Answer:
Step-by-step explanation:
19.
a) to find thhe x- intercept we make y=0
x² +4x -5 = 0
(x+5)(x-1) =0
x+5=0 so x=- 5
x-1 =0 so x= 1
b)
y-intercept is at (0, -5)
c)
axis of symmetry is at
x=-b/2a =-4/2*1 = -2
x= -2
d)
vertex is at (-2, -9) because x coordinate is on the axis of symmetry at -2 and
y= x² +4x -5= (-2) ² +4(-2) -5 = 4-8-5 = 4-13 = -9
Add them together
AC+CE= EA
24+13= 37
Answer:
length = 6 yards
width = 3.5 yards
Step-by-step explanation:
the length of a rectangle is 1 yard less than twice the width
LEt 'w' be the width of the rectangle
and 'l' be the length of the rectangle
length l = 2 times the width -1
so l = 2w -1
Area of the rectangle = length * width
Area = l * w
we know length is 2w-1 and given area = 21
21 = (2w-1) * w

subtract 21 on both sides

now solve for 'w'

0 = 2w(w+3)-7(w+3)
0= (2w-7)(w+3)
2w-7 = 0 and w+3 =0
w = 7/2 w=-3
width cannot be negative so we ignore w=-3
width w= 3.5
length = 2w-1= 2(3.5) - 1= 7-1=6
length = 6 yards
How to factor 175:
Find the factors of 175:
1, 5², 7
**Remember that factoring by prime numbers will get the job done more efficiently!**
Hope this helps!
Answer:

Step-by-step explanation:
The given expresion is

We want to evaluate this expression when x=3i
We substitute to obtain:

We simplify to get

Recall that

This implies that:


