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
If f(x) = 2x2 + 3 and g(x) = x2 - 7, find (f-9)(x).
O A. 3x2 - 10
O B. 3x2 - 4
O c. x2 + 10
O D. x² - 4
Plzzz helpp
Answers
Answer:
x^2 + 10
Step-by-step explanation:
f(x) = 2x^2 + 3
g(x) = x^2 - 7,
(f-g)(x) = 2x^2 +3 - ( x^2 -7)
Distribute the minus sign
= 2x^2 +3 -x^2 +7
Combine like terms
= x^2 +10
Find three consecutive integers that sums to 15. Show your equation and all work.
Answers
Answer:
4, 5, 6
Step-by-step explanation:
Represent the first number by x. Then the next two consecutive integers are x + 1 and x = 2.
THEN x + x + 1 + x + 2 = 15, WHICH REDUCES TO 3x + 3 = 15.
Then 3x = 12, and x = 4.
The consecutive integers are 4, 5 and 6.
Arithmetic Reasoning
4. A duplicator can make 75 copies of a letter per minute, and 300 copies from one master. After how long must the master sheet be changed?
a. 4 minutes
b. 5 minutes
C. 6 minutes
d. 15 minutes
Answers
Answer:
a. 4 minutes
Step-by-step explanation:
Since the duplicator makes 75 copies a minute, and can only make 300 copies from one master, we divide 300 copies by 75 copies, leaving us with four. So our answer is that the master sheet must be changed every 4 minutes.
Melanie makes $3.00 less per hour babysitting than her best friend, Carita. If the combined hourly rate of Melanie and Carita is $15.00, how much does Melanie make per hour? A. $3.00 B. $6.00 C. $9.00 D. $12.00
Answers
Answer:
B 6.00
Step-by-step explanation:
M= 6$
C= 9$
M+C= 6+9= 15$ per hour
ESTIMATED AND EXACT ANSWERS. Find the answers to these division problems. Use
compatible numbers to check your answer's accuracy. Look back to Lesson Three if you need
help with compatible numbers. (2 points each)
10. 903.6 - 25.1
Exact Answer:
Estimate:
11. 760.38 +0.38
Exact Answer:
Estimate:
Answers
Answer
10) 36
11)2001
Step-by-step explanation:
Answer:
10. 36 (exact answer), 30 or 30.16 (estimated answer).
11. 2001 (exact answer), Undefined, or 1900 (estimated answer).
Step-by-step explanation:
For number 10, the exact answer is 36 and the estimated is 30 or 30.16. Why?
-To have the exact answer we have to divide 903.6 ÷ 25.1 = 36.
-To have the estimated answer we have to round 903.6 and 25.1, as 903.6 is close to 900 and not 1,000, and 25.1 is close to 30 and not to 20. The equation is 900 ÷ 30 = 30.
-To make sure that the exact answer is correct, we have to multiple 25.1 and 36 = 903.6.
-To make sure that the estimated answer is correct, we have to multiple 30 and 30 = 900.
-But there's a problem, they can be two answers for the estimated answer 1). 30, and 2). 36.16. Process: 904 ÷ 25 = 36.16. Why? As they are decimal points, it may be that we have to round them but not the whole number, but the question doesn't specify how we have to round them, so I'm not so clear about it.
For number 11, the exact answer is 2001 the estimated is 1900 or Undefined. Why?
-To have the exact answer we have to divide 760.38 ÷ 0.38 = 2001.
-To have the estimated answer for the undefined we have to round 760.38 and 0.38, as 760.38 is close to 800 and not to 700, and 0.38 is close to 0 (0.00) and not to 1 (1.00). The equation is 800 ÷ 0.00 = Undefined.
-To make sure that the exact answer is correct, we have to multiple 2001 and 0.38 = 760.38.
-But there's a problem, they can be two answers for the estimated answer 1). Undefined, and 2). 19. Process: 760 ÷ 0.40 = 1900. Why? As they are decimal points, it may be that we have to round them but not the whole number, but the question doesn't specify how we have to round them, so I'm not so clear about it.
someone pls help mee
Answers
Answer:
-1/2
Step-by-step explanation:
The formula for slope is: y1-y2/x1-x2
The points given are: (x coordinate, y coordinate)
In the formula,
y1 is the y coordinate of the first point
y2 is the y coordinate of the second point
x1 is the x coordinate of the first point
x2 is the x coordinate of the second point
This said, we can plug our points in.
5-(-1)/-3-9
Simplify.
5+1/-12
6/-12
Divide both the numerator and denominator by -6.
-1/2
If X^2 = 4
Does X = 2 or X = -2
Answers
Answer:
Both.
