The required solution is correct. AB = 5.5.
Given that,
AB=[1+4.5]=5.5
To describe the expression and to determine whether the expression is correct or not.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
here,
Simplifying the given expression, AB = 1 + 4.5
AB = 1 + 4.5
Addition property of alike terms
AB = 1.00 + 4.50
AB = 5.50
AB = 5.5
Thus, the required solution is correct. AB = 5.5
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Write the equation in standard form of the line that has x-intercept 3 and y-intercept 5
Answer:
[tex] 5x + 3y = 15 [/tex]
Step-by-step explanation:
The x-intercept is 3, so the ordered pair of that point is (3, 0).
The y-intercept is 5, so the ordered pair of that point is (0, 5).
We need the equation of the line that passes through points (3, 0) and (0, 5). Also, from the y-intercept, we know that b = 5 in the slope-intercept form of the equation of a line,
y = mx + b
b = 5
We now have:
y = mx + 5
We can find the slope using the two given points.
[tex] m = \dfrac{y_2 - y_1}{x_2 - x_1} = \dfrac{5 - 0}{0 - 3} = -\dfrac{5}{3} [/tex]
[tex] y = -\dfrac{5}{3}x + 5 [/tex]
Now we change the equation into standard form,
ax + by = c
[tex] y = -\dfrac{5}{3}x + 5 [/tex]
Multiply both sides by 3.
[tex] 3y = -5x + 15 [/tex]
Rearrange terms.
[tex] 5x + 3y = 15 [/tex]
help with homework pls asap
The claimed made by Lawrence Summers that the women have a lower standards deviation IQ than men is not correct since only 0.15% population has IQ score more than 145
IQ, or intelligence quotient, is a measure of your ability to reason and solve problems. It reflects how well you did on a specific test compared to other people of your age group. While tests may vary, the average IQ on many tests is 100, and 68% of scores lie between 85 and 115.
Given that, suppose an IQ of 145 or higher is required to be a researcher at a top notch research institution
Use the idea of standard deviation, the Empirical Rule, and the fact that the mean and standard deviation IQ of humans is 100 and 15, respectively, to explain summer's argument.
Approximately 99.7% of the data will lie within 3 standard deviations of the mean. That is, approximately 99.7% of the data lie between α-3β and
IQ scores between = α-3β and α+3β
IQ scores = 100-3x15 and 100+3x15
= 55 and 145
We can see that approximately 99.7% of the population has IQ scores between 55 and 145
only 0.15% population has IQ score more than 145
Hence the claimed made by Lawrence Summers that the women have a lower standards deviation IQ than men is not correct since only 0.15% population has IQ score more than 145.
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Answer:
Lawrence Summers' assertion that women have a lower IQ standard deviation than men is untrue because only 0.15% of the population has an IQ higher than 145.
Step-by-step explanation:
Lawrence Summers' assertion that women have a lower IQ standard deviation than men is untrue because only 0.15% of the population has an IQ higher than 145.
Your capacity for reasoning and problem-solving is measured by your IQ, or intelligence quotient. It displays how well you performed on a certain test in comparison to other individuals in your age group. The average IQ on several tests is 100, and 68% of scores fall between 85 and 115, notwithstanding test variations.
Given that, let's assume that a prestigious research institute requires researchers to have an IQ of at least 145.
Explain summer's contention using the concept of standard deviation, the Empirical Rule, and the facts that human IQ has a mean of 100 and a standard deviation of 15, respectively.
The data will be within 3 standard deviations of the mean in about 99.7% of the cases. In other words, 99.7% of the values fall between -3 and
IQ scores ranging from -3 to +3
IQ scores are 100 x 3 x 15 and 100 x 3 x 15.
= 55 and 145
We can observe that between 55 and 145 is the range in which 99.7% of the population falls.
Only 0.15 percent of people have an IQ higher than 145.
Since just 0.15% of the population has an IQ score higher than 145, Lawrence Summers' claim that women have a lower standard deviation IQ than men is untrue.
Find the coordinates of the midpoint M and the distance between L(-4,5) and N(5,-3). Round to the nearest tenth, if necessary.
Answer:
Step-by-step explanation
x1 = X sub-one, y1 = Y sub-one, x2 = x sub-two, y2 = y sub-two
Midpoint Formula
M (x1 + x2/2, y1 + y2)/2)
-4 = x1, 5 = y1 and 5 = x2, -3 = y2
L(-4,5) and N (5,-3)
-4 + 5/2 = 1/2 or 0.5
5 + (-3)/2 = 2/2 = 1
Midpoint : (1/2, 1)
Consider the equation 2y-5x = 30. Determine the x-intercept.
