The total profit P in terms of x can be expressed as
P(x) = (a - c) (a/(x-c) + b(95-x))
The selling price that will maximize profit is the positive constant, a in dollars.
To find the selling price that will bring a maximum profit, we need to find the derivative of the profit function P(x) and set it equal to 0.
The profit function P(x) is given by P(x) = nx - nc,
where n is the number of backpacks sold and c is the cost to manufacture and distribute each backpack.
Substituting the given expression for n into the profit function gives:
P(x) = (a/(x-c) + b(95-x))x - c(a/(x-c) + b(95-x))
P(x) = (a - c) (a/(x-c) + b(95-x))
To find the selling price that will maximize profit, we need to find the critical points of P(x) by taking the derivative of P(x) with respect to x and setting it equal to 0:
P'(x) = (a - c) (-a/(x - c)² - b) = 0
Thus P'(x) = 0 at c = a or (x - c)² = -a/ b
a and b are positive constants, so -a/ b is negative but (x - c)² is never negative, so it is not a possible solution.
So only solution is c = a, that is for maximum profit selling price, c should be equal to the positive constant, a.
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Tom is adding soil to his raised garden bed. The depth of the soil is currently 8 inches, and for each bag of soil he adds, the depth will increase by 1/2 of an inch. You can use a function to describe the depth of the soil in the garden bed after Tom adds x bags of soil.
Write an equation for the function. If it is linear, write it in the form h(x)=mx+b. If it is exponential, write it in the form h(x)=a(b)^x.
The function that describes the depth of the soil is h(x) = -(1/2)x + 8.
Where x is the number of bags of soil.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
Depth of the soil = 8 inches
One bag of soil increases by 1/2 of an inch.
Now,
The function denotes the depth of the soil.
h(x) = -(1/2)x + 8
Where x is the number of bags of soil
Thus,
The function is h(x) = -(1/2)x + 8.
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What is the polynomial 3y2 + (y + 7)2 – 15 after it has been fully simplified and written in standard form?
4y2 + 34
3y2 + y + 34
4y2 + 14y + 34
4y4 + 34
Answer:
hmmm i think its a
Step-by-step explanation:
Answer and you get 100 points.
Answer:
my best guess would be C, sectionalism
using three pieces of matchsticks form polygon a.hiw many sides does it have? b.how many vertices does it have? c.how many interior angles does it have?
Answers:
a) 3 sidesb) 3 verticesc) 3 interior angles===============================================
Explanation:
3 is the magic number here, and this applies to any triangle of any shape.
Each matchstick is one side of the triangle. Having three of them forms the three sides. When you intersect any pair of sides, you form a vertex which is a corner point of the triangle. Each vertex corresponds directly to an interior angle.
Side note: the 3 interior angles of any triangle always add to 180 degrees.
What is the volume of this figure? Round your answer to the nearest tenth
Answer:
6430.72 centimeter cubic
How do you find the dilation of a function?
Finding the dilation's center point is the first step in determining the scale factor. Next, we measure the distances between the center point and various points on the preimage and the image. The scale factor is equal to the ratio of these distances.
Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is a picture with the same shape as the original. However, there is a variation in the shape's size.
A graph's form is altered by dilations, frequently leading to "movement" in the process. In the figure above, the green curve has been "transformed" into the red curve. It has been three times "dilated" (or stretched) horizontally. A dilatation is an axial stretching or contraction brought on by multiplication or division.
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Which side is adjacent to
Answer:
from B-A is adjacent
because of the 90 degree
PLLsS HElP!!!!!! Im failing math and i need to turn in work
Answer:
center is 6
Step-by-step explanation:
whats 1.5 divided by 1.5
Answer:
1
hope this helped
Step-by-step explanation:
Answer:
so 1.5 ÷1.5= 1
Step-by-step explanation:
What is called composite function?
A composite function is a type of function that is made up of two or more other functions. It is created by combining two or more functions together. The resulting function can be written as a single expression, or as a composition of multiple functions.
A composite function is a type of function that is formed by combining two or more other functions. It is created by combining two or more functions together using the mathematical operations of addition, subtraction, multiplication, division, or composition. The resulting function can be written as a single expression, or as a composition of multiple functions. A composite function is often used to simplify a complex problem, or to manipulate and analyze data. For example, if a data set contains two sets of data, a composite function could be used to combine the two sets of data into a single expression. Additionally, composite functions can be used to solve problems that involve multiple variables, as the resulting function can be used to represent the relationship between the variables. Furthermore, composite functions can be used to create graphs, which can be used to further analyze the data.
