The absolute value function g(x) = |x − 2| − 4 is reflected over the x-axis, and then translated 2 units right and 2 units down to become g′(x). The quadratic function f(x), graphed below, is translated 2 units left and 5 units up to become f′(x). Which of these two transformed functions has a larger maximum and what is the value of this maximum?
Answers
The given function is
\(g(x)=\lvert{x-2}\lvert-4\)When reflected across the x-axis and translate 2 units right, and 2 units down, then its image will be
\(\begin{gathered} g^{\prime}(x)=-\lvert{x-2-2}\rvert-4-2 \\ g^{\prime}(x)=-\lvert{x-4}\rvert-6 \end{gathered}\)Then its maximum vertex is (4, -6)
Since the maximum value is the y-coordinate of the maximum point, then
Its maximum value is -6
From the graph, we can see that the maximum point of f(x) is (-2, -4)
Since it will translate 2 units left and 5 units up, then
Subtract 2 from the x-coordinate, and add 5 to the y-coordinate of f(x) to find the maximum point of f'(x)
\((-2+2,-4+5)=(0,1)\)The maximum point of f'(x) is (0, 1)
The maximum value of f'(x) is 1
Since 1 > -6, then
f'(x) > g'(x)
f'(x) has a larger maximum and it is 1
The answer is C (3rd choice)
Related Questions
Farmer Johnson raises cows and chickens. For some reason he does not remember how many of each
animal he has, but does remember that he counted 54 heads and 140 feet.
How many of each kind of animal does he have?
Answers
38 times 2 equals 76 and 16 times 4 equals 64. 64 plus 76 equals 140.
Answer:
Step-by-step explanation:
Let the number of cows = x
Let the number of chickens = y
4x + 2y = 140
x + y = 54
Multiply the second equation by 2
2x + 2y = 108
Now write the new equation under the first equation and subtract.
4x + 2y = 140
2x + 2y = 108 Subtract
2x = 32 Divide by 2
x = 32/2
x = 16
There are 16 cows and 38 chickens.
Check
16 * 4 = 64
38 * 2 = 76
Total 140
Determine any point(s) of intersection of the equations algebraically. Then use a graphing utility to verify your results. y = x^2 - x + 1
Answers
The point of intersection will be the x, and y coordinates where the two lines cross.
To determine the point(s) of intersection algebraically, we need to find the solutions of the system of equations:
y = x² - x + 1
We can re-arrange the equation to solve for x:
x² - x + 1 - y = 0
We can then use the quadratic formula to find the solutions:
x = (1 ± √(1 - 4(1)(-y)))/2
x = (1 ± √(1 + 4y))/2
Now we can substitute values for y to find the x-coordinates of the points of intersection.
To verify the results, we can use a graphing utility to graph both equations and visually see where they intersect.
The point of intersection will be the x, and y coordinates where the two lines cross.
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Newton sleeps 9hours each night. How many hours does he sleeps in 1 week
Answers
Mrs. Lewis received her paycheck this week in the amount of $535.75. She spent $76.98 on groceries, she paid her $59.95 phone bill and she spent $22.45 at the movies. How much did she have left over?
Answers
Answer:
376.37
Step-by-step explanation:
Answer:
376.37
Step-by-step explanation:
6. George is learning about mosaics in art class. His teacher passes out small square tiles and
encourages the students to cut up the tiles in various angles. George's first cut tile looks like
this:
B
b. Solve for m.
c. What is the measure of angle MLE?
(% m)
L
Write an equation relating angle MLE with angle ELB.
d. What is the measure of angle ELB?
2(m+5)*
M
Answers
The value of m is 32, the measure of the angle ∠ MLE is 16° and the measure of ∠ ELB is 74°.
What is angle?
An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles.
Given:
The measure of ∠ MLE = 1 / 2 m, ∠ ELB = 2 (m + 5)
Calculate the value of m as shown below,
∠ MLE + ∠ ELB = 90 (As given on figure)
1 / 2 m + 2 (m + 5) = 90
1 / 2 m + 2 m + 10 = 90
m + 4 m + 20 = 180
5 m = 180 - 20
m = 160 / 5
m = 32
Hence, ∠ MLE = 32 / 2 = 16°, and ∠ ELB = 2 (32 + 5) = 74°
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The complete question is attached below.
