2.

Angelina_Jolie [31]

Answer: x=(7√6)/2

Step-by-step explanation:

To find x, we would have to find the hypotenuse of the 45-45-90 triangle. First, we would have to find the hypotenuse by using the 30-60-90 triangle on top to find it.

For a 30-60-90 triangle, the hypotenuse is 2x in length. the x is the same in all sides. All you would have to do is to plug it in. The leg opposite of 60° is x√3 in length. the leg opposite of 30° is x in length.

Since we know that 7 is opposite of the 30° angle, we know that x is 7. Across fron 60° is the hypotenuse of the 45-45-90 triangle. That leg is x√3. We plug in x=7 and get 7√3.

The hypotenuse of the 45-45-90 triangle is x√2 and the legs are both x. We can set 7√3 equal to x√2 to find x of the missing side.

7√3=x√2 [divide both sides by √2]

x=(7√6)/2

Now, we know x=(7√6)/2.

8 0

3 years ago

What is the simplified form of x minus 2 over x squared plus x minus 6divided byx squared plus 5x plus 4 over x plus 4?

tatyana61 [14]

Answer:

$\dfrac{1}{x^2+4x+3}$

Step-by-step explanation:

You have asked for the simpilfied form of ...

$x-\dfrac{2}{x^2}+x-\dfrac{6}{x^2}+5x+\dfrac{4}{x}+4$

That would be ...

$\dfrac{7x^3+4x^2+4x-4}{x^2}$

We suspect that's not what you meant. Parentheses are required for grouping when you write math expressions in text form. They work best using math symbols instead of words. We think you mean

... ((x -2)/(x^2 +x -6))/((x^2 +5x +4)/(x +4))

_____

Maybe you want to simplify ...

$\displaystyle\frac{\left(\frac{x-2}{x^2+x-6}\right)}{\left(\frac{x^2+5x+4}{x+4}\right)}=\frac{(x-2)(x+4)}{(x-2)(x+3)(x+4)(x+1)}\\\\=\frac{1}{(x+1)(x+3)}=\frac{1}{x^2+4x+3}$

_____

Comment on simplifying rational expressions

Division of fractions works the same whether you're working with numbers or polynomials (or anything else). Dividing by something is the same as multiplying by its inverse (reciprocal).

(a/b)/(c/d) = (a/b)·(d/c)

I learned this as "invert and multiply". I've recently seen it referred to as "copy dot flip", meaning you copy the numerator, use a dot symbol to indicate multipication, then flip the denominator (make its reciprocal) to become what you're multiplying by.

8 0

3 years ago

Samples of skin experiencing desquamation are analyzed for both moisture and melanin content. The results from 100 skin samples

zheka24 [161]

Answer: a. 0.40 b. 0.23 c . 0.435 d . 0.25

Step-by-step explanation:

melanin content Total

high low

moisture high 13 10 23

content low 47 30 77

Total 60 40 100

Let A denote the event that a sample has low melanin content, and let B denote the event that a sample has high moisture content.

a) Total skin samples has low melanin content = 10+30=40

P(A)= $\dfrac{40}{100}=0.40$

b) Total skin samples has high moisture content = 13+10=23

P(B) = $\dfrac{23}{100}=0.23$

c) A ∩ B = Total skin samples has both low melanin content and high moisture content =10

P(A ∩ B) = $\dfrac{10}{100}=0.10$

Using conditional probability formula , $P (A|B)=\dfrac{P(A\cap B)}{P(B)}$

$P (A|B)=\dfrac{0.10}{0.23}=0.434782608696\approx0.435$

d) $P (B|A)=\dfrac{P(A\cap B)}{P(A)}$

$P (B|A)=\dfrac{0.10}{0.40}=0.25$

8 0

3 years ago

A fund earns a nominal rate of interest of 6\% compounded every two years. Calculate the amount that must be contributed now to

Nesterboy [21]

Answer:

$712.

Step-by-step explanation:

We have been given that a fund earns a nominal rate of interest of 6% compounded every two years. We are asked to find the amount that must be contributed now to have 1000 at the end of six years.

We will use compound interest formula to solve our given problem.

$A=P(1+\frac{r}{n})^{nt}$ , where,