The difference between the following term is 7 and explicit rule is
[tex]a_{n}=-17+7n[/tex]
What is Explicit rule?Explicit rule is a rule that you can solve without needing the previous term.
How Should Explicit Formula Be Written?The nth term in the series is where the explicit formula can be expressed. The explicit formula of the sequence for the arithmetic progression a, a + d, a + 2d, a + 3d,...a + (n - 1)d is formed by the nth term. An = a + (n - 1)d is the explicit formula for this arithmetic series. The explicit formula can also be calculated for the harmonic and geometric sequences.
Here, [tex]a_{n}=-17+7n[/tex]
put n = 1
[tex]a_{n}[/tex]= =-17+7(1)
= -17+7
=-11 which is the first term
similarly for n = 4
-17+7(4)
= -17+ 28 =11 which is the fourth term.
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$11.49 for 3 packages
Answer:
3.83
Step-by-step explanation:
11.49 divided by 3 is 3.83
The sales tax rate is 10%. If Bill buys a globe priced at $14.80,
what will be the total cost including tax?
`suppose it took jacques 85 days to read the novel he read the same number of pagers per day
The number of pages that Jacques read per day is 7 pages.
How to calculate the number of days?From the information, Jacques has 595 pages of book to read and it took him 85 days to read the novel.
The number of pages will be the entire pages divided by the number of days used. This will be:
= Number of pages / Number of days
= 595 / 85
= 7
Therefore, Jacques read 7 pages per day.
The complete question is given below.
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Jacques has 595 pages of book to read. Suppose it took Jacques 85 days to read the novel, how many number of pages did he read per day.?
Help please it's going to be due soon):
Answer:
(2,1)
Step-by-step explanation:
Its the only pair that when plugged in would give you 13
3(2) + 7(1) =13
6 + 7 = 13
Find three consecutive odd integers such that the sum of the smaller two is three times the largest increased by seven.
Consecutive odd numbers are odd integers that are separated by 2 and come after one another. If the number x is odd, then the numbers x + 2, x + 4, and x + 6 are also odd.
Explain about the consecutive odd integers?The next two odd consecutive integers are (2n + 3) and (2n + 5) if 2n + 1 is an odd number. For illustration, assume that 2n + 1 is the odd number 7. Its successive numbers are identified as (7 + 2) and (7 + 4), or 9 and 11.
Three consecutive odd numbers that are 3, 5, and 7 are all prime. Three successive odd numbers that are not all prime are 109, 111, and 113 (111=37 times 3).
Answer
Let x - 2, x, and x + 2 be the three odd numbers.
x - 2 + x = 3(x + 2) + 7
2x - 2 = 3x + 6 + 7
2x - 2 = 3x + 13
3x - 2x = -2 - 13
x = -15
The three successive odd numbers are 17, 15, and 13, respectively.
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3. What are the approximate zeros of the function f(x) = x³ - 2x²-3x+1?
(round to tenth place)
The approximate zeros of the function f(x) = x³ - 2x²-3x+1 (round to tenth place) are -1.2 and 0.3.
What are Zeros of a Function?A function's zeros are the values of its variables that result in the function equaling 0. (f(x) = 0). The zeros of a function are the points on the x-axis where the graph intersects the x-axis. To put it another way, the zeros of a function are the x-intercepts of its graph.
Given:
We have f(x) = x³ - 2x²-3x+1
To determine the real zeros of the function f(x), we have f(x) = 0.
Using a graph to find the solutions for x(round to tenth place) are,
x₁ = -1.199 ≈ -1.2
x₂ = 0.286 ≈ 0.3
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Suppose point P divides the directed line segment XY so that the ratio of XP to PY is 3 to 5. Describe the point that divides directed line segment YX so that the ratio of YP to PX is 5 to 3.
The point that divides the directed line segment YX so that the ratio of YP to PX is 5 to 3 is P.
According to the question,
We have the following information:
Point P divides the directed line segment XY so that the ratio of XP to PY is 3 to 5.
Now, when the line segment XY is inverted to call the line segment YX then the point P is still there.
And the point P divided the line segment in the same way but the difference is that the measurement are taken from the other side. But the point P has not been removed because it is common in YP and PX and YX (as we observe even from the name of these smaller segments) is the line segment.
Hence, P is the point dividing the line segment YX into the given ratio.
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The Safari Restaurant is giving away gift bags. They have 24 magnets and 36 pencils. They want all the bags to be the same so that each bag has the same number of magnets and the same number of pencils. What is the greatest number of gift bags that the restaurant can make using all of the supplies?