Find the center and radius of this
circle:
(x + 13)²+(y + 2)² = 81
Center = ([?],[])
Radius = []
Enter
![Find the center and radius of thiscircle:(x + 13)+(y + 2) = 81Center = ([?],[])Radius = []Enter](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/yiKujknhPhoPRvVw6YYpsObEwyRdqFJv.png)
Answers
The center of the circle is (13, 2)
The radius of the circle is 9
How to find the radius of the circleTo find the center and radius of the circle described by the equation:
(x + 13)² + (y + 2)² = 81
We can compare with the standard form of the equation of the circle which is
(x - h)² + (y - k)² = r²
it can be deduced that
-h = 13, h = -13
-k = 2, k = -2
r² = 81, r = 9
This is the equation for a circle with center at (13, 2) and radius 9. So the center of the circle is (13, 2) and the radius is 9.
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Answer:
Center = (-13,-2)
Radius = 9
find the measures of GH and CH.
Answers
The length of the lines GH and CH are 16 units and 12 units.
What is a line?A line is an object in geometry that is infinitely long and has neither width nor depth nor curvature. Since lines can exist in two, three, or higher-dimensional spaces, they are one-dimensional objects. The term "line" can also be used to describe a line segment in daily life that has two points that serve as its ends. In geometry, lines are drawn with arrows at either end to indicate that they extend indefinitely. Two line points can be used to name a line (for example, AB) or just a letter, usually in lowercase (for example, line m ). The ends of a line segment are two.So, the measure of lines GH and CH:
We know that AC ⊥ GH hence cuts GH in two equal lines.
GB = BH GB is 8 units then BH is also 8 units.GB = BH = 8 units.But,
GH = GB + BHGH = 8 + 8GH = 16 unitsWe can observe that △GCH is an isosceles triangle.
GC = CHGC = CH = 12 unitsTherefore, the length of the lines GH and CH is 16 units and 12 units.
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In a 30-60-90 triangle, the length of the side opposite the 30 degree angle is 8. Find the length of the side opposite the 60 degree angle.
Answers
Answer:
The length of the side opposite the 60 degree angle 'c' = 4
Step-by-step explanation:
Step(i):-
Given data ∠A = 90° , ∠B = 60° and ∠C = 30°
Given data the length of the side opposite the 30 degree angle is 8
let 'a' = 8
step(ii):-
By using sine rule formula in properties of triangle
\(\frac{a}{Sin A} = \frac{b}{Sin B} = \frac{c}{Sin C} = 2 R\)
\(\frac{a}{Sin A} = \frac{c}{Sin C}\)
\(\frac{8}{Sin 90} = \frac{c}{Sin 30}\)
cross multiplication , we get
\(\frac{8 X sin 30}{Sin 90} = c\)
we know that trigonometry formulas
sin 30° = \(\frac{1}{2}\) and sin 90°= 1
C = 8 X 1/2 = 4
conclusion:-
The length of the side opposite the 60 degree angle 'c' = 4
It’s a bonus question on a work sheet I need your help.
Answers
Answer:
I think 5 because they both go into it
1.
(03.03 MC)
A biologist is studying the growth of a particular species of algae. She writes the following equation to show the radius of the algae, f(d), in mm, after d days:
f(d) = 11(1.01)d
Part A: When the biologist concluded her study, the radius of the algae was approximately 11.79 mm. What is a reasonable domain to plot the growth function? (4 points)
Part B: What does the y-intercept of the graph of the function f(d) represent? (2 points)
Part C: What is the average rate of change of the function f(d) from d = 2 to d = 7, and what does it represent? (4 points)
Answers
Answer:
sept one
Step-by-step explanation:
On a coordinate plane, f (x) = x cubed + 4 curves up
through (2, negative 3), has an inflection point at (0, 4),
and curves up through (1, 5). G (x) = Rootindex 3
StartRoot x minus 4 EndRoot curves up through
(negative 4, negative 2), has an inflection point at (4, 0),
and curves up through (5, 1).
Consider the function show. Explain why the graph of a
function and its inverse are reflections over the line
y=x.
O The ordered pairs (a, b) of a function are (-a, -b) for
the inverse function.
O The ordered pairs (a, b) of a function are (-b, -a) for
the inverse function.
O The ordered pairs (a, b) of a function are (a, b) for
the inverse function.
O The ordered pairs (a, b) of a function are (b, a) for
the inverse function.
Answers
Answer: B
Step-by-step explanation:
I just solved it
The correct answer is . The ordered pairs (a, b) of a function are (b, a) for the inverse function.
Which expression is equivalent to the given expression? Assume the denominator does not equal zero.
