The functions have the same x-intercept and the same end behaviour as x approaches infinity.
We are given two functions, f(x) and g(x). A function connects an input with an output. It is analogous to a machine with an input and an output. And the outcome is somehow connected to the input.
The function f(x) is represented in the graph. The function g(x) is represented by the data in the table. We have to find the correct comparison between the two functions.
The comparison is to be done on the basis of the lengths of the x-intercept and y-intercept and the end behaviour of both functions. From the given values, we conclude that the x-intercepts for both functions are the same, but the y-intercepts are different. The end behaviour of both functions becomes similar as x approaches infinity.
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[If f(x) = x and g(x) = 1/2 f(x) , how does the graph of g compare to the graph of f?]
We can notice that the graph of function g(x) = 1/2 f(x) is below the graph of function f(x) = x in the 1st quadrant but above in the 3rd quadrant, and they both intersect at 0.
What are graphs?In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.Charts and graphs come in a variety of styles. Line graphs, bar graphs and histograms, pie charts, and Cartesian graphs are likely the four most popular types. They serve quite diverse purposes and are best suited for very different uses.So, the difference in the graph of the given functions:
f(x) = x g(x) = 1/2 f(x)Plot on the graph as follows:
(Refer to the graph attached below)
Therefore, we can notice that the graph of function g(x) = 1/2 f(x) is below the graph of function f(x) = x in the 1st quadrant but above in the 3rd quadrant, and they both intersect at 0.
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A full-grown monarch caterpillar weights 0.75 grams, has a length of 5 centimeters, and is about 2.5 centimeters around. How can the surface area of the caterpillar be estimated?
A ___ can be used to model the surface area of the caterpillar. Based on the model, the caterpillar has an approximate surface area of ___ square centimeters.
The choices for the first blank are:
*rectangular prism
*triangular prism
*sphere
*cylinder
The choices for the second blank are:
*13.5
*6.75
*49.1
*117.8
A Cylinder can be used to model the surface area of the caterpillar with Surface area of 117.3 cm²
A full-grown monarch caterpillar is of cylinder shape . so , the option 4th is correct for first blank.
Surface area of cylinder is 2πrh + 2πr²
where r is radius of circle and h is height of cylinder
here , length of caterpillar is 5cm and radius is 2.5cm
Surface area = 2πrh + 2πr²
= 2π(5)(2.5) + 2π(2.5)²
= 2π(12.5) + 2π(6.25)
putting π = 3.14
=78.5+39.25
=117.8 cm²
Rewriting the sentence
A cylinder can be used to model the surface area of the caterpillar. Based on the model, the caterpillar has an approximate surface area of 117.8 square centimeters.
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Answer: A Cylinder can be used to model the surface area of the caterpillar with Surface area of 117.8 square centimeters
(if your on PLATO) if not then 117.8
Wing Ko replaces watch bands. He is paid $24.60 per band How many bands must he replace to eam at least $122.50 per day?
To earn at least $122.50 per day, Wing Ko must replace 5 watch bands
Here, we want to find the number of bands that Wing Ko must replace to earn at least $122.50 per day
Let the number of watch bands be x
Using mathematical relatio to represent this inequality, we have;
[tex]\begin{gathered} 24.\text{ 6 }\times\text{ x }\ge\text{ 122.50} \\ 24.6x\text{ }\ge\text{ 122.50} \\ \\ x\text{ }\ge\text{ }\frac{122.5}{24.6} \\ \\ x\text{ }\ge\text{ 4.97} \\ \\ x\text{ }\ge\text{ 5} \end{gathered}[/tex]at a butcher shop, hilda bought 7 1/4 lb of beef she left with 18 9/20 lb of meat express the numbers of pounds of pork she bought using a decimal
Using mathematical operations, we can conclude that the pound of pork the girl brought was 11.2 pounds.
What are mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value.The operation's arity is determined by the number of operands. The rules that specify the order in which we should solve an expression involving many operations are known as the order of operations. PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition Subtraction (from left to right).So, the pounds of pork the girl bought:
Beef bought: 7¼Total meat: 18 9/20Calculate pork as:
18 9/20 - 7¼369/20 - 29/4369 - 5(29)/20369 - 145/20224/2011.2Therefore, using mathematical operations, we can conclude that the pound of pork the girl brought was 11.2 pounds.
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Please fill the gaps in!!
Answer:
[tex]2 {d}^{2} + 5d - 7 [/tex]
[tex](2d + 7)(d - 1)[/tex]
What is the value of x?
