The function relationship is a quadratic function
How to determine the function type?The function is given as:
x y
-5 17
-4 7
-3 1
-2 -1
-1 1
Remove the x values:
y: 17 7 1 -1 1
Calculate the difference between the consecutive y values
Difference: 10 6 2 -2
Because the first difference are not equal, it means that the function is not a linear function.
Calculate the difference between the above differences
Difference: 4 4 4
Because the second differences are equal, it means that the function is a quadratic function.
Hence, the function relationship is a quadratic function
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The amount of trash, in tons per year, produced by a town has been growing linearly, and is projected to
continue growing according to the formula P(t) = 75 + 4t. Estimate the total trash that will be produced
over the next 8 years by interpreting the integral as an area under the curve.
tons
The total trash that will be produced over the next 8 years will be 107 trash
Functions and valuesGiven the function that represents the amount of trash, in tons per year, produced by a town has been growing linearly, and is projected to
continue growing according to the formula P(t) = 75 + 4t
The total trash that will be produced over the next 8 years is expressed as:
p(8) = 75 + 4(8)
p(8) = 75 + 32
p(8) = 107
Hence the total trash that will be produced over the next 8 years will be 107 trash
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Find the equations for a helix that has a radius of 8, a height of 12 and does exactly two complete revolutions (starting at the xy-plane).
By the equations according to the cylindrical system of coordinates, the equation for a helix are x = 8 · cos (2π · t /T), y = 8 · sin (2π · t /T) and z = 6 · (t/T).
How to derive the equations of a helix in cylindrical form
According to the cylindrical system of coordinates, helix can be described by the following equations:
Radius
x = r · cos (2π · t /T) (1)
y = r · sin (2π · t /T) (2)
Height
z = H · (t/T) (3)
Where T is the period of one complete revolution.
If we know that r = 8 and H = 6, then the equations for the helix is:
x = 8 · cos (2π · t /T)
y = 8 · sin (2π · t /T)
z = 6 · (t/T)
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At a sale, coats were sold for $184 each. If the coats originally cost $200 each, what percentage of its original price was a coat sold for?
Answer:
92%
Step-by-step explanation:
sale price is 184.
original price was 200.
184/200 = 0.92
Multiply by 100 to change to a percent.
0.92 × 100 = 92
184 is 92% of 200.
The coat was sold for 92% of its original price.
Answer:
92%
Step-by-step explanation:
What percentage of 200 is 184 ?
184 / 200 * 100% = 92%
0.403 divided by 100 what is the quotient
Answer: 0.403 / 100 = 0.00403
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The function g(x) = -2x +3 compare the slopes and y-intercepts
The slope of the function in discuss is -2 and the y-intercept of the function is; 3.
What is the slope and y-intercept of the function?The slope which is simply a measure of the rate of change can be obtained by comparison of the function given to the slope-intercept form of a linear function.
f(x) = mx + c
Hence, the slope of the function is -2 and it's y-intercept (point of intersection with the y-axis) is; (0,3).
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PLS HURRRYYYyyyyyyyydhsbsbd
Answer:
116.5027
Step-by-step explanation:
degree/360 *pie * radius^2
5. Which number is the base in the expression 8.3^6?
Answer:
8.3
Step-by-step explanation:
In 8.3^0.6, the base is the number that is being raised to the exponent. So, 8.3 is the base, and 0.6 is the exponent.
Brainliest, please :)
HELP ASAP 15 POINTS!!!
What is the solution to this equation?
6(x-5)=4x+20
Answer:
x = 25Step-by-step explanation:
What is the solution to this equation?
6 * (x - 5) = 4x + 20
6x - 30 = 4x + 20
2x = 20 + 30
2x = 50
x = 50 : 2
x = 25
-------------------
check
6 * ( 25 - 5) = 4 * 25 + 20
6 * 20 = 100 + 20
120 = 120
the answer is good
Answer:
x=25Step-by-step explanation:
6(x-5) 4x+20
Distribute.
