What is the range of the function f(x) = 3x2 + 6x – 9
The range of a function is the set of all possible output values. For the quadratic function f(x)=3x²+6x-9, because it forms an upward opening parabola, its range will start from its vertex point and continue to infinity. The range of this function will be y ≥ -6.
Explanation:This student is asking about the range of a given quadratic function. In the context of mathematics, the term 'range' refers to the set of all possible output values (y-values) of a function. For your function, f(x) = 3x² + 6x - 9, this is a quadratic function, so it forms a parabola when graphed. Given the positive coefficient of x², the parabola opens upwards.
Therefore, the lowest point (also known as the vertex) of the parabola will provide the minimum value of the range - since the parabola continues indefinitely upwards, there's no maximum value. For a quadratic function in the form f(x) = ax² + bx + c, you can find the x-coordinate of the vertex using the formula -b/2a.
Applying this to your function, we get x = -6 / (2*3) which simplifies to -1. You can then substitute this x-value into the function to find the minimum y value: f(-1) = 3*(-1)² + 6*(-1) - 9 = -6. Thus, the range of the function f(x) = 3x² + 6x - 9 is y ≥ -6.
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Is the fraction 1/15 a terminating or repeating decimal?
The fraction 1/15 is a repeating decimal because, when converted, it results in the repeating pattern 0.0666..., where the digit 6 repeats indefinitely.
When the fraction 1/15 is converted to a decimal, it results in the repeating decimal 0.0666..., where the digit 6 repeats indefinitely.
This happens because 1 divided by 15 gives a quotient of 0.0666..., and the 6 in the decimal representation repeats infinitely.
In other words, the division process doesn't terminate or end, and the same pattern of digits repeats endlessly after the decimal point.
This repeating pattern signifies that the fraction 1/15 cannot be expressed as a finite decimal and will always have repeating digits when written in decimal form.
Therefore, 1/15 is classified as a repeating decimal rather than a terminating one.
Rewrite the fraction as a decimal 57/5
factorise tis please.
[tex] (x+3)^{2} +2(x+3)[/tex]
Find each unit cost
$12 for 4 square yards
$3.45 for 3.7 oz
$9 for 5 L
Gretchen and Ezia received equal scores on a test made up of multiple choice questions and an essay. Gretchen got 18 multiple choice questions correct and received 19 points for her essay. Ezia got 15 multiple choice questions correct and received 31 points for her essay.
How many points was each multiple choice question worth?
Answer:
Each question had 4 points.
Step-by-step explanation:
Let the questions be x points each. As both Gretchen and Ezia received equal scores, we can write the equation as:
18x+19=15x+31 (Let the questions be x points each)
Solving for x;
[tex]18x-15x=31-19[/tex]
=> [tex]3x=12[/tex]
Dividing both sides by 3;
x = 4
Hence, each question had 4 points.
What is the slope of a line parallel to 10x - 5y = 8?
What is the slope of a line parallel to 4x + 2y = 5?
What is the slope of a line perpendicular to x - 3y = 9?
What is the slope of a line perpendicular to x - 5y = -10?
What is the slope of a line parallel to 4x + y = -1?
A) m = -5
B) m = 2
C) m = -3
D) m = -4
E) m = -2
Benny has saved 42 quarters from washing cars how many cents does Benny have
Rewrite the following without an exponent ₋7⁻¹.
Which of the following are true statements?
Check all that apply.
A. The graph of ƒ(x)=-1/2√x will look like the graph of ƒ(x)=√x but will reflect it about the x-axis and shrink it vertically by a factor of 1/2.
B. The graph of ƒ(x)=-1/2√x will look like the graph of ƒ(x)=√x but will shrink it horizontally by a factor of 1/2.
C. ƒ(x)=-1/2√x has the same domain but a different range as ƒ(x)=√x.
D. The graph of ƒ(x)=-1/2√x will look like the graph of ƒ(x)=√x but will shrink it vertically by a factor of 1/2.
...?
