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2 years ago

Factor the following: 2x2+9x+9

Mathematics

2 answers:

ryzh [129]2 years ago

8 0

Answer: (2x+3)(x+3)

Step-by-step explanation:

Looking at this, you know that it must look something like

(? +3)(?+3) , because they must multiply to 9. The ?s must multiply to 2x^2, the most plausible values being 2x and x, ending us up with (2x+3)(x+3)

Semenov [28]2 years ago

6 0

Answer:

(x + 3) (2x + 3)

Step-by-step explanation:

2x^2+9x+9

2x^2 + 3x + 6x + 9

x(2x +3) + 3 (2x + 3)

(x + 3) (2x + 3)

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3 years ago

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The circular bases of the traditional teepees of the Sioux and Cheyenne tribes have a diameter of about 15 ft. What is the area

LenaWriter [7]

if the diameter is 15, its radius is half that, or 7.5

$\bf \textit{area of a circle}\\\\A=\pi r^2~~\begin{cases}r=radius\\[-0.5em]\hrulefill\\r=7.5\end{cases}\implies A=\pi 7.5^2\implies A=56.25\pi \\\\\\A\approx 176.71459\implies A = \stackrel{\textit{rounded up}}{177}$

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3 years ago

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What is the slope of a line perpendicular to the line with equation 2x+3y=9

zheka24 [161]

Answer:

<h2> $slope = \frac{3}{2} \\$ </h2>

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

To find the slope of the perpendicular line we must first find the slope of the original line

The original line is

2x + 3y = 9

3y = - 2x + 9

$y = - \frac{2}{3} x + \frac{9}{ 3} \\ \\ y = - \frac{2}{3} x + 3$

Since the lines are perpendicular to each other the slope of the perpendicular line is the negative inverse of the original line

So the slope of the perpendicular line is

$slope = \frac{3}{2} \\$

Hope this helps you

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3 years ago

Find the value of x in each case:

Margaret [11]

Answer:

x = 11°

4x = 44°

Step-by-step explanation:

Line BC || Line EF... (given)

BF is transversal.

$\angle BFG + \angle BFE = 180\degree\\.. (straight \: line \: \angle 's) \\ + \angle BFE = 180\degree\\\angle BFE = 180\degree-147\degree \\\angle BFE = 33\degree\\$

$\angle BED$ is exterior angle of $\angle EBF$

Hence, by remote interior angle theorem of triangle, we have:

$m\angle BED = m\angle EBF + \angle BFE \\4x = x + 33\degree \\4x - x = 33\degree \\3x = 33\degree \\x = \frac{33}{3}\\\huge \purple {\boxed {x = 11\degree}} \\4x = 4\times 11\degree \\\huge \orange{\boxed {4x = 44\degree}}$

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3 years ago

We select n + 1 diﬀerent integers from the set { 1 , 2 , ··· , 2 n } . Provethat there will alwaysbe two among the selected inte

just olya [345]

Answer:

See answer below

Step-by-step explanation:

From the set

{1,2,3,4...2n} we have 2n numbers in total , n are odd and n are even , therefore for a sample of n+1 numbers , we have at least 1 even number and 1 odd number.

Then

it the set includes 1 , the largest common divisor is 1 for 1 and the other numbers

if the set includes 3, there will be always a number that is not divisible by 3. Even we construct a set of n+1 numbers that are multiple of 3 , the largest number would be 3*(n+1)= 3*n+3 > 2*n (out of bounds) , therefore we are forced to take other number that is not divisible by 3 → the largest common divisor of that number with 3 is 1

If the set includes any other prime number → the largest common divisor of that with any other is 1

For the remaining odd numbers N, they can be factorised into other 2 odd common divisors N₂ and n₂ :

N = N₂*n₂ , since n₂ ≥ 2 → N₂ < N

then the even N₂ also should be contained in the set

therefore also for N₂

N = N₃*n₃ → N₃ < N₂

therefore if we continue , we would obtain a number even Nn that has no smaller common divisors → since we cannot take all the multiples of N min ( because Nmin*(n+1)= Nmin*n+Nmin > 2*n for Nmin≥2) → there is at least a number in the sample of n+1 integers whose largest common divisor is 1

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3 years ago