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Savatey [412]
3 years ago
9

Find the equation of the line that is perpendicular to the given line and passes through the given point. Enter the right side o

f the equation as a single fraction. y = 5x − 1 2 ; (3, 3)
Mathematics
2 answers:
xenn [34]3 years ago
4 0
To answer this question we need to know two things, 1) a linear equation is written as y=mx+b. and 2) a perpendicular line is the negative reciprocal of the given slope. So, with this in mind, we now know that the new slope is -1/5x. In order for the equation to pass through the given points (3,3), we need to plug it in with the new equation. We plug both x and y with 3 while leaving the y-intercept to be variable b. 3=-1/5(3)+b. Now, we solve this equation by isolating the variable. -1/5*3 is -3/5, and we add this to 3, so it will be 3 3/5. This will be our new y-intercept. The equation is now y=-1/5x+3 3/5. 
scZoUnD [109]3 years ago
3 0
Y = 5x - 12....the slope here is 5. A perpendicular line will have a negative reciprocal slope. To find the negative reciprocal, u flip the slope and change the sign. So we have 5 or 5/1.....flip the slope making it 1/5.....change the sign making it -1/5. So the perpendicular line will have a slope of -1/5.

y = mx + b
slope(m) = -1/5
(3,3)....x = 3 and y = 3
now we sub into the formula and find b, the y int
3 = -1/5(3) + b
3 = -3/5 + b
3 + 3/5 = b
15/5 + 3/5 = b
18/5 = b

so ur equation is : y = -1/5x + 18/5
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3 years ago
A biology test is worth 100 points and has 36 questions.
Ad libitum [116K]

Answer:

(a) 7 essays and 29 multiple questions

(b) Your friend is incorrect

Step-by-step explanation:

Represent multiple choice with M and essay with E.

So:

M + E= 36 --- Number of questions

2M + 6E = 100 --- Points

Solving (a): Number of question of each type.

Make E the subject of formula in M + E= 36

E = 36 - M

Substitute 36 - M for E in 2M + 6E = 100

2M + 6(36 - M) = 100

2M + 216 - 6M = 100

Collect Like Terms

2M - 6M = 100 - 216

-4M = - 116

Divide both sides by -4

M = \frac{-116}{-4}

M = 29

Substitute 29 for M in E = 36 - M

E = 36 - 29

E = 7

Solving (b): Can the multiple questions worth 4 points each?

It is not possible.

See explanation.

If multiple question worth 4 points each, then

2M + 6E = 100 would be:

4M + xE = 100

Where x represents the number of points for essay questions.

Substitute 7 for E and 29 for M.

4 * 29 + x * 7 = 100

116 + 7x = 100

Subtract 116 from both sides

116-116 + 7x = 100 -116

7x = 100-116

7x = -16

Make x the subject

x = -\frac{16}{7}

Since the essay question can not have worth negative points.

Then, it is impossible to have the multiple questions worth 4 points

<em>Your friend is incorrect.</em>

6 0
2 years ago
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