30 points if answered
Answer: 20
Step-by-step explanation: They are both equal to each other, so 3x+50=6x-10. Then just solve for x by canceling out both sides.
Can anyone help with this? Thanks
The surface area of the prism is 1440 mm²
Given,
Triangular prism
Height of the prism = 32 mm
Base of the prism = 24 mm
Length of the prism = 7 mm
We have to find the surface area of the prism;
Surface area, SA = bh + (b₁ + b₂ + b₃) l
Here,
Base, b = 24 mm
Height, h = 32 mm
Length, l = 7 mm
b₁ = 24 mm
b₂ = 32 mm
b₃ = [tex]\sqrt{b_{1} ^{2} + b_{2} ^{2} }[/tex] = [tex]\sqrt{24^{2}+ 32^{2} }[/tex] = [tex]\sqrt{576 + 1024}[/tex] = √1600 = 40 mm
Then,
Surface Area = bh + (b₁ + b₂ + b₃) l
SA = 24 x 32 + (24 + 32 + 40) 7
SA = 768 + 96 x 7
SA = 768 + 672
SA = 1440 mm²
That is,
The surface area of the prism is 1440 mm²
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What is the remainder when x2 + 15x + 9 is divided by x + 5 ?0 -41O 49O 42O 59
When a polynomial is dived by x - a, to find the remainder, we can plug is x = a into the equation and find the remainder.
When it is divided by x + a, the remainder is found by plugging in x = -a.
Now, the polynomial here is:
[tex]x^2+15x+9[/tex]It is divided by x + 5, so we need to plug in x = -5 to get the remainder, which is:
[tex]\begin{gathered} x^2+15x+9 \\ (-5)^2+15(-5)_{}+9 \\ =-41 \end{gathered}[/tex]The remainder is - 41, 1st answer choice.
A supervisor finds the mean number of miles that the employees in a department live from work. He finds x Overbar = 29 and s = 3.6. Which mileage is within a z-score of -1.5?
The mean number of miles that the employees in a department live from work is 24.
What is a z-score?
The z-score is a numerical measurement used in statistics of the value's relationship to the mean of a group of values, measured in terms of standards from the mean.
The z-score is given as
x = 29
s = 3.6
z = -1.5
Then the mean will be
[tex]-1.5 = \frac{29-u}{3.6}[/tex]
μ = 29 - 5.4
μ = 23.6 ≅ 24
Hence the answer is the mean number of miles that the employees in a department live from work is 24.
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Two and six-tenths times a number, x, plus 5 is y.
Answer:
2,6x +5 = y
Step-by-step explanation:
Don’t know if you wanted the equation, but this is how it’s written
Evaluate the expression shown below and write your answer as a fraction in simplest form.
\frac{4}{5}\div\frac{9}{5}\cdot\frac{7}{3}
5
4
÷
5
9
⋅
3
7
The rules of BODMAS are useful in calulating mathematical expressions involving many operators. The given expression can be simplified as a simple fraction 28 / 27.
What are the rules of BODMAS?The rules of BODMAS can be understood by the full form of the name. B stands for bracket, O for of, D for division, M for multiplication, A for addition and S stands for subtraction. For a mathematical expression involving the combination of any of these operators the priority will be given to the letter that comes first.
The given expression can be written as,
4 / 5 ÷ 9 / 5 × 7 / 3
In the given expression there are three fractions separated by the sign of multiplication and division.
As per the rule of BODMAS, the division operator has the priority over multiplication operator.
Apply the rule mentioned above in the given expression to get,
4 / 5 ÷ 9 / 5 × 7 / 3
= 4 / 5 × 5 / 9 × 7 / 3
= 4 / 9 × 7 / 3
= 28 / 27.
Hence, the given expression is simplified to get the result as 28 / 27.
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Find the quotient of -20x9 and 2x³.
Answer:
-20x9= -180. 2 to the power of three =8 if you want the quotient it would be -22.5
Step-by-step explanation:
Find the 54th term of the following arithmetic sequence.15, 22, 29, 36,...
The length of the base of an isosceles triangle is x. The length of a leg is 5x−4. The perimeter of the triangle is 102. Find x.
In the given isosceles triangle, the value of x is 10 units.
What is a triangle?A triangle is a polygon with three edges and three vertices. It belongs to the basic geometric shapes. A triangle having vertices A, B, and C is known as triangle ABC. Any three locations in Euclidean geometry that are not collinear result in a distinct triangle and a distinct plane.So, the value of 'x' will be:
Given triangle is an isosceles triangle. Then,
x + 5x - 4 + 5x - 4 = 10211x - 8 = 10211x = 102 + 811x = 110x = 110/11x = 10Therefore, in the given isosceles triangle, the value of x is 10 units.
