Graph with their Turning Point is shown with different degree of different degree Equation
What is Turning Point?Where a graph changes, either from increasing to decreasing, or from decreasing to increasing, is called a turning point.
How to find Turning Point?Factorization Technique
The turning point of the parabola lies exactly at the midway between the (two) x-intercepts of a quadratic function, as shown by the fact that a vertical line of symmetry divides the parabola into two equal half and crosses it. In light of this, we can use a factorisation-based method to locate the solution of a quadratic equation. The process involves five steps.
Step 1: By looking at the coefficient of x2, determine if the graph is a minimum or maximum;
Factorize the supplied quadratic function in Step 2 and set it to Zero;
Step 3: Define the function's antecedents;
Take the midpoint of the pair of roots to find the x-coordinate of the turning point in step 4;
2 turning points
Let f(x)=x³+ax²+bx+c, where the coefficients a, b and c are real numbers. The figure below shows a section of the graph of y=f(x). The curve has two distinct turning points; these are located at A and B, as shown.
But there is come limitations in this case too, a function has to follow certain conditions to have two turning points.
3 turning points
If we get 4 roots of any equation it may be containing 3 turning Points.
With some limitations in this as well.
4 turning points
If we get 5 roots of any quadratic equation it may be containing 4 turning points with some limitations in this as well.
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what is the solution to 2x^2+x+3=0
The solutions of the quadratic equation are:
x = (-1 + i√23)/4
x = (-1 - i√23)/4
How to solve the quadratic function?For a general quadratic:
a*x^2 + b*x + c = 0
The solutions are given by the quadratic formula
[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]
Here we have the quadratic equation:
2x^2 + x + 3 = 0
[tex]x = \frac{-1 \pm \sqrt{1^2 - 4*2*3} }{2*2} \\\\x = \frac{-1 \pm \sqrt{-23} }{4}[/tex]
So we will have two complex solutions, these are:
x = (-1 + i√23)/4
x = (-1 - i√23)/4
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(3+2)to the power of 2 + 4x8*
Pls help asap
Does anyone know the answer?
Answer:
d = 5m
Step-by-step explanation:
Look at point (1, 5).
When the number of months is 1, the amount in dollars is 5.
The amount in dollars is always 5 times the number of months.
d = 5m
........ i need help past due
Part a: y = -6x + 5 is : Not proportional.
Part b: y = 7/8x proportional: proportionality constant = 7/8.
Explain the term proportional relation?Relationships among two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportionate relationship, each variable is consistently equal to the other's constant value. The "constant of proportionality" is the name of this constant.For the stated question;
Part a: y = -6x + 5
To check the proportional relation, put value of 'x' and find the corresponding value of 'y'.
The ratio = y/x must be same.
For x = 1, y = -1
y/x = -1
And, for x = 2, y = 7
y/x = 7/2
Thus, ratio is not equal, Not proportional.
Part b: y = 7/8x
For x = 1, y = 7/8
y/x = 7/8
Now, For x = 2, y = 14/8
y/x = 7/8, both ratios are equal.
Thus, y = 7/8x proportional: proportionality constant = 7/8.
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Please answer with the equation
The perimeter of a rectangle is 80 inches. The width of the rectangle is 5 less than triple the width?
The length is 28.75 inch and width is 11.25 inch.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
Perimeter= 80 inches
let the width be x.
length= 3x- 5
Now, perimeter of a rectangle = 2( l+ w)
80= 2( x+ 3x- 5)
40 = 4x -5
45 = 4x
x= 11.25
and, length = 3(11.25)- 5 = 28.75
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Graph y=1/2x=+1
Use the table or identify m and b if it helps you graph.
Answer: 1/3
Step-by-step explanation:
Consider Y= F(x) =2- 3x. using the space determine the equation that represents the inverse of f(x) 
Answer: [tex]f^{-1}(\text{x}) = \frac{2-\text{x}}{3}\\\\[/tex]
===============================================
Work Shown:
[tex]f(\text{x}) = 2-3\text{x}\\\\\text{y} = 2 - 3\text{x}\\\\\text{x} = 2 - 3\text{y}\\\\\text{x} + 3\text{y} = 2\\\\3\text{y} = 2-\text{x}\\\\\text{y} = \frac{2-\text{x}}{3}\\\\f^{-1}(\text{x}) = \frac{2-\text{x}}{3}\\\\[/tex]
-----------------
Explanation:
The process to find the inverse involves this outline.
Replace f(x) with y.Swap x and y.Solve for y.This process is followed in the "work shown" portion above.
