The minimum value of the given function f(x) = 16x² −16x+28 is 24.
What are the Maxima and Minima of a Function?The curve of a function has peaks and troughs called maxima and minima. A function may have any number of maxima and minima. Calculus allows us to determine any function's maximum and lowest values without ever consulting the function's graph.
To find the minimum value of the function f(x) = 16x² −16x+28 using the derivative method, you can start by taking the derivative of the function. The derivative of a quadratic function is given by:
f'(x) = 2ax + b
In this case, the derivative of the function f(x) is:
f'(x) = 2×16x - 16
To find the minimum value, we need to find the x value that makes the derivative equal to zero. Setting the derivative equal to zero and solving for x gives us:
216x - 16 = 0
32x = 16
x = 0.5
Now that we have the value of x that minimizes the function, we can plug this value back into the original function to find the minimum value:
f(0.5) = 16×(0.5)² - 16(0.5) + 28 = 4 - 8 + 28 = 24
Therefore, the minimum value of the function is 24.
Learn more about the Maxima and Minima of a Function here:
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Add fractions with unlike denominators
A charity is selling brooms to raise funds. Each box has 10 brooms. Each broom is sold for $ 15 . If the charity earns $ 50 profit for each box of brooms, how much does each box of brooms cost the charity, in dollars?
Answer:
Total cost= $100
Step-by-step explanation:
Giving the following information:
Each box has 10 brooms. Each broom is sold for $ 15
The charity earns $ 50 profit for each box of brooms.
First, we need to calculate the total revenue per box:
Total revenue per box= 10*15= $150
Now, the total cost:
Total cost= total revenue - total income
Total cost= 150 - 50
Total cost= $100
4. Right triangle LMN is shown on the coordinate grid below. Which of the following is the length, in units, of line segment MN?
Answer:
The answer is B.
Step-by-step explanation:
1 1 - 12 A vehicle uses 8 gallons of gasoline to travel 2 miles. At this rate, how many miles can the vehicle travel per gallon of gasoline?
Answer:
4 gallons of gasoline per 1 mile
Step-by-step explanation:
Answer:12 miles per gallon.
Solve for x "Enter the value for x that makes this
true.
– 2 = – 1/2 ( - 12x – 10)
Tell whether x and y
are proportional. If so, find the constant of proportionality.
8 = xy
Answer:
Step-by-step explanation:
y is inversely proportional to x; if x increases, y decreases.
Without more info it is not possible to find the constant of proportionality. Recheck the original numerical values. Think: 8 = kxy. You need to know x and y to find the value of k.
I need help subtracting integers!! THIS IS TIME SENSITIVE!!
1. John earns 12% for each house he sells.
If he sells a house for $52,000 , what is his commission?
|
Answer:
6240
Step-by-step explanation:
52,000*12%=6240
4.
Which equation is an identity?
A. 5y + 5 = 5y – 6
B. 8 – (6v + 7) = –6v – 1
C. 3w + 8 – w = 4w – 2(w – 4)
D. 6m – 6 = 7m + 9 – m
Answer: C. 3w + 8 – w = 4w – 2(w – 4)
(3w - w) + 8 = 4w - 2w -2(-4)
2w + 8 = 2w + 8
Step-by-step explanation:
City A and City B are 540 miles apart on a map. The scale on the map is 1inch:60 miles. How many inches apart on the map should City A and City B measure. Explain how you would solve this problem. What would the final answer be?
Answer: 9 inch
Step-by-step explanation:
Given
Distance between city A and city B is 540 miles
Scale on the map is 1 inch: 60 miles i.e. 1 inch on the map is equivalent to 60 miles in the real situation
suppose the distance between city A and B on the map is x
[tex]\therefore \dfrac{1}{60}=\dfrac{x}{540}\\\\\Rightarrow x=\dfrac{540}{60}=9\ in.[/tex]
Therefore, the distance between city A and B is 9 in.
What is the height, x, of the equilateral triangle?
Given:
The figure of an equilateral triangle with side length 14 in.
To find:
The height x of the equilateral triangle.
Solution:
We know that the height of an equilateral triangle is:
[tex]h=\dfrac{\sqrt{3}}{2}a[/tex]
Where, a is the length of side of the equilateral triangle.
It is given that the height of the triangle is [tex]x[/tex].
Putting [tex]a=14,h=x[/tex] in the above formula, we get
[tex]x=\dfrac{\sqrt{3}}{2}(14)[/tex]
[tex]x=\sqrt{3}(7)[/tex]
[tex]x=7\sqrt{3}[/tex]
Therefore, the height of the triangle is [tex]x=7\sqrt{3}[/tex].
Which expressions are equivalent to 8^x-2? Select all that apply.
(picture below)
Help me, pretty please
Answer:
The surface area is 8
and volume is 12.
Let me know if wrong!! :))
Step-by-step explanation:
Hello! Could y’all please explain why this is Decay and not growth?
