Which function grows at the fastest rate for increasing values of x?
h(x)=2x
f(x)=4x2+9x
g(x)=18x
Answers
The blue curve (f(x)) may start out below the others, but quickly surpasses them.
Answer:
Option 2. f(x) = 4x² + 9x
Step-by-step explanation:
In this question we have to tell which function grows at the fastest rate for increasing values of x.
1) h(x) = 2x It's a linear function increasing with the value of x.
2). f(x) = 4x²+9x It's a function representing parabola. Moreover the value of the function increases exponentially as the function is in the form of quadratic equation.
3). g(x) = 18x it's again a linear function.
Therefore out of three functions Function 2 will grow at the fastest rate for increasing values of x.
Related Questions
one method of estimating is to
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Hope this helps!
(20 Pts) What is the value of h when the function is converted to vertex form? Note: Vertex form is p(x)=a(x−h)^2+k . p(x)=x^2−14x+29
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PLEASE ANSWER THIS EASY MATH QUESTION!!
WILL PROVIDE THE ANSWERS BELOW!!!
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twice the measure of an angle's complement less 6 is equal to 124 find the measure of the angle
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Answer
you work it out the same way the first guy did, except instead of
2 (180-x) - 6 = 124, it's
2(90-x) -6 = 124.
the first guy divided by the supplement instead of the complement.
Step-by-step explanation:
To find the measure of the angle, you can use the equation 2(90 - x) - 6 = 124, where x represents the angle. By solving for x, you can determine that the measure of the angle is 25 degrees.
Explanation:To find the measure of the angle, we can use the information provided in the question. Let's let the measure of the angle be x degrees. The complement of the angle can be found by subtracting the measure of the angle from 90 degrees, since the sum of an angle and its complement is always 90 degrees. Therefore, the complement of the angle is 90 - x degrees.
According to the given equation, twice the measure of the angle's complement less 6 is equal to 124. We can write this as 2(90 - x) - 6 = 124. Now we can solve for x:
2(90 - x) - 6 = 124
180 - 2x - 6 = 124
-2x + 174 = 124
-2x = -50
x = 25
Therefore, the measure of the angle is 25 degrees.
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WHAT IS 2 400 000 written as a standard form?
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Hope this helps
Given: ΔABC ≅ ΔFDE. . What is the length of segment DE rounded to the nearest tenth?. . 3.2. . 4.2. . 2.2. . 3.6. .
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[tex]d= \sqrt{( x_{2}- x_{1})^2 + ( y_{2}- y_{1})^2 } [/tex]
[tex]d= \sqrt{(1)^2 + (-3)^2 } [/tex]
[tex]d= \sqrt{1+9 } [/tex]
[tex]d= \sqrt{10 } [/tex]
[tex]d= 3.2[/tex]
The length of segment DE is 3.2
Answer:
The length of segment DE is 3.2 (A)
Step-by-step explanation:
Mark has 36 drawings of horses and 4 drawings of spaceships. write and solve an equation to find how many times as many drawings of horses he has as spaceships.
Answers
4x = 36
Dividing both sides by 4:
x = 9
Hope this helps!
(I need 20 letters)
Question 2: A circular picture is 8 inches in diameter. Part A What is the area of the picture in square inches? A. 4π square inches B. 8π square inches C. 16π square inches D. 32π square inches Part B A frame that is 2 inches wide surrounds the picture. What is the total area of the picture and the frame in square inches? A. 4π square inches B. 12π square inches C. 36π square inches D. 40π square inches
really important please answer correctly
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_______________________________________________________
Part A) The correct answer is: [C]: " 16 [tex] \pi [/tex] square inches " .
_______________________________________________________
Part B) The correct answer is: [C]: " 36 [tex] \pi [/tex] square inches " .
_______________________________________________________
Note:
_______________________________________________________
Part A)
_______________________________________________________
The formula for the area, "A", of a circle:
A = [tex] \pi * r^2 [/tex] ;
in which:
" A = area of the circle" ;
" r = radius of the circle" ;
Note: radius, "r" = d / 2 ; in which: "d" is the diameter of the circle ;
Given: " d = 8 in " ; " r = (8 in) / 2 = 4 in " ;
_________________________________________________
A = [tex] \pi [/tex] * (4 in)² = [tex] \pi [/tex] * 4² * (in)² ;
= [tex] \pi [/tex] * (4*4) * (in²) ;
= [tex] \pi [/tex] * 16 * in² ;
________________________________________________________
→ which is: Answer choice: [C]: " 16 [tex] \pi [/tex] square inches " .
