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:

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Related Questions

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.
Explanation: 2000 • 38/108 = 703 19/27, and you can not have 19/27 of a person.

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Sorry, couldn't help in Q. 10

The question seems undefined or I haven't seen this question before.

Answer using scientific notation

0,00000000023 x 140000000
830000 x 0,00000034
0,00000042 x 0,0000081

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

= 2.3 x 10^-10 x 1.4 x 10^8

= 3.22 x 10^-2

2. 830000 x 0.00000034

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

= 0.2822

= 2.822 x 10^-1

3. 0.00000042 x 0.0000081

= 4.2 x 10^-7 x 8.1 x 10^-6

= 3.402 x 10^-12

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.
__________

Answers

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

If we want to find how much she needs to make to earn $600, we can divide 600 by 75. This gives us 8. So, she will need to sell $8000 in order to earn $600

1 point
10.) Tampa is about 275 miles from Tallahassee. How far about would they
be on a map with a scale of 1 in. = 15 mi?
20 inches
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O
19.24 inches
18.33 inches

Answers

Answer:

18.33

Step-by-step explanation:

its easy divide 275 ÷ 15 = [18.33]333333333333 the only number you need is [18.33]333333333333

and boom that simple you get your answer

Is s = 7 a solution to the inequality below s < 2 yes​

Answers

Answer:

No

Step-by-step explanation:

No, because s is less then 2. 7 is not less then 2.

‘Hope that helps! :)

Answer:

no

Step-by-step explanation:

s<2

s=7

7>2

A candy store sells 25 types of candy. Out of these 25 types, 12 contain chocolate. What percent of the candy types sold contain chocolate?

Answers

Answer:

Step-by-step explanation:

[tex]Percentage of chocolate candy = \dfrac{12}{25}*100\\\\ = 12*4\\\\[/tex]

= 48%

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

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.

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!2

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[tex]\large\red{┈──┈──┈──┈──┈──┈──┈──┈──┈─}[/tex]

The best option is B.

B. The rate of change of the cost of the taxi ride is 3.00 per minute.

Candace is considering trying the Spice Tea. What is the greatest number of 1-pound bags of Dark Roast coffee she can buy with
$52, if she also buys 0.5 pound of the Spice Tea and 2 pounds of the Morning Blend coffee?

Answers

Answer:

Step-by-step explanation:

69

Whoever answers in simplest form gets brainliest, 5 stars, and a thanks. Please help asap.

Answers

Answer:

18.725

Step-by-step explanation:

4 5/8 = (4*8 + 5) /8 = 37/8

10 7/10 = (10*10 + 7) / 10 = 107/10

3 2/5 = (3*5 + 2) / 5 = 17/5

lcm of 8, 10, 5 is 40

37/8 + 107/10 - 17/5

= (37*5 + 107*4 - 17*8) / 40

= (185 + 428 + 136) / 40

= 749/40

= 18.725

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

Find two consecutive odd integers such that thrice the smaller is 92 more than the larger
Nonsense Answer = Report
Innocent Answer but no Answer = Report
Answer with Solution = Heart, 5 Star, and Brainliest

Answers

Answer:

A = 47

B = 49

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.

We are also told that

3A - 92= B

Use this last expression for B in the first equation:

B = A + 2

3A - 92 = A + 2

2A = 94

A = 47

B must therefore be 47 + 2 = 49

Check:

1)  A + 2 = B?  YES

2)  3A - 92= B?

    3*47 - 92 = 49?

      141 - 92 = 49   YES

3) Are they both odd consecutive integers?  YES

     

A = 47

B = 49

the greatest common factor of 12x^2y^3 and 24xy^2 is

Answers

Answer:  (12xy^2)

Step-by-step explanation:

12x^2y^3

(12xy^2)*(xy)

24xy^2

(12xy^2)*(2)

The greatest common factor of the expressions 12x²y³ and 24xy² will be 12xy².

What is the greatest common factor?

Simply said, it is the biggest common element. The highest consistent element in the above example is 15, making 15 the greatest common factor amongst 15, 30, and 105. The biggest chunk of the common factors is called the "Greatest Common Factor" (of two or more numbers).

The expressions are given below.

