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3 years ago

The proper scientific notation for 676,000,000,000 is?

1 answer:

7 0

6.76 x 10^11
this is because when you are placing something in a scientific notation you basically move the decimal place behind the last hole number in this case 6. and count the remaining numbers behind the decimal such as .76,000,000,000 which there 11 counting 76 with the zeros. then you place the number of places behind the decimal as an exponent of 11 and keep all real numbers besides 0 as your other half

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Which ordered pair is a solution to the system of linear equations 1/2x-3/4y=11/60 and 2/5x+1/6y=3/10

Leona [35]

Answer:

( $\frac{2}{3} , \frac{1}{5}$ )

Step-by-step explanation:

The fastest way to do this is to convert both equations into slope-intercept form and graph it to find the solution point. If you wanted to do this algebraically, you might want to start out by getting rid of the fractions and using either substitution or elimination to find x and y.

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3 years ago

Which of the following is equivalent to -2/3?

arlik [135]

Answer:

Step-by-step explanation:

-2/3 = -4/6 = -6/9 = -8/12

= -10/15 = -12/18 = -14/21 = -16/24

= -18/27 = -20/30 = -22/33 = -24/36

= -26/39 = -28/42 = -30/45 = -32/48

= -34/51 = -36/54 = -38/57 = -40/60

= -42/63 = -44/66 = -46/69 = -48/72

= -50/75 = -52/78 = -54/81 = -56/84

= -58/87 = -60/90 = -62/93 = -64/96

= -66/99 = -68/102 = -70/105 = -72/108

= -74/111 = -76/114 = -78/117 = -80/120

= -82/123 = -84/126 = -86/129 = -88/132

= -90/135 = -92/138 = -94/141 = -96/144

= -98/147 = -100/150 = -102/153 = -104/156

= -106/159 = -108/162 = -110/165 = -112/168

= -114/171 = -116/174 = -118/177 = -120/180

= -122/183 = -124/186 = -126/189 = -128/192

= -130/195 = -132/198 = -134/201 = -136/204

= -138/207 = -140/210 = -142/213 = -144/216

= -146/219 = -148/222 = -150/225 = -152/228

= -154/231 = -156/234 = -158/237 = -160/240

= -162/243 = -164/246 = -166/249 = -168/252

= -170/255 = -172/258 = -174/261 = -176/264

= -178/267 = -180/270 = -182/273 = -184/276

= -186/279 = -188/282 = -190/285 = -192/288

= -194/291 = -196/294 = -198/297 = -200/300

5 0

3 years ago

Find the lateral area of the figure geometry

Arlecino [84]

Answer:

A) 420 in²

Step-by-step explanation:

The lateral surface area excludes the area of top and bottom faces.

Given is the right pentagonal prism with side length of 7 in and height of 12 in.

<u>The lateral area is:</u>

L = Ph = 5*7*12 = 420 in²

Correct choice is A

6 0

2 years ago

Another word for x-intercepts?

Nina [5.8K]

Answer:

X-intercepts are also called zeros, roots, solutions, or solution sets.

5 0

3 years ago

Solve the following recurrence relation: <br> <img src="https://tex.z-dn.net/?f=A_%7Bn%7D%3Da_%7Bn-1%7D%2Bn%3B%20a_%7B1%7D%20%3D

-Dominant- [34]

By iteratively substituting, we have

$a_n = a_{n-1} + n$

$a_{n-1} = a_{n-2} + (n - 1) \implies a_n = a_{n-2} + n + (n - 1)$

$a_{n-2} = a_{n-3} + (n - 2) \implies a_n = a_{n-3} + n + (n - 1) + (n - 2)$

and the pattern continues down to the first term $a_1=0$ ,

$a_n = a_{n - (n - 1)} + n + (n - 1) + (n - 2) + \cdots + (n - (n - 2))$

$\implies a_n = a_1 + \displaystyle \sum_{k=0}^{n-2} (n - k)$

$\implies a_n = \displaystyle n \sum_{k=0}^{n-2} 1 - \sum_{k=0}^{n-2} k$

Recall the formulas

$\displaystyle \sum_{n=1}^N 1 = N$

$\displaystyle \sum_{n=1}^N n = \frac{N(N+1)}2$

It follows that

$a_n = n (n - 2) - \dfrac{(n-2)(n-1)}2$

$\implies a_n = \dfrac12 n^2 + \dfrac12 n - 1$

$\implies \boxed{a_n = \dfrac{(n+2)(n-1)}2}$

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2 years ago