Answer:
The correct answer is The graph of f(x) is horizontally stretched.
Step-by-step explanation:
We can tell it is horizontally stretched by the fact that there is a coefficient of less than 1 in the front.
We know that (-4, 6) isn't a vertex, because it is in vertex form. The vertex is the opposite of the number being added to x and the y value is the constant. Since the constant is -6, it is not a vertex.
The negative coefficient in the front makes it open down, so it doesn't open up.
The domain should be all real numbers as there is no number that cannot be put into the equation.
Graph the function and analyze it for domain, range, continuity, increasing or decreaseing behavior, symmetry, boundedness, extrema, asymptotes, and end behavior.
f(x) = 3 * 0.2^x
Answer:
[tex]f(x) = 3 \cdot 0.2^x[/tex]
Step-by-step explanation:
[tex]f(x) = 3 \cdot 0.2^x[/tex]
Domain of f: "What values of x can we plug into this equation?" This makes sense for all real numbers so the domain is [tex]\mathbb{R}[/tex]
Range of f: "What values of f(x) can we get out of the function?" From the graph we see we can get any real number greater than 0 out of the function by choosing a suitable x-value in the domain. The range is therefore [tex](0, \infty)[/tex].
Continuity: Since the graph is one, unbroken curve (i.e. a curve that can be drawn in one movement without taking your pen off the paper). We see that "roughly speaking" the function is continuous.
Increasing or decreasing behaviour: For all x in the domain, as x increases, f(x) decreases. This means the function exhibits decreasing behaviour.
Symmetry: It is clear to see the graph of f(x) has no symmetry.
Boundedness: Looking at the graph we see it is unbounded above as when we choose negative values, the graph of f(x) explodes upwards exponentially. Choose a value of x, plug it in, next choose (x-1), plug this in and we observe [tex]f(x-1) > f(x)[/tex] for all x in the domain.
The function is however bounded below by 0: no value of x in the domain exists which satisfies [tex]f(x) < 0[/tex].
Extrema: As far as I can tell, there are no turning points on the curve. (Is this what you mean by extrema?)
Asymptotes: Contrary to the curve's appearance, there are no vertical asymtotes for this curve. The negative-x portion of the curve is just growing so quickly it appears to look like an asymptote. There is a value of f(x) for all x<0. There is however a horizontal asymtote: [tex]y=0[/tex].
End behaviour: As [tex]x \rightarrow \infty, f(x) \rightarrow 0[/tex]. As [tex]x \rightarrow -\infty, f(x) \rightarrow +\infty[/tex]
The function f(x) = 3*0.2^x is a decaying exponential function, with a domain of all real numbers and a range of (0, ∞). It is continuous, decreasing and has a horizontal asymptote at y=0.
Explanation:The function f(x) = 3*0.2^x is an exponential function with a base of 0.2. Here we're multiplying the function by a coefficient of 3.
Domain: The domain of an exponential function is always all real numbers. So, the domain is (-∞, ∞).
Range: Since this is a decaying exponential function, the output will always be between 0 (which will never actually be reached) and positive infinity. So, the range is (0, ∞).
Continuity: An exponential function is always continuous, meaning there are no holes or jumps in the graph.
Increasing or Decreasing Behavior: Since the base of the exponential (0.2) is less than 1, this function is always decreasing.
Symmetry: Exponential functions are not symmetric.
Boundedness: This function is bounded below by 0.
Extrema: There are no maximum or minimum points in this function. However, it is worth noting that the function gets closer and closer to y=0 as x goes to infinity, but never reaches it. This is sometimes considered a minimum.
Asymptotes: An asymptote is a line that the graph approaches but never reaches. For this function, the x-axis, or y = 0, is the horizontal asymptote.
End behavior: As x approaches positive infinity, y approaches 0; as x approaches negative infinity, y approaches positive infinity.
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What is the equation of the line in standard form which has slope -2/5 and y-intercept 10?
Answer: y = -2/5x + 10
Step-by-step explanation:
The equation of a line is y=mx+b. In this problem, m (the slope) is -2/5 and b (the y-intercept) is 10.
Me. Ellis is a teacher who tutors after school. Of the students he tutors, 30% need help in computer science and 70% need assistance in math. Of the students who need help, 40% are enrolled in Mr. Ellis's class during the school day. Of the students that need help in math, 25% are enrolled in his class during the day. What percent of the after school students are enrolled in Mr. Ellis's classes?
