In the diagram below, \overline{ST} ST is parallel to \overline{PQ} PQ. If STST is 55 more than QTQT, RT=10RT=10, and PQ=15PQ=15, find the length of \overline{QT} QT. Figures are not necessarily drawn to scale. State your answer in simplest radical form, if necessary.PQRTS
Answers
The length of the [tex]\overline{QT}[/tex] can be determined using the given information and
the relationship between corresponding sides of similar triangles.
[tex]\underline{\overline{QT} = 5}[/tex]Reasons:
The given parameters are;
[tex]\overline{ST} \parallel \overline{PQ}[/tex]
ST = QT + 5
RT = 10
PQ = 15
Required: The length of [tex]\overline{QT}[/tex]
Solution:
Using the relationship between corresponding sides of similar triangles, ΔRST and ΔRPQ, we have;
[tex]\displaystyle \frac{\overline{ST}}{\overline{RT}} = \mathbf{\frac{\overline{PQ}}{\overline{RQ}}}[/tex]RQ = QT + RT
Therefore;
[tex]\displaystyle \frac{\overline{ST}}{\overline{RT}} = \mathbf{\frac{\overline{PQ}}{\overline{QT} + \overline{RT}}}[/tex]Which gives;
[tex]\displaystyle \frac{\overline{QT} + 5}{\overline{RT}} = \frac{\overline{PQ}}{\overline{QT} + \overline{RT}}[/tex]
Plugging in the known values gives;
[tex]\displaystyle \frac{\overline{QT} + 5}{10} = \mathbf{\frac{15}{\overline{QT} + 10}}[/tex]
[tex](\overline{QT} + 5) \times (\overline{QT} + 10) = 10 \times 15[/tex]
[tex]\overline{QT}^2 + 10\cdot \overline{QT} + 5\cdot \overline{QT} + 50 = 10 \times 15[/tex]
[tex]\overline{QT}^2 + 15\cdot \overline{QT} + 50 - 150= 0[/tex]
[tex]\mathbf{\overline{QT}^2 + 15\cdot \overline{QT} -100} = 0[/tex]
Factorizing with a graphing calculator gives;
[tex](\overline{QT} -5) \cdot (\overline{QT} + 20)= 0[/tex]
[tex]\mathbf{\overline{QT} = 5} \ or \ \overline{QT} = -20[/tex]
Therefore, given that [tex]\overline{QT}[/tex] is a natural number, we have;
[tex]\underline{\overline{QT} = 5}[/tex]
Learn more about similar triangles here:
https://brainly.com/question/4268470
Related Questions
A new bank customer with $3,000 wants to open a money market account. The bank is offering a simple interest rate of 1.3% How much interest will the customer earn in 30 years
Answers
The formula for simple interest is A=P(1+rt)
A is the final amount
P is the initial amount
r is the rate
t is the amount of time
If you plug the information given into the formula:
3,000(1+1.3•30)=120,000
3,000 is the initial amount
1.3 is the rate
30 is the amount of time
120,000 is the final amount
The question asks how much interest the customer will earn, not what the final amount in the account will be.
Given that, you would subtract the initial amount to find out how much the customer earned.
120,000-3,000=117,000
hope this helps!
What happens if I find the sum of two even numbers
Answers
I don't know what you mean by this but you'll just get a value larger than the two sums that you added
5 + 7 = 12
3 + 4 = 7
Answer:
The sum will always be even
Step-by-step explanation:
how is the answer 4??
Answers
Answer:
see below
Step-by-step explanation:
log sqrt5 (25) = y
we know that loga (b) = c can be rewritten as a^c = b
sqrt(5) ^ y = 25
Rewriting sqrt(5) as 5^1/2 and 25 as 5^2
5^1/2 ^ y = 5^2
we know a^b^c = a^ (b*c)
5 ^ 1/2y = 5^2
1/2y = 2
y = 4
At the end of which day does Tyler have 2750 feet left to climb?
Answers
worth 30 pts pls helppp
Answers
Answer:
Step-by-step explanation:
it is blank
Please help...........
Answers
Answer:
4
Step-by-step explanation:
your answer is 4 because
2*4 = 8
5*4 = 20
7*4 = 28
8*4 = 33
f(1) = 4
f(x) = f(x-1) + 3
Find f(2)
Answers
f(2)= f(2-1)+3
f(2)=f(1)+3
Please help thankssssss
Answers
[tex]0,2a^{2}b^3 . (-5a^3b)^2 = 0,2a^{2}b^3 . 25a^6b^2 = 5a^8 b^5[/tex]
ok done. Thank to me :>
What is 10,000 written as a power of 10?
