Decide whether the word problem represents a linear or exponential function. Circle either linear or exponential. Then, write the function formula.
Answers
a. The given table is
Notice, the value of x increases at equal intervals of 1
Also, the value of y increases at an equal interval of 3
This means for the y values the difference between consecutive terms is 3
Also, for the x values, the difference between consecutive terms is 1
Hence, the table represents a linear function
The general form of a linear function is
[tex]y=mx+c[/tex]Where m is the slope
From the interval increase
[tex]m=\frac{\Delta y}{\Delta x}=\frac{3}{1}=3[/tex]Hence, m = 3
The equation becomes
[tex]y=3x+c[/tex]To get c, consider the values
x = 0 and y = 2
Thi implies
[tex]\begin{gathered} 2=3(0)+c \\ c=2 \end{gathered}[/tex]Hence, the equation of the linear function is
[tex]y=3x+2[/tex]b. The given table is
Following the same procedure as in (a), it can be seen that there is no constant increase in the values of y
Hence, the function is not linear
This implies that the function is exponential
The general form of an exponential function is given as
[tex]y=a\cdot b^x[/tex]Consider the values
x =0, y = 3
Substitute x = 0, y = 3 into the equation
This gives
[tex]\begin{gathered} 3=a\times b^0 \\ \Rightarrow a=3 \end{gathered}[/tex]The equation become
[tex]y=3\cdot b^x[/tex]Consider the values
x =1, y = 6
Substitute x = 1, y = 6 into the equation
This gives
[tex]\begin{gathered} 6=3\cdot b^1 \\ \Rightarrow b=\frac{6}{3}=2 \end{gathered}[/tex]Therefore the equation of the exponential function is
[tex]y=3\cdot2^x[/tex]c. The given table is
As with (b) above,
The function is exponential
Using
[tex]y=a\cdot b^x[/tex]When
x = 0, y = 10
This implies
[tex]\begin{gathered} 10=a\cdot b^0 \\ \Rightarrow a=10 \end{gathered}[/tex]The equation becomes
[tex]y=10\cdot b^x[/tex]Also, when
x = 1, y =5
The equation becomes
[tex]\begin{gathered} 5=10\cdot b^1 \\ \Rightarrow b=\frac{5}{10} \\ b=\frac{1}{2} \end{gathered}[/tex]Therefore, the equation of the exponential function is
[tex]y=10\cdot(\frac{1}{2})^x[/tex]
Related Questions
Debra will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $50 and costs anadditional $0.15 per mile driven. The second plan has an initial fee of $59 and costs an additional $0.11 per mile driven.for what amount of driving do the two plans cost the same? i need the answer for miles and cost
Answers
First plan cost is modeled as:
50 + 0.15x
where x are the miles driven
Second plan cost is modeled as:
59 + 0.11x
If the two plans cost the same, then:
50 + 0.15x = 59 + 0.11x
0.15x - 0.11x = 59 - 50
0.04x = 9
x = 9/0.04
x = 225 miles
which corresponds to a cost of:
50 + 0.15*225 = $83.75
What is the value of sinθ given that (3, −7) is a point on the terminal side of θ?
Answers
Solution
[tex]\begin{gathered} \text{ using pythagoras theorem} \\ \\ OB=\sqrt{OA^2+AB^2}=\sqrt{3^2+7^2}=\sqrt{58} \\ \\ \Rightarrow\sin\theta=\frac{AB}{OB}=-\frac{7}{\sqrt{58}}=-\frac{7\sqrt{58}}{58} \end{gathered}[/tex]Determine if the proportion is true 1/6= 3/18 Proportion is not true Proportion is true
Answers
Question: Determine if the proportion is true 1/6= 3/18
Solution:
we have the following equation that it may be true or false:
[tex]\frac{1}{6}\text{ = }\frac{3}{18}[/tex]But, the above equation is equivalent to:
[tex]1\text{ x 18 = 3 x 6}[/tex]But 1x 18 = 18, and 3x 6 = 18 so the above equation is equivalent to
[tex]18\text{ = 18}[/tex]The above equality always is true, so we can conclude that the proportion is true.
Suppose the purr of a cat has a sound intensity that is 320 times greater than the threshold level. Find the decibel value for this cats purr. Round to the nearest decibel.
