The profit from a business is
described by the function
P(x) = -5x² + 30x + 8, where x
is the number of items made,
in thousands, and P(x) is the
profit in dollars. How many
items will maximize the profit?
Answers
First of all we will understand the question!!
The question is saying that you are given a function and you have to find the value of x which will give the maximum profit... Lets solve it by finding the extrema using the vertex
[tex] \rm \: p(x) = - 5 {x}^{2} + 30x + 8[/tex]
Identify the coefficients a and b of the quadratic function[tex] \rm \: p(x) = { - 5x}^{2} + 30x + 8 \\ \rm \: a = - 5 \: and \: b \: = 30[/tex]
Since a<0, the function has the maximum value at x, calculated by substituting a and b into x=-b/2a[tex] \rm \: x = \frac{30}{ 2 \times (- 5)} [/tex]
Solve the equation for x[tex] \rm \: x = 3[/tex]
The maximum of the quadratic function is at x=3Related Questions
[tex]\huge\fbox\green{question}[/tex]
#Combine the members of the following sets to from new sets.Show the members in diagrams
a)A={Mine,Shine,Hari} and B={Ram,Sita,Dolma}
b)M={3,6,9,12>and N={5,10,15,20}
c)A={Mari,Rahlm,Bishnu}and B={Bishnu, Kishan,Dorge}
d)C={4,8,12,16,20} and F={8,16,24,32}
Answers
Refer to the attachment
4(9^0+48(2)^-3)
Please explain how
Answers
Answer:
4(9^0+48(2)^-3) I think it's like this
What are the coordinates of the image of vertex G after
a reflection across the line y = x?
O (-4,-5)
O (4, 5)
O (-5,4)
O (5, 4)
Answers
Answer:
(- 5, 4 )
Step-by-step explanation:
under a reflection in the line y = x
a point (x, y ) → (y, x ) , then
G (4, - 5 ) → G' (- 5, 4 )
The coordinates of the image of vertex G are (-5, 4)
What is line of reflection?When reflecting a figure in a line or in a point, the image is congruent to the pre image. A reflection maps every point of a figure to an image across a fixed line. The fixed line is called the line of reflection.
here, we have,
Let us revise some cases of reflection
If the point (x, y) reflected across the x-axis , then its image is (x, -y)
If the point (x, y) reflected across the y-axis , then its image is (-x, y)
If the point (x, y) reflected across the line y = x , then its image is (y, x)
If the point (x, y) reflected across the line y = -x , then its image is (-y, -x)
From the given figure
∵ The line of the reflection is y = x
→ That means we will switch the coordinates of the point to find its image
∵ The coordinates of vertex G are (4, -5)
∴ The x-coordinate = 4 and the y-coordinate = -5
→ Switch the two coordinates
∴ The coordinates of its image G' are (-5, 4)
∴ The coordinates of the image of vertex G are (-5, 4)
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make r the subject and find the value
Answers
[tex]~~~~~~~~\dfrac{1}{R} = \dfrac{1}{R_1} + \dfrac 1{R_2}\\\\\\\implies \dfrac 1{R_2} = \dfrac{1}{R } - \dfrac 1{R_1}\\\\\\\implies \dfrac 1{R_2} = \dfrac{R_1 -R}{RR_1}\\\\\\\implies R_2 = \dfrac{RR_1}{R_1-R}\\\\\\\text{When}~ R= 24~ \Omega ~ \text{and}~ R_1 = 30~ \Omega,\\\\R_2 = \dfrac{24 \times 30}{30-24}~\Omega\\\\\\~~~~~=\dfrac{720}{6}~ \Omega\\\\\\~~~~= 120~ \Omega[/tex]
PLEASE HELP!!! Use the vertical line to test to determine if the relation whose graph is provided is a function
Answers
Answer:
This graph does not represent a function.
Step-by-step explanation:
The vertical line test describes how, in order to be a function, there must be only one output for every input. Remember, the input of a function is the "x" value and the output is the "y" value.
Because of the circular nature, this graph does not represent a function. As you can see, there are "x" values which could correspond with mutliple "y" values. For example, when x = 2, there are two "y" values: y = -1 and y = -5.
an athlete covers a distance of 0.4 km in completing one round . how many rounds does he make if he runs a total of 8.4 km distance ?
Answers
Answer:
21 rounds
Step-by-step explanation:
[tex]1[/tex] [tex]round = 0.4km[/tex]
[tex]Total[/tex] [tex]distance = 8.4km[/tex]
[tex]8.4/0.4[/tex]
[tex]=21[/tex]
The number of rounds he makes, if he runs a total of 8.4 km distance.
Solution:[tex]\large\boxed{R=\frac{Total \: distance}{Distance \: covered \: in \: 1 \: round}}[/tex]
So, we'll have to divide the total distance covered by distance covered in 1 round.
Let's substitute according to the formula.
[tex]R= \frac{8.4}{0.4}[/tex]
= 21 rounds
Hence, the number of rounds he makes, if he runs a total of 8.4 km distance is 21
Ernest’s favorite lunch is a turkey, lettuce, and tomato sandwich Ernest can make the sandwich using either white bread or wheat bread Sometimes he adds cheese, pickles, or mayonnaise in any combination, but other times he doesn’t add anything Ernest says that there are 8 different ways to make his favorite sandwich Is he correct? Explain
Answers
Answer:
Ernest is wrong, because the sandwich can be made in 6 different ways (lunch > sandwich: white bread > cheese, pickles, mayonnaise ; wheat bread > cheese, pickles, mayonnaise) and the lunch can be made in 8 different ways.
As seen in the picture. Any help is appreciated :)
Answers
Can someone please help me figure out these 10th grade geometry arc problems? ANY help appreciated, but please explain how you got your answer! Will reward brainly and 5 stars + thanks!
Answers
Answer:
Step-by-step explanation:
What is the contrapositive of the statement below?
x⇒y
Answers
Answer:
Answer: A. The contrapositive of the statement will be :
Step-by-step explanation:
The contrapositive of an if-then statement "p then q' is given by :
"If not q then not p".
The given statement is
Then the contrapositive of the statement will be :
Hence, A is the right option.
Wren is at the grocery store buying fruit. She buys x pounds of apples for $1.68 per pound. She buys 2 fewer pounds of grapes for $2.48 per pound. The cost of the fruit, before tax, is $13.76. How many pounds of each fruit is she buying?
A.
2.8 pounds of apples and 4.8 pounds of grapes
B.
3.3 pounds of apples and 1.3 pounds of grapes
C.
3.8 pounds of apples and 1.8 pounds of grapes
D.
4.5 pounds of apples and 2.5 pounds of grapes
Answers
Answer:
A.
Step-by-step explanation:
Wren is at the grocery store buying fruit. She buys x pounds of apples for $1.68 per pound. She buys 2 fewer pounds of grapes for $2.48 per pound. The cost of the fruit, before tax, is $13.76. How many pounds of each fruit is she buying?
A.
2.8 pounds of apples and 4.8 pounds of grapes
B.
3.3 pounds of apples and 1.3 pounds of grapes
C.
3.8 pounds of apples and 1.8 pounds of grapes
D.
4.5 pounds of apples and 2.5 pounds of grapes
1) the length of a rectangle is equal to triple the width. if the perimeter of the rectangle is 86 centimeters, what
are its dimensions?
Answers
Step-by-step explanation:
the perimeter is
2×length + 2×width = 86
length = 3×width
now we use the second equation as variable identity in the first equation :
2×3×width + 2×width = 86
6×width + 2×width = 86
8×width = 86
width = 86/8 = 43/4 = 10.75 cm
length = 3×width = 3×10.75 = 32.25 cm
The theoretical probability of selecting a consonant at random from a list of
letters in the alphabet is 21. Wayne opens a book, randomly selects a letter on
the page, and records thé fetter. He repeats the experiment 200 times. He Fins
(consonant) = 60%. How does the theoretical probability differ from the
experimental probability? What are some possible sources for this discrepancy?
Answers
Vowels = {a, e, i, o, u}
There are 5 vowels out of 26 letters in the English alphabet. This leaves 26-5 = 21 consonants.