Answer:
This is an Exponential Decay
Step-by-step explanation:
A = 1200(0.85)⁶
The above expression is an Exponential Decay because 0.85 is less than 1
The formula for Exponential Decay
= y = a (1 - r)^t
We equate both equation together
Where
a = 1200
1 - r = 0.85
t = 6
Solving for r
1 - r = 0.85
r = 1 - 0.85
r = 0.15
Converting to Percentage
r = 15% decay rate
HELP ME PLEASE AND PLEASE ATTACH THE ANSWER BELOW (NO LINKS!!)
Answer:
D
Step-by-step explanation:
Answer:
1885
Step-by-step explanation:
Volume = Base x Height
Please help me FAST
Answer:
I believe it's either equation one or three. hope that helps :)
Nancy had 333 dollars to spend on 9 books. After buying them she had 18 dollars. How much did each book cost ?
Answer:
35 dollars
Step-by-step explanation:333-18=315 dollars
315/9=35 dollars for each book
A. Yes
B.no
Answer: yes!!!!!!!
Write an equation of the line with a slope of -3 and a y-intercept of 0
Answer:
-3/9=07+90
Step-by-step explanation:
Answer: y = 0x+3 or y = 3
The slope is 0 and the y intercept is 3. So m = 0 and b = 3.
Plug those into y = mx+b to get y = 0x+3, and that simplifies to y = 3.
This graphs out a horizontal line that passes through the two points (0,3) and (1,3).
The difference of c and 7 is less than or equal to 17.
| c - 7 | 《 17
- 17 《 c - 7 《 17
add sides 7
- 17 + 7 《 c - 7 + 7《 17 + 7
simplification
- 10 《 c《 24
Answer:
c - 7 ≤ 17
c ≤ 24
Step-by-step explanation:
The difference of c and 7 can be written as c - 7 or 7 - c.
Now, since c - 7 is less than or equal to 17, you need to add ≤ to imply that it's less than or equal to 17.
As always, write the 17 on the other side. Now you have an inequality.
If you just need the equation, it's c - 7 ≤ 17.
But if you want to solve for c, it would be c ≤ 24.
(bring the like terms together and isolate c.)
Tanya has a $50 gift card to spend on Amazon. She wants an airpod case cover for $12.
She also wants to buy some bracelets for $9.50 each. How many bracelets can she buy
without going over?
Answer:
She can buy 3 bracelets.
Step-by-step explanation:
$50 (Total price) - $12 (Airpod case) = $38
$38 - $9.50 (Bracelets) = $28.5
$28.5 - $9.50 = $19
$19 - $9.50 = $9.5
Suppose that $3500 is placed in an account that pays 16% interest compounded each year. Assume that no withdrawals are made from the account. Follow the instructions below. Do not do any rounding.
Liz goes on holiday to South Africa
Liz wants to change £850 into south african rand
she wants to get as many 200 rand notes as possible
The exchange rate is £1=18.53 rand
Work out the greatest number of 200 rand notes that liz can get for £850
Answer:
82 notes
Step-by-step explanation:
The computation is shown below:
Given that
£1= 18.53 rand
and since Linz has £850 so he would get the equivalent of
= $890 × 18.53
= 16,491.7 rands
Now he wants the 200 rand notes so we considered it as the highest note
So, the greatest no of 200 notes would be
= 16,491.7 ÷ 200
= 82.45
= 82 notes
Which cords are congruent
Answer:
A chord is a line segment with endpoints on the circle. le Conjecture tells us that the central angles determined by the congruent chords are equal in measure
Step-by-step explanation:
5) To find the slope of the trend line below, Riley chose
the points (1, 35) and (2, 25).
−6, −3, 2, 9, 18, . . . nth term
Answer:
Your answer would be
X^2-7
Step-by-step explanation:
Hope it helps .
Good luck .
Find the slope of the line that passes through each pair of points.
S (3, -6) and T (1, 4)
Answer:
Slope= -5
Step-by-step explanation:
Use the formula, (y2-y1)/(x2-x2)
4-(-6)/1-3 = 10/-2
10/-2 = -5
Therefore -5 is the slope
help please with math!
Answer:
1/2
Step-by-step explanation:
If you do this:
20:2=10
14:2=7
12:2=6
You get dimensions of smaller triangle which is a half from bigger one.
Answer:
scale factor is 1/2
Step-by-step explanation:
notice that the sides of ΔABC are one-half of the length of the sides 0f ΔDEF
Which galaxy is the farthest from Earth?
galaxy a
galaxy b
galaxy c
galaxy d
Answer: Galaxy c is the farthest
Step-by-step explanation:
Suppose each cube in this figure is a -inch cube. Select all that are true.
The dimensions of this prism are 3 inches × 2 inches × 2 inches.
The volume of this prism is 15 cubic inches.
The volume of this prism with -inch unit cubes is the volume of the prism with 1-inch cubes.
There are 96 cubes in the prism.
Answer:
Can you attach the figure?
Step-by-step explanation: