Answers
The value of unknown variable x in the right angled triangle is equal to approximately 20 units.
To find the value of x using the concept of similar triangles,
Use the property that in a right triangle, the altitude drawn from the right angle to the hypotenuse creates three similar triangles.
In triangle QRS, m∠R = 90°.
RS = x (unknown).
RT is an altitude on hypotenuse QS.
ST = 9.
QT = 16.
Now, set up the following ratios for the similar triangles:
In triangle QRT:
QR / QT = RT / ST
In triangle QRS:
QR / QS = RS / ST
Since triangle QRS is a right triangle, we can use the Pythagorean Theorem to find the value of QR:
QR² + RS² = QS²
QR² + x²= (QT + ST)²
QR² + x² = (16 + 9)²
QR²+ x² = 25²
Now, let's use the first similarity ratio to find QR in terms of ST:
QR / QT = RT / ST
QR / 16 = RT / 9
QR = (RT × 16) / 9
Since triangle QRT is also a right triangle, we can use the Pythagorean Theorem again:
QR² + RT² = QT²
((RT × 16) / 9)² + RT² = 16²
(RT² ×256) / 81 + RT²= 256
(RT² ×256 + 81 × RT²) / 81 = 256
(RT² × 337) / 81 = 256
RT² = (256 ×81) / 337
RT² ≈ 61.771
RT ≈ √61.771
RT ≈ 7.859
Now, substitute RT back into the expression for QR:
QR = (RT× 16) / 9
QR = (7.859 × 16) / 9
QR ≈ 13.927
Finally, substitute QR into the Pythagorean Theorem equation we obtained earlier to find the value of x:
QR² + x² = 25²
(13.927)² + x² = 625
193.931 + x² = 625
x² = 625 - 193.931
x² ≈ 431.069
x ≈ √431.069
x ≈ 20.059
Therefore, the value of x in the right triangle is approximately 20 units.
Learn more about triangle here
brainly.com/question/2773823
#SPJ6
Related Questions
Read the following two statements. Then, if possible, use the Law of Detachment to draw a conclusion. If Robbie wants to save money to buy a car, he must get a part-time job. Robbie started a new job yesterday at a grocery store. Robbie wants to save money. Robbie wants to buy a car. not possible If Robbie wants to save money, he must get a part-time job.
Answers
Final answer:
Using the Law of Detachment, we can conclude that Robbie wants to save money because he started a new job and the first condition states that he needs a job to save for a car.
Explanation:
Using the Law of Detachment, we can draw a conclusion from the following two statements:
If Robbie wants to save money to buy a car, he must get a part-time job.Robbie started a new job yesterday at a grocery store.Since Robbie started a new job, which is assumed to be part-time, we can conclude that Robbie wants to save money, as per the first statement which sets up a condition that needs to be fulfilled in order to save money. The specific intention of buying a car is not directly established, but it's often implied that people save for larger investments or expenses. The Law of Detachment only allows us to conclude propositions that directly follow from the given condition. Therefore, the direct conclusion we can draw here, based on the given statements and the Law of Detachment, is that Robbie wants to save money.
Final answer:
According to the Law of Detachment, Robbie wants to buy a car since he wants to save money and he has started a new job.
Explanation:
The Law of Detachment states that if we have a conditional statement of the form "If p, then q", and we know that p is true, then we can conclude that q is also true. In this case, let's analyze the given statements:
1. If Robbie wants to save money to buy a car, he must get a part-time job.
2. Robbie started a new job yesterday at a grocery store.
From statement 1, we can see that Robbie wanting to save money is the condition (p), and getting a part-time job is the conclusion (q). Since statement 2 confirms that Robbie has started a new job, which satisfies the condition (p), we can use the Law of Detachment to conclude that Robbie wants to save money (q) and therefore Robbie wants to buy a car (q). So, the conclusion is: that Robbie wants to buy a car.
Solve the equation for z and approximate the value of z
0.5*e^4z =13
Answers
hich is an example of a proportional relationship?
A.The yogurt shop charges .30 per pound.
B.The yogurt shop charges .30 per pound plus $1.00 for the cup.
C.John ran 2 miles in 15 minutes then ran 3 miles in 20 minutes.
D.The car travelled 40 mph for half an hour and then travelled 60 mph for 2 hours
Answers
Maybelle looked at a hotel. She waited a week before she decided to book nights at that hotel, and now the prices have increased. The original price was $1195. The price for the same room and the same number of nights is now $2075. What is the percent increase? Round to the nearest whole percent. Explain and Show your work.
-20 points. Better yet, 30 points!! Please help!
Diff in price = %
_________ _________ thats the formula i think...
original price 100
Answers
Plug in to get (2075-1195)/1195*100
880/1195*100
.7364*100
73.64% rounding we get
74%
The solution to f - (-4) = 12 is f = 8.