Answers
Answer:
B
Step-by-step explanation:
\(\dfrac{a^{m}}{a^{n}}=a^{m-n} \ if \ m > n\\\\\\ \dfrac{a^{m}}{a^{n}}=\dfrac{1}{a^{n-m}} \ if \ n > m\\\)
\(\dfrac{16r^{6}z^{3}}{8r^{2}z^{6}}=\dfrac{2r^{6-2}}{z^{6-3}}\\\\ =\dfrac{2r^{4}}{z^{3}}\)
help pleaseeeeeeeeeeeeeeeeee
Answers
20N pushing against another 20N pushing cancels each other out, subsequently balancing the forces.
he table represents a linear equation. A two column table with 5 rows. The first column, x, has the entries, negative 10, negative 5, 10, 15. The second column, y, has the entries, 8, 7. 4, 3. Which equation shows how (–10, 8) can be used to write the equation of this line in point-slope form?
Answers
Equation of the line in point slope form passing through (-10,8) for the given coordinates (-10,8), (-5, 7) , (10,4), (15,3) of linear equation is
(y - 8)=(-1/5)(x+ 10).
As given,
Given points of linear equation: (-10,8), (-5, 7) , (10,4), (15,3)
Consider (x₁, y₁)=(-10,8) and (x₂ ,y₂)=(-5,7)
Slope 'm'=(y₂-y₁)/(x₂-x₁)
=(7-8)/(-5+10)
=-1/5
Equation of line passing through (-10,8) in point slope form:
y-y₁=m(x-x₁)
⇒(y -8)=(-1/5)(x+10)
⇒y=1/5(-x+30)
Therefore, equation of the line in point slope form passing through (-10,8) for the given coordinates (-10,8), (-5, 7) , (10,4), (15,3) of linear equation is
(y - 8)=(-1/5)( x + 10).
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Are all intersecting lines perpendicular? Draw a picture to help explain your answer
Answers
Not all intersecting lines are perpendicular.
What are perpendicular lines?Perpendicular lines require a 90-degree angle of intersection, creating the formation of right angles.
Nonetheless, unlike perpendicular lines that necessitate exactly 90 degrees of intersections, other types of driven lines can be at varying angles beside these.
As such, it is critical to highlight that in general intersecting lines come with different angles of intersection, and only those featuring exact 90-degree angle of intersection become normal cases of intersecting lines, becoming one among many subtypes existing today.
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Determine the intercepts of the line
X_______
Y_______
Answers
Answer:
-250, and 100
Step-by-step explanation:
The intercepts of the line are the points where line intersects the x-axis and y-axis .
the x intercept is at point (-250, 0)
the y intercept is at point (0, 100)
A $550 T.V is discounted by 30%. It is then discounted another 10%
Answers
Answer:
$346.5
Step-by-step explanation:
10% of $550 is 55
3*55 = 165
550 - 165 = $385
10% of $385 is 38.5
385 - 38.5 = $346.5
Have a nice day! :-)
3. Journalise the following transactions:
(i) Paid 2,000 in cash as wages on installation of a machine.
(ii) Sold goods to Mr. Chopra at a list price of ₹4,000. Sales
subject to 10% Trade Discount and 5% Cash discount if payment
is made immediately, Mr. Chopra availed of cash discount.
Answers
These are the two transactions that are given in the question and the journalizing of these transactions are explained with the appropriate steps and accounts.
The solution for the journalizing of the given transactions can be found below:
Journalizing refers to the recording of business transactions in the journal. In the process of journalizing, all transactions are recorded in the journal in a systematic way.
Journal is the first place where every transaction is recorded systematically.
The transaction is a business exchange in which one entity provides value to another entity in exchange for a specific item, service, or asset.
Transaction
(i) is paid Rs 2000 in cash as wages on the installation of the machine. This transaction can be journalized as follows: Journal of Transactions Date Particulars LF Amount (Dr.) Amount (Cr.) DD/MM/YYYCash a/c………………………Dr.2000To wages a/c2000 (Being cash paid as wages on the installation of the machine)Transaction
(ii) sold goods to Mr. Chopra at a list price of Rs 4,000. The sale is subject to a 10% trade discount and a 5% cash discount if the payment is made immediately, Mr. Chopra availed cash discount.
This transaction can be journalized as follows: Journal of Transactions Date Particulars LF Amount (Dr.) Amount(Cr.) DD/MM/YYYMr. Chopra a/c………………………Dr.3,420To Sales a/c4,000 (Being sales made to Mr. Chopra on a discount) To Trade Discount a/c400 (Being Trade Discount allowed to Mr. Chopra) Cash Discount a/c180 (Being cash discount allowed to Mr. Chopra) To Mr. Chopra a/c180 (Being cash received from Mr. Chopra) To CGST a/c90(Being CGST charged on sales) To SGST a/c90(Being SGST charged on sales)
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The temperature fell 36oF in 9 hours. If the temperature fell at the same rate every hour, which represents the change in temperature each hour?
