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3 years ago

What is the length of line segment EF? Enter your answer, as a decimal rounded to the nearest tenth, in the box.

Mathematics

2 answers:

Zielflug [23.3K]3 years ago

6 0

2^2 + 3^2 = 4 + 9 = 13
EF = √13 = 3.6

answer
3.6

Nadya [2.5K]3 years ago

5 0

Answer:

3.6 units.

Step-by-step explanation:

We have been given an image of a coordinate plane. We are asked to find the length of line segment EF.

We will use distance formula to solve our given problem.

$\text{Distance}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Upon substituting our given values in above formula we will get,

$\text{Distance}=\sqrt{(-1--3)^2+(-2-1)^2}$

$\text{Distance}=\sqrt{(-1+3)^2+(-3)^2}$

$\text{Distance}=\sqrt{(2)^2+(-3)^2}$

$\text{Distance}=\sqrt{4+9}$

$\text{Distance}=\sqrt{13}$

$\text{Distance}=3.60555\approx 3.6$

Therefore, the length of line segment EF is 3.6 units.

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3 years ago

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Answer:

Step-by-step explanation:

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3 years ago

The function f(x)f(x) is a quartic function and the zeros of f(x)f(x) are -6−6, -5−5, -2−2 and 11. Assume the leading coefficien

Luden [163]

<h2>Answer: </h2>

$\boxed{f(x) = 11x^4 + 22x^3 - 1001x^2 - 5632x - 7260}$

<h2>Explanation: </h2>

A quartic function is a function given by the the following equation in standard form:

$f(x)=a_{4}x^4+a_{3}x^3+a_{2}x^2+a_{1}x+a_{0} \\ \\ \\ Where: \\ \\ a_{4},a_{3},a_{2},a_{1},a_{0} \ \text{are constant} \\ \\ \text{and} \ a_{4} \ \text{is the leading coefficient}$

From the statement we must assume the leading coefficient of f(x) is 11, so:

$a_{4}=11$

The zeros are:

$x=-6 \\ \\ x=-5 \\ \\ x=-2 \\ \\ x=11$

So, we can write:

$f(x)=11(x-(-6))(x-(-5))(x-(-2))(x-11) \\ \\ \\ So: \\ \\ \mathrm{Rule}:-\left(-a\right)=a \\ \\ \\ Then: \\ \\ f(x)=11\left(x+6\right)\left(x+5\right)\left(x+2\right)\left(x-11\right)$

$Expand:\left(x+6\right)\left(x+5\right):\ x^2+11x+30: \ \text{Distributive Property} \\ \\ \\ Then: \\ \\ f(x)=11\left(x^2+11x+30\right)\left(x+2\right)\left(x-11\right) \\ \\ \\ Expand:\left(x^2+11x+30\right)\left(x+2\right):\ x^3+13x^2+52x+60: \ \text{Distributive Property} \\ \\ \\ Then: \\ \\ f(x)=11\left(x^3+13x^2+52x+60\right)\left(x-11\right)$