In the diagram below, TU is parallel to QR. If TU is 6 more than Q T, T S=12, and Q R=18, find the length of QT. Figures are not necessarily drawn to scale. State your answer in simplest radical form, if necessary.
Answers
The value of the missing side QT using the similar triangles concept is;
QT = 6
How to solve similar triangles?We are given;
TU is parallel to QR.
TS = 12
QR = 18
Now, TU is 6 more than QT, Thus;
TU = QT + 6
From the concept of similar triangles, we can say that;
QS/TS = QR/TU
Plugging in the relevant values gives us;
(12 + QT)/12 = 18/(QT + 6)
(12 + QT)(QT + 6) = 18*12
QT² + 18QT + 72 - 216 = 0
QT² + 18QT - 144 = 0
Solving this using online quadratic equation calculator gives;
QT = 6
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Related Questions
Choose the function that represents the data in the table.
Answers
Answer:
f(x)= 2x- 3
Step-by-step explanation:
f(2) = 2(2) -3
f(2) = 1
I hope it helps.
What's the difference between a whole, integer, rational, and irrational number?
Answers
Integers are all negative numbers, 0, and all positive numbers.
Rational numbers are numbers including whole numbers, natural numbers, and integers.
Irrational numbers are all numbers that aren’t Rational numbers, like 3.141596...
I NEED HELP ASAP PLEASEEEE THANK YOUU.
Answer each of the following questions. However, you should show all steps
to illustrate the process that you used to get your results.
1). Bill likes to walk his dog on the sidewalk that goes around the edge of the
city park. The park is a square and each side has a length of 500 feet.
Approximately, how many times does Bill need to walk around the park in
order to complete a 5-mile walk?
2). Jamie is doing some baking. He needs exactly 2 cups of sugar for his
recipe. When he looks in his utensil drawer, though, he can only find a 1-
tablespoon measuring spoon. Jamie knows that that there are 2 tablespoons
in 1 ounce and 8 ounces in 1 cup. How many tablespoons of sugar will Jamie
need for his recipe?
3)Erin is moving into a new house and has rented a moving truck to haul her belongings from the old house to the new house. During the trip from the old house to the new house, she had to cross a bridge that has a 10-ton weight limit. She knows that the moving truck has an empty weight of 12600 pounds and she knows that her belongings weigh approximately 6000 pounds. Is it safe for Erin to cross the bridge in the moving truck? Justify your answer.
4) how many liters of a fluid can be contained in a 5 gallon bucket?
Answers
1) 14 times to complete a 5-mile walk. 2) 8 tablespoons of sugar Since 2 tablespoons make up 1 ounce and 8 ounces make up 1 cup 3) Since her weight is less than the bridge's weight limit of 10 tons, it is safe for Erin 4) One gallon is equal to 3.785 liters, so 5 gallons is equal to:18.925 liters fluid
what is weight limit ?
A weight limit is the maximum weight that is allowed for a particular object, structure, vehicle, or mode of transportation, beyond which it may not be safe or legal to operate.
what is fluid?
In general, fluid is any substance that can flow and take the shape of its container. Fluids can be gases or liquids, and they are distinguished from solids by their ability to flow and lack of resistance to shear stress.
In the given question,
1) To determine how many times Bill needs to walk around the park to complete a 5-mile walk, we need to first find the total distance around the park. Since the park is a square with sides of 500 feet, the total distance around the park is:
4 x 500 feet = 2000 feet
2000 feet / 5280 feet/mile = 0.3788 miles
To complete a 5-mile walk, Bill would need to walk:
5 miles / 0.3788 miles per park loop = 13.199 park loops
Rounding up to the nearest whole number, Bill would need to walk around the park approximately 14 times to complete a 5-mile walk.
2) Since 2 tablespoons make up 1 ounce and 8 ounces make up 1 cup, we can convert tablespoons to cups as follows:
2 tablespoons/1 ounce x 1 cup/8 ounces = 0.25 cups/tablespoon
Therefore, Jamie would need:
2 cups / 0.25 cups/tablespoon = 8 tablespoons of sugar
3) To determine if it is safe for Erin to cross the bridge in the moving truck, we need to calculate the total weight of the truck and her belongings. Since 1 ton is equal to 2000 pounds, the weight of the moving truck and her belongings in tons is:
(12600 pounds + 6000 pounds) / 2000 pounds/ton = 9.3 tons
Since this weight is less than the bridge's weight limit of 10 tons, it is safe for Erin to cross the bridge in the moving truck.