Answers
The decibel value for this cats purr round to the nearest decibel is; 25
How to calculate the decibel level?Decibel (dB) is a unit for expressing the ratio between two physical quantities, such as measuring the relative loudness of sounds. One decibel (0.1 bel) is equal to 10 times the common logarithm of the power ratio.
Decibels are a unit of measure used to describe how loud a sound is. Now, I₀ is the intensity of threshold sound, which is sound that can barely be perceived by the human ear.
The loudness of a sound, in decibels, with intensity I is given by;
dB = 10 log₁₀(I/I₀)
We are given the intensity of a cat’s purr as I = 320I₀
Thus;
dB = 10 log₁₀(320I₀/I₀)
dB = 10 log₁₀(320)
dB = 25.05 ≈ 25
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At which of the following points do the two equations f(x)=3x^2+5 and g(x)=4x+4 intersect?A. (0,5)B. (1,8)C. (0,4) D. (8,1)
Answers
Given the equations:
[tex]\begin{gathered} f(x)=3x^2+5 \\ \\ g(x)=4x+4 \end{gathered}[/tex]Let's find the point where both equations intersect.
To find the point let's first find the value of x by equation both expression:
[tex]3x^2+5=4x+4[/tex]Now, equate to zero:
[tex]\begin{gathered} 3x^2+5-4x-4=0 \\ \\ 3x^2-4x+5-4=0 \\ \\ 3x^2-4x+1=0 \end{gathered}[/tex]Now let's factor by grouping
[tex]\begin{gathered} 3x^2-1x-3x+1=0 \\ (3x^2-1x)(-3x+1)=0 \\ \\ x(3x-1)-1(3x-1)=0 \\ \\ \text{ Now, we have the factors:} \\ (x-1)(3x-1)=0 \end{gathered}[/tex]Solve each factor for x:
[tex]\begin{gathered} x-1=0 \\ Add\text{ 1 to both sides:} \\ x-1+1=0+1 \\ x=1 \\ \\ \\ \\ 3x-1=0 \\ \text{ Add 1 to both sides:} \\ 3x-1+1=0+1 \\ 3x=1 \\ Divide\text{ both sides by 3:} \\ \frac{3x}{3}=\frac{1}{3} \\ x=\frac{1}{3} \end{gathered}[/tex]We can see from the given options, we have a point where the x-coordinate is 1 and the y-coordinate is 8.
Since we have a solution of x = 1.
Let's plug in 1 in both function and check if the result with be 8.
[tex]\begin{gathered} f(1)=3(1)^2+5=8 \\ \\ g(1)=4(1)+4=8 \end{gathered}[/tex]We can see the results are the same.
Therefore, the point where the two equations meet is:
(1, 8)
ANSWER:
B. (1, 8)
What is the average rate of change of the function f(x) = 2x^2 + 4 over the interval (-4,-1] ?
Answers
The average rate of change is:
[tex]\frac{f(-1)-f(-4)}{-1+4}=\frac{f(-1)-f(-4)}{3}[/tex][tex]f(-1)=2(-1^2)+4=6[/tex][tex]f(-4)=2(-4^2)+4=2(16)+4=36[/tex]then computing the first formula, the average rate of change of f(x) is
[tex]\frac{6-36}{3}=-10[/tex]Simplify 17(z-4x)+2(x+3z)
Answers
Answer:
23z-66x
Step-by-step explanation:
Look at the attachment please :D
LE Answer two questions about Systems A and B: System A System B 3.7 +12y = 15 x+4y=5 10y = -2 73 - 10y = -2 1) How can we get System B from System A? Choose 1 answer: A Replace one equation with the sum/difference of both equations B Replace only the left-hand side of one equation with the sum/difference of the left-hand sides of both equations C Replace one equation with a multiple of itself D Replace one equation with a multiple of the other equation 2) Based on the previous answer, are the systems equivalent? In other words, do they have the same solution? Choose 1 answer: А Yes B No
Answers
The first equation from System A is what is called a linear combination of the first equation of System B: the equation are equivalent.
System A equation is equal to the System B equation multiplied by a factor of 3 on both sides, so they contain the same information.
