a. Plot the data for the functions f(x) and g(x) on a grid.
b. Identify each function as linear, quadratic, or exponential, and use complete sentences to explain your choices.
c. Describe what happens to the function values in each function as x increases from left to right.
d. At what value(s) of x are the function values equal? If you cannot give exact values for x, give estimates.
Answers
For the given tables, we have that:
a. The grids are given at the end of the answer.
b. The functions are classified as follows: f(x) exponential, g(x) linear.
c. When x increases by one unit from left to right, we have that:
f(x) is multiplied by 4.g(x) is increased by 1.d. The functions are equal for a value between 1 and 2, as at x = 1 g(x) is greater while at x = 2 f(x) is greater.
Exponential and linear functionsThe difference between exponential and linear functions is in the rate of change, as:
Linear functions change by a constant amount when x changes by 1.Exponential functions change by a common ratio when x changes by 1.Hence the functions are classified as follows:
f(x) exponential: when x increases by 1, y is multiplied by 4.g(x) linear: when x increases by 1, y increases by 1.We have one exponential and one linear function, so it is quite difficult to solve an equation to verify where they are equal. We have that:
At x = 1, g(x) > f(x).At x = 2, f(x) > g(x).This means that at one point between x = 1 and x = 2, they intersected, that is, they had the same function values.
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Related Questions
How many terms are in this expression?
7a+ 1 + 8b
Answers
Answer:
3
Step-by-step explanation:
There are 3 terms. The terms are separated by + signs. They can also be separated by - signs.
The terms are 7a, 1, 8b.
If there was a minus sign in front of the term you need to keep it with the term because it is a negative term.
Answer:
There are a total of 3 terms
Step-by-step explanation:
A term is either a single number or variable, or the product of several numbers or variables. Terms are separated by a + or - sign in an overall expression. We are basically counting how many individual mathematical expressions
7a is a term
1 is a term, and it's a constant
8b is a term
Which statement best describes how to slice a cone so that the resulting cross section is an ellipse
Answers
Cutting at less than a right angle to the axis but more than the angle made by the side of the cone produces an ellipse.
Therefore, with this above statement, the statement which best describes how to slice a cone so that the resulting cross-section is an ellipse is
A plane slicing the cone diagonally without intersecting the base
The correct option, therefore, is OPTION B
Colton has $67,696 in a savings account that earns 2% interest per year. The interest is not compounded. How much interest will he earn in 1 year?
Answers
Colton has $67,696 in a savings account that earns 2% interest per year. The interest is not compounded. How much interest will he earn in 1 year?
we know that
2%=2/100=0.02
so
To find out the amount of interest, multiply the total amount by the percentage in decimal form
(67,696)*0.02
=$1,353.92Determine whether the given value is from a discrete or continuous data set.When a car is randomly selected, it is found to have a gas tank that can hold 19.9 gal.
Answers
Explanation
We are asked to determine if the question is a continuous or discrete data set
The discrete data set is a data set that can be counted
Continuous data set are data that can be measured
For the given question, the answer will be option A
jim is six feet tall, and his shadow is $16$ feet long. the flagpole he is standing next to casts a shadow that is $72$ feet long. how tall is the flagpole, in feet?
Answers
The height of the flagpole is 27 feet.
Given,
If two triangles are similar, sides of these triangles will be proportional.
Height of the flagpole = h feet
Shadow castes by the flagpole = 72 feet
Height of the person = 6 feet
Shadow casted by the person = 16 feet
By using the property of similar triangles,
Hence, h/6 = 72/16
h = (6×72)/ 16
h = 27 feet
Therefore, The height of the flagpole is 27 feet.
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Element X decays radioactively with a half life of 5 minutes. If there are 860 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 230 grams? y = a(.5) k
Answers
The amount of time it would take Element X to decay to a mass of 230 grams is 9.5 minutes.
