The table below shows the values of f(x) and g(x) for different values of x. One of the functions is a quadratic function, and the other is an exponential function. Which function is most likely increasing quadratically? x f(x) g(x) 1 3 3 2 6 9 3 11 27 4 18 81 5 27 243 f(x), because it grows faster than g(x) g(x), because it will not intersect f(x) g(x), because it grows slower than f(x) f(x), because it grows slower than g(x)
Answers
Answer:
D
Step-by-step explanation:
Exponential functions always will end up being bigger than quadratic functions and since g(x) is probably the exponential it makes f(x) the quadratic because it is growing slower than the function g(x)
The function g(x) increases faster than the function f(x). Then the correct option is D.
What is a function?The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.
The table below shows the values of f(x) and g(x) for different values of x.
One of the functions is a quadratic function, and the other is an exponential function.
The quadratic function f(x) will be
f(x) = ax² + bx + c
At x = 1, f(x) will be 3
a + b + c = 3 ...1
At x = 2, f(x) will be 6
4a + 2b + c = 6 ...2
At x = 3, f(x) will be 11
9a + 3b + c = 11 ...3
On solving equations 1, 2, and 3, we have
a = 1, b = 0, and c = 2
Then the quadratic function will be
f(x) = x² + 2
The exponential function g(x) will be given as
g(x) = abˣ
At x = 1, g(x) will be 3
ab = 3 ...4
At x = 2, g(x) will be 9
ab² = 9 ...5
From equations 4 and 5, we have
a = 1 and b = 3
Then the exponential function will be
[tex]\rm g(x) = 3^x[/tex]
More about the function link is given below.
https://brainly.com/question/5245372
Related Questions
can someone explain step by step what to do next? I am trying to find the vertex, focus, and directrix of this parabola.
y=2x^2
y=2x^2 im using this equation (x-h)^2=4p(y-k)
y/2=x^2
this is my problem I dont know where to put y/2 in the equation I am using
Answers
Answer:
Hey hi how are you can you be my friend please..Step-by-step explanation:
And can you give me a fever can you please just marks me as brainliests please..Answer:
Step-by-step explanation:
Parabola: y=2x²
Let say (a,b) the focus and y=k the directrix.
[tex]formula\ to\ use:\ \boxed{y=\dfrac{(x-a)^2}{2(b-k)} +\dfrac{b+k}{2} }\\\\\left \{\begin {array}{ccc}a&=&0\\2&=&\dfrac{1}{2(b-k)} \\\dfrac{b+k}{2} &=&0\\\end {array} \right.\\\\\\\left \{\begin {array}{ccc}a&=&0\\b-k&=&\dfrac{1}{4} \\b+k &=&0\\\end {array} \right.\\\\\\\left \{\begin {array}{ccc}a&=&0\\b&=&\dfrac{1}{8} \\k &=&\dfrac{-1}{8} \\\end {array} \right.\\\\\\focus=(0,\dfrac{1}{8} )\\\\directrix:\ y=\dfrac{-1}{8}[/tex]
What is the simplified form of square root 400 x to the power 100
Answers
Step-by-step explanation:
[tex]thank \: you[/tex]
Answer:
20x⁵⁰
Step-by-step explanation:
With the equation √400x¹⁰⁰
we need to take the square root away separately
√400 = √20*20 = 20
Then with x¹⁰⁰
√x¹⁰⁰ = √x⁵⁰*x⁵⁰ = x⁵⁰
So √400x¹⁰⁰ = 20x⁵⁰
hope this helps
Find the axis of symmetry of the graph of
y = x2 + 2x + 2
A- x= 1
B- y=1
C- x= -1
D- y=-1
Answers
Answer:
x = -1
Step-by-step explanation:
The graph's turning point is at ( -1 , 1 ), therefore the line of symmetry is at x = -1.