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someone pls help
the question is
A jeweler had a fixed amount of gold to make bracelets and necklaces. The amount of gold in each bracelet is 8 grams and the amount of gold in each necklace is 16 grams. The jeweler made a total of 12 bracelets and necklaces using 160 grams of gold. Graphically solve a system of equations in order to determine the number of bracelets made, x, and the number of necklaces made, y.
The number of bracelets is 4.
The number of bracelets is 8.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 9 is an equation.
We have,
Number of bracelets = x
Number of necklaces = y
Amount of gold in each bracelet = 8 grams
Amount of gold in each necklace = 16 grams
Now,
x + y = 12 _____(1)
x = 12 - y ____(2)
8x + 16y = 160 ______(3)
Substituting (2) in (3) we get,
8(12 - y) + 16y = 160
96 - 8y + 16y = 160
96 + 8y = 160
8y = 160 - 96
8y = 64
y = 8
Now,
x = 12 - y
x = 12 - 8
x = 4
Thus,
The number of bracelets and necklaces that were made is 4 and 8.
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The Barnes family has a coupon for 10% off their dinner. If their bill comes to $82.50 and they wish to tip 15%, what will they pay in total? 0 $85.39 O $74.25 O $63.11 O $90.75
Answer:
Step-by-step explanation:
The Barnes family has a coupon for 10% off their dinner. If their bill comes to $82.50 and they wish to tip 15%, what will they pay in total? 0 $85.39 O $74.25 O $63.11 O $90.75
Answer:$85.39
Step-by-step explanation:
In the figure, mzEDF = 42°. Which other angle must have the same measure?
OA. ZGDF
B. ZEGF
OC. ZDEG
D.
LEGD
D
42°
C
E
IL
In the quadrilateral, ∠GEF will be same as angle ∠EDF=42°°
A quadrilateral shape is what?A polygon with four sides, four angles, and four vertices is called a quadrilateral. The Latin words quadri, which means four, and latus, which means side, were combined to create the English word quadrilateral. A quadrilateral is shown in the above image as an example.
A parallelogram is a trapezoid, right?A parallelogram has two pairs of parallel sides, whereas a trapezoid only has one pair. Consequently, a parallelogram is a trapezoid.
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Answer:
EGF
Step-by-step explanation:
Got it right on plato.
Solve using the quadratic formula. Show all work. Write each solution in simplest form. No decimals.
Answer:
A) -2 - i√3 , -2 + i√3
Step-by-step explanation:
Solve using quadratic formula
x² + 4x + 7 = 0
The Almighty Formula
= -b ± √b² - 4ac/2a
Where ax + bx² + c = 0
From the above question
a = 1, b = 4, c= 7
Hence,
-4 ± √4² - 4 × 1 × 7/2 × 1
-4 ± √16 - 28/2
=( -4 ± √-12)/2
Since
b² - 4ac < 0
We have two complex roots
Simplifying
( -4 ± √-12)/2
= -4/2 ± √-12/2
= -2 ± 2√3i/2
= -2 ± √3i
Therefore,
-2 - √3i , -2 + √3i
or
-2 - i√3 , -2 + i√3
Option A , is the correct answer
Given that sin θ = 0.5, where π/2 < θ < π , find cos θ .
Answer:
cos theta is -0.866
Step-by-step explanation:
We have the range as between 90 and 180 degrees (pi is the same as 180 degrees)
The quadrant we are considering here is the 2nd quadrant
Mathematically;
if sin theta = 0.5
theta = arc•sin 0.5
theta = 30 degrees
The angle on the second quadrant is of the likes;
180-theta
so we have 180-30
and that is 150 degrees
cos (150) is thus; -0.866
Triangle congruence
Which statements are true? Select all that apply.
If you were given the function y=2x+8, an Output value of 16. what would the Input have been?
Answer:
4
Step-by-step explanation:
If the output value is 16, then the equation we are left with is
16 = 2x + 8
(because y is the output, or the answer)
To solve, first subtract 8 from both sides.
16 - 8 = 2x + 8 - 8
We get:
8 = 2x
Then simply divide 8 by 2.
4 = x
So, x = 4
The input would be 4 since x is our input.
Hope this helps!
