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4 years ago

Two lines are perpendicular if they are para el and cross

Mathematics

1 answer:

eduard4 years ago

3 0

Answer:

If they create a 90 degree angle then yes.

You might be interested in

Find an nth-degree polynomial function with real coefficients satisfying the given conditions.

lesya692 [45]

Answer:

$\displaystyle f(x) = -2(x-2)(x^2+4)$

Step-by-step explanation:

We want to find a third degree polynomial with zeros x = 2 and x = 2i and f(-1) = 30.

First, note that by the Complex Root Theorem, since x = 2i is a root, x = -2i must also be a root.

Hence, we will have the three factors:

$\displaystyle f(x) = a(x-(2))(x-(2i))(x-(-2i))$

Where a is the leading coefficient.

Expand and simplify the second and third factors:

$\displaystyle \begin{aligned} (x-(2i))(x-(-2i)) &= (x-2i)(x+2i) \\ \\ &= x(x-2i)+2i(x-2i) \\ \\ &= (x^2 - 2ix) + (2ix - 4i^2) \\ \\ &=x^2 + 4\end{aligned}$

Hence:

$\displaystyle f(x) = a(x-2)(x^2+4)$

Since f(-1) = 30:

$\displaystyle \begin{aligned} f(x) &= a(x-2)(x^2+4) \\ \\ (30) &= a((-1)-2)((-1)^2+4) \\ \\ 30 &= -15a \\ \\ a&= -2\end{aligned}$

In conclusion, third degree polynomial function is:

$\displaystyle f(x) = -2(x-2)(x^2+4)$

5 0

3 years ago

Solve this please show your work <3

Nookie1986 [14]

Given:

The expression is

$\sqrt[3]{48}=\sqrt[3]{8\cdot \_\_}=$

To find:

The simplified form of the expression.

Solution:

We have,

$\sqrt[3]{48}=\sqrt[3]{8\cdot \_\_}=$

The expression $\sqrt[3]{48}$ can be written as

$\sqrt[3]{48}=\sqrt[3]{8\cdot 6}$

$\sqrt[3]{48}=\sqrt[3]{8}\cdot \sqrt[3]{6}$ $[\because \sqrt[3]{ab}=\sqrt[3]{a}\sqrt[3]{b}]$

$\sqrt[3]{48}=2\cdot \sqrt[3]{6}$

$\sqrt[3]{48}=2\sqrt[3]{6}$

Therefore, $\sqrt[3]{48}=\sqrt[3]{8\cdot 6}=2\sqrt[3]{6}$ .

5 0

3 years ago

You are choosing numbers from the set S ={A, B, C, D, E, F, G, H}. Let x = the number of ways to choose 3 letters from S without

postnew [5]

Given set S = {A, B, C, D, E, F, G, H}
There are 8 elements in set S and we are to choose 3 letters at random, the number of ways to choose such is x. It is simply similar to choosing 5 letters at random, which is also equal to x. Since order doesn't matter, n! / (n-m)! where n = 8 and m = 3, which is 336 ways.

6 0

3 years ago

Once each day, Erika tracks the depth of the water in her local creek. Her first nine measurements, in inches, are: 16, 15, 13,

solniwko [45]

Answer:

Median = 13

Step-by-step explanation:

We are given the following data:

16, 15, 13, 12, 17, 14, 11, 9, 11

Formula:

$Median:\\\text{If n is odd, then}\\\\Median = \displaystyle\frac{n+1}{2}th ~term \\\\\text{If n is even, then}\\\\Median = \displaystyle\frac{\frac{n}{2}th~term + (\frac{n}{2}+1)th~term}{2}$