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We know that the bionomial must be \((2x + y)^2\), that way the 2 2x's multiply out to \(4x^2\)

Expanding the bionomial out as is gives us: \(4x^2+2xy+2xy+y^2\)

We want the 2 2xy's to sum to 14x, so we have the equation: \(4xy= 14x\). Solving for y, we find \(y = {7 \over2}\)

Now, we have to findsubsitute this in, and expand. 

Hint: The co-efficent will be \(y^2\)

\(If\ 5^x=100,wath\ is\ the\ value\ of\ 5^{x+2}\ ?\)

Hello Guest!

\(5^x=100\\ x\cdot lg\ 5=2\)

\(x=\frac{2}{lg\ 5}\\ 5^{\frac{2}{lg\ 5}+2}=\color{blue}2500\)

  !

Answered here: https://web2.0calc.com/questions/coordinates_83752

Answered here: https://web2.0calc.com/questions/pls-haaaaalp_1

Note that \(5^{x+2} = 5^x \times 5^2\)

We know that \(5^x = 100\), so \(5^{x+2} = 100 \times 5^2 = \text{____}\)

Hi Guest!

\(m^3 + 24m^2 - 2022 = 3^{(n)}\)

I graphed

\(f(m)=m^3 + 24m^2 - 2022 -3^n=0\\ n\in \{0,1,2,\ ...\}\)

The zeros in the graph are approximately

\(m\in \{-17,-15,\ 8\}.\)  

By trying with the exponents

\(n\in\{0,1\}\) 

I found that the function with the integers

\(m\in \{-17,-15,\ 8\}\) 

gives the value zero.

Greatings

  !

Thanks, but I solved it and the answer was 13/25.

MaxWong answered this question on the link provided, and according to him, the answer is \(13 \over 50\)

Here is the answer: https://web2.0calc.com/questions/probability_11169#r1

And here is the link to the graph: https://www.desmos.com/calculator/t08bdptj6k

I don't see the graph. Are you sure this is correct?

See the answer and the Graph here:  https://web2.0calc.com/questions/probability_11169#r1

BE = 15/2.

alternatively, POLYNOMIAL is a series of terms linked together by addition and subtraction

It says it's wrong...

Using geometric probability, the answer is 11/20.

16 = 2⁴.

The question is basically asking how many even (divisible by 2) numbers are between 1 and 100 inclusive. 

There are 50 even numbers in between 1 and 100.

There are 50 numbers n in between 1 and 100 inclusive such that n/16 is reducable.

Note that k CANNOT be equal to zero.

One root is \(x = {-7 + \sqrt{49-12k} \over 6}\), while the other is \(x = {-7 - \sqrt{49-12k} \over 6}\).

Their reciprocals are \(6 \over -7+\sqrt{49-12k}\) and \(6 \over -7-\sqrt{49-12k}\).

Adding those gives this nice expression: - \(7 \over k\) 

This is equal to one.

-7/k = 1

k = -7

I assume that the buses are all the same size.

259 - 27 = 232

232/8 = 29

There were 29 kids in each bus. 

Wedge.

Cube both sides: 

3 - x = -27/8

\(x = 3 + {27\over8}\)

\(x={51\over 8}\)

Note that f(x) will always put out a value greater than or equal to four for an imput of less than or equal to four. 

For x<=4:

f(f(x)) = a(f(x))+b = a(8 - x) + b = x

We want (a,b) such that a(8 - x) + b = x for x<=4.

-ax + 8a + b = x

There is only one term on the left that contains x, which means that it must be equal to x. The only value of a that would do that is a = -1.

x - 8 + b = x

b = 8

a + b = 7

(I didn't check this, it could be wrong)

The sum of the exterior angles is always 360 degrees. This means that the exterior angles of this triangle are 90 degrees, 135 degrees, and 135 degrees. This would make the interior angles 90 degrees, 45 degrees, and 45 degrees, which makes the smallest angle 45 degrees.

I believe if you graph it on a graphing application of some sort the answer should be pretty clearly \((-\infty, \infty)\).

This is equal to (1-x²)¹⁰, since (1+x)^10 x (1-x)^10 = ((1+x)(1-x))^10.

A binomial raised to any power n has n+1 terms (assuming nothing simplifies).

There will be 10+1= 11 terms upon combining all like terms (I think).

\(x = \dfrac{15}{4}\)

LCM of 180 and 1 = 180
GCD of 180 and 1 = 1
LCM of 90 and 2 = 90
GCD of 90 and 2 = 2
LCM of 60 and 3 = 60
GCD of 60 and 3 = 3
LCM of 45 and 4 = 180
GCD of 45 and 4 = 1
LCM of 36 and 5 = 180
GCD of 36 and 5 = 1
LCM of 30 and 6 = 30
GCD of 30 and 6 = 6
LCM of 20 and 9 = 180
GCD of 20 and 9 = 1
LCM of 18 and 10 = 90
GCD of 18 and 10 = 2
LCM of 15 and 12 = 60
GCD of 15 and 12 = 3