Which graph shows the solution to the system of inequalities? y<1/2x-2 y≤-2x+4

Answers

Answer 1

Answer:

First of all, we need to graph the equation of the two lines and find each region separately.

The first line is:

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

This line has been plotted in the first figure below. To find the feasible region, let's take a random point and test the inequality, so let's take $(0,0)$

$y<(1)/(2)x-2 \n \n 0<(1)/(2)(0)-2 \n \n 0<-2 \ False!$

Since for (0,0) the inequality is false, then the region for this inequality is not where the point (0, 0) lies, but the other region, that is, the one under the line as indicated in the second figure. Keep in mind that points on the border of this region, that is, points that lies on the line aren't included in the region because the symbol < tells us that the equality is not included.

The second line is:

$y=-2x+4$

This line has been plotted in the third figure below. To find the feasible region, let's take (0,0) again, so let's take $(0,0)$

$y\leq -2x+4\n \n 0\leq -2(0)+4 \n \n 0<4 \ True!$

Since for the point (0,0) the inequality is true, then the region for this inequality is where this point lies as indicated in the fourth figure. Keep in mind that points on the border of this region, that is, points that lies on the line are included in the region because the symbol ≤ tells us that the equality is included.

_____________________

Finally, the solution to the system of inequalities is the one where the red and blue region overlap as indicated in the fifth figure below.

Answer 2

Answer:

Step-by-step explanation:

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A bag contains yellow marbles in red marbles 65 in total. The number of yellow marbles is five more than four times the number of red marbles. How many yellow marbles are there?

Answers

Answer: there would be 52 yellow marbles

Step-by-step explanation:

Ok we know that there is 65 marbles in total? Right? So then we’d take 65 and think, what could we divide this by and start guessing and estimating numbers. (I guessed 5, one because it’s divisible by 65, two there is 5 times more yellow marbles than red marbles.) So 5 divided by 65 is 13. But, in order to find the amount of yellow marbles, we need to subtract the whole number by the amount of red marbles. (So 65-13 =?) if you subtract that you get 52 yellow marbles. :)

A set of golf clubs is on sale for $150.00, which is 70% off of its original price. What was the original price of the golf clubs?

Answers

Answer:

$\$500$

Step-by-step explanation:

Let

x------> the original price of the golf club

we know that

$100\%-70\%=30\%$

$30\%=(30)/(100)=0.30$

$0.30x=150$ ------> linear equation that can be used to find the original price

solve for x

Divide by $0.30$ both sides

$0.30x/0.30=150/0.30$

$x=\$500$

Since it is 70% OFF, then $150.00 is 30% of the original price.

Divide it all by 3,
$50.00 is 10%,
therefore $500.00 is the original price!

Use an egg carton model to add fractions. Draw eggs in the cartons to show and solve the problem. Then fill in the blank to show the answer. 1/2 + 1/6 =

Answers

Well 1/2 is the same as 3/6 and you have 1/6 do draw an egg carton with 6 spaces and then draw 3/6 (which is 3 eggs) and draw 1/6 (which is one egg) so you'll have a total of 4 eggs in the carton

Find the value of x. if necessary round to the nearest tenth. a=27 sq inIf question isn't answered in 5 mins im only giving 30 points fam

Answers

do you mean X is A.

BTW did you get the question from Khan Academy.

a farm raises cows and chickens. the farmer has a total of 42 animals. one day he counts the legs of all animals of his animals and realizes he has a total of 114. how many cows does the farmer have? how many chickens?

Answers

Let's call cows x, and chickens as y.

Cows have 4 legs
Chickens have 2 legs.

Let's make two equations from the information they gave us!

x + y = 42
4x + 2y = 114

Now, let's multiply the first equation by 4.

4x + 4y = 168
4x + 2y = 114

Now, subtract the second equation from the first one.

4x - 4x + 4y - 2y = 168 - 114

4y - 2y = 168 - 114

2y = 54

y = 27

Now, plug y = 27 into either equation and solve for x.

x + y = 42

x + 27 = 42

x = 42 - 27

x = 15

There are 15 cows and 27 chickens.

How far can the mouse travel in one hour?

Answers

The mouse would travel 16.2 miles per hour.

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