No matter how far it is moved away, the midline of a function stays the same. because a sinusoidal function is involved.
What is amplitude ?A function's amplitude is the distance that the graph of the function moves above and below its midline. The value of the amplitude when graphing a sine function is comparable to the value of the sine coefficient. the greatest displacement or distance that a point on a wave or vibrating body can travel in relation to its equilibrium position A wave or vibration's amplitude or peak amplitude is a gauge of how far from the central value it deviates. All amplitudes are positive numbers.
given
( A)if pendulum were pulled away from its resting position, then Amplitude is the distance from its resting position to the end where it was released.
Amplitude is the same distance it was pulled away if more distance was pulled away then Amplitude is more.
(B). The midline of function s will not change, it will same irrespective of the distance pulled away. Because it's a sinusoidal function.
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by means of the definition, find the derivative of the function 'F' f(x)=6
We know that the derivative means the rate of change of the function. Graphically, this means that the derivative is the slope of the graph of that function.
How do you find the derivatives by using the Definition?The derivative of a function is the slope of the curve for the specified function. Physically speaking, the derivative of a function is the instantaneous rate of change of a function with respect to the variable at a location.
A securities with a price that is based on or derived from one or more underlying assets is referred to as a derivative. A contract between two or more parties based on the asset or assets constitutes the derivative itself. Changes in the underlying asset's value affect its value.
The instantaneous pace at which a function changes with regard to one of its variables is known as the derivative. Finding the slope of the tangent line to the function at a certain location is equal to doing this.
lim/h→0f(x+h)−f(x)h=f'(x).
lim/h→06−6/h=0.
f'(x)=limΔx→0
f'(x)=limΔx→0
f(x+Δx)−f(x)Δx=
f'(x)=limΔx→06−6Δx=0
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How do you find the length of the third leg of a triangle?
The third side of the triangle can be found out by using the Pythagoras theorem or the Heron's formula.
When there is a right angle triangle (A triangle whose on angle is of 90 degrees) then we use the Pythagoras theorem to find the third side.
The relation says that the sum of the square of the base and perpendicular is equal to the square of the hypotenuse.
In case of the scalene triangle the heron's formula is used to find out the value of the third side of the triangle.
There are several methods also present to find the value of the third side of the triangle.
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Enrique earns 101010 points for each question that he answers correctly on a geography test. Write an equation for the number of points, yyy, Enrique scores on the test when he answers xxx questions correctly.
On his first geography test, Enrique answered 333 questions correctly. On his second test, Enrique answered 777 questions correctly.
Place points on the graph to show Enrique's first and second geography test.
An equation for the number of points y, and the correct answers x is y = 10x.
Define the term equation?One mathematical expression makes up a term. It could be a single variable (a letter), a single number (negatively or positively), or a number of variables multiplied but just never added as well as subtracted.
For the stated question-
Since Enrique receives 10 points for every question on the a geography test that is answered properly,Again for number of points, "y," Enrique receives on the test if he successfully answers "x" questions, we must formulate an equation.Consequently, the total points earned equal the total points earned for each question. number of questions with accurate responses.
Consequently, points earned = 10x
y = 10x.
First geography test: x = 3
y = 10*3 = 30
Second geography test: x = 7
y = 10*7 = 70
Thus, the graph for the enrique's first and second geography test is plotted.
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The correct question is-
Enrique earns 10 points for each question that he answers correctly on a geography test. Write an equation for the number of points, y Enrique scores on the test when he answers x questions correctly.
On his first geography test, Enrique answered 3 questions correctly. On his second test, Enrique answered 7 questions correctly.
Place points on the graph to show Enrique's first and second geography test.
What is a polynomial of degree 4 called?
A polynomial of degree 4 is called bi-quadratic polynomial.
Bi-quadratic polynomial
A biquadratic equation is a polynomial equation with degree 4, and it strictly does not consist of any term with degrees 3 and 1.
Polynomial
A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division
Degree of polynomial
The degree of a polynomial is defined as the highest exponent of a monomial within a polynomial. Thus, a polynomial equation having one variable which has the largest exponent is called a degree of the polynomial.
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Draw a quadrilateral aBCD whose vertices are A (0,0) B(5,0), C(3,2) and D (0,2)
A graph of quadrilateral ABCD whose vertices are A (0, 0) B(5, 0), C(3, 2) and D (0, 2) is shown in the image attached below.