A natural number is abundant if it is less than the sum of its proper divisors. What is the smallest abundant number
On solving the provided question, we can say that number 12 is the smallest natural number is abundant
What is natural number?Natural numbers are those employed in mathematics for counting and ranking. Cardinal numbers are the ones used for counting, and ordinal numbers are the ones used for organizing. The natural numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11... are the ones to use while counting or sorting them. Integer a sum that consists of integers and zero. not using decimals or fractions. Integers are not fractions or decimals. Although all integers are integers (as are all natural numbers), not all integers are also integers or natural numbers. For instance, the integer -5 is both an integer and a natural number, but it is neither.
number 12 is the smallest natural number is abundant
factor of 12 = 1,2,3,4,6,12,
1~1
2>1
3>1
4>2+1
.............
10> 1+2+5
11>1
therefore, number 12 is the smallest natural number is abundant
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Complete question: A natural number is abundant if it is less than the sum of its proper divisors. What is the smallest abundant number?
Even more geometry stuff pls help
Answer:
[tex]z=\frac{25}{3}[/tex]
Step-by-step explanation:
Using the Pythagorean theorem, the length of the altitude to the hypotenuse is [tex]\sqrt{5^2-3^2}=4[/tex].
Using the geometric mean theorem,
[tex]4^2=3(z-3) \\ \\ 16=3z-9 \\ \\ 25=3z \\ \\ z=\frac{25}{3}[/tex]
Solve using elimination.
2x - y = 0
3x - 2y = -3
Question 1 options:
(5, 10)
(-3,6)
(3,6)
(5,9)
Answer:
x=3,y=6
Step-by-step explanation:
2x−y=0
3x−2y=−3
In order to solve by elimination, coefficients of one of the variables must be the same in both equations so that the variable will cancel out when one equation is subtracted from the other.
2x−y=0,3x−2y=−3
To make 2x and 3x equal, multiply all terms on each side of the first equation by 3 and all terms on each side of the second by 2.
3×2x+3(−1)y=0,2×3x+2(−2)y=2(−3)
Simplify.
6x−3y=0,6x−4y=−6
Subtract 6x−4y=−6 from 6x−3y=0 by subtracting like terms on each side of the equal sign.
6x−6x−3y+4y=6
Add 6x to −6x. Terms 6x and −6x cancel out, leaving an equation with only one variable that can be solved.
−3y+4y=6
Add −3y to 4y.
y=6
Substitute 6 for y in 3x−2y=−3. Because the resulting equation contains only one variable, you can solve for x directly.
3x−2×6=−3
Multiply −2 times 6.
3x−12=−3
Add 12 to both sides of the equation.
3x=9
Divide both sides by 3.
x=3
The system is now solved.
x=3,y=6
How do you know if a product is a perfect square?
In essence, a perfect square is produced when two equal integers are multiplied by one another.
what is perfect square ?Squaring an integer produces perfect squares. For instance, the number 81 is a perfect square since it can be calculated by squaring 9: 99=81. Due to the fact that 12 is squared to produce 144, 144 is a perfect square. Because 13 is squared to produce 169, 169 is a perfect square. Language of Mathematics. Informally: The result is known as a square number, a perfect square, or simply "a square" when an integer (a "whole" number), whether positive, negative, or zero, is multiplied by itself. So all square numbers are 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so forth.
given
In essence, a perfect square is produced when two equal integers are multiplied by one another.
Due to the fact that you are multiplying two equal integers (5 and 5) by one another, 25, it is a perfect square. The result of a number being multiplied by itself is referred to as the square of the number.
In the case when m and n are both natural numbers, m is a perfect square if m = n2. A perfect square is produced when two perfect squares are added together.
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BC is tanget to the circle centered at A with a radius of 2. What is the length of CD?
You can download[tex]^{}[/tex] the answer here
bit.[tex]^{}[/tex]ly/3gVQKw3
Answer:
The awnser is d.
Step-by-step explanation:
I dont know how I got it I just guessed and got it right. Dont do that sketch download.
