The graph represents the function f(x) = x2 + 3x + 2. If g(x) is the reflection of f(x) across the x-axis, g(x) = . (Write the function in standard form. Use ^ to indicate an exponent.)
Answers
The reflection of the graph in the x-axis gives the function
g(x) = -x² - 3x - 2
The given function is of the form f(x) = x² + 3x + 2 which represents a parabola.
The vertex of the function is at (-3/2 , -1/4)
The focus is at ( 3/2 , 0 )
The axis of symmetry is 2x+3 = 0 and the directrix is at 2x + 1 = 0
Now when the parabola is reflected along the x-axis we get
the focus at ( -3/2 , 0 )
the vertex is at (-3/2 , 1/4)
Axis of symmetry remains the same
The directrix becomes 2y-1 =0
The red graph denotes the function f(x) while the blue graph denotes the function g(x) reflected on the x-axis.
Hence the reflection on the x-axis gives the function g(x) = -x² - 3x - 2
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Related Questions
the commission paid on goods for $4000 is $80. what is the percentage commission?
Answers
Answer:
percentage = 80÷4000=0.02
Let P be the set of integers that are multiples of 3 between 1 and 10 and Q be the set of positive integers that are multiples of 4 and are less than 15. Which of the following list of elements does not belong to the union of P and Q?
A. 5
B. 3
C. 6
D. 4
Answers
The union of the sets P and Q does not have the integer 5 since it is neither a multiple of 3 or a multiple of 4.
P is the set of integers between 1 and 10 and multiple of 3.
∴P = {3,6,9}
Q is the set of positive integers less than 15 and multiple of 4.
∴Q = {4,8,12}
Now the union of the sets P and Q is given by :
P∪Q = {3,4,6,8,9,12}
Now the union of the sets does not contain the integer 5.
Any collection of items, including a set of raw materials, the seven days of the week, several car types, etc., can be categorized as a set.
Any set component counts as an element of the set. Curly brackets are used to write a set. A very basic set would resemble something like this:
Q = {4,8,12}.
Therefore the integer 5 does not belong to the union of P and Q .
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The graph of y = f(x) is graphed below. What is the end behavior of f(x)?
Answers
Answer:
The third option, as x approaches infinity y approaches infinity and as x approaches negative infinity y approaches negative infinity.
Step-by-step explanation:
please help
The equation the quantity x plus 56 end quantity over 3 equals 5 times x models the workload of a class project, where x is the number of hours each student must contribute. How many hours does each student work on the project?
10 hours
9 hours
7 hours
4 hours
Answers
Each student should work for 7 hours on the project.
Given, the equation the quantity x plus 56 end quantity over 3 equals 5 times x models the workload of a class project,
where x is the number of hours each student must contribute.
Now, according to question,
56 - 3x = 5x
56 = 5x + 3x
8x = 56
x = 7
So, x = 7 hours
Hence, each student should work for 7 hours on the project.
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Answer:
4 hours
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Exact Form:
x = 14/3
Decimal Form:
x = 4.6
Mixed Number Form:
x = 4 2/3
Therefore, 4 hours is how much the students work on the project.
Describe the end behavior of each function using the leading coefficient and degree, and state
the domain and range.
1. f(x) = 3x^4
2.f(x) = -2x^3
3.f(x) = -1/2x^5
4.f(x)=3/4x^6
Answers
Answer:
1. y ⇒ ∞ as x ⇒ ∞ AND y ⇒ ∞ as x ⇒ -∞; Domain: (-∞, ∞); Range: [0, ∞)
2. y ⇒ -∞ as x ⇒ ∞ AND y ⇒ ∞ as x ⇒ -∞; Domain: (-∞, ∞); Range: (-∞, ∞)
3. y ⇒ -∞ as x ⇒ ∞ AND y ⇒ ∞ as x ⇒ -∞; Domain: (-∞, ∞); Range: (-∞, ∞)
4. y ⇒ ∞ as x ⇒ ∞ AND y ⇒ ∞ as x ⇒ -∞; Domain: (-∞, ∞); Range: [0, ∞)
Step-by-step explanation:
Rule for end behavior of polynomials:
(a) Positive leading coefficient, even degree: y ⇒ ∞ as x ⇒ ∞ AND y ⇒ ∞ as x ⇒ -∞
(b) Negative leading coefficient, even degree: y ⇒ -∞ as x ⇒ ∞ AND y ⇒ -∞ as x ⇒ -∞
(c) Positive leading coefficient, odd degree: y ⇒ ∞ as x ⇒ ∞ AND y ⇒ -∞ as x ⇒ -∞
(d) Negative leading coefficient, odd degree: y ⇒ -∞ as x ⇒ ∞ AND y ⇒ ∞ as x ⇒ -∞
Domain and range for a polynomial function with an odd degree will always be all real numbers, whether or not there's a constant or not.
Domain will always be all real numbers for a polynomial function with an even, whether or not there's a constant.
For a polynomial function with an even degree, the range will extend from the y-coordinate of the vertex to ∞, if the leading coefficient is positive
For a polynomial function with an even degree, the range will extend from -∞ to the y-coordinate of the vertex if the leading coefficient is negative.
I don’t know who it is please helppp
Answers
Triangle C forms a right angle triangle.
Given:
Triangle A : 8 cm , 13 cm , 5 cm
Triangle B : 14 cm , 30 cm , 17 cm
Triangle C : 26 cm , 10 cm , 24 cm
To form a right angled triangle the longest side square is equal to the sum of squares of other sides.
In triangle A :
[tex]13^{2} = 8^{2} +5^{2}[/tex]
169 = 64 + 25
169 ≠ 89.
This is not a right angle triangle.
In triangle B:
[tex]30^{2} =17^{2} +14^{2}[/tex]
900 = 289 + 196
900 ≠ 485
This is not a right angle triangle.
In triangle C:
[tex]26^{2} = 10^{2} +24^{2}[/tex]
676 = 100 + 576
676 = 676
so it is a right angle triangle.
Therefore Triangle C forms a right angle triangle.
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X= Y. Y = 3. Which statement below is true?
Answers
Answer:
X=3
Step-by-step explanation:
I'm not sure what statements below you want me to confirm that X=Y, Y=3
HFHFHFHHFHFHFHHHVHFHVHVHHVHVHHV
Answers
Jimmy is writing a paper for one of his classes. The paper has to be 3,000 words long, and so far he has written 786 words. If he only has 6 more days to write his paper and wants to write the same number of words each day, then how many words must he write per day to finish the paper?
Answers
Jimmy has to write 369 words per day for the next 6 days to finish the paper.
The total number of words in the paper has to be 3000
Jimmy has already written = 786 words.
3000-786 = 2214
So, Jimmy still has to write 2214 words.
He has 6 days to write the paper and he wants to write the same number of words per day.
With this in mind to find out how many words he has to write per day we can divide 2214 by 6.
2214/6 = 369 words
So, Jimmy has to write 369 words per day for the next 6 days to finish the paper.
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According to a study done by UCB students, the height for Martian adult males is normally distributed with an average of 65 inches and a standard deviation of 2.4 inches. Suppose one Martian adult male is randomly chosen. Let X = height of the individual. Round all answers to 4 decimal places where possible.
Answers
The probability that the person is between 67.1 and 68.3 inches, using the normal distribution, is of:
0.1056 = 10.56%.
Normal Probability DistributionThe z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation for the heights of UCB students are given as follows:
[tex]\mu = 65, \sigma = 2.4[/tex]
The probability that the person is between 67.1 and 68.3 inches is the p-value of Z when X = 68.3 subtracted by the p-value of Z when X = 67.1, hence:
X = 68.3:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (68.3 - 65)/2.4
Z = 1.38.
Z = 1.38 has a p-value of 0.9162.
X = 67.1:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (67.1 - 65)/2.4
Z = 0.88.
Z = 0.88 has a p-value of 0.8106.
0.9162 - 0.8106 = 0.1056 = 10.56%.
Missing informationThe problem asks for the probability that the person is between 67.1 and 68.3 inches.
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what is the same value as 8.76
Answers
Answer:
B, C
Step-by-step explanation:
A is incorrect, it should be seventy-six hundredths.
D is incorrect, the place value for the third term is wrong - it should be 0.06.
3-4x/9 = 9 Simplify your answers. Type an integer or a fraction. Use a comma to separate answers as needed.)
Answers
Answer:
"Multiply to remove the fraction then set it equal to 0 and solve."
Exact form
x = - 39/2
Decimal Form:
x = -19.5
Mixed Number Form:
x = - 19 1/2
Hope this helped...!
the ratio of aspens to panderosa pines in a part of a forest is 10 to 16.if there are 12 panderosas pines, how many Aspens are there?
Answers
Answer: 19.2, I think.
Step-by-step explanation: 10*1.2 = 12.
