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Goryan [66]
3 years ago
11

Can someone please help on number 20? WILL MARK YOU AS BRAINIEST. (can you also show how you do the problem?) :(

Mathematics
1 answer:
PSYCHO15rus [73]3 years ago
5 0

Answer:

x =(22-√196)/6=(11-7)/3= 1.333

Step-by-step explanation:

(3x2 -  22x) +  24  = 0

The first term is,  3x2  its coefficient is  3 .

The middle term is,  -22x  its coefficient is  -22 .

The last term, "the constant", is  +24

Step-1 : Multiply the coefficient of the first term by the constant   3 • 24 = 72

Step-2 : Find two factors of  72  whose sum equals the coefficient of the middle term, which is   -22 .

     -72    +    -1    =    -73

     -36    +    -2    =    -38

     -24    +    -3    =    -27

     -18    +    -4    =    -22    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -18  and  -4

                    3x2 - 18x - 4x - 24

Step-4 : Add up the first 2 terms, pulling out like factors :

                   3x • (x-6)

             Add up the last 2 terms, pulling out common factors :

                   4 • (x-6)

Step-5 : Add up the four terms of step 4 :

                   (3x-4)  •  (x-6)

            Which is the desired factorization

Equation at the end of step 2:

 (x - 6) • (3x - 4)  = 0

STEP 3:

Theory - Roots of a product

3.1    A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

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Angle θ is in standard position. If (8, -15) is on the terminal ray of angle θ, find the values of the trigonometric functions.
nikitadnepr [17]

Answer:

* sin Ф = -15/17     * cos Ф = 8/17      * tan Ф = -15/8

* csc Ф = -17/15    * sec Ф = 17/8      * cot Ф = -8/15

Step-by-step explanation:

Lets revise the trigonometric function of angle Ф

- Angle θ is in standard position

- Point  (8, -15) is on the terminal ray of angle θ

- That means the terminal is the hypotenuse of a right triangle x and y

  are its legs

∵ x-coordinate is positive and y-coordinate is negative

∴ angle Ф lies in the 4th quadrant

- The opposite side of angle Ф is the y-coordinate of the point on the

  terminal ray of angle Ф and the adjacent side to angle Ф is the

  x-coordinate of that point

∵ The length of the hypotenuse (h) = √(x² + y²)

∴ h = √[(8)² + (-15)²] = √[64 + 225] = √[289] = 17

∴ The length of the hypotenuse is 17

- Lets find sin Ф

∵ sin Ф = opposite/hypotenuse

∵ The opposite is y = -15

∵ The hypotenuse = 17

∴ sin Ф = -15/17

- Lets find cos Ф

∵ cos Ф = adjacent/hypotenuse

∵ The adjacent is x = 8

∵ The hypotenuse = 17

∴ cos Ф = 8/17

- Lets find tan Ф

∵ tan Ф = opposite/adjacent

∵ The opposite is y = -15

∵ The adjacent = 8

∴ tan Ф = -15/8

- Remember csc Ф is the reciprocal of sin Ф

∵ csc Ф = 1/sin Ф

∵ sin Ф = -15/17

∴ csc Ф = -17/15

- Remember sec Ф is the reciprocal of cos Ф

∵ sec Ф = 1/ cos Ф

∵ cos Ф = 8/17

∴ sec Ф = 17/8

- Remember cot Ф is the reciprocal of tan Ф

∵ cot Ф = 1/tan Ф

∵ tan Ф = -15/8

∴ cot Ф = -8/15

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