How to determine the amount of time to decay?Mathematically, the mass of a radioactive element that is remaining after time (t-hours) is given by this exponential function:
A(t) = A₀·e^{t/τ}
Where:
A(t) represents the mass remaining or current mass measured in grams.A₀ represents the initial mass measured in grams.τ is the time constant measured in minutes.t represents the half-life or time to decay measured in minutes.Next, we would determine the time constant by using this mathematical expression:
Time constant, τ = t/ln2
Time constant, τ = 5/0.6932
Time constant, τ = 7.2130 minutes.
Now, we can determine the amount of time to decay by making half-life (t) the subject of formula as follows:
A(t) = A₀·e^{t/τ}
Half-life, t = -τ·ln(A(t)/A₀)
Substituting the parameters into the formula, we have;
Half-life, t = -7.2130·ln(230/860)
Half-life, t = -7.2130 × ln(0.2674)
Half-life, t = -7.2130 × -1.3190
Half-life, t = 9.51 ≈ 9.5 minutes.
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G(x)=|x-2|
How do u solve this?
Answers
Your weekly base salary is $150. You earn $20 for each cell phone that
you sell.
a. What is the minimum amount you can earn in a week?
b. Write and solve an inequality that represents the number of cell phones
you must sell to make at least $630 a week.
c. Write and solve an inequality that represents the number of cell phones
you must sell to make at least $750 a week.
d. The company policy is that as a part-time employee, the maximum
you can earn each week is $950. Write and solve an inequality that
represents the number of cell phones you can sell each week.
Answers
The minimum that could be earned is $150. The required inequalities are solved below:
What is an inequality?
An inequality in mathematics is a relationship that makes a non-equal comparison between two integers or other mathematical expressions. It is most commonly used to compare the sizes of two numbers on a number line. There are multiple notations used to denote various types of inequalities: The symbol a b indicates that an is smaller than b. The symbol a > b indicates that an is more than b. In either scenario, a and b are not equal. These are characterized as stringent inequalities because an is either strictly less than or strictly bigger than b. Equivalence is not allowed.
(a) The minimum that could be earned is $150.
(b) The required inequality is given as 150+20x≥630
or, 20x≥630-150
or, x≥480/20
or, x≥24
(c) The required inequality is given as 150+20x≥750
or, 20x≥750-150
or, x≥600/20
or, x≥30
(d) The required inequality is given as 150+20x≤950
or, 20x≤950-150
or, x≤800/20
or, x≤40
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10 < w/6 solve the inequality for w and simplify your answer as much as possible
Answers
Answer:
60
Step-by-step explanation:
10 x 6 < w
60 < w
that answers it
Answer: Multiply to remove the fraction, then set equal to
0
and solve.
Inequality Form:
w
>
60
Interval Notation:
(
60
,
∞
)
A blueprint for the floor of a natural history museum is shown.
The scale of the museum to the blueprint is 20 yd to 1 in. What
is the area of the floor of the actual Great Hall?
Answers
The journey through the difficult process of learning to read is described by the Reading Scale. It provides teachers with different perspectives on and analytical tools for their observations of children's growing abilities, knowledge, and comprehension of the reading process.
Give an example to explain what scale is.Develop Areas Dinosaur Special Using Scale Read the issue below and attempt to resolve it.
Wonderful exhibit hall A natural history museum's floor plan is displayed.
3/4 in The The museum is 20 yards to one inch in scale with the blueprint.
What Ocean Hall's floor area is the genuine Great Hall's?Space 3/4 in TRY IT Math Resource Kit paper with two sets of numbers, a grid, ribbon, and yarn ADVERTISE IT Why did you select that method of location, for example?
Share: I used the approach I did because.
3/4 : 20 yds
3/4 ×20/1 ÷60/4 = 15 yds
1 (3/4) = 7/4
7/4 × 20/1 = 140/4 = 35 yds.
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The area of a rectangular field is 5082 yd². If the length of the field is 77 yards, what is its width?
Answers
Answer:
The width is 66 yardsStep-by-step explanation:
Area of rectangle formula:
A = lw, where l- length, w- widthGivenA = 5082 yd²,l = 77 yd.SolutionFind the width by substituting the given values:
5082 = 77ww = 5082/77w = 66 ydHELP PLEASE FASTTTTTTTT
Answers
I put it into a distance calculator.
