The given sequence 10,20,30,40, ........... forms an arithmetic sequence. The common difference is found to be 10.
How does the AP arithmetic progression succession?The difference between the two mathematical orders is a fixed value in Arithmetic Progression (AP). Another name for it is Arithmetic Sequence.
We'd come around a few specific words in AP that were labeled as:
The first term (a)Common difference (d)Term nth (an)The total of first n terms (Sn)Some formulas related to AP are-
The AP could be defined in terms of common differences, as shown below: a, a + d, a + 2d, a + 3d, a + 4d, ………. ,a + (n – 1) d.The procedure for appraising an AP's n-th term is as follows: an = a + (n − 1) × dThe following is the arithmetic progression sum: Sn = n/2[2a + (n − 1) × d].Now, for the stated sequence is: 10,20,30,40, ...........
Let us suppose the first term is'a₁' = 10.
Let us suppose 'a₂' = 20 is the second term.
Let us suppose the third term is 'a₃' = 30.
Let us suppose the fourth term be 'a₄' = 40.
d = a₂ - a₁
Substitute the values;
d = 20 - 10 = 10 ........(equation 1)
Now consider the other set;
d = a₃ - a₂
d = 30 - 20 = 10 .......(equation 2)
Comparing equation 1 and 2, the common difference is same.
Thus, the given sequence forms an AP.
The common difference is found to be 10.
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-7 (3y)+2(-4y+-4)
Can someone please help me !!!!!!!!!!!!!!!1
The simplified form of the expression is -29y - 8
Expansion of expressionLinear equations are equations that has a linear degree of 1. For instance the expression y =mx + b has a linear degree of 1.
Given the linear equation below:
-7 (3y)+2(-4y+-4)
When solving linear equation, first we will need to expand the expression first.
-7 (3y)+2(-4y+-4)
-21y + 2(-4y) + 2(-4)
Simplify the resulting expression
-21y -8y. - 8
-29y - 8
Hence the simplified form of the expression is -29y - 8
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Physical science
You decide to race your best friend around the track to see who's the better runner. You travel 400 meters in 8.2 seconds. Your best friend covers the same distance but does it in 7.8 seconds. Calculate the speed of each of you, and determine who is the father runner.
The best friend is the faster runner as his speed is 51.28 m/s while my speed is 48.78 m/s.
Speed is defined as the distance travelled by someone or something in unit time. The SI unit of speed is meters per second. The speed is calculated by dividing the distance travelled by the total time taken to travel said distance.
Given the distance travelled by both of the friends is 400 meters.
Now The first friend travels this distance in 8.2 seconds:
Therefore speed is calculated by distance ÷ time
or, speed = 400 ÷ 8.2
or , speed = 48.7804... m/s
or, speed ≈ 48.78 meters per second
And the best friend travels this distance in 7.8 seconds:
Therefore speed is calculated by distance ÷ time
or, speed = 400 ÷ 7.8
or , speed =51.2820... m/s
or, speed ≈ 51.28 meters per second
Therefore by comparing both the speeds we can conclude that the best friend is the faster runner.
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Solve each equation.
p⁴+32=12 p²
The solutions of the given polynomial equation p⁴+32=12 p² is p = {-2√2, 2√2, -2, 2}.
The given polynomial equation is:
p⁴+32=12 p²
Subtract both sides by 12 p²
p⁴ + 32 -12 p² = 12 p² 12 p²
p⁴ -12 p² + 32 = 0 ...... (1)
Let x = p², then equation (1) becomes
x² -12x + 32 = 0
This is a quadratic equation.
Factorize:
x² -12x + 32 = 0
⇔ (x - 8 ) (x - 4) = 0
Take:
x - 8 = 0
x = 8
p² = 8
p = ±√8 = ±2√2
Take:
x - 4 = 0
x = 4
p² = 4
p = ±√4 = ±2
Hence the solution is p = {-2√2, 2√2, -2, 2}
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Find the eighth term of each geometric sequence. 2/3, 4/9, 8/27 . . . . .
The eighth term of the given geometric sequence is 256/6561.
What is a geometric progression?A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.
Given: 2/3, 4/9, 8/27...
As we can observe, each successive term of the geometric sequence is 2/3 of the previous one.
Thus, r = 2/3 and a₁ = 2/3.
The formula used to find the nth term of a geometric sequence is given by: [tex]a_n=a_1(r^{n-1})[/tex]
For n = 8, [tex]a_8=\frac{2}{3}(\frac{2}{3})^7=\frac{2}{3}^8=\frac{256}{6561}[/tex]
Thus, the eighth term of the given geometric sequence is 256/6561.