What are the types of quadrilateral?In Geometry, there are different types of quadrilateral and these include the following:
ParallelogramSquaresRectangleRhombusTrapeziumNext, we would use an online graphing calculator to construct (plot) quadrilateral ABCD on a cartesian coordinate based on the given vertices. Also, you should enter the value for each vertices of quadrilateral ABCD on the x-coordinate and y-coordinate respectively as shown in the table.
By critically observing the graph of quadrilateral ABCD, we can reasonably infer and logically deduce that it represents a trapezium.
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Latifa writes down a number
She says
If i find the cube root of that number and then quadruple the answer,I get 16
What number did Latifa write down?
Answer:
64?
Step-by-step explanation:
Basically the idea is we suppose the number she thinks of is "x"
She says that if she cube roots the number and then quadruples it (means multiply by 4 I think) she gets 16. We set this up as equation below:
[tex]4\sqrt[3]{x} = 16\\\sqrt[3]{x} = 4\\x = 4^{3}\\ x= 64[/tex]
This is my best guess, not totally sure sorry
What is the coefficient of 5x² in 5x² 5x?
The coefficient of expression 5x^2 in 5x^2 5x is 5.
The coefficient of 5x^2 in 5x^2 5x is the number that is multiplied with 5x^2. In this expression, the number multiplied with 5x^2 is 5, so the coefficient of 5x^2 is 5.
The expanded expression is 5x^2 5x = 5x^3 + 5x^2. The coefficient of 5x^2 in this expression is still 5.
The coefficient of 5x^2 in 5x^2 5x is the number that is multiplied with 5x^2. When we expand the expression 5x^2 5x, it becomes 5x^3 + 5x^2. The number that is multiplied with 5x^2 in this expression is still 5, so the coefficient of 5x^2 is 5.
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A small radio transmitter broadcasts in a 31 mile radius. If you drive along a straight line from a city 41 miles north of the transmitter to a second city 42 miles east of the transmitter, during how much of the drive will you pick up a signal from the transmitter
On solving the provided question, we can say that the slope's the intersection points are: (20.698, 42.197) and (43.998,16.527), the transmitter is within range between those to points along the line.
what is slope?A line's slope determines how steep it is. A mathematical equation for the gradient is called "gradient overflow" (the change in y divided by the change in x). The slope is the ratio of the vertical change (rise) between two points to the horizontal change (run) between those same two spots. When a straight line's equation is written as y = mx + b, the slope-intercept form of an equation is employed to express it. The y-intercept is located at a location where the line's slope is m, b is b, and (0, b). For instance, the slope of the equation y = 3x - 7 and the y-intercept (0, 7).The line's slope is m. b is b at the point where the y-intercept is, and (0, b). As an illustration, the equation y = 3x - 7 has a slope of 3, and its y-intercept is (0, 7).
city - north at (0,65)
city-east at (59,0)
Slope is m=(-65/59)
[tex]B= y - mx = 65 - (-65/59)(0) = 65[/tex]
The equation of the line between the cities is y = (-65/59)x + 65
[tex]x^2 + ( (-65/50)x + 65) )^2 = 47^2[/tex]
the intersection points are:
(20.698, 42.197) and (43.998,16.527)
The transmitter is within range between those to points along the line.
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Which graph represents the equation y equals one half times x minus 1?
graph of a line passing through the points negative 2 comma negative 2 and 0 comma negative 1
graph of a line passing through the points negative 2 comma 0 and 0 comma 1
graph of a line passing through the points negative 2 comma negative 3 and 0 comma negative 2
graph of a line passing through the points negative 4 comma 0 and 0 comma 2
The correct graph which represents the equation y = 1/2x - 1 is,
⇒ Graph of a line passing through the points negative 2 comma negative 2 and 0 comma negative 1.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The equation is,
⇒ y = 1/2x - 1
Now, After draw the equation we get;
Graph of a line passing through the points (-2, - 2) and (0, - 1).
Thus, The correct statement is,
⇒ Graph of a line passing through the points negative 2 comma negative 2 and 0 comma negative 1.
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Lesson 1. 12
At an ocean depth of 10 meters, a buoy bobs up and then down 6 meters from the ocean's depth.
Ten seconds pass from the time the buoy is at its highest point to when it is at its lowest point.
Assume at x= O the buoy is at normal ocean depth.
Find the following:
Period =
Equation of the mideline:
Amplitude =
Maximum =
Minimum =
For the described situation, y = 6sin ( (π / 10) x ) - 10 is the sine function.