Answer: x = -1
Step-by-step explanation:
The formula to find the axis of symmetry in a function y = ax² + bx + c is:
[tex]x=\frac{-b}{2a}[/tex]
For y = x² + 2x + 2, where:
a = 1b = 2c = 2The axis of symmetry would be:
[tex]x=\frac{-b}{2a} =\frac{-2}{2(1)} =\frac{-2}{2} =-1[/tex]
Find the slope of the line tangent to the graph of x²+2xy² +3y=31 at the point (2, -3)
Answers
9514 1404 393
Answer:
22/21
Step-by-step explanation:
Taking the derivative, we have ...
2x·dx +2y²·dx +4xy·dy +3·dy = 0
dx(2x +2y²) +dy(4xy+3) = 0
At the given point, this is ...
dx(2·2 +2·(-3)²) +dy(4·2·(-3) +3) = 0
22dx -21dy = 0
dy/dx = 22/21
The slope of the tangent at the point of interest is 22/21.
A missile travels at a constant rate of 15,000
feet per minute. How many hours would it
take to travel 9.0 X 10^8(ten to the 8th power)feet?
Answers
Answer: 1000 hours.
Step-by-step explanation: To travel 9 x 10^8 feet, it would take (9 x 10^8)/15000 minutes. This equals 60000 minutes. We divide this number by 60 to convert to hours. This equals 1000 hours.
A 5 ounce bottle of juice cost $1.35 and an 8 ounce bottle of juice cost $2.16 a what is the unit cost per ounce of juice and b what is the better buy
Answers
Answers:
First bottle's unit cost = 27 cents per oz
Second bottle's unit cost = 27 cents per oz
Both have the same unit cost.
----------------------------------------
Work Shown:
unit cost = price/(number of ounces)
1st bottle unit cost = (1.35)/(5) = 0.27 dollars per oz = 27 cents per oz
2nd bottle unit cost = (2.16)/(8) = 0.27 dollars per oz = 27 cents per oz
Both lead to the same unit cost. Therefore, you can pick either option and it doesn't matter.
What is the area of the trapezoid shown below?
2
15
12
help fast please!!!
Answers
Answer:
78 units2
Step-by-step explanation:
The Area of the triangle is 54 units2
The rectangle on the side has an area of 24 units2.
Add them together, and you get 78.
I hope this helps!
pls ❤ and give brainliest pls
Please help me to find out the answer
Answers
9514 1404 393
Answer:
44.66 in
Step-by-step explanation:
The side opposite the marked angle is given, and the side adjacent to it is the one wanted. The relevant trig relation is ...
Tan = Opposite/Adjacent
Solving for the Adjacent side, we find ...
Adjacent = Opposite/Tan
PQ = (29 in)/tan(33°) ≈ 44.66 in
IV. Round to the nearest ten thousand
31. 41,876
32. 260,098
33. 91,975
34. 207,865
35. 462,876
Answers
40,000
260,000
90,000
210,000
460,000
Step-by-step explanation:
Look at the ten thousandth digit and determine if the number next to it to the right is greater than 5 or equal to 5 or less than 5. If greater than 5 or equal round up but if not round down
What is the three hundred and twenty six to the nearest ten
Answers
Hi there!
»»————- ★ ————-««
I believe your answer is:
330
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
We are rounding the number 326 to the nearest tens.
The '2' is in the tens place, and the '6' is to the right of the digit.
Since the '6' is greater than or equal to 5, then we would round up.
326 ≈ 330
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
14 a and b please help
Answers
Step-by-step explanation:
14a. One method is two solve for x. Edit: I accidentally press sent. Repost the question and I'll answer it.
Please help!!!!!!!!!!!!!!!
Answers
Step-by-step explanation:
[tex]\triangle{ABC}[/tex] is similar to [tex]\triangle{ADE}[/tex] so we can write the ratio
[tex]\dfrac{x}{6+4} = \dfrac{2}{6}[/tex]
Solving for x, we get
[tex]x = \left(\dfrac{2}{6}\right)(10) = \dfrac{10}{3}[/tex]
The mean number of years employees stay with a company is 12 years with a population standard deviation 4 years. The distribution of years has a left skewed shape. The probability that the mean years of staying in the company for a randomly selected sample of 36 will be more than 14 years is
Answers
Answer:
sorry for doesn't know the answer
40 points! Find the distance UV between the points U (2,-2) and V (-5, -3). Round your answer to the nearest tenth, if necessary.