Answers
Answer:
4°F
Step-by-step explanation:
If the temperature fell 36°F in 9 hours, then;
36°F= 9hours
to get the change in temperature in 1 hour, we will say;
x°F = 1 hr
Since we have
36°F= 9hours
x°F = 1 hr
Cross multiply
9x = 1*36
9x = 36
x = 36/9
x = 4°F
Hence the change in temperature each hour is at 4°F
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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compare fractions
HELP, GIVING BRAINLIEST
Answers
Answer:
a) 5/6
b) 7/8
c) 3/4
Step-by-step explanation:
Draw models for the fractions provided and compare.
Hope this helps.
Answer:
5/6<6/7 3/4<5/6>7/8 2/3>3/4>7/12
2
Let g(x) = x + 4x-7.
What is g(x) in graphing form?
(x + 2) - 7 = 4
O g(x) = (x + 2)²-7
Onone of the answer choices
x² + 4x-7=0
O g(x) = (x + 2)² - 11
Answers
The graphing form of the function g(x) is: C) none of the answer choices.
The function g(x) = \(x^2 + 4x - 7\)is already in the standard form of a quadratic equation. In graphing form, a quadratic equation can be represented as y =\(ax^2 + bx + c,\) where a, b, and c are constants.
Comparing the given function g(x) =\(x^2 + 4x - 7\)with the standard form, we can identify the coefficients:
a = 1 (coefficient of x^2)
b = 4 (coefficient of x)
c = -7 (constant term)
Therefore, the graphing form of the function g(x) is:
C) none of the answer choices
None of the given answer choices (A, B, D, or E) accurately represents the graphing form of the function g(x) =\(x^2 + 4x - 7\). The function is already in the correct form, and there is no equivalent transformation provided in the answer choices. The given options either represent different equations or incorrect transformations of the original function.
In graphing form, the equation y = \(x^2 + 4x - 7\) represents a parabolic curve. The coefficient a determines the concavity of the curve, where a positive value (in this case, 1) indicates an upward-opening parabola.
The coefficients b and c affect the position of the vertex and the intercepts of the curve. To graph the function, one can plot points or use techniques such as completing the square or the quadratic formula to find the vertex and intercepts. Option C
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The resultant of two forces acting at a point at right angles to each other is 240 pounds. Determine the horizontal force makes an angle of 56° with the resultant.
Answers
HORIZONTAL FORCE = 134.4 pounds
4.1 A bag contains 6 red, 4 green, 2 yellow and 3 blue balls. In each case, give the ratio (in simplest form) of the asked number of balls in the bag.( 4 ) 4.1.1 The number of red balls to the number of green balls.
Answers
The number of red balls to the number of green balls is 3 : 2
How to determine the ratio?The distribution of the balls is given as:
6 red, 4 green, 2 yellow and 3 blue balls
The number of red balls to the number of green balls is represented as:
Ratio = Red : Green
So, we have:
Ratio = 6 : 4
Simplify
Ratio = 3 : 2
Hence, the number of red balls to the number of green balls is 3 : 2
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the value of a varies directly at the square of the value of b, and b=3 when a=10. find the value of a when b=9
Answers
Answer:
answer = 90
Step-by-step explanation:
General equation: a = k*b^2
Specifically: 10 = k*(3)^2 = 9 k
Solving for k: k = 10/9
Then a = (10/9)b^2. If b = 9, then a = (10/9)(9)^2 = 90 (answer)
Use what you know about intersecting lines to label the missing and
picture below.
35°
X
type of angle pair:
zoom in
X =
OManeuvering the Middle LLC, 2016, 2022
Answers
Answer:
x = 145
Step-by-step explanation:
x and 35° lie on a straight line and are supplementary angles , sum to 180°
x + 35 = 180 ( subtract 35 from both sides )
x = 145
Mr. George has 5 bookcases in his classroom. Each bookcase has 3 shelves. Each
shelf has 20 books. How many total books are on Mr. George's 5 bookcases?
CLEAR
SUBMIT
300 books
160 books
100 books
60 books
Answers
Answer:
300
Step-by-step explanation:
Please see the attached.
Answers
Answer:
min: 56
lower quartile: 70
median: 74
upper quartile: 80
max: 86
If there are 3 red marbles, 2 blue marbles, 4 white marbles and 6 black marbles in a bag. What is the probability of you randomly selecting a black marble ?
Help me please
Answers
Answer:
6/15 chance
Step-by-step explanation:
or 40% chance
A painter charges $15.66 per hour, plus an additional amount for the supplies. If he made $190.08 on a job where he worked 7 hours, how
much did the supplies cost?
A $27.15
B. $90.46
C. $109.62
OD. $80.46