________________________________________________________
Part B)
________________________________________________________
We now have a circular frame with a thickness of "2 inches"
surrounding the original circle. This adds "4 inches" to the diameter of that of the original circle in "Part A" —
{Note: "2 inches on one side of the circle" ; PLUS "2 inches on the other side of the circle" ; equals "4 inches".}.
The diameter, "d", of this "new circle" ;
= "8 inches (that of the previous circle)" , PLUS "4 inches" , equals "12 inches" .
→ d = 12 in. ;
The radius , "r" :
→ r = d/2 = 12 in / 2 = 6 in.
→ r = 6 in.
The area, "A" of a circle:
______________________________________________________
A = [tex] \pi [/tex] * r² ;
= [tex] \pi [/tex] * (6 in)² ;
= [tex] \pi [/tex] * (6²) * (in²) ;
= [tex] \pi [/tex] * (6*6) * (in²) ;
= [tex] \pi [/tex] * (36) * (in²) ;
_______________________________________________________
→ which is: Answer choice: [C]: " 36 [tex] \pi [/tex] square inches " .
_______________________________________________________
Carpet sells for $3 per square foot and will cost you $810 to recarpet your rectangular room. if your room is 18 feet long, how many feet wide is it?
Answers
Area of the room is 270 square feet.
Area = 270 square feet, length = 18 feet
Area = Length x Width
270 = 18 x width
Width = 280 ÷ 18
Width = 15 feet
The room is 15 feet wide.
Find the percent of increase from 4.5 inches to 13.5 inches.
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Final answer:
To calculate the percent of increase from 4.5 inches to 13.5 inches, subtract the original value from the new value, divide by the original value, and then multiply by 100, resulting in a 200% increase.
Explanation:
To find the percent of increase from one number to another, you can use the formula: (New Value - Original Value) / Original Value × 100%. Applying this to the question, the original value is 4.5 inches, and the new value is 13.5 inches.
Calculate the increase: 13.5 - 4.5 = 9 inches.Divide the increase by the original number: 9 / 4.5 = 2.Convert this to a percentage by multiplying by 100: 2 × 100% = 200%.Therefore, the percent of increase from 4.5 inches to 13.5 inches is 200%.
Which graph represents the function on the interval [−3, 3] ?
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floor(0.1) -3 = -3 . . . . only the lower-left graph has this point.
The lower-left selection is appropriate.
Javier bought a 20 oz smoothie that contains 450 total calories how many calories does a smoothie contain per ounce
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1 oz = 450 ÷ 20
1 oz = 22.5 calories
Match each correlation coefficient with the type of association it indicates between the variables x and y.
r = 0.9
r = -1.0
r = -0.6
r = 0.1
a perfect linear association in which y increases as x increases
a perfect linear association in which y decreases as x increases
a strong linear association in which y increases as x increases
a strong linear association in which y decreases as x increases
a moderate linear association in which y increases as x increases
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A value of 0.9 would indicate that the correlation is positive. Since it's also close to the value 1, it would also tell us that the correlation of y and x is strong. Therefore, r = 0.9 would be a strong linear association in which y increases as x increases.
r = -1.0
Since the value of r is negative, this would mean that the correlation is also negative. Furthermore, the value of r is also at the minimum point which is -1.0 thus this would tell us that the correlation is a perfect linear association in which y decreases as x increases.
r = -0.6
Likewise, this r value is also negative thus allowing us to know that y will decrease as x increases. The value of r, which is -0.6, is also close to -1.0. This allows us to tell that it is a strong relationship. Therefore, r = -0.6 is a strong linear association in which y decreases as x increases.
r = 0.1
For this correlation, the r value is positive. This would indicate that the value of y will increase as x increases. Since the r value is only 0.1, we cannot say that it is a strong relationship since it is far from the maximum value for a perfect relationship which is 1. Therefore, r = 0.1 is a moderate linear association in which y increases as x increases.
r = 0.9 (a strong linear association in which y increases as x increases)
r = -1.0 (a perfect linear association in which y decreases as x increases)
r = -0.6 (a moderate linear association in which y decreases as x increases)
r = 0.1 (no linear association or a very weak association)
Given f(x) = 3x+4 . What is f(8)
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Comment the correct answer.
f(x)=3x+4
f(8)=3(8)+4
f(8)= 24+4
f(8)=28
hope that helps!!
