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Snowcat [4.5K]
2 years ago
14

A) Determine the functions whose graphs are parallel to the graph of the function y=0.5x+10 and intersect the graph of the funct

ion y= -1.5x. The functions are expressed by the formulas.
y = -1.5x + 6, y = 0.5x-6

I WILL AWARD 75 POINTS !

B) Determine the functions whose graphs are parallel to the graph of the function y=0.5x+10 and intersect the graph of the function y= -1.5x. The functions are expressed by the formulas.


y = 0.5x+4, y = 0.5x, y = 3+1.5x

Please answer somebody. Someone help
Mathematics
1 answer:
Sonbull [250]2 years ago
3 0

We want to find parallel lines to the given lines, such that also meet some given restrictions.

The solutions are:

A) y = 0.5*x - 6

B) two solutions:

    y = 0.5*x + 4

    y = 0.5*x

Before start answering, a general line is given by:

y = a*x + b

Where a is the slope and b is the y-intercept.

Another line will be parallel this if and only if it has the same slope and a different y-intercept.

A) We want to find a line that is parallel to y = 0.5*x + 10 and that intersects y = -1.5*x

So we want another line with a slope of 0.5, then the correct option is:

y = 0.5*x - 6

How do we know that this intercepts the other line?

Because if two lines have different slopes, then the lines are not parallel, meaning that at some given point the lines intercept.

B) Similarly, now we want a line parallel to:

y = 0.5*x + 10

And that intersects:

y = -1.5*x

The correct options are the ones with slope equal to 0.5, then we have two correct options:

y = 0.5*x + 4

y = 0.5*x

If you want to learn more, you can read:

brainly.com/question/16701300

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I need help with this work
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G. 245.04cm²

Step-by-step explanation:

The shortest way to solve this problem would be:

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or

total surface area = 2 * π * r * (r + h).

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Radius = 3

Height = 10

The radius is half the diameter

TSA = Total surface area

TSA = 2 π 3(3+10)

TSA = (2)(3.141593)(3)(3+10)

TSA = (6.283185)(3)(3+10)

TSA = 18.849556(3+10)

TSA = (18.849556)(13)

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TSA = 245.04

Or you could do the longer way, which would be:

Step 1: Find the surface area of the curved part of the cylinder

Surface Area (Curved) = 2 x π x Radius x Height

Step 2: Find the surface area of the two ends of the cylinder

Surface Area (Ends) = 2 x π x Radius²

Step 3: Add the surface are of the curved part to the surface area of the ends

Surface Area (Total) = Surface Area (Curved) + Surface Area (Ends)

For the cylinder in the picture:

A cylinder has a height of 10 and a diameter of 6

Hence, Radius = d/2 = 6/2 = 3 cm

Surface Area (Curved) = 2 x pi x 3 x 10

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Surface Area (Ends) = 56.548668

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245.04 is the result of rounding 245.044227 to the nearest hundredth

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A quality analyst of a tennis racquet manufacturing plant investigates if the length of a junior's tennis racquet conforms to th
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Answer:

Confidence interval : 21.506 to 24.493

Step-by-step explanation:

A quality analyst selects twenty racquets and obtains the following lengths:

21, 25, 23, 22, 24, 21, 25, 21, 23, 26, 21, 24, 22, 24, 23, 21, 21, 26, 23, 24

So, sample size = n =20

Now we are supposed to find Construct a 99.9% confidence interval for the mean length of all the junior's tennis racquets manufactured at this plant.

Since n < 30

So we will use t-distribution

Confidence level = 99.9%

Significance level = α = 0.001

Now calculate the sample mean

X=21, 25, 23, 22, 24, 21, 25, 21, 23, 26, 21, 24, 22, 24, 23, 21, 21, 26, 23, 24

Sample mean = \bar{x}=\frac{\sum x}{n}

Sample mean = \bar{x}=\frac{21+25+23+22+24+21+25+21+23+ 26+ 21+24+22+ 24+23+21+ 21+ 26+23+ 24}{20}

Sample mean = \bar{x}=23

Sample standard deviation = \sqrt{\frac{\sum(x-\bar{x})^2}{n-1}}

Sample standard deviation = \sqrt{\frac{(21-23)^2+(25-23)^2+(23-23)^2+(22-23)^2+(24-23)^2+(21-23)^2+(25-23)^2+(21-23)^2+(23-23)^2+(26-23)^2+(21-23)^2+(24-23)^2+(22-23)^2+(24-23)^2+(23-23)^2+(21-23)^2+(21-23)^2+(26-23)^2+(23-23)^2+(24-23)^2}{20-1}}

Sample standard deviation= s = 1.72

Degree of freedom = n-1 = 20-1 -19

Critical value of t using the t-distribution table t_{\frac{\alpha}{2} = 3.883

Formula of confidence interval : \bar{x} \pm t_{\frac{\alpha}{2}} \times \frac{s}{\sqrt{n}}

Substitute the values in the formula

Confidence interval : 23 \pm 1.73 \times \frac{1.72}{\sqrt{20}}

Confidence interval : 23 -3.883 \times \frac{1.72}{\sqrt{20}} to 23 + 3.883 \times \frac{1.72}{\sqrt{20}}

Confidence interval : 21.506 to 24.493

Hence Confidence interval : 21.506 to 24.493

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B={(2,2),(4,2),(6,2),(2,4),(2,6),(1,3),(1,5),(1,1),(3,1),(3,3),(3,5),(4,4),(4,6),(5,1),(5,3),(5,5),(6,4),(6,6)}

C={(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,3),(2,5),(3,3),(3,5),(3,4),(3,6),(4,1),(4,3),(4,5),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,3),(6,5)}.

A∩B:{(2,2),(4,2),(6,2),(2,4),(2,6),(4,4),(4,6),(6,4),(6,6)}

A∪B={(1,2),(2,2),(4,2),(6,2),(2,4),(2,6),(4,4),(4,6),(6,4),(6,6),(3,2),(5,2),(1,4),(3,4),(5,4),(1,6),(3,6),(5,6),(1,3),(1,5),(1,1)(3,1),(3,3),(3,5),(5,1),(5,3),(5,5)}

A∩C={(1,2),(1,4),(1,6),(3,2),(3,4),(3,6),(5,2),(5,4),(5,6)}

Step-by-step explanation:

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2 years ago
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