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3 years ago

Solve the system 2x+y=-3 -2y=6+4x

Mathematics

1 answer:

ANEK [815]3 years ago

6 0

Answer:

Step-by-step explanation:

Write out the 2 equations:

2x + y = -3

-2y = 6+4x

-You then pick a variable that you want to solve for. I chose to solve for y because it would be a bit easier.

-2y = 6 + 4x

-Divide both sides by -2 to isolate the variable

(-2y) / -2 = (6 + 4x) / -2

-it comes out to y = -3 -2x

-Now that you have the y you can plug in the value into the second equation.

2x + y = -3 ---> 2x + (-3 -2x) = -3

This can be simplified to:

2x - 3 - 2x = -3

The 2x's cancel out because there is a +2x and a -2x. You are left with a

-3 = -3. If you add 3 to both sides of the equation you end up with 0 = 0, which can be simplified to just 0.

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3 years ago

Write the slope intercept form of the equation of the line through the given point with the given slope through (-2,5),slope-3/2

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3 years ago

On Saturday Keisha ran 2.758 kilometers. On Sunday she ran 1.78 kilometers. How Much farther did she run on Saturday than on Sun

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3 years ago

Read 2 more answers

Given f(x) = the quantity of 2x minus 2 divided by 4, solve for f−1(3).

spin [16.1K]

Given: f(x)=(2x-2)/4
find f^-1(3)?
we need to find the inverse of f(x), so
x=(2y-2)/4
2y-2=4x
y-1=2x
y=2x+1
so, then f^-1(x)=2x+1
f^-1(3)=2(3)+1
=6+1
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so, the answer is 7

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3 years ago

A random sample of 100 observations from a quantitative population produced a sample mean of 22.8 and a sample standard deviatio

natima [27]

Answer:

We conclude that the population mean is 24.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 24

Sample mean, $\bar{x}$ = 22.8

Sample size, n = 100

Alpha, α = 0.05

Sample standard deviation, s = 8.3

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 24\\H_A: \mu \neq 24$

We use Two-tailed z test to perform this hypothesis.

Formula:

$z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }$

Putting all the values, we have

$z_{stat} = \displaystyle\frac{22.8 - 24}{\frac{8.3}{\sqrt{100}} } = -1.44$

We calculate the p-value with the help of standard z table.

P-value = 0.1498

Since the p-value is greater than the significance level, we accept the null hypothesis. The population mean is 24.

Now, $z_{critical} \text{ at 0.05 level of significance } = \pm 1.96$

Since, the z-statistic lies in the acceptance region which is from -1.96 to +1.96, we accept the null hypothesis and conclude that the population mean is 24.

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3 years ago