To confirm the answer, let g(x) be the inverse of f(x).
If they were inverses of each other, then these two properties would hold true:
f( g(x) ) = xg( f(x) ) = xHere's the verification for the first part.
[tex]f(\text{x}) = 2-3\text{x}\\\\f(g(\text{x})) = 2-3*g(\text{x})\\\\f(g(\text{x})) = 2-3*\frac{2-\text{x}}{3}\\\\f(g(\text{x})) = 2-(2-\text{x})\\\\f(g(\text{x})) = 2-2+\text{x}\\\\f(g(\text{x})) = \text{x}\\\\[/tex]
I'll let you do the other confirmation.
In Japan, the ratio of vending machines to people is 1 to 24. In the city of Osaka there are about 2,400,000 people. How many banding machines are there in Osaka?
From the given ratio, there is a total of 100,000 vending machines in Osaka.
What is the ratio?
By comparing two amounts of the same units, the ratio can be used to calculate how much of one item is included in the other. There are two different categories for ratios. The first is a part-to-part ratio, whereas the second is a part-to-whole ratio.
Given, the ratio of vending machines to people is 1 to 24
That means, for every vending machine, there are 24 people.
In the city of Osaka, there are about 2,400,000 people.
So, the number of vending machines = 2400000/24 = 100000
Hence, there is a total of 100,000 vending machines in Osaka.
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If co(x)= 2/3 and x i in quadrant I, then find exact value for (without olving for x) in(2x)
If cos x= 2/3 and x is in quadrant I, then the exact value of sin(2x) is (4/3)sin x.
What is trigonometry?A branch of mathematics called trigonometry examines the connections between triangles' angles and sides. It is predicated on the idea of right triangles, where one angle is 90 degrees and two sides are perpendicular to one another. The six fundamental functions of trigonometry—sine, cosine, tangent, cotangent, secant, cosecant. These values of functions can be used to address real-world angle and length issues, such as determining the height of a structure or the distance between two locations. Calculus, geometry, and other areas of mathematics are all strongly connected to trigonometry.Modeling actual phenomena like item motion, wave behaviour, and light dispersion is possible with these functions. Physics, engineering, and astronomy are just a few of the disciplines that use trigonometry extensively.
How to solve?
In quadrant I, cos x = 2/3 and sin x > 0.
sin(2x) = 2sin x cos x
sin(2x) = 2 * 2/3 * (sin x)
sin(2x) = (4/3)sin x
If sin x > 0, then sin(2x) = (4/3)sin x > 0.
The exact value of sin(2x) is (4/3)sin x
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Use the reciprocal property to solve for a 36/15 8/a
Applying reciprocal property the equation 36 / 5 = 8 / a is solved to find the value of a as 10/9
What is reciprocal property?The definition of reciprocal in mathematics is the inverse of a value or a number.
If n is a real number, then 1/n will be n's reciprocal.
Therefore, we must change the number to its upside-down form. For instance, 1 divided by 9 is the reciprocal of 9, or 1/9.
The result of multiplying a number by its reciprocal now equals one. multiplicative Inverse is another name for it.
Similarly, 36 / 5 = 8 / a
the reciprocal is 5 / 36 = a / 8
cross multiplying
5 * 8 = 36 * a
36a = 40
a = 40 / 36
a = 10/9
The value of a is 10/9
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on average a customer waits 10 minutes in a queue and customers arrive at the rate of two per minute. how many customers are waiting in the queue on average
The average number of customers waiting in the queue is 20
In this question, we have been given that the customers arrive at the rate of two per minute.
On average a customer waits 10 minutes in a queue.
We need to find the number of customers waiting in the queue on average.
Assume that the average number of customers waiting in the queue is N.
We have the average Rate of Arrival = 2 customers per minute
So, by the formula for average waiting time under the Single-Server Queue Model,
10 = N/2
N = 10 * 2
N = 20
The average number of customers waiting according to the single-server queue model given the above conditions is 20
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Consider the line -7x-3y = 1.
Find the equation of the line that is perpendicular to this line and passes through the point (-7, 4).
Find the equation of the line that is parallel to this line and passes through the point (-7, 4).
Note that the ALEKS graphing calculator may be helpful in checking your answer.
Equation of perpendicular line:
Equation of parallel line:
0
X
0=0
S
Answer:
Parallel: Y= -7/3x - 37/3
Perpendicular: Y=3/7x + 7
Step-by-step explanation:
Use the formula: Y - Y1 = M(X - X1) Plug in -7 as X1 and 4 as Y1 and your M value is your slope. (-7, 4) where it passes from.
Remember when the slope is parallel it's always the same slope in this case -7/3
When perpendicular flip it and change the sign 3/7
Triangle ABC is translated 4 units to the right and 3 units down.
What are the coordinates of the new triangle?
Responses
(−2,3),(3,1),(−2,1)
( − 2 , 3 ) , ( 3 , 1 ) , ( − 2 , 1 )
(−2,0),(3,−2),(−2,−2)
( − 2 , 0 ) , ( 3 , − 2 ) , ( − 2 , − 2 )
(0,−2),(−2,3),(2,−2)
( 0 , − 2 ) , ( − 2 , 3 ) , ( 2 , − 2 )
(−6,0),(−6,−2),(−1,−2)
Hence, the coordinates of the new triangle are [tex]A(2,0),B(7,-2),C(2,-2)[/tex].
What is the coordinates?
A pair of numbers that describe the position of a point on a coordinate plane by using the horizontal and vertical distances from the two reference axes. Usually represented by [tex](x,y)[/tex] the x-value and y-value.
Here given coordinates are
[tex](-2,3),(3,1),(-2,1)\\\\(-2,0),(3,-2),(-2,-2)\\\\( - 2 , 0 ) , ( 3 , - 2 ) , ( - 2 , -2 )[/tex]
Suppose [tex]a[/tex] units on the horizontal and [tex]b[/tex] units on the vertical. Then, the new coordinate become
[tex]A(x,y)=A(x+a,y+b)[/tex]
As per the question triangle [tex]ABC[/tex] is translated [tex]4[/tex] units to the right and [tex]-3[/tex]units down.
So, [tex]a=4,b=-3[/tex] and the coordinates are
[tex]A(-2,3),B(3,1),C(-2,1)\\\\[/tex]
Then,
[tex]A(-2+a,3+b)=A(-2+4,3-3)=A(2,0)\\\\B(3+a,1+b)=B(3+4,1-3)=B(7,-2)\\\\C(-2+a,1+b)=C(-2+4,1-3)=C(2,-2)[/tex]
Hence, the coordinates of the new triangle are [tex]A(2,0),B(7,-2),C(2,-2)[/tex].
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solve each of these equations.
Answer:
a.) x=6 b.) y=-7 c.) a=0.25
Step-by-step explanation:
a.) 2(3x+2)=2x+28
6x+4=2x+28
subtract 4 on both sides
6x=2x+24
subtract 2x on both sides
4x=24
divide both sides by 4
x=6
b.) 5y+13=-43-3y
add 43 on both sides
5y+56=3y
subtract 5y on both sides
56=-8y
divide both sides by 8
-7=y or y=-7
c.) 4(2a+2)=8(2-3a)
8a+8=16-24a
add 24a on both sides
32a+8=16
subtract 8 on both sides
32a=8
divide both sides by 32
a=0.25
(hope you understood how I solved for each equation..)
Andrei has a glass tank. First, he wants to put in some marbles, each of which has a volume of 0. 40. 040, point, 04 liters. Then, he wants to fill the tank with water until it's completely full. If he uses 505050 marbles, he will have to add 333333 liters of water. What is the volume of the tank?.
The total Volume of tank = 35 liters
What is Volume ?In three dimensions, everything takes up some space. What is being measured here is the area's volume. The volume of an object is the area occupied inside its three-dimensional boundaries. Sometimes it is referred to as the
According to the Given information
Volume of each marble = 0.04 liters
Number of marbles to be put in the water tank = 50 marbles
Volume of 50 marbles = 0.04 × 50 = 2 liters
Volume of water added to the tank = 33 liters
Total Volume of tank = 2 liters + 33 liters
= 35 liters
SO,
The total Volume of tank = 35 liters
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PLS HELP Which function has the same slope as the graph of the function represented by the table.
The slope of the given function is 0.25. The function that has the same slope is y = 0.25x + 5. Option B is the correct option.
What is a function?
A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
Given table is
x 0 1 2 3
y -0.5 -0.25 0 0.25
The slope of a function that passes through the points (x₁, y₁) and (x₂, y₂) is m = (y₂ - y₁)/(x₂ - x₁)
Assume that x₁ = 0, y₁ = -0.5, x₂ = 1, y₂ = -0.25
The slope of the function is [-0.25 - (-0.50)]/(1 - 0) = 0.25
Now compare the equation y = -0.25x - 2 with y = mx + c
m = -0.25
The slope of the function is -0.25.
Now compare the equation y = 0.25x + 5 with y = mx + c
m = 0.25
The slope of the function is 0.25.