Answer: Yes. The systems are equivalent as their equations are equivalent.
determine the -domain- and -range- of the graphanswer in interval notation
Answers
Explanation: Let's consider two things
- Domain = represented by the minimum and maximum x-values
- Range = represented by the minimum and maximum y-values
Step 1: Let's take a look at the picture below
As we can see above
max x-value = + ∞
min x-value = - ∞
max y-value = 4
min y-value = - ∞
Final answer: So the final answer is
[tex]\begin{gathered} \text{domain}\Rightarrow(-\infty,+\infty) \\ \text{range}\Rightarrow(-\infty,4) \end{gathered}[/tex].
The Caldwell family placed a large back-to-school order online. The total cost of the clothing was $823,59 and the shipping weight was 32 lb. 10 oz. They live in the LocalZone (shipping = $5.87, plus $. 11 per lb. for each lb. or fraction of a lb. above 15 lbs.) and the sales tax rate is 7.5%. Find the total cost of the order.$864.43$876.77$893.21o $901.22None of these choices are correct.
Answers
The breakdown of fees paid by the Caldwell family are calculated and shown below;
[tex]\begin{gathered} \text{Total cost of clothing = \$823.59} \\ \text{Sales tax = 7.5\% of \$823.59} \\ =\frac{7.5}{100}\times823.59=61.769 \\ \text{Sales tax = \$61.77} \\ \\ \text{Shipping fe}e \\ \text{Total weight of item = 32lb 10oz }\approx\text{ 33lb} \\ \text{The excess weight above 15lbs = 33 - 15=18lbs} \\ \text{Shipping cost on the extra 18lbs = \$0.11}\times18=1.98 \\ \text{Total cost on shipping = \$5.87+\$1.98=\$7.85} \end{gathered}[/tex]The total cost of the order will now be
Total cost of clothing = $823.59
Shipping cost = $7.85
Sales tax = $61.77
TOTAL = $823.59 + $7.85 + $61.77 = $893.21
Therefore, the total cost of the order is $893.21
Choose the correct translation for the following statement.It must exceed seven.Ox<7Ox57Ox>7Ox27
Answers
Solution:
Given that a value or quantity must not exceed ten, let x represent the value or quantity.
Since it must not exceed 10, this implies that
[tex]x\leq10[/tex]The second option is the correct answer.
Zales sells diamonds for $1,100 that cost $800. What is Zales’s percent markup on selling price? Check the selling price.
Answers
Zales's percent markup on the selling price as required in the task content is; 37.5%.
Percentages and markup priceIt follows from the task content that the percent markup on the selling price be determined according to the given data.
Since the cost of diamonds is; $800 while the diamonds sell for $1,100. It follows that the markup on the selling price of the diamonds is;
Markup = Selling price - Cost price.
Hence, we have;
Markup = 1,100 - 800.
Therefore, the markup is; $300.
On this note, the percent markup can be determined as follows;
= (300/800) × 100%.
= 37.5%.
Ultimately, the percent markup on the diamonds is: 37.5%.
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Hurry Will give 75 points
(Score for Question 3: of 4 points)
3. The equation y = 14x describes the amount of money Louis earns, where x is the number of hours he works
and y is the amount of money he earns.
The table shows the amount of money Carl earns for different numbers of hours worked.
Carl's Earnings
Time (h)
Money earned
($)
Hours 3 5 8 10
Money 54 90 144 180
(a) How much money does Carl earn per hour? Show your work.
(b) Who earns more per hour? Justify your answer.
(c) Draw a graph that represents Carl's earnings over time in hours. Remember to label the axes.
Answer:
Carl earns 18 dollars an hour, we can get this by dividing the money earned by time which gets your answer.
Answers
Part a: Carl earning per hour is $18.
Part b: More Money is earned by Carl.
Part c: The graph that represents Carl's earnings is drawn.
What is termed as the equation?A mathematical statement consisting of two expressions joined by an equal sign is known as an equation. 3x - 5 = 46 is an example of an equation. We have the value for the variable x as x = 17 after solving this equation.For the given question,
The amount of the money Louis have is defined by the equation.
y = 14xx is the number of hours.y is the amount of money.Carl's Earnings
Time (h) Hours 3 5 8 10
Money earned($) 54 90 144 180
Part a: Carl earning per hour.
