The value of all things needed to create the good or service

A line, y = mx + b, passes through the point (10, 3) and is parallel to the line 2x+5y=12.

slava [35]

We have been given that a line $y=mx+b$ passes through the point (10, 3) and is parallel to the line $2x+5y=12$ . We are asked to find the y-intercept of the line.

First of all we will rewrite our given equation in slope-intercept form as:

$2x-2x+5y=12-2x$

$5y=-2x+12$

$\frac{5y}{5}=-\frac{2}{5}x+\frac{12}{5}$

$y=-\frac{2}{5}x+\frac{12}{5}$

We know that slope of parallel lines is equal, so slope of parallel line to our given line would be $-\frac{2}{5}$ .

Now we will use slope-intercept form of equation to find y-intercept.

$y=mx+b$ , where,

m = Slope,

b = The y-intercept.

Let us substitute $m=-\frac{2}{5}$ and coordinates of point $(10,3)$ in above equation as:

$3=-\frac{2}{5}(10)+b$

$3=-2(2)+b$

$3=-4+b$

$3+4=-4+4+b$

$7=b$

Therefore, the y-intercept is 7 and our required equation would be $y=-\frac{2}{5}x+7$ .

5 0

3 years ago

Find 4 consecutive odd numbers such that twice the sum of the least 2 numbers is 40 less than three times the sum of the greates

ANTONII [103]

4 consecutive odd numbers....x, x + 2, x + 4, x + 6

2(x + x + 2) = 3(x + 4 + x + 6) - 40
2(2x + 2) = 3(2x + 10) - 40
4x + 4 = 6x + 30 - 40
4x + 4 = 6x - 10
4x - 6x = -10 - 4
-2x = - 14
x = -14/-2
x = 7

x + 2 = 7 + 2 = 9
x + 4 = 7 + 4 = 11
x + 6 = 7 + 6 = 13

ur numbers are : 7,9,11,13 <==

4 0

4 years ago

How do I factorise 2t^2 + 5t +2

alekssr [168]

$2t^2+5t+2\\\\a=2;\ b=5;\ c=2\\\\\Delta=b^2-4ac;\ if\ \Delta > 0\ then\ t_1=\frac{-b-\sqrt\Delta}{2a}\ and\ t_2=\frac{-b+\sqrt\Delta}{2a}\\\\\Delta=5^2-4\cdot2\cdot2=25-16=9;\ \sqrt\Delta=\sqrt9=3\\\\t_1=\frac{-5-3}{2\cdot2}=\frac{-8}{4}=-2;\ t_2=\frac{-5+3}{2\cdot2}=\frac{-2}{4}=-\frac{1}{2}\\\\2t^2+5t+2=2(x+2)(x+\frac{1}{2})$

5 0

3 years ago

15 PTSS EASY I PROMISE FOR BRAINIEST!!!The distance from Newtown to Oldtown on the highway is (6x2 + 2x – 2) miles. Using the ba

devlian [24]

For this case we have to subtract the two distances (subtract the polynomials) and the difference will be given by the shorter miles of the second route.

$6x ^ 2 + 2x-2- (5x ^ 2-8x-6) =$