The theoretical probability of getting a consonant is 21/26 = 0.8077 = 80.77% approximately
Wayne found the empirical probability of a consonant as 60% which is quite a distance away from the 80.77% mentioned. The discrepancy is likely because vowels are tended to be used quite often in many words.
Words that are composed of consonants only are quite rare, but they do happen. Example: "fly" is a word with only consonants. I'm considering y to be a consonant.
PLEASE HELP ASAP
i couldn’t get it to write correctly so I inserted photo
Answers
When h is one-half and j is one-third, g is 4. if g varies jointly with h and j, what is the value of g when h is 2 and j is 3? 4 6 24 144
Answers
Answer:
D) 144Giveng varies jointly with h and jg = 4 when h = 1/2, j = 1/3To findValue of g when h = 2 and j = 3Joint variation:g = khj, where k- coefficient
Use given values of h and j, and find the value of k:
4 = k*(1/2)(1/3)4 = (1/6)kk = 4*6k = 24The equation is now:
g = 24hjFind the value of g when h is 2 and j is 3:
g = 24*2*3 = 144Correct choice is D
Answer:
D. 144
Step-by-step explanation:
i donnt know ..............
Answers
Answer:
7
Step-by-step explanation:
[tex]\dfrac 13(15+6)\\\\\\=\dfrac{21}3\\\\\\=7[/tex]
The Ratio of two numbers is 3/5, and their sum is 104. What are the 2 numbers?
Answers
Answer:
39 and 65
Step-by-step explanation:
the ratio of the two numbers is 3 : 5
sum the parts of the ratio, 3 + 5 = 8 parts
divide the sum by 8 to find the value of one part of the ratio
104 ÷ 8 = 13 ← value of 1 part of the ratio , then
3 parts = 3 × 13 = 39
5 parts = 5 × 13 = 65
the two numbers are 39 and 65
Solve the equation for x
z=m+x-y a)x=-z+m+y b)x=z-m+y c)x=z+m-y d)x=z+y+m
Answers
Answer:
x = z - m + y
Step-by-step explanation:
Given:
[tex]\displaystyle \large{z = m+x-y}[/tex]
To solve for x-term, we have to isolate it. We can do by subtracting m-term both sides and add y-term both sides.
[tex]\displaystyle \large{z-m+y=m+x-y-m+y}\\\\\displaystyle \large{z-m+y=x}\\\\\displaystyle \large{x=z-m+y}[/tex]
Therefore, the answer to this question is x = z - m + y
Please let me know if you have any questions regarding my answer or explanation!
A six-sided die is rolled seven times. What is the probability that the die will show an even number at least six times?
Answers
Answer:
Step-by-step explanation:
Explanation
On a 6 sided die, there are three even numbers (2,4,6)
That's 1/2 the number on the die.
So getting 6 even numbers is
P(6) = 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 0.00781
Where did that extra 1/2 come from? Well one of the numbers thrown was an odd number, and it has to be counted.
P(7) = the same answer. 0.00781
Total 0.0156
Can someone else explain how to do problems like this?
Answers
The answer is A , for determining range look at Y-axis only from down to up .For this question we can also say
range: [1,7] , if both ends of the line are arrows it means the line goes from negative infinity to positive infinity (which means range is all real numbers) , but if the point is include just like this graph the points will be also include in range , but if the points are an empty circle the points won't be include for writing range
hope it helps
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Use the following triangles to determine the trig ratios below simplify all fractions rationalize and simplify all radicals and convert all decimals answers to fractions
Answers
What is this function written in vertex form? f(x) = (x –1)2 – 7 f(x) = (x 1)2 – 7 f(x) = (x –1)2 – 5 f(x) = (x 1)2 – 5
Answers
The vertex form of all expressions is given below.
We have given that the expressions
We have to write the function in vertex form.
What is the vertex form of the equation?
The vertex form of a quadratic function is given by f (x) = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.
