caramel

Assuming Point I is in the interior of angle GHU....because there isn't a diagram or any confirmation.

The angle addition postulate states that if Point D is in the interior of Angle ABC, then Angle ABD + Angle CBD = Angle ABC.

Applying this to your problem, gives: (12x+1) + (-11+8x) = 60

Combine like terms: 20x-10=60

Solve for x: 20x=70

x=7/2, or 3.5

You can check your work by plugging x in for the angles, and seeing if sum of the angles equals 60 or not.

12(3.5)+1=43

-11+8(3.5)=17

43+17=60, meaning that its correct.

You solve this by factoring the first polynomial x^2+13x+30.

When factoring that into (x+a)(x+b), you want ab to equal 30, and a+b to equal 13.

This is the case for all quadratics, ax^2+bx+c, into the factored form (x+m)(x+n). m+n=b, and mn=c.

To start factoring the first polynomial, find the factors of 30, and then add those factors together to see if they equal 13.

The factors cannot be negative in this case because both b and c are positive. 

3*10=30, and 3+10=13, so 10 and 3 are a and b. (However, we don't know the order yet).

x^2-9, is a special case. Both terms are squares, and they are being subtracted.

m^2-n^2=(m+n)(m-n)

In this case, x is our 'm', and 3 is our 'n', therefore x^2-9=(x+3)(x-3).

(x+3) is the overlapping factor between the two polynomials, meaning that b is 3, a is 10, and c is -3.

a+b+c=10+3-3=10

There isn't an image....'shown below'

Hi! The answer would be a fraction; the numerator being the number of specific possibilies (product of numbers spun being even), and the denomerator being the total possibilities. Since there are 4 sectors and the spinner is spun 3 times, the denomerator would be 4 * 4 * 4 = 64. Using what you previously said about the different scenarios with even and odd numbers, you quickly find out that the only way for the product of 3 numbers to be odd is when all three numbers are odd (leaving the rest of the probabilitys [even x even x even, even x even x odd, and odd x odd x even] to result in even numbers). Since it is easier to find the probability of the product being odd, we can do that and then subtract our answer from the total at the end. In all the spins, 2 numbers out of the 4 are odd, so there are 2 options per spin. That means that there are 2 * 2 * 2 = 8 possibilities. (1*1*1, 1*1*3, 1*3*1, 1*3*3, 3*1*1, 3*1*3, 3*3*1, and 3*3*3). That means that 64-8=56 of the 64 spins will be even, so the answer is 56/64 or 7/8....I think at least

Oh, I get it now! So a would be 49, right?

Not 100% sure on this answer....

ACB

ACFDEB

ACDEB

ADEB

ADCB

ADFCB

3 from AC....because you can go straight down, and cross to the other side in 2 ways, and 3 from AD... for similar reasons.

Because only the first year and second year of a dog's life are calculated differently, you can add 15 and 9, subtract that from 44, and then divide the result by 5 to find Rocky's real age.

15+9=24

44-24=20

20/5=4

4+2 (15 and 9)=6

So Rocky's actual age is 6.

Alex just multiplies a dog's age by 7, so Alex would say that Rocky is 6 * 7 =42 years old.

Hope you found this useful!

If M is the midpoint of side AB, and AB and CD are parallel (because the shape is a square), then doesn't that mean that AM and DC are parallel and don't intersect? I might be misunderstanding the problem though...

According to the Pythagorean Theorem, its not possible for a right triangle to have sides whose lenghts are 4, 4, and 3....

Cos is adjacent/hypotnuse meaning that 3 is the 'adjacent' and 5 would be the hypotenuse. Using the Pythagorean Theorem (of the knowledge of Pythagorean Triples), you find that the other side of the right triangle is 4. Tan is opposite/adjacent. 'Opposite' would be 4, and 'adjacent' would remain 3. That means that tan B is 4/3. 

The area of a trapezoid is (b1+b2)/2 * h, where b1 and b2 are the two bases and h is the height. In other words, the area is the average of the bases of the trapezoid multiplied by the height of the trapezoid. From the information given, we can solve for the other base by plugging the other values into the equation of the area of a trapezoid. (10+x)/2 * 4 = 48. Divide both sides by 4: (10+x)/2=12, multiply both sides by 2: (10+x)=24, subtract both sides by 10: x=14. This means that the measure of the other base of the trapezoid is 14.

I'm assuming that by "3x^2+5x=7=0" you mean 3x^2+5x-7=0. Because this quadratic isn't easily factorable (or solvable via the difference of squares), we can use the quadratic formula. Through the quadratic formula, we find that the solutions to the equation are (-5+sqrt{109})/6 and (-5-sqrt{109})/6. Squaring both expressions gives (67-5sqrt{109})/18 and (67+5sqrt{109})/18. The square roots cancel out, which gives 134/18, simplifying to 67/9.