Answer:a=-2
b=5
Step-by-step explanation:
[tex]\frac{a}{b} =\frac{\frac{-1}{4} }{\frac{5}{8} } \\\frac{a}{b} =\frac{-1}{4}*\frac{8}{5}\\\frac{a}{b}=-2/5[/tex]
I jsut need some answers thank you mwa
A scientist collected a sample of data on cactus heights. the data were rounded to the nearest foot. if the minimum score was 4 feet and the range was 6 feet, what was the maximum score? The answer is 9.
I found this question here on brainly but an expert said the answer is 10 but that is wrong. I tried commenting to say that the answer is 9 but couldn't figure out how to comment so I just posted this question with the answer for anyone who needs the answer. :) The answer is 9, I received points for it being correct.
Answer: the maximum score was 10 feet.
Step-by-step explanation:
here's a step-by-step explanation:
Identify the minimum score: The minimum score is given in the problem as 4 feet.
Identify the range: The range is also given in the problem as 6 feet.
Calculate the maximum score: To find the maximum score, we simply need to add the minimum score and the range.
Maximum score = Minimum score + Range
Maximum score = 4 feet + 6 feet
Maximum score = 10 feet
So the maximum score was 10 feet.
pls help
About 3,500 tourists visit the Granite Falls overlook each year. After the construction of a new nature center with exhibits and hands-on activities, that number is expected to increase 5% each year. Assuming the same growth continues, you can use a function to approximate the number of annual visitors to the overlook x years after the nature center is built.
Write an equation for the function. If it is linear, write it in the form f(x)=mx+b. If it is exponential, write it in the form f(x)=a(b)^x.
Answer:
Step-by-step explanation:
Here's a step by step explanation for writing a function to approximate the number of annual visitors to the overlook x years after the nature center is built:
Start by defining the initial number of visitors as the baseline. We'll call this y0 and set it equal to 3,500 tourists:
y0 = 3,500
Define the rate of growth as a percentage increase. We're told that the number of visitors is expected to increase by 5% each year, so we'll call this rate "r" and set it equal to 0.05:
r = 0.05
Write the equation for exponential growth. The formula for exponential growth is given by:
y = y0 × (1 + r)^x
where x is the number of years after the nature center is built.
So, the equation for the function in this case would be:
f(x) = 3,500 × (1 + 0.05)^x
This function models the expected number of annual visitors to the overlook x years after the nature center is built. The function is exponential because the number of visitors is multiplied by a constant factor (1 + 0.05) raised to a power (x) at each time step.
estimate the percent of 18% of 48
Answer:8.64
Step-by-step explanation:
Answer:
8,64
Step-by-step explanation:
[tex]\frac{18}{100}[/tex]*48=8,64
Find the value of sin D rounded to the nearest hundredth, if necessary.
The value of the trigonometric equation sin D = 0.923
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the triangle be represented as ΔBCD
Now , the measure of BC = 24
The measure of side CD = 10
So , the measure of hypotenuse BD = √ ( BC )² + ( CD )²
Substituting the values in the equation , we get
The measure of BD = √ ( 576 ) + 100
The measure of BD = √ ( 676 )
The measure of BD = 26
Now , from the trigonometric relations ,
sin θ = opposite / hypotenuse
Substituting the values in the equation , we get
sin D = 24 / 26
On simplifying the equation , we get
sin D = 0.923
Hence , the equation is sin D = 0.923
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For the following distribution of quiz scores, how many individuals took the quiz?
x f
5 6
4 5
3 5
2 3
1 2
a. 5
b. 10
c. 15
d. 21
The answer is not one of the given choices. The correct answer is 73.
To find the total number of individuals who took the quiz, we need to add up the frequency (f) for each score (x) and then take the sum:
5(6) + 4(5) + 3(5) + 2(3) + 1(2) = 30 + 20 + 15 + 6 + 2 = 73
Therefore, the answer is not one of the given choices. The correct answer is 73.
Frequency distributions are portrayed as frequency tables or charts. Frequency distributions can show either the actual number of observations falling in each range or the percentage of observations. In the latter instance, the distribution is called a relative frequency distribution.
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Someone pls help me with the bottom question 30 points
Answer: 9/4
Step-by-step explanation:
A scale factor is the number by which all components of an object are multiplied in order to create a proportional enlargement or reduction.