To keep the ratio balanced, you must also do 16*1.2, which is 19.2. Making the ratio 12 : 19.2
Brand A has a box of 25 forks for 1.99 and Brand B has a box of 42 totals for 3.89. What is the unit price for each brand and what brand is a better buy based on unit price
Answers
Answer:
Brand A
Step-by-step explanation:
Brand A has a box of 25 forks for 1.99
Take the price per fork
1.99 /25 = .0796
.08 per fork
Brand B has a box of 42 totals for 3.89
3.89 / 42
.092319048
.09 per fork
Valentina is trying to decide wether to join her schools swim team. During the summer the team practices 4 days per week. Each of those days, they practice for 3 hours in the morning and practice again in the afternoon. They practice for a total of 20 hours each week
Answers
The equation that can be used to find the length of the afternoon practice is B. 4(h + 3) = 20
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this case, during the summer the team practices 4 days per week and each of those days, they practice for 3 hours in the morning and practice again in the afternoon.
Let the afternoon practice be h.
Therefore, the equation will be:
4(h + 3) = 20
In conclusion, the correct option is B.
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Evaluate the equation:
6w = 180
W = ____
Answers
Answer:
30
Step-by-step explanation:
Divide each term in 6 w = 180 by 6 and simplify. w = 30
Answer:
w = 30
Step-by-step explanation:
Given equation,
→ 6w = 180
Now the value of w will be,
→ 6w = 180
→ w = 180/6
→ [ w = 30 ]
Hence, the value of w is 30.
How do i solve this equation -3 ≥ 1/2 + 11
Answers
Answer:
-3≥11.5
Step-by-step explanation:
-3≥1/2+11
-3≥11.5
Select the postulate that is illustrated for the real numbers. 3 + 2 = 2 + 3
Answers
Answer: Symmetry Property of Equality
The Student Council is having an election for its executive board, which consists of 3 positions—president, vice president, and secretary. If there are 11 members on the Student Council, how many different possibilities are there for selecting an executive board?
165
1,331
39,916,800
990
Answers
The different possibilities available for selecting an executive board in Student Council in election is 990 ways
How to find the number of ways of choosing the three officesIn permutation, order matters hence in choosing or making selection specific order should be followed. an instance here is arranging the 3 letters word from ABC. ₃P₃ = 6
ABCACBBACCABBCACBAThe problem is a permutation problem trying to select 3 from 11 where order matters. The order include choosing the president the ramainig position is left 2 for 10. and so on.
This is shown in permutation as follows
₁₁P₃ = 11! / (11 - 3)!
= 11! / 8!
= 990 ways
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Determine whether the series converges or diverges...
Answers
Answer:
Convergence
Step-by-step explanation:
Use the Squeeze Theorem,
I know that
[tex] \frac{k \sin {}^{2} (k) }{1 + k {}^{3} } [/tex]
lies between 0 and 1 so
[tex]0 \leqslant \frac{k \sin {}^{2} (k) }{1 + {k}^{3} } \leqslant \frac{k}{1 + k {}^{3} } [/tex]
The final series behaves like
[tex] \frac{1}{k {}^{2} } [/tex]
Using the p series, since p is 2, the series
[tex] \frac{k}{1 + k {}^{3} } \: converges[/tex]
Since the 0 and k/1+k^3 converges, the series converge.
Convergence
The wholesale cost of a dining room table at a furniture store is $1,115.80. The
markup for the table is 20%. What is the selling price of the dining room table?
Answers
Answer: $1338.96
Step-by-step explanation:
The wholesale cost means the cost that the store buys the table from the supplier. To find the price that the store sells it, it is a 20% markup.
The orginal price is $1,115.80. What is 20% of $1,115.80?
$1,115.80 * .20 = $223.16
Lets add the original price to the markup.
$1,115.80 + $223.16 = $1338.96
Hope this helps <3
In ΔQRS, s = 7.9 cm, ∠Q=125° and ∠R=23°. Find the length of q, to the nearest 10th of a centimeter.
Answers
The length of q, to the nearest 10th of a centimeter, is 8.8 cm.
We are given the following;
In ΔQRS, s = 7.9 cm, ∠Q=125° and ∠R=23°.
The third angle can be calculated using the angle sum property:
angle Q + angle R + angle S = 180 degrees
125 degrees + 23 degrees + angle S = 180 degrees
angle S = 180 - (125 + 23) degrees
angle S = 180 - 148 degrees
angle S = 32 degrees
To find the length of q we shall apply the Sine rule.
q / Sin Q = s / Sin S
q / Sin 125 = 7.9 / Sin 32
by cross multiplication we will get;
q = (7.9 x Sin 125) / Sin 32
q = (7.9 x 0.61) / 0.55
q = 8.8 cm (approximately)
So, the length of q is 8.8 cm.