Now compare the equation y = 4x - 5 with y = mx + c
m = 4
The slope of the function is 4.
Now compare the equation y = -4x + 34 with y = mx + c
m = -4
The slope of the function is -4.
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50000x6000000000000 what is it?
Answer: 300000000000000000
Step-by-step explanation:
50000x6000000000000 can be written as 3 times 10^17
So the answer is 300000000000000000
Please help!!! And show your work or not I don’t care I need the answers
Answer:
Step-by-step explanation:
1. Lin, Tyler, and Jada's information is missing.
2. 9 1/8 = 73/8
1 2/8 = 10/8
73/8 - 10/8 = 63/8.
His shoe length was 63/8 inches.
50 POINTS IF ANSWERED PLSS!!!!!
Mr. Hansen has three sticks that measure 5 inches, 10 inches, and 17 inches. If he connects the sticks ends, will the three sticks form a triangle?
Answer:
This would not form a triangle
Step-by-step explanation:
due to the triangle inequality theorem, in order to find out if three numbers can form a triangle, you have to have each pair of numbers add up to more than the remaining number. The first combination added is 5+10 which is 15, and that is not greater than 17, so the answer is no, this is not a triangle.
hope this helps! :3
6/22, 3:45 PM
Kris said, "The Rawlings Rockets basketball team does not have any really tall players." These are the players'
heights in inches:
70, 77, 75, 68, 88, 70, and 72.
a. Which number does not seem to fit this set of data? 1
b. Do you agree or disagree with Kris?
2
Answer:
a. 88
b. I disagree with Kris
Step-by-step explanation:
88 is by far the biggest outlier here being 11 numbers away from the second highest being 77. This means there is one kid that is much higher than the rest of the group.
please help it about calculus
The question is based on the calculus and the derivative for given equation [tex]t^{4} - 24t^{2} \\ \\[/tex] is t = 0.
What is calculus?Calculus is a discipline of mathematics that focuses on rates of change, to put it simply. For instance, you could wish to determine how quickly an automobile will slow down when it approaches a stop sign. Calculus can assist you in calculating that change. Calculus introduces movement into math, that's correct!
Calculus is a tool used by engineers to calculate things like rates of change and areas; in fact, calculus is the mathematical "backbone" for dealing with problems where variables change with time or some other reference variable. Calculus is concerned with two basic operations: differentiation and integration.
We are given
x(t) = [tex]t^{4} - 24t^{2} \\ \\[/tex]
we need to find its derivative only then we can comment on its increasing decreasing nature
x'(t) = [tex]4t^3 -48t\\\\[/tex]
we will check where derivative is zero
[tex]4t^3 - 48t = 0\\\\4t^2(t-4) = 0\\\\\\t = 0 \\\\t = 4\\[/tex]
hence increasing for all x E R except interval (0,4)
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what is the least amount of money you can spend if you want to increase the computer performance by 25%, assuming that you can improve one or all the
$150 is the least amount of money you can spend if you want to increase the computer performance by 25%, assuming that you can improve one or all the components in the computer.
What is RAM?RAM is a type of volatile memory, which means that data is only stored there while the chip is powered and is completely erased when the computer is turned off. In gigabytes, RAM memory is measured (GB).
Random access memory is referred to as RAM. Because the data may be swiftly read and updated in any sequence, it is termed random access. Compared to previous storage devices like CD-RWs, which access data in a slower, predetermined order, this is faster.
There are much more methods through which we can improve computer performance but by spending the least amount of money we can do it by upgrading your RAM. We can upgrade the RAM of the system to 8 GB and 16 GB. If we want to upgrade the RAM to 8 GB then it can be done for around $75 and If we want to upgrade the RAM to 16 GB then it can be done for around $150.
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The complete question is as follows:
What is the least amount of money you can spend if you want to increase the computer performance by 25%, assuming that you can improve one or all the components in the computer?
A recently televised broadcast of a popular television show had a 15 share, meaning that among 5000 monitored households with TV sets in use, 15% of them were tuned to the show. A 0.01 significance level is used to test an advertiser’s claim that among the households with TV sets in use, less than 20% were tuned in to the show. Find the P-value.
