The length is 6 inches.
The width is 1 foot = 12 inches.
The perimeter is (6 + 12 + 6 + 12) = 36 inches (3 feet) .
"14 inches" is false.
37 would be the answer.....
Answer:
The answer is 2. 2 is the only number that can't change. There is no x or ^.
Answer:
1) ![2y^{2}+4y-9](https://tex.z-dn.net/?f=2y%5E%7B2%7D%2B4y-9)
2) ![18x^{5}y^{4}z](https://tex.z-dn.net/?f=18x%5E%7B5%7Dy%5E%7B4%7Dz)
3) ![6x^{5}-12x^{4}+9x^{3}](https://tex.z-dn.net/?f=6x%5E%7B5%7D-12x%5E%7B4%7D%2B9x%5E%7B3%7D)
4) 40
5) ![x^{3}-7x^{2}+3x+36](https://tex.z-dn.net/?f=x%5E%7B3%7D-7x%5E%7B2%7D%2B3x%2B36)
Step-by-step explanation:
1) Distribute the negative sign that is outside the parentheses and then you must add like terms, as following:
![(y^{2}-3y-5)-(-y^{2}-7y+4)=y^{2}-3y-5+y^{2}+7y-4=2y^{2}+4y-9](https://tex.z-dn.net/?f=%28y%5E%7B2%7D-3y-5%29-%28-y%5E%7B2%7D-7y%2B4%29%3Dy%5E%7B2%7D-3y-5%2By%5E%7B2%7D%2B7y-4%3D2y%5E%7B2%7D%2B4y-9)
2) According to the Product property of exponents, when you multiply powers with the same base, you must add the exponents. Then:
![(6xy^{3}z)(3x^{2}yx^{2})=18x^{5}y^{4}z](https://tex.z-dn.net/?f=%286xy%5E%7B3%7Dz%29%283x%5E%7B2%7Dyx%5E%7B2%7D%29%3D18x%5E%7B5%7Dy%5E%7B4%7Dz)
3) Apply the Distributive property and the Product property of exponents. Then, you obtain:
![-3x^{3}(-2x^{2}+4x-3)=6x^{5}-12x^{4}+9x^{3}](https://tex.z-dn.net/?f=-3x%5E%7B3%7D%28-2x%5E%7B2%7D%2B4x-3%29%3D6x%5E%7B5%7D-12x%5E%7B4%7D%2B9x%5E%7B3%7D)
4)
is a square of a sum, then, by definition you have:
![(a+b)^{2}=a^{2}+2ab+b^{2}](https://tex.z-dn.net/?f=%28a%2Bb%29%5E%7B2%7D%3Da%5E%7B2%7D%2B2ab%2Bb%5E%7B2%7D)
Then:
![(4a+5)^{2}=(4a)^{2}+2(4a)(5)+5^{2}=16a^{2}+40a+25](https://tex.z-dn.net/?f=%284a%2B5%29%5E%7B2%7D%3D%284a%29%5E%7B2%7D%2B2%284a%29%285%29%2B5%5E%7B2%7D%3D16a%5E%7B2%7D%2B40a%2B25)
The coefficient of the second term is the number in front of the variable <em>a.</em> Then, the answer is: 40
5) Apply the Distributive property and the Product property of exponents, then, oyou must add the like terms:
![(x-4)(x^{2}-3x-9)=x^{3}-3x^{2}-9x-4x^{2}+12x+36=x^{3}-7x^{2}+3x+36](https://tex.z-dn.net/?f=%28x-4%29%28x%5E%7B2%7D-3x-9%29%3Dx%5E%7B3%7D-3x%5E%7B2%7D-9x-4x%5E%7B2%7D%2B12x%2B36%3Dx%5E%7B3%7D-7x%5E%7B2%7D%2B3x%2B36)
Answer:
a = ![\sqrt{7}](https://tex.z-dn.net/?f=%5Csqrt%7B7%7D)
Step-by-step explanation:
I think your question is missed of key information, allow me to add in and hope it will fit the original one.:
<em>Suppose ABC is a right triangle with sides a, b, and c and right angle at C. Find the unknown side length using the Pythagorean theorem and then find the values of the six trigonometric functions for angle B. when b=3 and c=4</em>.
My answer:
We will Pythagoras theorem, which states that the sum of squares of two legs of a right triangle is equal to the square of the hypotenuse of right triangle. Because the question says that ABC is a right triangle.
![a^2+b^2=c^2](https://tex.z-dn.net/?f=a%5E2%2Bb%5E2%3Dc%5E2)
Given that: b=3 and c=4
![a^2+3^2=4^2a^2+9=16a^2+9-9=16-9a^2=7](https://tex.z-dn.net/?f=a%5E2%2B3%5E2%3D4%5E2a%5E2%2B9%3D16a%5E2%2B9-9%3D16-9a%5E2%3D7)
so a =
We know that tangent relates opposite side of a right triangle with adjacent side.
![\text{tan}(B)=\frac{a}{b}\\\text{tan}(B)=\frac{\sqrt{7}}{3}](https://tex.z-dn.net/?f=%5Ctext%7Btan%7D%28B%29%3D%5Cfrac%7Ba%7D%7Bb%7D%5C%5C%5Ctext%7Btan%7D%28B%29%3D%5Cfrac%7B%5Csqrt%7B7%7D%7D%7B3%7D)
Please have a look at the attached photos.