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Rus_ich [418]
1 year ago
10

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Find the gradient of the linear relation
Mathematics
2 answers:
vladimir1956 [14]1 year ago
8 0
  • 3y-5x=10

Isolate y

  • 3y=5x+10
  • y=5/3x+10/3

Compare to slope intercept form y=mx+b

Slope=m=5/3

kompoz [17]1 year ago
7 0

Answer:

\dfrac{5}{3}

Step-by-step explanation:

To find the gradient (slope) of the given <u>linear relation</u>, use <u>arithmetic operations</u> to isolate y:

Given relation:

3y-5x=10

Add 5x to both sides:

\implies 3y-5x+5x=10+5x

\implies 3y=5x+10

Divide both sides by 3:

\implies \dfrac{3y}{3}=\dfrac{5}{3}x+\dfrac{10}{3}

\implies y=\dfrac{5}{3}x+\dfrac{10}{3}

<u>Slope-intercept form of a linear equation</u>

y = mx+b

where:

  • m is the slope (gradient)
  • b is the y-intercept

Comparing the rewritten equation with the slope-intercept formula, the gradient (slope) of the given linear relation is ⁵/₃.

Learn more about linear equations here:

brainly.com/question/27317293

brainly.com/question/27781455

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The length of segment XY is 9 cm. Which statements regarding triangle XYZ are correct? Check all that apply.
Dominik [7]

<u>Answer-</u>

  • YZ = 9 cm
  • XZ=9\sqrt2
  • XZ is the longest segment in triangle XYZ.

<u>Solution-</u>

Triangle XYZ is a right angle triangle with ∠Y=90°

Triangle XYZ is also an isosceles triangle, as

∠X =45°= ∠Z

Therefore, triangle XYZ is a right angle isosceles triangle.

So,

XY = YZ = 9 cm

Applying Pythagoras theorem,

\Rightarrow XZ^2=XY^2+YZ^2\\\\\Rightarrow XZ^2=9^2+9^2\\\\\Rightarrow XZ^2=2\times 9^2\\\\\Rightarrow XZ=\sqrt{2\times 9^2}=9\sqrt2

In a right angle triangle, always the hypotenuse is the largest. So XZ is the longest segment in triangle XYZ.


6 0
3 years ago
Read 2 more answers
What is the distance between the points located at 7 and -1 1/2 on the number line?
Temka [501]

Answer:

8 1/2

Step-by-step explanation:

They are on opiate sids of zero so add the absolute values together to get  1/2

7 0
3 years ago
Given the points P(2,-1) and Q(-9,-6), what are the coordinates of the point on directed line segment PQ that partitions PQ in t
gayaneshka [121]

ANSWER

( -  \frac{23}{5} , - 4)

EXPLANATION

Given the points P(2,-1) and Q(-9,-6),the coordinates of the point that partition the directed line segment PQ in the ratio 3:2 is given by

x = \frac{ mx_2+nx_1}{m + n}

y= \frac{ my_2+ny_1}{m + n}

Where m=3 and n=2

x = \frac{ 3 ( - 9)+2(2)}{3+ 2}

x = \frac{  - 23}{5}

y= \frac{ 3( - 6)+2( - 1)}{3 + 2}

y= \frac{  - 20}{5}  =  - 4

The point is

( -  \frac{23}{5} , - 4)

4 0
3 years ago
Fractorise the following (a-b)²+(a-b)​
Lisa [10]

Step-by-step explanation:

taking common (a-b)

so we get the answer

5 0
3 years ago
Please help me, I don’t wanna fail..
balandron [24]
The answer is 8.7 cm
8 0
3 years ago
Read 2 more answers
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