MATHEMATICS HIGH SCHOOL

The line y =3x-5 meet x-axis at the point M. The line 3y+2x=2 meets y-axis at point N. Find the equation of the line joining M and N in the form ax + by + c = 0 where: a,b,c are integers.

Answers

Answer 1

Answer:

Answer-

The line equation is,

$\boxed{\boxed{6x+15y-10=0}}$

Solution-

The line $y =3x-5$ meets x-axis at the point M, i.e M is the x-intercept of this line. At the x-intercept y=0, so

$\Rightarrow 0 =3x-5$

$\Rightarrow 3x=5$

$\Rightarrow x=(5)/(3)$

So, coordinate of M is $((5)/(3),\ 0)$

The line $3y+2x=2$ meets y-axis at point N, i.e N is the y-intercept of this line. At the y-intercept x=0, so

$\Rightarrow 3y+2(0)=2$

$\Rightarrow 3y=2$

$\Rightarrow y=(2)/(3)$

So, coordinate of N is $(0,\ (2)/(3))$

The line joining M and N can be found out by applying two point formula of straight line,

$\Rightarrow (y-y_1)/(y_2-y_1)=(x-x_1)/(x_2-x_1)$

$\Rightarrow (y-0)/((2)/(3)-0)=(x-(5)/(3))/(0-(5)/(3))$

$\Rightarrow (y)/((2)/(3))=(x-(5)/(3))/(-(5)/(3))$

$\Rightarrow -(5)/(3)y=(2)/(3)(x-(5)/(3))$

$\Rightarrow -5y=2(x-(5)/(3))$

$\Rightarrow -5y=2x-(10)/(3)$

$\Rightarrow 2x+5y-(10)/(3)=0$

As it is given that all the coefficients are integers, so multiplying with 3

$\Rightarrow 6x+15y-10=0$

Answer 2

Answer:

Solution: As given line y =3x-5 meet x-axis at the point M.

On x axis y coordinate is zero.

Put y =0 in above equation, we get →x = 5/3

∴ Coordinate of M is (5/3,0).

As, also given , line 3y+2x=2 meets y-axis at point N.

On y axis , x coordinate is zero.

Substituting , x=0 in above equation, gives y =2/3.

Coordinate of point N is (0,2/3).

Equation of line passing through two points (a,b) and (p,q) is given by

→ $(y-b)/(x-a) =(q-b)/(p-a)$

Or as X intercept = 5/3, and Y intercept = 2/3

Equation of line in intercept form is → $(x)/(a) + (y)/(b) =1$ , where a and b is X intercept and y intercept respectively.

So, line passing through (5/3,0) and (0,2/3) is given by

→ $(x)/((5)/(3)) + (y)/((2)/(3))=1$

→ $(3x)/(5) + (3y)/(2) =1$

→ 6 x + 15 y =10 [Taking LCM of 5 and 2 which is 10]

→ 6 x + 15 y -10=0, which is equation of the line joining M and N in the form ax + by + c = 0 where: a,b,c are integers.

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The area of a rectangle is 77 yd2, and the length of the rectangle is 3 yd more than twice the width find the dimensions of the rectangle

Answers

Let the width be x.

Length is 3 more than twice the width = 2x + 3

Area = x*(2x + 3)

x*(2x + 3) = 77

2x² + 3x = 77

2x² + 3x - 77 = 0 This is a quadratic equation. Solve by factorization.

Multiply first and last coefficients: 2*-77 = -154

We look for two numbers that multiply to give -154, and add to give the middle coefficient +3

Those two numbers are 14 and -11.

Check: 14*-11 = -154 14 + -11 = 14 - 11 = +3

We replace the middle term of +3x in the quadratic expression with 14x -11x

2x² + 3x - 77 = 0

2x² + 14x -11x - 77 = 0

2x(x + 7) - 11(x + 7) = 0

(2x - 11)(x + 7) = 0

2x - 11 = 0 or x + 7 = 0

2x = 0 + 11 x = 0 - 7

2x = 11 x = -7

x = 11/2 = 5.5

The solutions are x = -7 or 5.5.

Since we are solving for length of rectangle, x can't be negative. So we do away with x = -7.

x = 5.5 is the only valid solution.

Recall width = x = 5.5,
Length = 2x + 3 = 2*5.5 + 3 = 11 + 3 = 14

Therefore length = 14 yards, and width = 5.5 yards.

PLEASE HELP AND PLEASE DONT GUESS!!!!Sharon has some one-dollar bills and some five-dollar bills. She has 14 bills. The value of the bills is $30. Solve a system of equations using elimination to find how many of each kind of bill she has.
A. 4 five-dollar bills, 10 one-dollar bills
B. 3 five-dollar bills, 15 one-dollar bills
C. 5 five-dollar bills, 5 one-dollar bills
D. 5 five-dollar bills, 9 one-dollar bills

Answers

the answer is A
cause in the question says Sharon has 14 bills . and the whole amount is 30$ so . the only answer that is correct is A . you may think D is correct too , but you should notice that the sum of the bills is not 30 $

Please help me !! Answer both correctly for a brainliest and also a thanks ! Don't answer if you don't know it .

Answers

1. Exponential
2000 times 2= 4000 (60)
4000 times 2= 8000 (120)
8000 times 2= 16000 (180)
16000 times 2= 32000 (240)
2. pull a 2x out of everything
answer is b

Attached it how i did it!
~Good Luck~!

What is the least common denominator of 1/3 and 5/11? 25 points

Answers

The leas common denominator is 33

The solution of the equation 2d - 6 = 5 is _____.

Answers

If you would like to solve the equation 2 * d - 6 = 5, you can do this using the following steps:

2 * d - 6 = 5
2 * d = 5 + 6
2 * d = 11 /2
d = 11/2
d = 5 1/2

The correct result would be 5 1/2.

$2d-6=5\n\nAdd\ 6\ on\ both\ sides.\n\n2d=11\n\nDivide\ by\ 2\ on\ both\ sides.\n\nd= (11)/(2)\n\nd=5(1)/(2)$

$\sf\ Answer:\ {\boxed{d=5(1)/(2)}}$

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