Answer: 18
Step-by-step explanation:
Remove 2 from 36 and remove 1 from 24 until you get to 0.
2+2+5+6+7+8+9+0+8+9+8+7+8+9
Answer:
88
Step-by-step explanation:
you add all of them together
answer the answer is 88
Step-by-step explanation:
add two at a time then add all answers togher and u get 88
what are the two types of function used to form the rational function ?
GET 20 PONITS IF U HELP ASAP
Decide which sprinter is running faster per second:
Sprinter A: 1.4 feet in 3 seconds
Sprinter B: 2.8 feet in 5 seconds
Answer:
Sprinter B is going faster.
Step-by-step explanation:
Sprinter A is moving at a rate of 1.4 feet every 3 seconds, or about 0.47 feet every second.
Sprinter B is moving at a rate of 2.8 feet every 5 seconds, or 0.56 feet every second.
Therefore, Sprinter B is moving at a quicker pace.
Answer: The answer is Sprinter B.
Step-by-step explanation:
First I did 2.8 / 5 = .56 secs.
for the A
B I did 1.4 / 3 = .47 secs
So, B is the faster sprinter.
Amy, ravi, and bob have a total of $127 in their wallets. bob has 4 times what ravi has. ravi has $7 less than amy. how much do they have in their wallets
Amy has $ 27, Bob has $ 80 and Ravi has $ 20 amounts in their wallets.
Finding unknown quantity using Linear Equation:
A mathematical statement used to find an unknown quantity in a given problem is known as a Linear Equation. Here to represent the unknown quantity we will use variables like x, y, and so on.
Here we have,
Amy, Ravi, and Bob have a total of $127 in their wallets.
Since we don't know the amount of each person we represent them with different variables
Let 'a' be Amy's amount
'b' be Bob's amount
'r' be Ravi's amount
Then the total amount a + b + r = 127 -----(1)
Given that,
Bob has 4 times what Ravi has
=> b = 4r ----(2)
Ravi has $7 less than Amy
=> r = a - 7 ----(3)
From (2) and (3)
b = 4(a - 7)
b = 4a - 28 ----(4)
Now substitute (3) and (4)
=> a + 4a - 28 + a - 7 = 127
=> 6a - 35 = 127
=> 6a = 162
=> a = 27
From (3)
r = a - 7 = 27 - 7 = 20
From (2)
b = 4r = 4(20) = 80
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can someone help me here please! thankyou
Answer:
AUB = {0,1,2,3,4,6,8}
B∩C = Nil
Xc∩Yc = {February, April, August, September, November, December}
(YUZ)c= {February, March, April, May, August}
the symbol c stands for complement in the solution.
Step-by-step explanation:
union is combining all the elements of sets A and B
AUB = {0,1,2,3,4,6,8}
intersection is combining only the common elements present in both B and C
B∩C = Nil
complement of a set is the number of elements that are not present in the set.
Xc = {January, February, April, August, September, November, December}
Yc= {February, March, April, May, August, September, October, November, December}
Xc∩Yc = {February, April, August, September, November, December}
Y∪Z = {January, June, July, September, October, November, December}
(YUZ)c= {February, March, April, May, August}
the symbol c stands for complement in the solution.
Answer:
A⋃B = {0, 1, 2, 3, 4, 6, 8} B⋂C = { } . . . (the empty set) X'⋂Y' = {Feb, Apr, Aug, Sep, Nov, Dec} (Y⋃Z)' = {Feb, Mar, Apr, May, Aug}Step-by-step explanation:
Given various set definitions, you want to find the union and the intersection of specific pairs of sets.
We find it convenient to list the set contents in such a way that we can readily identify elements in one set or another, neither, or both. That is what we have done in the attachment.
1. A⋃BThe union of sets A and B will be the list of elements in either set. That is, if an element is included in set A or in set B, it is included in their union. An element is only listed once, even if it appears in both sets.
A⋃B = {0, 1, 2, 3, 4, 6, 8}
2. B⋂CThe intersection of sets B and C will be the list of elements contained in both sets. Set B is even digits, and set C is odd digits. Since there are no digits that are both even and odd, their intersection is the empty set.
B⋂C = { } . . . (the empty set)
3. X'⋂Y'The intersection of the complements of sets X and Y is the list of elements of U that are not in either set.
X'⋂Y' = {Feb, Apr, Aug, Sep, Nov, Dec}
4. (Y⋃Z)'The complement of the union of Y and Z is the list of elements of U that are not in either of sets Y or Z. This is effectively the same as Y'⋂Z'.
(Y⋃Z)' = {Feb, Mar, Apr, May, Aug}
__
Additional comment
We have elected to abbreviate the month names for problems 3 and 4. Your answer may need to spell them out completely to match the problem statement.
What is the equivalent expression of 4.32÷0.16?
The equivalent expression of 4.32÷0.16 is 0.27.
What are equivalent expressions?Equivalent expressions are expressions that perform the same function notwithstanding their appearance. In mathematics, equivalent expressions are expressions that are the same even if they appear to be different. When the values are entered into the expression, however, both formulations produce the same result. If the terms in both expressions are identical, the expressions are equal.Given:
Expression = 4.32÷0.16
We have to determine the equivalent expression of 4.32÷0.16.
4.32÷0.16 (multiply both the terms by 100 to remove decimals)
432 ÷ 16
= 0.27
Therefore, the required equivalent expression is 0.27 respectively.
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what color is your buggati?
Answer: yellow
Step-by-step explanation:
ITS THE RIGHT ANSWER IMAOAO
Answer:
Bugatti veyron is available in 10 different colours
Step-by-step explanation:
Light blue pear,black-M,mocca brown, black blue-M ,lemon and Light red.
what is 121 divided by 12.75
Answer:
9.49
Step-by-step explanation:
this is the answer hope it helps
Find the indicated value using the given functions
The correct option is b: 2 ∛(5 - 1) , is the value of the composite inverse function.
What is meant by the inverse of the function?An inverse function, also known as an anti function, is a function that can be reversed into another function. Simply put, if any function "f" takes x to y, then its inverse will take y to x. The inverse function is signified by f-1 or F-1 if the function is signified by 'f' or 'F'. Here, (-1) should not be confused with exponent or reciprocal.For the given question,
The functions as given as;
f(x) = x/3 + 1
g(x) = x³
Now, the find the composite function f o g (x).
Put the value of g(x) at the place of x in f(x).
f o g (x) = x³/8 + 1
Let the obtained composite function be y.
y = f o g (x) = x³/8 + 1
Find the value of x in terms of y.
y = x³/8 + 1
y - 1 = x³/8
8(y - 1) = x³
taking cube root.
x = 2 ∛(y - 1)
Now, substitute the value of x in place of y.
(f o g )⁻¹(x) = 2 ∛(x - 1)
Now, put the value of x as 5.
(f o g )⁻¹(x) = 2 ∛(x - 1)
(f o g )⁻¹(5) = 2 ∛(5 - 1)
Thus, the value of the composite inverse function is obtained as 2 ∛(5 - 1).
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In his spare time, Kim likes to go cycling. He cycles partly on paved surfaces and partly off-road, through hilly and wooded areas. He cycles at 25km/h on paved surfaces and at 10 km/h off-road. One day, he cycled 41 km in 2 hours. How far did he cycle on the paved road and how far off-road?
Kim travelled 35 km on a paved surface and 6 km off-road which took 1.4 hours and 0.6 hours respectively
Speed of Kim when cycling on paved surfaces: 25 km/hr
Speed of Kim when cycling off-road = 10 km/hr
Distance covered by Kim = 41 km
Time is taken by Kim = 2 hours
Let x be the time Kim travels on a paved surface, and y represents the time off-road
Using the formula:
Speed = Distance/Time
Distance travelled by Kim on paved surface = 25*x
Distance travelled by Kim off-road = 10*y
x + y = 2-------(1)
25x + 10y = 41-------(2)
Multiplying equation (1) with 25 and equating with (2) we get:
25x + 25y = 50
25x + 10y = 41
15y = 9
y = 0.6 hours
x = 1.4 hours
Distance travelled on paved surface = 25*1.4 = 35 km
Distance travelled off-road = 10*0.6 = 6km
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x + 3/4 > - 1/3 Solve the inequality for x.
Simplify your answer as much as possible.
Answer:
x > -13/12
Step-by-step explanation:
x + 3/4 > - 1/3
x + 9/12 > -4/12
x > -13/12
-1/3 = -4/12
3/4 = 9/12
Answer:
x > - 13
12
Step-by-step explanation:
[tex]x + \frac{3}{4} > - \frac{1}{3} \\ x + \frac{3}{4} - \frac{3}{4} > - \frac{1}{3} - \frac{3}{4} \\ x > \frac{ - 4 - 9}{12} \\ x > - \frac{13}{12} [/tex]
a rectangle is h units wide it length is 3 units more than the width
Answer:
I think that you have to find the length and width of the rectangular
What is the equation in standard form has a graph that passes through the point (5,-3) and has a slope of 6/5
Considering the definition of a line, the equation of the line that passes through the point (5, -3) and has a slope of 6/5 is y= 6/5x -9.
