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3 years ago

What is the solution set of the system {2x - 3y =19 and 7x +4y = -6?

1 answer:

6 0

{ 2x-3y=19
{ 7x+4y=-6

{ 2x=19+3y
{ 7x=-6-4y

{ x=19/2+3/2y
{ x=-6/7-4/7y

19/2+3/2y=-6/7-4/7y
y=-5

x=-6/7-4/7(-5)
x=2

(x,y) = (2,-5)

Solution Check
{ 2 · 2-3(-5)=19
{ 7 · 2+4(-5)=-6

{ 19=19
{ -6=-6

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Please help and explain part A B and C

Umnica [9.8K]

Part A you would just distribute your 3 to your X and your 5. After doing that you would get 3x+15+x=4x. Next you would combine like terms, meaning combine your x's together that is on the same side of your equal sign. So you would add 3x and x. When finished with that you would get, 4x+15=4x. You would then subtract your 4x on both sides of your equal sign. You then would get 15=0 which is no solution.

Part B you would distribute your 4 to your 1 and -x. After doing this your equation should then look like 4-4x=5x+8. Next you would try to get your like terms together. You would add 4x on both sides of your equal sign. Your equation should then look like 4=9x+8. Next you would subtract your 8 on both sides of the equal sign because your getting your terms together. Your equation should then look like, -4=9x. This answer would be one solution.

Part C you would combine your like terms, meaning add your 2x and x together to get your equation looking like, 3x+5=5+3x. You can tell just by looking at this equation it's going to be a infinite number of solutions.

Hope this helps! (:

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Solnce55 [7]

Answer:

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Which graph represents the following system of inequalities?

Korolek [52]

The graph of the two given system of inequalities y > 2x - 5

y < -3x is; Attached below

<h3>How to graph Inequalities?</h3>

We are given two inequalities;

y > 2x - 5

y < -3x

The graph that represents the 2 inequalities has been attached and from the graph, we see that;

The slope of the dotted line is negative

The x- intercept of the dotted line is the point (0,0)

The y- intercept of the dotted line is the point (0,0)

The solution of the system of inequalities is the shaded pink area between the two dotted lines.

Read more about Inequality Graphs at; brainly.com/question/13635292

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2 years ago

A recipe submitted to a magazine by one of its subscribers’ states that the mean baking time for a cheesecake is 55 minutes. A t

EastWind [94]

Answer:

$t=\frac{59.4-55}{\frac{3.239}{\sqrt{10}}}=4.296$

The degrees of freedom are given by:

$df=n-1=10-1=9$

The p value for this case is given by:

$p_v =P(t_{(9)}>4.296)=0.001$

And for this case the p value is lower than the significance level so we have enough evidence to reject the null hypothesis and then we can conclude that true mean is higher than 55.

Step-by-step explanation:

Information given

We have the following data: 54 55 58 59 59 60 61 61 62 65

The sample mean and deviation can be calculated with the following formulas:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

$s=\sqrt{\frac{\sum_{i=1}^n (X-i -\bar x)^2}{n-1}}$

$\bar X=59.4$ represent the sample mean

$s=3.239$ represent the sample standard deviation

$n=10$ sample size

$\alpha=0.05$ represent the significance level

t would represent the statistic

$p_v$ represent the p value

System of hypothesis

We want to test if the true mean is higher than 55, the system of hypothesis would be:

Null hypothesis: $\mu \leq 55$

Alternative hypothesis: $\mu > 55$

Replacing the info given we got:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

And replacing the info given we got:

$t=\frac{59.4-55}{\frac{3.239}{\sqrt{10}}}=4.296$

The degrees of freedom are given by:

$df=n-1=10-1=9$

The p value for this case is given by:

$p_v =P(t_{(9)}>4.296)=0.001$

And for this case the p value is lower than the significance level so we have enough evidence to reject the null hypothesis and then we can conclude that true mean is higher than 55

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3 years ago