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s344n2d4d5 [400]
2 years ago
7

Which of the following describes the graph of 2x + 4y < 16?

Mathematics
1 answer:
kherson [118]2 years ago
6 0
<h3>Answer: A) Dashed line, shaded below</h3>

=============================================================

Explanation:

2x + 4y < 16 solves to y < -0.5x+4 when you isolate y. The inequality sign does not change direction because we divided both sides by a positive value (in this case, 4).

The graph of y < -0.5x+4 will be the same as the graph of 2x+4y < 16

To graph y < -0.5x+4, we graph y = -0.5x+4 which is a straight line that goes through the two points (0,4) and (2, 3). This is the boundary line of the inequality shaded region. The boundary line is a dashed line because we are not including points on the boundary that are part of the solution set. We only include these boundary points if the inequality sign has "or equal to".

We then shade below the dashed boundary line to indicate points below the boundary line. The shading is done downward due to the "less than" sign.

---------------------

Perhaps another method to find what direction we shade is we can try out a point like (0,0). The point cannot be on the boundary line.

Plug those coordinates into either equation. I'll pick the second equation

y < -0.5x+4

0 < -0.5*0+4

0 < 0+4

0 < 4

The last inequality is true, so the first inequality is also true when (x,y) = (0,0). Therefore, the point (0,0) is in the shaded region. The point (0,0) is below the boundary line y = -0.5x+4

So this is another way to see that the shaded region is below the boundary line.

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John looked at his bank account and noticed that he had $2,029.90 in his account. All that he could remember is that he created
Over [174]

We will have that for the previous year, he had in the account:

m_{y6}=2029.90-\frac{2029.90\cdot6}{100}\Rightarrow m_{y6}=1908.106

For the year previous to that one, he had:

m_{y5}=1908.106-\frac{1908.106\cdot6}{100}\Rightarrow m_{y5}=1793.61964

For the previous year to that, he had:

m_{y4}=1793.61964-\frac{1793.61964\cdot6}{100}\Rightarrow m_{y4}=1686.002462

For the year previous to that one, he had:

m_{y3}=1686.002462-\frac{1686.002462\cdot6}{100}\Rightarrow m_{y3}=1584.842314

For the second year that the money was in the account, there was:

m_{y2}=1584.842314-\frac{1584.842314\cdot6}{100}\Rightarrow m_{y2}=1489.751775

And the orinial ammount of money that was in the account was:

m_{y1}=1489.751775-\frac{1489.751775\cdot6}{100}\Rightarrow m_{y1}=1400.366669

From this, we know that Jhon had originally $1400.37 in the bank account.

6 0
8 months ago
A social media website had 350,000 followers in 2010. The number y of followers
Zolol [24]

Answer:

a) y(t) = 350(1.02)^t

b) 394 thousand = 394,000 people will be following the website in 2016

Step-by-step explanation:

Exponential equation for an amount:

The exponential equation for an amount after t years has the following format:

y = y(0)(1+r)^t

In which y(0) is the initial value and r is the growth rate, as a decimal.

A social media website had 350,000 followers in 2010. The number y of followers increases by 2% each year.

This means that: y(0) = 350, r = 0.02

a. Write an exponential growth function that represents the number of followers t years after 2010

In thousands:

y(t) = 350(1 + 0.02)^t

y(t) = 350(1.02)^t

b. How many people will be following the website in 2016?

2016 is 6 years after 2010, so this is y(6).

y(6) = 350(1.02)^6 = 394.2

Rounding to the nearest thousand:

394 thousand = 394,000 people will be following the website in 2016

5 0
3 years ago
Rafael has 3 times as many blue marbles as he does red marbles . He has a total of 124 marbles. How many read marbles and how ma
34kurt
<span>A quarter of the marbles are red, so there are 124/4 = 31 red marbles. The rest are blue, so there are 124 - 31 = 93 blue marbles.</span>
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3 years ago
Karen has 7 over 8cup of ice cream. How many 1 over 3cup servings can she make?
AlexFokin [52]
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3 0
3 years ago
Read 2 more answers
15% of customers that come to your
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Answer:

Number of customers (double taco)= 45

Step-by-step explanation:

Giving the following information:

Double taco order rate= 15% = 0.15

Total number of customers= 300

<u>To calculate the number of customers that order two tacos, we need to use the following formula:</u>

Number of customers (double taco)= Double taco order rate*total number of taco

Number of customers (double taco)= 0.15*300

Number of customers (double taco)= 45

7 0
2 years ago
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