Enter your response in the boxes.
2.
-5r = 30
_52 = 30
- 30
x =
The value of the x-intercept is -6
According to the question we have been the equation which is :
2y - 5x = 30 (1)
The general expression of slope intercept form is given as :
y = mx + c
where, m = slope
c = y-intercept
To find the value of x-intercept we will write equation (1) as an equation for x that is
-5x =-2y + 30
Dividing both the sides by -5 we get
x = 2/5y + (-6)
Which is in the form of slope intercept form which is
x = my + c and the x- intercept will be c = -6
Hence the x-intercept is -6
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What equation, in point-slope form, matches the graphed line shown? line that goes through (-3, -6) and (2, -2)
PLEASE HELP ASAP!! :0
The equation, in point-slope form, matches the graphed line shown is y + 2= 0.8(x - 2)
How to determine what equation, in point-slope form, matches the graphed line shown?The points on the line are given as
(-3, -6) and (2, -2)
Calculate the slope (m) of the line using
m = (y2 - y1)/(x2 - x1)
So, we have
m = (-2 + 6)/(2 + 3)
Evaluate
m = 0.8
The linear equation is then represented as
y - y1 = m(x - x1)
So, we have
y + 2= 0.8(x - 2)
Hence, the equation, in point-slope form, matches the graphed line shown is y + 2= 0.8(x - 2)
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How to make 10 + 4 x 12 -6 34
Answer:
(10 + 4) * (12 - 6) = 84Step-by-step explanation:
(10 + 4) * (12 - 6) = 34= 14 * 6 = 34= 84 ≠ 34The original one is false, with the answer being 84.
If there is 6 A of current through the filament of a lamp, how many coulombs of charge move through the filament in 1.75 s?
In 6A, 10.5 coulomb of charge is moved through the filament in 1.75 seconds.
What is charge?The electrical current that flows across conducting wires is carried by electrons, which are tiny particles. Negatively charged particles are electrons.
Charge is expressed in coulombs, or C.
The charge of an electron is 1.6 x[tex]10^{-19}[/tex]C.
The connection between current I and charge amount Q
Charged particle flow is what makes up an electric current.
One ampere of current flows when one coulomb of charge passes through a certain place in a circuit once every second.
The magnitude of an electric current affects how quickly charges flow.
I =[tex]\frac{quantity of charge(Q)}{Time taken (t)}[/tex]
Given: current I= 6A at time t=1.75s,
I = Q / t
Q = I x t
Q = 6 x 1.75
Q = 10.5 coulomb
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Adventure Travel has an Adjusted Trial Balance for Year Ended December 31, 20XX with the following account balances:
DEBITS: Cash: 25,000; Accounts Receivable: 15,000; Office Supplies: 4,300; Office Equipment: 29,600
CREDITS: Accumulated depreciation - office equipment: 5,000; Salaries Payable: 2,800; Long-term notes payable: 22,200; Common Stock: 20,000; Retained Earnings: 10,260
DEBIT: Cash Dividends: 1,000
CREDITS: Fees Earned: 75,000
DEBITS: Salaries Expense: 32,800; Rent Expense: 16,800; Depreciation expense - office equipment: 3,960; Advertising expense: 4,000; Office supplies expense: 2,800.
Total Debits = 135,260; Total Credits = 135,260
You have prepared the financial statements for December 20XX. Now, it is time to make the closing entries.
We will close the revenue accounts first: what dollar amount will I record for the debit and credit accounts? Specify as a whole number.
The closing entries to record the given transaction is: Debit Fees earned $75,000, Credit Income summary $75,000.
Closing journal entriesAdventure Travel journal entries
1. Debit Fees earned $75,000
Credit Income summary $75,000
2. Debit Income summary $60,360
Credit Salaries expense $32,800
Credit Rent expense $16,800
Credit Depreciation expense-Office equipment $3,960
Credit Advertising expense $4,000
Credit Office supplies expense $2,800
3. Debit Income summary $14,640
($75,000 - $60,360)
Credit A. Garcia, Capital $14,640
4. Debit A. Garcia, Capital $1,000
Credit A. Garcia, Withdrawals $1,000
Therefore the closing entries to record the given transaction is: Debit Fees earned $75,000, Credit Income summary $75,000.
