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x = 39

The answer is 76 cm^2.  Hope this helps!

Hey there, Guest!

Step 1: Multiply both sides by x+2.

\(14x+22=−3x^2−7x−2\)

\(14x+22−(−3x^2−7x−2)=−3x^2−7x−2−(−3x^2−7x−2)\)

\(3x^2+21x+24=0\)

Quadratic Formula:

\(x=\frac{−b±√b2−4ac}{2a}\)

\(x=\frac{-7}{2}+\frac{1}{2}\sqrt{17}\)

And that's the answer.

Hope this helped! :)

7 + 1 = 8

What's going on here?

Maybe this could help you:

(n+1)(n+2)(n+3) = 120.

Now solve for n.

7 + 6 ==13 boys and girls

6 / 13  x  5 / 12 ==5 / 26 probability of chosen students are 2 boys.

I can find only 2 such integers:

x ==2  and  8

There are 12 such integers:

568 , 576 , 656 , 688 , 696 , 768 , 776 , 856 , 888 , 896 , 968 , 976 , Total =  12 such integers.

Point D is the midpoint of median AM of triangle ABC. Point E is the midpoint of AB, and point T is the intersection of BD and ME. Find the area of triangle DMT if [ABC] = 160.

[DMT] = 1/12[ABC] = 13¹/₃

In triangle ABC, the angles A, B, C form an arithmetic sequence. if A = 17 degrees, then what is angle C, in degrees?

A + B + C = 180

17 + (17 + d) + (17 + 2d) = 180

d = 43             ( d => common difference )

Angle C = 103 degrees

Put a 12 in the box.  

Then you'll have 18x • 2 = +36x   

                 and  3x • –12 = –36x  

                 and together they total zero.  

_.

The possible values are 36 and -36.

t=

−25x2+30x−35/

5x2−6x+7

The sequence is as folllows:

1,  5,  17,  53,  161,  485,  1457,  4373  - that is it.

Just 2 multiples  of 5 < 10,000, and that is: 5  and  485.

Thanks for providing us with the solution abc ...

I am sure a number of us will examine it   

The GP is as follows:

3,  9,  27,  81,  243,................a(2007) ==3^2007 mod 10^10 ==9,532,282,187 - these are the last 10 digits of a(2007)

Find the set of values a.

Hello Guest!

\(range\ of\ f(x,a)=\mathbb R\ |\ \color{blue}a\in \mathbb R\)

  !

What is the largest number k less than 1000 such that the remainder is 1 when k is divided by each of 3, 4, and 5?

Hello Guest!

\(15\times 3\cdot 4\cdot 5=900\\ 16\times 3\cdot 4\cdot 5=960\\ 17\times 3\cdot 4\cdot 5=1020\\ k=16\times 3\cdot 4\cdot 5+1\)

\(k=961\)

  !

FV=PV x  [1  +  R]^N

FV==10,000 x  [1  +  0.046]^2

FV==10,000 x [1.046]^2

FV==10,000 x   1.094116

FV==$10,941.16 - principal + interest over 2 years.

$10,941.16  -  $10,000 ==$941.16 - interest earned over 2 years.

Volume(cylinder)  =  pi · radius² · height  =  pi · radius² · height  =  pi · x² · y

Volume(cone)  =  (1/3) · pi · radius² · height  =  (1/3) · pi · (3x)² · h  =  3 · pi · x² · h

Volume(cylinder)  =  Volume(cone)     --->     pi · x²​ · y  =  3 · pi · x² · h     --->     h  =  (1/3) · y  

If  cos(B) = 6/10, then  AB = 6.

Using the Pythagorean Theorem,  AC = 8.

Then, tan(C) = opposite / adjacent  =  6/8  =  3/4

Using 6, you get:  (3x + 2)(12x - 6)  =  36x² - 6x - 12  which is not a binomial.

If you use 8, you get:  (3x + 2)(12x - 8)  =  36x² -16  which is a binomial.

Note that the ratio:  3/2  =  12/8.

The number of ways to choose 0 girls from a group of 7 girls is:  ₇C₀

The number of ways to choose 2 boys from a group of 6 boys is:  ₆C₂

The number of ways to choose 2 students from a group of 13 students is:  ₁₃C₂ 

So, the probability is:  ₇C₀  x  ₆C₂  / ₁₃C₂