Instructions: Find the value of the trigonometric ratio. Make sure to simplify the fraction if needed.

Answers

Answer 1

Answer:

30/34

Step-by-step explanation:

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Four milliliters of ink A is added to 10 milliliters of ink B, forming a mixture of inks. Ink A contains 10% blue pigment. Ink B contains an unknown percentage of blue pigment. The mixture of the two inks contains 35% blue pigment.

Answers

We will assume that B contains higher percentage of blue pigment than the mixture ( because A contains lower). First we will subtract:
35-10=15 and then: x-35
So we will make the proportion:
4 : 10 = (x-35) : 15
4 * 15 = 10(x-35)
60=10 x- 350
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Answer: Ink B contains 41 % of blue pigment.

If triangle RST is congruant to triangle ABC, the measure of angle A equals x^2-8x, and the measure of angle C equals 4x-5, and the measure of angle R equals 5x+30 find the measure of angle C [ only an algebraic solution can receive full credit.]

Answers

In any statement like this one: $\triangle RST \cong \triangle ABC$ you can assume that the points match up in the order that you are given them.
This means that $\angle A \cong \angle R$ .
We know that $m\angle A = x^2-8x$ and $m\angle R=5x+30$ , and because they are congruent we can set the two equal to each other.

$x^2-8x=5x+30$
Let's get everything to one side.
$x^2-13x-30=0$
Let's solve by factoring, since it's easy to do with these whole numbers.
We're looking for two number thats add to -30 and multiply to -13...
These would be -15 and 2.
Since our leading coefficient (_x²) is 1, we can factor straight to (x-15)(x+2).
Here's what it would look like if you went through all the steps anyways, though.
$x^2-15x+2x-30=0$
$x(x-15)+2(x-15)=0$
$(x+2)(x-15)=0$
Any value which causes either factor to equal 0 is a solution.
(The second factor wouldn't matter b/c 0 times anything is still 0)
Therefore x = -2 or 15.
Only one of these is possible, however!
If you use x = -2, you will find that the angle measure 4x-5 is negative, which is impossible. In this case, x must be 15.

Let's find the measure of angle C.
$m\angle C=4x-5\ where\ x=15\nm\angle C=4(15)-5\nm\angle C=60-5\n\boxed{m\angle C = 55\°}$

   ΔRST ≡ ΔABC
      <R = <A
   (5x + 30)° = (x² - 8x)°
      5x + 30 = x² - 8x
-x² + 5x + 30 = x² - x² - 8x
-x² + 5x + 30 = -8x
+ 8x    + 8x
-x² + 13x + 30 = 0
x = -(13) ± √((13)² - 4(-1)(30))
   2(-1)
x = -13 ± √(169 + 120)
      -2
x = -13 ± √(289)
   -2
x = -13 ± 17
   -2
x = -13 + 17 U x = -13 - 17
   -2    -2
x = 4 U x = -30
     -2    -2
x = -2    x = 25

<C = 4x - 5    U <C = 4x - 5
<C = 4(-2) - 5 U <C = 4(25) - 5
<C = -8 - 5       U <C = 100 - 5
<C = -13°       U <C = 95°

or

      ΔRST ≡ ΔABC
      <A + <C = <R
   (x² - 8x)°+ (4x - 5)° = (5x + 30)°
       (x² - 8x) + (4x - 5) = (5x + 30)
   (x² - 8x + 4x - 5) = (5x + 30)
         x² - 4x - 5 = 5x + 30
      - 5x    - 5x
   x² - 9x - 5 = 30
   - 30 - 30
       x² - 9x - 35 = 0
x = -(-9) ± √((-9)² - 4(1)(-35))
       2(1)
x = 9 ± √(81 + 140)
      2
x = 9 ± √(221)
2
x = 9 ± 14.86
      2
x = 9 + 14.86 U x = 9 - 14.86
       2 2
x = 23.86 U x = -4.14
   2 2
x = 11.93 U x = -2.07

What is the exact value of sin(15)

Answers

The correct answer is √6-√2/4, or B.

I just took the unit test review and got it correct :)

the sum of three consecutive integer is 88. identify the variable and write an equation the describes the situation.

Answers

Lets say that you take n as the integer. Now you'll add it with 3 numbers. n+(n+1)+(n+2)=88. Now add 'em up, the sum is 3n+3=88. Take the 3 to the other side and subtract it from 88 which is 85. Now it'll be n= 85/3

What is the slope of a line perpendicular to x - 5y = -10?What is the slope of a line parallel to 4x + y = -1?

What is the slope of a line perpendicular to x - 3y = 9?

What is the slope of a line parallel to 10x - 5y = 8?

What is the slope of a line parallel to 4x + 2y = 5?

Answers

slope of line perpendicular to : x - 5y = -10
-5y = -x - 10
y = 1/5x + 2.....slope here is 1/5...perpendicular line needs a negative reciprocal slope. All that means is flip the slope and change the sign.
1/5......flip.....5/1.....change the sign....-5/1...or just -5 <== answer

slope of line parallel to 4x + y = -1
y = -4x - 1...slope here is -4....parallel lines will have the same slope
answer is : -4

slope of line perpendicular to x - 3y = 9
-3y = -x + 9
y = 1/3x - 3....slope = 1/3.....flip...3/1....change sign...-3 <== answer

slope of line parallel to 10x - 5y = 8
-5y = -10x + 8
y = 2x - 8/5....slope = 2....parallel lines have same slope...answer = 2

slope of line parallel to 4x + 2y = 5
2y = -4x + 5
y = -2x + 5/2.....slope = -2

y=-4x would be parallel to 4x + y = -1

y=-3x would be perpendicular to x - 3y = 9

y=-2x would be parallel to 10x - 5y = 8

y=2x would be parallel to 4x + 2y = 5

What is the squareroot of 343

Answers

Well, first of all, every positive number has two square roots.
Their digits are the same, but one is positive and one is negative.

The square root of 343 is an irrational number, so it can't ever be
exactly written with digits. As a decimal, it never ends or repeats,
and as a fraction, it can't be written at all.

The positive square root starts out 18.52025... and keeps going forever.

The other square root is the negative of that same number.
When you multiply either of them by itself, the product is close
to 343 . The more decimal places you include, the closer it gets,
but it can never be exactly 343 .

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