Answer:
-12a³b²c ( 2bc² + 7a)
Step-by-step explanation:
To factorize, we must separate the highest common factors between the products that make up the given expression. To get the highest common factor between the two products,
-24a3b3c3 = -2 * 2 *2 * 3 * a³ *b² *b * c² * c
- 84a4b2c = -2 * 2 *3 * 7 * a³ * a *b² * c
The common elements are -2, 2, 3, a³, b², c
The product of the common elements
= -12a³b²c
Hence, factorizing
-24a3b3c3 - 84a4b2c = -12a³b²c ( 2bc² + 7a)
Answer:
-3
Step-by-step explanation:
2a - 6 = 4a
subtract 2a giving you -6 = 2a
divide by 2 from both sides so that a will be by itself
giving you -6 ÷ 2 = a
-6 ÷ 2 = -3
so a = -3
55°
Step-by-step explanation:
110+15+x =180
x = 180 - 125
x = 55°
Answer:
2a) -2
b) 8
Step-by-step explanation:
<u>Equation of a parabola in vertex form</u>
f(x) = a(x - h)² + k
where (h, k) is the vertex and the axis of symmetry is x = h
2 a)
Using the equation of a parabola in vertex form, a parabola with vertex (2, -6):
f(x) = a(x - 2)² - 6
If one of the x-axis intercepts is 6, then
f(6) = 0
⇒ a(6 - 2)² - 6 = 0
⇒ 16a - 6 = 0
⇒ 16a = 6
⇒ a = 6/16 = 3/8
So f(x) = 3/8(x - 2)² - 6
To find the other intercept, set f(x) = 0 and solve for x:
f(x) = 0
⇒ 3/8(x - 2)² - 6 = 0
⇒ 3/8(x - 2)² = 6
⇒ (x - 2)² = 16
⇒ x - 2 = ±4
⇒ x = 6, -2
Therefore, the other x-axis intercept is -2
b)
Using the equation of a parabola in vertex form, a parabola with vertex (2, -6):
f(x) = a(x - 2)² - 6
If one of the x-axis intercepts is -4, then
f(-4) = 0
⇒ a(-4 - 2)² - 6 = 0
⇒ 36a - 6 = 0
⇒ 36a = 6
⇒ a = 6/36 = 1/6
So f(x) = 1/6(x - 2)² - 6
To find the other intercept, set f(x) = 0 and solve for x:
f(x) = 0
⇒ 1/6(x - 2)² - 6 = 0
⇒ 1/6(x - 2)² = 6
⇒ (x - 2)² = 36
⇒ x - 2 = ±6
⇒ x = 8, -4
Therefore, the other x-axis intercept is 8
Answer:
50, 58, 66
Step-by-step explanation:
it looks like a (+8) pattern