What is the sine function?The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths.
They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.
Asin(Bx)+C is the usual sine function formula.
A buoy bobs 6 meters up and down.
That is, the amplitude of the buoy shifts by 6 meters both vertically and horizontally.
A=6 Amplitude
The x-axis distance that constitutes one complete oscillation is known as the period.
We are aware that it takes a buoy 10 seconds to go from its greatest position to its lowest point (half oscillation).
20 seconds make up the complete oscillation period.
⇒ 20 (B) = 2π
B=2π /20
= π/ 10
Given that the buoy is 10 meters under the ocean's surface, C equals –10.
Using the formula's whole range of values:
⇒y = 6sin ( (π/ 10) x ) - 10
The midline is the initial point.
x=0 is the first point.
⇒y=6sin(0)-10
y= -10
The line is drawn from the origin at y = -10.
Either the highest or smallest value is at the second point.
Therefore, (5,-4) and (15, -16.)
Therefore, for the described situation, y = 6sin ( (π / 10) x ) - 10 is the sine function.
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Complete question:
At an ocean depth of 10 meters, a buoy bobs up and then down 6 meters from the ocean's depth. Ten seconds pass from the time the buoy is at its highest point to when it is at its lowest point. Assume at x = 0 the buoy is at normal ocean depth. Use the sine tool to graph the function. The first point must be on the midline and the second point must be a maximum or minimum value on the graph closest to the first point.
Linear equation and linear system
Answer:
Step-by-step explanation:
you have studied this in grade 8 grade 9 and grade 10 if you are studying under CBSE, so, better call textbook
Suppose that X ∼ Geom(p) and Y ∼ Geom(r) are independent. Find the probability P (X < Y )
The value of P(X<Y) could be p(1−q) / p+q−pq if X ∼ Geom(p) and Y ∼ Geom(r) are independent
What is probability ?
Probability could be defined as the ratio of number of favourable outcomes and total number of outcomes.
Given ,
X ∼ Geom(p) and Y ∼ Geom(r) are independent.
P(X<Y)=P(⋃1≤k<n,n∈N{X=k,Y=n})
=∑1≤k<n,n∈NP(X=k,Y=n)
=∑n=1∞∑k=1n−1P(X=k)P(Y=n)
=∑n=1∞∑k=1n−1p(1−p)k−1q(1−q)n−1
=pq∑n=1∞(1−q)n−11−(1−p)n−1p
=q∑n=1∞(1−q)n−1(1−(1−p)n−1)
=1−q / ∑n=1∞[(1−q)(1−p)]n−1
=1−q / 1−(1−p)(1−q)
=1−(1−p)(1−q)−q / 1−(1−p)(1−q)
=p(1−q) / p+q−pq.
Hence, The value of P(X<Y) could be p(1−q) / p+q−pq if X ∼ Geom(p) and Y ∼ Geom(r) are independent.
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The question is in the picture I would appreciate if you could explain how to get the answer thank you.
The equation that is modeled to the situation is x - 2y + 2 = 0 and the slope of the line is 1/2.
The slope of an equation:
A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in determining if the lines are parallel, perpendicular, or none at all.
The slope intercept form of a line is y = mx + c
Where, c - y-intercept and m - the slope of the line
Given that
The cost of using the internet at an internet cafe is equal to a fee plus a certain rate per minute.
4 minutes of internet costs $ 3
8 minutes of internet costs $ 4
[ We can represent the given situation as given below ]
And the coordinates formed are (4, 3) and (8, 4)
The slope of the line formed = (4 - 3)/(8 - 4) = 1/4
Let y = mx + c be the equation to the model situation
=> y = (1/2)x + c
=> 2y = x + c ---- (1)
As we know (1) will pass through (4, 3)
=> 2(3) = 4 + c
=> 6 = 4 + c
=> c = 6 - 4
=> c = 2
=> 2y = x + 2
=> x - 2y + 2 = 0
Therefore,
The equation that is modeled to the situation is x - 2y + 2 = 0 and the slope of the line is 1/2.
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If a piece of luggage has a height of 20.5 inches and a length of 14.75 inches, what is the maximum width
allowed for that piece of luggage?
A)9.75in
B)10.2in
C)10.25in
D)11.8in
The maximum possible width of the box will be equivalent to
w = (V/302.4).
What is the volume of the cuboid?The volume of cuboid is given by -
V{C} = Length x Breadth x Height
Given is a piece of luggage has a height of 20.5 inches and a length of 14.75 inches.
We can write the volume of the box as -
V{b} = L x B x H
Assume the volume of the box is {V} cubic inches and its width be {w} inches. So, we can write the inequality as -
(20.5 x 14.75 x w) = V
w = (V/302.4)
Therefore, the maximum possible width of the box will be equivalent to
w = (V/302.4).
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Write a polynomial function in standard form
-6,0,0,2
what is the legend of variables of combined gas law
The combined gas law for a gas is discussed below.
What is a gas?Gas is one of the four fundamental states of matter – the others being solid, liquid, and plasma. A pure gas may be made up of individual atoms, elemental molecules made from one type of atom, or compound molecules made from a variety of atoms.Given is the combined gas law.
The ideal combined gas law is given by →
PV = nRT
Where -
{P} = pressure {T} = temperature {V} = volume
{n} = number of moles {R} = gas constant
Non ideal gases are often modelled by the Van der Waals equation as →
(p + n²a/V²)(V - nb) = nRT
Where -
{a} and {b} = constants for a particular gas
{p} = pressure {v} = volume
{n} = number of moles {t} = temperature
{R} = gas constant
Therefore, the combined gas law for a gas is discussed above.
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Sandra has taken 3 Test this Quarter. She has scored an 78%, 76%, and a 93%. Sandra wants
to earn at least and 85% for the Quarter. What score will she need to earn on her Final Test in
order for her to Average at least an 85% for the Quarter? Then Explain what your answer
means.
*****This Question is similar to Question #8 in Thursdays Homework Quiz.
1. Write an Equation or Inequality you use to help you solve this Question. 5 pts.
2. Solve the Equation or inequality. 5 pts.
3. Explain what your answer means based on your solution you get. 10 pts.
Sandra needs to score at least 87.67% to get an average score of 85%.
What is average?Let's look at the average formula in more detail in this part and use some examples to illustrate how it may be used. The following is an example of the average formula for a specific set of data or observations: Average = (Sum of Observations) ÷ (Total Numbers of Observations).
Given, Sandra has taken 3 Test this Quarter. She has scored an 78%, 76%, and a 93%.
Now as per the question she needs 85%.
The average of the 1st three tests is 78+76+93/3 = 247/3 = 82.33
Now to get 85%, we have to average out as 82.33+x/2 = 85
x+82.33 = 85*2 = 170
x = 170-82.33 = 87.67
Hence, Sandra needs to score at least 87.67% to get an average score of 85%.
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convert 20% profit into profit amount
Answer: To convert 20% profit into a profit amount, you would multiply 20% by the revenue or cost of the item or service.
Let's say,
You have revenue of $1000
So,
20/100 * 1000 = $200
So the 20% profit on the revenue of $1000 is $200.
It's important to note that profit is the amount of money you make after you subtract your costs from your revenue. It's the amount you have left after all the expenses, taxes and other deductions are made.
Step-by-step explanation:
Mrs. Read can knit one pair of children's mittens with a ball of yarn six inches in diameter. How many pairs of identical mittens can she knit with a ball of yarn twelve inches in diameter
She can knit total 8 pairs of identical mittens with a ball of yarn twelve inches in diameter
In the given question, Mrs. Read can knit one pair of children's mittens with a ball of yarn six inches in diameter.
We have to find how many pairs of identical mittens she can knit with a ball of yarn twelve inches in diameter.
The radius of a ball of yarn six inches in diameter is
r = 6/2 = 3 inches
The radius of a ball of yarn twelve inches in diameter is
r = 12/2 = 6 inches
Now, the volume of the six inches yarn = [tex]\frac{4}{3} \pi r^3[/tex]
The volume of the six inches yarn = [tex]\frac{4}{3} \pi (3)^3[/tex]
The volume of the six inches yarn = 36π
Now, the volume of the twelve inches yarn = [tex]\frac{4}{3} \pi r^3[/tex]
The volume of the twelve inches yarn = [tex]\frac{4}{3} \pi (6)^3[/tex]
The volume of the twelve inches yarn = 288π
Now we finding the numbers of pairs of identical mittens she can knit with a ball of yarn twelve inches in diameter
= 288π/36π
= 8
Hence, she can knit total 8 pairs of identical mittens with a ball of yarn twelve inches in diameter.
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On a negatively skewed curve, which is true?
The statistical model is not good, and this is true for a negatively skewed curve.
What means negatively skewed curve?It is a statistical term implies that a curve is skewed at the left side.
