weigh 6 ounces each. How many smaller bars are there?
Answers
Explanation: 2 1/4 lb. to ounces is 36 ounces. Divide it by 6 and it makes 6 smaller bars.
Answer:
There are 6 smaller bars
Each banana weighs 1/2 pound. How many bananas are there in 3 pounds?
Answers
Answer:
6
Step-by-step explanation:
3 divided by 1/2 is equal to 6
Answer:
6 bananas are in 3 pounds.
Step-by-step explanation:
Each banana is 0.5 pound, and keep adding more bananas until you reach 3 pounds.
Mrs. Dombrowsky bought 27 books for the
class. What was the cost for one book if she
spent a total of $67.50?
Answers
Answer:
$2.50
Step-by-step explanation:
67.50/27 = 2.50
Answer:
$2.50
67.50/27 = 2.50
Step-by-step explanation:
