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]
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worth 30 pts pls helppp
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Answer:
Step-by-step explanation:
it is blank
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
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.
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f(1) = 4
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Answers
f(2)= f(2-1)+3
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PLS HELP AMSWER ANYONE PLS ILL GIVE BRAINLKEST THANKS
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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.
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Answers
Answer:4
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
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Answer:
Refer to the attachment
Soo :
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4b = 180
b = 45
[tex] \: [/tex]
2a + 3b = 325
2a + 3(45) = 325
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Answers
Answer: T=16 ± 0.12 ° CA Aw
Step-by-step explanation:
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The graph below shows the time it takes Michael to solve 30 multiplication
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Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
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Answer:
the answer shows in the picture, sorry, I tried to type it but it would come out different.
Step-by-step explanation:
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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.
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Step-by-step explanation:
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Answer:
4
Step-by-step explanation:
your answer is 4 because
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Step-by-step explanation:
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Answer:
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Answer:
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Answer:
A) monthly percentage rate = 1.45%
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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.
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Answer:
see below
Step-by-step explanation:
log sqrt5 (25) = y
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Step-by-step explanation:
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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.
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I hope this helps!
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
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convert cents to dollars (move decimole point over left 2 units)
25000 = 250 dollars
At the end of which day does Tyler have 2750 feet left to climb?
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A shark is 205 feet below sea level, it rises 80 feet towards sea level, then 25 points
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Captionless Image
Answers
Answer:
165 feet below sea level.
Step-by-step explanation:
205 - 80 = 125
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