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(90/5)+(78x34)
90 divided by 5
The dimensions of a rectangular monitor screen are such that its length is 3 in. more than its width. If the length were doubled and if the width were decreased by 1 in., the area would be increased by 104in^(2) . What are the length and width of the screen?
The length and width of the screen is 9.71 inch and 12.71 inch.
What is a rectangle?A Rectangle is a four sided-polygon, having all the internal angles equal to 90 degrees. The two sides at each corner or vertex, meet at right angles.
Area of triangle = Length * Width
Let L be the length and W be the width of the rectangle.
Now it is given that,
Dimensions of a rectangular monitor screen are, its length is 3 in. more than its width.
⇒ L + 3 = W
Therefore area is given as,
A = L * W
Put the value of W we get,
A = L * (L + 3)
Now, If the length were doubled and if the width were decreased by 1 in, the area would be increased by 104 in^2
Length = 2L
Width = W - 1
Thus area becomes,
A' = 2L(W - 1)
Now, the area would be increased by 104 in^2
A' = A + 104
Putting the value of A in A' we get,
A' = L * (L + 3) + 104
Now putting the value of A' we get,
2L(W - 1) = L * (L + 3) + 104
Expanding we get,
2LW - 2L = L^2 + 3L + 104
Since L + 3 = W
Thus, putting W in above we get,
2L(L + 3) - 2L = L^2 + 3L + 104
Expanding the brackets we get,
2L^2 + 6L - 2L = L^2 + 3L + 104
Solving we get,
2L^2 + 4L = L^2 + 3L + 104
Taking all the terms together we get,
2L^2 + 4L - L^2 - 3L - 104 = 0
Solving alike terms we get,
L^2 + L - 104 = 0
Solving the above equation we get,
L = 9.71 inch, -10.71 inch
Since, Length cannot be negative
Thus,
L = 9.71 inch
Put the value of L in W we get,
9.71 + 3 = W
⇒ W = 12.71 inch
Thus the required value of length and width is,
Length = 9.71 inch
Width = 12.71 inch
Thus, the length and width of the screen is 9.71 inch and 12.71 inch.
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given the function F described by f(x)=
Drag each equation to show if it could be a correct first step to solving the equation
9(x+2)=90.
Answer:
Is there more information
Step-by-step explanation:
I'll ll answer if there is
Answer:
Do the distributive property; your new equation will be 9x + 18 = 90
Step-by-step explanation:
The first step to the problem 9(x + 2) = 90 is the distribute property. Since we don't know what x is we can't add it to 2. Instead we do the distributive property, which is when you multiply the outside number to the terms inside the parenthesis.
The equation will then be: 9x + 18 = 90
! --- Note: I'm not too sure what you are trying to ask because your question is unclear but hope this helps in some way
----------------------------------------------------------------------------------------------------
! --- If you are also looking for what x is, x = 8
What is the formula for x^2-11x+10
Answer:
In the expression
[tex] {x}^{2} - 11x + 10[/tex]
a in the formula will be substituted for 1
b in the formula will be substituted for -11
c in the formula will be substituted for 10
Whats the Estimate of 110x298???
Answer:
33000
Step-by-step explanation:
To estimate the product of two numbers, round the individual numbers to numbers that you can multiply mentally.
Round 298 to the nearest hundred → 300.
(We don't need to round 110 as it is a multiple of 10, and therefore easy to multiply mentally).
Therefore,
⇒ 110 × 298 ≈ 110 × 300
To multiply 110 by 300, separate the 110 into 100 + 10:
⇒ 110 × 300 = (100 + 10) × 300
Apply the distributive property of multiplication:
⇒ (100 + 10) × 300 = 100 × 300 + 10 × 300
To multiply a number by 100, add two zeros.
To multiply a number by 10, add one zero.
Therefore:
⇒ 100 × 300 + 10 × 300 = 30000 + 3000 = 33000
Check
110 × 298 = 32780
32780 rounded to the nearest thousand is 33000.
PLEASE HELP WITH THIS QUESTION! ILL GIVE BRAINLYEST
Also pls explain how u got ur answer since I literally don't get it..
Step-by-step explanation:
the cost for n shirts is c=15+9(n-1)
c=15+9n-9 simplify
c=9n+6
n represents the number of shirts
so for the cost of 2 shirts, n=2
c=9(2)+6
c=24
therefore it costs $24 for 2 shirts
for the cost of 5 shirts, n=5
c=9(5)+6
c=51
therefore the cost of 5 shirts is $51
1 shirt = $15
2 shirts =$24
3 shirts =$33
24-15 =9
33-24=9
so 9 is the common difference which means each additional shirt is $9 more than the price of all the previous shirts
Geometry Unit 2 Lesson 2 Homework
In questions 1-5, determine the type of reasoning for each statement.
