The slowest rate of change that is the slowest for the training program is: 3 minutes per day.
What is the Rate of Change of a Function?In a given function that is expressed in slope-intercept form as .f(x) = mx + b, the rate of change of the function is represented as "m", while the starting or initial value is represented as "b" in the equation.
Given that Rachel increases the time she runs by 3 minutes for each day, then, the rate of change per day for the training program or Rachel is 3.
Given that the function .f(x) = 5x + 30 represents the minutes Nicole runs per day in the training program, then the rate of change is represented as "5" in the equation. This means that each day, Nicole increases her time of running by 5 minutes as compared to 3 minutes per day that Rachel increases her daily runs.
3 minutes per day is slower than 5 minutes per day, in order words, the slowest rate of change is therefore: 3 minutes per day.
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Can I please get answer for a and b. I just need the answers. Thanks
When we have a function and want to evalueate it for some "x", we just substitute every "x" with the value in parenthesis. So, to evaluate f(a + 2), we have x = a + 2, so we need to substitute every "x" in the function with a + 2:
[tex]f(a+2)=(a+2)^2-2(a+2)+1[/tex]Now, to simplify, we first need to use the distributive property on the second parenthesis and evaluate the binomial in the first:
[tex]f(a+2)=a^2+4a+4-2a-4+1[/tex]Now, we group the like-terms and add them:
[tex]\begin{gathered} f(a+2)=a^2+4a-2a+4+4+1 \\ f(a+2)=a^2+2a+1 \end{gathered}[/tex]For yhe other one, Let's do each term and then make the substraction:
[tex]\begin{gathered} f(a+h)=(a+h)^2-2(a+h)+1 \\ f(a+h)=a^2+2ah+h^2-2a-2h+1 \\ f(a+h)=a^2+h^2+2ah-2a-2h+1 \end{gathered}[/tex][tex]f(a)=a^2-2a+1[/tex]So:
[tex]\begin{gathered} f(a+h)-f(a)=a^2+h^2+2ah-2a-2h+1-(a^2-2a+1) \\ f(a+h)-f(a)=a^2-a^2+h^2+2ah-2a+2a-2h+1-1 \\ f(a+h)-f(a)=h^2+2ah-2h \end{gathered}[/tex]please help meeee i am lost
Answer:
The sum of a sequence is known as a series. Thus means a harmonic series is infinite with no limit
An artist wants to earn a revenue of $2700 by selling paintings for $30 each and sculptures for $45 each
The most appropriate choice for equation of line in slope intercept form x intercept = 90
y intercept = 60
Domain = {0, 3, 6, 9, ....., 90}
Range = {0 , 2, 4,...., 88}
What is equation of line in slope intercept form?
Equation of line in slope intercept form is written as y = mx + c, where m is the slope of the line and c is the y intercept of the line.
The distance from origin to the point where the line cuts the x axis is the x intercept and the distance of origin to the point where the line cuts the y axis is the y intercept.
Here,
Selling price of one painting = $30
Selling price of x paintings = $30x
Selling price of y sculptures = $45
Selling price of y sculptures = $45y
Total revenue = $(30x + 45y)
By the problem,
30x + 45y = 2700
a)
For x intercept, y = 0
30x = 2700
x = [tex]\frac{2700}{30}[/tex]
x = 90
x intercept is $90
For y intercept, x = 0
45 y = 2700
y = [tex]\frac{2700}{45}[/tex]
y = 60
y intercept is 60
b)
In 30x + 45y = 2700
Since x represents the number of paintings sold and y represents the number of sculptures sold, then x and y has to be integers.
If x = 0 , y = [tex]\frac{2700}{45}[/tex] = 60
If x = 3, y = [tex]\frac{2700 -90}{45} = 58[/tex]
If x = 6, y = [tex]\frac{2700 -180}{45} = 56[/tex]
If x = 9, y = [tex]\frac{2700 -270}{45} = 54[/tex]
_______________________________
If x = 90 , y = [tex]\frac{2700 -2700}{45} = 0[/tex]
Domain is the values of x
Domain = {0, 3, 6, 9, ....., 90}
Range is the values of y
Range = {0 , 2, 4,...., 88}
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Complete Question
The diagram with the questions have been attached below
Find the vertex of the parabola y=2x^2+8x+7.
