Answer:
f(n)=8n-63
15th term=57
Step-by-step explanation:
goes up by 8 each time therefore the coefficient of n is 8
take for example the 1st term,8n would be 8, to get to -55 from 8 you would have to subtract 63, therefore the nth term is 8n-63.
point slope that is parallel and passes through (-1,-1)
The equation of line parallel to the given line is y = x + 2
Given,
The points that the line passes, (x, y) = (-1, -1)
Slope of the line, m = 1
We have to find the equation of line that is parallel to the given line.
Slope of parallel lines will be same.
So, equation be like:
y = mx + b
y = 1x + b
Here, we can use points and find y intercept:
That is,
-1 = 1 × -1 + b
-1 = -1 + b
b = 1 + 1
b = 2
So, the equation of line be like, y = 1x + 2
That is,
The equation of line parallel to the given line is y = x + 2
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Question Progress
Homework Progress
12/
Biscuits can be bought in packets of 12 or packets of 18.
All biscuits are identical in size and quality.
Packet of 12 biscuit
for £0.78
Which packet represents better value?
Show how you decide.
Packet of 18 biscuits
for £1.25
Answer:
Answer:
The pack of 12
Step-by-step explanation:
1.25÷18=0.0694
0.78÷12=0.065
The packet of 12 biscuit have better value.
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The cost of Packet of 12 biscuit = £0.78
The cost of Packet of 18 biscuit = £1.25
Now,
Since, The cost of Packet of 12 biscuit = £0.78
Hence, The cost of Packet of 1 biscuit = £0.78/12
= £0.065
And, The cost of Packet of 18 biscuit = £1.25
Hence, The cost of Packet of 1 biscuit = £1.25/18
= £0.0694
Thus, The packet of 12 biscuit have better value.
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8. Stavros has 22 coins in his piggy bank, all dimes and quarters. Altogether, the
coins are worth more than $3.40. At least how many coins are quarters? At most,
how many of the coins are dimes?
Stavros has 9 at least quarters and 13 at most coins.
Define inequality.In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign (≠)" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
Given Data
Stavros has 22 coins in his piggy bank, all dimes and quarters. Altogether, the coins are worth more than $3.40.
He only has quarters and dimes in his possession. For quarters and dimes, assign variables.
Let x = the quantity of dime
Let y = the quantity of quarters.
Create an inequality and equation to depict the scenario.
We can use an equation because he has exactly 22 coins.
x + y = 22
He has more than $3.40 in his total, thus we can apply an inequality.
0.10x + 0.25y > 3.40
To figure out how many of each coin he possesses, we apply the substitution approach. In order to express the inequality in terms of x, substitute the equation into the inequality.
0.10x + 0.25(22 - x) > 3.40
The inequality can now be resolved.
0.10x + 5.5 - 0.25x > 3.40
-0.15x + 5.5 > 3.40
-0.15x > -2.1
x > 14
In an equation where we divide by a negative coefficient, We reverse the sign in inequality.
x < 14
Stavros has a maximum of 13 dimes.
The value of x can then be substituted into the equation since an equation provides you the most precise and minimal value you can have.
y = 22 - 13
y = 9
Stavros has 9 quarters and 13 dimes.
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As a part of a lesson on earthquakes a science class is researching the movement if a nearby fault line. the line moved 3/5 of an inch during the past year and 7/8 of an inch the year before. how far did the fault line move in all?
find the larger of 2 consecutive intergers if 4 times the smaller is 53 more than 3 times the larger
The larger of the two consecutive numbers is 57
What is a consecutive number?
Numbers that follow one another sequentially are known as consecutive numbers. Every time there are two numbers, there is a difference of 1 between them. If n is a number, then examples of consecutive numbers would be n, n+1, and n+2. and 1, 2, 3, 4, 5, and so on.
From the question,
Let's say the smaller integer is x
Then the larger integer will be (x + 1)
According to the question,
4 times the smaller = 4x
3 times the larger = 3(x + 1)
⇒ 4x = 3(x + 1) + 53
⇒ 4x - 3x = 56
⇒ x = 56
(x + 1) = 57
Therefore, the larger of the two consecutive numbers is 57
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-calculati
5+2
7
7
-
3
8
8
13
8
52
5+1
3
7
3
1
ام اس
2
5
32
5
اران
3
7
2
3 5
1
4
41
Answer:
Step-by-step explanation:
Use this calculator to add or subtract time (days, hours, minutes, seconds) from a starting time and date. The result will be the new time and date based on the ...
