The power symbols are missing.
I can infere that the product intended to simplify is (7^8) * (7^-4)., because that permits you to use the rule of the product of powers with the same base.
That rule is that the product of two powers with the same base is the base raised to the sum of the powers is:
(A^m) * (A^n) = A^ (m+n)
=>(7^8) * (7^-4) = 7^ [8 + (- 4) ] = 7^ [8 - 4] = 7^4, which is the option 3 if the powers are placed correctly.
Answer:
1. x = -1.5y
2. 5 (2x-3)
3. p = 4
Step-by-step explanation:
1) Simplifying
7x + 2y + -3x + 4y = 0
Reorder the terms:
7x + -3x + 2y + 4y = 0
Combine like terms: 7x + -3x = 4x
4x + 2y + 4y = 0
Combine like terms: 2y + 4y = 6y
4x + 6y = 0
Solving
4x + 6y = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-6y' to each side of the equation.
4x + 6y + -6y = 0 + -6y
Combine like terms: 6y + -6y = 0
4x + 0 = 0 + -6y
4x = 0 + -6y
Remove the zero:
4x = -6y
Divide each side by '4'.
x = -1.5y
Simplifying
x = -1.5y
2)
Common factor
10x - 15
5 (2x-3)
3) Simplifying
5p = 3p + 8
Reorder the terms:
5p = 8 + 3p
Solving
5p = 8 + 3p
Solving for variable 'p'.
Move all terms containing p to the left, all other terms to the right.
Add '-3p' to each side of the equation.
5p + -3p = 8 + 3p + -3p
Combine like terms: 5p + -3p = 2p
2p = 8 + 3p + -3p
Combine like terms: 3p + -3p = 0
2p = 8 + 0
2p = 8
Divide each side by '2'.
p = 4
Simplifying
p = 4
There is only one solution in the given equation -y2 − [-5y − y(-7y − 9)] − [-y (15y + 4)] = 0. In solving this problem, apply first PEMDAS (parenthesis, exponents,multiplication, division, addition, subtraction). Then equation will transform into -y2+5y-7y2-9y+15y2+4y=0. Combine terms with same power and achieve 7y2=0. Divide both sides with 7 and perform square root of zero. Since the root is zero, we have one solution of the given equation which is y=0.
Given the figure of a regular pyramid
The base of the pyramid is a hexagon with a side length = 6
The lateral area is 6 times the area of one of the side triangles
So, the side triangle has a base = 6
The height will be:
![\begin{gathered} h^2=6^2+(\frac{\sqrt[]{3}}{2}\cdot6)^2=36+27=63 \\ h=\sqrt[]{63} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20h%5E2%3D6%5E2%2B%28%5Cfrac%7B%5Csqrt%5B%5D%7B3%7D%7D%7B2%7D%5Ccdot6%29%5E2%3D36%2B27%3D63%20%5C%5C%20h%3D%5Csqrt%5B%5D%7B63%7D%20%5Cend%7Bgathered%7D)
so, the lateral area =
![6\cdot\frac{1}{2}\cdot6\cdot\sqrt[]{63}=18\sqrt[]{63}](https://tex.z-dn.net/?f=6%5Ccdot%5Cfrac%7B1%7D%7B2%7D%5Ccdot6%5Ccdot%5Csqrt%5B%5D%7B63%7D%3D18%5Csqrt%5B%5D%7B63%7D)
Total height of lumber, H = 10 1/2 feet = 21/2 feet .
Height of side panel, h = 5 2/3 feet = 17/3 feet .
Now,
Extra lumber required, L = 2 × Height of side panel - Total height of lumber
![L=[2\times (\dfrac{17}{3})]-\dfrac{21}{2}\\\\L = \dfrac{5}{6}\ feet](https://tex.z-dn.net/?f=L%3D%5B2%5Ctimes%20%28%5Cdfrac%7B17%7D%7B3%7D%29%5D-%5Cdfrac%7B21%7D%7B2%7D%5C%5C%5C%5CL%20%3D%20%5Cdfrac%7B5%7D%7B6%7D%5C%20feet)
Therefore, extra lumber required is 
feet.
Hence, this is the required solution.