Answer: There are 82.5% after school students who are enrolled in his classes.
Step-by-step explanation:
Let the total number of students be 100
Percentage of students who need help in computer science = 30%
So, number of students who need help in computer science = 30
Percentage of students who need help in maths = 70%
So, number of students who need assistance in maths = 70
Of the students who need help,
40% are enrolled in Mr. Ellis's class during the school day,
So, it means 60% are enrolled in his class after the school day.
Number of students who are enrolled in his class after the school day = 60
Number of students who need help in Maths is given by
[tex]\frac{70}{100}\times 60=42[/tex]
Of the students that need help in maths, percent of students are enrolled in his class during the day = 25%
So, number of students who need help in maths and enrolled in his class after school hours
[tex]\frac{75}{100}\times 42=31.5[/tex]
Number of students who need help in computer science and enrolled in his class after school hours
[tex]\frac{30}{100}\times 60=18[/tex]
Therefore, there are [tex]31.5+18=49.5[/tex] students who joined his class after school hours,
Percentage of the after students who are enrolled in Mr. Ellis's classes is given by
[tex]\frac{49.5}{60}\times 100=82.5\%[/tex]
Hence, there are 82.5% after school students who are enrolled in his classes.
29.5% of the after-school students are enrolled in Mr. Ellis's classes.
1. Calculate the percentage of students who need help in computer science and are enrolled in his class:
- 30% of the students need help in computer science.
- 40% of those students are enrolled in his class during the school day.
[tex]\[ \text{Percentage of students needing help in computer science and enrolled in his class} = 30\% \times 40\% = 0.3 \times 0.4 = 0.12 = 12\% \][/tex]
2. Calculate the percentage of students who need help in math and are enrolled in his class:
- 70% of the students need help in math.
- 25% of those students are enrolled in his class during the school day.
[tex]\[ \text{Percentage of students needing help in math and enrolled in his class} = 70\% \times 25\% = 0.7 \times 0.25 = 0.175 = 17.5\% \][/tex]
3. Combine the two percentages to find the total percentage of after-school students enrolled in his classes:
- 12% of the total students are those who need help in computer science and are in his class.
- 17.5% of the total students are those who need help in math and are in his class.
Thus, the total percentage of after-school students enrolled in Mr. Ellis's classes is:
[tex]\[12\% + 17.5\% = 29.5\%\][/tex]
George does not like the fact that his neighborhood makes it mandatory to pay a yearly fee to use the pool. He conducts a survey of all the neighborhood families to help support his case that the yearly fee should be voluntary. The survey asks questions about pool usage and financial statistics of the families. Is this a valid survey? Why or why not?
A) No, George should only survey families that support his view.
B) No, George should attach information about why the fee should be voluntary.
C) Yes, since George is trying to convince the board to change the requirement he needs results to support his opinion.
D) Yes, since George is surveying all of the families in his neighborhood he is getting the opinions of the entire population.
Answer:
I would pick the letter C
Step-by-step explanation:
Solve the equation 22=2p -2
Answer:
p = 12
Step-by-step explanation:
add 2 to both sides of the equation
24 = 2p ( divide both sides by 2 )
p = 12
Answer: p=2
Step-by-step explanation:
22=2p-2
You add two to 22 which will give you 24
24=2p
You want to divide the 2 to get the letter by itself
12=2
A fruit stand has to decide what to charge for their produce. They decide to charge $5.30 for 1 apple and 1 orange. They also plan to charge $14 for 2 apples and 2 oranges. We put this information into a system of linear equations.
Can we find a unique price for an apple and an orange?
Answer:
We cannot find a solution to the system of equations.
a+b = 5.30
2a + 2b = 14
Step-by-step explanation:
Let a = the price of an apple
let b = price of an orange
a+b = 5.30
2a + 2b = 14
Multiply the first equation by 2
2a+ 2b = 10.60
Subtract the second equation
2a+2b = 10.60
-2a+2b = 14
---------------------------
0 = -3.40
This is never true so there is no solution
Answer:
Can we find a unique price for an apple and an orange?
Choose 1 answer:
CORRECT (SELECTED)
No; the system has no solution.
Step-by-step explanation:
See attached!
a business reports a net income of -6,291 over a 9 month period. What is the average income per month for that period
Find the range of values of x such that the quadratic function f(x)=(x+5)^2-16 is positive.