Answers
Answer:
the answer shows in the picture, sorry, I tried to type it but it would come out different.
Step-by-step explanation:
10,000 = 10x10x10x10 = 10 4. Notice that the exponent of the ten is simply the number of the zeros.
Hope this helped:)
The large number 10,000 written as a power of 10 as 10⁴.
The given large number is 10000.
Scientific notation is a method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power such as 1.56×10⁷.
Here, the number 10000 can be written as 10⁴.
Therefore, the number 10,000 written as a power of 10 as 10⁴.
To learn more about the Scientific notation visit:
https://brainly.com/question/18073768.
#SPJ6
need help please i’m struggling to solve
Answers
I can't give a very good answer as I don't know what resources are available to you, but this is what I managed to find with a ti-84 calculator.
[tex]y=-31.24+1.34x[/tex]
If you want a better step-by-step, tell me what's in that 'open statistics calculator' option and I'll see what I can figure out.
edit: missed that second part of the question
Using this equation to calculate a test grade with a homework grade of 90:
[tex]y=-31.24+1.34(90)=89[/tex]
Mai is making personal pizzas. For 4 pizzas, she uses 10 ounces of cheese. How much does she use on 1 pizza. How much does she use on 15 pizzas.
Answers
Answer:
32.5
Step-by-step explanation:
10 ounces is in 4 pizzas so if we want 15 pizzas we need to count up
4 can not fit into 15 so we have to stop at 12 pizzas.
Now we need to add 3 pizzas
:Note: that one pizza is 2.5 of an ounce out of 10 ounces
so after you add the 3 pizzas you have 15 but that wasnt 4 pizzas so you have 2.5 ounces left over you add those ounces to the 30 you got from the 12 ounces which you have 30 and add it to the ounces left over
2.5 + 30 = 32.5
Pleaseee help me A medical equipment industry manufactures X-ray machines. The unit cost C (the cost in dollars to make each X-ray machine) depends on the number of
machines made. If x machines are made, then the unit cost is given by the function (x) -0.8x? - 256x+29,444. What is the minimum unit cost?
Do not round your answer.
Answers
Answer: 8,964
Step-by-step explanation: x= -b/2a. So, -(-256)/2(0.8)= 160. Plug in 160 to the whole equation.
0.8(160)^2 -256(160)+29444
=8,964
Find the slope (-10,-3) (7,2)
Answers
Answer:
Let (-10,-3) be (x1, y1)
and (7, 2) be (x2, y2).
Slope = [tex]\frac{y2-y1}{x2-x1}[/tex]
Substitute in values:
[tex]\frac{2-(-3)}{7-(-10)} =\frac{5}{17}[/tex]
Answer:
5/17
Step-by-step explanation:
Slope = Change in /Change in X
Slope = 2 - (-3) / 7 - (-10)
Slope = 5/17
-Chetan K
A shark is 205 feet below sea level, it rises 80 feet towards sea level, then 25 points
drops 40 feet. What is the current elevation?
Captionless Image
Answers
Answer:
165 feet below sea level.
Step-by-step explanation:
205 - 80 = 125
125 + 40 = 165
The area of the hexagon pictured above is ___ units2. Round answer
to the hundredths.
Answers
Answer:
The formula for the area of a hexagon is Area = (3√3 s2)/2; where 's' is the length of one side of the regular hexagon. The formula for the area of a hexagon can also be given in terms of the apothem as, Area of hexagon = (1/2) × a × P; where 'a' is the length of the apothem and 'P' is the perimeter of the hexagon.
Q(x)=-1/2x-3; q(x)=-4
Help
Answers
Answer:4
Step-by-step explanation:
Does the following relationship represent a function?
A. Yes
B. No
Answers
30 POINTS, I NEED FAST AND CORRECT ANSWERS PLEASE!!!!
The average cost of a compact car at a certain dealership over the last 5 years has ranged from $14,000
to $16,000. Suppose you were going to plot these points on a coordinate grid.
(a) What is a good scale to use for the y-axis? Explain your reasoning.
(b) What is a good interval to use for the y-axis? Explain your reasoning.
Answers
Answer:
Plz give brainliest
Step-by-step explanation:
I believe
A) 0 - 20,000
B) Interval= 2000 or 3000
Will give brainly crown
Jared’s average daily balance for last month was $560. The finance charge was $8.12.
a. What was the monthly percentage rate?
b. What was the APR?