At the beginning of the spelling bee there were 60 participants. One-third of the participants were eliminated during the first round. One-fourth of the remaining participants were eliminate during the second round. One-sixth of the remaining participants were eliminated during the third round. How many participants were still cmpeting at the beginning of the fourth round?
Answers
.
First round:
1/3 of 60 = 20
or
60 x 1/3
= 60/3
= 20
60 - 20 = 40
There are 20 participants that are eliminated on the first sound and 40 participants to move on to the second sound.
.
Participants = 40
Second round:
1/4 of 40 = 10
or
40 x 1/4
= 40/4
= 10
40 - 10 = 30
There are 10 participants that are eliminated on the second round and 30 participants that is moving on to the next round.
.
Participants = 30
Third round:
1/6 of 30 = 5
or
30 x 1/6
= 30/6
= 5
30 - 5 = 25
There are 5 participants that are eliminated on the third round and 25 participants to move on to the fourth round.
:)
By subtracting the eliminated participants in each round from the original number, it is determined that 25 participants were still competing at the beginning of the fourth round.
To find out how many participants were still competing at the beginning of the fourth round of the spelling bee, we need to perform some calculations based on the given percentages of participants eliminated in each round.
In the first round, one-third of the 60 participants were eliminated. This is 60 / 3 = 20 participants eliminated. So, 60 - 20 = 40 participants remained after the first round.In the second round, one-fourth of the remaining participants were eliminated. This is 40 / 4 = 10 participants eliminated. So, 40 - 10 = 30 participants remained after the second round.In the third round, one-sixth of the remaining participants were eliminated. This is 30 / 6 = 5 participants eliminated. So, 30 - 5 = 25 participants remained.Therefore, 25 participants were still competing at the beginning of the fourth round.
A light bulb manufacturing machine produces 72 light bulbs per minute. How much time would it take to make 5400 light bulbs?
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It would take 75 minutes for the machine to make 5400 light bulbs.
The ordered pairs below represent a function
(-2,-17.5),(5,8.75),(0,-10),(-1,-13.75),(3,1.25)
What is the rate of change of the function?Round to the nearest hundreth if necessary. PLEASE HELP ASAP WILL AWARD BRAINLIEST!!!
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If you plot the points, you will see that they are linear. The rate of change is equal to the slope between the points. Since the slope is the same between all of them, pick two points and find the slope.
(8.75 - (-17.5) / ( 5 - (-2))
26.25 / 7
3.75
Answer:
The answer is 3.75.
Step-by-step explanation:
I did this before
Find the two numbers whose sum is 29 and whose difference is 15
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Please help me I have 2 questions.
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.. A = (1/2)*h*P
You also know that a regular pentagon's perimeter (P) is 5 times the length of one side (s).
.. 37.2 m^2 = (1/2)*(3.2 m)*(5s)
.. 37.2 m^2 = (8 m)*s
.. (37.2 m^2)/(8 m) = s = 4.65 m
The length of one side is 4.65 m.
2) There are several ways you can figure this, all giving the same result.
a) The side length will be (12 cm)*√2, and the area is the square of that:
.. A = ((12 cm)*√2)^2 = 144 cm^2 * 2 = 288 cm^2
b) The area is half the product of the diagonal lengths.
.. A = (1/2)*(2*12 cm)^2 = (1/2)*576 cm^2 = 288 cm^2
c) The area is 4 times the area of the right triangle with sides of 12 cm.
.. A = 4*(1/2)*(12 cm)^2 = 2*144 cm^2 = 288 cm^2
d) The area is 4 times the area of one triangle with central angle 90°.