6x-30 = 4x+20
Subtract 4x from each side.
6x-4x-30 = 4x-4x+20
Simplify.
2x-30=20
Add 30 to both sides.
2x-30+30 = 20+30
Simplify.
2x = 50
Divide both sides by 2
2x/2 = 50/2
Simplify
x = 25
So, x = 25!
Which represents the inverse of the function
f(x) = 4x?
h(x) = x + 4
h(x) = x-4
h(x) = =x
h(x) =÷x
b) Some economists in the cOuntry are proposing mandatory wage and price controls to combat inflation, but others claim such controls are ineffective. Suppose it is established that 40% of all adults in the country favour wage and price controls. If 5 adults are selected at random, find the probability that: i. At least 3 favour wage and price controls?
Answer:
3/5
Step-by-step explanation:
40% of all adults favor wage and price controls, that means that 4 out of every 10 adults favor them. Therefore, if 5 adults are selected at random, the probability that at least 3 of them favor wage and price controls is 3/5 or 60%.
What type of system of linear equations is this?
y = -5x-4
y=1/2x+3
A. consistent and independent
B. consistent and dependent
C. inconsistent
D. independent and inconsistent
Answer:
B
Step-by-step explanation:
consistent and dependent
A force F = (4x i +3y) N acts on an object as the object moves in the x direction from the origin to x =5.00 m. Find the work done.
The work done is 100 + 15y Joules
How to find the work doneThe formula for determining the work done is given as;
Work done = force × distance
We have;
Force = (4x + 3y)
Distance = x = 5.00m
Work done = (4x + 3y) × x
Work done = 4x^ 2 + 3xy
Let's substitute the value of 'x'
Work done = 4 × 5 × 5 + 3 × 5 × y
Work done = 100 + 15y Newton
Thus, the work done is 100 + 15y Joules
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Don't know, could someone help me!!
Answer:
[tex]\boxed{A=1~~\land~~B=-4}[/tex]
Step-by-step explanation:
I use formulas:
[tex]\boxed{\dfrac{x^{n} }{x^{m} } =x^{n} \div x^{m} =x^{n-m} }[/tex]
[tex]\dfrac{t^{2} }{t^{6} } =t^{2}\div t^{6}=t^{2-6}=\boxed{t^{-4}}\\\\t^{-4} =1\cdot t^{-4} ~~\land~~At^{B} ~~\Rightarrow ~~A=1~~\land~~B=-4[/tex]
Find x.
please help!
Answer:
37
Step-by-step explanation:
Since the lines are parallel,
2x + 106 = 180
2x = 74
x = 37
Answer:
x = 37°
Step-by-step explanation:
∠ a = 2x [Corresponding angles]
106° + ∠ a = 180° [Angles on a straight line]
∴ 106° + 2x = 180°
⇒ 2x = 74°
⇒ x = 37°
3
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3
Tiles
31/50 42√/2
Pairs
972
448
3,528
4,050€
43/7 4√3
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3/4
738
Submit
Answer:
I need detailed question
Which expressions represent purely real numbers and which expressions represent non-real complex numbers?
All rights reserved.
-289
i9
√(-18)
4- 321² 2 √-49
3 +2i
Purely Real Number
Non-real Complex Number
An expression is defined as a set of numbers, variables, and mathematical operations.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
From the given expression the numbers can be classified as,
Real Numbers
-289i⁹ = -14-32i² = 36Non-real / Complex Number
3 + 2i2 - √-49 = 2 - 7iLearn more about Expression:
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IF Sin =p what is then cos^2x
Answer:
4r2
Step-by-step explanation:
2v 3qsdwg3
A computer manufacturer built a new facility for assembling computers. There were construction and new equipment costs. The company paid for these costs and made combined profits of $80 million after 4 years, as shown in the graph:
There is a graph of a line with Years on the x axis and Profits in millions on the y axis that passes through 1, negative 100 and 4, 80.