For 3 hours Carl earns $54.
For one hour-$54/3 = $ 18.
Part b: More Money is earned by-
For 1 hours Carl earns $8.
For 1 hour Louis earning is y = 14×1 = $14.
Thus, Carl earns more.
Part c: The graph that represents Carl's earnings over time in hours is drawn.
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3 1/2 berry and pinaple pies
times 2 rasberry pies
Answers
3 1/2 x 2 = 7
Determine the value for which the function f(u)= -9u+8/ -12u+11 in undefined
Answers
ANSWER
[tex]\frac{11}{12}[/tex]EXPLANATION
A fraction becomes undefined when its denominator is equal to 0.
Hence, the given function will be undefined when:
[tex]-12u+11=0[/tex]Solve for u:
[tex]\begin{gathered} -12u=-11 \\ u=\frac{-11}{-12} \\ u=\frac{11}{12} \end{gathered}[/tex]That is the value of u for which the function is undefined.
Please help me step by step
Answers
The value of the function f(x) at x = 0 is found as -1.
What is meant by the term function?A function is described as the connection between such a set of inputs that each have one output. A function is a relationship between inputs in which each input is linked to exactly one output. Every function does have a domain and a codomain, as well as a range. In general, a function is denoted by f(x), where x would be the input. A function's general representation is y = f(x). In mathematics, a function is a special relationship between inputs (the domain) and outputs (the codomain), where each input has precisely one output and the output could be traced all the way back to its input.For the given question,
The graph of the function f(x) = -x² + 4x - 1 is given.
For finding the value of f(x) at x = 0, check the y-coordinate of the graph when x = 0.
Put x = 0 in the given function.
f(0) = -0² + 40 - 1
f(0) = - 1
Thus, the value of the function f(x) at x = 0 is found as -1.
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cuales son los dos numeros enteros cuyo producto es 294 y cuyo cociente es 6?
Answers
1.- You need two equations
- x*y = 294
- x/y = 6
2.- Solve for x
x = 6y
(6y)y = 294
3.- Simplifying
6y^2 = 294
-Solve for y
y^2 = 294/6
Find the domain of the rational function.f(x)=x−1/x+4
Answers
Given:
[tex]f(x)=\frac{x-1}{x+4}[/tex][tex]\begin{gathered} \text{Let, x+4=0} \\ x=-4 \end{gathered}[/tex]Domain:
[tex]-\infty<-4<\infty[/tex][tex](-\infty,-4)\cup(-4,\infty)[/tex]Skis are listed by a manufacturer for $850, less trade discounts of 35% and 18%. What further rate of discount should be given to bring the net price to $446?
Answers
The Solution:
The listing price of the Skis by a manufacturer is $850.
A trade discount of 35% was allowed.
[tex]\begin{gathered} 35\text{ \% of \$850=0.35}\times850=\text{ \$297.50} \\ \text{Price}=850-297.50=\text{ \$552.50} \end{gathered}[/tex]Allowing an extra discount of 18%, we get
[tex]\begin{gathered} 18\text{ \% of \$}552.50=0.18\times552.50=\text{ \$99.45} \\ \text{Price}=552.50-99.45=\text{ \$453.05} \end{gathered}[/tex]We are required to find what further rate of discount should be given to bring the net price to $446.00
[tex]\begin{gathered} 453.05-446.00=7.05 \\ To\text{ find the required percentage of discount, we have} \\ \frac{7.05}{453.05}\times100=0.0155612\times100=1.55612\approx1.56\text{\%} \end{gathered}[/tex]Therefore, the correct answer is 1.56%
Convert: 1200 liters =kiloliters
Answers
We have from the question 1200 liters, and we need to convert it into kiloliters.
To find the equivalent in kiloliters to 1200 liters, we can proceed as follows:
1. Find the equivalent between these two measures:
[tex]1\text{ kiloliter=}1000\text{ liters}[/tex]2. Then we have:
[tex]\begin{gathered} 1200liters*\frac{1kiloliter}{1000liters}=\frac{1200}{1000}\frac{liters}{liters}kiloliters=1.2kiloliters \\ \\ \end{gathered}[/tex]Therefore, in summary, we can conclude that 1200 liters are equivalent to 1.2kiloliters.