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help meeeeeeeeeeeeeee pleaseeeeeee
Answer: Width = 5.7 feet, Length = 10.5 feet
Step-by-step explanation:
Let the width be w. Then, the length is 2w-0.9.
[tex]w(2w-0.9)=59.85\\\\2w^2 -0.9w-59.85=0\\\\w =\frac{-(-0.9) \pm \sqrt{(-0.9)^2 -4(2)(-59.85)}}{2(2)}\\\\w =5.7\\\\\implies 2w-0.9=10.5[/tex]
55 POINTS!!!
1. Identify the set of ordered pairs that represents y as a function of x.
Responses
{(−1, 0), (−1, 1), (−2, 2), (0, 3)}
{(−1, 1), (−2, 0), (−3, 4), (−3, 3)}
{(0, 0), (1, 1), (2, 2), (3, 3)}
{(0, 0), (1, 0), (2, 4), (2, 3)}
2. Which table represents y as a function of x?
Responses
x y
0 1
0 2
1 3
2 3
x y
1 0
2 0
3 1
3 2
x y
−1 −1
0 −1
2 0
3 2
x y
−1 −1
−1 0
0 2
2 3
Answer:
1) B, 2) C
===========
As per definition, functions have only one y-value per x-value.
Let's test it with given sets and tables.
Part 1A) {(−1, 0), (−1, 1), (−2, 2), (0, 3)} - Not a function x = - 1 repeatedB) {(−1, 1), (−2, 0), (−3, 4), (−3, 3)} - Not a function x = - 3 repeatedC) {(0, 0), (1, 1), (2, 2), (3, 3)} - FunctionD) {(0, 0), (1, 0), (2, 4), (2, 3)} - Not a function x = 2 repeatedPart 2A)
x y
0 1
0 2
1 3
2 3
Not a function, x = 0 is repeatedB)
x y
1 0
2 0
3 1
3 2
Not a function, x = 3 is repeatedC)
x y
−1 −1
0 −1
2 0
3 2
FunctionD)
x y
−1 −1
−1 0
0 2
2 3
Not a function, x = - 1 repeated1) The set of ordered pairs that represents y as a function of x is;
B; {(−1, 1), (−2, 0), (−3, 4), (−3, 3)}
2) The table that represents y as a function of x is; Table 3
How to Interpret Ordered Pairs?An ordered pair is defined as a composition of the x coordinate called the abscissa and the y coordinate called the ordinate having two values written in a fixed order within parentheses.
1) The first function given as {(−1, 0), (−1, 1), (−2, 2), (0, 3)} ; This cannot be regarded as a function because the input x = - 1 is repeated with different output values.
The second function {(−1, 1), (−2, 0), (−3, 4), (−3, 3)} ; This cannot be regraded as a function because the input x = -3 is repeated with different output values.
The third function {(0, 0), (1, 1), (2, 2), (3, 3)}; This is a function because each input has unique output values.
The fourth function {(0, 0), (1, 0), (2, 4), (2, 3)} ; This cannot be regraded as a function because the input x = 2 is repeated with different output values.
2) Table 1 cannot be regarded as a function because the input x = 0 is repeated with different output values.
Table 2 cannot be regarded as a function because the input x = 3 is repeated with different output values.
Table 3 is a Function because each input has unique output values.
Table 4 cannot be regarded as a function because the input x = -1 is repeated with different output values.