Answers
[tex]\\ \sf\longmapsto UV=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]\\ \sf\longmapsto UV=\sqrt{(-5-2)^2+(-3+2)^2}[/tex]
[tex]\\ \sf\longmapsto UV=\sqrt{(-7)^2+(-1)^2}[/tex]
[tex]\\ \sf\longmapsto UV=\sqrt{49+1}[/tex]
[tex]\\ \sf\longmapsto UV=50[/tex]
Find the length of BC in the figure below.
Answers
And triangle ADC, ED=8 which is half of 12. So BC has to be half of AB, making length BC 6
Answer:
BC = 6 units
Step-by-step explanation:
In triangle ACD, BE || CD (given)
Therefore, by Basic Proportionality Theorem, we have:
[tex]\frac{AE}{ED} =\frac{AB}{BC} \\ \\ \therefore \: \frac{16}{8} = \frac{12}{BC} \\ \\ \therefore \: \frac{2}{1} = \frac{12}{BC} \\ \\ \therefore \: BC = \frac{12}{2} \\ \\ \therefore \: BC =6 \: units[/tex]
Please answer this and show the work/explain.
2/7m - 1/7 = 3/14
Answers
Please help almost done will give brainliest
x and y are related.
х
-2
-1
0
1
2
3
y
-4
-4.5
-5
-5.5
-6
-6.5
y = -0.5x + [?]
Enter the answer that belongs in [?].
Answers
Answer:
-5
Step-by-step explanation:
y = -0.5x + [?]
The equation is put in slope intercept form
slope intercept form: y = mx + b
where m = slope and b = y intercept
We want to find the y intercept.
the y intercept is the value of y when x = 0
looking at the table when x = 0, y = -5 so the y intercept is -5.
In other words -5 belongs in [?]
each week a train travels the same route 47 times about how many times does the train travel the route 43 weeks?
Answers
1,500 times
200 times
150 times
2,000 times
Answers
Answer:
Roughly 2,000 times
Step-by-step explanation:
47 x 43 = 2,021
Thank You
A triangle has two sides of lengths 8 and 10. What value could the length of
the third side be? Check all that apply.
Answers
Answer:
8, 10, 4, 7
Step-by-step explanation:
Missing side = x
Rules for x:
It should be less than the sum of the other two sides
It should be greater than the difference of the other two sides
8 + 10 = 18
10 - 8 = 2
2<x<18
8, 10, 4, 7
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Solve -9 < 4x + 3 5 19.
Answers
Answer:
C -3 < x ≤ 4
Step-by-step explanation:
-9 < 4x + 3 ≤ 19.
Subtract 3 from all sides
-9-3 < 4x + 3-3 ≤ 19-3
-12 < 4x ≤ 16
Divide by 4
-12/4 < 4x/4 ≤ 16/4
-3 < x ≤ 4
What's 955 ÷ 35 ?
[tex]955 \div 35[/tex]
Answers
Answer:
Hello
Step-by-step explanation:
955÷35
27.2857142857
Or
35/955
35)955(27
-945
________
10
I hope this works♥️
Solve for h: W = 5h - 90 (must show step by step)
Answers
Answer:
[tex]W = 5h - 90 \\ 5h = W + 90 \\ h = \frac{W + 90}{5} [/tex]
Answer:
h = w+90/ 5
Step-by-step explanation:
5h-90=w
5h/5= w+90/5
h= w+90/5
Let X1 and X2 be independent random variables. Suppose the mean and variance of X1 are 1 and 1, respectively. Suppose, the mean and variance of X2 are 4 and 8 respectively. What is the standard deviation of X2 - 3X1
Answers
Since X₁ and X₂ are independent, we have
Var[X₂ - 3X₁] = Var[X₂] + (-3)² Var[X₁]
Var[X₂ - 3X₁] = 8 + 9 × 1
Var[X₂ - 3X₁] = 17
Then the standard deviation of X₂ - 3X₁ is the square root of the variance, √17.
