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3 years ago

In which quadrants do solutions for the inequality y ≤ 2/7x +1 exist?

Mathematics

2 answers:

valina [46]3 years ago

8 0

I know this isnt an answer, however! the other answer is wrong i'm doing the quiz right now and i did that one and got no points whatsoever.

Just so nobody else has do their quiz again!

viktelen [127]3 years ago

3 0

All four quadrants

<h2>Explanation:</h2>

We have the following inequality:

$y \leq \frac{2}{7}x+1$

So the first step we need to perform is to plot the line:

$y = \frac{2}{7}x+1$

$If \ x=0 \\ \\ y=\frac{2}{7}(0)+1 \\ \\ y=1 \\ \\ \\ If \ y=0: \\ \\ 0=\frac{2}{7}(x)+1 \\ \\ x=-\frac{7}{2}=-3.5$

So the line passes through the points:

$(0,1) \ and \ (-3.5,0)$

To find the shaded region, let us take a point, namely, the origin and test it in the inequality:

$y \leq \frac{2}{7}x+1 \\ \\ 0\leq \frac{2}{7}(0)+1 \\ \\ 0\leq 1 \ True!$

Since this is true, then the shaded region includes this point. This is shown below and <em>as you can see the solutions exist in all four quadrants.</em>

<h2>Learn more:</h2>

Inequalities: brainly.com/question/12890742

#LearnWithBrainly

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By selling a stool for rupees 67.50,a carpenter loses 10%.how much percent would he gain or lose by selling it for rupees 82.50.

valentina_108 [34]

Let the actual value of the stool be x.

So if the carpenter sells the stool x rupees he neither loses, now wins anything.

67.50 is the value x - 10% of x, that is:

67.50=x-0.1x
67.50=0.9x

x=67.50/0.9=75 (rupees) is the actual value of the stool.

Selling the stool for 82.50 rupees, the carpenter clearly would make a profit, say of y% of that actual value, that is y%*75.

So using the same method:

82.50=75+y%*75

y%*75=82.50-75=7.5

we can make the calculations, but clearly 7.5 is 10% of 75

Answer: 10% gain.

8 0

3 years ago

Calculate the sample mean and sample variance for the following frequency distribution of heart rates for a sample of American a

spin [16.1K]

Answer:

$Mean = 68.9$

$s^2 =18.1$ --- Variance

Step-by-step explanation:

Given

$\begin{array}{cccccc}{Class} & {51-58} & {59-66} & {67-74} & {75-82} & {83-90} \ \\ {Frequency} & {6} & {3} & {11} & {13} & {4} \ \end{array}$

Solving (a): Calculate the mean.

The given data is a grouped data. So, first we calculate the class midpoint (x)

For 51 - 58.

$x = \frac{1}{2}(51+58) = \frac{1}{2}(109) = 54.5$

For 59 - 66

$x = \frac{1}{2}(59+66) = \frac{1}{2}(125) = 62.5$

For 67 - 74

$x = \frac{1}{2}(67+74) = \frac{1}{2}(141) = 70.5$

For 75 - 82

$x = \frac{1}{2}(75+82) = \frac{1}{2}(157) = 78.5$

For 83 - 90

$x = \frac{1}{2}(83+90) = \frac{1}{2}(173) = 86.5$

So, the table becomes:

$\begin{array}{cccccc}{x} & {54.5} & {62.5} & {70.5} & {78.5} & {86.5} \ \\ {Frequency} & {6} & {3} & {11} & {13} & {4} \ \end{array}$

The mean is then calculated as:

$Mean = \frac{\sum fx}{\sum f}$

$Mean = \frac{54.5*4+62.5*3+70.5*11+78.5*13+86.5*4}{6+3+11+13+4}$

$Mean = \frac{2547.5}{37}$

$Mean = 68.9$ -- approximated

Solving (b): The sample variance:

This is calculated as:

$s^2 =\frac{\sum (x - \overline x)^2}{\sum f - 1}$

So, we have:

$s^2 =\frac{(54.5-68.9)^2+(62.5-68.9)^2+(70.5-68.9)^2+(78.5-68.9)^2+(86.5-68.9)^2}{37 - 1}$

$s^2 =\frac{652.8}{36}$

$s^2 =18.1$ -- approximated

5 0

3 years ago

Describe the dimensions of two different prisms that each have a volume is 2,400 cubic centimeters

Phantasy [73]

One prism with a volume of 2400 might have a rectangular base with a length of 4 and a width of 5, as well as a height of 120.

V = l x w x h
V = 4 x 5 x 120
V = 2400

This prism would essentially look like a really tall rectangle, since the height is such a large number. I wouldn't accurately represent the units on graph paper, if I were you. Just label the sides with the numbers I gave you.

Another prism with a volume of 2400 might be a rectangular prism with a length of 8, a width of 10, and a height of 30.

V = l x w x h
V= 8 x 10 x 30
V = 2400

This would also be a tall rectangle, although it isn't as tall. Keep in mind that l x w x h is only the volume formula for a rectangular prism. I only used rectangular prisms because they would be the easiest for this example. A triangular prism has a different volume formula.

3 0

3 years ago

What is 5/16 x 246/1000

rosijanka [135]

Fraction form 41/400
decimal form .1025

8 0

3 years ago

What are 3 consecutive numbers that is the sum of -27.please be right.use odd numbers

qaws [65]

You're asking for three consecutive odd numbers, then
Let, the numbers = x, x+2, x+4

It is given that, x + x+2+ x+4 = -27
3x + 6 = -27
3x = -27 - 6
x = -33/3
x = -11
Then, x+2 = -9 & x+4 = -7

In short, Your Numbers would be: -7, -9,-11

Hope this helps!

6 0

3 years ago