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The length of a rectangle is 3 more than twice the width. Which of the following represents the length of the rectangle if the perimeter is 42 inches? 2(x) +2(2x+3)=42
Answer:
Step-by-step explanation: if the width is x then the length is 2x+3
The perimeter is 2x+2(2x+3)=42
then 6x+6=42
6x=36
x=6
Then the length is 2*6+3=15
help meeeeeeeeeeeeeee pleaseeeeeee
Answer: 2.5, 5.4
Step-by-step explanation:
[tex]-16t^2 +126t=213\\\\16t^2 -126t+213=0\\\\t =\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(213)}}{2(16)}\\\\t \approx 2.5, 5.4[/tex]
6) How long will it take for an investment to double in value if it earns 4.75% compoundedcontinuously?A) 14.593 yearsB) 15.711 years C) 23.129 years D) 7.296 years
A quantity that is compounded continuously follows the next equation:
[tex]A=Pe^{rt}[/tex]Where:
[tex]\begin{gathered} A=\text{ amount in time ''t''} \\ P=\text{ initial amount} \\ r=\text{ rate of interest in decimal form} \\ t=\text{ time} \end{gathered}[/tex]Now, the interest rate in decimal notation is determined by dividing the percentage by 100:
[tex]r=\frac{4.75}{100}=0.0475[/tex]Now, we are asked to determine the time required for the quantity to double. Therefore, we need to determine "t" when:
[tex]A=2P[/tex]Substituting in the formula we get:
[tex]2P=Pe^{rt}[/tex]Now, we can cancel out the "P":
[tex]2=e^{rt}[/tex]Now, we solve for "t". First, we take the natural logarithm to both sides:
[tex]ln2=lne^{rt}[/tex]Now, we use the following property of logarithms:
[tex]lnx{}^y=ylnx[/tex]Applying the property we get:
[tex]ln2=rtlne[/tex]We have that:
[tex]lne=1[/tex]Therefore:
[tex]ln2=rt[/tex]Now, we divide both sides by "r":
[tex]\frac{ln2}{r}=t[/tex]Now, we substitute the value of "r":
[tex]\frac{ln2}{0.0475}=t[/tex]Solving the operations:
[tex]14.593=t[/tex]Therefore, the right option is A.
What is the mean daily snowfall 8,3,12,1,1
Answer:25
Step-by-step explanation:
1. you place the numbers in order from least to greatest so 1,1,3,8,12
2. then you add those all up
3.then you divide how many numbers there are together
1+1+3+8+12=25
then you divide by 5 because that's how many numbers are shown for the daily snow fall
HOPE THIS HELPS
Solve each equation by graphing. Verify youranswer algebraically.
12. 5-8x=16- 8x
21. 12x +132 = 12x- 100
Answer:
12. 0 = 11
No Solution
21. 0 = -132
No Solution
Step-by-step explanation:
12.
5 - 8x = 16 - 8x
-8x + 5 = -8x + 16
- 5 = - 5
-8x = -8x + 11
-8x = -8x
0 = 11
No Solution
21.
12x + 32 = 12x - 100
- 32 - 32
12x = 12x - 132
-12x -12x
0 = -132
No Solution
mDE= ?Use O, A to find mDE , given that BF is a diameter of O. A.
STEP 1: Identify and Set Up
We are required to get the angle subtended by the arc DE.
We first acknowledge that it is part of the angles in a quadrant as this will help us find it.
STEP 2: Execute
First find angle DAE
[tex]\begin{gathered} Angle subtended by DE = 45 degreesSolve the following system for y: 2x+y=43x−12y=−4
On solving the equation 2x+y=-4 and 43x-12y=-4 for y we get the value of y=-164/67 as the definition of solution of equation says "A solution to an equation is a number that can be plugged in for the variable to make a true number statement".
What is system of equation?A group of equations involving one or more variables is known as a system of equations. The variable mappings that cause all component equations to be satisfied or intersected are the solutions to systems of equations.
Here,
2x+y=-4
43x-12y=-4
43(2x+y=-4)
2(43x-12y=-4)
86x+43y=-172
86x-24y=-8
subtracting equation,
67y=-164
y=-164/67
As stated in the definition of equation solution, "A solution to an equation is a number that can be plugged in for the variable to make a true number statement," we arrive at the value of y=-164/67 after solving the equations 2x+y=-4 and 43x-12y=-4 for y.
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If
C
=
−
x
+
2
C=−x+2 and
D
=
x
2
+
8
x
−
1
,
D=x
2
+8x−1, find an expression that equals
3
C
+
3
D
3C+3D in standard form.
The expression that equals 3C+3D in standard form is:
x²+7x+1
Given:
C = -x+2
and D = x²+8x-1
we are asked to find out an expression which equals 3C+3D in standard form.
based on the conditions, formulate:
3C+3D
substitute C and D values.
⇒ 3(-x+2) + 3(x²+8x-1)
Apply multiplicative distribution law:
⇒ open the parenthesis.
⇒ -3x+6+3x²+24x-3
calculate the product or quotient
⇒ arrange the like terms.
⇒ 3x²+21x+3
⇒ Reduce the terms.
⇒ x²+7x+1
Hence we get the equation in standard form.
