MATHEMATICS HIGH SCHOOL

True or false? The equation (x y)^2 is always equal to x^2 y^2.

Answers

Answer 1

Answer:

Hello!

Answer:

$\Large \boxed{\sf True}$

Step-by-step explanation:

→ We want to find if the expression (xy)² is equal to x²y².

→ Let's simplify the expression:

→ We know that $\sf (a * b)^n$ is equal to $\sf a^nb^n$ .

In our expression:

$\sf a = x\nb = y\nn = 2$

→ So the expression is equal to:

$\sf x^2 y^2$

Conclusion:

The expression (xy)² is equal to x²y².

So the answer is true.

Answer 2

Answer:

Answer:

True

Step-by-step explanation:

(xy)²

= xy × xy

= x × x × y × y

= x² × y²

= x²y² ← True

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Line AB contains points A (0, 1) and B (1, 5). The slope of line AB is

Answers

For any points (x1, y1) and x2, y2)
the slope od the line joining them is
(y2-y1)/(x2-x1)

I would have say Slope = (5-1)/(1-0)= 4

so the rise = 5-1, run = 1-0

which is still 4

Which operation should be completed first ? 36÷4×3-2

Answers

36/4
PEMDAS
Parentheses
Exponents
Multiplication Division whichever comes first in the equation
Addition Subtraction whichever comes first in the equation

You should divide first, then multiply, then you subtract.

For which system of equations is (2, 2) a solution? A.–3x + 3y = 0
x + 6y = 10B.–2x + 5y = –6
4x – 2y = 4C.5x – 2y = –6
3x – 4y = 2D.2x + 3y = 10
4x + 5y = 18

Answers

$A.)\n\n-3x + 3y = 0\nx + 6y = 10 \ / *3\n\n-3x + 3y = 0\n3x + 18y = 30\n+------\n21y =30 \ / :21\n \ny=(30)/(21)=(10)/(7)\n\nnot \ true$

$B.)\n\n-2x + 5y = -6 \ / \cdot 2\n4x - 2y = 4\n \n-4x + 10y = -12 \n4x - 2y = 4 \n+-------- \n8y=-8\ /:8\n \ny=-1\n \n not \ true$

$C.\n\n5x - 2y = -6 \ / \cdot 2\n3x - 4y = 2 \n \n 10x - 4y = -12 \n 3x- 4y = 2\n+------\n13x=-11 \ / :13\n \nx=-(11)/(13)\n\n not \ true$

$D.)\n\n2x + 3y = 10\ / \cdot (-2)\n4x + 5y = 18\n\n-4x -6y =-20\n4x + 5y = 18\n+-------\n-y = -2 \ / \cdot (-1)\n \ny=2$

$2x + 3*2 = 10\n \n2x=10-6 \n \n2x=4 \ / :2 \n \n x=2 \n \n true$

$x=2\ \ \ and\ \ \ y=2\n\nA.\ \ \ \ \ \ x + 6y = 2+6\cdot2=2+12=14 \neq 10\n\nB.\ \ \ \ \ -2x + 5y =-2\cdot2+5\cdot2=-4+10=6 \neq -6\n\nC.\ \ \ \ \ \ \ 5x-2y =5\cdot2-2\cdot2=10-4=6 \neq -6\n\nD.\ \ \ \ \ \ \ 2x + 3y =2\cdot2+3\cdot2=4+3= 10\nand\ \ \ \ \ \ 4x + 5y = 4\cdot2+5\cdot2=8+10=18\n\nAns.\ (2,\ 2)\ is\ a\ solution\ for\ system \ D$

How do I get (tan^2(x)-sin^2(x))/tan(x) equal to (sin^2(x))/cot(x)

Answers

$LHS\n \n =\frac { \tan ^( 2 ){ x-\sin ^( 2 ){ x } } }{ \tan { x } } \n \n =\frac { 1 }{ \tan { x } } \left( \tan ^( 2 ){ x-\sin ^( 2 ){ x } } \right)$

