Consider the quadratic function f(x) = x2 – 8x – 4. What is the value of the leading coefficient?8 оооо
4
Answers
Answer:
x = 4 + 2 sqrt(5) or x = 4 - 2 sqrt(5)
thus :
8
Step-by-step explanation:
Solve for x over the real numbers:
x^2 - 8 x - 4 = 0
Hint: | Solve the quadratic equation by completing the square.
Add 4 to both sides:
x^2 - 8 x = 4
Hint: | Take one half of the coefficient of x and square it, then add it to both sides.
Add 16 to both sides:
x^2 - 8 x + 16 = 20
Hint: | Factor the left hand side.
Write the left hand side as a square:
(x - 4)^2 = 20
Hint: | Eliminate the exponent on the left hand side.
Take the square root of both sides:
x - 4 = 2 sqrt(5) or x - 4 = -2 sqrt(5)
Hint: | Look at the first equation: Solve for x.
Add 4 to both sides:
x = 4 + 2 sqrt(5) or x - 4 = -2 sqrt(5)
Hint: | Look at the second equation: Solve for x.
Add 4 to both sides:
Answer: x = 4 + 2 sqrt(5) or x = 4 - 2 sqrt(5)
Answer:
-8 or option A
Step-by-step explanation:
2023
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9e + 4 = -5e + 14 + 13e
Answers
Answer:
e = 10
Step-by-step explanation:
In this problem we are told to solve for e. This means we need to isolate the variable e, leaving it completely by itself on one side of the equation.
9e + 4 = -5e + 14 + 13e
We can do this multiple ways, but I will show you how I would do it.
First I would subtract 4 from both sides.
9e + 4 = -5e + 14 + 13e
9e = -5e + 14 + 13e - 4
We can simplify the right side of the equation down by subtracting four from 14.
9e = -5e + 10 + 13e
Next, let's simplify our algebraic expressions. We can subtract 5e from 13e (or add -5e to 13e whatever tickles your fancy)
-5e + 13e = 8e
9e = 8e + 10
Now we subtract algebraic expression 8e from both sides
9e - 8e = 10
All of our expressions with the variable e are now on one side but we aren't done yet. Compute 9e - 8e.
9e - 8e = 10
1e = 10
or
e = 10
We have isolated e! Our final answer is e = 10
Answers
Answer:
(a) 720 ways
(b) 120 ways
(c) 24 ways
Step-by-step explanation:
Given
--- number of letters
Solving (a): Number of arrangements.
We have:
So, the number of arrangements is calculated as:
This gives:
This gives:
Solving (b): DA as a unit
DA as a unit implies that, we have:
[DA] N C E R
So, we have:
So, the number of arrangements is calculated as:
This gives:
This gives:
Solving (c): NCE as a unit
NCE as a unit implies that, we have:
D A [NCE] R
So, we have:
So, the number of arrangements is calculated as:
This gives:
This gives:
5(2x - 9) + 3 =-
Answers
Answer:
Step-by-step explanation:
5(2x-9)+3
10x - 45 +3
10x - 42
x- 4.2
Answers
Answer:
the 2nd one
Step-by-step explanation:
Answers
We have then:
We now look for the amount of watermelons that people ate.
We have then:
Therefore, the amount of watermelon remaining is:
We note that the amount of watermelon remaining is equal to 8.5 pounds.
Answer:
the amount of leftover watermelon is: equal to 8.5 pounds
The amount of leftover watermelon is equal to 8.5 pounds
Explanation:
1- getting the total weight of the watermelon:
The total weight of the watermelon will be the summation of the weights of the 5 watermelons he bought.
This means that:
Total weight = 8.25 + 9.25 + 8.875 + 9.625 + 10.75
Total weight = 46.75 pounds
2- getting the weight of the eaten watermelon:
We know that at the party, there were 153 people and each ate 0.25 of a pound of watermelon.
This means that:
amount eaten = 153 * 0.25
amount eaten = 38.25 pounds
3- getting the weight of the leftover:
weight of leftover = total weight - amount eaten
We have:
Total weight = 46.75 pounds
amount eaten = 38.25 pounds
Therefore:
weight of leftover = 46.75 - 38.25
weight of leftover = 8.5 pounds
Hope this helps :)
Reflection: in the line y=−1
Answers
The image of triangle △RST after the glide reflection, which involves a translation of (x, y) → (x - 3, y) followed by a reflection in the line y = -1, is △R'S'T' with vertices R'(1, -2), S'(4, -5), and T'(3, -6).
To graph triangle △RST with vertices R(4, 1), S(7, 3), and T(6, 4), and its image after the glide reflection, we'll follow these steps:
Start by plotting the original triangle △RST using the given vertices:
R(4, 1)
S(7, 3)
T(6, 4)
Now, let's apply the translation to every vertex of the triangle.
The translation (x, y) → (x - 3, y) shifts each point 3 units to the left (in the negative x-direction).
Apply this translation to each vertex:
R' = (4 - 3, 1) = (1, 1)
S' = (7 - 3, 3) = (4, 3)
T' = (6 - 3, 4) = (3, 4)
Next, we'll apply the reflection in the line y = -1 to the translated vertices. The reflection in this line flips each point across the line.
To do this, we'll calculate the distance between each point and the line y = -1 and then move the same distance in the opposite direction.
R'' is reflected across the line y = -1 to (1, -2).
S'' is reflected across the line y = -1 to (4, -5).
T'' is reflected across the line y = -1 to (3, -6).
Now, we have the vertices of the image triangle △R'S'T'.
You can plot these points on the same graph as the original triangle to visualize the glide reflection transformation.
For similar question on image of triangle.
#SPJ3
Answer:
Step-by-step explanation:
Points R(4,1) S(7,3) T(6,4) after translation
R(4-3, 1) S(7-3, 3) T(6-3, 4)
R'(1, 1) S'(4, 3) T'(3, 4)
Points R'(1, 1) S'(4, 3) T'(3, 4) after reflection
R''(1, -3) S''(4, -5) T''(3, -6)