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3 years ago

Solve the following system of equations: −2x + y = 1 −4x + y = −1

2 answers:

6 0

Hello!

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

You can subtract these equations from each other to eliminate y

2x = 2

Divide both sides by 2

x = 1

Put this into one of the original equations

-2(1) + y = 1

Combine like terms

-2 + y = 1

Add 2 to both sides

y = 3

The answer is D) (1, 3)

Hope this helps!

Jlenok [28]3 years ago

3 0

Answer:

d. (1,3)

Step-by-step explanation:

We will use the substitution method to solve this system of linear equations with two unknowns.

First, we will have to choose any variable from some equation and clear it.

I will use the first equation, with the variable "y"

$-2x+y=1\\y=1+2x$

We will substitute this equation in the second equation. Every time we find the value of "y", let's replace.

$-4x+y=-1\\-4x+(1+2x)=-1$

We will solve this equation to find the value of "x"

$-4x+1+2x=-1\\-2x=-1+1\\-2x=-2\\x=\frac{-2}{-2} \\x=1$

Now, the found value of "x" will replace it in any of my two initial equations.

$-2(1)+y=1\\$

and we solve

$-2+y=1\\y=1+2\\y=3$

Thus, the result of this system of equations is

(1,3)

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Halloween Candy Halloween is Kelly's favorite holiday of the year! Based on experience, Kelly knows that on average, each house

LuckyWell [14K]

Using the <u>normal distribution and the central limit theorem</u>, it is found that there is an approximately 0% probability that the total number of candies Kelly will receive this year is smaller than last year.

Normal Probability Distribution

In a normal distribution with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

It measures how many standard deviations the measure is from the mean.
After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.
By the Central Limit Theorem, for n instances of a normal variable, the mean is $n\mu$ while the standard deviation is $s = \sigma\sqrt{n}$ .

In this problem:

Mean of 4 candies, hence $\mu = 4$ .
Standard deviation of 1.5 candies, hence $\sigma = 1.5$ .
She visited 35 houses, hence $n = 35, \mu = 35(4) = 140, s = 1.5\sqrt{4} = 3$

The probability is the <u>p-value of Z when X = 122</u>, hence:

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{122 - 140}{3}$

$Z = -6$

$Z = -6$ has a p-value of 0.

Approximately 0% probability that the total number of candies Kelly will receive this year is smaller than last year.

A similar problem is given at brainly.com/question/24663213

6 0

2 years ago

State the domain of the function.

boyakko [2]

Hi there! The domain of a function refers to the values that can be validly input for x. In laymen's terms, domain is the x-values that exist on a graph of the equation.

If we were to plug in y=-2x+5 into a calculator that shows an infinite graph, we would see that the line of the equation would extend both ways infinitely! This means that all real numbers can be inputs for x, because for every x value that exists there is a corresponding y value.

This means that D. All real numbers, is your answer.

Hope it helps! :)

6 0

3 years ago

I’m honestly done with math

rewona [7]

Answer:

15.

Step-by-step explanation:

8x - 10 = 110 (vertical angles are equal in measure).

8x - 10+ 10 = 110 + 10

8x = 120

x = 120 /8

x = 15.

3 0

3 years ago

PLEASE PEOPLE, HELP ME!! Geometry

Oksanka [162]

I use the sin rule to find the area

A=(1/2)a*b*sin(∡ab)

1) A=(1/2)*(AB)*(BC)*sin(∡B)
sin(∡B)=[2*A]/[(AB)*(BC)]

we know that
A=5√3
BC=4
AB=5
then

sin(∡B)=[2*5√3]/[(5)*(4)]=10√3/20=√3/2
(∡B)=arc sin (√3/2)= 60°

now i use the the Law of Cosines

c2 = a2 + b2 − 2ab cos(C)

AC²=AB²+BC²-2AB*BC*cos (∡B)

AC²=5²+4²-2*(5)*(4)*cos (60)----------- > 25+16-40*(1/2)=21

AC=√21= 4.58 cms

the answer part 1) is 4.58 cms

2) we know that

a/sinA=b/sin B=c/sinC

and

∡K=α

∡M=β

ME=b

then

b/sin(α)=KE/sin(β)=KM/sin(180-(α+β))

KE=b*sin(β)/sin(α)

A=(1/2)*(ME)*(KE)*sin(180-(α+β))

sin(180-(α+β))=sin(α+β)

A=(1/2)*(b)*(b*sin(β)/sin(α))*sin(α+β)=[(1/2)*b²*sin(β)/sin(α)]*sin(α+β)

A=[(1/2)*b²*sin(β)/sin(α)]*sin(α+β)

KE/sin(β)=KM/sin(180-(α+β))

KM=(KE/sin(β))*sin(180-(α+β))--------- > KM=(KE/sin(β))*sin(α+β)

the answers part 2) are

side KE=b*sin(β)/sin(α)
side KM=(KE/sin(β))*sin(α+β)
Area A=[(1/2)*b²*sin(β)/sin(α)]*sin(α+β)

5 0

3 years ago

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:

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

5 0

3 years ago