.. A = 4*(1/2)*(12 cm)^2*sin(90°) = 2*144 cm^2*1 = 288 cm^2
The area of the square is 288 cm^2.
PLEASE HELP ME ON THIS
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After receiving $42, the new domain (that Albert can afford) is from 80 to 147.
A tour group charges a flat price for a tour of up to 20 people. The cost per person varies inversely with the number of people. If five people pay 135 each, what must 15 people pay per person.
Answers
15 people must pay 45 unit currency each
Explanation:
Assume that the number of people is x and that the price per person is y.
We are given that the cost per person varies inversely with the number of people.
This means that as the number of people (x) increases, the cost per person (y) decreases and vice versa
This can be translated into the following equation:
y = k / x
where k is the constant of proportionality.
Now, we need to get k.
We are given that:
for number of people (x) = 5, the charge per person (y) is 135.
Substitute with this in the above equation to get k as follows:
y = k / x
135 = k / 5
k = 135 * 5 = 675
The equation now became:
y = 675 / x
Finally, we want to get the cost per person (y) when the number of people (x) is 15.
All we have to do is substitute in the above equation to get the y as follows:
y = 675 / x
y = 675 / 15
y = 45
This means that, for a group of 15 people, each one will pay 45 unit currency
Hope this helps :)
find the geometric mean of the pair of numbers 36 and 4
Answers
The geometric mean of the pair of numbers 36 and 4 is calculated by getting the square root of the product of the two numbers, which gives us the geometric mean as 12.
Explanation:To find the geometric mean of the pair of numbers 36 and 4, we use the formula for the geometric mean of two positive numbers, which is the square root of the product of the two numbers.
When we multiply 36 and 4 we get 144. So, the geometric mean of 36 and 4 is the square root of 144, which equals 12.
Therefore, the geometric mean of the numbers 36 and 4 is 12.
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Is it possible to take a cross section of a tetrahedron and get an octagon? Why or why not?
A.) Yes, because an octagon has eight sides, which is twice the number of faces on a tetrahedron.
B.) Yes, because a tetrahedron is symmetric about its center.
C.) No, because the only cross section that can result from a tetrahedron is a triangle.
D.) No, because the number of sides on the resulting shape cannot exceed the number of faces on the solid.
Answer: D.) No, because the number of sides on the resulting shape cannot exceed the number of faces on the solid.
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A tetrahedron is another name for a triangular prism. When you look at a tetrahedron it only has 4 different sides. If you take a cross section, the largest number of sides that you could have would be 4. There is no way to get an 8 sided octagon.
Option (D) No, it is not possible to take a cross section of a tetrahedron and get an octagon because the number of sides on the resulting shape cannot exceed the number of faces on the solid. A tetrahedron, having only four faces, cannot have a cross section with eight sides like an octagon.
The question asks if it is possible to take a cross section of a tetrahedron and get an octagon. A tetrahedron is composed of four triangular faces, six edges, and four vertices. It is the simplest of all the ordinary convex polyhedra and the only one with fewer than 5 faces. The provided options suggest various reasons why an octagon could or could not result from a cross section of a tetrahedron. The correct answer is D: No, because the number of sides on the resulting shape cannot exceed the number of faces on the solid.
A cross section that intersects a solid will typically not have more sides than the number of faces of the solid itself. Since a tetrahedron has only four faces, any cross-section made through it cannot naturally have more than four sides, thus it cannot result in an octagon, which has eight sides. The concept of symmetry or the fact that an octagon has twice as many sides as a tetrahedron does not relate to the possibility of such a cross section.
What is the domain of y = cos θ?
A. [-1, 1]
B. [0, infinity]
C. All real numbers
D. 2pi,
Answers
Answer:
Option C - All real numbers
Step-by-step explanation:
Given : Function [tex]y=\cos \theta[/tex]
To find : The domain of given function ?
Solution :
Domain is defined as the set of values for which function is defined.
We have given the function,
[tex]y=\cos \theta[/tex]
We know, for any value of [tex]\theta[/tex] the function [tex]y=\cos \theta[/tex] is defined.
Which means the set of all real numbers defined the given function i.e. [tex]x\in(-\infty,\infty)[/tex]
Therefore, Option C is correct.