Answer:
f(x)=(x−5)2−16
Set the polynomial equal to y
to find the properties of the parabola.
y=(x−5)2−16
Use the vertex form, y=a(x−h)2+k
, to determine the values of a, h, and k
.
a=1
h=5
k=−16
Since the value of a
is positive, the parabola opens up.
Opens Up
Find the vertex (h,k)
.
(5,−16)
Find p
, the distance from the vertex to the focus.
Tap for more steps...
14
Find the focus.
Tap for more steps...
(5,−634)
Find the axis of symmetry by finding the line that passes through the vertex and the focus.
x=5
Answer:
x > -1 or x < -9
Step-by-step explanation:
(x + 5)^2 must be > 16 for f(x) to be positive.
(x + 5)^2 > 16
Taking square roots:-
x + 5 > 4
x > -1 (answer)
or x + 5 < -4
x < -9 (answer)
ll the members of a construction crew work at the same pace. Six of them working together are able to pour foundation in 22 hours. a How many hours would this job take if the number of workers decreased by factor of 2?
Answer:
44 hours
Step-by-step explanation:
Decreasing the people by a factor of 2 means we have 3 people
The job takes 6* 22 = 132 people hours
When we decrease the people, it will take more hours
132 people hours = 3 people * t hours
Divide each side by 3
132/3 = 3t/3
44 = t
It will take 44 hours
WHATS THE ANSWERS PLS TELL MEH PLS
Answer: 3) 9 7/10 (C)
4) 26 1/12 pounds (A)
5) 17 5/6 miles (D)
Answer:
3. C
4. A
4. D
Step-by-step explanation:
3)
When adding two fractions, you must add them with the same denominator. This means finding the lowest common multiple of 10 and 5, which is 50. Simply multiply each fraction by the denominator of the opposite fraction:
[tex]\frac{4}{5} * 10 = \frac{40}{50}[/tex]
[tex]\frac{9}{10} * 5 = \frac{45}{50}[/tex]
Add the two fractions together:
[tex]\frac{40}{50} + \frac{45}{50} = \frac{85}{50} = 1 \frac{35}{50} = 1 \frac{7}{10}[/tex]
7 + 1 + 1 + 7/10 = 9 7/10
4)
Again, make the denominator the same number by multiplying the fraction by the denominator of the other fraction:
[tex]\frac{3}{4} * 3 = \frac{9}{12}[/tex]
[tex]\frac{1}{3} * 4 = \frac{4}{12}[/tex]
9/12 + 4/12 = 13/12 = 1 1/12
10 + 15 + 1 + 1/12 = 26 1/12
5)
Again, multiply the fraction by the denominator of the opposite fraction:
[tex]\frac{1}{2} * 3 = \frac{3}{6}[/tex]
[tex]\frac{1}{3} * 2 = \frac{2}{6}[/tex]
3/6 + 2/6 = 5/5
7 + 6 + 4 + 5/6 = 17 5/6
evaluate each using the values given.
(z)(yx)^2+z; use x=2,y=2, and z=2
A.40
B.36
C. 34
D. 35
Put the values of x = 2, y = 2 and z = 2 to the expression (z)(yx)²+z:
[tex](2)(2\cdot2)^2+2=(2)(4)^2+2=(2)(16)+2=32+2=34[/tex]
Answer: C. 34Emily and a friend bought 2 tickets to see a soccer game each ticket costs 8.25 dollars the friends paid a toatal of 24.50 dollars which included a parking fee what percent increase represents the change when the parking fee is included?
Answer:
48 percent increase
Step-by-step explanation:
in the diagram, HE ||GF. Find DF
Answer:
WOwwwzerzzzzZZZZZZZZZZZZZZZZZZZZ
50 is 125% of what number? 12.5 40 62.5 112.5
Answer:
40
Step-by-step explanation:
divide by 5 if there is a decimal it is wrong
12.5/5=2.5
62.5/5=12.5
40/5=8
112.5/5=22.5
(8/9)^-2 without an exponent
Answer:
81/64 or 1 17/64
Step-by-step explanation:
A negative exponent means to flip the fraction
(8/9) ^-2
(9/8)^2
81/64
Changing this to a mixed number
1 17/64
Carrie is looking for a job cutting hair. One option is self-employment at The Belmont Salon, where she would pay $438 per month to rent a station and keep all her earnings. Another option is to work at a franchise, where she just have to pay $2 for every haircut. if she performed a certain number of haircuts every month, the amount paid to either salon would be the same. how much would Carrie pay? how many haircuts would that be? ( Can you also show the steps please?)
