Answer:
Step-by-step explanation:
X^2-6x+5=x^2-5x-x+5=x(x-5)-(x-5)=(x-5)(x-1)
Then we have (x-5)(x-1)=0 if x=5 or x=1.
Intersections on x are points (1,0) and (5,0), middle is (3,0).
Intersection with y is when put x=0 in equation, so you will get y=0-6*0+5, y=5. The point is (0,5).
From picture symmetry is line x=3.
Answer:
angle CAB = 113.8 degree
angle ABC = 35.6 degree
angle BCA = 30.6 degree
Step-by-step explanation:
Given data:
A(1, 0, −1),
B(5, −3, 0),
C(1, 5, 2)
calculate the length of side by using the distance formula
so
AB = (5,-3,0) - (1,0,-1) = (4,-3,1)
AC= (1,5,2) - (1,0,-1) = (0,5,3)
|AB|
|AC| =
From following formula, calculate the angle between the two side i.e Ab and AC
AB.AC = |AB|*|AC| cos ∠CAB
(4,-3,1).(0,5,3)
4*0 -3*5 +1*3
-12 =
cos ∠CAB = - 0.404
angle CAB = 113.8 degree
BA =B- A = (1,0,-1) - (5,-3,0) = (-4,3,-1)
BC = (1,5,2)-(5,-3,0) = (-4,8,2)
|BA| = \sqrt{(26)}
|BC|
BA.BC = |BA|*|BC|* cosABC
(-4,3,-1).(-4,8,2) =
16+24-2
cos ∠ABC = 0.813
angle ABC = 35.6 degree
we know sum of three angle in a traingle is 180 degree hence
sum of all three angle = 180
angle BCA + 35.6 + 113.8 = 180
angle BCA = 30.6 degree
There are 80 nickels and 120 dimes and 300 quarters in piggy bank
<em><u>Solution:</u></em>
Given that,
For every 2 nickels there are 3 dimes ,
So, ratio of nickel to dime will be 2 : 3
Also for every 2 dimes there are 5 quarters
So, ratio of dime to quarters is 2 : 5
Let us first find the ratio of nickles to dimes to quarters
nickel : dime = 2 : 3
dime : quarters = 2 : 5
So,
Thus nickel : dime : quarters = 4 : 6 : 15
Now, let the number of nickel be 4x
Let the number of dimes be 6x
Let the number of quarters be 15x
From given question,
There are 500 coins in all.
number of nickel + number of dimes + number of quarters = 500
4x + 6x + 15x = 500
25x = 500
x = 20
Thus,
number of nickel = 4x = 4(20) = 80
number of dimes = 6x = 6(20) = 120
number of quarters = 15x = 15(20) = 300
Thus there are 80 nickels and 120 dimes and 300 quarters in piggy bank