The function at its maximum value will be at point (11,4) and its value is 52 which can be derived keeping in mind the constraints that have been given.
Maximizing a functionThe maximum value of any kind of a function is the place where the said function reaches its highest point, or vertex, on a graph. If your kind of quadratic equation has something as a negative of a term, it will also have a maximum value.
There are a bit of three ways to find that maximum, depending on which form of a quadratic function you have got.
Herein we can find the closed region ABC from the three equations or constraints given
and can mark the points as
A = (5,4)
B = (5, 12)
C = (11, 4)
if we put up the values of the points, we get
at (11, 4), Z = 4 x 11 + 2 x 4
=52 that is the maximum value amongst the three.
Thus, the maximum point of the function can be calculated as (11,4)
How do you extract out the maximum or minimum value of a function?We will at first set out the first derivative of the function to absolute zero and then solve for x to get the exact critical point.
If we then take the second derivative or f’’(x), there in we can find out whether this point will be a maximum or minimum. If the second derivative is seen as positive, it will be a minimum value
What is the maximum value of a function called?The maximum or minimum value that is calculated over the entire function is called an “Absolute” or “Global” maximum or minimum of the function.
There is presence of only one global maximum (and only one global minimum) but there can be several that is more than one local maximum or minimum
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Write the quadratic equation that has roots √3 +1/2 and √3 −1/2 , if its coefficient with x^2 is equal to 9
The quadratic equation that has roots √3 + 1 / 2 and √3 - 1 / 2 and a leading coefficient of 9 is y = 9 · x² - 18√3 · x + 99 / 4.
How to find the quadratic equation associated with given real roots and leading coefficient
In this problem we must determine the quadratic equation such that its roots are √3 + 1 / 2 and √3 - 1 / 2 and whose leading coefficient is equal to 9. This can be found by substituting on factor form:
y = a · (x - r₁) · (x - r₂)
Where:
a - Leading coefficient.r₁, r₂ - RootsIf we know that r₁ = √3 + 1 / 2, r₂ = √3 - 1 / 2 and a = 9, then the quadratic equation is:
y = 9 · (x - √3 - 1 / 2) · (x - √3 + 1 / 2)
y = 9 · [x² - (√3 - 1 / 2) · x - (√3 + 1 / 2) · x + 3 - 1 / 4]
y = 9 · (x² - 2√3 · x + 11 / 4)
y = 9 · x² - 18√3 · x + 99 / 4
The quadratic equation is y = 9 · x² - 18√3 · x + 99 / 4.
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what is the exact value of tan (-3pi/4)
Answer:
1
Step-by-step explanation:
The owner of a video store has determined that the profits P of the store are approximately given by
The profit of the store is represented by the quadratic formula:
[tex]P(x)=-x^2+90x+52[/tex]Where
P is the profit
x is the number of videos rented
The coefficients of the parabola are:
a= -1 (coefficient of the quadratic term)
b= 90 (coefficient of the x-term)
c=52 (constant)
The value of a is negative, which indicates that the parabola opens downwards and that its maximum value is represented by the vertex.
To determine the maximum profit, you have to determine the coordinates of the vertex.
First, calculate the x-coordinate of the vertex, to do so you have to use the following formula:
[tex]x_v=-\frac{b}{2a}[/tex]Replace it with the values of the coefficients a=-1 and b=90
[tex]\begin{gathered} x_v=-\frac{90}{2\cdot(-1)} \\ x_v=-\frac{90}{-2} \\ x_v=45 \end{gathered}[/tex]Second, replace x=45 in the equation to determine the y-coordinate of the vertex:
[tex]\begin{gathered} y_v=P(45) \\ y_v=-(45^2)+90\cdot45+52 \\ y_v=-2025+4050+52 \\ y_v=2077 \end{gathered}[/tex]The y-coordinate of the vertex represents the maximum profit.
So the maximum profit is $2077, the correct option is option A.
Write a rational expression to determine how many cubbies high the book shelf will be.
Answer:
[tex]\frac{x^2-8x-65}{x+1}[/tex]
Explanation:
The height of each small division is x + 1, and the total height is x² + 6x + 5. Then, the number of small division is the total height divided by the small division height.
use the function f=8v to find the value of f when v =8
EXPLANATION
Given the function f= 8v
And the v-value = 8
Replacing this on the equation:
f= 8*8 = 16
Answer: f=16
The diagram represents a ramp in the shape of a right triangle and the lengths of two of its sides in feet. What is the length of the round in feet?