The graph shows the depth, y, in meters, of a shark from the surface of an ocean for a certain amount of time, x, in minutes:A graph is titled Distance Vs. Time is shown. The x axis is labeled Time in minutes and shows numbers 0, 1, 2, 3, 4, 5. The y axis is labeled Distance from Ocean Surface in meters. A straight line joins the points C at ordered pair 0,66, B at ordered pair 1, 110, A at ordered pair 2, 154, and the ordered pair 3, 198.Part A: Describe how you can use similar triangles to explain why the slope of the graph between points A and B is the same as the slope of the graph between points A and C. (4 points)Part B: What are the initial value and slope of the graph, and what do they represent? (
Answers
We are given a graph that shows the depth in meters (y) as a function of the time in minutes (x).
Part A:
Points A, B, and their projection in the point (2, 110) form a similar triangle with the triangle formed by points A, C, and the point (2, 66).
write the equation of the line in slope-intercept form given the follow[tex]slope = - \frac{5}{4} \: y - intercept \: (0 \: - 8)[/tex]
Answers
Let's begin by identifying key information given to us:
[tex]\begin{gathered} slope=-\frac{5}{4}\: \\ y-intercept\: (0\: -8) \end{gathered}[/tex]The point-slope equation is given by:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-intercept\: (0\: -8)\Rightarrow(x_1,y_1)=(0,-8) \\ (x_1,y_1)=(0,-8) \\ m=-\frac{5}{4} \\ y-\mleft(-8\mright)=-\frac{5}{4}(x-0) \\ y+8=-\frac{5}{4}x-0 \\ y=-\frac{5}{4}x-8 \\ \\ \therefore\text{The slope-intercept form is }y=-\frac{5}{4}x-8 \end{gathered}[/tex]The side-by-side boxplots show consumer ratings of name brand and store brands of peanut butter.
name brands
al The median of name brands peanut butter is
grester thas the median of store
brands. (Hint* greater than or less than)
b) Approximately
% of name brands peanut butter data values are
greater than the median of the store brands peanut butter data values.
Answers
a. Median for name brands is greater than the median for store brands data values in the boxplots given.
b. Approximately 75% of the data values of name brands is greater than the median of the data values of store brands.
How to Find the Median of a Data in a Boxplot?A boxplot displays the distribution of a data such that the median is represented by the vertical line that divides the rectangular box.
25% of a data distribution is represented by the beginning of the edge of the box, while 50% is represented by the median, and 75% is represented by the point at the end of the edge of the box in the boxplot.
Therefore:
a. The median of name brands peanut butter is approximately 82-83.
The median of store brands is approximately less than 80.
Thus, we can conclude that, the median for name brands is greater than the median for store brands.
b. The median for store brands is approximately below 25% of the data values for name brands. Therefore, we would conclude that, approximately 75% of name brands data value are greater, compared to the median of the store brands data value.
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Find the sum of the arithmetic series given a₁ =A. 650B. 325C. 642D. 1266Reset SelectionPrevious Jixt45, an=85, and n = 5.
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: write the given details
[tex]a_1=45,a_n=85,n=5[/tex]STEP 2: Write the formula for calculating the sum of arithmetic series
STEP 3: Find the sum
By substitution,
[tex]\begin{gathered} S_n=5(\frac{45+85}{2}) \\ S_n=5(\frac{130}{2})=5\times65=325 \end{gathered}[/tex]Hence, the sum of the series is 325
4y - 6 = 2y + 8how to solve this equation
Answers
To solve this equation, we need to collect like terms
To collect like terms, we bring the terms similar to each other to the same side
In this case, the value having y will be brought to same side of the equation
Kindly note that if we are bringing a particular value over the equality sign, then the sign of the value has to change
This means if negative, it becomes positive and if positive, it becomes negative
Proceeding, we have
4y - 2y = 8 + 6
2y = 14
divide both sides by 2
2y/2 = 14/2
y = 7
The value of y in this equation is 7
A box of a granola contains 16.8 ounces . It cost $5.19 . What is the cost , to the nearest cent , of the granola per ounce ? A . $0.12 B . $0.31 C . $3.24
Answers
The cost per unit ounce is obtained by computing the quotient:
[tex]c=\frac{C}{N}.[/tex]Where:
• c is the cost per unit ounce,
,• C is the cost,
,• N is the number of ounces that you get for C.