Missing: ام اس اران 41
what is the volume of the following triangular prism? 288 ft^3480 ft^396 ft^3576 ft^3
The volume of the triangular prism = base area x height
Since its base is a right triangle, then
[tex]B\mathrm{}A=\frac{1}{2}\times leg_1\times leg_2[/tex]From the figure leg1 = 6 ft and leg2 = 8 ft
[tex]\begin{gathered} BA=\frac{1}{2}\times6\times8 \\ BA=24ft^2 \end{gathered}[/tex]Now multiply it by the height of the prism
Since its height = 12 ft, then
[tex]\begin{gathered} V=24\times12 \\ V=288ft^3 \end{gathered}[/tex]The answer is A
Graph the line that passes through the point (1,-1) and is parallel to another line whose slope is 1 .
Answer:
The image is inserted below.
Step-by-step explanation:
The blue line is the line that passes through the point (1,-1) which is marked as A on the graph.
The green line is the new line you need to graph that is parallel to the original line and has a slope of 1.
Premises:
If you have a cat, then it will chase mice.
You have a cat.
Conclusion:
Your cat will chase mice.
The Law of ________
By law of syllogism the statement is true. Your cat will chase mice.
What are premises?
premises is a statement taken to be true and used as a basis for argument or reasoning.
Here it is given that :
If you have a cat, then it will chase mice. is the given statement.
Let p is you have a cat
q is chase mice.
r is cat will chase mice.
by the law of syllogism Your cat will chase mice. because (1) If p , then q . (2) If q , then r . Then we can derive a third true statement: (3) If p , then r .
Hence by law of syllogism the statement is true.
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The amount in Ebony's bank account B(d) is a function of the number of days d since she opened the account.
The graph segments representing her day-by-day bank balance. Although there are no labeled tick marks on the graph, you can answer the questions by using the additional given information as well as your general knowledge of graphs of functions.
a) Domain of the function 0 ≤ d ≤ 21 (0,21)
Range of the function 0 ≤ B ≤ 400 (0,400)
b) Estimate to the nearest hundreds for B(0) is 200
c) Ebony's bank balance first reached $0 on day 12 can be shown as functional notation as - we can add the number 12 below the first point reaching the horizontal axis.
d) Ebony's bank balance remained $0 from day 12 through day 15. The segment which represents the information is - segment 4.
(a) Domain: the collection of values used as input or arguments for the function.
Range: Either the codomain or the function's image is mentioned.
For three weeks, Ebony's bank account was active (21 days). then the domain is 0 ≤ d ≤ 21 (here 'd' refers to day)
Her highest balance was $400 and her lowest was zero, so the range is 0 ≤ B ≤ 400. (Here, 'B' refers to Balance)
(b) When d = 0, the graph's highest point, which represents her highest balance of $400, is displayed. This means that on the first day, the point will probably only be half as high as the highest point. Therefore, we may calculate the nearest hundred for B(0) is about equal to 0.5 * 400 = 200.
(c) In other words, the line of the function first touches the horizontal axis at d = 12; the balance first reached $0 on day 12. Below the first point that reaches the horizontal axis, we can add the number 12.
(d) From day 12 through day 15, the bank balance stayed at zero dollars; this is shown by the vertical axis of segment 4 of graph 4.
COMPLETE QUESTION:
The amount in Ebony's bank account B(d) is a function of the number of days(d) since she opened the account. The graph shows segments representing her day-by-day bank balance. Although there are no labeled tick marks on the graph, you can answer the questions by using the additional given information as well as your general knowledge of graphs of functions. (Score for Question 1;_ of 4 points) 1. Ebony kept her bank account open for only 3 weeks, and the graph shows the entire 3 weeks. During that time, her greatest balance was $400.
(a) Give the domain and range of the function. 0 ≤ d ≤ 21 domain; 0 ≤ B ≤ 400
(b) Give an estimate to the nearest hundreds for B(0). Explain how you determined your estimate and tell what B(0) means in the context of the situation.