4) One gallon is equal to 3.785 liters, so 5 gallons is equal to:
gallons x 3.785 liters/gallon = 18.925 liters
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The radius of a circle is 18 millimeters. What is the circle's area?
Answers
Area = π × ( radius )^2
Area = π × ( 18 )^2
Area = π × 324
Area = 324 π mm^2
If you get this you are a critical thinker.
I enter the garden.
There are 34 people.
You kill 30.
How many people are in the garden.
Good luck!
If you get it correct your answer will be deleted and l will message you to continue the game.
Don't play if you are not going to continue party poopers!
I won against Lisa Swensrud
Answers
Answer:
5
Step-by-step explanation:
Because when you walk in there is now 35 people 35 - 30 = 5
There are 34 people in the garden.
In order to answer the question, you've to think critically, it should be noted that even if 30 people are killed, they are still in the garden.Also, the fact that you entered the garden still makes the total number 34. Therefore, in this situation, the total number of people in the garden is 34.Read related ink on:
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Give the name of the parent function of y = 2[x-5]
Answers
The parent function of the transformed function is y = f ( x ) = x
Given data ,
Let the parent function be represented as f ( x )
Now , the value of f ( x ) is
The transformed function is represented as y
where y = 2 ( x - 5 )
On simplifying , we get
y = 2( x - 10 )
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
The function is shifted horizontally left by 10 units and multiplied by a scale factor of 2 units.
Hence , the parent function is f ( x ) = x
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A recipe uses 5 cups of flour for every 2 cups of sugar.
How much sugar is used for 1 cup of flour?
How much flour is used for 1 cup of sugar?
How much flour is used with 7 cups of sugar?
How much sugar is used with 6 cups of flour?
Answers
Answer:
2.5
Step-by-step explanation:
5 divided by 2= 2.5
Answer:
2.5
Step-by-step explanation:
SOLVE FOR VARIABLE PLEASE HELPP ASAP!!:)))
Answers
Answer:
x=24
Step-by-step explanation:
180-96=84
2x+x+12=84
3x+12=84
3x=72
x=24
Answer:
x=24°
Step-by-step explanation:
180-96=84
2x+x+12=84
3x+12=84
-12 -12
3x=72
3x/3=72/3
x=24
hopefully this helps :)
PLEASE HELP. ITS ALGEBRA
Answers
Answer: the y intercept is 330. the rate of change is -55. the domain is infinity since it is linear i'm pretty sure
Step-by-step explanation:
27 + 36
A.
9(3 + 4)
B.
(9 × 3)(9 × 4)
C.
(9 + 3)(9 + 4)
D.
9 + (3 × 4)
Answers
Answer:
It's A
Step-by-step explanation:
Using process of elimination B is wrong because even though you get 37 and 36 it multiplies them because of a lack of addition symbol. C is also wrong because it would turn out to be 12 x 13 which is larger than C so that's not it. in D 3x4 is 12 but it's added to 9 not multiplied so that's wrong which leaves you with A which is 9(3 + 4) = 63 and 27 + 36 = 63
Evaluate the expression
Answers
The exclamation mark at the end of any number indicates a factorial. You may be able to find this button in your calculator, though where it is varies.
A factorial is the product of the integer and all of the integers below it (greater than 0).
So, 9 factorial = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
6 factorial = 6 x 5 x 4 x 3 x 2 x 1
We can immediately eliminate the numbers that are the same on the top and bottom, since this is a fraction. That leaves us with the following multiplication problem to solve.
9 x 8 x 7 = 504
Hope this helps!
Rectangle 1 has length x and width y. Rectangle 2 is made by multiplying each dimension of Rectangle 1 by a factor of K, where k > 0. ( Answer Part A, Answer Part B, and Answer Part C. ( Will Mark Brainliest and do not repaste another students answer on Brainly or any other website or you'll be reported. Thank you.
Answers
\(\bold{\huge{\underline{\pink{ Solution }}}}\)
Given :- Rectangle 1 has length x and width yRectangle 2 is made by multiplying each dimensions of rectangle 1 by a factor of k Where, k > 0 Answer 1 :-Yes, The rectangle 1 and rectangle 2 are similar .
