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Lelechka [254]
3 years ago
14

2q-r=p, r=q-s, p=q+2r prove s=2r

Mathematics
1 answer:
kipiarov [429]3 years ago
8 0

Answer:

s=2r

Step-by-step explanation:

Solution:

Given;

2q-r=p

r=q-s

or,q=r+s

p=q+2r

To prove: s=2r

Now,

2q-r=p

or,2(r+s)-r=q+2r

or,2r+2s-r=r+s+2r

or,r+2s=3r+s

or,s=2r

PROVED

If you want any other solutions follow me

THANK YOU

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(03.01 MC)
vekshin1

Answer:

Option (1) will be the answer.

Step-by-step explanation:

Coordinates of the points A and B lying on the line f are (0, 2) and (2, 0) respectively.

Slope of the line f,

m_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}

m_{1}=\frac{2-0}{0-2}

m_{1}=-1

After dilation of line f by a scale factor of 2, coordinates of A' and B' will be,

Rule for dilation,

(x, y) → (kx, ky)

Where k = scale factor

A(0, 2) → A'(0, 4)

B(2, 0) → B'(4, 0)

Slope of line f',

m_{2}=\frac{0-4}{4-0}

m_{2}=-1

Since, m_{1}=m_{2}=-1

Therefore, both the lines f and f' will be parallel.

Option (1) will be the answer.

6 0
3 years ago
Which is the approximate solution for the system of equations 3x+4y=2 and 4x+y=-4
harina [27]

3x+4y=2\qquad\text{subtract 3x from both sides}\\\\4y=-3x+2\qquad\text{divide both sides by 4}\\\\y=-\dfrac{3}{4}x+\dfrac{2}{4}\to y=-\dfrac{3}{4}x+\dfrac{1}{2}\\\\for\ x=0\to y=-\dfrac{3}{4}(0)+\dfrac{1}{2}=0+\dfrac{1}{2}=\dfrac{1}{2}\to\left(0,\ \dfrac{1}{2}\right)\\\\for\ x=2\to y=-\dfrac{3}{4}(2)+\dfrac{1}{2}=-\dfrac{3}{2}+\dfrac{1}{2}=-\dfrac{2}{2}=-1\to(2,\ -1)\\--------------------------------\\

4x+y=-4\qquad\text{subtract 4x from both sides}\\\\y=-4x-4\\\\for\ x=0\to y=-4(0)-4=0-4=-4\to(0,\ -4)\\\\for\ x=-1\to y=-4(-1)-4=4-4=0\to(-1,\ 0)\\\\Answer:\ \boxed{A.\ (-1.4,\ 1.5)}

6 0
3 years ago
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Mariana [72]

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6 0
2 years ago
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What is the equation of the line in slope intercept form through (-5,-3) and (6,1) ?
erastovalidia [21]

y - y1 = m (x - x1)

where m is the slope and (x1 , y1) is the point given

m = (y2-y1)\(x2-x1)

we have  <span>(-5,-3) and (6,1)

so: m = (1- -3) / (6- -5) = (1+3)/(6+5) = 4/11

and the equation of the line is:
</span>y - y1 = m (x - x1)
y-1 = 4/11 (x-6)

simplify:

y = 4/11 x - 24/11 +1

y= \frac{4}{11} x -  \frac{13}{11}

I hope that helps!



8 0
3 years ago
Eduardo rides his bicycle for 6 hours. What was Eduardo's average speed if he rides a distance of 84 miles? Use the formula d =
german
D = r x t
replace the d with 84 and replace the t with 6 hours
divide 84 by 6 = 84/6
get the quotient 14
84 = 14 x 6
5 0
3 years ago
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