In a statistical data for a certain distribution, we can get a negatively skewed curve when most of the data values are located on the right side of the distribution graph. The high concentration of values on the right side of distribution curve forms a long tail in the negative direction.
Which is true for negatively skewed curve?In general, negatively skewed curve is not good because it expresses the tendency of left tail events. Negatively skewed curves indicate a poor return from an investment. That means a person might be earn lower or no profit from his business. In case of an exam scores, negative skewed data value implies the question was too easy to perform better than usual.
In a word, left skewed or negatively skewed curve or data values inform us to be aware about the current statistical model and inspire us to take proper steps for wellbeing.
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3.5 x 4 + 11 x 2.2 = 38.2 i used a calculator already but i need to show i how got the answer i dont know if i can give the brain thing
Step-by-step explanation: To solve this equation, you'll need to use the order of operations to determine the correct sequence of steps to follow. The order of operations is a set of rules that specifies the order in which calculations should be performed in a math problem. It helps to prevent ambiguity and ensures that all calculations are performed consistently.Here is the order of operations:Perform any calculations inside parentheses or brackets first.Perform all multiplications and divisions, working from left to right.Perform all additions and subtractions, working from left to right.Using this order, we can solve the equation as follows:3.5 x 4 + 11 x 2.2 = 14 + 11 x 2.2
3.5 x 4 + 11 x 2.2 = 14 + 24.2
3.5 x 4 + 11 x 2.2 = 38.2Therefore, the solution to the equation is 38.2.
Using BODMAS,
B-Bracket
O-Of
D-Division
M-Multiplication
A-Addition
S-Subtraction
Multiplication comes first before addition, so
3.5×4=17
+
11×2.2=24.2
17+24.2=41.2
The average price for houses in the area is $280,000, and the standard deviation is $12,000. What is
the price of a house whose z score is 2.5?
When working with a normal distribution, you can use the z-score to determine how many standard deviations away from the mean a certain data point is.
Given that the average price for houses in the area is $280,000 and the standard deviation is $12,000, we can use the z-score formula to find the price of a house whose z-score is 2.5:
z = (x - mu) / sigma
where x is the price of the house, mu is the mean price of houses in the area, and sigma is the standard deviation of the price of houses in the area.
In this case, we are looking for the value of x, which is the price of a house whose z-score is 2.5, so we can rearrange the formula to solve for x:
x = (z * sigma) + mu
x = (2.5 * $12,000) + $280,000
x = $350,000
So the price of a house whose z-score is 2.5 is $350,000
It's worth noting that the value of Z-Score 2.5 is considered an outlier, it is usually very rare to find houses that far from the average and standard deviation.
what is x if 2/9+x=11/18?
Answer:
x = 7/18
Step-by-step explanation:
what is x if 2/9+x=11/18?
2/9 + x = 11/18
x = 11/18 - 2/9
x = 63/162
x = 7/18
check
2/9 + 7/18 = 11/18
11/18 = 11/18
the answer is goodAngle AOB is a central angle with a measure of 110 degrees.
What is the measure of its arc AB?
The most accurate value for AB is 37.699111843077516 (approximately)
How to measure arc?The measure of an arc is directly related to the measure of the central angle that intercepts it. The measure of an arc is equal to the measure of its central angle, multiplied by the radius and divided by the degree of the circle.
Since, radius is not given let's assume it 20.
In this case, the central angle AOB has a measure of 110 degrees, and the radius of the circle is 20. Therefore, the measure of the arc AB is:
AB = (110/360) * 20 * 2 * π
or
AB = (110/360) * 20 * π
where π is the mathematical constant (approximately equal to 3.14).
So, the measure of the arc AB is (110/360) times the circumference of the circle, or (110/360) of the total length of the circumference.
The most accurate value for AB is 37.699111843077516 (approximately)
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A train moving at a constant speed travels 325 mi in 8 hr. At this rate, how many miles does the train travel in 12 hr?
ANSWER ASAP!!!
Answer:
Step-by-step explanation:
In 12 hours, the train will travel 487.5 miles
8/325=40.625
40.625 x 12 = 487.5
Radicals please help
On solving the provided question, we can say that - the radicals are as follows be = 3x^2|y| sqrt(7x)
what are radicals?The square root or nth root symbol is called a radical. Expressions with square roots are referred to as root expressions. A radical's radicand is a number or phrase that appears there. The radicals 7, 2y+1, and so on are examples. The following phrases can also be used to describe radicals: Radical equations are equations contained within of radicals. The term "root expression" refers to the expression found inside the square root. Examples of radical representations are the numbers 2, 372, 2x+7, and 41p.
here,
the radicals will be - 7xy ∛(xy^2)
and 3x^2|y| sqrt(7x)
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How do you prove a number is irrational?