(c) Ebony's bank balance first reached $0 on Day 12. How would you show that information in function notation? B(12) = 0
(d) Ebony's bank balance remained at $0 from Day 12 through Day 15. As you count segments from the left, which segment on the graph1, 2, 3, 4, 5, or 6 represents that information? Explain how you know. 4th segment
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The equation $f\left(x\right)=2x-9$ translated 6 units up is $g\left(x\right)=$ .
The equation f(x) = 2x - 9 translated 6 units up, then the equation g(x) = 2x-3
The equation is
f(x) = 2x - 9
Then it is translated 6 units up
The translation is the process of moving the shape to left/right of up or down. During the translation process the shape and size of the graph will not change. In translation we are only changing the coordinates of the points of the shape.
Here it is translated 6 units up.
During the upward motion it will be positive
g(x) = f(x) + 6
Substitute the value of f(x)
g(x) = 2x-9 + 6
g(x) = 2x-3
Hence, the equation f(x) = 2x - 9 translated 6 units up, then the equation g(x) = 2x-3
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Write the equation in standard form, x(x+3)=0
Answer:
x²+3x=0
Step-by-step explanation:
Just distribute and simplify.
Skylar bought 23 chicken wings for $32.20. How much would it cost for 13 wings?
If Skylar bought 23 chicken wings for $32.20 then the cost of 13 wings would be using the concept of estimation.
As per the question statement, Skylar bought 23 chicken wings for $32.20. We are supposed to calculate the cost of 13 wings. We will use the concept of estimation.
Cost of 23 wings = $32.20
Cost of 1 wing = $32.20/23 = $1.40
Therefore cost of 13 wings = $1.40 * 13 = $18.20
So, if Skylar bought 23 chicken wings for $32.20 then the cost of 13 wings would be using the concept of estimation.
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Divide.
(24x³ - 2x² + 3x-9) ÷ (6x - 5)
Your answer should give the quotient and the remainder.
Answer: 4x^2 + 3x + 3
Step-by-step explanation:
The daily changes in the barometric pressure for four days are −0.05, 0.09, −0.04, and −0.08 inches. The mean change after five days is −0.01 inch. What is the change on the fifth day? Write your answer as a decimal.
The change on the fifth day is 0.03.
What is a mean?A mean simply means the average of.a set of numbers.
Based on the information given, let the change in the fifth day be x. This will be illustrated as:.
= (-0.05 + 0.09 - 0.04 - 0.08 + x)/ 5 = -0.01
Crops multiply
-0.08 + x = -0.05
Collect like terms
x = -0.05 + 0.08
x = 0.03
The change is 0.03.
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There are two cars, green car (gc) and a blue car (bc). gc is $15 plus $0.50 per mile driven, bc is $25 plus $0.15 per mile. how many miles do both cars have to drive to cost the same amount?
The number of miles that both the green car and the blue car have to drive to cost the same amount is equal to 28.5 miles.
The number of miles both cars have to travel to cost the same amount can be determined using an algebraic expression. An algebraic expression can be defined as a mathematical equation consisting of both letters and numbers.
As the green car (gc) cost $15 plus $0.50 per mile and the blue car (bc) costs $25 plus $0.15 per mile, an algebraic expression for this problem can be given as follows;
15 + 0.50(x) = 25 + 0.15(x)
Solving for x;
0.50x - 0.15x = 25 - 15
0.35x = 10
x = 10 / 0.35
x = 28.5
Hence, both cars have to drive 28.5 miles to cost the same amount.
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Lisa is saving for college. The account is modeled by the function:
f(x) = 250(1.25)x^, when x represents how many years she has saved.
Xavier is also saving for college. His account is modeled by this table:
X 0 1 2 3
g(x) 200 270 364.5 492.08
Answer the following questions:
A. After 5 years, how much does Lisa's account have in it?
B. After 5 years, how much does Xaviers account have in it?
C. What is the positive difference in their accounts after 5 years?
Using exponential functions, it is found that:
a) Lisa's account has $763 after 5 years.
b) Xavier's account has $897 after 5 years.
c) The difference is of $134.
What is an exponential function?An exponential function is modeled according to the following rule:
[tex]y = ab^x[/tex]
In which the parameters are described as follows:
a is the initial value of the function, that is, the value of the function when x = 0.b is the rate of change of the function.Lisa's function is already given, while for Xavier's, the parameters are given as follows:
a = 200, b = 270/200 = 1.35.