In order to participate in school sports, students must have a minimum GPA of a 2.0. Jim has a GPA of 2.75, therefore he can participate in school sports.
Every Tuesday that Yolanda's family has visited a specific local restaurant, the kids' meals have been free. When Yolanda's family visits that restaurant next Tuesday, the kids' meals will be free.
A new movie director has grossed over 250 million for each of his first three movies. When his fourth movie is released, it will gross over 250 million.
The type of reasoning for each statement is as follows:
Statement 1 is deductive reasoningStatement 2 is abductive reasoningStatement 3 is abductive reasoningWhat is deductive reasoning?
Deductive reasoning is the type of reasoning that follows a more general statement to reach a specific conclusion. The conclusions of inductive reasoning is most likely true. This is the type of reasoning used in mathematics.
What is inductive reasoning?Inductive reasoning uses a more specific statement and arrive to a general conclusion. It is goes from bottom to up. The conclusion here is strongly persuasive to be true but still has false probability
For instance, in the second statement "Every Tuesday that Yolanda's family has visited a specific local restaurant, the kids' meals have been free" This does not logically mean the kids' meal is free but it is assumed to be free as it has been happening. more like taking a specific events that has happened for a while and assume it will always be so.
What is abductive reasoning?
Abductive reasoning is the type of reasoning that follows an incomplete observation to reach a more likely conclusion. The conclusions of abductive reasoning is more of a probability. This is the type of reasoning used in used in our day to day events.
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i know how to do a and b, but how do i do c and d? thanks
Answer:
1c 12
1d 4x - 3
2c 10x + 20
2d 60x² + 160x + 100
3c
Domain is -3 ≤ x ≤ 3
Range is -2 ≤ g(x) ≤ 2
Step-by-step explanation:
Question 1 : f(x) = 2x - 3
1c. 3 - f(-3)Question 2: f(x) = 8x + 10, g(x) = 2x
2c: 2f(x) - 3g(x)Mr. Brown is buying bottles of water for the volunteers of an event he is managing. He already has 17 bottles in his office and needs a total of 350 bottles of water. They are sold in cases of 24 . Write an equation to show how many more cases of water he needs.
An equation to show the additional number of cases of water Mr. Brown needs is y = 24x - 3, where y = 333 bottles and x = 14.
What is an equation?An equation is a mathematical statement that claims that two mathematical expressions are equal.
An equation contains the equation symbol (=).
Data and Calculations:The number of bottles in his office = 17 bottles
The total number of bottles required = 350 bottles
The total number of additional bottles of water required, y = 333
1 case of water bottles = 24 bottles
The equation to show the additional cases required is y = 24x - 3, where y = 333 bottles and x = 14.
Check:
y = 24x - 3
333 = 24(14) - 3
333 = 336 - 3
333 = 333
Thus, an equation to show the additional number of cases of water Mr. Brown needs is y = 24x - 3, where y = 333 bottles and x = 14.
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A fair die is rolled 5 times what is the probability that no 1 and no 6 among the rolls
The probability of getting no 1 and no 6 is 0.01%
There are six possible outcomes in a role. Since no 1 and 6 are to be rolled. There would only be 4 possible outcomes.
So, the chance of rolling no 1 and 6 is
Since we have 5 rolls. Then we have: 1/6×1/6×1/6×1/6×1/6 = =0.00013
Therefore, the probability of rolling no 1 and 6 is approximately 0.01%.
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it's that a proposition is true.
he probability of an occasion is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.[note 1]] the upper the probability of an event, the more likely it's that the event will occur. an easy example is the tossing of a fair (unbiased) coin. Since the coin is fair, the 2 outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could even be written as 0.5 or 50%).
These concepts are given an axiomatic mathematical formalization in probability theory, which is employed widely in areas of study such as statistics, mathematics, science, finance, gambling, AI, machine learning, computing, theory of games, and philosophy, for instance, draw inferences about the expected frequency of events. applied mathematics is also used to describe the underlying mechanics and regularities of complex systems.
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E
D
A
In the diagram above, why is m/EFD = m/BFC?
O If two angles are supplementary, then their measures are equal.
O If two angles are vertical, then they are congruent.
