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2 years ago

The graph of a linear relationship passes

Mathematics

1 answer:

Evgen [1.6K]2 years ago

3 0

Answer:

The equation of the linear relationship is y = 3x + 2 ⇒ B

Step-by-step explanation:

<em>To solve the question substitute the x in the equation by the x-coordinate of each point to find y, if y equals the y-coordinate of the point, then the point is on the graph of the equation</em>

∵ y = 2x + 3

→ Use the first point (0, 2)

∵ x = 0

→ Substitute x by 0 in the equation

∴ y = 2(0) + 3

∴ y = 0 + 3 = 3

∵ The y-coordinate is 2

∴ The point (0, 2) does not lie on the graph of the relationship

∴ The equation y = 2x + 3 doesn't represent the equation of the relationship

∵ y = 3x + 2

→ Use the first point (0, 2)

∵ x = 0

→ Substitute x by 0 in the equation

∴ y = 3(0) + 2

∴ y = 0 + 2 = 2

∵ The y-coordinate is 2

∴ The point (0, 2) lies on the graph of the relationship

→ Use the second point (1, 5)

∵ x = 1

→ Substitute x by 1 in the equation

∴ y = 3(1) + 2

∴ y = 3 + 2 = 5

∵ The y-coordinate is 5

∴ The point (1, 5) lies on the graph of the relationship

→ Use the third point (3, 11)

∵ x = 3

→ Substitute x by 3 in the equation

∴ y = 3(3) + 2

∴ y = 9 + 2 = 11

∵ The y-coordinate is 11

∴ The point (3, 11) lies on the graph of the relationship

→ Use the fourth point (2, 7)

∵ x = 2

→ Substitute x by 2 in the equation

∴ y = 3(2) + 2

∴ y = 6 + 2 = 8

∵ The y-coordinate is 7

∴ The point (2, 7) doesn't lie on the graph of the relationship

∴ The equation of the linear relationship is y = 3x + 2

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Answer:

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Step-by-step explanation:

Given:

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To find the total milkshakes sold.

Solution:

Let the total number of milkshakes sold on Monday be = $x$

Percentage of milkshakes with whipped cream added to them = 70%

Number of milk shakes with added whipped cream can be given as:

⇒ $70\% \textrm{ of the total number of milkshakes}$

⇒ $70\% x$

⇒ $\frac{70}{100}x$ [Representing percent in fraction form]

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We know that the number of milkshakes with whipped cream added to them = 210.

So, we have:

$0.7x=210$

Solving for $x$

Dividing both sides by 0.7

$\frac{0.7x}{0.7}=\frac{210}{0.7}$

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Solution:

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$$= \frac{1+\cos^2 x}{\sin^2x}$

Using the identity: $1=\cos ^{2}(x)+\sin ^{2}(x)$

$$=\frac{\cos ^{2}x+\cos ^{2}x+\sin ^{2}x}{\sin ^{2}x}$

$$=\frac{\sin ^{2}x+2 \cos ^{2}x}{\sin ^{2}x}$ ------------ (1)

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Using the identity: $\cot (x)=\frac{\cos (x)}{\sin (x)}$

$$=1+2\left(\frac{\cos x}{\sin x}\right)^{2}$

$$=1+2\frac{\cos^{2} x}{\sin^{2} x}$

$$=\frac{\sin^2 x + 2\cos^{2} x}{\sin^2 x}$ ------------ (2)

Equation (1) = Equation (2)

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Hence proved.

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