The point (16, 12) lies on the terminal side of an angle. find cos, tan, and sin

Answers

Answer 1

Answer: The terminal side means that it's 16 to the right and 12 up. Which means that the triangle made from this has the sides of 16 and 12 and the hypotenuse is 20 units long. Theta, in this case, would have 16 as it's adjacent and 12 as it's opposite.
Therefore, using the Pythagorean identities:
$sin(\theta) = (12)/(20) = \boxed{(3)/(5)} \n\ cos(\theta) = (16)/(20) = \boxed{(4)/(5)} \n\ tan(\theta) = (12)/(16) = \boxed{(3)/(4)}$

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What is x/3+10=15 using two step

Solve for x. −4/9 x 7=−71/8 x 9

Answers

-4/9 x + 7 = -71/8 x + 9
-4/9 x + 71/8 x = 9 - 7
607/72 x = 2
x = (2 x 72)/607 = 144/607

Elia is training for her first marathon. she currently runs 10 mi. per week, and wants to increase her mileage by 2 mi. every week. if elia keeps to her training schedule write a formula to define the number of miles she runs each week. ( 1 point)

Answers

Answer: Required expression is given by

$y=8+2x$

Step-by-step explanation:

Since we have given that

Number of miles per week Elia is training for her first marathon = 10 miles

According to question, we have given that she wants to increase her mileage by 2 miles every week.

so, Equation becomes

10,12,14,16..........

Let the number of weeks be x

Since it forms an Arithmetic sequence,

As we know the formula for nth term :

$a_x=10+(x-1)2\n\ny=10+2x-2\n\ny=8+2x$

So, our required expression will be

$y=8+2x$

Answer:

y=2x+8

Step-by-step explanation:

Given is the number of miles per week Elia is training = 10 miles

And she wants to increase her mileage by 2 miles every week. Means the next week she will run 12 miles, next week she will run 14 miles and so on.

The series goes like this 10,12,14 and so on. This forms an arithmetic sequence.

Let the number of weeks be represented by x

The formula for nth term :

a = d (n - 1) + c, where d is the common difference between consecutive terms, and c = a1.

So, equation becomes a=10+(x-1)2

y=10+2x-2

y=8+2x or y=2x+8

Hence, the formula is : y=2x+8

Which radical expression is equivalent to 3^3/4

Answers

The numerator of the fraction is the power of the number and the denominator is the root of the number. This is expressed as follows:

⁴√(3)³

Answer:27

Step-by-step explanation:

It is given that A = {1, 2, 3, 4, 7} and B = {2, 4, 8, 10).
(i) List all the elements in A∩B in set notation.
(ii) Draw a Venn diagram to represent the sets A and B.

Answers

Answer:

(i) A∩B = {2,4}

(ii) I don't know how to attach pictures in brainly so i can't send the veen diagram

A teacher wrote the equation 3y + 12 = 6x on the board. For what value of b would the additional equation 2y = 4x + b form a system of linear equations with infinitely many solutions?b = –8
b = –4
b = 2
b = 6

Answers

Answer: First option.

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

$y=mx+b$

Where "m" is the slope of the line and "b" is the y-intercept

We need to write each equation in Slope-Intercept form:

First equation

$3y + 12 = 6x\n\n3y=6x-12\n\ny=2x-4$

Second equation

$2y = 4x + b \n\ny=2x+(b)/(2)$

Since, by definition, a system of linear equations has infinitely many solutions when the lines are the same, we can say that:

$y=y\n\n2x-4=2x+(b)/(2)$

Then, solving for "b", we get:

$-4=(b)/(2)\n\n(-4)(2)=b\n\nb=-8$

Answer:

-8

Step-by-step explanation:

Just took test lol

Faye and Andrew have written down the same negative number.Faye squares the number then multiplies by 2 and adds 4.
Andrew multiples the number by 21 then subtracts the result from 40.
They both finish with the same answer. What was the number?

Answers

x - the number

Faye squares the number: x²
then multiplies by 2: 2x²
and adds 4: 2x²+4

Andrew multiplies the number by 21: 21x
then subtracts the result from 40: 40-21x

They both finish with the same answer, so the results are equal.
$2x^2+4=40-21x \n2x^2+21x+4-40=0 \n2x^2+21x-36=0 \n2x^2+24x-3x-36=0 \n2x(x+12)-3(x+12)=0 \n2x-3=0 \ \lor \ x+12=0 \n2x=3 \ \lor \ x=-12 \nx=(3)/(2) \ \lor \ x=-12$

The number is negative so x=-12.

The number is -12.

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