Attempt 1 of 2

zepelin [54]

Answer:

Step-by-step explanation:

i). $\frac{48a^3}{6a}=\frac{6\times 8\times a\times a^2}{6a}$

$=\frac{6a}{6a}\times 8a^2$

= 8a²

ii). $\frac{72a^3b^4c^5}{8ab^2c^3}$ = $\frac{8\times 9\times a\times a^2\times b^2\times b^2\times c^2\times c^3}{8ab^2c^3}$

= $\frac{8ab^2c^3}{8ab^2c^3}\times 9a^2b^2c^2$

= 9a²b²c²

8 0

2 years ago

In ΔWXY, the measure of ∠Y=90°, XW = 53, YX = 28, and WY = 45. What is the value of the cosine of ∠X to the nearest hundredth?

kotegsom [21]

The value of ∠X = 58.11°, If ΔWXY, the measure of ∠Y=90°, XW = 53, YX = 28, and WY = 45.

Step-by-step explanation:

The given is,

In ΔWXY, ∠Y=90°

XW = 53

YX = 28

WY = 45

Step:1

Ref the attachment,

Given triangle XWY is right angled triangle.

Trigonometric ratio's,

$Cos$ ∅ $= \frac{Adj}{Hyp}$

For the given attachment, the trigonometric ratio becomes,

$Cos$ ∅ $= \frac{XY}{XW}$ .....................................(1)

Let, ∠X = ∅

Where, XY = 28

XW = 53

Equation (1) becomes,

$Cos$ ∅ $= \frac{28}{53}$

$Cos$ ∅ = 0.5283

∅ = $cos^{-1}$ (0.5283)

∅ = 58.109°

Result:

The value of ∠X = 58.11°, If ΔWXY, the measure of ∠Y=90°, XW = 53, YX = 28, and WY = 45.

4 0

3 years ago

How does one find the inverse function of f(x)= <img src="https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3x-1%7D" id="TexFormula1" tit

lisabon 2012 [21]

Answer:

$\displaystyle f^{-1}(x)=\frac{1+x}{3x}$

Step-by-step explanation:

<u>The Inverse of a Function</u>

The procedure to find the inverse of the function is:

* Write the function as a two-variable equation:

$\displaystyle y=\frac{1}{3x-1}$

* Solve the equation for x.

Multiply by 3x-1

$y(3x-1)=1$

Divide by y:

$\displaystyle 3x-1=\frac{1}{y}$

Sum 1:

$\displaystyle 3x=\frac{1}{y}+1$

Operate the right side:

$\displaystyle 3x=\frac{1+y}{y}$

Divide by 3:

$\displaystyle x=\frac{1+y}{3y}$

* Swap the variables:

$\displaystyle y=\frac{1+x}{3x}$

Write back into function form:

$\boxed{\displaystyle f^{-1}(x)=\frac{1+x}{3x}}$

7 0

3 years ago

Given m∥n .

frosja888 [35]

Answer: heres the answer for future people lel

8 0

3 years ago

Simplify polynomial

Kay [80]

Answer:

j² - 5j²k - 2

Step-by-step explanation:

3j² - j²k - 6 - 4j²k - 2j² + 4

To simplify this polynomial, we can collect like terms. A term is number(s) or variable(s) that are grouped together by multiplication. <u>Like terms have the same variable and exponent</u>.

We have three groups of like terms:

The j-squares (j²), the j-squared k (j²k) and the constants (no variable).

Remember to include the negatives!

The j-squares are: 3j² ; -2j²

The j-squares k are: - j²k ; - 4j²k

The constants are: - 6 ; 4

Simplify:

3j² - j²k - 6 - 4j²k - 2j² + 4

Rearrange the polynomial by like terms

= (- j²k - 4j²k) + (3j² - 2j²) + (- 6 + 4)

Add or subtract the like terms

= (-5j²k) + (j²) + (-2)

Remove brackets and rearrange so the negative is not first

= j² + - 5j²k + - 2

Simplify where two signs are together. Adding a negative is subtraction.

= j² - 5j²k - 2 Simplified

8 0

3 years ago