O If two angles are complementary, then they are congruent.
OIf two angles are a linear pair, then they have equal measure.
F
O If a ray bisects an angle, then it divides it into two congruent angles.
40°
ВА
C
Answer:
O If a ray bisects an angle, then it divides it into two congruent angles.
Step-by-step explanation:
Please help me with this question asap. it’s due tonight
The horizontal line passing through the point (2/3, 1/2) is represented by the equation y = 1/2.
What is slope intercept form?y=mx+c
where m is the slope.
As stated in the problem the line is horizontal. This means that its slope is zero.
y-y1=m(x-x1)
y-1/2=0(x-2/3)
y-1/2=0
y=1/2.
Mathematically it means that it is a line parallel to the x-axis and passing through y = 1/2.
The horizontal line passing through the point (2/3, 1/2) is represented by the equation y = 1/2.
Therefore horizontal line passing through the point (2/3, 1/2) is represented by the equation y = 1/2.
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PLS HELP I WILL GIVE BRAINLIEST
Find the x-intercept and the y-intercept of each line. Express the answers as ordered
pairs.
x+4y=12
x-intercept is
y - intercept is
An architect has designed two tunnels. Tunnel A is modeled by x2 + y2 + 28x + 52 = 0, and tunnel B is modeled by x2 – 36x + 16y + 68 = 0, where all measurements are in feet. The architect wants to verify whether a truck that is 8 feet wide and 13.5 feet high can pass through the tunnels.
Part A: Write the equation for Tunnel A in standard form and determine the conic section. Show your work. (4 points)
Part B: Write the equation for Tunnel B in standard form and determine the conic section. Show your work. (4 points)
Part C: Determine the maximum height of each tunnel. Is the truck able to pass through either tunnel without damage? If so, which tunnel(s) and why? Show your work. (7 points)
Considering the equations of a circle and of a parabola, we have that:
a) Tunnel A is a circle, with it's radius meaning that both the width and the height are of 12.
b) Tunnel B is a parabola, with it's vertex and it's roots meaning that it has a width of 32 feet and a height of 16 feet.
c) The maximum height of Tunnel A is of 12 feet and of Tunnel B is of 16 feet, hence, since the height of the truck is of 13.5 feet, it can pass through Tunnel B without damage, as it's height is greater than 13.5 feet.
What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
For Tunnel A, the equation is given by:
x² + y² + 28x + 52 = 0
Completing the squares:
(x + 14)² + y² = -52 + 14²
(x + 14)² + y² = 144.
Hence:
Tunnel A is a circle, with it's radius meaning that both the width and the height are of 12.
What is the vertex of a quadratic equation?A parabolic(quadratic) equation is modeled by:
y = ax^2 + bx + c
The vertex is given by:
[tex](x_v, y_v)[/tex]
In which:
[tex]x_v = -\frac{b}{2a}[/tex][tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]For Tunnel B, the equation is given as follows:
x² - 36x + 16y + 68 = 0.
16y = -x² + 36x - 68.
Simplifying by 16:
y = -0.0625x² + 2.25x - 4.25.
Hence the coefficients are a = -0.0625, b = 2.25, c = -4.25, and the maximum height is:
[tex]y_v = -\frac{(2.25)^2 - 4(-0.0625)(-4.25)}{(-0.0625)} = 16[/tex]
The width is the difference between the roots, which, using a calculator, are:
2 and 34, hence the width is of 32 feet, as 34 - 2 = 32.
Hence:
Tunnel B is a parabola, with it's vertex and it's roots meaning that it has a width of 32 feet and a height of 16 feet.
For item c, considering the previous items, we have that:
The maximum height of Tunnel A is of 12 feet and of Tunnel B is of 16 feet, hence, since the height of the truck is of 13.5 feet, it can pass through Tunnel B without damage, as it's height is greater than 13.5 feet.
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How do I solve this problem?
Answer:
y = 16(x +2)
Step-by-step explanation:
The equation of the tangent to a curve at a point can be written using the point-slope form of the equation for a line. The point is (x, f(x)), and the slope is the derivative, f'(x).
