Answer:x=6
Step-by-step explanation:Step-1 : Multiply the coefficient of the first term by the constant 1 • 18 = 18
Step-2 : Find two factors of 18 whose sum equals the coefficient of the middle term, which is -9 .
-18 + -1 = -19
-9 + -2 = -11
-6 + -3 = -9 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -6 and -3
x2 - 6x - 3x - 18
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-6)
Add up the last 2 terms, pulling out common factors :
3 • (x-6)
Step-5 : Add up the four terms of step 4 :
(x-3) • (x-6)
Which is the desired factorization
Answer:
y+1=3(x-4)
Step-by-step explanation:
Hi there!
We are given a slope of 3 and a point (4,-1).
We need to find the equation of the line in point-slope form
Point-slope form is given as y-y1=m(x-x1), where m is the slope, and (x1,y1) is a point
We have all of the needed information to substitute into the formula
First, let's label the values of everything to avoid any confusion
m=3
x1=4
y1=-1
now substitute into the formula *remember, the formula has SUBTRACTION, and we have a NEGATIVE number, so we'll end up subtracting a negative*
y--1=3(x-4)
simplify
y+1=3(x-4)
That's it!
Hope this helps :)
Answer:
Step-by-step explanation:
The graph is done using Desmos. Just by substitution x = 1 will force the graph to go to y = 0, but graphs are not always that good. This one gets 1.111
to get y = 0. I'd use 1 if you had to answer it and a computer will mark it.
Answer:
444 adult ticket
763 student ticket
Step-by-step explanation:
let a = number of adult ticket
let s = number of student ticket
s+a=1207
5a+s=2983
get s by itself in the 1st equation so you can plug it into the 2nd
s+a=1207
-a -a
s=1207-a
5a+(1207-a)=2983
solve for a
4a+1207=2983
-1207 -1207
4a= 1776
444
this is adult ticket amount
subtract this from 1207 to get student amount
1207-444=763
Answer:
m∠BCD = 90°
∠BCD is a right angle
Step-by-step explanation:
<em>If a ray bisects an angle, that means it divides the angle into two equal parts in measure</em>
∵ Ray CE bisects ∠BCD
→ Means divide it into two angles BCE and ECD which equal in measures
∴ m∠BCE = m∠ECD = 
m∠BCD
∵ m∠BCE = 3x - 6
∵ m∠ECD = 2x + 11
→ Equate them to find x
∴ 3x - 6 = 2x + 11
→ Add 6 to both sides
∵ 3x - 6 + 6 = 2x + 11 + 6
∴ 3x = 2x + 17
→ Subtract 2x from both sides
∵ 3x - 2x = 2x - 2x + 17
∴ x = 17
∵ m∠BCE = m∠BCD
→ Substitute x in the measure of ∠BCE to find it, then use it to
find m∠BCD
∵ m∠BCE = 3(17) - 6 = 51 - 6
∴ m∠BCE = 45°
∵ 45 = m∠BCD
→ Multiply both sides by 2
∴ 90 = m∠BCD
∴ m∠BCD = 90°
→ The measure of the acute angle is less than 90°, the measure of
the obtuse angle is greater than 90°, and the measure of the
right angle is 90°
∴ ∠BCD is a right angle