Answer:
61 feet
Explanation:
The length of the ramp is the hypotenuse of the right triangle formed.
To find the hypotenuse, use the Pythagorean Theorem:
[tex]\begin{gathered} Hypotenuse^2=Base^2+Altitude^2 \\ x^2=60^2+11^2 \end{gathered}[/tex]Take the square root of both sides:
[tex]\begin{gathered} x=\sqrt{60^2+11^2} \\ x=\sqrt{3721} \\ x=61\text{ ft} \end{gathered}[/tex]The length of the ramp is 61 feet.
Using the idea of the Empirical Rule for a normal distribution, explain what percent of individuals would fall in the given range. iܒܫܡܗ Si The range of IQ scores from 80 to 120, when the mean IQ score is 100 and the standard deviation is 10.
SOLUTION
Answer = 95.5%
From this information given.
We have a mean value of 100 and a standard deviation value of 10
To obtain the range from 80 to 120.
This will be moving 2(S.D) to the left and 2(S.D) to the right of the mean.
From theory, values within 2S.D from the mean, represent 95.5% of the given data.
Therefore, the percent of individuals that would fall in the given range is
95.5%
Together, Nora and Addison own 152 shares of stock. Nora has 4 less than three times Addison's amount. How many shares does each girl have?
The number of shares that Nora has is 113.
The number of shares that Addison has is 39.
How many shares do they have?Let x represent the amount of shares that Addison has
Shares that Nora has = 3x - 4
The sum of shares they both have : 3x - 4 + x = 152
In order to determine the value of x, take the following steps:
Combine similar terms together: 3x + x = 152 + 4
Add similar terms: 4x = 156
Divide both sides by 4 : x = 156/ 4 = 39
Shares that Nora has = 3(39) - 4
117 - 4 = 113
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My answer I correct or no please help
The product of 8 and a number k increased by 12 , 8K+12
What is algebraic expression?Using letters or alphabets to represent numbers without giving their exact quantities is the idea behind algebraic expressions. The principles of algebra taught us how to express an unknown value using letters like x, y, and z. These letters are referred to here as variables. Variables and constants can both be used in an algebraic expression. Any amount that is added before a variable and then multiplied by it is referred to as a coefficient.An algebraic expression is one that has been constructed using integer constants, variables, and algebraic operations. For instance, the algebraic formula 3x2 2xy + can algebraic symbol or set of symbols that includes one or more integers, variables, and arithmetic operationsTo learn more about Algebraic expression refer to:
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How much was the decrease dollar? How much was in his account the end of last year?
Explanation
We are given the following information:
• Amount at the beginning of an investment = $5500
,• Percent decrease = 24.6%
We want to determine the decreased amount in dollars and the amount in his account at the end of the year.
We can determine the decreased amount with the formula below:
[tex]Decreased\text{ }amount\text{ }=Percent\text{ }decrease\text{ }\times Amount[/tex]Therefore, the decreased amount can be calculated as:
[tex]\begin{gathered} Decreased\text{ }amount=24.6\%\times5500 \\ Decreased\text{ }amount=\frac{24.6}{100}\times5500=1353 \end{gathered}[/tex]Hence, the decreased amount is $1353.
At the end of last year, the amount left in his account can be calculated as follows:
[tex]undefined[/tex]Hence, the year-end amount is $4147.
A group of 60 students arerandom randomly selected to take a one minute fitness test using a jump rope 30 students are in first grade and 30 students are in 7th grade the following following status information is calculated using the number of jumps completed him one minute they sell me samples what interest rate can be used
we get that the final price of a 16-ounce smoothie is:
[tex]3.69+1.06+0.94-0.75=4.94[/tex]$4.94
Find the mean of these numbers: 5, 11, 2, 12, 4, 2Need solution :D
SOLUTION
We want to find the mean of the numbers 5, 11, 2, 12, 4, 2
To do this, we add the numbers and divide by the total numbers.