Hi i hope this helps you out
What is an equation of the line that passes through the point (8,0)(8,0) and is parallel to the line x-4y=20x−4y=20?
The equation of the line that passes through the point (8, 0) is parallel to the line x - 4y = 20 is 1/4x - y = 2
Given,
The equation of the line: x - 4y = 20
The points which the line passes through, (x₁, y₁) = (8, 0)
We have to find the equation of the line parallel to the given line.
The formula for the slope intercept form:
(y - y₁) = m(x - x₁)
m is the slope of the line.
Lets find the slope of the line given.
x - 4y = 20
x = 20 + 4y
x - 20 = 4y
y = (x - 20) / 4
y = 1/4x - 5
Here, slope of the line is 1/4
Now, substitute the slope of the line and (x₁, y₁) in the slope intercept formula to get the equation of line parallel to the given line
(y - y₁) = m(x - x₁)
(y - 0) = 1/4(x - 8)
y = 1/4x - 8/4
y = 1/4x - 2
1/4x - y = 2
Therefore,
The equation of the line that passes through the point (8, 0) is parallel to the line x - 4y = 20 is 1/4x - y = 2
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Select the correct answer.
What is the product of (7) (-16)(-7) (-1)?
A.
B.
-7
9
B. -16
C. -
D. 192
The product of (7) (-16)(-7) (-1) is - 784 by using simple multiplication.
What is multiplication?Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. The symbols for multiplication are a cross (x), an asterisk (*), and dot (.). You seem to utilize the cross a lot when you write in your notebooks. In both algebra and computer languages, the asterisk and dot are symbols (higher mathematics).
7 × -16 = -112
-112 × -7 = 784
784 × -1 = -784
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the sum of two consecutive natural number is 36 find the number
Hi someone please help me and thanks have a great day.Hi someone please help me and thanks have a great day. Hi someone please help me and thanks have a great day.
Given data:
The given figure is shown.
For figure A, the expression for sin(A) is,
[tex]\begin{gathered} \sin A=\frac{7}{18} \\ A=\sin ^{-1}(\frac{7}{18}) \\ =22.885^{\circ} \\ \approx23^{\circ} \end{gathered}[/tex]Thus, the value of angle A is 23 degrees.
(b)
The vaue of tan(A) is,
[tex]\begin{gathered} \tan (A)=\frac{14}{12} \\ A=\tan ^{-1}(\frac{7}{6}) \\ =49.398^{\circ} \\ \approx49^{\circ} \end{gathered}[/tex]Thus, the value of A is 49 degrees.
(c)
The value of cos(A) is,
[tex]\begin{gathered} \cos (A)=\frac{6}{10} \\ A=\cos ^{-1}(0.6) \\ \approx53^{\circ} \end{gathered}[/tex]Thus, the value of A is 53 degrees.
(d)
The value of tan(A) is,
[tex]\begin{gathered} \tan A=\frac{20}{28} \\ \tan A=\frac{5}{7} \\ A=\tan ^{-1}(\frac{5}{7}) \\ =35.53^{\circ} \\ \approx35^{\circ} \end{gathered}[/tex]Thus, the measurement of angle A is 35 degrees.
I'm re-posting because I need to turn this in soon! Please help! Thanks :)
The slope of g(x) is -3 and the g(x) is reflected across the x-axis
The table of values is
x f(x) = x g(x) = -3x
0 0 0
1 1 -3
2 2 -6
How to complete the blanks in the question?From the question, we have the definition of the functions to be
f(x) = x and g(x) = -3x
Also, we have the following x values from the blank table of values
x = 0, 1 and 2
Next, we calculate f(x) and g(x) at these x values
For the function f(x), the values are
f(0) = 0, f(1) = 1 and f(2) = 2
For the function g(x), the values are
g(0) = 0, g(1) = -3 and g(2) = -6
The next step is to calculate the slope and the transformation
Recall that
f(x) = x and g(x) = -3x
Generally, the form of a linear equation is
y = mx
Where m is the slope
This means that the slope of g(x) is -3
Lastly, the negative sign in g(x) = -3x implies that the graph is reflected across the x-axis or the y-axis
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Miss sheet,owner of the Bedspread shop knows his customers will pay no more than $145 for a comforter Misu wants a 40percent markup on selling price what is most that Misu can pay for a comforter?
