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

In The Diagram Below, \overline{ST} ST Is Parallel To \overline{PQ} PQ. If STST Is 55 More Than QTQT,

Answers

Answer 1

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


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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

1/216×(27x³-8y³)

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Answer:

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Step-by-step explanation:

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Answers

Answer: -6, 3

[] Our two integers will be x and y

        With this in mind,

                 x + y = -3

                 x * y = -18

[] Let's think about the factors of -18

        Then we will think about which ones could add up to 3

                 1 & 18, 2 & 9, 3 & 6 are factors of 18 (one being negative results in -18)

                 Well 1 and 18 cannot make 3, same for 2 and 9, that leaves us with 3 and 6.

[] Last, we will test

        You can see our test shows this solution works!

                 -6 + 3 = -3

                 -6 * 3 = -18

Have a nice day!

  I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

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Step-by-step explanation:

Answer:

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Step-by-step explanation:

At a certain high school, 38 out of 108 students surveyed have a pet at home. If there are 2,000 students in the school, estimate the number of students in the school who have a pet at home.

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Answer: About 703-704 students.
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Francis graphs the system of equations to determine its solution.


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Enter your answer by filling in the boxes.

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Answer:

Step-by-step explanation:

3x+2y=12   x= −2/ 3 y+4

3x-y=3    x= 1 /3 y+1

i hope this helps in anyway :/

The solution of the system of linear equations 3x + 2y = 12 and 3x − y = 3 is (x = 2, y = 3)

What is a Linear Equation?

If it is written in the form of ax + by + c = 0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero.

Given that the system of linear equations;

3x + 2y = 12 and 3x − y = 3 is

Solving the equations by elimination, we get

x = 2 and y = 3

Hence, The solution of the system of linear equations 3x + 2y = 12 and 3x − y = 3 is (x = 2, y = 3)

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Answer:

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Step-by-step explanation:

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Answers

Answer:

[tex]y = - \frac{4}{3} x + 3[/tex]

Step-by-step explanation:

slope-intercept form

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Answer:

Step-by-step explanation:

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Answers

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Step-by-step explanation:

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12x²y³ and 24xy²

The factor of the expression 12x²y³ is given as,

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Nonsense Answer = Report
Innocent Answer but no Answer = Report
Answer with Solution = Heart, 5 Star, and Brainliest

Answers

Answer:

A = 47

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Step-by-step explanation:

Let the two consecutive odd integers be A and B

We know that B = A + 2, and that A is odd.

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Use this last expression for B in the first equation:

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2A = 94

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B must therefore be 47 + 2 = 49

Check:

1)  A + 2 = B?  YES

2)  3A - 92= B?

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3) Are they both odd consecutive integers?  YES

     

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Answers

Answer:

x = 18 and x = 30

Step-by-step explanation:

The 3 angles lie on a straight line and sum to 180° , that is

90 + x + 4x = 180

90 + 5x = 180 ( subtract 90 from both sides )

5x = 90 ( divide both sides by 5 )

x = 18

-------------------------------------

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Answer:

Using the slope-intercept form, the slope is 4 4 .

Answer: Using the slope-intercept form, the slope is 4 4 .

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Answer(s):

Exact Form: x + 2 y − 3 z = 15 , 2 x − 2 z = 6 , 3 2 3

Mixed Number Form: x + 2 y − 3 z = 15 , 2 x − 2 z = 6 , 3 2 3

Improper Fraction Form: x + 2 y − 3 z = 15 , 2 x − 2 z = 6 , 11 3

Decimal Form: x + 2 y − 3 z = 15 , 2 x − 2 z = 6 , 3. ¯ 6

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Answer:

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The sale of cars in a particular month is decreased by 20% is $3060. What was the sale of cars before reduction.​

Answers

Answer:

$3672

Step-by-step explanation:

3060 x 20% = 612

612 + 3060 = 3672

Katrina wants to earn at least $600 this week in commission. What is the minimum amount she needs to sell in order to earn $600 if she earns a 7.5% commission on everything she sells? Round your answer to the nearest dollar if necessary.
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Answer:

$8000

Step-by-step explanation:

For every $1000 Katrina sells, she earns $75. This is becuase when we multiply what she sold by her commision price, we get what she made

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Answer:

6/12 or 1/2

Step-by-step explanation:

Multiply Across

Numerators 3 x 2 = 6

3 x 4 = 12

6/12

(or 1/2, simplified)

[tex] \\ \frac{3}{4} \times \frac{2}{3} [/tex]

[tex] \\ = { \cancel{ \frac{3}{4} }} \times { \cancel{ \frac{2}{3} }}[/tex]

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Answers

Answer:

1. 3.22 x 10^-2

2. 2.822 x 10^-1

3. 3.402 x 10^-12

Step-by-step explanation:

1. 0.00000000023 x 140000000

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= 3.22 x 10^-2

2. 830000 x 0.00000034

= 8.3 x 10^5 x 3.4 x 10^-7

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= 2.822 x 10^-1

3. 0.00000042 x 0.0000081

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simplify, (xy+yz)² - 2x²y²z² and find the value when x=-1, y=2 and z=1

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Simplify:

We have

(xy + yz)² - 2x²y²z

If,

x = -1, y = 2 and z = 1

Putting value:

(xy + yz)² - 2x²y²z

➡ (-1×2 + 2×1)² - 2×-1²×2²×1

➡ (-2 + 2)² - 2×1×4×1

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POINT out the correct ANSWER (Free_

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Answer:

40...................................

Answer:

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If given DG ≅ JK, which congruence postulate or theorem must you use before proving FG ≅ HK?

Answers

Answer:

  the correct answer choice is marked (AAS)

Step-by-step explanation:

All the corresponding angles are marked congruent. If one corresponding side is marked congruent, you can claim AAS or ASA congruence for the triangles: one side and two angles. Of these, AAS is among the answer choices.

You must use AAS to show triangle congruence before claiming FH ≅ HK by CPCTC.

the average attendance at a club fell by 7% in 2015. if 2030 fewer people went in 2015, how many went in 2014?​

Answers

Answer:

300

Step-by-step explanation:

All you had to be is take 2030 and divide by 7 percents

a
What is the equation of the line that passes through the point (3, 2) and has a slope
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Answers

Answer:

y=2/3x

Step-by-step explanation:

Hi there!

We want to find the equation of the line that passes through the point (3,2) and has a slope of 2/3

We can write the equation of the line in slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept

Since we are already given the slope, we can substitute it into the equation as m

y=2/3x+b

Now we need to find b

Since the equation passes through the point (3,2), we can plug its values into the equation to solve for b

Substitute 3 as x and 2 as y into the equation:

2=2/3(3)+b

Multiply

2=2+b

Subtract 2 from both sides

0=b

Substitute 0 as b into the equation

y=2/3x+0

Simplify:

y=2/3x

Hope this helps!

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