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3 years ago

Compare 4.6, 2.8..., square root 17, 3.9..., square root 8

1 answer:

7 0

1. Square root 17= 289, Square root 8= 64.
$289 = 289.00 \: \: 64 = 64.00$
$4.6 > 2.8$
$289.00 > 64.00$
$289.00 > 4.6$
$4.6 > 3.9$
$2.8 < 3.9$
Least to greatest:
2.8, 3.9, 4.6, 64.00, 289.00

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What will be the value in twenty years of $1000 invested at the end of each year for the next twenty years?

denis23 [38]

The formula for yearly compound interest is A(1 + r)^t

Where is A = 1000, r = 8%, t = 20

$1000(1 + .08)^{20} = 4660.96$

The answer is $4660.96

3 0

3 years ago

Blake is playing a racing game on his computer. The game tracks the locations of objects using and y coordinates (see graph belo

Anvisha [2.4K]

<h3>Answer: 2.2 units</h3>

============================================

Explanation:

I'll define these point labels

B = Blake's starting position
F = finish line
C = the third unmarked point of the triangle

The locations of the points are

B = (-8,1)
C = (-6,-3)
F = (4,-2)

Use the distance formula to find the distance from B to C

$B = (x_1,y_1) = (-8,1) \text{ and } C = (x_2,y_2) = (-6,-3)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-8-(-6))^2 + (1-(-3))^2}\\\\d = \sqrt{(-8+6)^2 + (1+3)^2}\\\\d = \sqrt{(-2)^2 + (4)^2}\\\\d = \sqrt{4 + 16}\\\\d = \sqrt{20} \ \text{ ... exact distance}\\\\d \approx 4.47214 \ \ \text{... approximate distance}\\\\$

Segment BC is roughly 4.47214 units long.

Following similar steps, you should find that segment CF is approximately 10.04988 units long.

If Blake doesn't take the shortcut, then he travels approximately BC+CF = 4.47214+10.04988 = 14.52202 units. This is the path from B to C to F in that order.

---------

Use the distance formula again to find the distance from B to F. This distance is about 12.36932 units. He travels this amount if he takes the shortcut.

Subtract this and the previous result we got

14.52202 - 12.36932 = 2.1527

That rounds to 2.2

This is the amount of distance he doesn't have to travel when he takes the shortcut.

In other words, the track is roughly 2.2 units shorter when taking the shortcut.

Side note: Replace "units" with whatever units you're working with (eg: feet or meters).

7 0

3 years ago

Use the function f(x) = 4x2 − 7x − 15 to answer the questions. Part A: Completely factor f(x). (2 points) Part B: What are the x

makkiz [27]

Answer:

Part A: f(x) = 4·x² - 7·x-15 = (x - 3)·(4·x + 5)

Part B: The x-intercepts are x = 3 and -1.25 #

Part C: As x approaches ∞, y approaches ∞, as x approaches -∞, y approaches ∞

Part D: The graph is a u-shaped quadratic equation graph passing though the x-intercept points -1.25 and 3 on the x-axis and the y-intercept point -15 on the y-axis. Both sides of the symmetrical graph curve extending to infinity

Step-by-step explanation:

The function 4·x² - 7·x-15

To factorize the expression, we have at the 0 factors;

$x = \dfrac{-b\pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}$

Where;

a = 4, b = -7, c -15, substituting gives;

$x = \dfrac{-(-7)\pm \sqrt{(-7)^{2}-4\times 4\times (-15)}}{2\times 4} = \dfrac{7\pm 17}{8} = 3 \ or -1.25$

Which gives;

(x - 3)·(x + 1.25) = (x - 3)·(4·x + 5)

f(x) = 4·x² - 7·x-15 = (x - 3)·(4·x + 5)

Part B: The x-intercepts are the point where y = 0, which are x = 3 and -1.25 as shown above

Part C: As x approaches ∞, y approaches ∞, as x approaches -∞, y approaches ∞

Part D: With the the nature of the function as y approaches ∞ and -∞ the graph is a u-shaped graph of a quadratic equation passing though the points -1.25 and 3 on the x-axis and the point -15 on the y-axis.

6 0

3 years ago

Find the arc length of the semicircle. Either enter an exact answer in terms of π or use 3.14 for π and enter your answer as a d

inna [77]

Answer:

hope this helps you