The numbers are 6 in numbers, so the mean
[tex]\begin{gathered} mean=\frac{5+11+2+12+4+2}{6} \\ =\frac{36}{6} \\ =6 \end{gathered}[/tex]Hence the answer is 6
The ------------- of a circle is a line segment that joins two points on the circumference of the circle and passes through the centre of the circle
Solution
The Diameter of a circle is a line segment that joins two points on the circumference of the circle and passes through the centre of the circle
Aliyah's school is selling tickets to the annual dance competition. On the first day of ticket sales
the school sold 8 senior citizen tickets and 15 child tickets for a total of $266. The school took in
$168 on the second day by selling 8 senior citizen tickets and 8 child tickets. What is the price
each of one senior citizen ticket and one child ticket?
Each senior citizen ticket costs $7.
One child's ticket costs $14.
Describe algebra.
Algebra is one of the numerous subfields of mathematics. The study of mathematical symbols and the rules for employing them in formulas is commonly referred to as algebra, which runs across almost all of mathematics.
S represents the senior citizen ticket cost.
C is the child's ticket cost.
Price is expressed as USD per ticket.
8S + 15C = 266
8S + 8C = 168
Subtract both equations now to get rid of S
8S + 15C = 266
8S + 8C = 168
———————————-
7C = 98
C = 98/7
C = $14
Changing the value of C in the first
8S + 15(14) = 266
8S + 210 = 266
8S = 266 - 210
8S = 56
S = 56 / 8
S = $7
Hence, $7 is the price for senior citizen
And, $14 is the price for child
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Factor the following expression completely.x4 - 16
Given:
[tex]x^4-16[/tex]Required:
To factor the given expression.
Explanation:
Consider the given expression
[tex]x^4-16[/tex]Now
[tex]\begin{gathered} x^4-16=(x^2)^2-(4^)^2 \\ \\ =(x^2-4)(x^2+4) \\ \\ =(x^2-2^2)(x^2+4) \\ \\ =(x-2)(x+2)(x^2+4) \end{gathered}[/tex]Final Answer:
[tex]x^4-16=(x-2)(x+2)(x^2+4)[/tex]Which expression is equivalent to -5/3 x
Answer:
-1 2/3 x
Step-by-step explanation:
This is not that difficult. But I suggest that you provide answer options.
pls mark brainliest
Andre graphed the parent function f(x) and
1
a new line d(x). If d(x) will have a slope of 4
and a y-intercept of 9, write a function to
represent d(x) as a transformation of f(x).
Answer:Its d(x)=1/4f(x)+9, mate
Step-by-step explanation:I just guessed and got it correct lol, also its "1/4" as a fraction
find an equation parallel to y=-8 and passing through (-6, -7)
Given:
an equation is given as y = -8.
Find:
we have to find an equation parallel to the given equation and passing through (-6, -7).
Explanation:
Compare the given equation with y = mx + b,
we find that slope ,m = 0 ,
the equation of the line passing through (-6,-7) is
y - (-7) = m( x - (-6))
y + 7 = 0(x + 6)
y + 7 = 0
y = -7
Therefore, y = -7 is an equation which is parallel to y = -8 and passing through ( -6, -7).
The graph of both y = -8 and its parallel equation y = -7 which passes through (-6, -7) is given as below
Red line represents the equation y = -8
and blue line represents the equation y = -7 passes through the point (-6,-7).
Therefore, the equation of the line parallel to y = -8 and passing through (-6,-7) is y = -7.
I have no clue how to get the different
The distance between the two given points X(-3,3) and Z(4,4) in the given cartesian plane is XZ = √50 = 7.07 units.
As per the question statement, we are supposed to calculate the distance between the two given points X(-3,3) and Z(4,4) in the given cartesian plane. We know that the distance between any two points in the plane is given by:
d=√((x2 – x1)² + (y2 – y1)²), where "d" is the distance between the points (x1,y1) and (x2,y2). Using this formula to find the distance between the two given points X(-3,3) and Z(4,4).
XZ = √((4 +3)² + (4 – 3)²)
XZ = √((7)²+ (1)²)
XZ = √(50)
XZ = 7.07 units
Cartesian Plane: A Cartesian coordinate system in a plane is a system of coordinates that specifically identifies each point by a pair of numerical coordinates with one on X-axis and other on Y-axis. These numerical coordinates are the signed distances from two fixed perpendicular lines to the point, measured in the same unit of length.To learn more about Cartesian Plane click on the link given below:
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The points R, S, T and U all lie on the same line segment, in that order, such that the ratio of RS:ST:TURS:ST:TU is equal to 1:1:4.1:1:4. If RU=54,RU=54, find RS.RS.