Answer:
A
C
Step-by-step explanation:
Here we must compare a function and its transformation, we will see that the correct options are A and C.
First, we must define the transformations that we will be using here.
Reflection about the x-axis:
For a function f(x) a reflection about the x-axis is written as:
g(x) = -f(x)
Vertical contraction.
For a function f(x) a vertical contraction of scale factor k is written as:
g(x) = k*f(x)
So here we start with:
ƒ(x)=√x
Then we reflect it about the x-axis to get:
ƒ(x)=-√x
Then we shrink it by a scale factor k = 1/2
ƒ(x) = (-1/2)*√x
From this, we can see that the correct options are:
A. The graph of ƒ(x)=-1/2√x will look like the graph of ƒ(x)=√x but will reflect it about the x-axis and shrink it vertically by a factor of 1/2.
And C is also true, because we have a reflection about the x-axis, the range changed from positive values to negative values, so:
C. ƒ(x)=-1/2√x has the same domain but a different range as ƒ(x)=√x.
Is also a correct option.
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Express this amount in dozens. (Use decimal form.) 7.5 cupcakes
...?
-17x 15 6x - 23 = 10 - 8x
what do real number include?
Suppose the first term of a geometric sequence is multiplied by a nonzero constant, c. What happens to the following terms in the sequence? What happens to the sum of this geometric sequence? (This question has one right answer.) Give an example of a geometric sequence to illustrate your reasoning. (Many answers are possible.)
6 times the sum of 3 consecutive odd intergers is -18
If 32% of a number is 64, what is the number?
A student reads 3/5 of a book in 30 minutes. if the student is reading at the same speed in 40 minute how much of the book will the student read
Choose what the expressions below best represent within the context of the word problem.
The length of a rectangle is 12 inches more than its width. What is the width of the rectangle if the perimeter is 42 inches?
x best represents .
x + 12 best represents .
The sum of the interior angles, s, in an n-sided polygon can be determined using the formula s = 180(n – 2), where n is the number of sides. Benita solves this equation for n and writes the equivalent equation n = s/180 + 2.
Using this formula, how many sides does a polygon have if the sum of the interior angles is 1,260°?
_______ sides
the answer is 9 hope it helps
$9.00 for 3 pairs of socks
If a 100(degree) arc of a circle has a length of 8 inches, to the nearest inch, what is the radius of the circle?
If you divide 6! by 4! you are evaluating
P(6, 4)
P(4, 6)
P(6, 2)
Lian and her younger sister Ella are 4 years apart. The sum of their ages is 20. Let l be Lian’s age in years and let e be Ella’s age in years. The system of linear equations that models the scenario is: l – 4 = e l + e = 20 How old is each sister?
Answer:
Lian is 12 years old and Ella is 8 years old.
Step-by-step explanation:
Lian and her younger sister Ella are 4 years apart.
The sum of their ages is 20.
Let L be Lian’s age in years.
Let E be Ella’s age in years.
The system of linear equations that models the scenario is:
[tex]L-4=E[/tex] this gives [tex]L=E+4[/tex]
[tex]L+E=20[/tex]
Putting L=E+4 in the second equation
[tex]E+4+E=20[/tex]
[tex]2E=20-4[/tex]
[tex]2E=16[/tex]
So, [tex]E=8[/tex]
Now we have , L+E=20
[tex]L+8=20[/tex]
So, [tex]L=12[/tex]
Therefore, Lian is 12 years old and Ella is 8 years old.
Is my answer correct?
Write an exponential function to model this situation: a population of 420 animals decreases at an annual rate of 21%. Then predict the value of the function after 5 years (to the nearest whole number).
Answer:
[tex]y=420\cdot (0.79)^x[/tex]
The value of the function after 5 years would be 129.
Step-by-step explanation:
We have been that a population of 420 animals decreases at an annual rate of 21%. We are asked to write an exponential function for our given problem.
