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Troyanec [42]
3 years ago
12

Write the equation of a line in slope intercept form that is perpendicular to the line y = –4x and passes through the point (2,

6).
Mathematics
1 answer:
Gnesinka [82]3 years ago
6 0

1. If the line that we are searching for is perpendicular to the line y = -4x, this means that the gradient of our line and the gradient of the perpendicular line will multiply to give -1. Thus if we call the gradient of our line m, then:

m*(-4) = -1

-4m = -1

m = 1/4

2. Since we know that m = 1/4 and we have a point (2,6) on our line, we can use the formula y - y1 = m(x - x1) to find the equation of our line, where (x1, y1) is the coordinates of a point on the line. Thus:

y - y1 = m(x - x1)

y - 6 = (1/4)(x - 2)

y - 6 = (1/4)x - 2/4 (Expand (1/4)(x - 2))

y = (1/4)x - 1/2 + 6 (Simplify 2/4 and add 6 to each side)

y = (1/4)x + 11/2 (Evaluate -1/2 + 6)

Slope-intercept form is given by y = mx + c. As our equation is already in this form, there is nothing more to do. Thus, the answer is y = (1/4)x + 11/2

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The mean of a set of 5 numbers is 12. One of the numbers in the set is 16. If 16 is removed from the list, what is the new mean?
Reil [10]

The new mean is 11

Step-by-step explanation:

The mean = sum of the numbers ÷ numbers

  • The mean of a set of 5 numbers is 12
  • One of the number is 16
  • We need to find the new mean if 16 is removed from the set of numbers

∵ The set has 5 numbers

∵ The mean of the 5 numbers is 12

- Substitute these values in the rule of the mean above

∴ 12 = sum of the numbers ÷ 5

- Multiply both sides by 5

∴ 60 = sum of the numbers

∵ One of the number is 16

∵ 16 is removed from the set of the number

- Subtract 16 from the sum and the numbers will be four numbers

∵ The new sum = 60 - 16

∴ The new sum = 44

∵ The set has 4 numbers

∴ The new mean = 44 ÷ 4 = 11

The new mean is 11

Learn more:

You can learn more about the mean in brainly.com/question/5069437

#LearnwithBrainly

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3 years ago
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never [62]

Answer:

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BlackZzzverrR [31]
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Solve the following equation for 0° ≤ θ < 360°. Use the "^" key on the keyboard to indicate an exponent. For example, sin2x w
Margarita [4]

Answer: 2sin^2x+sin2x+cos2x=0 ..... (1).

By using the trigonometric identities below :

sin2x=2sinxcosx

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We substitute the trigonometric identities into (1).

2sin^2x+2sinxcosx+cos^2x-sin^2x=0

By combining like terms .

sin^2x+2sinxcosx+cos^2x=0.....(2)

The equation (2) is equivalent to the following expression (3).

(sinx+cosx)(sinx+cosx)=0 .....(3).

sinx+cosx=0

cosx=-sinx

divide both sides by cosx

1=-sinx/cosx

-1=sinx/cosx

sinx/cosx=tanx

substitute

-1=tanx

tanx=-1

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tan135º=-1 (one answer)

tan315º=-1 (second answer)

Step-by-step explanation:

Please refer to the trigonometric identities used and explained above .

5 0
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Answer:

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Step-by-step explanation:

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