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First: write it as a single common fraction:  1/2 + 3/4  ==>  2/4 + 3/4  ==>  5/4

5/4  as a ratio is  5:4

A common denominator is 12; multiply each term times 12:

  12(2x/3) + 12(x/2) - 3(12) = 12(3x/4) + 2(12)

  8x + 6x - 36 = 9x + 24

  14x - 36 = 9x + 24

    5x  =  60

      x  =  12

cos = adj/hyp           sin = opp/hyp 

1)  For angle B, adj = 7 and hyp = 25; so cos B  =  7/25  = .28  

     This works; but A = 90 - B.

2)  Isn't correct; cos B = .28 not .96

3)  For angle A, opp = 7 and hyp = 25; so sin A  = 7/25 = .28 and B is found by 90 - A.

By FOIL,  (a - 4b)(a + 4b)  =  a² + 4ab - 4ab - 16b²  =  a² - 16b²

Draw a right triangle from the plane (point A) parallel to the ground to a point right above the airport (point C) and from point C down to the airport (point B) and then from point B back to point A.

There is a right angle at point C.

AC = 4 miles 

angle A is 6.5 degrees (the angle of elevation is the same as the angle of depression)

In right triangle ACB, you know angle A and its adjacent side, AC. You need to know its opposite side CB.

tan = opp/adj    --->    tan 6.5  =  x / 4   --->  x = 4 · tan(6.5)

Solve for x.

If you can read 11 pages in 1/2 hour, then you should be able to read 22 pages in 1 hour (twice the number of pages in twice the time).

The rate is 22 pages per hour.

1)  You have a triangle, call the angles A, B, and C, with opposite sides a, b, and c.

Let a = 15, b = 25, and c = 36. The angle between sides a and b is angle C.

Since you have SSS, use the Law of Cosines:

     c²  =  a² + b² - 2·a·b·cosC

     36²  =  15² + 25² - 2·15·25·cosC

   1296  =  225 + 625 - 750·cosC

   1296  =  850 - 750·cosC

     446  =  -750·cosC

  -0.594666  =  cosC

  angle C  =  126.5 degrees

2)  One formula for the area of a triangle is  A  =  ½·a·b·sinC

     Use the process of problem #1, to find the angle, then place the values into this            equation.

Thank you Cphill .. 

but I think that this sentence Suffice 

" has at least one solution '' 

The one solution is  x  =  2.

I look at this problem this way:

         y = invSin(x+2)  --->  sin(y)  = x + 2  --->  x = sin(y) - 2.

The sin is only defined for values at least as large as -1 and no larger than +1; so sin(y) is pinned in this way:  -1 <= sin(y) <= 1;       this means that  x >= -3  and  x <= -1.

0.7 is the answer

Thank you, CPhill! :)

2(e)(f) = (2)*(9)*(6)  = 108

The factored form of  9  is  3 x 3  =  3²

The factored form of  12  is  2 x 2 x 3  =  2²·3  

The answer is the number created by each base to its largest exponent:                              LCM  =  3² · 2²  =  36.

(Ignore the  3  from the second number because there is a  3²  in the first number.)

.7                    

what is a bear?

5/16 + 15/16:

Since they have the same denominator, add their numrators and write this answer over the common denominator:

5/16 + 15/16  =  (5 + 15)/16  =  20/16

This can be reduced; both the numerator and denominator can be divided by 4, leaving the answer of  5/4  or  1 1/4 

$$\frac{4.62\times 10^7}{1.2\times 10^4}=\frac{4.62\times 10^{7-4}}{1.2}=\frac{4.62\times 10^3}{1.2}=3.85\times 10^3=3850$$

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The statement sqrt(5²) just means take the square root of 5².

The statement sqrt(5²,5) means take the fifth root of 5².  This can also be written as ⁵√(5²)  or (5²)^1/5

The statement sqrt(5²,5)⁵ means take the fifth root of 5² and then raise it to the power 5.

Now the fifth root of something, say x, raised to the power of 5 is just the original something, x, from the definition of fifth root.  So the fifth root of 5² raised to the power of 5 is just  5², or 25 (press = on the calculator to see this).

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The Intermediate Value Theorem says that , in some interval [a, b], if f(a) and f(b) have opposite signs, then f(x) has at least one "root" in this interval. (As long as f(x) is continuous on the interval !!)

So

f(0) = (0)^3 + 4(0) - 4 = -4

and

f(1) = (1)^3 + 4(1) - 4 =  1

Then, at x=0 the function lies below the x axis, and at x =1, the function lies above the x axis........and since polynomials are always continuous, this function must cross the x axis on [0,1]

So...this tells us that this ploynomial has at least one"zero" (root) on the interval [0, 1]....In other words, whatever this value is, it makes f(x) = 0......(the "0" in the problem is correct !!!......)

Well...there is another way....

Note...... √5 / 2  = √(4*1.25) / 2  = (√4/2) * √1.25 = (2/2)* √1.25 = √1.25

And check for yourself that √1.25 = √5 / 2  !!!!

√5 / 2   ??????