The segment RS has a length of 9 units
How to determine the length of the segment RS?From the question, the partition of the line segment is given as
RS : ST : TU = 1 : 1 : 4
Where the endpoints of the line segments are R and U
This means that the length RS can be calculated using the following equation
Length RS = Ratio of RS/Sum of the ratios x The length of RU
Substitute the known values in the above equation
So, we have
Length RS = 1/(1 + 1 + 4) x 54
Evaluate the sum
Length RS = 1/6 x 54
Evaluate the products
Length RS = 9
Hence, the length of the segment RS is 9 units
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NEED HELP ASAP
The graph compares the ages of 100 randomly selected visitors at a beach in January and in July. Select from the drop-down menu to correctly complete the statement. On average, visitors in January were Choose... years older than visitors in July.
From the given box and whisker plot, On average, visitors in January were 10 years older than visitors in July.
How to Interpret Box and Whisker Plot?A box and whisker plot is a graph plot that indicates whether a distribution is skewed and whether there are potential unusual observations (outliers) in the data set.
Now, the way to interpret it is as follows;
The left side of the box is the lower quartile. The right side of the box is the upper quartile. The box covers the interquartile interval, where 50% of the data is found.The vertical line that split the box in two is referred to as the median. The whiskers are the two lines outside the box, that go from the minimum to the lower quartile and then from the upper quartile to the maximum.Now, looking at the box and whisker plot for January and July, we can say that those in January are approximately 10 years older than those in July.
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pls help me with this ill give brainlist
HELPP Natasha is eating her backyard. The backyard is square in shape and has an area of 4,096 feet. What is a length of one side of Natasha's backyard?
We will determine how to evaluate the side length of a square given its area.
A square is a four sided 2D planar figure with all its sides at right angles and equal in magnitude as follows:
The side a square are all equal and will be denoted by a variable as follows:
[tex]\text{Side of a square = x}[/tex]We will now express the Area of the square in terms of its side length using the basic definition as follows:
[tex]\text{Area of square = Length}^2[/tex]We will now express the above in terms of the side length variable ( x ) as follows:
[tex]\text{Area of square = x}^2[/tex]We are given that Natasha's garden has the following area:
[tex]\text{Area of square = 4096 ft}^2[/tex]Now we will equate the result of area of a square with the side length ( x ) terms as follows:
[tex]4096=x^2[/tex]Evaluate(solve) the above the equation for the variable ( x ) by taking a square root on both sides of the equation as follows:
[tex]\begin{gathered} \sqrt{x^2}\text{ = }\sqrt{4096} \\ \textcolor{#FF7968}{x}\text{\textcolor{#FF7968}{ }}\textcolor{#FF7968}{=}\text{\textcolor{#FF7968}{ }}\textcolor{#FF7968}{\pm}\text{\textcolor{#FF7968}{ 64}} \end{gathered}[/tex]For practical sense, the variable ( x ) denotes the magnitude of the side length of the square which can not be negative. Hence, we have only solution for the side length ( x ) as follows:
[tex]\textcolor{#FF7968}{x}\text{\textcolor{#FF7968}{ = 64 feet}}[/tex]
Factor Sums and Differences of cubes 27x^3 - 64y^3
SOLUTION
The given question is
[tex]27x^3-64y^3[/tex]Simplify the expression
[tex]3^3x^3-4^3y^3=(3x)^3-(4y)^3[/tex]The difference of two cubes is given as
[tex]x^3-y^3=\mleft(x-y\mright)\mleft(x^2^{}+xy+y^2\mright)[/tex]Hence the given expression becomes
[tex](3x)^3-(4y)^3=(3x-4y)((3x)^2+3x(4y)+(4y)^2)[/tex]This gives
[tex](3x-4y)(9x^2+12xy+16y)[/tex]Para medir temperaturas podemos utilizar distintas escalas, las más utilizadas son las de grados centígrados y las de grados Fahrenheit, sabemos que 0 C es equivalente a 32F y 20C es equivalente a 68F, si conocemos que la relación entre ambas variables responde una función lineal
A) Encontrar la expresión de la función que permita transformar grados Fahrenheit a Centigrados
B) Encontrar la expresión inversa a la anterior
AYUDA PORFAVOR DOY LO QUE SEA POR ESTO
Using linear functions, it is found that:
a) The expression to convert from Fahrenheit to Celsius is: y = 5x/9 - 160/9.
b) The inverse expression is: y = 9x/5 + 32.