Hope this will help.
Answer: I think it’s C
Karina is baking bread. she buys a small bag of flour that contains 2 2/3 cups of flour. the recipe calls for 2 5/7 cups of flour. does she have enough flour to bake the bread? explain how she can compare the fractions to know for sure.
Answers
Using approximation, the two are the same and she contains enough flour.
What is meant by the unitary method?The unitary technique entails finding the value by multiplying the single value and then solving the problem using the initial value of a single unit. If an event may take place in m different ways and a second event can take place in n different ways after it, then the two events that follow can take place in m n different ways.
Given that Karina buys a small bag of flour that has 2 2/3 cups of flour. The recipe calls for 2 5/7 cups of flour.
1) 2 2/3 cups of flour.
= ((2 × 3)+2)/3
= 2.666
Therefore, she get 2.666
2) 2 5/7 cups of flour.
= ((2 × 7) + 5)/7
= 2.714
Therefore, she get 2.714
Using approximation, the two are the same and she has enough flour.
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Select all the intervals where f is decreasing.(Choice A)-5
Answers
Looking at the graph
we have that
Decreasing intervals are
(-infinite, -2.5) and (1.75, infinite)
so
Verify each option
A ----> is true
B ---> is not true
C ---> is true
D ---> is not true
The answer is A and CDetermine the coordinates of Q(6, −4) after a reflection in the line x=2
Answers
The coordinates of (6, -4) after a reflection in the line x = 2 are:
(-4, -4)
What are the coordinates after the reflection?If we have a point (x, y) and we do a reflection in the line x = a, the new coordinates of the point will be:
(a - x, y)
In this case, we have (6, -4) and the line of reflection is x = 2, then the coordinates after the reflection are:
(2 - 6, -4) = (-4, -4)
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for her final project, stacy plans on surveying a random sample of 50 students on whether they plan to go to florida for spring break. from past years, she guesses that about 10% of the class goes. is it reasonable for her to use a normal model for the sampling distribution of the sample proportion? why or why not?
Answers
It is not reasonable to use a normal model for the sampling distribution of the sample because the data doesn't meet the success or failure consideration.
How to illustrate the information?The sample has a size of 50 students. The probability that she guesses that about 10% of the class goes is 10%
This will be illustrated as:
1 - p = 1 - 10% = 1 - 0.10 = 0.90
np = 50 × 0.1 = 5. This implies the number of successes.
In this case, the number of successes is less than 10. This is because 5 is less than 10. Therefore, the data doesn't meet the condition.
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(b)The graph of y = g(x) is shown. Draw the graph of g(2x). Will award 100 Brainly points
The points of the graph is (0,0) (2,-4) and (4,-2)
Answers
Using the stated transformation, the graph of g(2x) is given at the end of the answer.
Horizontal stretch and compressionAn horizontal stretch or an horizontal compression happens when a constant is multiplied at the domain of the function, as follows:
g(x) = f(ax).
The definition of stretch or compression depends on the value of the constant a, as follows:
If a > 1, it is a compression by a factor of 1/a.If a < 1, it is a stretch by a factor of 1/a.In this problem, the rule is:
f(x) = g(2x).
Meaning that f(x) is an horizontal compression by a factor of 1/2 of g(x), and then the vertices are given as follows:
(0,0).(1,-4).(2,-2).That is, in each vertex, the x-coordinate was divided by 2, and thus the graph with these vertices is given at the end of the answer.
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A bag contains 3 red, 4blue, 4 yellow, and 5 green marbles only yellow marbles will be added tp the bag. how many yellow marbles should be added to the bag to make the probability of choosing yellow marble 1/3?
Answers
Two yellow marbles are added to the bag to make the probability of choosing a yellow marble 1/3 .
There is a bag containing five green marbles, three red marbles, and four blue marbles and four yellow marbles.
The probability that a given event will happen is expressed as a number between 0 and 1 where 0 means there is no chance of the event occurring and 1 means that the outcome is certain.
There are a total of 16 marbles in the bag (5 + 3+ 4+4 = 16). This means that the probability of drawing a marble of a particular color is the number of marbles of that color divided by the total number of marbles in the bag.