Step-by-step explanation:
[tex]x^2=4[/tex]
[tex]x=\±\sqrt{4}[/tex]
[tex]x=\± 2[/tex]
Answer:
Yes
Step-by-step explanation:
If,
X² = 4
Taking square root on both sides
[tex]\sqrt{x^2} = \sqrt{4}[/tex]
So, It becomes
X = ±4
Either
X = 2 OR X = -2
For every 2 adults there are 7 kids. There are a total of 180 people. How many adults and kids are there out of the 180 total?
Answers
Answer:
40 adults and 140 kids
Step-by-step explanation:
Answer:
40 adults
Step-by-step explanation:
40 adults and 140 kids
20 times 7 is 140
40 plus 140 is 180
Which rhetorical technique is the speaker using? A.appeal B.overstatement C.parellelism D.shift
Answers
Answer:
From what chapter of a book?
Step-by-step explanation:
Answer:
he is making an appeal to someone to do something about something that he knows would be good for everyone
Step-by-step explanation:
What is the result of subtracting the second equation from the first?
-2x + y = 0
-73 + 3y = 2
Answers
Answer:
The result is 2x + 2y - 73 = 2.
-73 + 3y = 2 (equation 2)
First of all, rearrange and simplify equation so they’re in the format of y= ax + b.
Equation 1
-2x + y = 0
y = 2x + 0
y = 2x
Equation2:
-73+3y=2
3y = 2 + 73
3y = 75
3y/3 = 75/3
y= 25
Subtract second equation from first:)
y= 2x - 25
Hope this helped :)
Mr.Brown is planting trees in a field that is one mile long and 2 miles wide. How much is his field.
Answers
Answer:
Step-by-step explanation:
Wtwtettete
Answer:
2 miles squared.
Step-by-step explanation:
A= length times width
A= 1 mile times 2 miles
A= 2 miles squared
Which statement describes whether a right triangle can be formed using one side length from each of these squares?
Area = 64 in
Area = 225 in
Area = 289 in
Yes, a right triangle can be formed because the sum of the areas of the two smaller squares does not equal the area of
the largest square
Yes, a right triangle can be formed because the sum of the areas of the two smaller squares equals the area of the
largest square
No, a right triangle cannot be formed because the sum of the areas of the two smaller squares does not equal the area
of the largest square.
Save and Exit
Set
Answers
Answer:
Step-by-step explanation:
The area of the given squares are
Area = 64 in
Area = 225 in
Area = 289 in
The length of each side of a square is determined by finding the square root of its area. For the first square, the length of its side is √64 = 8inches. For the second square, the length of its side is √225 = 15inches. For the third square, the length of its side is √289 = 17inches.
For a right angle triangle to be formed, Pythagorean theorem must be obeyed. Sum of the square of the smaller sides must equal the square of the longer side. Therefore,
8² + 15² = 17²
289 = 289
Therefore, the correct statement is
Yes, a right triangle can be formed because the sum of the areas of the two smaller squares equals the area of the largest square
Answer:
B
Step-by-step explanation:
I got this right in edge 2020. Hope this helped! ;)
SOMEBODY HELP ME OUT !!
Answers
Answer:
D
Step-by-step explanation:
Under a clockwise rotation about the origin of 90°
a point (x, y ) → (y, - x ) , thus
X(- 1, - 3 ) → X'(- 3, 1 )
Y(0, 0 ) → Y'(0, 0 )
Z(1, - 3 ) → Z'(- 3, - 1 )
In the section describing the survey methods, the report states, “For results based on the total sample of national adults, the margin of sampling error is ±4 percentage points at the 95% confidence level.” Interpret the meaning of this statement in terms of the poll. Use any statistic given in the report as an example to explain your interpretation.
Answers
Answer:
The interpretation of that same problem is listed throughout the section below on explanation.
Step-by-step explanation:
Interpretation:
Researchers seem to be confident with 95% that the sample selection standard error seems to be + as well as - 4 percent respectively. This same margin of sampling error would then decrease from either the mean or average value by four percentage points smaller or even larger, it describes the survey method.So that the above is the right answer.
Factor. x2−8x+16
(x+8)2
(x−4)2
(x+4)2
(x−8)2
Answers
Answer:
B
Step-by-step explanation:
[tex]x^2-8x+16= \\\\(x-4)(x-4)=\\\\(x-4)^2[/tex]
You can confirm this by working in reverse:
[tex](x-4)^2= \\\\(x-4)(x-4)=\\\\x^2-4x-4x+16=\\\\x^2-8x+16[/tex]
Hope this helps!
Answer:
(x−4)^2
Step-by-step explanation:
I did the test
What is the volume of a hemisphere with a radius of 40.7 in, rounded to the nearest tenth of a cubic inch?