True or False
Answers
if MN = PQ AND PQ = RS then MN = RS
Answers
How to solve 5x-9y=7 and -3x+7y=-5 using any method
Answers
The x value will give 0.5 and the y value will be equal to -0.5
I hope this helps.
YOU'RE WELCOME :D
PLZ HELP
Mrs. Kuss received a $50 Itunes gift card for her birthday. She bought one album for $9.99 and would like to see how much money she has left to buy single songs. If each song costs $1.29, how many songs can Mrs. Kuss buy with her remaining money? Show your work.
Answers
50.00-9.99 = 40.01
40.01 / 1.29 = 31.0
A packet of biscuits has a mass of 1 1/3 kg. Jason eats 2/5 of the packet. What is the mass of biscuits left?
Answers
2 / 5 = 6 / 15;
So. 11 / 3 - 2 / 5 = 55 / 15 - 6 / 15 = 49 / 15 = 3.26 kg is the mass of biscuits left.
The mass of biscuits left after Jason eats 2/5 of the packet is approximately 0.8 kg.
To find the mass of the biscuits left after Jason eats 2/5 of the packet, we need to calculate the mass of the biscuits he ate and then subtract it from the initial mass of the packet.
Given:
Mass of the packet of biscuits = 1 1/3 kg
First, let's convert 1 1/3 kg to an improper fraction:
1 1/3 = 3/3 + 1/3 = 4/3 kg
Now, to find the mass of the biscuits Jason ate, we can use the fact that he ate 2/5 of the packet:
Mass of biscuits Jason ate = (2/5) * (4/3) kg
Now, perform the multiplication:
Mass of biscuits Jason ate = (8/15) kg
To find the mass of biscuits left, we subtract the mass Jason ate from the initial mass of the packet:
Mass of biscuits left = 4/3 kg - 8/15 kg
To subtract fractions, we need to find a common denominator, which is 15 in this case:
Mass of biscuits left = (20/15) kg - (8/15) kg
Now, perform the subtraction:
Mass of biscuits left = 12/15 kg
Finally, let's simplify the fraction:
Mass of biscuits left = (12/15) * (1/3) kg
Mass of biscuits left ≈ 0.8 kg
Therefore, the mass of biscuits left after Jason eats 2/5 of the packet is approximately 0.8 kg.
For more details of mass :
https://brainly.com/question/22493549
#SPJ2
Johnny is reading a novel for the read-a- Thon. The ratio of the number of pages she read to the pages that remain to be read is 7:3. If the book contains 500 pages in all, how many pages did Johnny reed and how many pages remain left?
Answers
If one quart is the same amount as 2 pints, how many pints are in 8 quarts?
Numerical Answers Expected!
Answers
Answer:
16!
Step-by-step explanation: Hope this helps.... you made this in 2017 its 2020 now-
Which of the following list of ordered pairs is a function?!!!
Answers
Give the first four nonzero terms of the series about x=8 representing the function x^(1/3)
Answers
is (3,4) a solution of y=-x+5
Answers
4=y
4=-3+5
So no it’s not.
A trail is 2940 miles long. it begins in city a and ends in city
b. manfred has hiked three sevenths 3 /7 of the trail before. how many miles has he hiked?
Answers
Final answer:
Manfred has hiked 1260 miles of the trail, which is calculated by multiplying the total length of the trail (2940 miles) by the fraction of the trail he has completed (3/7).
Explanation:
To calculate the distance Manfred has hiked on the trail, we multiply the total length of the trail by the fraction of the trail he has completed. In this case, Manfred has hiked three sevenths (3/7) of the trail. The total distance of the trail is 2940 miles.
Distance Hiked = (Total Distance of Trail) × (Fraction of Trail Completed)
Distance Hiked = 2940 miles × (3/7)
Distance Hiked = 2940 miles × 0.4286
Distance Hiked = 1260 miles
Therefore, Manfred has hiked 1260 miles of the trail.
Bella babysits for two families each weekend. One family pays her $20. The other family pays her $22. Which expression represents the amount of money Bella has been paid after w weekends?
Answers
Please Help With This. What is the equation of the line shown in this graph? Answer your answer in the box.
Points are:
(-2,-3) (3,-3)
Answers
[tex]\bf \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-(-3)=0[x-(-2)] \\\\\\ y+3=0\implies y=-3[/tex]
If you know how to do this, can you show the work, please?
Thanks
Answers
-------------------------------------
-------------------------------------
Let x be the original side length of the square. The original area is therefore going to be x*x = x^2. For now we don't know the area but once we figure out x, we can compute the area.