The domain of [tex]y=\cos \theta[/tex] is all real numbers.
maria is planning a triangular garden she wants to build a fence around the garden to keep out the rabbits. the length of one side of the garden is 29 feet. if the angles of this side are 65 and 44 find the length of the fence needed to enclose the garden
Answers
Approximately 85.323 feet of fence is needed to enclose the garden.
To find the length of the fence needed to enclose Maria's triangular garden, we can use the Law of Sines since we know one side length and its opposite angle.
The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant:
[tex]\[ \frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)} \][/tex]
Where:
- a, b, c are the side lengths of the triangle.
- A, B, C are the angles of the triangle.
Given that one side length is 29 feet and its opposite angle is 65°, let's denote the other two angles as B and C . Since the sum of angles in a triangle is 180°, we can find angle C as 180° - 65° - 44° = 71°.
Now, we can use the Law of Sines to find the lengths of the other two sides:
[tex]\[ \frac{29}{\sin(65°)} = \frac{b}{\sin(44°)} \][/tex]
Solving for b:
[tex]\[ b = 29 \times \frac{\sin(44°)}{\sin(65°)} \][/tex]
b ≈ [tex]24.438 \text{ feet} \][/tex]
Similarly, we can find the length of side c using the same formula:
[tex]\[ \frac{29}{\sin(65°)} = \frac{c}{\sin(71°)} \][/tex]
[tex]\[ c = 29 \times \frac{\sin(71°)}{\sin(65°)} \][/tex]
c ≈ [tex]31.885 \text{ feet} \][/tex]
Finally, to find the total length of the fence needed, we sum up the lengths of all three sides:
[tex]\[ \text{Total fence length} = 29 + 24.438 + 31.885 \][/tex]
[tex]\[ \text{Total fence length}[/tex] ≈ [tex]85.323 \text{ feet} \][/tex]
So, approximately 85.323 feet of fence is needed to enclose the garden.
Suppose you invest $500 at an annual interest rate of 8.2% compounded continuously. How much will you have in the account after 15 years? (1 point)
$1,671.74
$17,028.75
$1,710.61
$8,140.92
Answers
A=Pe^(rt)
P=$500 r=8.2% n=15
A=500*e^(0.082*15)
=500*e^1.23
= 1710.61476814
Rounding off to the nearest hundredths, we have
A= $1,710.61
The expanded form 700,000 + 10,000+9 represents the whole number. 701,309. 713,009. 710,309. 713,090.
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123456780-646472.657
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Carolina is mowing lawns for a summer job. For every mowing job, she charges an initial fee plus $6 for each hour of work. Her total fee for a 4-hour job, for instance, is $ 32.
Answers
Carolina's charges can be represented by the linear equation y = 8 + 6x, where x represents hours worked and y represents the total fee charged for the service.
Explanation:The subject this question pertains to is Mathematics, specifically linear equations. Carolina's job can be modelled by a linear equation, where the independent variable is the number of hours worked and the dependent variable is the total fee charged.
In this case, Carolina charges an initial flat fee plus $6 per hour worked. Her total charge for a 4-hour job is $32, which means her initial fee can be deduced by subtracting four times her per-hour fee from the total fee, that is $32 - 4*$6 = $32 - $24 = $8. Therefore, the linear equation that models Carolina's job is y = 8 + 6x, where x is the number of hours worked and y is the total fee charged.
This is similar to the linear equation that represents Svetlana's tutoring job in Example 12.4, where each tutoring session earns her a one-time fee of $25 plus $15 per hour of tutoring, modeled by the equation y = 25 + 15x.
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bracelet costs $8. Simone is also buying a necklace for her mother for $18. She believes that her total will be $98. Which expression could be used to estimate the reasonableness of Simone’s total? 8 × $8 + $10 8 × $8 + $18 10 × $8 + $20 10 × $10 + $10
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i hope i helps
"She believes that her total will be $ 98"
To get to this we have:
10 × $ 8 + $ 20
Rewriting:
10 × $ 8 + $ 20
$ 80 + $ 20
$ 100
Rate approximately equal to $ 98 with an extra $ 2.
Answer:
An expression that could be used to estimate the reasonableness of Simone's total is:
10 × $ 8 + $ 20