Help me with this question please...
Each of the following statements is true or false. Which statements are true?
A. A triangle where at least two angles are acute is called an acute triangle.
B. Some polygons are neither convex nor concave.
C. The sum of the interior angles of a concave pentagon is $540^{\circ}.$
D. The interior angles of a regular $1000$-gon are greater than the interior angles of a regular $100$-gon.
E. The exterior angles of a regular $1000$-gon are greater than the exterior angles of a regular $100$-gon.
Answers
9514 1404 393
Answer:
A. False
B. False
C. True
D. True
E. False
Step-by-step explanation:
A. False -- any triangle has at least two acute angles, whether it is acute, right, or obtuse.
B. False -- by definition, any polygon that is not convex is concave.
C. True -- the angle sum is the same regardless of whether the pentagon is convex or concave. (Provided it is a "simple" polygon, with no crossing sides.)
D. True -- the measure of the interior angle of a regular polygon increases as the number of sides increases. (see E)
E. False -- the exterior angles of a regular polygon are 360° divided by the number of sides. As the number of sides increases, the measure of each exterior angle decreases. (Interior angles are the supplement of exterior angles, so they increase as the number of sides increases.)
solve the absolute value 4=1+(2-1/4w)
Answers
Nathan saves 5 1/4% of his weekly salary. Naban earns $380.00 per week. How much
does he save per week?
.
A.$19.95
B.$20.52
C.$21.95
D.$25.20
Answers
Answer:
19.95
Step-by-step explanation:
Take the amount of his salary and multiply by 5 1/4 %
380 * .0525
19.95
given that general term 7n+4
evaluate sum of 5th term and 5th term
Answers
[tex]\boxed{\sf t_n=7n+4}[/tex]
We have to find 5th term[tex]\\ \sf\longmapsto t_5=7(5)+4[/tex]
[tex]\\ \sf\longmapsto t_5=35+4[/tex]
[tex]\\ \sf\longmapsto t_5=39[/tex]
Rotation 90° counterclockwise around the origin of the point (-8,1)
Answers
the mass of 2bags of beans and
3 bags of salt is 410kgs
if the mass of 3bags of beans and
2bags of salt is 390kg find the
mass of each item.
Answers
Answer:
70kg- weight of the bag of beans, 90 kg- weight of the bag of salt
Step-by-step explanation:
Suppose the mass of a bag of beans - x kg, the mass of a bag of salt - y kg
The mass 2 bags of beans 2x, The mass 3 bags of salt 3y
2x+3y= 410
The mass of 3 bags of beans 3x, for 2 bags of salt it is 2y
3x+2y=390
We have system of equations (the equations are simultaneous)
2x+3y=410
3x+2y=390
2x= 410-3y
x=205-1.5y
3* (205-1.5y)+2y=390
615-4.5y+2y=390
2.5y= 225
y=90- the mass of the bag of salt
x= 205 - 1.5*90= 205-135= 70- the mass of the bags of beans
Levi decides to examine the effect of fertilizer on the growth of tomato plants. He chooses four plants for his experiment and applies varying amounts of fertilizer to three of them. He does not apply fertilizer to one plant.
Over a 15-day period, the plants receive fertilizer on Days 1, 4, 7, 10, and 13. Levi measures the height of all of his plants with a meterstick on Days 3, 6, 9, 12, and 15. He also makes sure to hold all experimental factors constant except for the fertilizer.
What is the dependent variable in Levi's experiment on tomato plants?
the amount of fertilizer given to the plants
the measurements of plant height
the days fertilizer was applied
the days plant height was measured
Answers
Answer:
Number 1
Step-by-step explanation:
I can answer the first one! The dependent variable is the measurement. The days in the independent and always the X variable
Answer:
Step-by-step explanation:
The measurement of the plant height. That (presumably) is dependent on the amount of fertilizer. Everything else is held constant (such amount of water, amount of sunlight, even distance from a window (constant heat), is held the same for all plants.