7 5/6 / 2 2/3
Leave as a mixed number
Answer:
2.9375
Step-by-step explanation:
7 5/6 / 2 2/3 = 47/16 = 2 15/16 = 2.9375
Given AC is the angle bisector of
proof below. Note that the last statement and reason have both been filled in for
you.
( must make AAS )
The proofing will be illustrated thus:
1. Seg. AC bisects ∠BAD 1. Given
2. (m=measure) m∠BAC=∠CAD 2. Definition of angle bisector
Therefore, m∠BAC≅∠CAD.
3. AC=AC 3. reflexive property
4. ∠ABC =∠ADC 4. Given
5. Triangle ABC≅Triangle ADC 5. Angle-Angle-Side (AAS postulate).
6. Therefore, BC=DC 6. CPCTC
What does AAS mean?It should be noted that AAS stands for Angle-Angle-Side. In this case, ehen two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle, then the triangles are said to be congruent
Corresponding parts of congruent triangles are congruent.
Here, the two pairs of angles correspond, but there is a shared side that is not between the angles.
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Given: AC bisects \angle BAD
Given: AC bisects \angle BAD
\angle ABC=\angle ADC
Write a two-column proof to prove= BC=DC
Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options.
The value of f(–10) = 82
The graph of the function is a parabola.
The graph of the function opens down.
The graph contains the point (20, –8).
The graph contains the point (0, 0).
The only correct option for the given quadratic function, is the graph of the function is a parabola. (there is only one correct option)
What is a quadratic function?A quadratic function is a polynomial function with one or more variables in which the highest exponent of the variable is two.
Given is a quadratic function f(x) = x² - 5x + 12, there are some options given, we need to select the option which are correct according to the given quadratic function,
So, firstly we will plot the graph of the given function,
From the graph, we get,
The function is a parabola which opens up, the points (20, -8) and (0, 0) do not lie in the graph,
Now, finding the value of f(-10), put x = -10
(-10)² - 5(-10) + 12 = 100+52+12 = 164
Hence, in the conclusion the only correct option for the given quadratic function, is the graph of the function is a parabola. (there is only one correct option)
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What is the perimeter of parallelogram WXYZ?
The perimeter is ]- (Type an integer or a decimal.)
The perimeter of the parallelogram is; 184
What is the perimeter of the parallelogram?In geometry, the perimeter of a shape is defined as the total length of its boundary.
Now, from the given image, we don't know the vertical sides XW and YZ and we can find it from Pythagoras theorem;
XW = √(68² - 60²)
XW = 32
Thus, the perimeter of the parallelogram is;
Perimeter = 2(32 + 60)
= 2 * 92
= 184
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A group of 500 middle school students were randomly selected and asked about their preferred television genre. A circle graph was created from the data collected.
a circle graph titled preferred television genre, with five sections labeled drama 14 percent, sports 22 percent, documentaries 24 percent, reality 20 percent, and sci-fi
How many middle school students prefer the Sci-Fi television genre?
100
80
72
20
Answer:
The answer is 100, see Step-by-step explanation:
Step-by-step explanation:
If anyone looks at the verified answer, its wrong and so are the comments under it. In the answer above it says "Sci-fi = 100-24-22-20-14=20" that is correct but the answer is not. 20 percent of 500 is 100 not 72 or 20, I don't know how anyone got those answers.
Use numerical evidence to estimate the value of the limit to at least 2 decimal places.
If the equation be [tex]$\lim _{x \rightarrow 6}\left(\frac{x^2-x-30}{x^2-3 x-18}\right)$$[/tex] then the value is 1.22222
What is meant by numerical evidence?The term "numerical evidence" describes information that is expressed in a numerical manner, such as numbers, quantities, or statistical data. It is thought to be objective and quantifiable, and it is used to support a claim or argument.
The quantity of sales made during a specific business quarter is an example of numerical data. Simply put, if the response includes a number, the data is quantitative (numerical).
Let the equation be [tex]$\lim _{x \rightarrow 6}\left(\frac{x^2-x-30}{x^2-3 x-18}\right)$$[/tex]
Simplifying the above equation, we get
[tex]$\frac{x^2-x-30}{x^2-3 x-18}= \frac{x+5}{x+3}$[/tex]
[tex]$=\lim _{x \rightarrow 6}\left(\frac{x+5}{x+3}\right)$$[/tex]
Plug in the value x = 6
= (6 + 5)/(6 + 3)
= 11/9 = 1.22222
Therefore, the equation of [tex]$\lim _{x \rightarrow 6}\left(\frac{x^2-x-30}{x^2-3 x-18}\right)$$[/tex] be 1.22222.
