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schepotkina [342]
3 years ago
11

6(a)If the gradient of the straight line

Mathematics
1 answer:
tensa zangetsu [6.8K]3 years ago
5 0

Answer:

(i) k =1

(ii) y-intercept is 7

Step-by-step explanation:

<u>Given line:</u>

  • ky = kx + x + 7

<u>Divide all terms by k to get slope-intercept form of the line</u>

  • y = (1 + 1/k)x + 7/k

<u>Since the gradient (slope) of the line is 2:</u>

  • 1 + 1/k = 2
  • 1/k = 1
  • k = 1

<u>The equation is now:</u>

  • y = 2x + 7

<u>y - intercept is found when x = 0</u>

  • x = 0 ⇒
  • y = 2*0 + 7
  • y = 7

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Preeta’s book has 300 pages. Each day she reads 10 more pages than the day before. She finishes her book in 6 days. How many pag
Scilla [17]

Step-by-step explanation:

1. if the number of pages in the 1st day is 'x', then the 2d day - 'x+10', the 3d day - 'x+20', the 4th day - 'x+30', the 5th day - 'x+40' and the last day - 'x+50' pages;

2. if the sum of all the pages is 300, then it is possible to make up the equation:

x+x+10+x+20+x+30+x+40+x+50=300;

3. x=25, it means:

1st day - 25;

2d day - 35;

3d day - 45;

4th day - 55;

5th day - 65;

6th day - 75 pages.

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2 years ago
Solve the expression: 45x+-3(4-6)
joja [24]
45x+6 is the answer

Simply
Subtract the numbers
45x-3(4-6)
45x-3(-2)
Multiply the numbers
Solution
45x+6
5 0
3 years ago
Read 2 more answers
What are the two ways you can find the distance between points (X1,Y1) and (x2,y2) in the coordinate
igomit [66]

The first (and most typical) way to find distance of two points is by using the distance formula.

distance=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2  }

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3 years ago
(x-1)(x-3)(x+5)(x+7)=297
mihalych1998 [28]

First simplify the expression into polynomial form,

(x-1)(x-3)(x+5)(x+7)=297

x^4+8x^3-10x^2-104x+105=297

x^4+8x^3-10x^2-104x-192=0

Now factor into,

(x-4)(x+8)(x^2+4x+6)=0

Which means the solutions are,

x-4=0\implies\boxed{x_1=4}

x+8=0\implies\boxed{x_2=-8}

and then two complex solutions because determinant of the third factor D\lt0,

x^2+4x+6=0

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(x+2)^2=-2\implies\boxed{x_3=i\sqrt{2}-2},\boxed{x_4=-i\sqrt{2}-2}

Hope this helps :)

5 0
3 years ago
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The interior angle of a regular polygon is five times its corresponding exterior angle. Find the
tiny-mole [99]

Answer:

12

Step-by-step explanation:

Regular polygon is one in which each angle and sides is congruent.

Sum of all the exterior angles of any polygon is 360.

Sum of all the  interior angles of any polygon is (2n-4)*90

where is n is the no. of sides of polygon.

Let n be the no. of sides of polygon required

Therefore,

Sum of all the  interior angles of  polygon = (2n-4)*90

since no of sides of polygon is n

therefore, value of each  interior angles of the polygon = (2n-4)*90/n  (A)

Sum of all the exterior angles of any polygon = 360.

value of each  exterior angles of the polygon = 360/n  (B)

Given that

The interior angle of a regular polygon is five times its corresponding exterior angle   (c)

using the statement A, B and C

(2n-4)*90/n = 5*360/n

1/n is common on both side, hence it gets cancelled.

(2n-4)*90 = 5*360

=> (2n-4) = 5*360 /90 = 20

=> 2n = 20+4 = 24

=> n = 24/2 = 12.

the  number of sides of the polygon is 12

6 0
3 years ago
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