12x²y³ and 24xy²

The factor of the expression 12x²y³ is given as,

12x²y³ = 12 × x × x × y² × y

The factor of the expression 24xy² is given as,

24xy² = 2 × 12 × x × y²

The common factors in both expressions are 12, x, and y². Then the greatest common factor will be given as,

⇒ 12 × x × y²

⇒ 12xy²

The best normal component of the articulations 12x²y³ and 24xy² will be 12xy².

More about the greatest common factor link is given below.

https://brainly.com/question/11221202

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Answers

Answer:

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3-0.72=3.72. add this decimal number to the whole number .final answer is 3.72

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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^∇^)

- Heather

Keith spent $8 on tomatoes. How many did he get? ​

Answers

Answer:

its got 6

Step-by-step explanation:

I REALLY DONT KNOW

Answer:

Step-by-step explanation:

Let t be the unit cost of the tomatoes:  e. g., t = $1.25/lb.

If Keith spent $8 on tomatoes, the number he bought would then be

   $8

------------- = 6.4 lb of tomatoes

$1.25/lb

Of course he couldn't buy 0.4 tomato, but this method of calculating how many tomatoes he could buy theoreticallyl is correct.

The general formula would be

   $8

------------   and the end result would be the number of pounds Keith could

  $t / lb                               buy for $8.

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!

POINT out the correct ANSWER (Free_

You get 35 points for free by answering one question
How many points do you get by answering this question?

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Answer:

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

Answer:

35 points because you said so O-O

HEYOOOOOO, HELLOOOO, PLEASE LOOK HERE, HELP NEEDED, LIKE NOW LOLOLOL Factor this expression completely, then place the factors in the proper location on the grid.

1/8 x^3 - 1/27 y^3

Answers

Answer:

1/8x³- 1/27y³

Step-by-step explanation:

1/216×(27x³-8y³)

1/216×(3x-2y)×(9x²+6xy+4y²)

1/216×(3x-2y)×(9x²+6xy +4y²)

hey can someone help with my assignment worth 80% of my grades

Answers

Answer:

Honestly the intercept should be on the axis

Step-by-step explanation:

Answer:

You didn't helped me with my question so no

Step-by-step explanation:

When a fish is selected at random from a tank, the probability that it has a green tail is
0.48, the probability that it has red fins is 0.28, and the probability that it has both a
green tail and red fins is 0.22. What is the probability that the selected fish will not have
a red fin or a green tail?
O 98%
O 2%
O 54%
O 46%

Answers

Answer:

I think the answer to your question is 2%

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

plz answer this fast plz u will give you brainly plz help me fast only 5min left to answer​

Answers

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

➡ (0)² - 8

➡ 0 - 8 = -8,answer

HELPPPPPPP

Find the value of x for both

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

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

The 2 angles are corresponding and congruent , then

x = [tex]\frac{1}{2}[/tex] x + 15 ( multiply through by 2 to clear the fraction )

2x = x + 30 ( subtract x from both sides )

x = 30

Answer:

1. x=18    2. x=30

Step-by-step explanation:

For 1. the equation would be x+4x =90 as it is a 90 degree angle

So 5x=90 then x = 18

For 2. The 2 angles are the same so we set them equal to each other

x=1/2x+15

2x=x+30

x=30

x+2y - 3z =15. 2x – 2z=6 x = 3. 2/3)-22 i dont know this answer pls help me???

Answers

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

Hope this helps, have a nice day/night! :D

What would the slope of a line perpendicular to y=-4x+5 equal?

Answers

Answer:

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

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

Explanation: so your answer is 4 4.

8x+6y=18
Put the following equation of a line into slope-intercept form, simplifying all fractions.


Answers

Answer:

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

Step-by-step explanation:

slope-intercept form

y= mx +c, where m is the slope and c is the y-intercept.

8x +6y= 18

Move everything that is not a y term to the right side of the equation:

6y= -8x +18

Divide both sides by 6 so that the coefficient of y is 1:

[tex]y = - \frac{8}{6} x + \frac{18}{6} [/tex]

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

Francis graphs the system of equations to determine its solution.


3x+2y=12
3x−y=3


What is the correct solution?


Enter your answer by filling in the boxes.

Answers

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)

For more reference on Linear Equation, click;

https://brainly.com/question/13738061

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what is 3/4 x 2/3 as a fraction

Answers

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]

[tex] \\ = \frac{1}{2} [/tex]

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