Answers
Answer:
[tex](\frac{4}{3} \pi 40.7^{3})/2[/tex]
[tex]\pi =3.14[/tex]
[tex](4*3.14*40.7^{3} )/3 = 282,261.5[/tex]
[tex](282,261.5)/2 = 141,130.7 in^{3}[/tex]
Step-by-step explanation:
1. Volume of sphere
[tex]V=\frac{4}{3} \pi r^{3}[/tex]
2. Volume of hemisphere
[tex]V=(\frac{4}{3} \pi r^{3} )/2[/tex]
The volume of hemisphere is 1,41,130.7 cubic inch.
What is hemisphere?The words hemisphere and sphere can be separated into hemi, which denotes half, and sphere, which refers to the mathematical 3D shape. Consequently, a hemisphere is a 3D geometric object that is made up of half of a sphere, with one side being flat and the other being a bowl-like shape. It is created by precisely cutting a spherical along its diameter, leaving behind two identical hemispheres.
Given the radius of hemisphere = 40.7 inches
to find the volume,
volume of hemisphere = 2/3πr³
volume of hemisphere = 2/3(3.14)(40.7)³
volume of hemisphere = 2/3(3.14)(67419.143)
volume of hemisphere = 1,41,130.7 cubic inch.
Hence the volume is 1,41,130.7 cubic inch.
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Which is the graph of the linear equation 3x – 4y = –12? On a coordinate plane, a line goes through points (0, 3) and (4, 0). On a coordinate plane, a line goes through points (negative 4, 0) and (0, negative 3). On a coordinate plane, a line goes through points (0, negative 3) and (4, 0). On a coordinate plane, a line goes through points (negative 4, 0) and (0, 3).
Answers
Answer:
On a coordinate plane, a line goes through points (negative 4, 0) and (0, 3).
Step-by-step explanation:
I graphed the equation on the graph below so you can where I got my answer.
Answer:
the answer is D
Step-by-step explanation:
hope this helps!
Wich property is represented by the equation shown below? 6 x 3 = 3 x 6 A) Multiplicative inverse property B) Multiplicative identity property C) Associative property of multiplication D) Commutative property of multiplication
Answers
Answer:
D) Communicative Property of Multiplication
Please give brainliest -3-
Which function shows a fabric with a price of $1.25 per square yard?
Answers
Answer: n=1.25x
Step-by-step explanation:
X represent the number of yards and n represent the total amount
The function which shows the fabric with a price of $1.25 per square yard will be y = 1.25x where x represents square yard and y represent the price of fabric.
What is a function?A certain kind of relationship called a function binds inputs to essentially one output.
A function can be regarded as a computer, which is helpful.
The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.
In other words, the function is a relationship between variables, and the nature of the relationship defines the function.
Given that the
Price of fabric = $1.25/ yard
Let's say the price of fabric = y
Square yard = x
Then y = 1.25x so it will be the correct answer.
For more about the function
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What is the area of this triangle?
Answers
Answer:
8 units^2
Step-by-step explanation:
The area of a triangle is given by
A = 1/2 bh
A = 1/2 (7-3) * (4-0)
= 1/2 4*4
= 8
Which of the following relations represents a function?
O A. {(1, 1), (1, 2), (1,3)}
O B. {(1, 1), (2, 1), (3, 1)}
O C. {(1, 1), (2, 2), (3, 3)}
O D. Both B and C.
Answers
OPTION NUMBER D IS CORRECT
D.Both B and C.
Step-by-step explanation:
function is the relation from set A to B such that every element of set A(domain) should have only 1 image in Set B(co domain).
4. A driver set a goal to earn $2,000 in March. He receives a base salary of $1,000 per month as well as a 20% commission for all sales in that month. What does his total sales have to be this month to reach his goal?
Answers
Answer:
X=$5,000
Step-by-step explanation:
You can write an equation in slope-intercept to find an answer.
y=0.2x+1000, 20% commission is the slope and the base pay is the y-intercept.
Now, just plug in 2,000 for y.
2,000=0.2x+1,000, subtract 1,000.
1000=0.2x, Multiply by 5 to get x by itself.
x = 5,000
Hope this helped youuuuu
Find x, y and z to the nearest hundredth.
Answers
Answer:
see explanation
Step-by-step explanation:
This is an example of the Altitude - on - Hypotenuse theorem.
The altitude that is perpendicular to the hypotenuse of a right triangle.
The two triangles formed are similar to the given triangle and to each other.
x² = (smaller part) × (larger part) of main hypotenuse
x² = 6 + 19 = 114 ( square root both sides )
x ≈ 10.68 ( nearest hundredth )
---------------------------------------------
y² = ( smaller part) × (whole part) of main hypotenuse
y² = 6 × 25 = 150 ( square root both sides )
y ≈ 12.25 ( nearest hundredth )
--------------------------------------------
z² = ( larger part) × (whole part) of main diagonal
z² = 19 × 25 = 475 ( square root both sides )
z ≈ 21.79 ( nearest hundredth )
7) Given that Sn=3-2^(-4n)
is the sum of the first n terms of a sequence.