In this problem we have:
• C = $5.19,
,• N = 16.8 ounces.
Computing the quotient, we get:
[tex]c=\frac{5.19}{16.8}\cong0.31[/tex]dollars per ounce.
Answer: B. $0.31
x + 4y = 4 2x + 4y = 8x=4y=-2
Answers
x + 4y = 4
2x + 4y = 8
x=4
y=-2
we know that
If a ordered pair is a solution of a equation, then the ordered pair must satisfy the equation
we have the ordered pair (4,-2)
Verify if the ordered pair is a solution of the given equations
Equation 1
x+4y=4
substitute the value of x and the value of y in the given equation
(4)+4(-2)=4
4-8=4
-4=4 ------> is not true
the ordered pair is not a solution of the equation
Equation 2
2x + 4y = 8
substitute the value of x and the value of y in the given equation
2(4)+4(-2)=8
8-8=8
0=8 -----> is not true
the ordered pair is not a solution of the equation
If A and B are two random events with probabilities of P(A) = 4/9, P(B) = 2/9, P(A ∩ B) = 1/9, calculate P(B|A).a.1/4b.3/4c. 1/2d.1
Answers
Answer:
A. 1/4.
Explanation:
Given two random events A and B:
[tex]\begin{gathered} P(B|A)=\frac{P(B\cap A)}{P(A)} \\ P(B\cap A)=P(A\cap B) \end{gathered}[/tex]Substitute the given values:
[tex]P(B|A)=\frac{\frac{1}{9}}{\frac{4}{9}}=\frac{1}{9}\div\frac{4}{9}=\frac{1}{9}\times\frac{9}{4}=\frac{1}{4}[/tex]The value of P(B|A) is 1/4.
The sum of two numbers is 40. If 2 is added to the larger number, theresult is equal to twice the smaller number. What are the two numbers?
Answers
We have 2 numbers. We can call them x and y, being x the smaller one.
The sum of this two numbers is 40, so we can write:
[tex]x+y=40[/tex]We know that if 2 is added to the larger number (that we name as y), the result is twice the smaller number, that would be 2x. Then, we can express this as:
[tex]y+2=2x[/tex]We can express y in function of x from the second equation and then replace it in the first equation to solve for x:
[tex]y+2=2x\Rightarrow y=2x-2[/tex][tex]\begin{gathered} x+y=40 \\ x+(2x-2)=40 \\ 3x-2=40 \\ 3x=40+2 \\ 3x=42 \\ x=\frac{42}{3} \\ x=14 \end{gathered}[/tex]Now, we can calculate y as:
[tex]\begin{gathered} y=2x-2 \\ y=2(14)-2 \\ y=28-2 \\ y=26 \end{gathered}[/tex]Answer: the two numbers are 14 and 26.
May I please get help with this math problem. I have been trying many times to find all correct answers to each length.
Answers
To draw a triangle, you cannot take three random line segments, they have to satisfy the triangle inequality theorems.
0. Triangle Inequality Theorem One: the lengths of any two sides of a triangle must add up to more than the length of the third side.
Procedure:
• Evaluating the first values given: (adding the two smallest values)
[tex]5.2+8.2=13.4[/tex]Now, we have to compare this addition with the bigger value. As 13.4 > 12.8, these can be side lengths of a triangle.
• Evaluating the second values given: (adding the two smallest values)
[tex]5+1=6[/tex]Comparing this addition with the bigger value, we can see that 6 < 10, meaning that these values cannot be side lengths of a triangle.
• Evaluating the third values given: (adding the two smallest values)
[tex]3+3=6[/tex]Comparing, we can see that 6 < 15. Therefore, these cannot be side lengths of a triangle.
• Evaluating the final values given:
[tex]7+5=12[/tex]We can see that 12 < 13, so these cannot be side lengths of a triangle.
Answer:
• 12.8, 5.2, 8.2: ,can be side lengths of a triangle.
,• 5, 10, 1: ,cannot be side lengths of a triangle.
,• 3, 3, 15: ,cannot be side lengths of a triangle.
,• 7, 13, 5: ,cannot be side lengths of a triangle.