Answer:
She would have to do 219 haircuts in a month for the costs to be the same, which would be $428.
Step-by-step explanation:
To find this we take the costs of the first place.
$438
Next we can look at the costs of the second place using x as the number of haircuts she'd do.
2x
Now we can set the two equal to each other to find the number of cuts.
438 = 2x
219 = x
Carrie would pay $438 and perform 219 haircuts each month.
Explanation:To find out how much Carrie would pay and how many haircuts that would be, we need to set up an equation.
Let's assume the number of haircuts per month is x.
For self-employment at The Belmont Salon, Carrie would pay a fixed monthly rent of $438, so her total cost would be $438.
For the franchise option, Carrie would pay $2 for every haircut. So the total cost would be 2x.
Setting up the equation: 438 = 2x
To solve for x, we divide both sides of the equation by 2:
x = 438 / 2 = 219
Therefore, Carrie would pay $438 and perform 219 haircuts each month.
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Mary had 74 dollars to spend on 7 books after buying them she had 11 dollars how much did each book cost
Answer: Each book costs $9
Step-by-step explanation:
74-11 = 63
63 divided by 7 = 9
That's the answer
Answer: $9
Step-by-step explanation: 74 - 11 = 63. 63 divided by 7 equals 9. So each book cost $9
A scuba diver was swiming at an elevation of -8 meters. A shark was swimming at an elevation of -29 meters. Find the diffrence between these two elevations.
The difference in elevations between a scuba diver at -8 meters and a shark at -29 meters is calculated as: -8 - (-29) = 21 meters.
Explanation:The subject in question involves finding the difference in elevations. In this context, the scuba diver is swimming at an elevation of -8 meters, and the shark is at -29 meters. To find the difference, we subtract the lower number (-8) from the higher number (-29).
However, due to the negative signs, the difference will be calculated as follows: -8 - (-29) = -8 + 29 = 21 meters. Therefore, the difference in elevations between the shark and the scuba diver is 21 meters.
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NEED A FAST ANSWER
The graph shows the value of a car at different years after Gianna purchased it.
Which answer is the best estimate for the average rate of change between Year 4 and Year 9?
−$900/year
−$450/year
−$330/year
−$180/year
Answer:
Step-by-step explanation:
2.) −$180/year
The average rate of change between Year 4 and Year 9 is -$180 per year.
A linear equation can be used to represent a non linear line. A linear equation is of the form:
y = mx + b
where y, x are variables, m is the slope of the line and b is the y intercept.
Let y represent the value of car after x years.
From the graph, at year 4, y = 2300, hence it is (4, 2300). At year 9, y = 1400, hence it is (9, 1400). Therefore:
[tex]Average\ rate\ of\ change=\frac{1400-2300}{9-4}= - 180[/tex]
Hence the average rate of change between Year 4 and Year 9 is -$180 per year.
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Order the numbers least to greatest 73/100, 2/5, 1/10
Final answer:
To order the given fractions from least to greatest: 73/100, 2/5, 1/10, convert them to decimals and arrange them in increasing order: 0.1, 0.4, 0.73.
Explanation:
To order the numbers least to greatest, we compare their values. Let's convert these fractions to decimals first:
73/100 = 0.732/5 = 0.41/10 = 0.1Now that we have the decimals, we can arrange them from least to greatest:
0.10.40.73Which symbol is the correct symbol for the figure shown
Answer:
The answer is c:
Step-by-step explanation:
A: RS can mean anything
B: both line segment continue
D: the line segments continue in both directions
slope= 9; intercept= 2
Answer:
y = 9x + 2
Step-by-step explanation:
The equation of a line with slope m and y-intercept b is
y = mx + b
If you were asked to write the equation of the line with slope = 9 and y-intercept = 2, then the equation is
y = 9x + 2
Answer:
y = 9x -2
Step-by-step explanation:
I need help 9-16!!Thank u!
Answer:9-16=-7
Step-by-step explanation:
he isosceles triangle has a perimeter of 7.5 m. Which equation can be used to find the value of x if the shortest side, y, measures 2.1 m?
Answer:
2x+ 2.1 = 7.5
x=2.7
Step-by-step explanation:
The perimeter of an isosceles triangle with sides x and y is
2x+y = P
I put y as the single side since the question said y is the shortest side. It should say shorter sides if the two sides with the same length are smaller than the third.