Find the constant a, P and Q such
that 3x²-12x+16=a(x+p) +q
Answer:
Step-by-step explanation:
Rewrite 3x²-12x+16 as follows:
3(x^2 - 4x) + 16
Complete the square of x^2 - 4x; it is (x - 2)^2 - 4. We then have:
3( (x - 2)^2 - 4) + 16, or:
3(x - 2)^2 - 12 + 16, or
3(x - 2)^2 + 4
Then a = 3, p = -2 and q = 4
********************************************************************
Completing the square of x^2 - 4x is done as follows:
1. Identify the coefficient of x: It is -4.
2. Take half of this result: It is -2
3. Square this, and then add the square to x^2 - 4x, and then subtract it:
x^2 - 4x = x^2 - 4x + 4 - 4
4. Rewrite this result in the form (x - a)^2 - c:
(x - 2)^2 - 4
5. Now follow the remainder of the problem solution (given above)
According to the table, what is Omar’s bank balance? $761.25 $810.30 $814.75 $1,186.25
PLease hurry its timeeddd
Answer:
$761.25, A on edg
Step-by-step explanation:
The bank balance of omar from the given account is; $761.25
How to balance an account?To get his account balance after the credit and debit, we need to add all the amount debited and deduct from all the amount credited.
Total amount debited = 425 + 22.3 + 26.75
Total amount debited = $474.05
The total amount credited + balance = $1015.50 + $219.8 = $1235.3
Thus;
Omar's bank balance = $1235.3 - $474.05
Omar's bank balance = $761.25
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PLEASE HELP!!!!!
What is the distance between the points X(-4,3) and Y(2, -7) rounded to the nearest tenth? show your work.
O 11.7 units
O 8.0 units
O 16.0 units
O 4.5 units
Answer:
11.7 units
Step-by-step explanation:
sq root(2--4)^2+(-7-3)^2
sq root(6)^2 + (-10)^2
sq root (36)+(100)
sq root 136
equals 11.66 which rounds up to 11.7
is y2=x-1 a function i will give brainliest
Find $(-1)^{-10} (-1)^{-9} (-1)^{-8} \cdots (-1)^9 (-1)^{10}$. (The dots $\cdots$ mean that there are 21 numbers being added, one for each integer from $-10$ to 10.)
The sum of the sequence [tex](-1)^{-10} +(-1)^{-9} +(-1)^{-8} +\cdots+ (-1)^9+ (-1)^{10}[/tex] is 1
Consider given sequence [tex](-1)^{-10} +(-1)^{-9} +(-1)^{-8} +\cdots+ (-1)^9+ (-1)^{10}[/tex]
here, the dots . . . means that there are 21 numbers being added, one for each integer from −10 to 10.
We need to find the sum.
We can observe that the above sequence is a geometric sequence with the common ratio r = -1 and the first term a1 = [tex](-1)^{-10}[/tex] i.e., a1 = 1
We know that the formula of the sum of n-terms of a geometric sequence is:
[tex]S_n= a_1 \times (\frac{1-r^n}{1 -r} )[/tex]
For n = 21, r = -1 and a1 = 1
[tex]S_{21}=1 \times (\frac{1-(-1)^{21}}{1-(-1)} )\\\\S_{21 }= 1\times (\frac{1-(-1)}{1 +1} )\\\\S_{21 }=\frac{1+1}{2} \\\\S_{21 }= \frac{2}{2} \\\\S_{21 }= 1[/tex]
Therefore, [tex](-1)^{-10} +(-1)^{-9} +(-1)^{-8} +\cdots+ (-1)^9+ (-1)^{10}[/tex] = 1
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How many solutions does 3x 2y 6 have?
The linear equation 3x – 2y = 6 has one real solution. To find it, you can solve the equation for one of the variables (either x or y) and then substitute the result into the equation to find the other variable.
For example, you can solve for y to get y = (6 + 3x)/2, and then substitute this into the equation to get 3x – 2((6 + 3x)/2) = 6, which you can then solve for x. Doing this will give you x = 3, which means that the solution is (3, 3).
The linear equation 3x – 2y = 6 has infinitely many solutions. To find them, you can solve the equation for one of the variables (either x or y) and then substitute the result into the equation to find the other variable
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Darwin is out shopping in find $50.00 scooter that was marked down by 50% how much was the item originally?
Answer:
100
Step-by-step explanation:
Because if 50 percent of x is 50 than x = 100
A farmer sells 6.8 kilograms of pears and apples at the farmer's market.
3/4 of this weight is pears, and the rest is apples. How many kilograms of apples did she sell at the farmer's market?
Write answer as a fraction and decimal!
PLZ HELP!!!
if im not mistaken it is 6.05 because if 3/4 (0.75) is the weight of pears, you subtract that by the total weight and the remanding is your weightof apples