According to the similarity theorem :-If the ratio of length and breath of both the triangles are same then the given triangles are similar.Let's Understand the above theorem :-
The dimensions of rectangle 1 are x and y
Now,
Rectangle 2 is made by multiplying each dimensions of rectangle 1 by a factor of k .Let assume the value of K be 5
Therefore,
The dimensions of rectangle 2 are
\(\sf{ 5x \:and \:5y }\)
Now, The ratios of dimensions of both the rectangle :-
\(\bold{Rectangle 1 = Rectangle 2}\)\(\bold{\dfrac{ x }{y}}{\bold{ = }}{\bold{\dfrac{5x}{5y}}}\)
\(\bold{\blue{\dfrac{ x }{y}}}{\bold{\blue{ = }}}{\bold{\blue{\dfrac{x}{y}}}}\)
From above,
We can conclude that the ratios of both the rectangles are same
Hence , Both the rectangles are similar
Answer 2 :-Here,
We have to proof that, the
Perimeter of rectangle 2 = k(perimeter of rectangle 1 )In the previous questions, we have assume the value of k = 5
Therefore,According to the question,
Perimeter of rectangle 1
\(\sf{ = 2( length + Breath) }\)
\(\bold{\pink{= 2( x + y ) }}\)
Thus, The perimeter of rectangle 1
Perimeter of rectangle 2
\(\sf{ = 2( length + Breath) }\)
\(\sf{ = 2(5x + 5y) }\)
\(\sf{ = 2 × 5( x + y) }\)
\(\bold{\pink{= 10(x + y) }}\)
Thus, The perimeter of rectangle 2
According to the given condition :-
Perimeter of rectangle 2 = k( perimeter of rectangle 1 )Subsitute the required values,
\(\sf{ 2(x + y) = 10(x + y)}\)
\(\bold{\pink{2x + 2y = 5(2x + 2y) }}\)
From Above,
We can conclude that the, Perimeter of rectangle 2 is 5 times of perimeter of rectangle 1 and we assume the value of k = 5.
Hence, The perimeter of rectangle 2 is k times of rectangle 1
Answer 3 :Here,
We have to proof that ,
The area of rectangle 2 is k² times of the area of rectangle 1.That is,
Area of rectangle 1 = k²( Area of rectangle) Therefore,According to the question,
Area of rectangle 1
\(\sf{ = Length × Breath }\)
\(\sf{ = x × y }\)
\(\bold{\red{= xy }}\)
Area of rectangle 2
\(\sf{ = Length × Breath }\)
\(\sf{ = 5x × 5y }\)
\(\bold{\red{ = 25xy }}\)
According to the given condition :-
Area of rectangle 1 = k²( Area of rectangle)\(\sf{ xy = 25xy }\)
\(\bold{\red{xy = (5)²xy }}\)
From Above,
We can conclude that the, Area of rectangle 2 is (5)² times of area of rectangle 1 and we have assumed the value of k = 5
Hence, The Area of rectangle 2 is k times of rectangle 1 .
Which equation can be used to solve a – 5 = 30?
a = 30 • 5
a = 30 ÷ 5
a = 30 – 5
a = 30 + 5
Answers
Answer:
last one
a = 30 + 5
a - 5 = 30
Step-by-step explanation:
here is your answer
Find the equation of the line passing through (1, 5) and parallel to y = 3x – 1.
(20 POINTS!!!!!!!! SHOW YOUR WORK PLEASE!!!!)
Answers
Answer:
y = 3x - 1
y = 3x + 2
Step-by-step explanation:
Here Is The Right Lined Up Answer,
If You Expected It As A Photo Lined For An
Easier Review I Don't Have The 'Capture Photo' Button
But I Can Reuse/Repost, Here It Is:
There You Are, I Hope This Helped You Out
Don't Get Stressed You WILL Get 100%
By: LocalLesMara
Write the geometric sequence in function notation.
4,2,1,1/2,1/4,...
A) AX) = (2) - (1/4)x - 1
OB) Ax) = (2) - (1/2)x - 1
C) Ax) = (4) · (/4)x - 1
D AX) = (4) · (1/2)x - 1
Answers
Answer:
D
Step-by-step explanation:
PLEASE HELP!!! due today!!
Answers
Answer:
The maximum distance between supports for the beam to support a weight of 1600 lb is also 4.5 feet.
