Since all triangles in these questions are similar, we use that the ratios of corresponding sides are equal
(1)
=
= ![\frac{5}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B4%7D)
solving
=
( cross-multiply )
5x = 36 ( divide both sides by 5 )
x = ![\frac{36}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B36%7D%7B5%7D)
solving
= ![\frac{5}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B4%7D)
4y = 30 ⇒ y = ![\frac{15}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B15%7D%7B2%7D)
(2)
let h be the height of the flagpole, then
= ![\frac{50}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B50%7D%7B4%7D)
4h = 275 ⇒ h = 68.75 feet
(3)
= ![\frac{93.5}{12.75}](https://tex.z-dn.net/?f=%5Cfrac%7B93.5%7D%7B12.75%7D)
12.75x = 561 ⇒ x = 44 feet
![x^2-y^2+z^2=2](https://tex.z-dn.net/?f=x%5E2-y%5E2%2Bz%5E2%3D2)
If
![y=2](https://tex.z-dn.net/?f=y%3D2)
, then you get
![x^2-2^2+z^2=2\iff x^2+z^2=6](https://tex.z-dn.net/?f=x%5E2-2%5E2%2Bz%5E2%3D2%5Ciff%20x%5E2%2Bz%5E2%3D6)
which is a circle in the x-z plane with radius
![\sqrt6](https://tex.z-dn.net/?f=%5Csqrt6)
.
If
![x=1](https://tex.z-dn.net/?f=x%3D1)
, then you get
![1^2-y^2+z^2=2\iff z^2-y^2=1](https://tex.z-dn.net/?f=1%5E2-y%5E2%2Bz%5E2%3D2%5Ciff%20z%5E2-y%5E2%3D1)
which is a hyperbola in the y-z plane.
If
![y=0](https://tex.z-dn.net/?f=y%3D0)
, you get another circle in the x-z plane defined by
![x^2+z^2=2](https://tex.z-dn.net/?f=x%5E2%2Bz%5E2%3D2)
, this time with radius
![\sqrt2](https://tex.z-dn.net/?f=%5Csqrt2)
.
If
![x=2](https://tex.z-dn.net/?f=x%3D2)
, then
![2^2-y^2+z^2=2\iffy^2-z^2=2](https://tex.z-dn.net/?f=2%5E2-y%5E2%2Bz%5E2%3D2%5Ciffy%5E2-z%5E2%3D2)
, another hyperbola in the y-z plane with branches perpendicular to the case where
![x=1](https://tex.z-dn.net/?f=x%3D1)
.
9/11 there is 11 in total and 9 blue and green marbles all together (brainliest if right pls)
Answer:
x⁴ + 3x³ - 5x + 1
Step-by-step explanation:
(x - 1)(x³ + 4x² + 4x - 1)
Same as writing....
x(x³ + 4x² + 4x - 1) - 1(x³ + 4x² + 4x - 1)
x⁴ + 4x³ + 4x² - x - x³ - 4x²- 4x + 1
x⁴ + 3x³ - 5x + 1