The average rate of change of R(t) over the time intervals [t, t + h] , where t is as indicated and h = 1, 0.1, and 0.01 are 210,100 and 100.
What is Differentiation?
Finding a function's derivative, or rate of change, is the process of differentiation in mathematics. The practical approach of differentiation can be performed utilising only algebraic operations, three fundamental derivatives, four principles of operation, and an understanding of how to manipulate functions, in contrast to the theory's abstract character.
Given function : R(t) = 240 + 30t^3
R'(t) = 90 t²
So, the average rate of change of R(t) is 90 t² .
Now, over the time interval [t, t + h], it will be as follows:
we know that, f'(t) = {f(t+h) - f(t)} / h
So, when h = 1, f'(1) = {f(1+1) - f(1)} / 1
= f(2) - f(1)
= 480 - 270 = 210
when h = 0.1 , f'(1) = {f(1+0.1) - f(1)} / 0.1
= {f(1.1) - f(1)} / 0.1
= (280 - 270) / 0.1 = 100
when h = 0.01 , f'(1) = {f(1+0.01) - f(1)} / 0.01
= {f(1.01) - f(1)} /0.01
= (271 - 270) / 0.01 = 100
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does anybody know the answers for these question?
The functions are solved for the inverses and matched as follows
1. not inverse function
2. not inverse function
3. inverse functions
4. not inverse function
5. not inverse function
6. not inverse function
How to find the inverse of the functions1. g(n) = -1/n + 1 and f(n) = -1/(n - 1)
say y = g(n) = -1/n + 1
y - 1 = -1/n
-y + 1 = 1/n
n = -1/(y - 1)
interchanging the variables
y = -1/(n - 1)
2. The cube root of 4 not in the inverse hence this is not inverse function.
3. g(x) = (x + 2)³ - 3 and f(x) = ∛(x + 3) - 2
say y = g(x) = (x + 2)³ - 3
y + 3 = (x + 2)³
x + 2 = ∛(y + 3)
x = ∛(y + 3) - 2
interchanging the variables
y = f(x) = ∛(x + 3) - 2 this is inverse functions
4.f(n) = 4/(n - 1) - 3 and g(n) = -2/n + 1
say y = f(n) = 4/(n - 1) - 3
y + 3 = 4/(n - 1)
1 / (y + 3) = (n - 1) / 4
4 / (y + 3) = n - 1
4 / (y + 3) + 1 = n
interchanging the variables
y = 4/(n + 3) + 1 this is not inverse functions
5. g(x) = 4/(x - 3) - 2 and f(x) = -2/(x + 1)
say y = g(x) = 4/(x - 3) - 2
y + 2 = 4/(x - 3)
1 / (y + 2) = (x - 3) / 4
4 / (y + 2) = x - 3
4 / (y + 2) + 3 = x
interchanging the variables
y = 4/(x + 2) + 3 this is not inverse functions
6. f(x) = 2/(x - 3) - 1 and g(x) = -3(-x + 2) - 2
say y = f(x) = 2(x - 3) - 1
y + 1 = 2/(x - 3)
1 / (y + 1) = (x - 3) / 2
2 / (y + 1) = x - 3
2 / (y + 1) + 3 = x
interchanging the variables
y = 1/(x + 1) + 3 this is not inverse functions
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The number of each type of ticket sold in the following situation: Tickets to a football game cost $5.oo if purchased before the day of the game. They cost $7.50 if purchased at the game. For a particular game, 600 tickets were sold and the receipts were $3500.
The number of each type of ticket sold in the following situation:
1. The tickets of $5.00 = 400
2. The tickets of $7.50 = 200
What is linear equation ?A linear equation is an algebraic equation in which the highest power of the variable is 1. In simple words, a linear equation is an equation in which the variables appear only in the first degree.
Linear equations can be written in the form:
y = mx + b
where y and x are variables, m is the slope (or rate of change), and b is the y-intercept (the point where the line crosses the y-axis).
Let x be the number of tickets sold before the day of the game and y be the number of tickets sold at the game.
Then we have:
x + y = 600 (the total number of tickets sold)
and
5x + 7.5y = 3500 (the total receipts from ticket sales)
To solve for x and y, we can use substitution.
Simplify and solve for y:
3000 - 5y + 7.5y = 3500,
2.5y = 500
y = 200
Substitute y = 200 back into the equation x + y = 600 to find x:
x + 200 = 600,
x = 400.
Therefore, 400 tickets were sold before the day of the game and 200 tickets were sold at the game.
