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3 years ago

Which of the following points lies on the line perpendicular to

Mathematics

1 answer:

sergij07 [2.7K]3 years ago

6 0

Answer:

Step-by-step explanation:

recall that perpendicular lines have slopes that are opposite reciprocals. if u don't know what opposite reciprocals are, according to study.com they are, "The term opposite reciprocals refers to two numbers that have opposite signs and are flipped fractions of each other." for example, 1/2 and -2 are opposite reciprocals.

also recall that the formula to find the slope of a line is m=y2-y1/x2-x1

to solve this problem, we need to go through all of the options and find the slope of that line using the given point and point (0,4). After that, we need to check if that slope is equal to 1. One is the opposite reciprocal of -1, and -1 is the slope of the equation y= -x+4. if the slope is equal to 1, the line will be perpendicular to the line y= -x+4.

lets do the math now:

option a)

m=y2-y1/x2-x1

m=12-4/6-0

m=8/6

m=4/3

this line isnt perpendicular to y= -x +4 cuz the slope is 4/3, which isnt equal to 1

option b)

m=y2-y1/x2-x1

m=0-4/6-0

m=-4/6

m= -2/3

this line isnt perpendicular to y= -x +4 cuz the slope is -2/3, which isnt equal to 1

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

ok girl i dont wanna do all the rest of the calculations. just keep doing the same thing with all the other options until you find something that has a slope of 1.

toodles! :)

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3 years ago

How do I solve tan(62) = 12/x?

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Answer:

x = 6/31 = 0.194

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

(62)-(12/x)=0

Step by step solution :

Step 1 :

Simplify ——

Equation at the end of step 1 :

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Step 2 :

Rewriting the whole as an Equivalent Fraction :

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Rewrite the whole as a fraction using x as the denominator :

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2.2 Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

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4.1 When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

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Here's how:

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Now, on the left hand side, the x cancels out the denominator, while, on the right hand side, zero times anything is still zero.

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Equations which are never true :

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This equation has no solution.

A a non-zero constant never equals zero.

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Add 6 to both sides of the equation :

31x = 6

Divide both sides of the equation by 31:

x = 6/31 = 0.194

Answer :

x = 6/31 = 0.194

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3 years ago

A professor wishes to discover if seniors skip more classes than freshmen. Suppose he knows that freshmen skip 2% of their class

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Answer:

We conclude that seniors skip more than 2% of their classes at 0.01 level of significance.

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We are given that a professor wishes to discover if seniors skip more classes than freshmen. Suppose he knows that freshmen skip 2% of their classes.

He randomly samples a group of seniors and out of 2521 classes, the group skipped 77.

Let p = percentage of seniors who skip their classes.

So, Null Hypothesis, $H_0$ : p $\leq$ 2% {means that seniors skip less than or equal to 2% of their classes}

Alternate Hypothesis, $H_A$ : p > 2% {means that seniors skip more than 2% of their classes}

The test statistics that will be used here is One-sample z proportion statistics;

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So, test statistics = $\frac{\frac{77}{2521} -0.02}{{\sqrt{\frac{\frac{77}{2521}(1-\frac{77}{2521})}{2521} } } } }$

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The value of the test statistics is 3.08.

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Therefore, we conclude that seniors skip more than 2% of their classes.

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