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IRISSAK [1]
3 years ago
6

Please help. WIll give brainliest if you explain

Mathematics
1 answer:
Eddi Din [679]3 years ago
5 0
The answer to 2 is <span>√30/5 or 1.09545

First, you multiply the numerator and denominator by </span>√5. 
√6x<span>√5=√30 
</span>√5x<span>√5=5 (when a square root of an expression is multiplied by itself, the result is that expression) Therefore, the answer is </span><span>√30/5 or 1.09545
</span>

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Expand the following using the Binomial Theorem and Pascal’s triangle. (x + 2)6 (x − 4)4 (2x + 3)5 (2x − 3y)4 In the expansion o
ivolga24 [154]
\bf (2x+3)^5\implies &#10;\begin{array}{llll}&#10;term&coefficient&value\\&#10;-----&-----&-----\\&#10;1&&(2x)^5(+3)^0\\&#10;2&+5&(2x)^4(+3)^1\\&#10;3&+10&(2x)^3(+3)^2\\&#10;4&+10&(2x)^2(+3)^3\\&#10;5&+5&(2x)^1(+3)^4\\&#10;6&+1&(2x)^0(+3)^5&#10;\end{array}

as you can see, the terms exponents, for the first term, starts at highest, 5 in this case, then every element it goes down by 1, till it gets to 0

for the second term, starts at 0, and every element it goes up by 1, till it gets to the highest

now, to get the coefficient, they way I get it, is "the product of the current coefficient and the exponent of the first term, divided by the exponent of the second term plus 1"

notice the first coefficient is always 1

so...how did we get 10 for the 3rd element?  well, 5*4/2
how did we get 10 for the fourth element?  well, 10*2/4


\bf (2x-3y)^4\implies &#10;\begin{array}{llll}&#10;term&coefficient&value\\&#10;-----&-----&-----\\&#10;1&&(2x)^4(-3y)^0\\&#10;2&+4&(2x)^3(-3y)^1\\&#10;3&+6&(2x)^2(-3y)^2\\&#10;4&+4&(2x)^1(-3y)^3\\&#10;5&+1&(2x)^0(-3y)^4&#10;\end{array}


\bf (3a+4b)^8\implies &#10;\begin{array}{llll}&#10;term&coefficient&value\\&#10;-----&-----&-----\\&#10;1&&(3a)^8(+4b)^0\\&#10;2&+8&(3a)^7(+4b)^1\\&#10;3&+28&(3a)^6(+4b)^2\\&#10;4&+56&(3a)^5(+4b)^3\\&#10;5&+70&(3a)^4(+4b)^4\\&#10;6&+56&(3a)^3(+4b)^5\\&#10;7&+28&(3a)^2(+4b)^6\\&#10;8&+8&(3a)^1(+4b)^7\\&#10;9&+1&(3a)^0(+4b)^8&#10;\end{array}

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like for example, the 7th element of (3a+4b)⁸ will then be 1032192a²b⁶
7 0
3 years ago
Read 2 more answers
Priya rode her bike 1250 feet. If her bike wheel has a diameter of 2.5 feet, how many times did her wheel make a full rotation?
Alex17521 [72]

Answer:

  • 159 times

Step-by-step explanation:

<h3>Given</h3>
  • d = 2.5 ft
  • Distance = 1250 ft
<h3>To find</h3>
  • Number of rotations
<h3>Solution</h3>

<u>Circumference of the wheel is the one full rotation:</u>

  • C = πd = 3.14*2.5 = 7.85 ft

<u>Number rotations:</u>

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<u>Correct option is</u> 159 times

5 0
3 years ago
Write the equation of the line that is the perpendicular bisector of the segment with endpoints (4, 1) and (2, -5)
Sedbober [7]

Answer:   \bold{y=-\dfrac{1}{3}x-1}

<u>Step-by-step explanation:</u>

(4, 1) & (2, -5)

First, find the slope (m) and then the perpendicular (opposite reciprocal) slope:

m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\\m=\dfrac{-5-1}{2-4} = \dfrac{-6}{-2}=3\quad \rightarrow \quad m_{\perp}=-\dfrac{1}{3}\\

Next, find the midpoint of (4, 1) and (2, -5):

Midpoint=\bigg(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\bigg)\\\\\\.\qquad \qquad=\bigg(\dfrac{4+2}{2},\dfrac{1-5}{2}\bigg)\\\\\\.\qquad \qquad=\bigg(\dfrac{6}{2},\dfrac{-4}{2}\bigg)\\\\\\.\qquad \qquad=(3, -2)

Lastly, input the perpendicular slope and the midpoint into the Point-Slope formula to find the equation of the line:

y - y_1 = m_{\perp}(x - x_1)\\\\y - (-2) = -\dfrac{1}{3}(x - 3)\\\\y + 2=-\dfrac{1}{3}x +1\\\\y =-\dfrac{1}{3}x - 1\\


6 0
2 years ago
Help me please I’m not sure about this
frutty [35]

easy, 36/6=6

6 people, right?

7 0
3 years ago
Read 2 more answers
A population, P, of birds is doubling in size each year, according to the model P = 100(2t), where t reperesents years. What was
mina [271]
The initial population size was 200
5 0
2 years ago
Read 2 more answers
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