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The complete question:
The number of each type of ticket sold in the following situation: Tickets to a football game cost $5.oo if purchased before the day of the game. They cost $7.50 if purchased at the game. For a particular game, 600 tickets were sold and the receipts were $3500. Find the number of tickets sold before the day of the game and the number of tickets sold at the day of the game?
Jade decided to rent movies for a movie marathon over the weekend. The
function g(x) represents the amount of money spent in dollars where x is the
number of movies. Does a possible solution of (6.5, $17.50) make sense for this
function? Explain your answer.
A solution (6.5, 17.50) does not make sense in the context of the problem, as the number of movies watched must be a non-negative integer.
How to interpret the ordered pair?The general format of an ordered pair is given as follows:
(x,y).
The meaning of an ordered pair (x,y) is that y = f(x), meaning that the numeric value of the function at the value of x is of y.
The variables for this problem are given as follows:
x: number of movies watched.g(x): amount of money spent.You can watch 1, 2, 3, ... and so on movies, a countable amount, hence 6.5 movies watched does not make sense in the context of this problem as decimal numbers are outside the function's domain.
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Jordan recorded the number of sit-ups he completed during the first 4 track practices. Which of Jordan's friends completed double the amount of sit-ups that Jordan completed during each practice?
The required proportionality relationship between Jordan and his friend for the sit-up is y = 2x.
What is proportionality?Proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.
Here,
Jordan recorded the number of sit-ups he completed during the first 4 track practices, we can establish the proportionality relationship between Jordan and his friend by comparing the number of sit-ups each completed during each practice.
Let's call the number of sit-ups that Jordan and his friend completed during each practice "x" and "y". Then, the number of sit-ups that his friend completed during each practice would be "2x".
The proportionality relationship between Jordan and his friend can be expressed as,
y = 2x
This means that for every 1 sit-up that Jordan completed, his friend completed 2 sit-ups, or that Jordan's friend completed twice the number of sit-ups that Jordan completed during each practice.
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A population of a town is 18,000 it decreases at a rate of 8% per year
Approximately it takes 6 years to the population be fewer than 11,000.
What is population growth and population decrease formula?If the constant decrease in population be R% per annum, then the population after n years = P(1-R/100)ⁿ.
Given that, A=11,000, rate of interest=8% and P=18,000.
Here, 11,000=18,000(1-8/100)ⁿ
11/18=(1-0.08)ⁿ
0.611=(0.92)ⁿ
Take the logarithm of both sides of the equation to remove the variable from the exponent.
Exact Form:
n=ln(0.611)/ln(0.92)
Decimal Form: n=5.90847701…
n=6
Therefore, approximately it takes 6 years to the population be fewer than 11,000.
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"Your question is incomplete, probably the complete question/missing part is:"
The population of a town is 18,000. it decreases at a rate of 8% per year. In about how many years will the population be fewer than 11,000?
calculate the interest and maturity value.
Interest Rates Term
Ordinary Exact (Days)
4%
Purpose
Drum Set
Used Car
Used Dirt Bike
School Tuition for Twins
Principal
$ 900.00
1,960.00
4,800.00
9,675.00
-
10
6%
9
Interest
45 a.$
30 a.
a.
123
275
a.
Maturity
Value
b. S
b.
b.
b.
The answers are:
a. For Drum Set: Interest = $0.98, Maturity Value = $900.98b. For Used Car: Interest = $2.88, Maturity Value = $1,962.88c. For Used Dirt Bike: Interest = $5.23, Maturity Value = $4,805.23d. For School Tuition for Twins: we can't calculate the interest or maturity value without the time period.How to calculate the interest and maturity valueTo calculate the interest and maturity value, we need to use the formula:
Interest = Principal x Rate x Time
Maturity Value = Principal + Interest
Where:
Principal is the initial amount investedRate is the interest rate as a decimalTime is the time period in yearsFor the given information, we have:
Drum Set:
Principal = $900.00
Rate = 4% = 0.04
Time = 10/365 = 0.0274 years (assuming an exact interest calculation based on days)
Interest = $900.00 x 0.04 x 0.0274 = $0.98
Maturity Value = $900.00 + $0.98 = $900.98
Used Car:
Principal = $1,960.00
Rate = 6% = 0.06
Time = 9/365 = 0.0247 years (assuming an exact interest calculation based on days)
Interest = $1,960.00 x 0.06 x 0.0247 = $2.88
Maturity Value = $1,960.00 + $2.88 = $1,962.88
Used Dirt Bike:
Principal = $4,800.00
Rate = 4% = 0.04
Time = 10/365 = 0.0274 years (assuming an exact interest calculation based on days)
Interest = $4,800.00 x 0.04 x 0.0274 = $5.23
Maturity Value = $4,800.00 + $5.23 = $4,805.23
School Tuition for Twins:
Principal = $9,675.00
Rate = 6% = 0.06
Time = not specified
We don't have the time period for this investment, so we can't calculate the interest or maturity value without that information.