Therefore the first equation
[tex]f(x)=(x-1)^2-7[/tex]
it can be written as
[tex]f(x)=1(x-1)^2+(-7)[/tex]
The second equation can be written as
[tex]f(x) = (x+1)^2 -7[/tex]
vertex for is,
[tex]f(x)=1(x-(-1))^2+(-7)[/tex]
The third equation is,
[tex]f(x) = (x -1)^2 - 5[/tex]
Vertex form is,
[tex]f(x)=1(x-1)^2+(-5)[/tex]
Forth equation is,
[tex]f(x) = (x +1)^2 +(- 5)[/tex]
Vertex form is,
[tex]f(x) =1 (x -(-1))^2 +(- 5)[/tex]
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Suppose that g(x) = f(x-4). Which statement best compares the grap
g(x) with the graph of f(x)?
Answers
The transformation of a function may involve any change. The graph of g(x) is the graph of f(x) shifted 4 units to the right.
How does the transformation of a function happen?The transformation of a function may involve any change.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units, y=f(x+c) (same output, but c units earlier)
Right shift by c units, y=f(x-c)(same output, but c units late)
Vertical shift
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
Stretching:
Vertical stretch by a factor k: y = k × f(x)
Horizontal stretch by a factor k: y = f(x/k)
As per the transformation of the function, if the function g(x) = f(x-4), then the graph of g(x) will be 4 units in the right of f(x).
Hence, the graph of g(x) is the graph of f(x) shifted 4 units to the right.
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How to find the sum of these terms. 1. 5x,12x,9x
2. -5x,19x,-7x
Answers
Answer:
just solve normally as if theres no x,
1. 26x
2. -7x
Jose wants to find the perimeter of triangle ABC. He uses the distance formula to determine the length of AC. Finish Jose’s calculations to find the length of AC.
What is the perimeter of triangle ABC? Round the answer to the nearest tenth, if necessary.
12.0 units
12.4 units
15.0 units
15.4 units
Answers
Answer:
15 units
Step-by-step explanation:
15.0
Which of the following is the solution of 5x - 6 = 44?
O x= -10
38
Ox=
x = -5
O x=
Ox-10
Answers
Work Shown:
5x-6 = 44
5x-6+6 = 44+6 ... see note 1
5x = 50
5x/5 = 50/5 ... see note 2
x = 10
note1: We add 6 to both sides to undo the -6note2: Divide both sides by 5 to undo the multiplication. Think of 5x as 5*x or "5 times x".STATISTICS in a recent year the mean score on the mathematics section of the SAT test was 515 and the standard deviation was 114. This means that people within one deviation of the mean have SAT math scores that are no more than 114 points higher or 114 points lower than the mean A. write an absolute value inequality to find the range of SAT mathematics test scores within one standard deviation of the mean B. what is the range of SAT mathematics test scores 12 standard deviation from the mean?
Answers
An absolute value inequality to find the range of SAT mathematics test scores within one standard deviation of the mean is; |x – 515| ≤ 114
How to Write Inequalities?
A) We are told that;
Mean score = 515
Standard deviation = 114
We are now given that people within one deviation of the mean have SAT math scores that are no more than 114 points higher or 114 points lower than the mean. Thus, the absolute value inequality is;
|x – 515| ≤ 114
B) The range of scores to within ±2 standard deviations of the mean is;
Range = 515 ± 2(114)
Range = 287 to 743
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Kellie thinks of a number, then doubles the number, and then multiplies the result by 3. If her final number is 65 more than her original number, then what was her original number I will give 70 points pls
Answers
Kellie's original number given the analogy and corresponding equation is 13
How to write and solve equation?let
the unknown number = x(x × 2) × 3 = x + 65
2x × 3 = 65 + x
6x = 65 + x
6x - x = 65
5x = 65
divide both sides by 5x = 65/5
x = 13
check:
6x = 65 + x
6(13) = 65 + 13
78 = 78
Therefore, the unknown number, x is 13
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20. Solve 3(5x − 4) < 15x.
All Real Numbers
x>-4
x<4
no solution
Answers
Answer:
No solution
Step-by-step explanation:
[tex]3(5x - 4) < 15x \\ 15x - 12 < 15x \\ 15x - 15x < 12 \\ 0 < 12[/tex]
answer?...............
Answers
Step-by-step explanation:
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