Step-by-step explanation:
We are given that weight P is inversely proportional to the distance D between the supports of the beam, and for this certain type of wooden beam, we have:
P = 7200/D
To find the distance between supports needed to carry 1600 lb, we can substitute P = 1600 in the above equation and solve for D:
1600 = 7200/D
D = 7200/1600
D = 4.5 feet
So the distance between supports needed to carry 1600 lb is 4.5 feet.
To find the maximum distance between supports for the beam to support a weight of 1600 lb, we can use the same equation and solve for P = 1600:
1600 = 7200/D
D = 7200/1600
D = 4.5 feet
Therefore, the maximum distance between supports for the beam to support a weight of 1600 lb is also 4.5 feet.
How many digits of PI are there exactly?
Answers
Answer:
100,000 Digits of Pi
Step-by-step explanation:
3.141592653589793238462643383279502884197169399375105820974944592307816406286 208998628034825342117067982148086513282306647093844609550582231725359....
Lengths of chord is 560cm and 640cm. The radius is 360cm. Work out length of the centre of the circle (O) to the crossing point of the chords.
Answers
The length of the center of the circle is approximately 391.9 cm
What is the length of the center of the circleLet's call the point where the two chords intersect point P. To find the length of the center of the circle to point P, we need to find the distance between point O (the center of the circle) and point P.
To do this, we first need to find the distance from point O to each chord. We can use the Pythagorean theorem to do this. Let's call the midpoint of the first chord point A, and the midpoint of the second chord point B. Then:
OA = √((360 cm)^2 - (280 cm)^2) = 160√2 cm
OB = √((360 cm)^2 - (320 cm)^2) = 40√17 cm
Next, we need to find the distance from each midpoint (A and B) to point P. We can use the formula for the length of a chord that passes through the center of a circle:
AP = BP = √(2r^2 - d^2)
where r is the radius of the circle and d is the length of the chord. Then:
AP = BP = √(2(360 cm)^2 - (560 cm)^2) = 320√2= 320√(2) cm
Now we can use the Pythagorean theorem again to find the distance from point O to point P:
OP = sqrt(OA^2 - AP^2) = √(160√2 cm)^2 - (320√(2) cm)^2) ≈ 391.9 cm
Therefore, the length of the center of the circle to the crossing point of the chords is approximately 391.9 cm.
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Answer: 280cm
Step-by-step explanation:
Use some graph paper and draw the question scaling it down by 0.01.
5.6cm 6.4cm and the radius 3.6cm.
Then multiply the answer by 100.
This is one way to get the answer, but I am sure there are more and one way to get to the 280cm.
Good luck, and share your ideas.
What is the equation of the line that is parallel to the line defined by the equation y = 3x−7 and goes through the point (4, 2)?
Answers
Answer:
\(y-2=3(x-4)\)
Step-by-step explanation:
Pre-SolvingWe are given a line contains the point (4, 2).
We also know that the line is parallel to y= 3x - 7.
We want to write the equation of this line.
Parallel lines have the same slopes.
First, let's find the slope of y = 3x - 7.
3 is in the place of where m (the slope) is, so that means it is the slope of that line.
It is also the slope of the line whose equation we want to write.
The equation of the line can be written in three ways:
Slope-intercept form, which is y=mx+b, where m is the slope and b is the y-intercept. Standard form, which is ax+by=c, where a, b, and c are free integer coefficients. a and b cannot be 0, and a is usually non-negative as well. Point-slope form, which is \(y-y_1=m(x-x_1)\), where m is the slope and \((x_1, y_1)\) is a point.All of these ways are valid, but for this problem, let's write the equation in point-slope form, as it is the easiest.
SolvingSubstitute 3 as m in \(y-y_1=m(x-x_1)\).
\(y-y_1=3(x-x_1)\)
Now, substitute 4 as \(x_1\) and 2 as \(y_1\).
\(y-2=3(x-4)\)
Topic: parallel and perpendicular lines
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What is the area of the square that measures 3.1 m on each side
Answers
The area of the square with a side length of 3.1 meters is 9.61 square meters.
To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.
Area of a square = side length × side length
Substituting the given side length into the formula:
Area = 3.1 m × 3.1 m
To perform the calculation:
Area = 9.61 m²
It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.
Remember, to find the area of any square, you simply need to multiply the length of one side by itself.
The area of the square with a side length of 3.1 meters is 9.61 square meters.
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College level Trigonometry any help will do
Answers
The distance between both houses is: 3839.75 ft
How to use law of cosines?The Law of Cosines is simply a numerical formula that relates the side lengths and points of any triangle. It expresses that the square of any side of a triangle is equivalent to the number of squares of the other different sides short two times the result of those sides and the cosine of the point between them.