1.9998
0.9999
0.0001
0.0002
The p-value of the given hypothesis is; 0.9999
How to find the p-value of the statistics?The formula for the z-score of proportions is;
z = (p^ - p)/√(p(1 - p)/n)
where;
p^ is sample proportion
p is population proportion
n is sample size
We are given;
p^ = 15% = 0.15
p = 20% = 0.2
n = 5000
Thus;
z = (0.15 - 0.2)/√(0.2(1 - 0.2)/5000)
z = -8.8388
From p-value from z-score calculator, we have;
P(Z < -8.8388) = 1 - 0.0001 = 0.9999
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Find the slope of the line that passes through (1, 1) and (7, 8).
Answer:
[tex] slope=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} [/tex]
[tex] slope=\frac{8-1}{7-1} [/tex]
[tex] slope=\frac{7}{6} [/tex]
slope = 7/6
help me please, please write what i put on the sides too and what i put in the bottom right please and thank youuuuu
The values obtained after solving the given equation is x = 6 and y = 10.
What is an equation?Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.
This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.
As per the information given in the question,
The given equations are,
-5x + 3y = 0 (i)
7x - 4y = 2 (ii)
Multiply equation (i) by -7 and equation (ii) by 5.
35x - 21y = 0 (iii)
35x - 20y = 10 (iv)
Now, solve the equation for y, because 35x in positive and 35x in negative cancel out each other.
-y = -10
y = 10
Substitute y = 10 in equation (i)
-5x + 3(10) = 0
-5x = -30
x = 30/6
x = 5
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You have two exponential functions. One has the formula h(x) = 3x – 2. The other function, g(x), has the graph shown below.
Which inequality below is true for all points on the indicated interval?
A g( x) ≥ h( x) on the interval –3 ≤ x ≤ 3
B g( x) ≥ h( x) on the interval –2 ≤ x ≤ 2
C g( x) ≤ h( x) on the interval –3 ≤ x ≤ 3
D g( x) ≤ h( x) on the interval –2 ≤ x ≤ 2
The correct statement regarding the exponential functions g(x) and h(x) is given as follows:
B g( x) ≥ h( x) on the interval –2 ≤ x ≤ 2.
What is an exponential function?The standard definition of an exponential function is given as follows:
y = ab^x.
In which the coefficients of the function are described as follows:
a is the y-intercept, the value of y at which the function crosses the y-axis.b is the rate of change of the exponential function.Function h(x) is defined as follows:
h(x) = 3^x - 2.
For the graphed function g(x), when x = 0, y = 4, hence the intercept of the function is given as follows:
a = 4.
When x = 1, y = 5, hence the rate of change of the function is obtained as follows:
b = 5/4.
b = 1.25.
Then function g(x) is given as follows:
g(x) = 4(1.25)^x.
Due to the higher intercept, g(x) ≥ h( x) at x = 0. This will change when they intersect, which from the image given at the end of the answer is at x = 1.906, which is approximately 2, hence statement B is correct.
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Which model represents the equation 6x = 18
Answer:
top right
Step-by-step explanation:
6x3=18
The population of a heard of buffalo after t
years is represented by the function
() = 2186(0.954)^t
What does the value 0.954 represent in this
situation?
a. The initial population of the town is 0.954
b. The population of the town increases by 0.954
each year.
c. The population of the town decreases by 0.954
each year.
d. The population of the town is 0.976 times the
population of the town in the previous year.
0.954 represents population of the town increases by 0.954 each year.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
The population of a heard of buffalo after t
years is represented by the function
[tex]f(x)=2186(0.954)^{t}[/tex]
We need to find the what does the value 0.954 represent in this
situation.
In the given function 2186 represent the initial population.
t represents the time in years
and 0.954 represents population of the town increases by 0.954 each year.
Hence, 0.954 represents population of the town increases by 0.954 each year.
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which age group has more variable finish times
Answer:
l
v
Step-by-step explanation:
80, 5, 30, 7, and 3,
A sign made of aluminum is in the shape of a pyramid. The base is a triangle with a base of 3 feet and a height of 5 feet. The height of the sign is 6 feet. The aluminum costs $8 per cubic foot. What is the cost of the sign?
A) $722
B) $240
C) $120
D) $168
The cost of the pyramid shape sign is $240.
What is a pyramid?A pyramid is a 3D figure that has a base made of a polygon and faces that are all triangular and connected. The conventional shape of a pyramid is created by joining each vertex of the base to a single common tip or apex. In this section, let's study more about pyramids.
We know the volume of a pyramid is (1/3)×length of the bese×width of the base×height.
∴ The volume of the pyramid with base length of 6feet, base width of 3feet and height 5 feet is,
= (1/3)×6×3×5 cubic feet.
= 30 cubic feet.
Given, The aluminum costs $8 per cubic foot.
∴ The total cost of the pyramid is = (30×8) = $240.
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