Hence his function is:
[tex]g(x) = 200(1.35)^x[/tex]
In 5 years, the amounts in each account will be given by the numeric values of the functions as follows:
Lisa: [tex]f(5) = 250(1.25)^5 = 763[/tex]Xavier: [tex]g(5) = 200(1.35)^5 = 897[/tex]The positive difference is given by the subtraction of the greater amount by the lesser amount, hence:
897 - 763 = $134.
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How much greater is the average temperature on Earth than the average temperature on Jupiter?
The average temperature on Earth is greater than the average temperature on Jupiter by 225°F.
By how many degrees Fahrenheit is the average temperature on Earth than the average temperature on Jupiter?The average temperature on earth is greater than the average temperature in Jupiter by 225°F. This can be obtained by getting the average temperatures as follows:
The average temperature on Earth is = 59°F
The average temperature on Jupiter is = -166°F.
Now we represent this in an equation as follows:
-166°F + x = 59°F
x = 59 - (-166)
x = 59 + 166
x = 225°F.
So, the figure with which the average temperature of the earth surpasses the average temperature of Jupiter is 225°F.
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Plot the points of the pre-image and graph the pre-image.
Given:
The Point is:
[tex]\begin{gathered} W(2,2) \\ \\ X(2,0) \\ \\ Y(0,1) \\ \\ Z(1,2) \end{gathered}[/tex]The scale factor is 3.
Find-:
Create the point W'X'Y'Z'
Explanation:-
The scale factor is 3.
So the point is:
[tex]\begin{gathered} W^{\prime}=3W \\ \\ W^{\prime}=3(2,2) \\ \\ W^{\prime}=(6,6) \end{gathered}[/tex]Point X' is:
[tex]\begin{gathered} X^{\prime}=3X \\ \\ X^{\prime}=3(2,0) \\ \\ X^{\prime}=(6,0) \end{gathered}[/tex]The point Y' is:
[tex]\begin{gathered} Y^{\prime}=3Y \\ \\ Y^{\prime}=3(0,1) \\ \\ Y^{\prime}=(0,3) \end{gathered}[/tex]The point Z' is:
[tex]\begin{gathered} Z^{\prime}=3Z \\ \\ Z^{\prime}=3(1,2) \\ \\ Z^{\prime}=(3,6) \end{gathered}[/tex]The graph of WXYZ.
The graph of W'X'Y'Z'
What percentage of the floor has been covered in tile? A. 14% B. 28% C. 56% D. 70%
Answer:
Answer down below!
Step-by-step explanation:
We have 25 squares in total, and 14 of them are fill, we can figure out it's percentage with division
25/14 = 0.56
We can do 0.56 *100 to get the percentage!
Which that will give you 56%
you've done a ton of original research for a statistics project, but you just can't prove your hypothesis that the majority of college students adore katy perry. rather than admit that only .9% of students can tolerate kp, you move the decimal point and declare that 90% of students are katycats. this is an example of:
This is an example of remix plagiarism.
Remix plagiarism includes collecting information from different sources, combing together into one work by using the method of paraphrasing, and claiming it as your work.
The person basically changes the language of the statements and fit the topic under his or her name. Here the hypothesis that majority of college students adore katy perry, rather use the statement "90% of students are katycats".
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A population numbers 17,000 organisms initially and decreases by 4% each year.
Suppose P represents population, and t the number of years of growth. Write an exponential model to represent this situation.
An exponential model to represent this situation [tex]P =17000 (0.96)^{t}[/tex]
What is exponential growth of population?Exponential growth occurs when a population's per capita growth rate remains constant regardless of population size, causing the population to grow faster and faster as it grows larger.
In exponential growth, the per capita (per individual) growth rate of a population remains constant regardless of population size, causing the population to grow faster and faster as it grows larger. In nature, populations may grow exponentially for a time, but they are eventually constrained by resource availability.
Given that,
P represents population, and
t the number of years of growth.
As we know,
P = [tex]a(b)^{t}[/tex]
[here 'a' is the initial amount of population and 'b' is the amount of growth or shrink]
To get 'b,' start at 1 and either add or remove the decimal growth rate depending on whether it is rising or decreasing.