Let ‘x’ number of additional yellow marbles be added to the bag.
Then, the required probability will be
(4 + x )/ (16+x ) = 1/3
=> 3(4+x) =16 +x
=> 12+3x = 16+x
=> 2x =4
=> x= 2
Hence, the required number of marbles is 2.
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What are we missing in the triangle in the picture?
Answers
Looking at the triangle, we missing a side. This side represents the leg.
Now, we can find this missing side using the Pythagorean Theorem because the half represents a right triangle.
- The hypotenuse is the largest side, then hypotenuse = 5ft.
Using
quick Sarah is walking diagonally across a park as modeled by the equation y = x − 1. Suppose Marcus starts walking at the point (0, 9) so his path is perpendicular to Sarah's. At what point will Sarah's path and Marcus's path intersect?
Answers
The Sarah's path and Marcus path will intersect at the point (5,4) .
In the question ,
it is given that
the park is modeled by the equation y = x − 1 .
On comparing with the slope intercept form ,
we get
the slope as 1 .
Since both the paths are perpendicular ,
the slope for Marcus path is -1 .
hence the equation of line with slope -1 and passing through the point (0,9) is y = (-1)x + c
9 = (-1)0 + c
9 = c
so equation is y = (-1)x + 9
So to find the point of intersection , we solve both the equations .
Substituting y = x − 1 in y = (-1)x + 9 ,
we get
x − 1 = (-1)x + 9
x - 1 = -x + 9
x + x = 9 + 1
2x = 10
x = 5
So, y = 5 - 1 = 4
the point of intersection is (5,4) .
Therefore , The Sarah's path and Marcus path will intersect at the point (5,4) .
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How do I know when to subtract or add or divide when it comes to the end of the solution?
Answers
Given a rectangular peice of paper
Length = 34 cm
Width = 16 cm
So, the area of the rectangle = 34 x 16 = 544 cm²
Two semicircles cut out of it
The diameter of the circle = d = 16 cm
So, the radius of the circle = r = d/2 = 8 cm
The area of the two semicircles = area of the complete circle
so, the area of the circle = πr² = 3.14 x 8² = 200.96 cm²
So, the area of the remaining paper = area of the rectangle - area of the circle
= 544 - 200.96 = 343.04 cm²
So, the answer will be Area = 343.04 cm²
10 POINTS! PLS HELP! If 4 < a < 5 and 5 < b < 8, which of the following best describes a-b?
a) between -4 and -8
b) between -4 and 0
c) between 2 and 3
d) between -1 and 0
I don't know how to do this, so pls explain how to do it in your answer :)
Answers
Answer:
Between -4 and 0
Step-by-step explanation:
Hey! I saw your most recent and I'm assuming it is this question we're talking about it so let's help you with that!
Let's start by looking at what each of them mean, the first one means that 4 is lower than a but a is lower than 5 (Inequality 1) The second one means 5 is lower than b but b is lower than 8 (Inequality 2). Now, in order to find out [tex]a-b[/tex], we need to find the largest and smallest value of [tex]a-b[/tex]. The reason why we do this is because we want to look for the range of what [tex]a-b[/tex] can give us and in finding the largest and smallest value, if we were to evaluate both inequality 1 and 2 using [tex]a-b[/tex], we know that it can't be beyond the largest value or smaller than the lowest value.
In order to figure out the largest possible value of [tex]a-b[/tex], we need to take the maximum x value of inequality 1 and subtract it by the minimum y value of inequality 2, so we get:
[tex]5-5=0[/tex]
In order to figure out the smallest possible value of [tex]a-b[/tex], we need to take the minimum x value of inequality 1 and subtract it by the maximum y value of inequality 2, so we get:
[tex]4-8=-4[/tex]
So, in this case! The answer is b) between -4 and 0
Answer:
B
Step-by-step explanation:
in professional tennis, the length of time that the strings of a tennis racquet last is distributed uniformly anywhere from 5 to 30 days. given that the strings are still not broken on day 15 since they were strung, what is the probability that the strings will not break for at least another 10 days? round your answer to 2 digits after the decimal.
