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rewona [7]
3 years ago
13

How do I solve these math problems

Mathematics
1 answer:
olchik [2.2K]3 years ago
6 0
Its simple. You collect like terms and put them on one side of the equation

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6(a)If the gradient of the straight line
tensa zangetsu [6.8K]

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>

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  • y = 2*0 + 7
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5 0
3 years ago
#11 i
Paraphin [41]

The area of a shape is the amount of space a shape can occupy, while the perimeter is the sum of its lengths.

  • <em>The perimeter is </em>18 + 3\sqrt 5 + 3\sqrt 2<em>units</em>
  • <em>The area of the sanctuary is 27 square units</em>

We have:

A = (5,7)\\B=(8, 7)\\C=(8, 1)\\D=( 1, 1)\\E=( 1, 4)\\F= ( 5,4)

<u>Perimeter</u>

See attachment for the layout of the sanctuary

BC = \sqrt{(8 - 8)^2 + (7 - 1)^2} = 6

EF = \sqrt{(1 - 5)^2 + (4 - 4)^2} = 4

FA = \sqrt{(5 - 5)^2 + (4 - 7)^2} = 3

From the attachment, the sides are

<em>AB, BF, FC, CD, DE and EA</em>

Start by calculating the length of each side using the following distance formula:

d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_2)^2}

So, we have:

AB = \sqrt{(5 - 8)^2 + (7 - 7)^2} = 3

BF = \sqrt{(8 - 5)^2 + (7 -1)^2} = \sqrt{45} = 3\sqrt 5

FC = \sqrt{(8 - 5)^2 + (1 -4)^2} = \sqrt{18} = 3\sqrt 2

CD = \sqrt{(8 - 1)^2 + (1 - 1)^2} = 7

DE = \sqrt{(1 - 1)^2 + (1 - 4)^2} = 3

EA = \sqrt{(1 - 5)^2 + (4 -7)^2} = 5

So, the perimeter (P) is:

P = AB + BF + FC + CD + DE + EA

P = 3 + 3\sqrt 5 + 3\sqrt 2 + 7 + 3 + 5

P = 18 + 3\sqrt 5 + 3\sqrt 2

<em>Hence, the perimeter is </em>18 + 3\sqrt 5 + 3\sqrt 2<em>units</em>

<u />

<u>Area</u>

To calculate the area, we need to divide the sanctuary into three.

  1. <em>Triangle ABF</em>
  2. <em>Triangle EFA</em>
  3. <em>Trapezium CDEF</em>

The area of ABF is:

Area = \frac 12 \times AB \times FA

Where:

AB = 3

FA = \sqrt{(5 - 5)^2 + (4 - 7)^2} = 3

Area = \frac 12 \times 3 \times 3

Area = \frac 92

The area of EFA is:

Area = \frac 12 \times EF \times FA

Where:

FA = 3

EF = \sqrt{(1 - 5)^2 + (4 - 4)^2} = 4

So:

Area = \frac 12 \times 4 \times 3

Area = 6

The area of CDEF is:

Area = \frac 12(CD + EF) \times DE

Where

CD = 7

EF = 4

DE = 3

So, we have:

Area = \frac 12 (7 + 4) \times 3

Area = \frac 12 \times 11 \times 3

Area = \frac {33}2

So, the area of the sanctuary is:

Area = \frac 92 + 6 + \frac {33}2

Area = \frac {9 +12 + 33}2

Area = \frac {54}2

Area = 27

<em>Hence, the area of the sanctuary is 27 square units</em>

Read more about areas and perimeters at:

brainly.com/question/11957651

8 0
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A quadratic equation of the form 0 = ax2 + bx + c has a discriminant value of 0. How many real number solutions does the equatio
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It is 3 though       ............
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