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Elza [17]
3 years ago
12

The answer to find QS

Mathematics
2 answers:
weqwewe [10]3 years ago
7 0

Since R is the midmoint of QS that means that QR and RS are equal to each other. So first you need to find x. There are many different ways to set up the equation to solve for x, but I'll show you the easiest one:

QR+QS=RT+QR

(2x-4)+(2x-4)=(8x-43)+(2x-4)

Combine like terms:

4x-8=10x-47

Isolate Variable:

4x-8=10x-47

-4x -4x

6x-47=-8

Isolate Constant:

6x-47=-8

+47 +47

6x=39

Divide:

x=6.5

Check Your Answer:

(Plug in 6.5 as x)

(4(6.5)-8)=(8(6.5)-43)+(2(6.5)-4)

18=18

olganol [36]3 years ago
3 0

Answer:

The measure of QS is 68 units.

Step-by-step explanation:

Given information: R is midpoint of QS, RS=2x-4, ST=4x-1, and RT=8x-43.

We need to find the value of QS.

From the given figure it is clear that points Q, R, S and T are collinear.

RT=RS+ST

8x-43=(2x-4)+(4x-1)

On combining like terms.

8x-43=(2x+4x)+(-4-1)

8x-43=6x-5

Isolate variable terms.

8x-6x=43-5

2x=38

Divide both sides by 2.

x=19

The value of x is 19.

It is given that R is midpoint of QS. It means R divides the line QS in two equal parts.

QS=2(RS)

QS=2(2x-4)

Substitute x=19 in the above equation.

QS=2(2(19)-4)

QS=2(38-4)

QS=2(34)

QS=68

Therefore the measure of QS is 68 units.

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8 0
3 years ago
for what value of k, the line joining 3x-ky+7=0 is perpendicular to the line joining (4 ,3) and ( 5, -3).
Schach [20]

Answer:

  • k = 18

=========

<h2>Given</h2>

<h3>Line 1</h3>
  • 3x - ky + 7 = 0

<h3>Line 2</h3>
  • Passing through the points (4, 3) and (5, - 3)

<h2>To find</h2>

  • The value of k, if the lines are perpendicular

<h2>Solution</h2>

We know the perpendicular lines have opposite reciprocal slopes, that is the product of their slopes is - 1.

Find the slope of line 1 by converting the equation into slope-intercept from standard form:

<u><em>Info:</em></u>

  • <em>standard form is ⇒ ax + by + c = 0, </em>
  • <em>slope - intercept form is ⇒ y = mx + b, where m is the slope</em>

  • 3x - ky + 7 = 0
  • ky = 3x + 7
  • y = (3/k)x + 7/k

Its slope is 3/k.

Find the slope of line 2, using the slope formula:

  • m = (y₂ - y₁)/(x₂ - x₁) = (-3 - 3)/(5 - 4) = - 6/1 = - 6

We have both the slopes now. Find their product:

  • (3/k)*(- 6) = - 1
  • - 18/k = - 1
  • k = 18

So when k is 18, the lines are perpendicular.

4 0
2 years ago
Which line has a slope of 2 and goes through (2, 10)?
garik1379 [7]
Y= 2x+6
You just have to go back wards from what you have. You already know the slope is 2 and slope is the change is y over the change in x. 2=2/1
So every time you take away 1 from x, you’re going to take away 2 from y.
(2,10) will become (1,8) which will be come (0,6).
You know have your y intercept (6)
So the equation for the line is y=2x+6
3 0
3 years ago
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Taya2010 [7]

Answer:

y= 0.05x

Step-by-step explanation

7.50 divided by 150 = 0.05

11.00 divided by 220 = 0.05

12.50 divided by 250 = 0.05

13.75 divided by 275 = 0.05

So the answer is y= 0.05x

8 0
4 years ago
Read 2 more answers
Please help !! Solve –2.5x ≤ 25
lutik1710 [3]

Answer:

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Step-by-step explanation:

–2.5x ≤ 25

Divide each side by -2.5, remembering to flip the inequality

–2.5x/-2.5 ≥ 25 /-2.5

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