What is a linear function?The slope-intercept representation of a linear function is given as follows:
y = mx + b
The coefficients of the function are described as follows:
m is the slope of the function, representing the rate of change of the output y in relation of the input x of the function.b is the y-intercept of the function, representing the numeric value of the function when the input x is of 0.For the conversion of Fahrenheit to Celsius, we have two points, as follows:
(32,0), (68, 20).
When the input increases by 36, the output increases by 20, hence the slope is calculated as follows:
m = 20/36 = 5/9
Hence:
y = 5/9x + b.
When x = 32, y = 0, hence the intercept b is calculated as follows:
0 = 5/9(32) + b
b = -5 x 32/9
b = -160/9
Hence the equation is:
y = 5/9x - 160/9.
To find the inverse expression, we exchange x and y and then isolate y, as follows:
x = 5/9y - 160/9.
5/9y = x + 160/9
5y = 9x + 160
y = 9x/5 + 32.
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2. Which pair of numbers has the least common multiple with the greatest value?
4 and 8
4 and 9
5 and 7
6 and 8
Answer:
4 and 9
Step-by-step explanation:
4 x 8 = 32
4 x 9 = 36
5 x 7 = 35
(6 x 4 = 24 and 8 x 3 = 24)
PLEASE HELP
A bag contains 42 red, 45 green, 20 yellow, and 32 purple candies. You pick one candy at random, find the probability that it is yellow or green.
p(Yellow or not green)= ?
Answer:
I think the answer is 94/139
Step-by-step explanation:
Answer:
65/139
Step-by-step explanation:
Total number of candies - 139
No of yellow and green - 65
Thus probability - 65/139
A circle has area of 361pi cm2 what is the circumference in centimeters of the circle
The area of the circle is given as:
[tex]A=\pi r^2[/tex]plugging the value given we have that:
[tex]\begin{gathered} 361\pi=\pi r^2 \\ r^2=361 \\ r=\sqrt[]{361} \\ r=19 \end{gathered}[/tex]Now, the circumference is given as:
[tex]C=\pi d[/tex]where d is the diameter of the circle. The diameter is twice the raidues, hence the diameter is 38, therefore the circumference is:
[tex]C=38\pi[/tex]Therefore the circumference is 38pi
Reflect (1, -3) over the y-axis.
Then translate the result down 1 unit.
What are the coordinates of the final point?
Answer:
(-1 , -4)
Step-by-step explanation:
Hello!
Refer to the graph for the reflection and translation.
The coordinates of the final point would be (-1,-4), given the x and y-values of the point.
Sammy and Teemu were trying to describe parts of the expression 1/2bh + 4.
• Teemu said," is a coefficient."
Sammy said, "The entire expression is the sum of 4 terms."
Who is correct?
Choose 1 answer:
B
Only Teemu
Only Sammy
Neither student is correct.
Both students are correct.
option (c) is correct.
What is the expression?An expression is a set of numbers or variables combined using the operations + , – , × or ÷ . Arithmetic expression that contains only numbers and mathematical operators and algebraic expression that contains variables, numbers and mathematical operators.
Given that,
An expression
1/2bh + 4
There are two terms in the first term b and h are variables and its coefficient is [tex]\frac{1}{2}[/tex] .
In the second term only 4 is a constant term.
It means this expression has two.
(a) Teemu said, "[tex]\frac{-1}{2}[/tex] is a coefficient"
In the first term [tex]\frac{1}{2}[/tex] is a coefficient of b and h.
(b) Sammy said, "The entire expression is the sum of 4 terms."
No this expression has only two terms.
Hence, Neither student is correct.
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Answer: Only teemu
Step-by-step explanation: Because 1/2 is the numerical factor in a product involving variables and although sammy said it is the sum of 4 terms, there is 2 in the expression.