Solve 3(4 – x) ≤ 54
1 answer:
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Given:
Triangle DEF
To find:
The perimeter of triangle DEF.
Solution:
Coordinate of D = (-1, 1)
Coordinate of E = (2, 1)
Coordinate of F = (-1, 4)
Distance formula:
<u>Distance of DE:</u>
Here,
d = 3 units
<u>Distance of EF:</u>
Here,
d = 4.2 units
<u>Distance of FD:</u>
Here,
d = 3 units
Perimeter of ΔDEF = DE + FE + FD
= 3 + 4.2 + 3
= 10.2 units
The perimeter of triangle DEF is 10.2 units.
Micah was asked to add the following expressions:
First, he combined like terms in the numerator and kept the common denominator
First step is correct. He added the like terms in the numerator, because the denominators are same.
So he got ,
In the next step, he cannot cancel out x^2 from the top and bottom . Because x-4 and 3x+2 are added with x^2
If we have x^2 is multiplied with other terms at the top and bottom , then we can cancel out x^2.
So Micah added the expression incorrectly. Final answer is not correct.
Answer:
B is true
Step-by-step explanation:
given f(x) = 2x² - x - 1 and g(x) = x - 1
A
If x = - 1 is a root then f(- 1) = 0
f(- 1) = 2(- 1)² - (- 1) - 1 = 2 + 1 - 1 = 2 ≠ 0 ← False
B
If (x - 1) is a factor then x = 1 is a root and f(1) = 0
f(1) = 2(1)² - 1 - 1 = 2 - 1 - 1 = 0
⇒ g(x) = x - 1 is a factor of f(x) ← True
C
If x = 2 is a root then f(2) = 0
f(2) = 2(2)² - 2 - 1 = 8 - 3 = 5 ≠ 0 ← False
D
=
Cancel the factor (x - 1) on the numerator/ denominator, leaving
= 2x + 1 with remainder 0 ≠ 2 ← False