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irga5000 [103]
3 years ago
15

Which statements are true about the linear inequality y > 3/4x – 2? Check all that apply. The slope of the line is –2. The gr

aph of y > 3/4 x – 2 is a dashed line. The area below the line is shaded. One solution to the inequality is (0, 0). The graph intercepts the y-axis at (0, –2).

Mathematics
1 answer:
pishuonlain [190]3 years ago
4 0
You can draw the area bounded by the unequality y\ \textgreater \  \frac{3}{4} x-2 in following way:

1. Draw a dashed line y=\frac{3}{4} x-2 with a slope \frac{3}{4} (a dashed, because all points from this line, for example when x=0, y=-2 do not belong to the area);

2. Define which part (under the line or over the line) is suitable by substituting values. For example, when x=0 and y=0 you obtain that 0\ \textgreater \  \frac{3}{4} \cdot 0-2 is a right unequality, that means that the point (0,0) is a solution and belongs to the area;

3. Shade that part of the plane to which point (0,0) belongs, you receive the area over the line (see image).

From the done steps you can see that only fourth statement is true.



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A piece of wire of length 6363 is​ cut, and the resulting two pieces are formed to make a circle and a square. Where should the
Lerok [7]

Answer:

a.

35.2792 cm from one end (The square)

And 27.7208 cm from the other end (The circle)

b. See (b) explanation below

Step-by-step explanation:

Given

Length of Wire ,= 63cm

Let L be the length of one side of the square

Circumference of a circle = 2πr

Perimeter of a square = 4L

a. To minimise

4L + 2πr = 63 ----- make r the subject of formula

2πr = 63 - 4L

r = (63 - 4L)/2π

r = (31.5 - 2L)/π

Let X = Area of the Square. + Area of the circle

X = L² + πr²

Substitute (31.5 - 2L)/π for r

So,

X² = L² + π((31.5 - 2L)/π)²

X² = L² + π(31.5 - 2L)²/π²

X² = L² + (31.5 - 2L)²/π

X² = L² + (992.25 - 126L + 4L²)/π

X² = L² + 992.25/π - 126L/π +4L²/π ------ Collect Like Terms

X² = 992.25/π - 126L/π + 4L²/π + L²

X² = 992.25/π - 126L/π (4/π + 1)L² ---- Arrange in descending order of power

X² = (4/π + 1)L² - 126L/π + 992.25/π

The coefficient of L² is positive so this represents a parabola that opens upward, so its vertex will be at a minimum

To find the x-cordinate of the vertex, we use the vertex formula

i.e

L = -b/2a

L = - (-126/π) / (2 * (4/π + 1)

L = (126/π) / ( 2 * (4 + π)/π)

L = (126/π) /( (8 + 2π)/π)

L = 126/π * π/(8 + 2π)

L = (126)/(8 + 2π)

L = 63/(4 + π)

So, for the minimum area, the side of a square will be 63/(4 + π)

= 8.8198 cm ---- Approximated

We will need to cut the wire at 4 times the side of the square. (i.e. the four sides of the square)

I.e.

4 * (63/(4 + π)) cm

Or

35.2792 cm from one end.

Subtract this result from 63, we'll get the other end.

i.e. 63 - 35.2792

= 27.7208 cm from the other end

b. To maximize

Now for the maximum area.

The problem is only defined for 0 ≤ L ≤ 63/4 which gives

0 ≤ L ≤ 15.75

When L=0, the square shrinks to 0 and the whole 63 cm wire is made into a circle.

Similarly, when L =15.75 cm, the whole 63 cm wire is made into a square, the circle shrinks to 0.

Since the parabola opens upward, the maximum value is at one endpoint of the interval, either when

L=0 or when L = 15.75.

It is well known that if a piece of wire is bent into a circle or a square, the circle will have more area, so we will assume that the maximum area would be when we "cut" the wire 0, or no, centimeters from the

end, and bend the whole wire into a circle. That is we don't cut the wire at

all.

7 0
3 years ago
Employees at a company are given £1,200 to spend on items for the office.
umka21 [38]

Answer:

380

Step-by-step explanation:

280 coffe machine

15 bag multiple for 40= 600 - 15%= 540

540+280=820

1200-820=380

3 0
3 years ago
a teacher plans a simulation to estimate the probability that a student will pick a vowel out of a bag of 26 tiles, each with a
Alex Ar [27]

Answer:

Yes

Step-by-step explanation:

Given that a teacher prepares 26 tiles with 5 vowels numbered 1 and 21 consonants numbered 2.

The probability for drawing vowel =\frac{5}{26}

Prob for consonant =\frac{21}{26}

If number of trials is atleast 30 we can expect reliable results.

Here the results are recorded for 120 times at random.

Since number of trials is large, we can expect a reliable and accurate results representing the actual probability.

This is because more the number of trials, the less would be the margin of error i.edeviationfrom the expected probability would be minimum

8 0
3 years ago
Read 2 more answers
Samuel made a list of his test scores: 88, 100, 92, 80, 85, 94, and 90. What is the lowest test score he can get on his next tes
yulyashka [42]

Answer:

he needs to get a 91 to have a mean score of 90

Step-by-step explanation:

add up all the known scores to get 629

let 's' = lowest test score

(629 + s) ÷ 8 = 90   [we divide by 8 because there are 7 known and 1 unknown score)

cross-multiply to get:

629 + s = 720

s = 720-629

s = 91

4 0
3 years ago
How to find irrational numbers between two numbers
Vaselesa [24]

Answer:

If A and B are two rational numbers such that A<B

Then X = A + (B-A)/π would be an example of an irrational number

such that A < X < B

Hope this helps

Please give me brainliest

8 0
3 years ago
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