Answers
Answer:
(a) 3.5
(b) x = 4
(c) -¹/₂
(d) -¹/₂
Step-by-step explanation:
Part (a)f(1) is the value of y when x = 1.
To find the value of y from a given value of x, find the position of x on the x-axis, then trace vertically until you meet the line. Once you meet the line, trace horizontally to the y-axis to find the corresponding value of y.
Therefore, f(1) = 3.5.
Part (b)To solve f(x) = 2, find the value of x when y = 2.
To find the value of x from a given value of y, find the position of y on the y-axis, then trace horizontally until you meet the line. Once you meet the line, trace vertically to the x-axis to find the corresponding value of x.
Therefore, the solution of f(x) = 2 is x = 4.
Part (c)The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:
[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]
Given interval: 2 ≤ x ≤ 4
Therefore:
a = 2b = 4[tex]\implies \dfrac{f(4)-f(2)}{4-2}=\dfrac{2-3}{4-2}=-\dfrac{1}{2}[/tex]
Part (d)The average rate of change between any interval of the given function will be the same as the graph is linear. Therefore, the average rate of change from 0 to 8 is the same as the rate found in part (c): -¹/₂.
Proof
The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:
[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]
Given interval: 0 ≤ x ≤ 8
Therefore:
a = 0b = 8[tex]\implies \dfrac{f(8)-f(0)}{8-0}=\dfrac{0-4}{8-0}=-\dfrac{4}{8}=-\dfrac{1}{2}[/tex]
Related Questions
Cual es el radio de 35 cm
Answers
Answer: 17.5
Step-by-step explanation:
Si un circulo tiene un diametro de 35 centimetros entonces para encontrar el radio se divide en 2. 35 /2 = 17.5
Can someone help plss
Answers
Answer= y=6x-3
Maddie and Cara each made a bowl of punch. Cara used 6 times as much lemonade as Maddie did. If Maddie used 2/3 of a cup of lemonade, how many cups of lemonade did Cara use?
Write your answer as a fraction or as a whole or mixed number.
Answers
Cara used 4 cups.
Maddie(M) used 2/3 of a cup.
Cara(C) used 6 times the amount M used.
M x 6 = C
2/3 x 6 = C
2/3 x 6 = 12/3 = C
12/3 = 4 = C
4 = C
Which model shows 4 × 5? 25 or 20 or 9 or 16 witch one? pls help marking brainly pritty pleaseeeeee
Answers
Answer:
20.
Step-by-step explanation:
Well, Multiplication is simple. 4*5 is 20, because you're basically writing and solving 5+5+5+5. 5 added to itself 4 times.
Hope this helps!
Side Note
If you have trouble with Division, the way to do it with this equation is:
You know our answer is 20 now, so what is 20/5? (20 divided by 5) This would be 4. This is the Inverse Property of Multiplication.
Please explain what the answers are for questions 2, 3, 4, 5, and 6 and how or just help me with the questions you know the answers to, thanks!
Answers
3.$5.22
4.59/10
5. 2.58 pounds
6.$20.55
<3 have a good day!
A small treasure chest is in the shape of a rectangular prism.
The length of the chest is y feet, the width ½ y feet, and the height
2y feet. The chest holds 8 cubic feet of treasure. What are the
dimensions of the treasure chest?
Answers
Answer:
length = 2ft
width = 1 ft
height = 4 ft
Step-by-step explanation:
V = LWH
V = (1/2)y × y × 2y
V = y³ = 8 ft³
y = 2
length = 2ft
width = (1/2)(2 ft) = 1 ft
height = 2(2 ft) = 4 ft
HELP ME WITH QUESTION B PLEASE!!!
Answers
Cavitation reduces a tree's ability to conduct water due to the formation of air bubbles in water, thereby reducing the hydraulic conductance of the tree.
How does cavitation affects a tree's ability to conduct water?Cavitation, also known as embolism, is said to occur when the tracheid or vessels of the xylem is being filled with bubbles of air. Cavitation is what is said to occur when air bubbles form in water during transpiration.
The effect of cavitation is the prevention of the upward pull of water, leading to a degradation of hydraulic conductance, such that the xylem water potential is reduced.
Learn more about cavitation here:
https://brainly.com/question/12975587
#SPJ1
two cities are 65 miles apart
a. if their distance on the map is 3 1/4 inches, find the scale of the map
b. on another map, the same cities are 6.5 inches apart. What is the new scale?
c. If the scale was 2 inches: 11 miles, how far apart would the same cities be on the map? Round to the nearest inch.
Answers
The scale is 1 inch represent 20 miles.
The new scale is 1 inch represents 10 miles
The distance on the map would be 11.8 inches.
What is the scale of the map?A scale drawing is a reduced form in terms of dimensions of an original image / building / object. A map is a scale drawing of a city.
The scale of a drawing is usually written in this format - length in the drawing, a colon (:), then the matching length on the original image.
Scale of the drawing = original dimensions / dimensions of the scale drawing
Initial scale = 65 ÷ 3 1/4
65 X 4/13 = 20
1 inch ; 20 miles
New scale = 65 / 6.5 = 1 10
1 inch : 10 miles
Length of the map = (2 x 65) / 11 = 11,8 inches
To learn more about scale drawings, please check: https://brainly.com/question/26388230
#SPJ1
3x-22°=90°
please help me ASAP
Answers
Answer:
about 37.33
Step-by-step explanation:
90+22=112/3 is x
x=37.33
the answers for 22, 24,and 25?
Answers
Answer:
22) -3jk+12k^2---------24)-3xy^4-7xy^3
Step-by-step explanation:
given h (x)=2x+4 find h(-1)
Answers
The required simplified value of the given expression h(-1) = 2.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
As given that,
h (x)=2x+4
Put x = -1
h(-1) = 2(-1) +4
h(-1) = 2
Thus, the required simplified value of the given expression h(-1) = 2.
Learn more about simplification here:
https://brainly.com/question/12501526
#SPJ2
Solve for u.
u +4=7
U =
Answers
in the above question we have to do addition and subtraction method. Therefore, u is equal to 3.
What is addition?Addition in math is a process of combining the two or more numbers. Addends are the numbers added, and the result or final answer we get after the process is called the sum. It is one of essential mathematical functions we use in our everyday activities. There are many situations in which we use to add the numbers. One of the most common everyday uses for adding the numbers is when we work with time or money—for example, adding up the bills and receipts.
An addition sentence is a mathematical expression that shows the two or more values added together and their sum. The two or more values that are added are called the addends. The parts of an addition sentence are the two or more addends, plus symbol(s), equal sign, and the sum.
From above question, it is given that:
u+4=7
so, u= 7-4= 3
To know more about addition visit: https://brainly.com/question/875080
#SPJ9
A ball is dropped from rest and takes 1.3 s to hit the ground. from what height was it dropped?
Answers
Initial velocity=0
Height=45m
G=10m/s^2
By the 2 nd equation of motion …(Under free fall)-
H = ut + 1/2 g t^2
45 = 0 + {1/2 * 10 * (t^2)} •: [0*t=0]
45 = 5 t^2
45/5 = t^2
9 = t^2
√9=t
3=t
Answer-: The time taken would be 1.3 seconds to reach the ground.
find the weighted average of the numbers 1 and 6, with weight four-fifths on the first number and one-fifth on the second number.
Answers
The weighted average of the numbers 1 and 6 is 2
What is weighted average of two numbers?
The weighted average of 1 and 6 in this instance, means the sum of the two numbers multiplied by their weights which are four-fifths and one-fourth respectively.
weighted average=(first number*weight of first number)+(second number*weight of second number)
first number=1
weight of first number= four-fifths=4/5
second number=6
weight of second number=one-fifth=1/5
weighted average=(1*4/5)+(6*1/5)
weighted average=2
Find out more about weighted average on:brainly.com/question/28293878
#SPJ1
show that 268 can be written as the sum of a power of 3 and a squared number
Answers
We have shown that 268 can be written as the sum of a power of 3 and a squared number.
We are given a number:
268
We need to show that it can be written as the sum of a power of 3 and a squared number.
We can write 268 as:
268 = 243 + 25
Now, factors of:
243 = 3 × 3 × 3 × 3 × 3
25 = 5 × 5
So, this can be rewritten as:
268 = 3 ⁵ + 5²
which is he sum of a power of 3 and a squared number
Therefore, we have shown that 268 can be written as the sum of a power of 3 and a squared number.
Learn more about power here:
https://brainly.com/question/847241
#SPJ9
Given the following informat
1
3. slope = y-intercept = -1
TT
Answers
The equation of straight line in the cartesian plane with slope and y-intercept of -1 is y+x+1=0
A straight line is an object in geometry that is indefinitely long and has neither breadth nor depth nor curvature.
The x-axis, a horizontal line, and the y-axis, a vertical line, are two perpendicular lines that split the number plane, also known as the Cartesian plane, into four quadrants. The origin is the location where these axes converge.The general equation of a line in the cartesian plane is given by the equation y = mx + c , where m is the slope and c is the y-intercept.The slope of a straight line is calculated by taking tan θ where θ is the angle made by the line with positive direction of x- axis.Given the slope = y-intercept= -1
Therefore m = -1 and c = -1 .
Substituting the values of m and c in the general equation of a straight line we get :
y = -x - 1
or, y + x+ 1 = 0
Therefore the equation of the straight line is y + x+ 1 = 0.
To learn more about straight line visit:
https://brainly.com/question/24143133
#SPJ9
the lengths of plate glass parts are measured to the nearest tenth of a millimeter. the lengths are uniformly distributed with values at every tenth of a millimeter starting at 590.1, and continuing through 590.9. determine the mean and variance of the lengths. (a) mean round your answer to two decimal places (e.g. 98.76). (b) variance round your answer to three decimal places (e.g. 98.765)
Answers
The mean is 590.45 and the variance is 0.053.
What is arithmetic mean and variance?
A mean refers to a representative of a list of numbers, usually the sum of the numbers divided by how many numbers are in the list.The expectation of a random variable's squared divergence from its population mean or sample mean is known as its variance.Now,
Adding together all the numbers and dividing by the total number of data points yields the mean:=> Sum of all the values = 590.1+590.2+590.3+590.4+590.5+590.6+590.7+590.8 = 4723.6
=> Since 8 data values are present,
=> Mean = 4723.6/8 = 590.45
We deduct each data value from the mean in order to calculate the variance. Next, we square this discrepancy to determine the average square:=> 590.1 - 590.45 = -0.35;
=> (-0.35)² = 0.1225
=> 590.2 - 590.45 = -0.25;
=> (-0.25)² = 0.0625
=> 590.3-590.45 = -0.15;
=> (-0.15)² = 0.0225
=> 590.4-590.45 = -0.05;
=> (-0.05)² = 0.0025
=> 590.5-590.45 = 0.05;
=> (0.05)² = 0.0025
=> 590.6-590.45 = 0.15;
=> (0.15)² = 0.0225
=> 590.7-590.45 = 0.25;
=> (0.25)² = 0.0625
=> 590.8-590.45 = 0.35;
=> (0.35)² = 0.1225
Thus, variance = [tex]\frac{(0.1225+0.0625+0.0225+0.0025+0.0025+0.0225+0.0625+0.1225)}{8}[/tex] = 0.42/8 = 0.0525 ≈ 0.053
To learn more about mean and variance, refer to the link: https://brainly.com/question/17082521
#SPJ4
Choose the system
for the graph
a)
(3x + 4y ≤ 12
(2x - 5y ≤ 10
(3x + 4y ≤ 12
2x - 5y ≥ 10
b)
:
(3x + 4y ≥ 12
c) (2x - 5y ≥ 10
(3x + 4y ≥ 12
d) (2x - 5y ≤ 10
Answers
Therefore, option (c) is the correct system for the graph based on the given options.
Based on the given options, the correct system for the graph would be option (c):
(2x - 5y ≥ 10
(3x + 4y ≥ 12
In option (c), both inequalities have the same orientation (greater than or equal to) and the same signs (+ and -) in front of the variables (x and y) as the original problem statement. This ensures that the inequalities maintain the same relationship.
Option (a) has one inequality with the opposite orientation (≤) compared to the original problem statement, which would result in an incorrect solution.
Option (b) has both inequalities with the opposite orientation (≥), which is also not consistent with the original problem statement.
Option (d) has one inequality with the opposite orientation (≤), which does not match the original problem statement.
For such more question on graph
https://brainly.com/question/19040584
#SPJ8
can someone answer this plssssssss
Answers
Answer:
y=-5x/2+4
Step-by-step explanation:
4y=-10x+16
y=-5x/2+4
In 9 hours, Donna reads 45 chapters of a book. What is her rate in chapters per hour?
Answers
Answer:
Donna reads an average of 5 chapters each hour.
Step-by-step explanation:
45/9=5
estimate the square root to the nearest tenth the square root of 11, and the square root of 62
Answers
The square root of 11 and 62 to the nearest tenth is 7.9 and 3.3 .
Given, the numbers are 11 and 62.
we are asked to determine the square root of the given numbers to the nearest tenth.
a. 11
Since the given number is not an even number, hence we can't get a whole number as the square root of 11.
we need to find the number whose square root is nearest to the number 11.
3 × 3= 9
9 is nearer to 11 whereas 4 × 4 = 16 gets greater than 11.
then dividing the number 11 by 3.we get:
√11 = 3.31662479 × 3.316622479
√11 = 3.31662479
√11 = 3.4 (rounding off to the nearest tenth)
b. 62
since we can't get the square root as a whole number so ,
we need to find the number whose square root is nearest to the number 62.
8 × 8 = 64
which gets greater than 62, hence we take 7 × 7 = 49
therefore, √62 = 7.874007874 × 7.874007874
√62 = 7.874007874
√62 = 7.9 (rounding off to the nearest tenth)
hence we get the square root of 11 and 62 as 3.3 and 7.9 respectively.
Learn more about Square root here:
brainly.com/question/98314
#SPJ9
1/18
In decimal equivalent rationam number
Answers
The decimal equivalent rational number of the given fraction 1/18 is 0.06
What are rational numbers?In arithmetic, a rational number is a number that can be represented as the quotient p/q of two integers such that q = 0. Aside from fractions, the set of rational numbers includes all integers, each of which can be written as a quotient with the integer as the numerator and 1 as the denominator.A rational number's decimal equivalent is the rational number in decimal form. We can find the decimal equivalent of a rational number in fraction form by dividing by the fraction.So, 1/18:
1/18 = 0.05555555555....
Rounding off to the nearest tenth we get: 0.06
(Refer to the diagram below for calculation)
Therefore, the decimal equivalent rational number of 0.06
Know more about rational numbers here:
https://brainly.com/question/1535013
#SPJ1
Select the correct answer. ethel is arranging rides so that 27 members of her club can go bowling. some people can ride in a van that belongs to the center where they meet. the rest must ride in cars. if 12 can go in the van, and 5 can go in each car, how many cars will they need? a. 3 cars b. 5 cars c. 7 cars d. 9 cars
Answers
There are 3 cars to be needed for the remaining 15 persons in Ethel club.
Unitary method:
Unitary method used to find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.
Given,
27 people will travel for bowling.
As there is only one van.
and in that one van only 12 people can go.
so remaining people will go by car
no. of people that they will go by car
=> 27 - 12 = 15
in one car 5 people can go
no. of cars needed to take people=no. of people/no. of cars
=> 15 / 5 = 3
Therefore 3 cars will be needed.
To know more about Unitary Method here.
https://brainly.com/question/28276953
#SPJ4
HELPPP 15 pointssssss mathhh
Answers
__
7
Hope this help
Hi! Can someone solve and tell me all the steps so I could understand how to do this?
Answers
Answer:
x = 12
AB = 39
AC = 24
Step-by-step explanation:
The sum of AB and BC is equal to the length of AC.
We can write the following equation based on this information :
AB + BC = AB rewrite the equation using given values
4x - 9 + 3x - 12 = 63 add like terms
7x - 21 = 63 add 21 to both sides
7x = 84 divide both sides by 7
x = 12 replace x with 12 in each expression to find the lengths
AB = 4x-9
AB = 4•12 - 9 and
AB = 39
BC = 3x -12
BC = 3•12-12 and
BC = 24
Please help, select all the perfect squares
Answers
Answer:
9 , 16x^2 , 4z and 100y^2 are perfect Squares!
_____________________________________
What are Perfect Squares?
A perfect square is a number that can be expressed as the product of an integer by itself or as the second exponent of an integer.
3 * 3 = 9
4 * 4 = 16
2 * 2 = 4
50 * 50 = 100
Therefore making those numbers perfect squares.
[NOTE: The numbers that are squared are still perfect squared, just a larger version!]
More information on perfect squares:
https://brainly.com/question/17735980?referrer=searchResults
Have a WONDERFUL day! (:
Answer:
Step-by-step explanation:
Perfect squares are: 100y^2, 16x^2, and 9
sqrt of 100y^2 is 10y
sqrt of 16x^2 is 4x
sqrt of 9 is 3
WILL MARK BRAINLIST WILL GIVE 5 STAR REVIEW
Answers
Answer: software, hardware, input device, operating system
Step-by-step explanation:
Answer:
windows-software
mouse-input device
microsoft word-operating system
motherboard-hardware
Step-by-step explanation:
Lois James' W-2 form is shown below.
રરરરર
1 Employed and code
PA
667438991
Acme, Inc
123 Man Street
Philadelphia, PA 19146
Lou James
632 Dodge Street
Philadelphia, PA 19145
Wage and Tax
Empre
471-29-2525
35-5427864
foW-2 Statement
Copy 1-For State, City, or Local Tax Department
A. $2018.40
D. $472.04
B. $32,554.76
C. $4465.71
32,554 76
999 43
2010
32,554 76
32,554 76
32.554 76
060
16 Laps
32,554 76
12e
the
124
4465 71
2018 40
Macato all
472 04
Department of the y
1400 18
How much did Lois have withheld from her yearly pay for Social Security?
20 Locatty cam
PHIL
ne Service
Answers
Answer:2018.40
Step-by-step explanation: i tried 472 and it was wrong and stated 2018 was correct.
Sally babysits for 3 hours on weekdays and charges $10 per hour. If she babysits for 65 days total, how much will she make?
Answers
If she babysits for 65 days total, she would make $1,950 in all
What is the earnings of Sally per day of babysitting?
The earnings that Sally realize from one day of babysitting is the pay per hour multiplied by the number of hours Sally works per day as shown below:
earnings per day=hourly rate*number of hours a day
hourly rate=$10
number of hours a day=3
earnings per day=$10*3
earnings per day=$30
Now, the earnings at she realizes from 65 days of babysitting can be determined as the earnings made in one day multiplied by the number of days she spent babysitting
earnings for 65 days=$30*65
earnings for 65 days=$1,950
Find out more about total earnings on:brainly.com/question/11436809
#SPJ1
To three decimal places, what is the volume of a cube (cm3) with an edge length of 0.843 cm?
Answers
The volume of cube whose edge length is 0.843 is 0.599 cubic centimeters.
According to the given question.
Length of the edge of the cube = 0.843 cm.
As we know that, a cube is a 3-D solid shape, which has 6 faces. A cube is one of the simplest shapes in three-dimensional space. All the six faces of a cube are squares, a two-dimensional shape.
And the volume of cube is calcualted by the formula
V = a^3
Where,
V is the volume of cube
And, a is the length of the edge of cube
Therefore,
The volume of the cube whose edge length is 0.843 cm
= (0.843cm)^3
= 0.599 cubic centimeters
Hence, the volume of cube whose edge length is 0.843 is 0.599 cubic centimeters.
Find out more information about volume of cube here:
https://brainly.com/question/11168779
#SPJ4