Point and slopeThe point where you want the tangent line has y-value ...
y = 2(-2)³ -8(-2) = 2(-8)+2(8) = 0 . . . . . point (x, y) = (-2, 0)
The slope at the point where you want the tangent is ...
y' = 2·3x² -8 = 6(-2)² -8 = 24 -8 = 16 . . . . . slope m = 16
Equation of the tangent lineThe point-slope equation of a line is ...
y -k = m(x -h) . . . . . line with slope m through point (h, k)
y -0 = 16(x -(-2)) . . . . . line with slope 16 through (-2, 0)
y = 16(x +2) . . . . . simplified
An equation of the tangent line is ...
y = 16(x +2)
Consider two markets: the market for cat food and the market for dog food. The initial equilibrium for both markets is the same, the equilibrium price is $6.50, and the equilibrium quantity is 35.0. When the price is $6.75, the quantity supplied of cat food is 59.0 and the quantity supplied of dog food is 101.0
Using the midpoint formula, calculate the elasticity of supply for dog food. Please round to two decimal places.
The elasticity of supply for dog food is 25.71
What is the elasticity of supply?Price elasticity of supply measures the responsiveness of quantity supplied to changes in price of the good.
Price elasticity of supply = midpoint change in quantity supplied / midpoint change in price
Midpoint change in quantity supplied = change in quantity supplied / average of both supply
change in quantity supplied= 101 - 35 = 66
average of both supply = (101 + 35 ) / 2 = 68
Midpoint change in quantity supplied = 66 / 68 = 0.97
Midpoint change in price = change in price / average of both price
Change in price = 6.75 - 6.50 = $0.25
Average of both price = (6.75 + 6.50) / 2 = $6.625
Midpoint change in price = 0.25 / 6.625 = 0.03774
Price elasticity of supply = 0.97 / 0.03774 = 25.71
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In the figure below angle m 1 =(x-6) and and angle m 2 =7x
Answer:
angle 1 = 6°
angle 2 = 84°
Step-by-step explanation:
since these 2 angles form 90°, they're called complementary
so when they're added they give 90°
x-6°+7x=90°, then we collect the like terms
x+7x=90°+6°, 8x=96°, divide both sides by 8 so we can get x
x=96/8, x=12, so now we substitute 12 in x so we can get the angles
FOR ANGLE 1:
12-6=6°
FOR ANGLE 2:
7(12)=84°
hope it helped, if it did mark me brainliest
Which is the following is an arithmetic sequence?
A. 6,13,19,32,51
B. 3,6,9,12,15
C. 3,5,8,13,21
D. 1,4,5,9,14
Answer:
Step-by-step explanation:
An arithmetic sequence also known as arithmetic progression is a sequence of numbers in which the difference between consecutive terms are always the same eg 1 5 9 13 17 , the difference is always 4
so THE ANSWER TO YOUR QUESTION IS B
geometry question, surface area of a triangular prism,
Answer:
282 [in²].
Step-by-step explanation:
all the details are in the attachment.
What is the turning point of the graph of ƒ(x) = |x| +4 ? (0,4) (0, – 4) (4,0) (-4, 0)
The turning point of the function f(x) = |x| + 4 lie on the y - axis and has coordinates (0, 4).
What is Turning point of a graph?A stationary point is called a turning point if the derivative changes sign (from positive to negative, or negative to positive ) at that point. There are two types of turning points - local maxima and local minima.
Given in the question is a modulus function -
f(x) = |x| + 4
In order to determine the turning point, we will first have to plot the graph of this function -
f(x) = |x| + 4
Now, we can write f(x) as -
f(x) = { (x + 4) for x ≥ 0 and (- x + 4) for x < 0} }
Alternatively, you can plot the graph of |x| and positive shift it by 4 units. Refer to the graph attached with the answer. From the graph you can see that after the coordinate (0, 4) the slope becomes positive. Slope of a line gives the rate of change of y with respect to x. So (0, 4) represents the turning point.
Therefore, the turning point of the function f(x) = |x| + 4 lie on the y - axis and has coordinates (0, 4).
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Use the diagrams. Name a pair of nonadjacent supplementary angles.
1. KJL
2. KJM
3. MJN
4. MJP
5. FGH
6. LJM
7. FGE
8. NJP
9. LJN
From the given diagram, the pair of angles that are non-adjacent and supplementary are given as follows:
5. FGH
6. LJM
What are non-adjacent and supplementary angles?Supplementary angles are angles whose measures add to 180º.Non-adjacent angles do not have a common arm neither a common vertex.Hence, we need one angle among vertices E, F, G and H, and other with vertices K, J, L, M, N, P, to guarantee the non-adjacency. The angles are:
5. FGH
6. LJM
As:
FGH = 124º.LJM = 56º.124 + 56 = 180º, meaning that they are supplementary.
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