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2 years ago

Solve the system using elimination. x + 2y = –6 3x + 8y = –20 (–4, –1) (–4, 4) (–1, –4) (3, 1)

Mathematics

2 answers:

Orlov [11]2 years ago

6 0

$x + 2y = - 6 > > > 3x = - 18 - 6y$
$- 18 - 6y + 8y = - 20 > > > 2y = - 2 > > y = - 1$
so x=4

LiRa [457]2 years ago

3 0

Answer: The required solution is x = -4 and y = -1.

Step-by-step explanation: We are given to solve the following system of equations by the method of Elimination :

$x+2y=-6~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\3x+8y=-20~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

Multiplying equation (i) by 3 , we have

$3(x+2y)=-6\times3\\\\\Rightarrow 3x+6y=-18~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)$

Subtracting equation (iii) from equation (ii), we get

$(3x+8y)-(3x+6y)=-20-(-18)\\\\\Rightarrow 2y=-20+18\\\\\Rightarrow 2y=-2\\\\\Rightarrow y=-\dfrac{2}{2}\\\\\Rightarrow y=-1.$

From equation (i), we get

$x+2\times(-1)=-6\\\\\Rightarrow x-2=-6\\\\\Rightarrow x=-6+2\\\\\Rightarrow x=-4.$

Thus, the required solution is x = -4 and y = -1.

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Your company has just taken out a 1-year installment loan for $72,500 at a nominal rate of 20.0% but with equal end-of-month pay

Mariulka [41]

Answer:

100% of the 2nd monthly payment go toward the repayment of principal.

Step-by-step explanation:

The loan taken is the Principal which is mentioned as $72,500 with interest at a nominal rate of 20%. Firstly, it is important to understand that nominal rate means <em>non-compounding </em>rate. Simply put will be a "<em>one-time charged" </em>rate on the loan. Since this is given as 20% of the Principal. It is calculated thus: $\frac{20}{100}$ × $\frac{72,500}{1}$ = $14,500. So the interest on the loan is $14,500. Added to the Principal the total amount to be paid back by the company becomes: $72,500 + $14,500 = $87,000. To pay back this amount at equal end-of-month installments in 1 year (12 months), we divide the total amount by 12. i.e $\frac{87000}{12}$ = $7250. This means, the monthly payment will be $7,250. Since the monthly payment pays only 10% of the initial principal $72,500. By the second month only 20% of the Principal would have been paid. So all of the monthly payment will go towards repaying the principal

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2 years ago

There are three choices of jellybeans - grape ,cherry and orange. if the probability of getting a grape is 3/10 and the probabil

muminat

When looking at probabilities, two ideas are always true.

1) Any probability is more than 0.

2) The sum of all the probabilites is 1.

Idea #2 works here. (For example, think of how a die has six things and the probability of each is 1/6. So 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 1.) Let G = the probability of grape, C = probability of cherry and O = the probability of orange. From Idea #2, G + C + O = 1. Since we know G and C, then

3/10 + 1/5 + O = 1.

3/10 + 2/10 + O = 1

5/10 + O = 1

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Thus, the probability of an orange jelly bean is 5/10 = 1/2.

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2 years ago

Complete the following multiplication exercises.

olga2289 [7]

43x7=301
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6x3=18
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30x3=90
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83x5=415
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29x4=116
761x9=6,849
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2 years ago

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Suppose that a jewelry store tracked the amount of emeralds they sold each week to more accurately estimate how many emeralds to

RUDIKE [14]

Answer:

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

And for this case the 95% confidence interval is given by (2.13; 2.37)

We have a point of estimate for the sample mean with this formula:

$\bar X = \frac{Upper+ Lower}{2}= \frac{3.37+2.13}{2}= 2.75$

And for the margin of error we have the following estimation:

$ME= \frac{Upper -Lower}{2}= \frac{3.37-2.13}{2}= 0.62$

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X$ represent the sample mean

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

And for this case the 95% confidence interval is given by (2.13; 2.37)

We have a point of estimate for the sample mean with this formula:

$\bar X = \frac{Upper+ Lower}{2}= \frac{3.37+2.13}{2}= 2.75$

And for the margin of error we have the following estimation:

$ME= \frac{Upper -Lower}{2}= \frac{3.37-2.13}{2}= 0.62$

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2 years ago

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Answer: x= 1/2k

Step-by-step explanation:

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2 years ago

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