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The table represents an exponential function. What is the multiplicative rate of change of the function? 2 5.
From the table which represents the exponential function , the multiplicative rate of change of function is (a) 1/5 .
The exponential function is expressed mathematically as : y = a(b)ˣ ;
where "a" is = initial value of function , and "b" is = multiplicative rate of change ;
We first substitute , the first two values from the exponential table ;
we get ;
⇒ 2 = a(b)¹
⇒ 2 = ab ,...,,....equation(1) ;
Now substituting the second value ,
we get ;
⇒ 2/5 = a(b)² ,....equation(2) ;
On dividing equation(2) by equation(1) ,
we get;
⇒ 2/(2/5) = ab/ab² ;
⇒ 5 = 1/b ;
⇒ b = 1/5 .
Therefore , the multiplicative rate of change is b = 1/5 .
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The given question is incomplete , the complete question is
The table represents an exponential function.
What is the multiplicative rate of change of the function ?
(a) 1/5
(b) 2/5
(c) 2
(d) 5
Find the length of CB
C is 22 and B is 20, then the length of CB is √(22² + 20²) = √(884) = 29.
What is length?Length is a measurement of size and it can be measured in a variety of waste including inches sentiment of metres feet miles and more. Playing these an important concept in mathematics, science and engineering and many others build it to used to calculate the dimensions of this area. And more it is also used to measure the time it takes to travel.
The length of CB can be determined by using the Pythagorean theorem, which states that the square of the length of the hypotenuse (the longest side of a right triangle) is equal to the sum of the squares of the other two sides. Since CB is the hypotenuse of a right triangle, the length of CB can be determined by solving the following equation:
C² + B² = CB²
Therefore, when given the lengths of sides C and B, the length of CB can be calculated by taking the square root of the sum of the squares of C and B.
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Landis cuts a foam block along the red line. When he looks at the newly
exposed face, what is the shape of the cross-section?
15 in
6 in
5 in
The shape of the newly cut cross section is option A. A rectangle, 5 inches by 6 inches.
What is Rectangle?Rectangle is a two dimensional shape or figure which consists of four sides and four angles and all the angles are right angles.
Opposite sides are equal.
It is clearly seen that the red line is passing along the length of the block.
So the new cross section cannot have the dimension 15 inches in any part.
And the width and height is not getting cut.
So the dimension will be 5 inches by 6 inches.
A square has all the sides equal.
Since both the dimensions are not equal it is a rectangle and not a square.
Hence the new cross section is A. A rectangle, 5 inches by 6 inches.
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The complete question is as follows and the image for the block is attached below :
Landis cuts a foam block along the red line. When he looks at the newly
exposed face, what is the shape of the cross-section?
A. A rectangle, 5 inches by 6 inches
B. A rectangle, 15 inches by 6 inches
C. A rectangle 5 inches by 15 inches
D. A square, 5 inches by 5 inches
What is the area of this parallelogram?
A:60cm
B:66
C:72
D:132
The area of the given parallelogram is 12 cm².
What is Parallelogram?A parallelogram is defined as a special type of quadrilateral that has both pairs of opposite sides parallel and equal.
The formula to calculate the area of a parallelogram can thus be given as,
Area of parallelogram = b × h square units
where b is the length of the base and h is the height
According to the given parallelogram ABCD, we have
Length of the base b = 5 + 9 = 14 cm
The height h = 8 cm
Area of parallelogram = b × h
Area of parallelogram = 14 × 8
Area of parallelogram = 112 cm²
Thus, the area of the given parallelogram is 12 cm².
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The question seems incomplete, the missing figure has been attached below.
Write an equation for the line that contains the points (4,-2) and (-2,0)
The linear equation that passes through the two given points is:
y = (-1/3)*x - 2/3
How to write the equation of the line with the two points?A general linear equation can be written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If a line passes through the points (x₁, y₁) and (x₂, y₂) then the slope can be written as:
a = (y₂ - y₁)/(x₂ - x₁)
Here we know that the line passes through (4, -2) and (-2, 0), then the slope is:
a = (0 + 2)/(-2 - 4)= 2/-6 = -1/3
y = (-1/3)*x + b
To find the value of b, we can replace the values of any of the points in the equation, if we use (-2, 0) we will get:
0 = (-1/3)*-2 + b
0 = 2/3 + b
-2/3 = b
The linear equation is y = (-1/3)*x - 2/3
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What is the surface area of the cylinder?
