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2 years ago

Solve the system of equations. It is an order pair.......... Remember to SHOW

Mathematics

2 answers:

lisabon 2012 [21]2 years ago

5 0

-3x + 2y = -3
4x - y = -1

2(4x - y = -1)

-3x +2y = -3
8x -2y = -2

-5x = -5
/-5

X = 1

Svetllana [295]2 years ago

5 0

Answer:

x = -1, y = -3

Step-by-step explanation:

Let's start by solving -3x + 2y = -3 for x.

-3x + 2y = -3

Subtract 2y from both sides of the equation.

-3x = -2y - 3

Divide both sides by -3.

x = -1/3(-2y - 3)

Multiply -1/3 by -2y - 3.

x = 2/3y + 1

Substitute 2/3y + 1 for x in 4x - y = -1

4(2/3y + 1) - y = -1

Multiply 4 by 2/3y + 1.

8/3y + 4 - y = -1

Add 8/3y to -y.

5/3y + 4 = -1

Subtract 4 from both sides of the equation.

5/3y = -5

Multiply both sides by 3/5.

y = -3

Substitute -3 for y in x = 2/3y + 1. Because the resulting equation contains only one variable, you can solve for x directly.

x = 2/3(-3) + 1

Multiply 2/3 by -3.

x = -2 + 1

Add 1 to -2.

x = -1

The system is now solved. x = -1, and y = -3.

Work check:

-3(-1) + 2(-3) = -3

3 + (-6) = -3 is true.

4(-1) - (-3) = -1

-4 - (-3) = -1

-4 + 3 = -1 is true.

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Which of the following could be the ratio of the length of the longer leg of a 30-60-90 triangle to the length of its hypotenuse

Aliun [14]

Answer:

Option C is correct.

Ratio of longer leg to hypotenuse is; $\sqrt{3} : 2$

Step-by-step explanation:

This is the special right angle triangle 30°-60°-90° as shown below in the figure.

The side opposite the 30° angle is always the shortest because 30 degrees is the smallest angle.

The side opposite the 60° angle will be the longer leg, because 60 degrees is the mid-sized degree angle in this triangle.

Finally , the side opposite the 90° angle will always be the largest side(Hypotenuse) because 90 degrees is the largest angle.

In 30°−60°−90° right triangle,

the length of the hypotenuse is twice the length of the shorter leg,also
the length of the longer leg is $\sqrt{3}$ times the length of the shorter leg.

Then:

the sides are in proportion i.e, $1:\sqrt{3} :2$

Therefore, the ratio of the length of the longer leg to the length of its hypotenuse is: $\sqrt{3} : 2$

7 0

3 years ago

Read 2 more answers

A soft-drink machine at a steakhouse is regulated so that the amount of drink dispensed is normally distributed with a mean of 2

AnnZ [28]

Answer:

$z=\frac{203-200}{\frac{15}{\sqrt{9}}}=0.6$

$p_v =P(z>0.6)=0.274$

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can't conclude that the true mean is not significantly higher than 200 at 5% of signficance.

Step-by-step explanation:

Data given and notation

$\bar X=203$ represent the mean height for the sample

$\sigma=15$ represent the population standard deviation

$n=9$ sample size

$\mu_o =200$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is higher than 200, the system of hypothesis would be:

Null hypothesis: $\mu \leq 200$

Alternative hypothesis: $\mu > 20$

If we analyze the size for the sample is < 30 but we know the population deviation so is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$z=\frac{203-200}{\frac{15}{\sqrt{9}}}=0.6$

P-value

Since is a one sided test the p value would be:

$p_v =P(z>0.6)=0.274$

Conclusion

8 0

3 years ago

An angle measures 29° . what is the measure of its complement?

Olenka [21]

Complementary angles add up to 90 so 90-29=the complement, which is 61.