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Which expression is equivalent to (14x)⁰y-⁷z?
The expression which is equivalent to (14x)⁰y-⁷z as required in the task content is; z / y⁷.
Laws of indicesIt follows from the task content that the expression which is equivalent to the given expression (14x)⁰y-⁷z is to be determined.
Recall from the laws of indices that a⁰ = 1 where a represents any mathematical entity.
Therefore, the resulting expression is;
1 • y -⁷ • z
= z • 1 / y⁷
= z / y⁷.
Ultimately, the resulting expression which is equivalent is; z / y⁷.
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what is the approximate side length of the largest square envelope that can be placed into the mailbox without bending it? you must round your answer to two decimal places.
The approximate side length of the largest square envelope that can be placed into the mailbox without bending it is 0.71x.
In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles of 90 degrees each. It is a two-dimensional shape that can be represented by a closed polygon with four straight sides and four right angles.
First, we need to measure the size of the mailbox. Let's say that the length of each side of the mailbox opening is "x" inches. We can then set up an inequality to find the maximum size of the side of the square envelope that can fit into the mailbox. The inequality is:
side length of square envelope ≤ x
This inequality tells us that the side length of the square envelope must be less than or equal to the size of the mailbox opening. We want to find the largest possible side length of the square envelope, so we'll use the "less than or equal to" symbol.
To find the largest possible side length of the square envelope, we'll use the value of "x" to set up an equation. We know that the diagonal of the square envelope will be equal to the length of the side of the square envelope multiplied by the square root of 2. Therefore, we can set up the following equation:
diagonal of square envelope = side length of square envelope × √2
We want to find the maximum side length of the square envelope, so we'll use the maximum value of the diagonal of the envelope. We know that the diagonal of the envelope must be less than or equal to the length of the mailbox opening (which is "x"), so we can set up the inequality:
side length of square envelope × √2 ≤ x
We can solve for the side length of the square envelope by dividing both sides of the inequality by the square root of 2:
side length of square envelope ≤ x/√2
To get the largest possible side length of the square envelope, we'll use the maximum value of "x". Therefore, the largest possible side length of the square envelope that can fit into the mailbox without bending is:
side length of square envelope ≤ x/√2 ≈ 0.71x
We can round this value to two decimal places, which gives us:
side length of square envelope ≈ 0.71x
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Which table of values satisfies the linear equation y=−34x −6?
The table of values satisfies the linear equation y = −3x/4 − 6 is: C. table C.
How to determine the solution?In order to determine which ordered pairs are valid and true solutions based on the given linear equation, we would have to test the given ordered pairs by substituting their values into the linear equation as follows;
For ordered pair (-4, -9), we have:
y = −3x/4 − 6
-9 = −3(-4)/4 − 6
-9 = 3 − 6
-9 = -3 (False).
For ordered pair (-8, -12), we have:
y = −3x/4 − 6
-12 = −3(-8)/4 − 6
-12 = 8 − 6
-12 = 2 (False).
For ordered pair (-4, -3), we have:
y = −3x/4 − 6
-3 = −3(-4)/4 − 6
-3 = 3 − 6
-3 = -3 (True).
For ordered pair (0, -6), we have:
y = −3x/4 − 6
-6 = −3(0)/4 − 6
-6 = 0 − 6
-6 = -6 (True).
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Complete Question:
Which table of values satisfies the linear equation y = −3x/4 − 6?
please help and explain
Find the equation of the line that cuts the x-axis at x = 1 and whose slope is -1.
The equation of the line that cuts the x-axis at x = 1 and has a slope of -1 is y = -x + 1.
What is slope-intercept form?The equation of a line in slope-intercept form is given by y = mx + b, where m is the slope of the line and b is the y-intercept, which is the point where the line crosses the y-axis.
Since the line has a slope of -1 and cuts the x-axis at x = 1, we can find the y-intercept by using the point-slope form of the line equation:
y - y₁ = m(x - x₁)
y - 0 = -1(x - 1)
y = -x + 1
So the equation of the line that cuts the x-axis at x = 1 and has a slope of -1 is y = -x + 1.
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30 minutes twice a day for 184 days how many gallons of water will be used in each hole
30 minutes twice a day for 184 days, total 368 gallons of water will be used in each hole.
Assuming that each hole uses one gallon of water per 30 minutes.
1 hole = 1 gallon of water
The total amount of water used in each hole over 184 days would be 184 gallons.
So, in 184 days = 184 gallons of water
This is because each hole would be watered twice a day for 184 days, which comes out to 368 separate waterings.
= 184 × 2
= 368 gallons
The total amount of water used would be 368 gallons.
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The complete question is:
How many gallons of water will be used in each hole if 30 minutes is spent twice a day for 184 days?
4. John and Mitchell are buying snack from the break cart at school. John bought 2 bags of chips and 3
candy bars for $8.50. Mitchell bought 4 bags of chips and 2 candy bars for $11. How much did each item
cost?
Define your variables. x =
Write a system of equations.
Solve using any method.
y=_
morgan is analyzing her data and notices that the value of her mean is quite a bit smaller than the value of her median. she asks for your help in interpreting these results. what would you tell her?
We can interpret from the results that the distribution of data might be negatively skewed.
In the given question it is mentioned that while Morgan was analyzing her data, she notices that the value of her mean is quite a bit smaller than the value of her median.
As we know that, in statistics, when the mean is smaller than the median and mode, it indicates a negatively skewed distribution.
A negatively skewed distribution or left skewed distribution is a type of distribution in which more values are concentrated on the right side of the distribution graph while the left side of the graph is longer.
Hence, we can interpret from these information that the distribution of data of Morgan are negatively skewed.
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In the diagram below, RA is parallel to ET, and RT is 21 units long. Find the length of ST.
Answer:
ST = 12 units
Step-by-step explanation:
Δ STE and Δ SRA are similar ( AA postulate ) , then the ratios of corresponding sides are in proportion, that is
[tex]\frac{ST}{SR}[/tex] = [tex]\frac{TE}{RA}[/tex] ( substitute values )
[tex]\frac{ST}{21-ST}[/tex] = [tex]\frac{8}{6}[/tex] ( cross- multiply )
6 ST = 8(21 - ST)
6 ST = 168 - 8 ST ( add 8 ST to both sides )
14 ST = 168 ( divide both sides by 14 )
ST = 12 units
1 Aiden paints an unassembled gift box to use for
his sister's birthday gift.
The base of the box measures 2 inches by5 inches. When assembled the box measures7 inches tall. If Aiden only paints the outside of the unassembled box, how many square inches will he paint?
A 64 in.²
B 70 in.²
C 118 in.²
D 126 in.²
read the story. clara snacked on a mix of almonds and pecans. she ate 3 almonds for every 1 pecan. pick the diagram that models the ratio in the story. if clara ate 10 more almonds than pecans, how many nuts did she eat altogether?
In all together, Clara ate 20 nuts.
A system of equations is a set of one or more equations involving a number of variables.
The solutions to systems of equations are the variable mappings such that all component equations are satisfied—in other words, the locations at which all of these equations intersect.
Given that Clara snacked on a mix of almonds and pecans. She ate 3 almonds for every 1 pecan. Clara ate 10 more almonds than pecans.
Let the number of pecans be x and the number of almonds is y.
We can write the system of equations as:
y = 3x
y = x + 10
Equating the value of {y}, we get -
3x = x + 10
2x = 10
x = 5 ...(1)
y = x + 10 = 15
y = 15 ...(2)
x + y = 15 + 5 = 20
Therefore, in together, Clara ate 20 nuts.
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**EASY POINTS**
2 part question:
1. There is a circular running path in the park. The diameter of the circle is 350 m. What is the length of one lap around the path?
2. Jimmy jogs 3 laps of the circle in question #1 every morning. How long does he jog in 5 days?
Answer:
The length of one lap around the path is 2π x 350 m, which is equal to 2200 m.
Jimmy jogs 2200 m x 3 laps x 5 days, which is equal to 33000 m or 33 km.
Step-by-step explanation:
Which parallelogram has the greatest area?
Area is the total space taken up by a flat (2-D) surface or shape. The area is always measured in square units.
To find the area of a parallelogram, we use this equation:
Base × height = areaNow that we have this equation, we can apply it to each parallelogram.
3 × 5 = 155 × 3 = 154 × 4 = 164 × 3 = 12Now, we can figure out which has the greatest area.