100 ft²
800 ft²
10 ft
10 ft
Select the correct answer.
A right angle triangle where ABC angle is 90° and angle ACB is 45°.
Which trigonometric ratio will not have the same value as sin A?
A.
cos A
B.
sin C
C.
tan C
D.
cos C
Reset Next
Trigonometric Ratios: Mastery Test
© 2023 Edmentum. All rights reserved.
Trigonometric ratio in option (c) tan C will not have the same value as sin A.
What are Trigonometric Functions?Trigonometric functions are defined as the periodic functions which relate an angle in a right angled triangle to the ratios of the length of two sides.
Given a right angled triangle ABC given below.
ABC angle is 90° and angle ACB is 45°.
Then angle BAC = 180° - (90° + 45°) = 45°
Since two angles are equal, it is an isosceles triangles.
So opposite sides to the equal angles are equal.
AB = BC
AC is the hypotenuse.
Sin A = Opposite side / Hypotenuse = BC / AC
(a) Cos A = Adjacent side / Hypotenuse = AB / AC = BC / AC
(b) Sin C = AB / AC = BC / AC
(c) Tan C = Opposite side / Adjacent side = AB / BC = BC / BC = 1, not equal to Sin A
(d) Cos C = BC / AC
Hence the option (c) is not equal to sin A.
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Use this table to answer the question. Round to the nearest percent.
Car Plane Train Total
Green 120 250 500 870
Blue 150 350 750 1250
Yellow 170 200 450 820
Red 200 300 300 800
Brown 220 450 320 990
Total 860 1550 2320 4730
What percent of Planes are Green?
There are 29% of the Planes are Green.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
Total number of green planes = 250
The total number of green vehicles = 870
The percent of green planes = (number of green planes/number of total green vehicles) x 100
The percent of green planes = (250/870) x 100
The percent of green planes = 0.2873 x 100
The percent of green planes = 28.73
Round to the nearest percent, and we get
The percent of green planes = 29%
Thus, 29% of Planes are Green.
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Use the coordinates below to determine if AABC and ADEF are congruent.
AABC: A(2, -8), B(-5, -2), C(-7, 3); ADEF: D(-9, 7), E(-11, 12), F(-2, 1)
AB=
DE=
BC=
EF=
AC=
DF=
Are the angles congruent? If yes, explain your reasoning and write a congruency statement.
No The triangles' are not congruent
How to determine if the triangles are congruentThe length of the corresponding sides should be equal and the length of sides is gotten using the equation:
The length of line in an ordered pair is calculated using the formula
d = √{(x₂ - x₁)² + (y₂ - y₁)²}
where
d = distance between the points
x₂ and x₁ = points in x coordinates
y₂ and y₁ = points in y coordinates
distance between points A(2, -8), B(-5, -2), C(-7, 3); and ΔDEF: D(-9, 7), E(-11, 12), F(-2, 1) are calculated as follows:
AB =√{(-2 + 5)² + (-8 + 2)²} = 6.71
DE = √{(-9 + 1)² + (7 - 12)²} = 9.43
BC = √{(-5 + 7)² + (-2 - 3)²} = 5.39
EF = √{(-11 + 2)² + (12 - 1)²} = 14.21
AC = √{(2 + 7)² + (-8 - 3)²} = 14.21
DF = √{(-9 + 2)² + (7 - 1)²} = 9.22
Examining the figures showing the side lengths shows that the two triangles are not congruent
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2023 Tax Year (Filing in 2024)
You are 25yr old and single with no kids/dependents.
You live in Florida.
Your job pays $84,649/yr.
You have no other sources of incomes.
Your itemized deductions come out to $10,211.
Your credits come out to $9.
Your tax-deffered retirement contributions come out to $3,288.
Calculate the total Federal Income Taxes and FICA paid.
If you are 25yr old and single with no kids/dependents. The total Federal Income Taxes is $11,218 and FICA paid is $6,478.