Which equation most closely represents the line depicted in the graph?
f(x) = 60x − 160
f(x) = −60x + 160
f(x) = −80x + 4
f(x) = 80x − 4
The equation that most closely represents the line depicted in the graph is; f(x) = 60x − 160
How to find the equation of a Graph?We're given a point of the graph (4, 80).
From the complete question seen online, we see that the profits increased $60 million per year. Thus, slope = 60.
Let us write the equation and find x and y intercepts.
y = 60x + b
Thus;
80 = 60*4 + b
80 = 240 + b
b = -160
Thus, the equation that most closely represents the line depicted in the graph is; f(x) = 60x − 160
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If you are driving at a rate of 55 miles per hour, about how many feet per second are you traveling?
290400 feet per second
0.015 feet per second
4840 feet per second
80.67 feet per second
In how many ways can 3 cards be chosen from a standard deck of 52 cards?
[tex]\displaystyle\\\binom{52}{3}=\dfrac{52!}{3!49!}=\dfrac{50\cdot51\cdot52}{2\cdot3}=22100[/tex]
First accurate commenter gets brainliest
Answer:
Graph #4 is the correct answer.
Step-by-step explanation:
Answer:
It is graph four
Step-by-step ex
The only correct corresponding set for -1,6 would be this graph
Which shows an equation in point-slope form of the line shown?
y−4=43(x−2)
y−2=34(x+6)
y−4=34(x−2)
y+2=43(x+6)
Number graph ranging from negative ten to ten on the x and y axes. A line passes through the labeled points (negative six, negative two) and (two, four).
Answer: Option (3)
Step-by-step explanation:
The slope of the given line is
[tex]\frac{-2-4}{-6-2}=\frac{-6}{-8}=\frac{3}{4}[/tex]
Thus, the answer must be Option (3)
7)Which statement is true?
A. The radius of a given circle is longer than its diameter.
B. The length of the radius is the same in all circles.
C. The circumference is always twice the radius.
D. All circles contain 360 degrees.
Answer:
D.
Step-by-step explanation:
A. The radius of a given circle is longer than its diameter.
False. The diameter is twice the radius.
B. The length of the radius is the same in all circles.
False. Since there are circles of many sizes, there are many different sizes of the radius.
C. The circumference is always twice the radius.
False. The circumference is 2π times the radius or π times the diameter.
D. All circles contain 360 degrees.
True.
A livestock pen is built in the shape of a rectangle that is 3 times as long as it is wide. The perimeter is 56 feet. If the material used to build the pen is $1.50 per foot for the longer sides and $2.75 per foot for the shorter sides (the shorter sides have gates, which increase the cost per foot), find the cost to build the pen.
The cost of the shorter and longer side of the rectangular pen is $19.25 and $31.50 respectively.
Perimeter of rectangleWidth = xLength = 3xPerimeter = 56 feetPerimeter = 2(length + width)
56 = 2(3x + x)
56 = 2(4x)
56 = 8x
x = 56/8
x = 7
So,
Width = x
= 7 feet
Length = 3x
= 3(7)
= 21 feet
Cost of material used for the shorter side = $2.75 × 7
= $19.25
Cost of material used for the longer side = $1.50 × 21
= $31.50
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Drag each graph to show which transformation was applied to the original figure.
Each graph is the result of one transformation.
Transformation is a process in which the dimensions or orientation of a given plane shape is changed. The required answers are:
Graph 1: Reflection
Graph 2: Translation
Graph 3: Rotation
Graph 4: Rotation
Graph 5: Translation
Graph 6: Reflection
Transformation is the process in which the dimensions or orientation is a given shape is changed. The major types are reflection, dilation, translation, and rotation.
