Reading  at the top from left to right

The first, third and fourth equations are growth

All the rest are decay

Population in 2023  =

4600 ( 1 - .017)^7   ≈ 

4080

(1,4), (-1,2) 

First....find the slope between these two points

[2 - 4 ]  / [ -1 - 1 ]  =     -2 / -2   = 1

Using either point  - I'll use  (1, 4)  - to write the equation, we have

y  =  1 ( x - 1)  +  4

y  =  x  - 1 + 4

y  = x + 3    in slope-intercept form

Population in 2006  =

440 (1.17)^6  ≈

1129  coyotes in 2006

Graph the line for 𝑦 − 1 = 7 𝑥 − 2 on the coordinate plane 

Solve for x:
x^2 + 4 x + 13 = 0

Subtract 13 from both sides:
x^2 + 4 x = -13

Add 4 to both sides:
x^2 + 4 x + 4 = -9

Write the left hand side as a square:
(x + 2)^2 = -9

Take the square root of both sides:
x + 2 = 3 i or x + 2 = -3 i

Subtract 2 from both sides:
x = -2 + 3 i or x + 2 = -3 i

Subtract 2 from both sides:

x = -2 + 3i    or    x = -2 - 3i

y -  1 = 7x - 2     add 1 to both sides

y  = 7x  -  1

The y intercept is at   (0, -1)

Let x  = 1  and  y = 7(1)  - 1    =  6

So....the points  (0, -1)   and  (1, 6 )  are on the graph

Plot these points and connect them with a line.....that will be your graph

Simplify the following:
1 + 1/2 + 2 + 3/8

Put 1 + 1/2 + 2 + 3/8 over the common denominator 8. 1 + 1/2 + 2 + 3/8 = 8/8 + 4/8 + (8×2)/8 + 3/8:
8/8 + 4/8 + (8×2)/8 + 3/8

8×2 = 16:
8/8 + 4/8 + 16/8 + 3/8

8/8 + 4/8 + 16/8 + 3/8 = (8 + 4 + 16 + 3)/8:
(8 + 4 + 16 + 3)/8

= 31/8

I just need some help learning this.

Solve for x over the complex numbers.

494 = h - 197

h = 494 +197 = 691 m

I don't know if there is a shortcut or some formula to calculate this? Maybe somebody else on this forum does.

However, it is very easy to write a very short and simple computer code to check all the numbers from 1 up to 1,000. When you do that, this is what you get:

25! mod [1 to 1,000] =0 are the following numbers:

(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 60, 63, 64, 65, 66, 68, 69, 70, 72, 75, 76, 77, 78, 80, 81, 84, 85, 88, 90, 91, 92, 95, 96, 98, 99, 100, 102, 104, 105, 108, 110, 112, 114, 115, 117, 119, 120, 121, 125, 126, 128, 130, 132, 133, 135, 136, 138, 140, 143, 144, 147, 150, 152, 153, 154, 156, 160, 161, 162, 165, 168, 170, 171, 175, 176, 180, 182, 184, 187, 189, 190, 192, 195, 196, 198, 200, 204, 207, 208, 209, 210, 216, 220, 221, 224, 225, 228, 230, 231, 234, 238, 240, 242, 243, 245, 247, 250, 252, 253, 255, 256, 260, 264, 266, 270, 272, 273, 275, 276, 280, 285, 286, 288, 294, 297, 299, 300, 304, 306, 308, 312, 315, 320, 322, 323, 324, 325, 330, 336, 340, 342, 343, 345, 350, 351, 352, 357, 360, 363, 364, 368, 374, 375, 378, 380, 384, 385, 390, 391, 392, 396, 399, 400, 405, 408, 414, 416, 418, 420, 425, 429, 432, 437, 440, 441, 442, 448, 450, 455, 456, 459, 460, 462, 468, 475, 476, 480, 483, 484, 486, 490, 494, 495, 500, 504, 506, 510, 512, 513, 520, 525, 528, 532, 539, 540, 544, 546, 550, 552, 560, 561, 567, 570, 572, 575, 576, 585, 588, 594, 595, 598, 600, 605, 608, 612, 616, 621, 624, 625, 627, 630, 637, 640, 644, 646, 648, 650, 660, 663, 665, 672, 675, 680, 684, 686, 690, 693, 700, 702, 704, 714, 715, 720, 726, 728, 729, 735, 736, 741, 748, 750, 756, 759, 760, 765, 768, 770, 780, 782, 784, 792, 798, 800, 805, 810, 816, 819, 825, 828, 832, 833, 836, 840, 847, 850, 855, 858, 864, 874, 875, 880, 882, 884, 891, 896, 897, 900, 910, 912, 918, 920, 924, 931, 935, 936, 945, 950, 952, 960, 966, 968, 969, 972, 975, 980, 988, 990, 1000)
Total = 358

Man! That is a lot of numbers!!! If there isn't a formula, how are you supposed to calculate all of this?

3.875

3 tosses    1/2  chance of each being heads = 3/2     3 pts for each   =  9/2

The idea is to factor the stuff under the radical into two pieces.

One piece is something that has a clear cube or 4th root and the other piece is the rest.

In the first one we want to break \(-54 n^7\) into pieces one of which we can simply take the cube root of.

\(\left(-3n^2\right)^3 = -27n^6\\ -54n^7 = -27n^6 \cdot 2n \\ \sqrt[3]{-54n^7} = \sqrt[3]{-27n^6 \cdot 2n} = -3n^2 \sqrt[3]{2n} \\ -\sqrt[3]{-54n^7} = -(-3n^2\sqrt[3]{2n}) = 3n^2\sqrt[3]{2n} \)

I'll do one more for you but I'd like to see you work these out yourself

\(-5\sqrt[4]{128x^4} = -5\sqrt[4]{2^7 x^4}=\\ -5\sqrt[4]{2^4 x^4 \cdot 2^3} = -5\cdot 2x\sqrt[4]{2^3} = \\ -10x \sqrt[4]{8}\)

it's fine now i got help thanks though! :)

I don't know if it's just me, but I can't see the image. It isn't working

Thanks but I still don't understand...

\(-\sqrt[3]{-54n^7} = \\ -((-1)\sqrt[3]{54n^7} = \\ \sqrt[3]{27n^6 \cdot 2n} = \\ 3n^2\sqrt[3]{2n}\)

the rest are similar, give them another try

I don't know

Example:

sqrt(80 P^3) = sqrt (16*5  p^2 * p)  =  4p sqrt(5p)

sqrt(50n^2) = sqrt (25*2 n^2) = 5n sqrt2

   Can you do the others?   

I think I got these ones so nevermind

Tricky question subject to interpretation

   is it     81% - 33 percentage points = 48 %

      or is it    81% - 33% OF 81% = 81 - .33(81) = 54. 27 %

Really does not matter....in this case you are subtracting a smaller number when you subtract 22%   vs 33% from 81

   so the SECOND one is the larger of the two.

81%-33%=48%

81%-22%=59%

59%>48%

33%>22%