Therefore, the parallelogram that has the greatest area is 3, or III.
Answer:
III
Step-by-step explanation:
the area (A) of a parallelogram is calculated as
A = bh ( b is the base and h the perpendicular height )
I
A = 3 × 5 = 15 units²
II
A = 5 × 3 = 15 units²
III
A = 4 × 4 = 16 units²
IV
A = 4 × 3 = 12 units²
parallelogram III has the greatest area
nonlinear transformation 1 point possible (graded) explore which, if any, transformations to and can improve the quality of the fit and reduce the residuals. what transformations give you the best fit?
Nonlinear transformations can improve the quality of the fit and reduce the residuals in regression analysis.
Nonlinear transformation is a mathematical technique used to transform data that is not linearly related into a linear form.
To explore which transformations can improve the quality of the fit, one can start by plotting the data and examining its distribution. Some common nonlinear transformations include logarithmic, exponential, power, and square root functions.
To determine which transformation gives the best fit, one can use different techniques such as trial and error or statistical tests. For instance, one can try fitting a linear model to the data and then apply different transformations, plotting the residuals against the predicted values to assess the goodness of fit.
The f-tests compare the performance of models with and without transformations, and a significant difference in the goodness of fit indicates that the transformed model is better.
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Shelly incorrectly solves the equation 4−2x=−2.
Answer:
x=3
Step-by-step explanation:
x=3
4-2x=-2
-2x=-6
x=3
Answer:
Positive
Step-by-step explanation:
She incorrectly solved it because 4-2x = 2 ( Positive )
the number of people living in baltimore is 183,000. the number of new active cases of tb occurring between january 1 and june 30, 2012 was 26. the number of active tb cases according to the city register on june 30, 2012 was 264. the incidence rate of active cases of tb for the 6-month period was:
The incidence rate of active cases of tb for the 6-month period was 0.00014
An incidence rate describes how quickly disease occurs in a population.
Incidence rate is the rate of new occurrence of a particular disease divided by the population of people at risk of the disease.
So for this question
The number of new active cases of tb occurring between January 1 and June 30, 2012 was 26
Population at risk in Baltimore is 183,000
Incidence rate = 26/183,000
The incidence rate of active cases of tb for the 6-month period was 0.00014 or 14 per 100,000 population.
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which statement about 4 √2x+4 √x+3=0 is true?
The statement that is true is: The equation 4 √2x + 4 √x + 3 = 0 has one solution, which is x = -1/2.
How to find the equation that is true?To determine which statement about 4 √2x + 4 √x + 3 = 0 is true, we need to solve the equation.
However, it is not possible to solve the equation exactly because it contains square roots. We can simplify the equation by multiplying both sides by the conjugates of the square roots, which eliminates the square roots.
Multiplying both sides by (2x + x + 3) / (2x + x + 3), we get:
(4 √2x + 4 √x + 3) * (2x + x + 3) / (2x + x + 3) = 0 * (2x + x + 3) / (2x + x + 3)
Expanding the left-hand side, we get:
12x + 6 = 0
Solving for x, we get:
x = -1/2
So, the statement that is true is: The equation 4 √2x + 4 √x + 3 = 0 has one solution, which is x = -1/2.
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Helppppppo meeeeeee plssssssssssssss
1)
it took
25 min : 35 mile
?? min : 70 mile
cross multiply we get 50 minutes
25 x 70 then divide by 35
2) we used:
4 cups : 90 batches
? cups. : 112.5 batches
cross multiply we get: 5 cups
112.5 x 4 then divide by 90
Evaluate Ix+yl, for x = 8 and y=-15.
7
23
-7
-23
Answer:
A.7
Step-by-step explanation:
You first have to add 8 and -15
Then, find the absolute value
So, the answer is 7
question 6 the area of the rectangle is 48x3y5 square inches. its width is 6xy2 inches. what is the length of the rectangle?
The length of the rectangle is [tex]8x^2y^3[/tex] inches when the area of the rectangle is [tex]48x^3y^5[/tex] square inches.
To find the length of the rectangle, we can use the formula for the area of a rectangle, which is:
Area = length x width
We are given that the area of the rectangle is [tex]48x^3y^5[/tex] square inches, and its width is [tex]6xy^2[/tex] inches. Therefore, we can substitute these values into the formula to get:
[tex]48x^3y^5 = length * 6xy^2[/tex]
Simplifying this equation, we can cancel out the common factors of 6x and [tex]y^2[/tex] on both sides to get:
[tex]8x^2y^3 = length[/tex]
Therefore, the length of the rectangle is [tex]8x^2y^3[/tex] inches.
