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4vir4ik [10]
3 years ago
6

Which statement is true about the graphs of the two lines y=-8x - 5/4 and y= 1/8x + 4/5? The lines are perpendicular to each oth

er because –8 and are opposite reciprocals of each other. The lines are perpendicular to each other because and are opposite reciprocals of each other. The lines are neither parallel nor perpendicular to each other because –8 and are not opposite reciprocals of each other. The lines are neither parallel nor perpendicular to each other because and are not opposite reciprocals of each other.
Mathematics
2 answers:
GREYUIT [131]3 years ago
4 0
Hi there!

The lines given in the problem are perpendicular to each other because they are opposite reciprocals. An opposite reciprocal is when the original slope (-8) is made opposite, which is negative or positive depending on the number (8) and is flipped upside down, or the numerator becomes the denominator and vice-versa (1/8). Opposite reciprocals are also shown by when the two slopes are multiplied together, it is equal to -1, showing that the lines are perpendicular. (-8/1 x 1/8 = -1)

Hope this helps!! :)
NNADVOKAT [17]3 years ago
3 0

Answer:

1. The lines are perpendicular to each other because -8 and 1/8 are negative reciprocals of each other.

Step-by-step explanation:  

We have been given equations of two lines as: y=-8x-\frac{5}{4} and y=\frac{1}{8}x+\frac{4}{5}. We are asked to choose the correct statement about our given lines.

We can see both equations of our given lines in slope-intercept form of equation: y=mx+b, where, m represents slope of line and b represents y-intercept.

We can see that the slopes of our lines are -8 and 1/8.

Since we know that the slopes of perpendicular lines are negative reciprocal of each other and -8 and 1/8 are negative reciprocal of each other.

Two numbers are negative reciprocal if their product is -1.

-8\times \frac{1}{8}=-1

Therefore, our given lines are perpendicular lines and 1st statement is the correct choice.

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Step-by-step explanation:

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Given : Sample size = 463

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\sigma=65\text{ minutes}

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Now, the 90% confidence interval for the population mean will be :-

118\ \pm\ 2.576\times\dfrac{65}{\sqrt{463}} \\\\\approx118\pm7.78=(118-7.78\ ,\ 118+7.78)=(110.22,\ 125.78)

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The equation x+53=15 can be solved by performing two operations on both sides.
Wewaii [24]
Hey!


You're right! This equation can definitely be solved by performing two operations on both sides. Let me show you how it's done.

First, let's write out our equation.

<span><em>Original Equation :</em>
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Now that that's done, we'll be performing two operations on both sides. The operation we'll want to do is subtracting both sides of the equation by 53. We do this to get x on its own.

<em>Original Equation :</em>
x + 53 = 15

<em>New Equation {Added Subtract 53 to Both Sides} :</em>
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Now we have to solve the equation. Let's do the left side first.

<em>Left Side of the Equation :</em>
x + 53 - 53 

<em>Left Side of the Equation {Solved} :</em>
x

Now, we'll solve the right side of the equation.

<em>Right Side of the Equation :</em>
15 - 53

<em>Right Side of the Equation {Solved} :</em>
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Now we can put both solutions to both sides of the equation together.

<em>New Equation :</em>
x = -38

Since this cannot be simplified any farther, this is our final answer. And that's it!

<em>So, now we know that in the equation x + 53 = 15,</em>  x = -38

Hope this helps!


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