The price that Misu can pay for a comforter based on the markup percentage is $103.57.
How to calculate the value?From the information, the Bedspread shop knows his customers will pay no more than $145 for a comforter Misu wants a 40 percent markup on selling price.
Let the selling price be represented as x. Based on the information given, this will be illustrated as:
x + (40% × x) = 145
x + 0.4x = 145
1.4x = 145
Divide
x = 145/1.4.
x = 103.57
The selling price will be $103.57.
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What is the product of -2 1/2 and -3 1/3?
A mixed fraction exists one that is represented by both its quotient and remainder.
Product of -2 1/2 and -3 1/3 is [tex]8\frac{1}{3}[/tex].
Product of 1 1/3 and -3 1/2 is [tex]-5\frac{5}{6}[/tex] .
How do you multiply fractions and mixed numbers in simplest form?A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction exists, for example, 2 1/3, where 2 is the quotient and 1 is the remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.
Step 1: Create an incorrect fraction from the jumbled number.Step 2: Separately multiply the denominators and numerators of the two fractions. Step 3: Simplify by removing the common elements to obtain the most basic version of the outcome. Step 4: Change the result back to a mixed number if it is an incorrect fraction.Product of -2 1/2 and -3 1/3 is [tex]8\frac{1}{3}[/tex].
Product of 1 1/3 and -3 1/2 is [tex]-5\frac{5}{6}[/tex] .
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Simplify the following expressions by using the properties of exponents. Assume none of the denominators is zero.
a^3 (2a^2 + 4bc^4)^ 0
The simplified form of the expression is a³ which is calculated by using the properties of exponents.
Exponentiation is a mathematical operation that involves the base number (b) and the exponent (or power) number (n), and is represented as bⁿ. Its pronunciation is "b (raised) to the (power of) n." Exponentiation corresponds to repeated base multiplication where n is a positive integer; so, bⁿ is the result of multiplying n bases.
Typically, a superscript to the right of the base indicates the exponent. Then, bⁿ is referred to as "b raised to the nth power," "b (raised) to the power of n," "the nth power of b," "b to the nth power," or, most succinctly, "b to the nth."
The given expression is a³(2a² + 4bc⁴)⁰.
From the properties of exponents we know that:
a⁰ = 1
Therefore the value of the part of the expression (2a² + 4bc⁴)⁰ is 1
Therefore the total value of the exponential expression is a³
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6. Suppose the class takes a test and the following averages are obtained: mean = 80, median= 90, and mode = 70. Tom, who scored 80, would like to know if he did better than half the class. What is your response?
We know that the mean is 80, the median is 90, and the mode is 70. This means that the majority of students got an 80 on the test.
However, the median is 90, which means half of the class is below 90 where Tom's grade is placed.
Hence, he did not do better than half of the class.Dalia's living room is 12 feet long and 10 feet wide. Her dining room
is also 10 feet wide. Write two equivalent expressions that each
represent the combined area of the two rooms.
10ft
12 ft-
Living
Room
xft-
Dining
Room
(120 + 10x) sq. feet or 10(12+x) sq. feet will be the combined area of the two rooms.
the given dimensions of the living room are given as follows,
length =12
width/breadth =10
thus the area of the living room will be,
length x breadth, i.e.
=12 x 10
=120 sq. feet
the given dimensions of the dining room are given as follows,
length= x
width/breadth=10
thus the area of the dining room can be calculated as
length x breadth
=10x sq. feet
Now, to calculate the combined area of both the rooms, we have to add the area of the dining room and the area of the living room,
that is,
(120 + 10x) sq. feet
What is area?
The area is the entire amount of space occupied by a flat (2-D) surface or an object's shape.
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What’s the correct answer answer asap i need help can somebody answer this question?
il give you brainlist
zjsjjsjsdsodss a sjsodisjww
I need help on these questions
Question 16
[tex](f(x), g(x))=x^2, (x-9)[/tex]
Note it wants the pair, so you just include the definitions of the functions, not f(x)= and g(x)=Question 17
[tex](f(x), g(x))=\sqrt{x}, 9+\sqrt{x}[/tex]
The values for first question are f(x) = x², g(x) = (x - 9) and for second question f(x) = √x, g(x) = 9 + √x.
A function may be defined as an expression in which for one value of input variable x there is only one value of output variable y. The input variable is called independent variable and output variable is called dependent variable. A composite function is the one which is written as a combination of two function. For two given functions f(x) and g(x) the composite functions are f(g(x)) and g(f(x)). In the first question the composite function is F(x) = (x - 9)². the parent functions will be f(x) = x² and g(x) = (x - 9).
in the second question the composite function is H(x) = √(9 + √x). The parent functions will be f(x) = √x and g(x) = 9 + √x.
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One year ago, Anne could run a mile in m minutes. Since then, her time hasdecreased by 16%. Write two different expressions that represent the number ofminutes it now takes Anne to run a mile, and show or explain why the expressionsare equivalent.
We know that
• Anne could run a mile in ,m, minutes.
,• Now, time has decreased by 16%.
The following expressions represent the number of minutes She uses to run a mile now.
[tex]\frac{16}{100}\cdot m[/tex]This expression represents 16% of m in fraction form.
[tex]0.16\cdot m[/tex]This expressed represents 16% of m in decimal form.
Both expressions are equivalent because they refer to the same percentage 16%. That is 0.16 and 16/100 are equivalent to 16%
Directions: Find the slope of the line that passes through the given point.
15.) (-8,-11) and (17,4)
16.) (10,-15) and (13,-17)
17.) (-6,-7) and (5,-7)
PLEASE HURRY
What is the value of the expression 45x − 16 if x is equal to −6?
Answer:
-286
Step-by-step explanation:
45(-6)-16
= -270 - 16
= -286
Step-by-step explanation:
45x - 16
x = -6
45(-6) - 16
-270 - 16
-286
Hope this helps! :)
Point DD is located at (-6,-5)(−6,−5) on the coordinate plane. Point DD is reflected over the xx-axis to create point D'D ′ . What ordered pair describes the location of D'?D ′ ?
The ordered pair that describes the location of N is (2,6)
Given:
N's coordinates are: (-2,-6)
Point N ′ is produced by reflecting point N over the y-axis.
By reflecting point N' over the x-axis, the final point N" is produced.
x , y = -x , y
N(-2 -6) = N'(2 6)
To locate the ordered pair describing where N" is located.
Point N's coordinates are (-2,-6). Point N ′ is produced by reflecting point N over the y-axis.
x , y = -x , y
N(-2 -6) = N'(2 6)
The resultant point N" is created by reflecting point N' over the x-axis.
The ordered pair for point N" is therefore (2,6) gives its location.
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The elephants at the zoo eat 3 1/6 buckets of bananas each day. The zookeeper bought 6 1/3 buckets of bananas. How many days will the bananas last?
Write your answer as a fraction or as a whole or mixed number.
The bananas will last 2 days at the zoo (found by division).
According to the question,
We have the following information:
The elephants at the zoo eat [tex]3\frac{1}{6}[/tex] buckets of bananas each day. The zookeeper bought [tex]6\frac{1}{3}[/tex] buckets of bananas.
Now, first we will find the number of days taken in eating 1 bucket of bananas.
[tex]3\frac{1}{6}[/tex] buckets = 1 day
Now, we will convert this mixed fraction into simple fraction.
19/6 buckets = 1 day
1 bucket = 1/(19/6) days
1 bucket = 6/19 days
Now, we have the total number of buckets as [tex]6\frac{1}{3}[/tex].
Now, after converting this mixed fraction, we have:
19/3 buckets
1 bucket = 6/19 days
19/3 buckets = (6/19)*(19/3)
19/3 buckets = 2 days
2 is a whole number.
Hence, the given buckets of bananas will last 2 days.
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The population of a town over the past 10 years can be represented with the equationy = 2450(1.07)? What is the rate of change?A) 1.07%B 2450C 7%D.0796
Let's begin by identifying key information given to us:
The population is represented by the equation:
[tex]y=2450\mleft(1.07\mright)[/tex]We will compare the equation for the population with the general exponential growth equation, we have:
[tex]\begin{gathered} f(x)=a(1+r)^x \\ where\colon \\ f(x)=exponential\text{ }growth\text{ }function \\ a=initial\text{ }amount \\ r=growth\text{ }rate \\ x=number\text{ }of\text{ }time\text{ }intervals \end{gathered}[/tex]Comparing, we have:
[tex]\begin{gathered} f(x)\Rightarrow y \\ a=2450 \\ (1+r)=1.07\Rightarrow r=1.07-1=0.07 \\ \Rightarrow r=0.07=7\text{\%} \\ \\ \\ \end{gathered}[/tex]Therefore, the rate of change is 7%. Hence, C is the answer
How many inches are in 4 feet 6 inches?
6 inches
54 inches
46 inches
48 inches
Answer:
54 inches
Step-by-step explanation:
There are 12 inches in 1 foot
12in = 1ft
There are 4 feet and 6 inches
If you break it down its 4×12
4 × 12 = 48
Add 6 inches
48 + 6 = 54
Therefore the answer would be 54 inches
Your welcome <3
How many zeroes are in the product of 40 x 107? O A. 6 B. 7 O C. 8 O D. 9
We need to count the number of zeros in a number multiplied by a power of 10. Which is shown below:
[tex]40\cdot10^7[/tex]The power of 10 will add a certain number of zeros, which is equal to the expoent of the power, in this case it's 7, but there is one more zero which is present in the "40", therefore the total number of zeros will be 8.
to find 24 times 17 i multiply 20 times 17 and add it to 4 times 17
Step-by-step explanation:
to find 24 times 17 i multiply 20 times 17 and add it to 4 times 17?
Yes, that is one way of doing it:
Your method:
20 × 17 = 340
4 × 17 = 68
340 + 68 = 408
The typical way of solving is:
24 × 17 = 408
Both return the correct answer.
Answer:
24 times 17 = 408
But if you multiply:
20 times 17 = 340 Then add that to:
4 times 17 = 68
340 + 68 = 408
You would get the same answer so this is correct!
Step-by-step explanation:
Hope it helps! =D
72.7% to nearest 10th percent
Answer:
72.7% to nearest 10th percent would be 73%!
Step-by-step explanation:
Hope it helps! =D
help meeeeeeeeeeeeeeeeeeeeeeee pleaseeeeee
Answer:
it would be 600
Write 8.94 in fractional notation. don't simplify
We have to write 8.94 in fractional notation without simplification.
For decimal values, we can convert them to fractions taking into account the number of decimals they have.
In this case, 8.94 has two decimals. Then, we can multiply it by a fraction 100/100, as 100 has two zeros.
Then, we will get:
[tex]8.94\cdot\frac{100}{100}=\frac{8.94\cdot100}{100}=\frac{894}{100}[/tex]This works beacuse we multiply the number 8.94 by a number that will make it become an integer (without decimals). To keep the value of the fraction equal to the decimal number, we have to divide by the same factor (in this case, 100).
This fraction can be simplified.
Answer: the fractional notation, without simplification, of 8.94 is 894/100.
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
[tex]P(0)=0.023(0)^3-0.289(0)^2+3.068(0)+55.170=55.17[/tex]
The table shows the number of restaurants in five different cities Cities numbers of restaurants Carlsbad 489 potters vale 261 little hath 282 edgbaston 216 barrow 317 how many more restaurants are there in Carlsbad than in barrow?
To answer this question, we will use the next table (obtained from the Question Tab):
City -------- Number of restaurants
Carlsbad 489
Potter Valley 261
Little Heath 282
Edgbaston 216
Barrow 317
If we want to know how many more restaurants there are in Carlsbad than in Barrow, we need to subtract the number of restaurants in Barrow from Carlsbad as follows:
[tex]489-317=172[/tex]From the table, we have that in Carlsbad there are 489 restaurants, while there are 317 in Barrow.
We can check this as follows:
In summary, we can say that there are 172 more restaurants in Carlsbad than in Barrow.