$\n \n =\frac { \cos { x } }{ \sin { x } } \left( \frac { \sin ^( 2 ){ x } }{ \cos ^( 2 ){ x } } -\frac { \sin ^( 2 ){ x\cos ^( 2 ){ x } } }{ \cos ^( 2 ){ x } } \right) \n \n =\frac { \cos { x } }{ \sin { x } } \left( \frac { \sin ^( 2 ){ x-\sin ^( 2 ){ x\cos ^( 2 ){ x } } } }{ \cos ^( 2 ){ x } } \right)$

$\n \n =\frac { \cos { x } }{ \sin { x } } \cdot \frac { \sin ^( 2 ){ x\left( 1-\cos ^( 2 ){ x } \right) } }{ \cos ^( 2 ){ x } } \n \n =\frac { \cos { x } }{ \sin { x } } \cdot \frac { \sin ^( 2 ){ x\cdot \sin ^( 2 ){ x } } }{ \cos ^( 2 ){ x } } \n \n =\frac { \cos { x } \sin ^( 4 ){ x } }{ \sin { x\cos ^( 2 ){ x } } } \n \n =\frac { \sin ^( 3 ){ x } }{ \cos { x } }$

$\n \n =\sin ^( 2 ){ x } \cdot \frac { \sin { x } }{ \cos { x } } \n \n =\sin ^( 2 ){ x } \cdot \frac { 1 }{ \frac { \cos { x } }{ \sin { x } } } \n \n =\sin ^( 2 ){ x } \cdot \frac { 1 }{ \cot { x } } \n \n =\frac { \sin ^( 2 ){ x } }{ \cot { x } } \n \n =RHS$

What are the solutions to the equation (x – 2)(x + 5) = 0?

Answers

A product of two (or more) factor can be zero if and only if at least one of the factors is zero.

In other words, you cannot multiply two non-zero real numbers, and have zero as a result.

So, if we want the product of these two factors to be zero, at least one of them has to be zero.

The first factor is zero if

$x-2 = 0 \iff x=2$

The second factor is zero if

$x+5 = 0 \iff x=-5$

The solutions to the equation are x = 2 and x = -5.

To find the solutions to the equation (x – 2)(x + 5) = 0, you need to set each factor equal to zero and solve for x. When the product of two factors is equal to zero, one or both of the factors must be equal to zero.

Set x - 2 = 0 and solve for x:

x - 2 = 0

x = 2

Set x + 5 = 0 and solve for x:

x + 5 = 0

x = -5

The solutions to the equation are x = 2 and x = -5. When you substitute these values back into the original equation, you get (2 - 2)(2 + 5) = 0 and (-5 - 2)(-5 + 5) = 0, both of which evaluate to 0, confirming that these are indeed the solutions.

To know more about equation:

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2) The Club Auto Parts Company has just recently been organized. It is expected to experience no growth for the next 2 years as it identifies its market and acquires its inventory. However, Club will grow at an annual rate of 5% in the third and fourth years and, beginning with the fifth year, should attain a 10% growth rate which it will sustain thereafter. The last dividend paid was $0.50 per share. Club has a cost of capital of 12%. What should be the present price per share of Club common stock?

Answers

Answer:

$20.84

Step-by-step explanation:

div 1 = $0.50

div 2 = $0.50

div 3 = $0.50 x 1.05 = $0.525

div 4 = $0.525 x 1.05 = $0.55125

years 5 and beyond we need to use the growing perpetuity formula:

stock price = [div 4 x (1 + g)] / (r - g) = ($0.55125 x 1.1) / (12% - 10%) = $30.32

now to determine the current value of the stocks we must calculate the present value of the future dividends and stock price:

stock price = $0.50/1.12 + $0.50/1.12² + $0.525/1.12³ + $0.55125/1.12⁴ + $30.32/1.12⁴ = $0.45 + $0.40 + $0.37 + $0.35 + $19.27 = $20.84

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