How to find the total Federal Income Taxes and FICA paid?First, you need to determine your taxable income.
Gross income: $84,649
Itemized deductions: $10,211
Tax-deferred retirement contributions: $3,288
Taxable income: $71,150
Next, you can use the tax brackets and rates for the 2023 tax year to calculate your federal income tax liability.
The first $10,950 is taxed at 10%: $1,095
The next $32,250 is taxed at 12%: $3,870
The next $28,425 is taxed at 22%: $6,253
The remaining $0 is taxed at 24%: $0
Total federal income tax liability: $11,218
b. For 2023, the Social Security tax rate is 6.2% on the first $147,000 of income, and the Medicare tax rate is 1.45% on all income.
Social Security tax: $5,240.80
Medicare tax: $1,237.20
Total FICA taxes: $6,478
Therefore the total Federal Income Taxes is $11,218 and FICA paid is $6,478.
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18.
Credit scores are made of _____.
credit history, payment history, debt ratio, and types of credit
creditworthiness
FICO
credit profile
Credit scores are made of credit history, payment history, debt ratio, and types of credit which is therefore denoted as option A.
What is a Credit score?This is referred to as a numerical expression based on a level analysis of a person's credit files, to represent the creditworthiness of an individual.
It is a prediction of how likely you are to pay a loan back on time based on information from your credit reports and has different components such as the credit history, payment history, debt ratio, etc.
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Question content area top
Part 1
Find the slope of the line if it is defined.
Through (6,5) and (6,-8)
Answer:
undefined or no slope.
Step-by-step explanation:
m is slope. slope is always change of y over change of x. this mean. y2-y1 divide by x2-x1. in this case y2 is -8, y1 is 5 and x2 is 6 and x1 is 6. remember the number in front the variable are base. the answer is undefined.
A worker earned a 3% increase in her annual salary for each of 5 years. They plan to continue working in
their position for an additional n years. If they continue to earn a 3% increase in their annual salary, which
statement describes the expression that can be used to calculate the total percent increase in their annual
salary from the first year to the last year?
A. The expression 1.035 can be used because (1.035)" = 1.035.
OB. The expression 1.035 ca
can be used because 1.035 x 1.03 = 1.035.
O C. The expression 1.035+ can be used because 1.035 x 1.03 = 1.035+
O D. The expression 1.035+ can be used because 1.035 +1.03n = 1.035+n.
Using an exponential function, it is found that the expression that can be used to calculate the total percent increase in their annual salary from the first year to the last year is given by:
P= 100%[([tex]1.03^{t}[/tex]) - 1]
What is an exponential function?An exponent refers to the number of times a number is multiplied by itself. For example, 2 to the 3rd (written like this: 23) means: 2 x 2 x 2 = 8. 23 is not the same as 2 x 3 = 6. Remember that a number raised to the power of 1 is itself.
here, we have,
An increasing exponential function is modeled by:
A(t)= A(0)[tex](1+r)^{t}[/tex]
In which:
A(0) is the initial value.
r is the decay rate, as a decimal.
As a percentage, the increase is modeled by:
P= 100%[[tex](1+r)^{t}[/tex] - 1]
In this problem, the growth rate is of r = 0.03, hence:
P= 100%[ [tex](1+0.03)^{t}[/tex]- 1]
P= 100%[[tex](1.03)^{t}[/tex]- 1]
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40 books are increased in the ratio 5:4 the new number of books are?
Answer:
50
Step-by-step explanation:
4x10=40.
5x10=50
Answer:
Step-by-step explanation:
To increase a quantity in a given ratio, we can follow these steps:
Step 1: Find the total increase in the quantity.
Suppose the original number of books is "b". The total increase in the number of books is 40, so:
b + 40 = b
Step 2: Divide the total increase into two parts in the given ratio.
In this case, the ratio is 5:4, so we can divide the increase of 40 into two parts in the ratio 5:4. Let's call the first part "x". Then, the second part is 40 - x.
The first part (5x) is 5 times the second part (4x), so:
5x = 4(40 - x)
Step 3: Solve for x.
Expanding the right side:
5x = 160 - 4x
Adding 4x to both sides:
9x = 160
Dividing both sides by 9:
x = 40/9
Step 4: Find the new number of books.
The first part of the increase (x) is 40/9, and the second part (40 - x) is 40 - 40/9 = 40 * 9/9 - 40/9 = 40 * 8/9. The new number of books is the original number plus the two parts of the increase:
b + 40/9 + 40 * 8/9 = b + 40
So, the new number of books is b + 40.
Sheet Metal Trades To determine the average thickness of a metal sheet, a Sheet metal worker measures it at five different locations. Her measurements are 0.0401, 0.0417, 0.0462, 0.0407, and 0.0428 in. What is the average thickness of the sheet?
The average thickness of the metal sheet is 0.0423 inches.
What do you mean by average?In statistics, the mean is a measure of central tendency of a set of data. It is also referred to as the arithmetic mean and is calculated by adding up all the values in the data set and dividing by the total number of values.
Mean = (sum of all values) / (number of values)
For example, suppose we have the following set of data: 5, 7, 9, 11, 13. To find the mean, we add up all the values and divide by the total number of values, which is 5 in this case:
Mean = (5 + 7 + 9 + 11 + 13) / 5
Mean = 9
Therefore, the mean of this data set is 9.
The mean is a commonly used measure of central tendency because it takes into account all the values in the data set and is sensitive to changes in the data. However, it can be affected by outliers or extreme values in the data set, which can skew the results.
To find the average thickness of the sheet, we need to add the five measurements together and then divide by 5 (the number of measurements):
Average thickness = (0.0401 + 0.0417 + 0.0462 + 0.0407 + 0.0428) / 5
Average thickness = 0.0423 in
Therefore, the average thickness of the metal sheet is 0.0423 inches.
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A small kitchen sink is 14in x 16in x 6in = 3584 cubic inches. If your water faucet in the kitchen is leaking 1 drop of water per second (volume of a typical drop is 0.05 ml ≈ 0.003 cubic inches), how long would it take for a clogged sink to fill and start overflowing. Write your answer in days.
A more accurate value would be 13.8271643518519
Round it however you need to.
======================================================
Explanation:
1 day = 24 hours
1 hour = 60 minutes
1 minute = 60 seconds
Let's see how many seconds there are in a day.
[tex]1 \text{ day} = (1 \text{ day})*\frac{24 \text{ hrs}}{1 \text{ day}}*\frac{60 \text{ min}}{1 \text{ hr}}*\frac{60 \text{ sec}}{1 \text{ min}}\\\\=\frac{24*60*60}{1*1*1}\text{ sec}\\\\=86,400\text{ sec}\\[/tex]
I set up those fractions so that the units "day", "hours", "minutes" cancel out. The only unit left over is "seconds".
There are exactly 86,400 seconds in 1 day.
This leads to the fact the sink fills up at a rate of 86,400 drops per day, since the leak rate is 1 drop per second.
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1 drop = 0.003 cubic inches approximately
x of those drops give a volume of 0.003x cubic inches, where x is some positive whole number. Set this equal to the volume of the sink and solve for x.
0.003x = 3584
x = 3584/0.003
x = 1,194,666.66666667 approximately
Round up to the nearest whole number to get 1,194,667
The sink starts to overflow when we have 1,194,667 drops of water in it.
Divide this over 86,400 mentioned earlier.
(1,194,667)/(86,400) = 13.8271643518519 approximately.
Round that however you need to. If for instance you round to 3 decimal places, then it would be 13.827
Please help!!!!! Due tomorrow need to understand how to properly do this question :(
The table offers an average rate of change greater than the average rate of change of the function f(x) = x² + 2 · x - 1.
How to determine the average rate of change of a function
In this problem we need to determine two average rates of change, one from an equation and another from a table. Graphically speaking, average rate of change is the slope of a line secant to a curve and it can be computed by secant line formula:
m = [f(2) - f(- 2)] / [2 - (- 2)]
First, we proceed to determine the average rate of change for the function f(x) = x² + 2 · x - 1:
f(- 2) = (- 2)² + 2 · (- 2) - 1
f(- 2) = 4 - 4 - 1
f(- 2) = - 1
f(2) = 2² + 2 · 2 + 1
f(2) = 9
m = [9 - (- 1)] / [2 - (- 2)]
m = 10 / 4
m = 5 / 2
m = 2.5
And the average rate of change of the table:
m = (6.25 - 0.16) / [2 - (- 2)]
m = 0.09 / 4
m = 609 / 400
m = 1.523
To learn more on average rates of change: https://brainly.com/question/17219001
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