Prove identity tan 3x−tan 2x−tanx = tan 3xtan 2xtanx

Answers

Answer 1

Answer: tan ( a + b ) = [ tan a + tan b ] / [ 1 - (tan a)*(tan b) ];

let be a = 2x and b = x;

=> tan 3x = [ tan 2x + tan x ] / [ 1 - (tan 2x)*(tan x) ] => (tan 3x)*[ 1 - (tan 2x)*(tan x) ] =

tan 2x + tan x => tan3x - tan 3xtan 2xtanx = tan 2x + tan x => tan 3x−tan 2x−tanx = tan 3xtan 2xtanx.

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Which represents the solution(s) of the system of equations, y = –x2 + 6x + 16 and y = –4x + 37? Determine the solution set algebraically.a.(3, 25)
b.(–3, 49)
c.(3, 25) and (7, 9)
d.(–3, 49) and (–7, 65)

Answers

Answer: c.(3, 25) and (7, 9)

y = –x^2 + 6x + 16 and y = –4x + 37

Plug in -4x+37 for y in first equation . It becomes

$-x^2 + 6x + 16= -4x+37$

Combine like terms. add 4x and subtract 37 on both sides

$-x^2 + 10x - 21=0$

Divide the whole equation by -1 to remove negative sign from -x^2

$x^2 - 10x + 21=0$

Now factor the left hand side

(x-7)(x-3) = 0

x-7 =0 and x-3=0

x= 7 and x=3

Now we find out y using y = –4x + 37

when x= 7 , then y=-4(7) +37 = 9

when x= 3, then y=-4(3) + 37 = 25

We write solution set as (x,y)

(7,9) and (3,25) is our solution set

TO determine the solution set of the equations given above, we can use substitution method. We do as follows:

y = –x2 + 6x + 16 and y = –4x + 37

–x2 + 6x + 16 = –4x + 37
-x^2 +10x -21 = 0
x = 7 and 3
y = 9 and 25

Therefore, option C is the correct answer.

Find the Surface Area of a cylinder with a base radius of 2 cm and a height of 3 cm. Use pi = 3.14

Answers

$A_S=2\pi r^2+2\pi rH\n\nr=2cm;\ H=3cm\n\nA_S=2\pi\cdot2^2+2\pi\cdot2\cdot3=2\pi\cdot4+2\pi\cdot6=8\pi+12\pi=20\pi\ (cm^2)\n\n20\pi\approx20\cdot3.14=62.8\ (cm^2)$

$S=2\pi r(r+h)\n S=2\cdot3.14\cdot2\cdot(2+3)\n S=12.56\cdot5\n S=62.8\ cm^2$

Find the volume of the given prism. round to the nearest tenth if necessary.

Answers

Volume of triangular prism = area of triangle x length.
Here, the triangle is an equilateral triangle with sides 14yds
Area of the triangle = 1/2 x 14 x 14 x sin 60 = 84.87 square yds
volume of the triangular prism = 84.87 x 25 = 2,121.8 cubic yds

Two sides of a triangle measure 8 cm and 15 cm. which could be the length of the third side?

Answers

something grater than 23.

Answer:28

Step-by-step explanation:

What is the area, in square, of the rectangle?Sides 2
----
9

Top and bottom 3
----
7

Answers

For the area of a square or rectangle you multiply the sides. So 2 times 9 is 18. And then for the other it would be 3 times 7, which is 21.

What are the perfect square trinomials?

Answers

A perfect square trinomial is

(square of one term) + (square of another term) + (double the product of the two terms)

Let's look at the following trinomial.

X² - 14x + 49

(x - 7) (x - 7)

(x - 7)²

This trinomial would be classified as a perfect square trinomial because it factors as two identical binomials which is (x - 7)². This means that any trinomial that factors as two identical binomials is called a perfect square trinomial.

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