Numerically, the Law of Cosines can be communicated as:
c² = a² + b² - 2abcos(C),
where:
c is the length of the side inverse to the point C, and an and b are the lengths of the other different sides.
Using law of cosines, the length AB is:
AB = 50² + 100² - 2(50 * 100) * cos 30
AB = 3839.75 ft
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andy’s saving account pays 0.3% more interest then marty’s. martys account earns 200 in interest. how much does interest does andy’s account earn?
1. 200.60
2. 203.00
3. 206.00
4. 230.00
Answers
200.60 interest does andy’s account earn.
Let x be the amount of interest earned by Andy's account.
According to the problem, Andy's account earns 0.3% more interest than Marty's account, which means that Andy's account earns the same amount plus an additional 0.3% of that amount. Mathematically, we can express this as:
x = 200 + 0.3% of 200
Simplifying the right-hand side of the equation, we get:
x = 200 + 0.003 × 200
x = 200.60
Therefore, the answer is option 1: 200.60.
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Which of the following points( X,Y) lies on the graph of 8X + 2Y = 24
Answers
Step-by-step explanation:
don't see any points to pick from however the following would lie on the graph
(0,12)
(1,8)
(2,4)
(3,0)
(4,-4)
find the slope of the line passing through the points (8,7) and (8, -6)
Answers
Step-by-step explanation:
slope= ( y2-y1) / (x2-x1)
slope=(-6-7)/(8-8)
slope=(-13)/0
undifined slope
an infinite slope is any line which runs parallel to the y-axis
Explain how to use Pascal's Triangle to expand the binomial (3x-4y)^11
Answers
The expansion of (3x-4y)¹¹ using Pascal's Triangle is:
177147x¹¹ - 2598156x¹⁰y - 17321040x⁹y² - 69284160x⁸y³ - 184757760x⁷y⁴ - 344881152x⁶y⁵ - 458941536x⁵y⁶ - 437944320 x⁴y⁷ - 291962880x³y⁸ - 129761280x²y⁹ + 34603008xy¹⁰ - 4194304y¹¹.
What is Pascal's Triangle?The triangle-shaped array of integers known as Pascal's triangle has one at the top and one on each of its two sides. Every new number has a value equal to the sum of the two numbers above it and is located between two other numbers and underneath them. Pascal's triangle is a triangular array of binomial coefficients that appears in algebra, combinatorics, and probability theory.In algebra, a triangle-shaped grouping of integers known as Pascal's triangle provides the coefficients for the expansion of any binomial formula, such as (x + y)ⁿ. Although it is much older, it bears the name of the French mathematician Blaise Pascal from the 17th century.So, the expression is:
(3x-4y)¹¹Now, use Pascal's Triangle to expand as follows:
(Refer table attached below for expansion)Therefore, the expansion of (3x-4y)¹¹ using Pascal's Triangle is:
177147x¹¹ - 2598156x¹⁰y - 17321040x⁹y² - 69284160x⁸y³ - 184757760x⁷y⁴ - 344881152x⁶y⁵ - 458941536x⁵y⁶ - 437944320 x⁴y⁷ - 291962880x³y⁸ - 129761280x²y⁹ + 34603008xy¹⁰ - 4194304y¹¹.
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Valeria and Christina both want to run for class president. In order to appear on the ballot,
they must collect a certain number of signatures. So far, Valeria has 26 signatures and
Christina has 53. Now, Valeria is collecting signatures at a rate of 6 per day, whereas
Christina is collecting 3 signatures per day.
Assuming that their rates stay the same, the two will eventually collect the same number of
signatures. How many signatures will they both have at that time? How many days will it
take?
Answers
Answer:
10 days
Step-by-step explanation:
questions and answer choices attached to photo, please help ASAP :)
Answers
Answer:
D
Step-by-step explanation:
10 x 10 x 29 x .5 = 1,450
Jorge paid $9 for a book that was originally $12. What was the % discount for the book
Answers
Answer:
25%
Step-by-step explanation:
12=100%
3=25%
9=75%
i need help with this question!
Answers
Answer:
\((3b)^{8}\)
Step-by-step explanation:
N/A
Please hurry:)
Which of the following is equivalent to…
Answers
Answer:
D
Step-by-step explanation: