Use the graph to find the average rate of change from x=-1 to x=1.
The average rate of change of f(x) over the interval is 3
What is the average rate of change of f(x) over the intervalFrom the question, we have the following parameters that can be used in our computation:
The graph
We have the interval to be
x=-1 to x=1.
From the graph, we have
f(-1) = -3
f(1) = 3
The average rate is then calculated as
Average rate = [f(1) - f(-1)]/[1 + 1]
Substitute the known values in the above equation, so, we have the following representation
Average rate = (3 + 3)/2
Evaluate
Average rate = 3
Hence, the average rate is 3
Read more about average rate at
brainly.com/question/17131025
#SPJ1
Simplify using properties of exponents and radicals. ^3√32a¹⁰b^6
The simplified expression is 4a⁵ * b³.
Describe exponents?Exponents are a way to represent repeated multiplication. The exponent of a number represents the number of times the base is multiplied by itself. For example, 2^3 means 2 multiplied by itself 3 times, or 2 * 2 * 2 = 8.
In general, if the base number is b and the exponent is n, then b^n represents b multiplied by itself n times. This can be written as b * b * ... * b (n times). The exponent can be any positive integer or zero, and the base can be any real number.
Exponents have several properties, including the following:
b^0 = 1 for any non-zero base b.
b^1 = b for any base b.
b^n * b^m = b^(n + m) for any base b and positive integers n and m.
(b^n)^m = b^(n * m) for any base b and positive integers n and m.
b^(-n) = 1 / b^n for any base b and positive integer n.
These properties help simplify and manipulate expressions with exponents.
We can simplify the expression using the properties of exponents and radicals as follows:
^3√32a¹⁰b⁶
= ^3√(2⁵ * 2¹ * a¹⁰ * b⁶) [since 32 = 2⁵ and 2¹]
= ^3√(2⁶ * a¹⁰ * b⁶) [using the property of exponents: a^m * a^n = a^(m+n)]
= 2^2 * ^3√(a¹⁰ *b⁶) [since 2⁶ = 2² * 2⁴]
= 2² * a⁵ * b³ [since (^3√(x))³ = x, and since a^m * b^m = (ab)^m]
= 4a⁵ * b³.
So, the simplified expression is 4a⁵ * b³.
To know more about expression visit:
https://brainly.com/question/27148036
#SPJ1
What is the slope of the line that runs through the two points? (-3, 1) (-17, 2)
Hello!
Answer:
The slope of the line that runs through the two points (-3,1) and (-17,2) is
[tex]m= - \frac{1}{14}[/tex]
Step-by-step explanation:
Use the formula of slope to find [tex]m[/tex]
Hope this helps!
Karen borrowed $1000 from a friend that agreed to charge her a very low interest rate of .25% per month. The deal is that Karen will pay back $1100 at the time when the interest brings the total up to that amount. How many months will Karen have before the total reaches
$1100?
months (ROUNDED TO THE NEAREST MONTH)
Answer:
The interest amount Karen needs to pay each month is $1000 * .0025 = $2.5.
So, she needs to pay $1100 - $1000 = $100 in interest.
Therefore, Karen will have to pay for 100 / 2.5 = 40 months.
Rounding to the nearest month, Karen will have to pay for 40 months.
Preform the multiplication. Simplify your answer if possible
(5 √(3) + √(15)) × (3 √(5) + √(15))
The simplified form for the given problem (5 √(3) + √(15)) × (3 √(5) + √(15)) is 45√(45).To solve the equation we are using the distributive property.
The property which states that the product of a number and the sum of two numbers is equal to the sum of the products of the number and each of the two numbers being added. Using this principle, the problem can be broken down into two separate products, (5 √(3) × 3 √(5)) and (5 √(3) × √(15)) + (√(15) × 3 √(5)).
The first part of the problem can be simplified by combining 5 and 3, which is 15. This leaves 15 √(15). The second part of the problem can be simplified by combining 3 and 5, which is 15. This leaves 15 √(15). Adding the two parts together results in 30 √(15). The √(15) can be multiplied by itself, which is 15. Multiplying 30 by 15 results in 45 √(45). The √(45) cannot be simplified any further, so the final answer is 45√(45).
To know more about distributive property refer to the link brainly.com/question/6276874
#SPJ4
What is one of the solutions to the following system?
StartLayout Enlarged left-brace 1st Row y minus 3 = x 2nd row x squared minus 6 x + 13 = y EndLayout
The solutions to the system of equations is given as follows:
(-1,2) and (8,11).
How to solve the system of equations?The system of equations for this problem is defined as follows:
y - 3 = x.x² - 6x + 13 = y.From the first equation, we have that:
y = x + 3.
Replacing on the second, we have that:
x² - 6x + 13 = x + 3.
x² - 7x - 16 = 0.
We can factor the expression as follows:
(x - 8)(x + 1) = 0.
Hence the solutions are:
x - 8 = 0 -> x = 8 and y = x + 3 = 11.x + 1 = 0 -> x = -1 and y = x + 3 = 2.More can be learned about a system of equations at https://brainly.com/question/30374328
#SPJ1
Answer: B
Step-by-step explanation:
edge 2023
Write the ratio in simplest form.
3:9
1:3
simplify the ratio and you would get 1:3
The area formula is A = πr2. Substitute the values of r (3.5 inches) and π (3.14) in the formula to find A: A = 3.14 × (3.5)2 square inches A = 38.465 square inches. The area of each light is about 38.465 square inches. What is the total area of all three circular lights?
The total area of all three circular lights is 115.395 square inches
What is the total area of all three circular lights?From the question, we have the following parameters that can be used in our computation:
A = 3.14 × (3.5)2 square inches A = 38.465 square inches. The area of each light is about 38.465 square inches.Using the above as a guide, we have the following:
The total area of all three circular lights = 3 * 38.465 square inches.
Evaluate
The total area of all three circular lights = 115.395 square inches.
Hence, the area is 115.395 square inches
Read more about area at
https://brainly.com/question/22972014
#SPJ1
The pair of linear equations is graphed below.
Which values for x and y will satisfy both linear equations?
x = 0, y = 7
x = – 7, y = 0
x = 3, y = – 4
x = – 4, y = 3
Answer:
(-4,3)
x = -4 and y = 3
Step-by-step explanation:
Set the two equation equal to each other and solve for x.
x + 7 = [tex]\frac{3}{4}[/tex] x + 6 Multiply all the way through by 4 to clear the fraction
4(x + 7) = 4( [tex]\frac{3}{4}[/tex] x + 6) Distribute the 4
4x + 4(7) = 4([tex]\frac{3}{4}[/tex]x) + 4(6)
4x + 28 = 3x + 24 [tex]\frac{4}{1}[/tex] x [tex]\frac{3}{4}[/tex] = [tex]\frac{12}{4}[/tex] = 3 ([tex]\frac{4}{1}[/tex] is another name for 4) subtract 3x from both sides
4x - 3x + 28 = 3x - 3x + 24
x + 28 = 24 subtract 28 from both sides
x + 28 - 28 = 24 - 28
x = -4
Substitute -4 for x in either of the two original equations and solve for y.
y = x + 7
y = -4 + 7
y = 3
Check
Substitute in -4 for x and 3 for y and see if we get true statements.
y = x + 7
3 = -4 + 7
3 = 3 checks
y = [tex]\frac{3}{4}[/tex] x + 6
3 = [tex]\frac{3}{4}[/tex] [tex](\frac{-4}{1})[/tex] + 6
3 = -3 + 6
3 = 3 cfhecks
what feature in tableau was used in the video above to help understand the interpretation of the large p-value of the variable spec.feats in the multiple linear regression model whose independent variables are size and spec.feats?
In the video, the presenter used Tableau to help interpret the large p-value of the variable spec. feats in the multiple linear regression model.
The presenter first used a scatter plot to visualize the relationship between size and spec. feats and included a regression line to represent the linear relationship between the two variables.
The presenter then used Tableau's Trend Lines tab to calculate the p-value of the spec. feats by providing the regression equation and data points.
This allowed the presenter to determine the p-value of the spec. feats were too large to be significant and thus concluded that spec. feats did not have a significant linear relationship with size.
For more questions like Tableau click the link below:
https://brainly.com/question/25531734
#SPJ4
What does paper folding have to do with exponents? Explain your reasoning.
Answer: Shows base 2 exponents
Step-by-step explanation: When there are no folds, the paper is at 2^0 which is one piece. The after one fold is 2^1 which is 2 and doubles after. This represents exponents with base 2.
A hot, humid coastal tropical atmosphere is one that forms over the Indian Pacific.
It's not fully accurate to say that. In many tropical and subtropical coastal places around the world, where warm, moist air from the ocean mixes with the land and creates high humidity and frequent rainfall, a hot, humid coastal tropical atmosphere prevails. This climate is not specific to the Indian or Pacific Oceans.
Are tropical regions hot and muggy?The majority of tropical regions are renowned for their year-round high temperatures and heavy precipitation. Tropical regions are humid because of the heavy rainfall and hot because of the high temperature.
In which region of India is it hot and humid?The tropical wet climate, often referred to as the tropical monsoon climate, dominates a section of the southwest lowlands that border the Malabar Coast, the Western Ghats, and southern Assam. It is the driest climate. Lakshadweep and the Andaman and Nicobar Islands, two of India's island territories, are also impacted by severe weather.
To know more about Tropical visit:
https://brainly.com/question/9339571
#SPJ1
HELP WILL GIVE BRAINLIEST
help me find the equations for the piece wise graph
The equations for the Piece Wise Graph is:
F(x) = -1/8x² - 2x -1 -8 ≤ x < -4
(x + 1) + 2 -4 < x < 4
What is a Piece Wise Graph?A piecewise function is one that has several curve parts in its graph. It signifies that it has several meanings based on the input value. A piecewise function, in other words, performs differently depending on the input.
To derive the above equation,
Set a square root function y = ax² + bx + C
7 = 64a = 8b +c a = -1/8
5 = 16a - 4b + c b = -2
-b/2a = -8 c = -1
So y = -1/8 x² - 2x -1
Absolute Value Function:
Right: y = x + 3
so y = (x+1) + 2
F(x) = -1/8x² - 2x -1 -8 ≤ x < -4
(x + 1) + 2 -4 < x < 4
Thus the piece-wise functions are computed in turn.
Learn more about piece-wise functions:
https://brainly.com/question/16984860
#SPJ1
The angles below are supplementary. What is the value of x? (5 points) A pair of supplementary angles is shown. One angle measures 3x + 40, and the other angle measures 80. a 16.6 b 20 c 26.7 d 40
Answer:
b) 20
Step-by-step explanation:
In supplementary angles, the sum of two angles add up to 180°
3x + 40 + 80 = 180
3x + 120 = 180
Subtract 120 from both sides,
3x = 180 - 120
3x = 60
Divide both sides by 3
x = 60 ÷ 3
[tex]\boxed{\bf x = 20^\circ}[/tex]
XYZ Tech wants to sell at least 40% more tablets this week than the 50 they sold last week. Which inequality describes this?
A. x ≥ 1.4(50) B. x > .4(50) C. x > 1.4(50)
The solution is Option A.
The inequality equation is x ≥ 1.4 ( 50 )
What is an Inequality Equation?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the inequality equation be represented as A
Now , the value of A is
The number of tablets XYZ Tech sold last week = 50 tablets
The number of tablets XYZ Tech needs to sell this week = 40 % more
So , number of tablets XYZ Tech needs to sell this week = 50 +( 40/100 )50
On simplifying the equation , we get
The number of tablets XYZ Tech needs to sell this week = 50 ( 1 + 0.4 )
The number of tablets XYZ Tech needs to sell this week = 1.4 ( 50 )
Now , they have to sell at least 40 % more
So , the inequality equation is x ≥ 1.4 ( 50 )
Hence , the inequality equation is x ≥ 1.4 ( 50 )
To learn more about inequality equations click :
https://brainly.com/question/11897796
#SPJ1
A total of
330
330 children and adults attended a school play. There were
21
21 times as many children in attendance as there were adults.
This situation is modeled by the given system of equations, where a represents the number of adults and c represents the number of children.
As a result, 315 pupils attended the school play.
What is equation?In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical phrase with two equal sides separated by an equal sign is called an equation. An example of an equation is 4 + 6 = 10.
Here,
The first equation in the system is given by the total number of attendees:
c + a = 330
The second equation is given by the number of children being 21 times the number of adults:
c = 21a
We can use substitution to find the value of a and then find the value of c. Substituting the second equation into the first equation, we get:
21a + a = 330
Combining the two terms on the left-hand side, we have:
22a = 330
Dividing both sides by 22, we have:
a = 15
So there were 15 adults in attendance at the school play. To find the number of children, we can use the second equation:
c = 21a = 21 * 15 = 315
So there were 315 children in attendance at the school play.
To know more about equation,
https://brainly.com/question/2228446
#SPJ4
There are 5,280 feet in a mile. Round answers to the nearest unit. a. How many miles does a car traveling at 42 mi/h go in one hour
The answers for questions G, H, K, and L are the same as questions C, D, K, and L, respectively, because the speed (65mi/h) remains constant.
A. 65 miles in one hour: If a car is traveling at 65 miles per hour (mi/h), then in one hour it will travel 65 miles.
B. 340,800 feet in one hour, 65 miles is equal to 5,280 x 65 = 340,800 feet.
C. 5,680 feet in one minute, 340,800 feet ÷ 60 = 5,680 feet in one minute.
D. 94.67 feet in one second, 5,680 feet ÷ 60 = 94.67 feet in one second.
E. 42 miles in one hour: If a car is traveling at 42 miles per hour, then in one hour it will travel 42 miles.
F. 221,760 feet in one hour, 42 miles is equal to 5,280 x 42 = 221,760 feet.
G. 5,680 feet in one minute.
H. 94.67 feet in one second.
I. x miles in one hour.
J. 5,280 x x feet in one hour:
K. (5,280 x x) ÷ 60 feet in one minute.
L. ((5,280 x x) ÷ 60) ÷ 60 feet in one second.
To learn more about constant please click on below link
https://brainly.com/question/14159361
#SPJ4
There are 5,280 feet in a mile. Round answers to the nearest unit.
A. How many miles does a car traveling at 65mi/h go in one hour?
B. How many feet does a car traveling at 65mi/h go in one hour?
C. How many feet does a car traveling at 65mi/h go in one minute?
D. How many feet does a car traveling at 65mi/h go in one second?
E. How many miles does a car traveling at 42mi/h go in one hour?
F. How many feet does a car traveling at 42mi/h go in one hour?
G. How many feet does a car traveling at 65mi/h go in one minute?
H. How many feet does a car traveling at 65mi/h go in one second?
i. How many miles does a car traveling at x mi/h go in one hour?
J. How many feet does a car traveling at x mi/h go in one hour?
K. How many feet does a car traveling at x mi/h go in one minute?
L. How many feet does a car traveling at x mi/h go in one second?
Maliyah buys a bus ticket to New Orleans, her favorite city in America. The original price of $120 . She uses a coupon code to get a 20% discount off of the original price . She is then charged a 6% tax on the discounted price . What is the final cost for Maliyah's bus ticket
By using the unitary method, the final cost of Maliyah's bus ticket after the discount and tax was $101.76.
The unitary method involves dividing the original price by the percentage discount and then multiplying the result by the percentage tax to find the final cost.
First, we will find the discounted price of the bus ticket. To do this, we divide the original price of $120 by 100 and multiply by 20 to find the discount amount.
=> $120 / 100 * 20 = $24.
So, the discount amount is $24.
Next, we subtract the discount amount from the original price to find the discounted price.
=> $120 - $24 = $96.
So, the discounted price of the bus ticket is $96.
Finally, we multiply the discounted price by the percentage tax of 6% to find the final cost. To do this, we divide the 6% tax by 100 and multiply by the discounted price.
=> 6 / 100 * $96 = $5.76.
So, the final cost of the bus ticket is
=> $96 + $5.76 = $101.76.
To knw more about unitary method here,
https://brainly.com/question/28276953
#SPJ4
HELP!!!!! Solve for the value of q
Answer:
q = 4
Step-by-step explanation:
The three angles shown lie on the same straight and are adjacent to each other.
Adjacent angles on a linear segment are called supplementary angles and their sum adds up to 180°
Plugging in the expressions for the three angles we get:
(8q + 1) + 90 + 57 = 180
==> 8q + 1 + 90 + 67 = 180
==> 8q + 148 = 180
==> 8q = 180 - 148
==> 8q = 32
q = 32/8 = 4
identify the term with coefficient -3
The term with the coefficient that is - 3 is - 3 x ²y.
How to find the coefficient ?In mathematics, a coefficient is a value expressed by a number or other symbol multiplied by the variable of a single term or the terms of a polynomial.
In this case therefore, the coefficient is the number that is next to the variables. The term that has the coefficient being - 3 is therefore - 3 x ²y where - 3 is the fixed value in the term.
Find out more on coefficients at https://brainly.com/question/28767308
#SPJ1
Options for this question include :
2xy-3x²y9 x³y²z²x²ythe population of a town increased by 1.5% per year from 1995 to 2015. the town's population at the beginning of 1995 was 16,112. what was the 1-year growth factor for the town's population?
The population of a town increased by 1.5% per year from 1995 to 2015. The town's population at the beginning of 1995 was 16112. The 1-year growth factor for the town's population is 1.49%.
The population of a town increased by 1.5% per year from 1995 to 2015.
So, rate of growth is 1.5%.
The town's population at the beginning of 1995 was 16112.
So, initial population is 16112.
And we have to calculate 1 year growth factor.
So, we will use the formula i.e.
x(t) = [tex]x_{o}[/tex] × (1 + r) t
Here, Initially the Population is [tex]x_{o}[/tex] =16112
Growth Rate (%) (r) = 1.5
Number of years (t)= 1
So, we get=
x(t)=16112 × (1+1.5) 1
x(t)=16353.67
To calculate growth factor = (Final population- Initial population/ Initial population) *100
= (16353.67-16112/16112) *100
=1.49%
Here is more information on growth rate: brainly.com/question/2639972
#SPJ4
Help please 40 points and brainlist if picked
Answer: x = 2, y = 5
Step-by-step explanation:
Step 1: Substitute y = -2x + 9. --> {2x + 9 = 4x - 3}
Step 2: Isolate x for the 2-sided equation. (x = 2) --> y = -2 · 2 + 9.
Step 3: Simplify. y = 5.
Hope this helped. :)
HELPPPP! i will give brainliest Find the measure of the missing angle.
The measure of the missing angle a is 155 degrees.
What is the measure of the missing angle?The sum of angles on a straight line is equal to 180 degrees.
From the diagram;
Supplement angle to a = 25°Angle a = ?Since the sum of angles on a straight line is equal to 180 degrees.
Supplement angle to a + angle a = 180
25° + a = 180°
Solve for a by subtracting 25° from both sides.
25° - 25° + a = 180° - 25°
a = 180° - 25°
a = 155°
Therefore, the measure of angle a is 155°.
Learn more about supplementary angles here: https://brainly.com/question/18164299
#SPJ1
the side lengths of an equiangular octagon are $1$, $2$, $3$, $4$, $1$, $2$, $3$, and $4$ in clockwise order. find the octagon's area.
The side lengths of an equiangular octagon are 1, 2, 3, 4, 1, 2, 3, and 4 in clockwise order so area of octagon is 11 + 12√2 square units.
The sides of octagon are 1, 2, 3, 4, 1, 2, 3, 4 as shown in the figure,
The area of the octagon = area of the rectangle - the area of the four right isosceles triangular corners.
A = (lxb) - 1/2[√2×√2 + √8×√8]x2
A = [(3+√2+√8)(1+√2+√8)] -1/2[√2×√2 + √8×√8 + √2×√2 + √8×√8]
A = 3 + 12√2 +7
A = 11 + 12√2
Therefore, The area of the octagon is 11 + 12√2 square units.
A closed two-dimensional shape having eight sides, eight vertices, and eight internal angles is known as an octagon. An octagon is referred to as a regular octagon if all of its sides and internal angles are of equal length; otherwise, it is referred to as an irregular octagon. The next sections also discuss the various octagon types, such as convex and concave octagons.
Learn more about Area of octagon:
https://brainly.com/question/860089
#SPJ4
what is the volume of the figure ?
The volume of the prism is 360cm³
What is volume of a prism?A prism is a solid shape that is bound on all its sides by plane faces. There are two types of faces in a prism. The top and bottom faces are identical and are called bases. A prism is named after the shape of these bases.
The volume of a prism is expressed as base area x height
The height = 10cm
base area = ½b×h
= ½ × 6× 12
= 36cm²
therefore;
volume = 36 × 10 = 360cm³
therefore the volume of the shape is 360cm³
learn more about volume of prism from
https://brainly.com/question/23766958
#SPJ1
what is the difference between a line spectrum and a continuous spectrum? provide an example of each.
A line spectrum refers to a type of spectrum where light is emitted at specific, discrete frequencies. A continuous spectrum, on the other hand, refers to a type of spectrum where light is emitted at all frequencies within a given range.
A line spectrum refers to a type of spectrum where light is emitted at specific, discrete frequencies. The light is emitted in a pattern of individual lines, hence the name "line spectrum." Hot gases or plasmas often produce this type of spectrum, and the lines represent specific energies of electrons in the gas.
An example of a line spectrum is the Hydrogen spectrum, which consists of a series of distinct lines of different colours that correspond to different energies of the electrons in a hydrogen atom.
A continuous spectrum, on the other hand, refers to a type of spectrum where light is emitted at all frequencies within a given range. The light is emitted in a smooth, continuous manner, hence the name "continuous spectrum." This type of spectrum is often produced by hot solid objects, such as the sun, and it represents a continuous range of energies.
An example of a continuous spectrum is the spectrum of light emitted by the sun, which spans a wide range of frequencies and has a smooth, continuous appearance.
To know more about Hydrogen spectrum, here
https://brainly.com/question/7586240
#SPJ4
WILL GIVE BRAINILEST
What is the Area and Perimeter? WILL MARK AS BRAINLIEST.
The area of the shape is x²+2x +1 and the perimeter is 4x +7
What is area and perimeter?The area is the region covered by shape or figure whereas perimeter is the distance covered by outer boundary of the shape. The unit of area is given by square unit or unit2 and unit of perimeter is same as the unit.
The area of the shape is :
The shape is sub divided into 4 with different areas x, x , x², and 1
Therefore the area of the shape = x²+x+x+1 = x²+2x+1
The perimeter is obtained by adding all the sides
x+x+x+x+1+1+1+1+1+1+1 = 4x+7
therefore the perimeter of the shape is 4x+ 7
learn more about area and perimeter from
https://brainly.com/question/25292087
#SPJ1
2. Given: q//r
q is perpendicular to s
Prove: r is perpendicular to s
Please leave an explanation to how you got your answer.
The candle that will burn out first is the yellow candle rather than the blue candle.
How long will it take for each candle to completely burn out?Blue candle:
1/4 inch per hour or 0.25 inches per hour
8 / 0.25 = 32 hours to completely burn out
Yellow candle:
1/2 inch per hour or 0.5 inches per hour
12 / 0.5 = 24 hours
What candle will burn out first?If the blue candle is lit 6 hours before the yellow candle then:
Blue candle: 32 - 6 = 26 hours left
Yellow candle: 24 hours left
This means the yellow candle will burn out first.
Learn more about time in https://brainly.com/question/28050940
#SPJ1