Answer:
Step-by-step explanation:
We see that the two terms share an x, so we can pull that out:
Now notice that we have a difference of squares (
). Given a difference of squares, 
, this can always be factored into 
. We can use this in this case: 
.
So, our final factorized form is: .
Hope this helps!
For x^3-11x^2+33x+45 , we can make it an equation so <span>x^3-11x^2+33x+45=0. Next, we can find out if -1 or -3 is a factor. If -1 is a factor, than (x+1) is factorable. Using synthetic division, we get
x^2-12x+45
___ ________________________
x+1 | x^3-11x^2+33x+45
- (x^3+x^2)
_________________________
-12x^2+33x+45
- (-12x^2-12x)
______________
45x+45
-(45x+45)
___________
0
Since that works, it's either B or D. We just have to figure out when
</span> x^2-12x+45 equals 0, since there are 3 roots and we already found one. Using the quadratic formula, we end up getting (12+-sqrt(144-180))/2=
(12+-sqrt (-36))/2. Since sqrt(-36) is 6i, and 6i/2=3i, it's pretty clear that B is our answer
(2x+1)=Jeremy´s age
(2x+3)=Sam´s age.
we suggest this equation:
(2x+1)(2x+3)=783
4x²+6x+2x+3=783
4x²+8x-780=0
x²+2x-195=0
We solve this quadratic equation:
x=[-2⁺₋√(4-4*1*(-195))]/2=(-2⁺₋28)/2
x₁=(-2-28)/2=-15 this solution is not valid.
x₂=(-2+28)/2=13
Jeremy´s age=2x+1=2*13+1=27
Sam´s age=2x+3=2*13+3=29
Answer:
x = 2.3
Measure of arc XY = 76° ⇒ answer (D)
Step-by-step explanation:
∵ arc XY congruent to arc YZ
∴ XY = YZ ⇒ chords subtended by equal arcs are equal
∴ 3x = 6.9 ⇒ x = 6.9/3
∴ x = 2.3
In ΔOXY
∵ OX = OY radii
∴ m∠OXY = m∠OYX
∵ m∠OXY = 52°
∴ m∠OYX = 52°
∵ The sum of angles of a Δ = 180°
∴ m∠XOY = 180 - 2 × 52 = 76°
∵ ∠XOY is central angle subtended by arc XY
∴ The measure of arc XY = m∠XOY = 76°
Answer:
Step-by-step explanation:
The formula for the surface area of a prism is obtained by taking the sum of (twice the base area) and (the lateral surface area of the prism). The surface area of a prism is given as S = (2 × Base Area) + (Base perimeter × height) where "S" is the surface area of the prism.