We know y =2.1 and P = 7.5
Substituting these values in, we get
2x+ 2.1 = 7.5
Subtract 2.1 from each side
2x+2.1 -2.1 = 7.5 -2.1
2x= 5.4
Divide each side by 2
2x/2 = 5.4/2
x = 2.7 m
Solve using elimination
2x+3y=12
-4x-6y=-24
[tex]\left\{\begin{array}{ccc}2x+3y=12&|\text{multiply both sides by 2}\\-4x-6y=-24\end{array}\right\\\underline{+\left\{\begin{array}{ccc}4x+6y=24\\-4x-6y=-24\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad0=0\qquad TRUE\\\\2x+3y=12\qquad\text{subtract 2x from both sides}\\\\3y=12-2x\qquad\text{divide both sides by 3}\\\\y=4-\dfrac{2}{3}x\\\\Answer:\ \text{It's the dependent system of equations}\\\\\left\{\begin{array}{ccc}x\in\mathbb{R}\\y=4-\dfrac{2}{3}x\end{array}\right[/tex]
Solving the system using elimination reveals that the two equations are dependent, resulting in infinitely many solutions since they represent the same line. There is no unique solution for x and y.
To solve the system of equations 2x + 3y = 12 and -4x - 6y = -24 using the elimination method, we aim to eliminate one variable by combining the equations. First, notice that the second equation is exactly -2 times the first equation. If we multiply the first equation by 2, we would have identical left-hand sides but with opposite signs, which would cancel out when added together.
Multiplying the first equation by 2 gives 4x + 6y = 24. Now, add this new equation to the second equation:
4x + 6y = 24-4x - 6y = -24Adding them results in 0 = 0, which indicates that the two equations are dependent, and the system has infinitely many solutions. This is because each equation is a multiple of the other, and they both represent the same line. Therefore, we cannot isolate x or y to find a unique solution. The system is consistent and dependent.
Soft drinks cost $1.89 and refills cost $0.25 each. With $3.80 to spend on the soft drink and refills, what is the maximum number of refills that you can get? refills
Which graph shows a dilation of a rectangle with the scale factor of 8/3
Answer:
Step-by-step explanation:
Rules for Dilations. In geometry, a transformation is an operation that moves, flips, or changes a shape to create a new shape. A dilation is a type of transformation that enlarges or reduces a figure (called the preimage) to create a new figure (called the image)
Answer:
D
Step-by-step explanation:
Kyle got in the elevator on the 7th floor. He rode up 2 floors and then down 5 floors. Which expression represents the floor Kyle is on now?
Answer:
7+2-5=f
Step-by-step explanation:
If he starts on the 7 floor, then he is seven above ground, and that would clarify as a positive number. He then goes up 2 floors, which means we would add 2 to the original number. Going down five would mean we would subtract, because he is getting closer to zero, which is ground level. F represents the floor he is on now.
Hope this helps! (Brainliest please!)
answer
4th floor
Step-by-step explanation:
7+2-5=4
Susie is visiting China from the U.S. One day she stopped by a market and found a stall selling tomatoes for 15.65 yuan per kilogram. If 1 yuan was worth 0.14 dollars that day, how much did the tomatoes cost in dollars per pound? Fill in the first two blanks with two of the ratios. Then write your answer rounded to the nearest hundredth in the last blank.
Answer:
1st blank is 0,14 dollars/1yuan, and 2nd blank is 1kg/2.2lb
Step-by-step explanation:
The tomatoes at the Chinese market would cost approximately $0.99 per pound, following the currency conversion rate from yuan to dollars and the weights conversion rate from kilograms to pounds.
Explanation:To find the cost in dollars per pound from yuan per kilogram, we should use both the conversion rate from yuan to dollars and the conversion rate from kilograms to pounds. In this case, we are given that 1 yuan is worth 0.14 dollars and that 1 kilogram is approximately 2.20462 pounds. Therefore, the cost in yuans per pound would be 15.65 yuan/kg divided by 2.20462 lbs/kg, which equals approximately 7.09 yuan/pound. After converting it to dollars, it'd be approximately 7.09 yuan/pound times 0.14 dollars/yuan which gives us approximately $0.99 per pound.
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is (1,9) a solution to the inequality y>6x+3
Put the coordinates of the point (1, 9) to the inequality y > 6x + 3:
9 > 6(1) + 3
9 > 6 + 3
9 > 9 FALSE
Answer: It's not a solution.