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3 years ago

( x, y) satisfies both equations y+18=x(x-3) and x=y+6

Mathematics

1 answer:

antoniya [11.8K]3 years ago

3 0

Answer:

(- 2, - 8 ) , (6, 0 )

Step-by-step explanation:

y + 18 = x(x - 3) ← distribute

y + 18 = x² - 3x → (1)

x = y + 6 → (2)

Substitute x = y + 6 into (1)

y + 18 =(y + 6)² - 3(y + 6) ← expand parenthesis using FOIL

y + 18 = y² + 12y + 36 - 3y - 18

y + 18 = y² + 9y + 18 ( subtract y + 18 from both sides )

0 = y² + 8y = y(y + 8)

Equate each factor to zero and solve for y

y = 0

y + 8 = 0 ⇒ y = - 8

Substitute these values into (2) and evaluate for x

y = 0 : x = 0 + 6 = 6 ⇒ (6, 0 )

y = - 8 : x = - 8 + 6 = - 2 ⇒ (- 2, - 8 )

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A sociologist wants to determine if the life expectancy of people in africa is less than the life expectancy of people in asia.

Colt1911 [192]

Answer:

The sample statistics are attached.

First, we need to determine the hypothesis.

The null hypothesis should be: $H_{o} : u_{africa} \geq u_{asia}$ .

The alternative hypothesis should be: $H_{a}: u_{africa}$

The next step is about calculating the t statistics based on the samples. This t test will give the probability value or p-value, which determines if there's enough to reject the null hypothesis. The formula we need to use to find the t-value is: $t=\frac{x_{1}-x_{2} }{\sqrt{\frac{s_{1} ^{2} }{n_{1} } +\frac{s_{2} ^{2} }{n_{2} } } }$

Replacing all the values into the formula, we have:

$t=\frac{52.4-58.1}{\sqrt{\frac{(7.4)^{2} }{45}+\frac{(8.8)^{2} }{35} } } \\t=\frac{-5.7}{\sqrt{1.2+2.2} } =\frac{-5.7}{1.8} =-3.2$

Therefore, the t-value is -3.2.

Now, we using a level of significance of 0.01, and a degree of freedom (df) of 34, we use the t-table to find the p-value for this results. (df = N -1; in this case, we take the smaller sample, which is 35, giving us 34 of df).

Therefore, according to the table attached, the p-value is less than 0.01, which is less than our level of significance. This result means that the null hypothesis is rejected. In other words, there's enough evidence to say that the life expectancy of people in Africa is less than the life of expectancy of people in Asia.

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4 years ago

You pull horizontally on a 50-kg crate with a force of 450 n and the friction force on the crate is 250 n. the acceleration of t

natka813 [3]

Hello AljakeVillena!

$\huge \boxed{\mathfrak{Question} \downarrow}$

You pull horizontally on a 50-kg crate with a force of 450 n and the friction force on the crate is 250 n. the acceleration of the crate is ?

$\large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}$

Given,

mass of crate = 50 kg
Force you pull it with = 450 N
Frictional force = 250 N
Acceleration = ?

__________________

Let's first find the total force/net force acting on the crate. The total force will be :-

450 N - 250 N = 200 N.

We subtracted the forces because both the forces act on opposite directions.

__________________

Now, let's find the acceleration of the crate. To find the acceleration we must divide the net force by the mass. So,..

Acceleration = Force/mass
a = F/m
a = 200/50
a = 4 m/s²

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So, the acceleration of the crate is 4 m/s².

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Hope it'll help you!

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3 years ago

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Alona [7]

Answer:

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3 years ago

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serious [3.7K]

Answer:

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zalisa [80]

Answer:

Step-by-step explanation:

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1 year ago