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3 years ago

(3,4) and (12,19) find the equation of the line that passes through it

Mathematics

1 answer:

harina [27]3 years ago

5 0

Answer:

The equation of the line will be:

$y=\frac{5}{3}x-1$

Step-by-step explanation:

Given the points

(3, 4)

(12, 9)

Finding the slope between (3, 4) and (12, 9)

$\left(x_1,\:y_1\right)=\left(3,\:4\right),\:\left(x_2,\:y_2\right)=\left(12,\:19\right)$

$\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{19-4}{12-3}$

$m=\frac{5}{3}$

The equation of the line can be obtained using the point-slope form of the equation of the line

$y-y_1=m\left(x-x_1\right)$

substituting the values m = 5/9 and the point (3, 4)

$y-4=\frac{5}{3}\left(x-3\right)$

$y-4+4=\frac{5}{3}\left(x-3\right)+4$

$y=\frac{5}{3}x-1$

Therefore, the equation of the line will be:

$y=\frac{5}{3}x-1$

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2 years ago

What is the solution to the equation 13.7y = 6.2y + 30?

il63 [147K]

Here, we are required to determine the solution to the equation: 13.7y = 6.2y + 30?

The solution to the equation is y = 7.5

The solution is thus,

13.7y = 6.2y + 30
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Therefore, y = 30/7.5 = 4

Therefore, y = 4 is the solution to the equation.

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3 years ago

A survey shows that 10% of the population is victimized by property crime each year. A random sample of 527 older citizens (65 y

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Answer:

The data provide sufficient evidence that older people are more likely to be victimized.

Step-by-step explanation:

H 0 : P = 0.10

H 1 : P > 0.10 (Right tailed test)

n = 527, P = 0.1235

The test statistics

x = P - p / $\sqrt{p*(1-p) / n}$

x = 0.1235 - 0.10 / $\sqrt{0.10 * 0.90 / 527}$

x = 0.0235 / $\sqrt{0.09 / 527}$

x = 0.0235 / $\sqrt{0.00017077798}$

x = 0.0235 / 0.0130682049264618

x = 1.798257689731729

x = 1.798

P value = [1 - p(Z > 1.7980] (Right tailed test)

P value = 0.036089

The P - Value is very small, so <u>reject H0</u>

Conclusion: The data provide sufficient evidence that older people are more likely to be victimized.

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3 years ago

Suppose the supply function for a certain item is given by S(q)= (q+6)2 and the demand funtion is given by D(q)= (1000)/(q+6).

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Step-by-step explanation: The equilibrium point on a demand and supply graph is the point at which demand equals supply. Better put, it is the point where the demand curve intersects the supply curve.

The supply function is given as

S(q) = (q + 6)^2

The demand function is given as

D(q) = 1000/(q + 6)

The equilibrium point therefore would be derived as

(q + 6)^2 = 1000/(q + 6)

Cross multiply and you have

(q + 6)^2 x (q + 6) = 1000

(q + 6 )^3 = 1000

Add the cube root sign to both sides of the equation

q + 6 = 10

Subtract 6 from both sides of the equation

q = 4

Therefore when q = 4, supply would be

S(q) = (4 + 6)^2

S(q) = 10^2

S(q) = 100

Also when q = 4, demand would be

D(q) = 1000/(4 + 6)

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