Simplify by using factoring: (2a+6b)(6b−2a)−(2a+6b)^2
Answers
The simplified expression is -8a² - 24ab.
Given expression: (2a + 6b)(6b - 2a) - (2a + 6b)^2
First, let's expand the squared term (2a + 6b)^2:
(2a + 6b)(6b - 2a) - (2a + 6b)(2a + 6b)
Now, we have a common factor of (2a + 6b) in both terms, so let's factor it out:
(2a + 6b)[(6b - 2a) - (2a + 6b)]
Now, simplify the expression inside the brackets:
(2a + 6b)[6b - 2a - 2a - 6b]
Combining like terms within the brackets:
(2a + 6b)[-4a]
Now, multiply the remaining terms:
-4a(2a + 6b)
-8a² - 24ab
Therefore, the simplified expression is -8a² - 24ab.
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Answer:
-8a(a+3b)
Step-by-step explanation:
(2a+6b)(6b−2a)−(2a+6b)^2
(2a+6b) {(6b−2a)−(2a+6b)(2a+6b)}
2(a+3b) (6b-2a-2a-6b)
2(a+3b) (-4a)
-2(a+3b) x 4a
-2 x 4a (a+3b)
-8a(a+3b)
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The base of an aquarium with given volume V is made of slate and the sides are made of glass. If slate costs five times as much (per unit area) as glass, find the dimensions of the aquarium that minimize the cost of the materials. (Let x, y, and z be the dimensions of the aquarium. Enter your answer in terms of V.)
The expression 3a + 2b + c / d gives the average number of points a team earns in d games by winning a games in regulation, b games in overtime and losing c games in overtime. What is the average number of points earned for a team that wins 10 games in regulation, wins 8 in overtime, loses 6 in overtime, and loses 4 in regulation?
EquationsSolve T = C(9+ AB) for B
PLEASEEE HELPPPSolve for x:
Answers
Answer:
It is better for the warriors to use man-to-man defense.
Step-by-step explanation:
The complete question is: The Westwood Warriors basketball team wants to score more points. To get better at scoring points the team is trying to improve its offensive strategies. Some opponents primarily use a zone defense, while others primarily use a man-to-man defense. When the Warriors play against teams that use a zonedefense they score an average of 67 points per game with a standard deviation of 8 points per game. When they play against teams that use a man-to-man defense they score an average of 62 points per game with a standard deviation of 5 points per game.
Since the Warriors started using their improved offensive strategies they have played two games with the following results.
Against the McNeil Mavericks
Maverick defense: zone
Warrior points: 77
Against the Round Rock Dragons
Dragon defense: man-to-man
Warrior points: 71
What is the Z-score of these values?
We are given that when the Warriors play against teams that use a zonedefense they score an average of 67 points per game with a standard deviation of 8 points per game. When they play against teams that use a man-to-man defense they score an average of 62 points per game with a standard deviation of 5 points per game.
We have to find the z-scores.
- Finding the z-score for the zone defense;
Let X = points score by warriors when they use zone defense
The z-score probability distribution for the normal distribution is given by;
Z = ~ N(0,1)
where, = mean score = 67 points
= standard deviation = 8 points
It is stated that the Warriors scored 77 points when they used zone defense, so;
z-score for 77 =
= = 1.25
- Finding the z-score for the zone defense;
Let X = points score by warriors when they use man-to-man defense
The z-score probability distribution for the normal distribution is given by;
Z = ~ N(0,1)
where, = mean score = 62 points
= standard deviation = 5 points
It is stated that the Warriors scored 71 points when they used man-to-man defense, so;
z-score for 71 =
= = 1.8
So, it is better for the warriors to use man-to-man defense.
Answers
Answer:
His daily fat intake is 40.824g.
His daily Vitamin D intake is 290.304 IU.
Step-by-step explanation:
The first step to solve this problem is finding the daily kcal intake of the dogs.
Each cup has 324 kcal, and he eats 3.5cups a day. So:
1 cup - 324 kcals
3.5 cups - x kcals
kcals.
His daily intake is of 1134 kcals.
The food contains 3.6 g of fat in 100 kcals of energy. what is his daily fat intake?
There are 3.6g of fat in 100 kcals of energy. How many g of fat are there in 1134 kcals?
3.6g - 100 kcals
xg - 1134 kcal
g
His daily fat intake is 40.824g.
The food contains 25.6 IU of Vitamin D3 in 100 kcals of energy. what is his daily Vitamin D inake?
Similar logic as above.
25.6IU - 100 kcals
x IU - 1134 kcal
IU
His daily Vitamin D intake is 290.304 IU.
Answers
Logx-log(x+13)=1
Step by step explanation please
Answers
Answer:
Step-by-step explanation:
Applying logarithm rule
Log A - Log B= Log(A/B). Division rule
Now, Logx-log(x+13)=1
Log(x/(x+13))=1
Assume that the log is a natural log whose base is 10.
Then apply logarithm law
Log10 base 10=1
Comparing this to Log(x/(x+13))=1
This implies that
x/(x+13)=10
x=10(x+13)
x=10x+130
x-10x=130
-9x=130
x=130/-9
x=-14.444
Answers
Answer: 2.72 i guess
Answers
This is about slope of tangents via derivatives.
A) m = 8a- 6a²
B) At (1, 11), equation of tangent is y = 2x + 9
At (2, 9), equation of tangent is y = 2x + 4
- The slope of a tangent to a curve is simply gotten by finding the first derivative of the function representing that curve.
- We are given the function; y = 9 + 4x² - 2x³
The slope will be;
m = y' = 8x - 6x²
A) At x = a; To find the slope we will just put a for x in the slope function;
Slope; m = 8a- 6a²
B) Slope is 8x - 6x²
At the point (1, 11);
Slope = 8(1) - 6(1²) = 2
Thus, equation of tangent line is; y - 11 = 2(x - 1)
⇒ y - 11 = 2x - 2
⇒ y = 2x - 2 + 11
⇒ y = 2x + 9
- At the point (2, 9);
Slope = 8(2) - 6(2²) = -8
Thus, equation of tangent line is; y - 8 = 2(x - 2)
⇒ y - 8 = 2x - 4
⇒ y = 2x - 4 + 8
⇒ y = 2x + 4
Read more at; brainly.com/question/18476507
y' = 8x - 6x^2
This is the slope in terms of x.
When x = a , the slope is
8a - 6a^2
(b) equation of tangent line at x1,y1
is y- y1 = (8x - 6x^2)( x - x1) , so at (1,11) it is
y - 11 = (8(1) - 6((1)^2) ) (x - 1)
y = 2(x - 1) + 11
y = 2x + 9 (answer)
At (2,9)
y - 9 = (16-24)(x - 2)
y - 9 = -8x + 16
y = -8x + 25 answer