In this case a = 17,000, it is the value of population at the time zero.
As the population decreases 4% each year, then b = 1-0.04 = 0.96
So, the equation becomes, P = [tex]17000 (0.96)^{t}[/tex]
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need asap pleaseeee
Which is the best definition of an equation?
A statement that can only be simplified.
A number, variable, or combination of numbers and variables with an addition sign.
A number, variable, or combination of numbers and variables that also includes a multiplication sign.
A statement where two expressions are joined with an equal sign.
Answer:
I think the answer is (A statement where two expressions are joined with an equal sign.)
Step-by-step explanation:
Let f(t) be outside temperature t hours after 12 PM. Explain the meaning of f (1)>f(7)
If f(t) be the outside temperature t hours after 12 PM, then the meaning of f(1)>f(7) is the outside temperature 1 hours after 12 PM is greater than outside temperature 7 hours after 12 PM.
The function f(t) be the outside temperature t hours after 12 PM
Therefore,
f(1) be the outside temperature 1 hours after 12 PM.
f(7) be the outside temperature 7 hours after 12 PM.
Then,
f(1)>f(7) is the outside temperature 1 hours after 12 PM is greater than outside temperature 7 hours after 12 PM.
Hence, if f(t) be the outside temperature t hours after 12 PM, then the meaning of f(1)>f(7) is the outside temperature 1 hours after 12 PM is greater than outside temperature 7 hours after 12 PM.
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5k-3(2k-2/3)-9=0 what is equal to k
[tex]5k - 6k + 2 - 9 = 0 \\ - k - 7 = 0 \\ - k = 7 \\ \frac{ - k}{ - 1} = \frac{7}{ - 1} \\ k = - 7[/tex]
ATTACHED IS THE SOLUTION
Solve for x.
5(2x - 1) = 6
a. x = 1/10
b. x = 11/10
c. x = 1/2
Answer:
b
Step-by-step explanation:
5(2x - 1) = 6 ← distribute parenthesis on left side
10x - 5 = 6 ( add 5 to both sides )
10x = 11 ( divide both sides by 10 )
x = [tex]\frac{11}{10}[/tex]
At the local dairy farm, Kareem buys a 32-oz container of yogurt for $2.56. Jonah buys a 6-oz container of yogurt for $0.48. Are the cost, y, in dollars and the amount of yogurt, x, proportional?
The quantities Choose... proportional.
The dollar cost y and the amount of yogurt are proportionate
The formula is y = 0.08x
If y fluctuates as directly as x, you may express it as y = kx.
Where k is the proportionality constant.
Determine the value of the proportionality constant. When y = 2.56 and x = 32, you get:
y = kx
k = y/x
k = 2.56/32
k = 0.08
The equation is then: y = 0.08
Check to see if they are directly proportionate. Substitute the amount of yogurt purchased by Jonah. The outcome must be $0,48:
y = 0.08 (6) (6)
y = 0.48
The cost and amount of yogurt are proportionate in a straightforward manner.
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Choose ALL answers that describe the quadrilateral PQRS if PQ = RS, QR =SP, and diagonals have equal length: PR = QS.
○ parallelogram
○ rectangle
○rhombus
○square
○ trapezoid
answer:It's a rectangle
Bacteria grow at a rate of 10% per hour in a petri dish. if there is initially one bacterium and a carrying capacity of 1 million cells, how long (in hours) does it take to reach 500,000 cells? (round your answer to two decimal places.)
Bacteria grow at a rate of 10% per hour in a petri dish. then Bacteria take 50 hour to reach 500000 cells
Bacteria grow at a rate of 10% per hour in a petri dish.
if there is initially one bacterium and a carrying capacity of 1 million cells, how long (in hours) does it take to reach 500,000 cells?
An initial population of bacteria contain 100000 cell.
The population grow 10% every 1 hours.
This gives us an idea that in another 1 hours we will have 100000 cells organisms.
10% 0f 100000=10000 in one hour
then 500000 grow in = 500000/10000
= 50 hour
Hence Bacteria take 50 hour to reach 500000 cells
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32 = 5v + 7 solve for v simplify your answer as much as possible
Answer:
v=5
Step-by-step explanation:
32=5v+7 minus 7 on both side
25=5v divide 5 on both side
5=v or v=5