d) You have a <u>difference of squares</u>:
49y² - 9 = (7y)² - 3²
Recall the identity,
a² - b² = (a - b) (a + b)
So,
49y² - 9 = (7y - 3) (7y + 3)
e) Pull out the common factor 3 from each term:
3x² - 3x - 90 = 3 (x² - x - 30)
Now use the <u>sum-product method</u>. Notice that we can write 30 = 5 • 6, and 5 - 6 = 1, so
3x² - 3x - 90 = 3 (x + 5) (x - 6)
f) Same as in (e), use the <u>sum-product method</u>. Notice that 42 = 7 • 6, and -7 - 6 = -13, so
x² - 13x + 42 = (x - 7) (x - 6)
First off we have x number of students in the robotics club, 12 more in the Science club, and 84 students in total. This means:
Robotics Club = x
Science Club = (x + 12)
Total = 84
Okay, so here's the equation:
x + (x + 12) = 84 ~ Add like terms.
2x + 12 = 84 ~ Subtract 12 by both sides.
2x = 72 ~ Divide both sides by 2.
x = 36 ~ Meaning that the Robotics Club has 36 members.
At this point you can do: 84 - 36 = 48 which gives you the number of members in the Science Club, though...:
36 + (36 + 12) = 84 ~ Add the two in the parenthesis to get your answer.
36 + 48 = 84 ~ 48 is the number of Students in the Science Club.
84 = 84
In conclusion: The Science Club has 48 students.
Hope that helps. ^ ^
{-Ghostgate-}
a. Dilation of 2nd equation by a factor of 12
b. The systems have the same solution, as dilations do not affect overall coordinates, changing side lengths but not angles
Answer:
2[(1 + 5x) (1 - 5x)]
Step-by-step explanation:
Given:
Expression
2 - 50x²
Find:
Factorization of the given expression
Computation:
2 - 50x²
By taking 2 as common
⇒ 2[1 - 25x²]
⇒ 2[(1)² - (5x)²]
We know that;
⇒ a² - b² = (a + b)(a - b)
In given expression;
⇒ a = 1
⇒ b = 5x
⇒ 2[(1)² - (5x)²]
2[(1 + 5x) (1 - 5x)]
Factorization of the given expression
2[(1 + 5x) (1 - 5x)]
Answer:
Roberta's boat started farther from the dock, but John's boat moves more quickly.
Step-by-step explanation:
