Answer:
3x(x - 4)(x + 2)
Step-by-step explanation:
Given
3x³ - 6x² - 24x ← factor out common factor of 3x from each term
= 3x(x² - 2x - 8) ← factor the quadratic
Consider the factors of the constant term (- 8) which sum to give the coefficient of the x- term.
The factors are - 4 and + 2, since
- 4 × 2 = - 8 and - 4 + 2 = - 2, thus
x² - 2x - 8 = (x - 4)(x + 2) and
3x³ - 6x² - 24x = 3x(x - 4)(x + 2)
Answer:
A) 37:191
B)191:154
Step-by-step explanation:\
A) Mary's Savings= 185 Rs
Mary's Income= 955 Rs
Ratio = 185:955
= 185/955
=37/191 ( INTO LOWEST TERMS )
=37:191
B) Mary's Income= 955 Rs
Mary's Expenditure= ?? = Income- Saving = 955-185= 770
Ratio= 955:770
= 955/770
= 191/154 ( INTO LOWEST TERMS )
= 191:154
Answer/Step-by-step explanation:
5. 21x + 4 = 22x - 2 (corresponding angles)
Collect like terms
21x - 22x = -4 - 2
-x = -6
divide both sides by -1
x = 6
6. (x + 72) + (x + 132) = 180 (linear pair)
x + 72 + x + 132 = 180
Add like terms
2x + 204 = 180
2x = 180 - 204
2x = -24
x = -12
7. 90 = 22x + 2 (vertical angles)
90 - 2 = 22x
88 = 22x
Divide both sides by 22
4 = x
x = 4
8. 12x + 10 = 13x + 3 (vertical angles)
Collect like terms
12x - 13x = -10 + 3
-x = -7
Divide both sides by -1
x = 7
9. 17x = 16x + 5 (alternate exterior angles)
17x - 16x = 5
x = 5
✔️17x
Plug in the value of x
17(5) = 85°
10. 21x - 6 = 20x (corresponding angles)
Add like terms
21x - 20x = 6
x = 6
✔️20x
20(6) = 120°
Simplify -5x + 12 - 7x to -12x + 12
-12x + 12 = -3(5x + 8)
Expand
-12x + 12 = -15x - 24
Add 15x to both sides
-12x + 12 + 15x = -24
Simplify 12x + 12 + 15x to 3x + 12
3x + 12 = -24
Subtract 12 from both sides
3x = -24 - 12
Simplify -24 - 12 to -36
3x = -36
Divide both sides by 3
x = -36/3
Simplify 36/3 to 12
<u>x = -12</u>
Answer:
19.714
Step-by-step explanation:
Given :
Yearly Tuition Frequency
12-16 5
17-21 4
22-26 3
27-31 2
We calculate the midpoint (x) = (lower + upper) / 2
The mean yearly tuition :
The midpoint (x) :
X ___ F ___ Fx
14 __ 5
19 __ 4
24 __ 3
29 __ 2
The mean = Σfx / Σf
Σfx / Σf = (14*5 + 19*4 + 24*3 + 29*2) / (5+4+3+2)
Mean = 276 / 14
Mean yearly tuition = 19.714