Reflection is a transformation method in which a given shape is flipped over a given reference point or line. Dilation is a transformation method that involves either increasing or decreasing the length of sides of a given shape.Translation is a transformation method that requires the movement of all points of a shape with respect to a given reference point or line.Rotation is a transformation method that involves the rotation of a given shape at a certain degree clockwise or counterclockwise.Thus the transformation process that was applied to the original figure for each graph is:
Graph 1: Reflection along the y-axis
Graph 2: Translation at 4 units in the -x direction
Graph 3: [tex]90^{o}[/tex] clockwise Rotation
Graph 4: [tex]180^{o}[/tex] clockwise Rotation
Graph 5: Translation
Graph 6: Reflection along the x-axis
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If f(x) = -3x - 5 and g(x) = 4x - 2, find (f+ g)(x).
Answer: x-7
Step-by-step explanation:
[tex]f(x)+g(x)=-3x-5+4x-2=\boxed{x-7}[/tex]
Periodic Deposit: $1000 at the end of each year Rate: 4.5% compounded annually Time: 11 years
The interest amount is $622.85
How to determine the interest amount?The given parameters are:
Principal, P =$1000 Rate, r = 4.5% compounded annually i.e. n = 1Time, t = 11 yearsThe interest amount is calculated as:
I = P(1 + r/n)^(nt) - P
This gives
I = 1000 * (1 + 4.5%/1)^(1 * 11) - 1000
Evaluate the products and the quotient
I = 1000 * (1 + 0.045)^(11) - 1000
Evaluate the sum
I = 1000 * (1.045)^(11) - 1000
Solve
I = 622.85
Hence, the interest amount is $622.85
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How do I Expand (2x − 1)^6
Answer:
well if u do this
(2x-1)(2x-1)(2x-1)(2x-1)(2x-1)(2x-1)
it would be the expanded form for (2x-1)^6
Step-by-step explanation:
i um learned it before so...
Which number can each term of the equation be multiplied by to eliminate the fractions before solving?
-3/4m-1/2=2+1/4m
2
3
4
5
To eliminate the fraction, we multiply by 4
How to eliminate the fractions?The equation is given as:
-3/4m-1/2=2+1/4m
Rewrite properly as:
[tex]-\frac{3}{4}m - \frac 12 = 2 + \frac 14m[/tex]
The denominators of the above fractions are 2 and 4
The LCM of 2 and 4 is 4
So, we multiply through by 4.
This gives
-3m - 2 = 8 + m
Hence, to eliminate the fraction, we multiply by 4
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A movie theater has a seating capacity of 167. The theater charges $5.00 for children, $7.00 for students, and $12.00 for adults. There are half as many adults as there are children. If the total ticket sales was $ 1198, How many children, students, and adults attended?
Child attend:
Student attend:
Adult attend:
Answer:
Child attend: 58
Studen attend: 80
Adult attend: 29
Step-by-step explanation:
a + c + s = 167 Eq. 1
12a + 5c + 7s = 1198 Eq. 2
a = c/2 Eq. 3
a = adult attend
c = children attend
s = students attend
Replacing Eq, 3 in Eq. 2:
12(c/2) + 5c + 7s = 1198
6c + 5c + 7s = 1198
11c + 7s = 1198
7s = 1198 - 11c
s = (1198 - 11c) / 7 Eq, 4
Replacing Eq, 3 and Eq, 4 in Eq, 1
c/2 + c + (1198-11c) / 7 = 167
7c/14 + 14c/14 + 2(1198-11c)/14 = 2338/14
7c/14 + 14c/14 + 2396/14 - 22c/14 = 2338/14
7c + 14c + 2396 - 22c = 2338
7c + 14c - 22c = 2338 - 2396
-1c = -58
c = -58/-1
c = 58
from Eq. 3
a = c/2
a = 58/2
a = 29
from Eq. 4
s = (1198-11c)/7
s = (1198 - 11*58)/7
s = (1198 - 638) / 7
s = 560/7
s = 80
Check:
from Eq, 1
58 + 29 + 80 = 167