Answer:
x = 3.87
Step-by-step explanation:
Using the right angle altitude theorem, we know that all three triangles are congruent, so the lengths of corresponding sides of the triangles are in proportion..
AD/DB = DB/DC
15/x = x/1
x² = 15
x = √15
x = 3.87
Answer: 54 mph
Step-by-step explanation:
d-the distance
s+9 - the speed to the conference
d=6*(s+9)
s- is the speed on the way back home
d=7*s
so 6*(s+9)=7*s
6s+54=7s
-6s -6s
54= 7s-6s
s=54 mph
Answer:
tkae j ad by f then subtracr the u then add the c then multply k then say u
Step-by-step explanation:
Answer:
a. ![(x - 3)^2 + 16](https://tex.z-dn.net/?f=%28x%20-%203%29%5E2%20%2B%2016)
b. ![8(x -7)^2](https://tex.z-dn.net/?f=8%28x%20-7%29%5E2)
c.
or ![(a+1)(a-1)(7x-6)](https://tex.z-dn.net/?f=%28a%2B1%29%28a-1%29%287x-6%29)
d.
or ![(x-2)(x+2)(x^2+3)](https://tex.z-dn.net/?f=%28x-2%29%28x%2B2%29%28x%5E2%2B3%29)
e. ![(a^n+b^n)(a^n-b^n)(a^{2n} +b^{2n})](https://tex.z-dn.net/?f=%28a%5En%2Bb%5En%29%28a%5En-b%5En%29%28a%5E%7B2n%7D%20%2Bb%5E%7B2n%7D%29)
Step-by-step explanation:
![a.\ (x + 1)^2 - 8(x - 1) + 16](https://tex.z-dn.net/?f=a.%5C%20%28x%20%2B%201%29%5E2%20-%208%28x%20-%201%29%20%2B%2016)
Expand
![(x + 1)(x + 1) - 8(x - 1) + 16](https://tex.z-dn.net/?f=%28x%20%2B%201%29%28x%20%2B%201%29%20-%208%28x%20-%201%29%20%2B%2016)
Open brackets
![x^2 + x + x + 1 - 8x + 8 + 16](https://tex.z-dn.net/?f=x%5E2%20%2B%20x%20%2B%20x%20%2B%201%20-%208x%20%2B%208%20%2B%2016)
![x^2 + 2x + 1 - 8x + 24](https://tex.z-dn.net/?f=x%5E2%20%2B%202x%20%2B%201%20-%208x%20%2B%2024)
Collect Like Terms
![x^2 + 2x - 8x+ 1 + 24](https://tex.z-dn.net/?f=x%5E2%20%2B%202x%20-%208x%2B%201%20%20%2B%2024)
![x^2 - 6x+ 25](https://tex.z-dn.net/?f=x%5E2%20-%206x%2B%2025)
Express 25 as 9 + 16
![x^2 - 6x+ 9 + 16](https://tex.z-dn.net/?f=x%5E2%20-%206x%2B%209%20%2B%2016)
Factorize:
![x^2 - 3x - 3x + 9 + 16](https://tex.z-dn.net/?f=x%5E2%20-%203x%20-%203x%20%2B%209%20%2B%2016)
![x(x -3)-3(x - 3) + 16](https://tex.z-dn.net/?f=x%28x%20-3%29-3%28x%20-%203%29%20%2B%2016)
![(x - 3)(x - 3) + 16](https://tex.z-dn.net/?f=%28x%20-%203%29%28x%20-%203%29%20%2B%2016)
![(x - 3)^2 + 16](https://tex.z-dn.net/?f=%28x%20-%203%29%5E2%20%2B%2016)
![b.\ 8(x - 3)^2 - 64(x-3) + 128](https://tex.z-dn.net/?f=b.%5C%208%28x%20-%203%29%5E2%20-%2064%28x-3%29%20%2B%20128)
Expand
![8(x - 3)(x - 3) - 64(x-3) + 128](https://tex.z-dn.net/?f=8%28x%20-%203%29%28x%20-%203%29%20-%2064%28x-3%29%20%2B%20128)
![8(x^2 - 6x+ 9) - 64(x-3) + 128](https://tex.z-dn.net/?f=8%28x%5E2%20-%206x%2B%209%29%20-%2064%28x-3%29%20%2B%20128)
Open Brackets
![8x^2 - 48x+ 72 - 64x+192 + 128](https://tex.z-dn.net/?f=8x%5E2%20-%2048x%2B%2072%20-%2064x%2B192%20%2B%20128)
Collect Like Terms
![8x^2 - 48x - 64x+192 + 128+ 72](https://tex.z-dn.net/?f=8x%5E2%20-%2048x%20-%2064x%2B192%20%2B%20128%2B%2072)
![8x^2 -112x+392](https://tex.z-dn.net/?f=8x%5E2%20-112x%2B392)
Factorize
![8(x^2 -14x+49)](https://tex.z-dn.net/?f=8%28x%5E2%20-14x%2B49%29)
Expand the expression in bracket
![8(x^2 -7x-7x+49)](https://tex.z-dn.net/?f=8%28x%5E2%20-7x-7x%2B49%29)
Factorize:
![8(x(x -7)-7(x-7))](https://tex.z-dn.net/?f=8%28x%28x%20-7%29-7%28x-7%29%29)