To verify our answer, we can substitute the length and width back into the formula for the area of a rectangle and check if it matches the given area:
Area = length x width = [tex](8x^2y^3) * (6xy^2) = 48x^3y^5[/tex]
Since this matches the given area, we can be confident that our answer is correct. Therefore, the length of the rectangle is [tex]8x^2y^3[/tex] inches.
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Which of the following shows 87 and 1/2% as a fraction? 7/8, 5/8, -8/75, none of these
On solving the provided question we can say that 7/8 show 87 and 1/2% as a fraction
what is fraction?Any number of equal parts or fractions can be used to represent a whole. Standard English fractions indicate how many units of a particular size there are. 8, 3/4. Whole contains fractions. The numerator to denominator ratio is a way of representing numbers in mathematics. Each of these is a simple fractional integer. A complex number has a fraction in its numerator or denominator. A proper fraction has a numerator that is smaller than the denominator. A fraction is a sum that is part of a grand total. It can be evaluated by breaking it down into smaller parts. For example, a whole number or half article is represented as 12.
7/8 show 87 and 1/2% as a fraction
87 and 1/2% should be written as 87.5%
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Jerome runs a clothing store. To mark their anniversary, they have a promotional offer for their customers. He has kept a box with five 10% discount coupons, eight 15% discount coupons, seven 20% discount coupons, six 25% discount coupons, and four 40% discount coupons. Every 30 minutes, one customer gets to draw a discount coupon from the box, use it on their purchase, and then place the coupon back into the box. Jerome predicts that when a customer draws a discount coupon from box without looking, the customer will draw a 10% discount coupon one-sixth of the time.
Yes, Jerome's prediction is true that customers will draw a 10% discount coupon one-sixth of the time.
What is probability?The possibility of the result of any random event is known as probability. This phrase refers to determining the likelihood that any given occurrence will occur.
Yes, Jeremore is correct.
It is given that a box has
Number of 10% discount coupons = 5
Number of 15% discount coupons = 8
Number of 20% discount coupons = 7
Number of 25% discount coupons = 6
Number of 40% discount coupons = 4.
The total coupons in the box = 5+8+7+6+4 = 30.
So, the probability that the customer will get a 10% coupon is
Number of 10% coupons/ Total coupons = 5/30= 1/6.
So, Jerome's prediction is true that customers will draw a 10% discount coupon one-sixth of the time.
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Which of the following statements about f(x)= -(x-4)² -1 are true? Select all that apply.
a) Vertex: (4, -1)
b) y-intercept: (0, -17)
c) x-intercept: (5, 0)
d) Axis of Symmetry: x = 4
e) x-intercept: (3, 0)
f) no x-intercepts
The following statements are true about the function f(x) = -( x-4) ² -1
1. The y intercept is (0,-17)
2. The axis of symmetry x = 4
3. The x intercept is (3,0)
What are quadratic function?A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero. The graph of a quadratic function is a curve called a parabola. Parabolas may open upward or downward and vary in "width" or "steepness", but they all have the same basic "U" shape.
The equation f(x) = -(x-4)² -1 can be expanded as
f(x) = -x²+8x-16-1 = -x²+8x-17
therefore when x = 0
the y-intercept = -17
therefore the y intercept = (0,-17)
The x intercept of the function,
when y = f(x) and y = 0
-(x-4)² = 1
-(x-4) = 1
-x+4 = 1
-x = -3
x = 3
the x intercept of the function is (3,0)
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Select all the angle relationships in △
△
ABC that are correct.
In ΔABC, we can conclude that m∠A < m∠C and m∠B < m∠A < m∠C. Hence, options a. and d. are the accurate solutions.
The angle opposite to the longest side of the triangle is the largest angle of the triangle, similarly, the angle opposite to the smallest side of the triangle is the smallest angle of the triangle.
In the given ΔABC, we have,
The longest side = AB = 3.1
The angle opposite to side AB = m∠C
The smallest side = AC = 2.9
The angle opposite to side AC = m∠B
side CB = 3
The angle opposite to side CB = m∠A
We have,
side AC < side CB < side AB
m∠B < m∠A < m∠C
From the given relations in the options provided, we get,
a. m∠A < m∠C
d. m∠B < m∠A < m∠C
are correct interpretations.
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The complete question is -
Select all the angle relationships in △ABC that are correct.