We know that an exponential function is in form [tex]y=a\cdot b^x[/tex], where,
a = Initial value,
b = For decay b is in form [tex]1-r[/tex], where, r represents decay rate in decimal form.
[tex]r=21\%=\frac{21}{100}=0.21[/tex]
[tex]y=a\cdot (1-r)^x[/tex]
[tex]y=420\cdot (1-0.21)^x[/tex]
[tex]y=420\cdot (0.79)^x[/tex]
Therefore, our required function would be [tex]y=420\cdot (0.79)^x[/tex].
To find the value of the function after 5 years, we will substitute [tex]x=5[/tex] in our function.
[tex]y=420\cdot (0.79)^5[/tex]
[tex]y=420\cdot 0.3077056399[/tex]
[tex]y=129.236368758[/tex]
[tex]y\approx 129[/tex]
Therefore, the value of the function after 5 years would be 129.
tan inverse cos x/1-sin x
write in simplest form? ...?
Find the first four terms of the infinite sequence defined explicitly by the following rule.
f(n)= 4n - 2
Scott and Harry went cycling every day. They increased the number of minutes of cycling every week as described below:
Scott: Cycled for 10 minutes every day in the first week, 15 minutes in the second week, 20 minutes in the third week, and 25 minutes in the fourth week.
Harry: Cycled for 10 minutes every day in the first week, 20 minutes in the second week, 40 minutes in the third week, and 80 minutes in the fourth week.
Which statement best describes the methods used by Scott and Harry to increase the time they spent cycling?
A. Scott's method is linear because the number of minutes increased by an equal number every week.
B. Harry's method is linear because the number of minutes increased by an equal factor every week.
C. Both Harry's and Scott's method is exponential because the number of minutes increased by an equal factor every week.
D. Both Harry's and Scott's method is exponential because the number of minutes increased by an equal number every week.
Answer:
(A)
Step-by-step explanation:
Scott cycled for 10 minutes in first week, 15 minutes in second week,20 minutes in third week and 25 minutes in the fourth week which maintains a consistency in the line as there is consistent slope when drawn on a graph.
On, the other hand, harry cycled for 10 minutes in first week, 20 minutes in second, 40 minutes in third and 80 minutes in fourth week in which there is no consistency in the timings according to the weeks. Therefore, only, scott's method is linear as the number of minutes increased by an equal factor every week.
Translate the phrase into a math expression. twenty divided by the sum of 4 and 1.
Which type of cause and effect graphic organizer would be best to identify why we use gasoline in our cars today and what we might use as fuel in the future?
a. Timeline
b. Flow chart
c. Both of these
d. None of these
Answer: The answer is (a) Timeline.
Step-by-step explanation: We are given four options out of which one is the cause and effective graphic organiser that best identifies why we use gasoline in our cars today and what we might use as fuel in the future.
The best option is Timeline, because they show the order of events, an event's place in history and identify events which lead up to, or cause, other events.
Flowcharts does not serve the purpose, because they do not clearly identifies the cause.
Thus, the correct option is (a).
A flow chart would be the best graphic organizer to identify why we use gasoline in our cars today and potential future fuels, as it clearly presents causes and effects in a non-linear way.
Explanation:The type of cause and effect graphic organizer that would be most effective in identifying why we use gasoline in our cars today and what we might use as fuel in the future is a flow chart. A timeline would be helpful in demonstrating a chronological progression of fuels, but a flow chart allows you to clearly lay out causes and effects in a non-linear way, which is more suitable for this topic as it involves multiple possibilities for future fuels. It can visually present the reasons why we use gasoline now and the different options we have for future fuels, alongside their possible effects or outcomes.
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A room in the shape of a rectangular prism measures 15 feet by xx feet by 12 feet. Write a simplified expression for the volume (in cubic feet) of the room.
Volume ==
ft3