![8((x -7)(x-7))](https://tex.z-dn.net/?f=8%28%28x%20-7%29%28x-7%29%29)
![8(x -7)^2](https://tex.z-dn.net/?f=8%28x%20-7%29%5E2)
![c.\ 7a^2x - 6a^2 - 7x + 6](https://tex.z-dn.net/?f=c.%5C%207a%5E2x%20-%206a%5E2%20-%207x%20%2B%206)
Factorize
![a^2(7x - 6) -1( 7x - 6)](https://tex.z-dn.net/?f=a%5E2%287x%20-%206%29%20-1%28%207x%20-%206%29)
![(a^2 - 1)(7x - 6)](https://tex.z-dn.net/?f=%28a%5E2%20-%201%29%287x%20-%206%29)
The answer can be in this form of further expanded as follows:
![(a^2 - 1^2)(7x - 6)](https://tex.z-dn.net/?f=%28a%5E2%20-%201%5E2%29%287x%20-%206%29)
Apply difference of two squares
![(a+1)(a-1)(7x-6)](https://tex.z-dn.net/?f=%28a%2B1%29%28a-1%29%287x-6%29)
![d.\ x^4 - x^2 - 12](https://tex.z-dn.net/?f=d.%5C%20x%5E4%20-%20x%5E2%20-%2012)
Express
as ![x^2](https://tex.z-dn.net/?f=x%5E2)
![(x^2)^2 - x^2 - 12](https://tex.z-dn.net/?f=%28x%5E2%29%5E2%20-%20x%5E2%20-%2012)
Expand
![(x^2)^2 +3x^2- 4x^2 - 12](https://tex.z-dn.net/?f=%28x%5E2%29%5E2%20%2B3x%5E2-%204x%5E2%20-%2012)
![x^2(x^2+3) -4(x^2+3)](https://tex.z-dn.net/?f=x%5E2%28x%5E2%2B3%29%20-4%28x%5E2%2B3%29)
![(x^2-4)(x^2+3)](https://tex.z-dn.net/?f=%28x%5E2-4%29%28x%5E2%2B3%29)
The answer can be in this form of further expanded as follows:
![(x^2-2^2)(x^2+3)](https://tex.z-dn.net/?f=%28x%5E2-2%5E2%29%28x%5E2%2B3%29)
Apply difference of two squares
![(x-2)(x+2)(x^2+3)](https://tex.z-dn.net/?f=%28x-2%29%28x%2B2%29%28x%5E2%2B3%29)
![e.\ a^{4n} -b^{4n}](https://tex.z-dn.net/?f=e.%5C%20a%5E%7B4n%7D%20-b%5E%7B4n%7D)
Represent as squares
![(a^{2n})^2 -(b^{2n})^2](https://tex.z-dn.net/?f=%28a%5E%7B2n%7D%29%5E2%20-%28b%5E%7B2n%7D%29%5E2)
Apply difference of two squares
![(a^{2n} -b^{2n})(a^{2n} +b^{2n})](https://tex.z-dn.net/?f=%28a%5E%7B2n%7D%20-b%5E%7B2n%7D%29%28a%5E%7B2n%7D%20%2Bb%5E%7B2n%7D%29)
Represent as squares
![((a^{n})^2 -(b^{n})^2)(a^{2n} +b^{2n})](https://tex.z-dn.net/?f=%28%28a%5E%7Bn%7D%29%5E2%20-%28b%5E%7Bn%7D%29%5E2%29%28a%5E%7B2n%7D%20%2Bb%5E%7B2n%7D%29)
Apply difference of two squares
![(a^n+b^n)(a^n-b^n)(a^{2n} +b^{2n})](https://tex.z-dn.net/?f=%28a%5En%2Bb%5En%29%28a%5En-b%5En%29%28a%5E%7B2n%7D%20%2Bb%5E%7B2n%7D%29)
You mean 60%of 5 1/2? that makes more sense...
i would do it like this:
![\frac{60}{100}* 5\frac{1}{2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B60%7D%7B100%7D%2A%205%5Cfrac%7B1%7D%7B2%7D%20%20)
(60% is the same as
![5\frac{1}{2}=\frac{11}{2}](https://tex.z-dn.net/?f=%20%205%5Cfrac%7B1%7D%7B2%7D%3D%5Cfrac%7B11%7D%7B2%7D)
(so that there is no confusion, i've put it into an improper fraction
now we can multiply:
![\frac{60}{100}* \frac{11}{2}=](https://tex.z-dn.net/?f=%20%5Cfrac%7B60%7D%7B100%7D%2A%20%5Cfrac%7B11%7D%7B2%7D%3D%20%20)
![\frac{6}{10}* \frac{11}{2}=](https://tex.z-dn.net/?f=%20%5Cfrac%7B6%7D%7B10%7D%2A%20%5Cfrac%7B11%7D%7B2%7D%3D%20%20)
![\frac{3}{5}* \frac{1}{2}=](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%7D%7B5%7D%2A%20%5Cfrac%7B1%7D%7B2%7D%3D%20%20)
![\frac{3*11}{10}=](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%2A11%7D%7B10%7D%3D%20%20)
![\frac{33}{10}=](https://tex.z-dn.net/?f=%20%5Cfrac%7B33%7D%7B10%7D%3D%20%20)
which is 3.3.
so 60% of 5 and a half is 3.3.