The original side length x is increased by 7 ft to jump up to (x+7) ft
At the same time, the other dimension is reduced to (x-2) ft, which is a decrease of 2 ft
The old square is x ft by x ft with area x*x = x^2
The new rectangle is (x+7) ft by (x-2) ft
Let's find the area of this rectangle
Have a look at the image attachment to see how to multiply out (x+7)*(x-2) using the box method
The terms in red are x^2, 7x, -2x and -14 which are found by multiplying the headers
x times x = x^2
x times 7 = 7x
-2 times x = -2x
-2 times 7 = -14
The like terms are 7x and -2x which combine to 5x
Overall the result of multiplying out (x+7)*(x-2) is x^2+5x-14
Note: we can get the same result if we use the FOIL or distribution rule. The box method is a handy way to visually keep track of all the terms.
-------------------------------------
The area of the rectangle, in terms of x, is x^2+5x-14
We are told that the area is 90 square feet
So equate the two expressions and solve for x
x^2+5x-14 = 90
x^2+5x-14-90 = 90-90
x^2+5x-104 = 0
(x-8)(x+13) = 0 ... see note below
x-8 = 0 or x+13 = 0
x = 8 or x = -13
note: find two numbers that multiply to -104 and add to 5. Those numbers are -8 and 13 which helps us factor
We ignore x = -13 as a negative side length makes no sense
The only practical root is x = 8
The side length of the original square is 8 feet
The area is
x*x = 8*8 = 64 square feet
We can check the answer by adding 7 to 8 to get 15, and subtracting 2 from 8 to get 6. The 8 by 8 square turns into a 15 by 6 rectangle. Since 15*6 = 90, we have confirmed the right answer.
Can someone please just explain what I need to do? I'm so confused
The length of a text messaging conversation is normally distributed with a mean of 10 minutes and a standard deviation of 4 minutes. What is the probability that a conversation lasts longer than 20 minutes?
Answers
1. Can √72 be completely simplified if it is broken up as √72=√9x8, explain why or why not?
2. How do you determine the result of taking the square root of a variable raised to an even power? For example √x∧28?
Answers
2. sqrt x = x^½. Rules of indices states for a power of a power, you times them.
so (x^28)^½ = x^14
HELP PLEASE:
What is the point-slope form of the line with slope 25 that passes through the point (−4, −7)?
y−7=2/5(x−4)
y+7=2/5(x+4)
y+4=2/5(x+7)
y−4=2/5(x−7)
Answers
slope(m) = 2/5
(-4,-7)....x1 = -4 and y1 = -7....pay attention to ur signs
now we sub
y - (-7) = 2/5(x - (-4)...not done yet
y + 7 = 2/5(x + 4) <===
Answer:
Correct option is:
y+7=2/5(x+4)
Step-by-step explanation:
The point-slope form of the line with slope m and passing through the point (x1,y1) is given by:
y-y1=m(x-x1)
Here, we are given line with slope m=2/5
and passing through (x1,y1)=(-4,-7)
i.e. x1= -4 and y1= -7
[tex]y-(-7)=\dfrac{2}{5}(x-(-4))[/tex]
[tex]y+7=\dfrac{2}{5}(x+4)[/tex]
Hence, Correct option is:
y+7=2/5(x+4)
What is the value of the expression when a = 4, b = 3 ,and c = 10?
3a/4b−c
1
4
6
12
Answers
What is the next term in the sequence 1/2 1/6 1/18 1/54
Answers
2*3=6
6*3=18
18*3=54
54*3=162
For an arithmetic sequence where a1 = 13 and the common difference is 3, find s7.
A. 162
B. 157
C. 154
D. 151
Answers
s7 means n=7
a7=7/2[2(13)+(7-1)(3)]=7/2(44)=154
Ans:C
Answer:
C. 154
Step-by-step explanation:
Here we have given that,
First Term a₁ = 13
Common Difference d = 3
Term (n ) = 7
so, we have arithmetic sequence: 13, 16, 19, 22,... and so on
Thus Sum of first 7 terms = [tex]\frac{n}{2} [2a+(n-1)d][/tex]
= 7÷2 [2*13 + (7 - 1)*3 ]
= 3.5 [ 26 + 21 ]
= 154
Brock is a plumber. He charges a flat rate of $40 to visit a house to inspect it's plumbing. He charges an additional $20 for every hour he spends inspecting or making repairs.
Which graph below correctly shows the price of using Brock's plumbing service vs time?
Answers
W is correct. the red line starts at 40 which is the initial fee
then it crosses 60 and 1.0 and 80 at 2.0 which is 20 dollars for 1 hour
which statement is equivalent to the inequality 14x-14>7x+7
Answers
14x - 7x > 7 + 14
7x > 21
x > 21/7
x > 3
cindy had a party. She invited two guests. Her guests each invited four guests, and then those guests each invited three guests.
Answers
Is 55.56 greater than 55.65? I'm in a hurry so answer quick
Answers
$40 is discounted into $32 what is the percent decrease
Answers
The function f(x) is shown in the graph.
What is the equation for f(x)?
Enter your answer in the box.
f(x)=_______
Answers
___________________________________