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What is the center and radius of -10x = -121 - y2 - x2 -22y
We need to find the center and the radius of
[tex]-10x\: =\: -121\: -\: y^2\: -\: x^2\: -22y[/tex]The general circle equation is the following
[tex](x-h)^2+(y-k)^2=r^2[/tex]where
(h,k) is the center and
r is the radius
1. rearrange the equation
[tex](x^2-10x)+(y^2+22y+121)=0[/tex]2. Add 25 on both sides
[tex](x^2-10x+25)+(y^2+22y+121)=25[/tex]3. Factor
[tex](x-5)^2+(y+11)^2=5^2[/tex]Now we have an equation that is very similar to the circle equation, so let's compare them
Center -> (h,k) = (5,-11)
radius -> r = 5
Which figures can have two sides of the same length, but are not parallelograms?quadrilateralrectanglesquareisosceles trapezoid
A Quadrilateral has four-sides, it is 2-dimensional (a flat shape), closed (the lines join up), and has straight sides.
We have special types of quadrilaterals which are,
1) Rectangle
2) Square
3) Rhombus
4) Parallelogram
5) Trapezium
6) Kite
Some types are also included in the definition of other types! For example a square, rhombus and rectangle are also parallelograms.
An isosceles trapezoid has left and right sides of equal length that join to the base at equal angles.
Below is the diagram of an Isosceles trapezoid
The first puzzle includes a treasure map. The treasure map is an xy coordinate grid with the origin markingthe center of the room as shown below. Two lines intersect to show the location of the next clue. The linesmust be added to the treasure map.The first line is represented by the equation y = 3x - 16.The graph of the second line passes through the points (1,7) and (4,1).North6s411WestEast112South4. What is the equation of the second line? Show how you found the equation.(Replace this text with your equation)(Replace this text with your work).
Given
(1,7) and (4,1)
[tex]\begin{gathered} M=\frac{y_2-y_1}{x_2-x_1} \\ M=\text{ }\frac{1-7}{4-1} \\ M=-\frac{6}{3} \\ M=-2 \\ \\ y-y_1=m\mleft(x-x_1\mright) \\ y-7=-2(x-1) \\ y-7=-2x+2 \\ y=-2x+2+7 \\ y=-2x+9 \end{gathered}[/tex]y=-2x+9
Ilya goes to the store with $1.40 in his pocket and $1.85 in his wallet. Which model shows how much money Ilya has all together?
The model is a linear function that shows $3.25 money that Ilya has all together
What is meant by a linear function?The phrase linear function relates to two distinct but related concepts in mathematics:
Some authors use the term "linear function" only for linear mappings that accept values in the scalar field; these are more frequently known as linear forms.
Calculus' "linear functions" qualify as "linear mappings" when (and only when) f(0,..., 0) = 0, or, equivalently, when the aforementioned constant b equals zero.
A linear function in calculus and related fields is one whose graph is a straight line, that is, a polynomial function of degree zero or one. The word affine function is commonly used to distinguish such a linear function from the other idea.
A linear function is also known as a linear map in linear algebra, mathematical analysis, and functional analysis.
Given,
Ilya goes to the store with $1.40 in his pocket and $1.85 in his wallet.
Total money=$1.40+$1.85
=$3.25
The model is a linear function that shows $3.25 money that Ilya has all together.
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Can you please help me out
ANSWER:
A. 2.2%
STEP-BY-STEP EXPLANATION:
We can calculate the probability using the quotient of the area of the small circle and the area of the entire rectangular sector, like this:
[tex]\begin{gathered} p=\frac{A_c}{A_r} \\ A_c=\pi\cdot r^2 \\ A_r=l\cdot w \end{gathered}[/tex]In the circle the radius is 6 inches and in the rectangle the length is 84 inches and the width is 60 inches.
Therefore we replace and we have:
[tex]\begin{gathered} A_c=3.14\cdot6^2=113.04 \\ A_r=84\cdot60=5040 \\ p=\frac{113.04}{5040}=0.022=2.2\text{\%} \end{gathered}[/tex]To save money for her son's college tuition, Mary invests $98 every month in an annuity that pays 6.1% interest, compounded monthly. Payments will be made at the end of each month. Find the total value of the annuity in 21 years.
Given
Monthly deposit = $98
Rate = 6.1%
Number of years = 21
Find
Total value of the annuity in 21 years.
Explanation
Total value of annuity is given by
[tex]FV=A[\frac{(1+\frac{r}{m})^{mt}-1}{\frac{r}{m}}][/tex]where FV is a future value
so ,
[tex]\begin{gathered} FV=98[\frac{(1+\frac{0.061}{12})^{12\times21}-1}{\frac{0.061}{12}}] \\ \\ \end{gathered}[/tex]now solve this to obtain the future value .
[tex]\begin{gathered} FV=98\times509.227229162 \\ FV=49904.26 \end{gathered}[/tex]Final Answer
Therefore , the future value is $49904.27