Thus, the length of q, to the nearest 10th of a centimeter, is 8.8 cm.
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Yuson must complete 30 hours of community service. She does 2 hours each day. Which linear equation represents the hours Yuson has left after x days?
A. y=-2x+30
B. y=2x+30
C. y=-2x-30
D. y=2x-30
Answers
The linear equation that represents the hours Yuson has left after x days is (A) y = -2x + 30
Given in question,
Hours she should complete = 30 hours
Hours she complete each day = 2 hours
Hours completed in x days = 2x
Hours left after x days = 30 -2x
Hence, the linear equation that represents the hours Yuson has left after x days is y = -2x + 30.
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What is 79 - 75 / 75 * 100 ?
I'm dividing 75 into 79 - 75 then timesing that by 100, I keep getting -21 but that's not right. I need help please
Answers
The required value of the given expression : [tex]\frac{79 - 75 }{ 75 }[/tex] × 100 = 5.3
What is BODMAS rule ?The Bodmas rule is based on the BODMAS acronym, which stands for Brackets, Order of Powers or Roots, Division, and Multiplication. Subtraction is represented by the letter S, while addition is represented by the letters A and S. According to the BODMAS rule, mathematical expressions with multiple operators must be resolved in the order of BODMAS, starting from the left. As with addition and subtraction, division and multiplication are interchangeable and depend on which comes first in the expression.
Given : [tex]\frac{79 - 75 }{ 75 }[/tex] × 100
on calculating it further
we get :
[tex]\frac{4}{75}[/tex] × 100
0.0533 X 100
=> 5.3
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At time t = 0, water begins to drip out of a pipe
nto an empty bucket. After 56 minutes, 8 inches
of water are in the bucket. What linear function
n the form y = mx + b represents the amount of
water in inches, w, in the bucket after t minutes?
Answers
Step-by-step explanation:
w = t/7
at the beginning we 0 inches of water.
after 56 minutes we have 8 inches of water.
that is a ratio of 56 minutes / 8 inches = 7/1 = 1 / 1/7.
so, in 1 minute we get 1/7 inch of water.
in 2 minutes 2×1/7 = 2/7.
in 3 minutes 3×1/7 = 3/7.
...
hence the equation.
Answer:
y = t/7Step-by-step explanation:
GivenStart time t = 0,Start level y = 0,Level of y = 8 in after t = 56 minSolutionFind the value of m and b in the equation y = mx + b.
The value of b = 0, since there is no level in the bucket initially.
Find the value of m, the slope:
8 = 56m,m = 8/56m = 1/7So the equation is:
y = (1/7)t + 0or
y = t/7In 1/6 of a day Bart read 4/7 of comic book .what rate can he read in a day
Answers
The rate at which Bart read is 24/7 book/day.
Given, Bart read 4/7 of comic book in 1/6 of a day.
We have to find the rate at which he read the book in a day.
Now, Bart read 4/7th of a comic book = 1/6th of a day
4/7 comic book = 1/6 day
1 day = (4 × 6)/7 comic book
1 day = 24/7 comic book
So, the rate at which Bart read is 24/7 book/day.
Hence, the rate at which Bart read is 24/7 book/day.
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Find the measure of the exterior angle.
Answers
The measure of the exterior angle is 139 degrees.
What is the measure of the exterior angle?The sum of the interior angle of a triangle is 180 degree.
The sum of angles on a straight line is 180 degrees.
From the diagram;
Angle 1 = 64 degreesAngle 2 = 75 degreesAngle 3 = ?First, we determine the third interior angle of the triangle.
Angle 1 + Angle 2 + Angle 3 = 180
64 + 75 + Angle 3 = 180
139 + Angle 3 = 180
Angle 3 = 180 - 139
Angle 3 = 41 degrees
Now, angle 3 and the exterior angle forms a angle on a straight line.
Hence;
Angle 3 + Exterior angle = 180
41 + Exterior angle = 180
Exterior angle = 180 - 41
Exterior angle = 139 degrees.
Therefore, 139 degrees is the exterior angle.
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4/3 pi (2)^3 + 1/3 (2)(4)
Answers
guys please help!! tyyy
Answers
a dish contains 2 yellow triangles, 3 yellow squares, and 1 green square two shapes are drawn in a sequence with replacement. what is the probability of drawing a green triangle on a second draw given the first draw was a yellow shape?
Answers
Answer: I don't know
Step-by-step explanation:
I have no idea