Answer: x=7
Step-by-step explanation: First you distribute the 12 to (10-x). That then gives you 15x+120-12x=141. Now you combine like terms. So you do 15x-12x=3x. Your new equation now is 3x+120=141. Subtract 120 from 141 and mark it out. That leaves you with 3x=21. Divide both sides by 3. Your final answer is x=7.
-1.331. -1.1 * -1.1 * -1.1
We'll represent Louise's, Tammy's, Delores's, and Sheryl's point values with 
, 
, 
, and 
respectively since each one is 1 point more than the last.
Add all of these values up and set it all equal to 
.
Now, simplify.
Subtract 
on both sides.
Divide both sides by 
.
Since Louise's score is , the answer is 
.
<h3>Double-checking</h3>
To verify our answer, add the point totals , 
, 
, and 
.
This equals , so we can be sure the answer is correct.
Answer:
Step-by-step explanation:
4.5b + 8.5c = 175
b + c = 22.......b = 22 - c
4.5(22 - c) + 8.5c = 175
99 - 4.5c + 8.5c = 175
-4.5c + 8.5c = 175 - 99
4c = 76
c = 76/4
c = 19......there are 19 cats
b + c = 22
b + 19 = 22
b = 22 - 19
b = 3 <==== there are 3 birds
Answer:
x = -2, x = 3 − i√8, and x = 3 + i√8
Step-by-step explanation:
g(x) = x³ − 4x² − x + 22
This is a cubic equation, so it must have either 1 or 3 real roots.
Using rational root theorem, we can check if any of those real roots are rational. Possible rational roots are ±1, ±2, ±11, and ±22.
g(-1) = 18
g(1) = 18
g(-2) = 0
g(2) = 12
g(-11) = 1782
g(11) = 858
g(-22) = -12540
g(22) = 8712
We know -2 is a root. The other two roots are irrational. To find them, we must find the other factor of g(x). We can do this using long division, or we can factor using grouping.
g(x) = x³ − 4x² − 12x + 11x + 22
g(x) = x (x² − 4x − 12) + 11 (x + 2)
g(x) = x (x − 6) (x + 2) + 11 (x + 2)
g(x) = (x (x − 6) + 11) (x + 2)
g(x) = (x² − 6x + 11) (x + 2)
x² − 6x + 11 = 0
Quadratic formula:
x = [ 6 ± √(36 − 4(1)(11)) ] / 2
x = (6 ± 2i√8) / 2
x = 3 ± i√8
The three roots are x = -2, x = 3 − i√8, and x = 3 + i√8.