To prove a number is irrational we divide the integer by another integer is the decimal is non terminating and non repeating then it will be a irrational number .
What are Irrational Numbers ?
The Irrational numbers can be defined a number that cannot be expressed as a fraction [tex]\frac{p}{q}[/tex] for any integers p and q.
The Irrational numbers have decimal expansions that do not terminate nor repeat (periodic) . Every transcendental number is an irrational number .
(i) To prove a number irrational when we divide an integer by another integer, and if decimal expansion does not terminate and do not repeat then it is an irrational .
(ii) if the number cannot be expressed in the form of [tex]\frac{p}{q}[/tex] , then also the number will be called as irrational numbers .
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Directions: The Johnson family is redesigning their backyard this spring. They want to include a sandbox area,
a swing set area, a patio area, a pool area and a grill area. Their plans for the yard layout in feet is shown in the
figure below. Use the figure and your knowledge of polynomials, perimeter, and area to solve the following:
1) The formula for area is,
⇒ Area of rectangle = Length × Width
And, The formula for perimeter is,
⇒ Perimeter = 2 (Length + width)
2) An expression for the length of the south side of the yard is,
⇒ Length = (5x + 2) + (x² - 9) + (x² - 7x + 12)
3) The simply expression for the length of the south side of the yard is,
⇒ Length = 2x² - 2x + 5
4) An expression for the perimeter of the pool area is,
⇒ Perimeter = 2 ( (x² + 10) + (8x + 8) )
5) 5) The simply expression for the perimeter of the pool area is,
⇒ Perimeter = 2x² + 16x + 36
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
The Johnson family is redesigning their backyard this spring. They want to include a sandbox area, a swing set area, a patio area, a pool area and a grill area.
Now,
1) The formula for area is,
⇒ Area of rectangle = Length × Width
And, The formula for perimeter is,
⇒ Perimeter = 2 (Length + width)
2) An expression for the length of the south side of the yard is,
⇒ Length = (5x + 2) + (x² - 9) + (x² - 7x + 12)
3) The simply expression for the length of the south side of the yard is,
⇒ Length = (5x + 2) + (x² - 9) + (x² - 7x + 12)
= 5x + 2 + x² - 9 + x² - 7x + 12
= 2x² - 2x + 5
4) An expression for the perimeter of the pool area is,
⇒ Perimeter = 2 ( (x² + 10) + (8x + 8) )
5) The simply expression for the perimeter of the pool area is,
⇒ Perimeter = 2 ( (x² + 10) + (8x + 8) )
= 2 (x² + 10 + 8x + 8)
= 2 (x² + 8x + 18)
= 2x² + 16x + 36
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Raul works at a movie theatre. The function f(x) represents the amount of money Raul earns per ticket, where x is the number of tickets he sells. The function g(x) represents the number of tickets Raul sells per hour, where x is the number of hours he works. Show all work to find f(g(x)), and explain what f(g(x)) represents.
f(x) = 2x2 + 16
g(x) = √5x^3
The required function that gives [tex]f(g(x))[/tex] that represents the total amount of money Raul earned is
[tex]f(g(x)) = 10x^{3}+16[/tex]
What is a function?
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.
Mostly functions are written as f(x) where x is the input of the function.
Given,
[tex]f(x) = 2x^{2}+16[/tex]
[tex]g(x)[/tex] = [tex]\sqrt{5x^{3} }[/tex]
If [tex]f(x)[/tex] represents amount of money Raul earns per ticket and [tex]g(x)[/tex] represents number of tickets Raul sells per hour, where x is the number of hours he works, then,
[tex]f(g(x))[/tex] represents the total amount of money Raul earned in a day.
To find [tex]f(g(x))[/tex], substitute value of [tex]g(x)[/tex] in the place of x in function [tex]f(x)[/tex] .
[tex]f(g(x))[/tex] = [tex]f[/tex]([tex]\sqrt{5x^{3} }[/tex])
= 2( [tex]\sqrt{5x^{3} }[/tex])² +16
= 10x³ + 16
Therefore the required function is [tex]f(g(x)) = 10x^{3}+16[/tex].
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