Answers
A travel trailer is bought at the price of $35,000. The value decreases at the rate of .25 every year (t). The exponential expression 35,000(0.75)t describes this situation. Find the value of the travel trailer after 5 years.
Answers
The value of the travel trailer after 5 years is $8306 .
in the question ,
it is given that
the price of the travel trailer(a) = $35000
rate of decrease(r) = 0.25
time (x) = 5 years
The exponential expression for the decrease in price after x years is given by the formula
price = a(1-r)ˣ
where, a is the initial amount ,
r is the decay rate ,
x is the time period .
Substituting the values from above in the formula ,
we get
price = 35000(1-0.25)⁵
= 35000(0.75)⁵
= 8305.664
≈8306
Therefore , the value of the travel trailer after 5 years is $8306 .
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Please someone answer this ty! :)
Answers
Answer:373248
Step-by-step explanation:
Answer:
Step-by-step explanation:
12*6=72
72^3=373248
freddy is having a fall harvant party for his friends they have 30 to decorate and 36 sets of material to make mini scarecrows how many kids decorate pumpkins and make scarecrows if he wants each person to have the same amount of crafts with nno left overs material
Answers
Based on the highest common factor, the number of kids that can decorate 30 pumpkins equally and make scarecrows from the materials without leftovers is 5.
What is the highest common factor?The highest common factor (HCF) is the number that can divide between 30 and 36 without a remainder.
Pumpkins Materials
Units 30 36
HCF 6 6
Average used 5 6
Thus, dividing 30 and 36 by their HCF of 6, respectively, shows that 5 kids can decorate the 30 pumpkins using 6 materials each to make the scarecrows.
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The number of kids who can decorate 30 pumpkins equally and make scarecrows from the materials without leftovers would be; 5.
What is factorization?factorization is the method of breaking a number into smaller numbers that multiplied together will give that original form.
The highest common factor (HCF) is defined as the number which can divide between 30 and 36 without a remainder.
Given that they have 30 to decorate and 36 sets of material to make mini scarecrows.
Their HCF is 6. The averages used are 5 and 6 respectively.
Hence, their HCF of 6, shows that 5 kids can decorate the 30 pumpkins by using 6 materials each to make the scarecrows.
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Sydney has a quarters and y dimes, having no less than 18 coins worth a maximum of $3.60 combined. A minimum of 4 of the coins are quarters and at least 16 of the coins are dimes. Solve this system of inequalities graphically and determine one possible solution.
HELP ME ASAP PLEASE!!!
Answers
Step-by-step explanation:
x + y = 18 We have at least 4 quarters
0.25x + 0.1y = 3.6
If we graph both equations, the point of intersection will give us our answer.
In this case, the lines intersect at the point (12, 6) which means I have 12 quarters and 6 dimes. This solution is correct as it also satisfies the condition of having at least 4 quarters.
(got this from another website, maybe it's wrong..
Wishing you the best!! )
please help me fill in the boxes its due tomorrow
Answers
Answer:
1- 80 miles
2- 3 hours
3- 35 mph
4- 180 miles
5- 5 hours
6- 15 mph
Step-by-step explanation:
if you travel at 40 miles every hour, then in 2 hours you'll travel 80 miles.
What is the arithmetic mean between 15 and 7?
Answers
Answer:
11
Step-by-step explanation:
How to find the arithmetic mean:
Add all numbers together, and divide by the amount of numbers.
Ans: 15 + 7 = 22
22 ÷ by amount of numbers =
22 ÷ 2 =
11
Ans = 11
Which expressions are equivalent to 46 ?Choose all answers that apply:A6 + 2(b + 26)B36 +62(26)
Answers
hello
to solve this question, we just have to find the expression that is equal to 4b
option A
[tex]b+2(b+2b)=b+2b+4b=7b[/tex]option a is incorrect
let's look at option B
[tex]3b+b=4b[/tex]option B is correct
and finally option C
[tex]2(2b)=4b[/tex]option C is correct
from the calculations above, option B and C are the right answers