Un is the n term.
a) Express Un+1 in terms of n.
b) Deduce that the
sequence is a geometric progression.
Answers
Answer:
Step-by-step explanation:
[tex]s_{n}=3-2^{-4n}\\s_{n+1}=3-2^{-4(n+1)}=3-2^{-4n} *2^{-4}\\s_{n+1}-s_{n}=3-2^{-4n}*2^-4-3+2^{-4n}[/tex]
[tex]=2^{-4n}-2^{-4n}*2^{-4}\\=2^{-4n}(1-2^{-4})\\=2^{-4n}(\frac{2^4-1}{2^4})\\=2^{-4n}\frac{15}{16}\\U_{n+1}=15*2^{-4(n+1)}[/tex]
Can someone please help me with this?
Answers
Answer:
3/4
Step-by-step explanation:
There are 12 marbles in the bag
9 marbles are not blue
P(not blue) = marbles that are not blue / total marbles
= 9/12 = 3/4
Your history teacher is going to give you a 92 point assessment. There are 2 point questions and 3 point questions. If there is a total of 40 questions on the assessment, how many questions are worth 2 points?
Answers
Solve the following equation : 2x+3x= 40
then, multiply the value of "x" by 2.
Hope it helps
To change a decimal to a fraction we route write the digit to the left or to the right of the decimal point over the appropriate power of 10
Answers
Answer:
The digit goes to the right of the decimal point
Step-by-step explanation:
If you had [tex]\frac{1}{10}[/tex], you would convert that to 0.1, which is equivalent to the fraction form. The one goes on the right of the decimal point.
some teachers traveled to school by car the table shows the number of teachers in the cars a) what was the modal number of teachers in a car b) what was the median number of teachers in a car c) what was the mean number of teachers in a car
Answers
Answer:
Step-by-step explanation:
since it is asking for the modal that means the most so it would be 3 teachers, and when asking the median we have to change the order so it would be 2,3,4,6 and we find the middle so it would be 3.5, and the mean is the total of the numbers divided by how many numbers there are so it would 2+6+4+3=
15/10 = 1.5
A mean is an arithmetic average of a set of observations. The model number, median, and mean of the number of teachers in a car are 3, 3, and 2.46667, respectively.
What is Mean?A mean is an arithmetic average of a set of observations. it is given by the formula,
Mean = (Sum of observations)/Number of observations
The given table can be written in the data form as 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4.
A.) The modal number is the mode of a given data set. Therefore, the mode of the given data set is 3.
B.) The median is the middle number of a given data set. Therefore, the median is 3.
C.) The mean is the average number of teachers in a car. Therefore, the mean is,
Mean = (1+1+1+2+2+2+2+3+3+3+3+3+3+4+4)/15 = 37/15 = 2.46667
Hence, the model number, median and the mean of the number of teachers in a car is 3, 3, and 2.46667, respectively.
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Solve the equation using the Quadratic Formula:
x2 + 6x + 3 = 0
Answers
Answer:
x = -2[tex]\frac{2}{3}[/tex]
Step-by-step explanation:
First we have to distinguish the numbers with x from the "normal" numbers.
2x and 6x are numbers with x.
3 and 0 are "normal" numbers.
Now we have to seperate them on different sides of the equal sign.
To do this, we can subtract 3 from the left side and then add it to 0 on the left side.
Therefore, the equation will now be 2x + 6x = -3.
Now we can add 2x and 6x together, making it 8x.
The equation will now be 8x = -3.
To find the product of x, we need to divide both sides together.
So 8 divided by -3 will make -2[tex]\frac{2}{3}[/tex].
Therefore, x is -2[tex]\frac{2}{3}[/tex].
Hope my explination makes sense :)
William, Nancy, and Edgar met at the lodge at 8 AM. William began hiking west at 3 mph. At 10 AM Nancy began hiking north at 5 mph and Edgar went east on a three wheeler at 12 mph. At what time was the distance between Nancy and Edgar 10 miles greater than the distance between Nancy and Willam? ____:____ AM/PM
Answers
Answer:
12:00 AM
Step-by-step explanation:
Taking the lodge as the center of the coordinate system, the position of each person is:
William: 6+3*t
Nancy: 5*t
Edgar: 12*t
where t is in hours after 10:00 am
Between the positions of William and Nancy, a right triangle is formed, where their distance is the hypotenuse.
WN = √[(5*t)² + (6+3*t)²]
Similarly, Between the positions of Nancy and Edgar:
NE = √[(5*t)² + (12*t)²]
If the distance between Nancy and Edgar is 10 miles greater than the distance between Nancy and Willam, then
NE = WN + 10
√[(5*t)² + (12*t)²] = √[(5*t)² + (6+3*t)²] + 10
With the help of the graph of this equation, we find that t = 1.95 or approximately 12:00 AM