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Line in this caseIn this case, you know:
The line has a slope of 6/5.The line passes through the point (5, -3).Substituting the value of the slope m, the line has the form: y=6/5x +b
Substituting the value of the point in the previous expression, the value of the ordinate to the origin b can be obtained:
-3= 6/5×5 + b
-3= 6 + b
-3 - 6= b
-9= b
Finally, the equation of the line is y= 6/5x -9.
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Graph the equation y=1/3x-2
Answer:
Start by putting a dot on -2 on the y-axis. Then go up 1 square and go across to the right three squares. Continue to do that to graph the equation.
Step-by-step explanation:
Start by putting a dot on -2 on the y-axis. Then go up 1 square and go across to the right three squares.
Answer:
Step-by-step explanation:
A wedding planning business is setting up for an event. They are expecting 120 guests to participate. The manager at the reception center says that there are two options for the size of the tables. Small tables seat 2 people and large tables seat 6 people. An equation that could be used to find the combination of large and small tables needed for the event is 2x+6y=120. Here is a graph of the equation.
You may select more than one answer:
If the wedding planner chose to use small tables only, then 20 tables would be needed.
If 15 small tables are used, 15 large tables will be needed.
If 5 fewe large tables are used, 15 more small tables would be needed.
If 30 small tables are used, 5 large tables would be needed.
If no large tables are used, 60 small tables would be needed.
Work out the missing number
a) 0.36 ÷
= 0.09
PLEASE HELP ASAP
Two clocks are turned on at the same time. One clock chimes every 15 minutes. The
other clock chimes every 25 minutes. In how many minutes will they chime together?
Answer:
In 75 minutes, both clocks will chime together.
Step-by-step explanation:
All you have to do is find the least common multiple of 15 and 25.
Multiples of 15:
15 x 1 = 15
15 x 2 = 30
15 x 3 = 45
15 x 4 = 60
15 x 5 = 75
Multiples of 25:
25 x 1 = 25
25 x 2 = 50
25 x 3 = 75
25 x 4 = 100
25 x 5 = 125
If you compare the two, you’ll find that 15 and 25 have a least common multiple of 75. So, in 75 minutes both clocks will chime at the same time
Solve for x with zero product propertyX^2 + 4x -27 = 5
Answer
[tex]\begin{gathered} Given\text{ }x^2+4x-27=5 \\ x^2+4x-27-5=5-5 \\ x^2+4x-32=0 \end{gathered}[/tex]Using factorization method
[tex]\begin{gathered} x^2+8x-4x-32=0 \\ x(x+8)-4(x+8)=0 \\ (x+8)(x-4)=0 \end{gathered}[/tex][tex]\begin{gathered} x+8=0\text{ }or\text{ }x-4=0 \\ x=-8\text{ }or\text{ }x=4 \end{gathered}[/tex]Therefore, x = -8 or x = 4
Solve the equation 5+10(x-9)<-103-(7-5x)
we have the inequality
5+10(x-9) < -103-(7-5x)
solve for x
apply distributive property left side and remove the parenthesis right side
5+10x-90 < -103-7+5x
Combine like terms
10x-85 < 5x-110
Group terms
10x-5x < -110+85
5x < -25
x< -25/5
x < -5
the solution is the interval (-inf, -5)
set builder notation
x| x < -5
-2 1/2 - 5 3-4 as a mixed number
Answer:
The distance between -2 1/2 and -5 3/4 Is
13/4.
2x - 3y +z = 7
4x + y + 2z=0
3x + 4y -z = -4
Answer:
x=1
y=-2
z=-1 ( substitute into equations)
A bicycle travels at a speed of 2,808 inches
per minute. The radius of each tire on the
bicycle is 3 feet. Approximately how many
revolutions does one of these tires make in 2 minutes?
(Use the approximation 22/7 for π.)
A. 12
B 25
C. 32
D. 46
Answer:
in a complete turn the wheel will travel the
expressed 2pi x radius or 2 x 3.14 x 28 or 175.84
circumference of the wheel. The circumference is cm x 3 (turns) = 527.52 cm or 572.52cm x 1in/2.54 cm x 1ft/12in or 18.78 ft or if you prefer meters 572.52 cm x 1m/100cm = 5.73 m
