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3 years ago

Find the length of segment JK with endpoints J(4, 8) and K(-1, -2). Leave the answer as a radical. Simplify if necessary

Mathematics

1 answer:

Alex777 [14]3 years ago

6 0

Answer:

The length of segment JK is 5 $\sqrt{5}$ ⇒ C

Step-by-step explanation:

The formula of the distance between the two points (x1, y1) and (x2, y2) is

d = $\sqrt{(x2-x1)^{2}+(y2-y1)^{2}}$

Let us use the formula above to solve the question

∵ Jk is a line segment

∵ J = (4, 8) and K = (-1, -2)

∴ x1 = 4 and y1 = 8

∴ x2 = -1 and y2 = -2

→ Substitute them in the formula above

∵ JK = $\sqrt{(-1-4)^{2}+(-2-8)^{2}}$

∴ JK = $\sqrt{(-5)^{2}+(-10)^{2}}$

∴ Jk = $\sqrt{25+100}$

∴ Jk = $\sqrt{125}$

→ Simplify the root

∵ 125 = 5 × 5 × 5

∴ $\sqrt{125}$ = 5 $\sqrt{5}$

∴ JK = 5 $\sqrt{5}$

∴ The length of segment JK is 5 $\sqrt{5}$

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Determine, using the intermediate value theorem, if the function F(x)=x^3+2x-1 has a zero on the interval [0,1]. Justify your an

SSSSS [86.1K]

Plug x = 0 into the function

f(x) = x^3 + 2x - 1

f(0) = 0^3 + 2(0) - 1

f(0) = -1

Note how the result is negative. The actual number itself doesn't matter. All we care about is the sign of the result.

Repeat for x = 1

f(x) = x^3 + 2x - 1

f(1) = 1^3 + 2(1) - 1

f(1) = 2

This result is positive.

---------------------------

We found that f(0) = -1 and f(1) = 2. The first output -1 is negative while the second output 2 is positive. Going from negative to positive means that, at some point, we will hit y = 0. We might have multiple instances of this happening, or just one. We don't know for sure. The only thing we do know is that there is at least one root in this interval.

To actually find this root, you'll need to use a graphing calculator because the root is some complicated decimal value. Using a graphing calculator, you should find the root to be approximately 0.4533976515

7 0

3 years ago

D₁ vide using x² - 2x² 2× +3× -5 by ×-3 using synthetic division. <br>

Vaselesa [24]

Answer:

Step-by-step explanation:

I think you are trying to use synthetic division for

$x^{4} -2x^{3} -2x^{2} +3x-5$ divided by x-3