Answers
Answer:
A) monthly percentage rate = 1.45%
B) APR = 17.4%
The monthly percentage rate was 1.45 % and the annual percentage rate was 17.4%.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
We have been given that Jared’s average daily balance for last month was $560. The finance charge was $8.12.
We have to determine the monthly percentage rate.
The monthly percentage rate is the percentage ratio of the finance charge to the average daily balance.
The monthly percentage rate = finance charge / average daily balance
The monthly percentage rate = $8.12 / $560 × 100
The monthly percentage rate = 0.0145 × 100
The monthly percentage rate = 1.45 %
The Annual percentage rate = 12 × monthly percentage rate
The Annual percentage rate = 12 × 1.45 %
The Annual percentage rate = 17.4 %
Therefore, the monthly percentage rate was 1.45 % and the annual percentage rate was 17.4%.
Learn more about the percentages here:
brainly.com/question/24159063
#SPJ5
Solve the equation. Linear Equations:Variable on Both Sides
-7x-3x+2=-8x-8
Solve it step by step
Answers
help me can you help with the second part
Answers
Answer:
12 packages with 2 toothbrushes and 3 soaps each
Step-by-step explanation:
Jodie wants to raise money for a school trip by selling raffle tickets at a basketball game. She sells each ticket for 50 cents, and she sells two and a half rolls of tickets. If each roll of ticket has 200 tickets, how much money did Jodie make?
Answers
Answer:
250 dollars
Step-by-step explanation:
t = tickets
t = 200
Two and a half rolls tickets = (200 x 2) + 200/2) = 400 + 100 = 500
500 tickets x 50 cents = 25000 cents
convert cents to dollars (move decimole point over left 2 units)
25000 = 250 dollars
the $5 are correct but it marked the .75 as wrong
Answers
PLS HELP AMSWER ANYONE PLS ILL GIVE BRAINLKEST THANKS
Answers
Answer:
5. w ≠ 8
Step-by-step explanation:
#1 is the expression for "The amount of water is greater than eight ounces." This technically means it differs from eight ounces, but it's too specific for what the question is asking.
#2 is the expression for "The amount of water is greater than or equal to eight ounces." It doesn't necessarily differ from eight ounces.
#3 is the expression for "The amount of water is less than eight ounces." Same issue as #1.
#4 is the expression for "The amount of water is greater than eight ounces." Same issue as #2.
#5 is the expression for "The amount of water is not equal to eight ounces." This is the correct expression as the only information we know is that it's not eight ounces.
HELP!!! Worth 50 points
Answers
Answer:
with what
Step-by-step explanation:
I am confused there is no question at all showing
Answer:
Answer:
The correct answer is C - 7.8 < 7 5/6 < 7.9
Step-by-step explanation:
First, convert 7 5/6 to decimal form --> 7.83.
If you don't know how to convert, think about what 5/6 is equal to and put it in decimal form. Add your decimal to the whole number, and there is your answer.
7.83 is in between 7.8 and 7.9, so it must be the answer.
I hope this helps!
Step-by-step explanation:
simplify 16v²÷2v²tlA
Answers
Hello
just a second
people reading this please complete because you will help me a lot.
I am an Indian girl my name is Lamer and am 13 years old.
I Just got this new device after working at a farm for 2 years.
I used to use brainly at my friend device she had money to buy brainly plus.
I cant please help me get points so I can get good marks and my dad let me complete my education instead of getting married.
PLEASE HELP!!!!
The graph below shows the time it takes Michael to solve 30 multiplication
flash cards over 7 attempts. In which attempts did he improve by more than 8
seconds from the previous attempt? Check all that apply.
Answers
Answer:
I think it's 2 and 5
Step-by-step explanation:
I hope this helps
Answer:
4,6,2,7
Step-by-step explanation:
In an experiment, the temperature of a sample is measured as 16 degrees Celsius. If the percent error is 0.75%, how can you report the temperature of the sample using the absolute error and the actual temperature value in degrees Celsius?
Answers
Answer: T=16 ± 0.12 ° CA Aw
Step-by-step explanation:
A youth group went on trip to EXPO Dubai Travelling in two Vans. The number of people in each van and the total cost of admission are shown in the table. Find the adult price and student price of admission
Answers
Answer:
Refer to the attachment
Soo :
2a + 3b = 325
2a + 7b = 505 -
-4b = -180
4b = 180
b = 45
[tex] \: [/tex]
2a + 3b = 325
2a + 3(45) = 325
2a + 135 = 325
2a = 325 - 135
2a = 190
a = 95
Awnser this for brainliest
Answers
Distance traveled in one complete orbit of the sun (one “year”) would be around 17,562,300,000 miles
hope this helps