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Simplified version of the equation in the pic please
Answer:
3[tex]x^{2}[/tex] + 4x + xy
Step-by-step explanation:
Basically just combining like terms
[tex] \large \bf \implies{ {3x}^{2} + xy + 4x} \\ [/tex]
Step-by-step explanation:Given :- 6x² + 6x - 3x² + xy - 2xTo Find :-Simplify itSolution :-Step 1) Combine the like terms
(6x² - 3x²) + (xy) + ( 6x - 2x )Step 2) Add/Subtract the terms
(3x²) + (xy) + (4x)Step 3) We have got the answer
3x² + xy + 4xThe table represents an absolute value function f(x). x f(x) −2 4 −1 3 0 2 1 1 2 0 3 1 4 2 5 3 6 4 What are the vertex and range of the function? Vertex (0, 2), Range: {y | 0 ≤ y < ∞} Vertex (0, 2), Range: {y | 2 ≤ y < ∞} Vertex (2, 0), Range: {y | 0 ≤ y < ∞} Vertex (2, 0), Range: {y | 2 ≤ y < ∞} Question 10(Multiple Choice Worth 4 points) (02.04 MC) A medical clinic is reducing the number of incoming patients by giving vaccines before flu season. During week 5 of flu season, the clinic saw 75 patients. In week 10 of flu season, the clinic saw 50 patients. Assume the reduction in the number of patients each week is linear. Write an equation in function form to show the number of patients seen each week at the clinic. f(x) = 5x + 100 f(x) = −5x + 100 f(x) = 25x + 75 f(x) = −25x + 75 Question 11(Multiple Choice Worth 4 points) (02.05 MC) Compare the slopes of the linear functions f(x) and g(x) and choose the answer that best describes them. a line labeled f of x passing through 0, negative 1 and 3, 1 x g(x) 0 2 5 4 10 6 The slope of f(x) is greater than the slope of g(x). The slope of f(x) is less than the slope of g(x). The slope of f(x) is equal to the slope of g(x). The slope of g(x) is undefined. Question 12(Multiple Choice Worth 4 points) (02.02 LC) If h(x) = −4x − 10, find h(−5). −30 1.25 10 −1 Question 13(Multiple Choice Worth 4 points) (02.04 MC) Write the equation of the line that passes through the points (1, 7) and (5, 15) using function notation. y = 2x + 5 y = 4x + 8 f(x) = 2x + 5 f(x) = 4x + 8 Question 14(Multiple Choice Worth 4 points) (02.05 LC) Which of the following statements best describes the effect of replacing the graph of y = f(x) with the graph of y = f(x − 9)? The graph of y = f(x) will shift up 9 units. The graph of y = f(x) will shift down 9 units. The graph of y = f(x) will shift left 9 units. The graph of y = f(x) will shift right 9 units. Question 15(Multiple Choice Worth 4 points) (02.03 MC) Choose the graph that correctly represents the equati
Using the absolute value function, linear functions and translations, we have that:
9. Vertex (2, 0), Range: {y | 0 ≤ y < ∞}
10. The equation is f(x) = -5x + 100.
11. The correct option is: The slope of f(x) is greater than the slope of g(x).
12. h(-5) = 10.
13. The equation is f(x) = 2x + 5.
14. The graph of y = f(x) will shift right 9 units.
What is the absolute value function?The absolute value function is defined by the following piecewise rule, depending on the input of the function:
|x| = x, x ≥ 0.|x| = -x, x < 0.It measures the distance of a point x to the origin, hence, for example, |-2| = |2| = 0, and has vertex(turning point) at (0,0). The range is from the y-coordinate of the vertex to positive infinity.
In item 9, from the table, the turning point is at (2,0), hence:
Vertex (2, 0), Range: {y | 0 ≤ y < ∞}
What is a linear function?A linear function is modeled by the following rule:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, the change in y divided by the change in x.b is the y-intercept, which is the the value of y when the function crosses the x-axis, that is, when x = 0.For item 10, we have that:
The initial amount is of 100 patients, as 75 + 25 x 5 = 100 hence b = 100.The reduction is of 5 patients in a week(25 patients reduction in 5 weeks = 5 a week), hence m = -5.Then:
The equation is f(x) = -5x + 100.
For item 11, the slope is given by change in y divided by change in x, hence:
f(x): (1 - (1))/(3 -0) = 2/3 = 0.67.g(x) = (4 - 2)/(5 - 0) = 0.4.Hence:
The correct option is: The slope of f(x) is greater than the slope of g(x).
For item 12, we have that:
h(x) = -4x - 10.
Hence, when x = -5:
h(-5) = -4(-5) - 10 = 20 - 10 = 10.
Hence:
h(-5) = 10.
For item 13, we have that when x changes by 4, y changes by 8, hence the slope is:
m = 8/4 = 2.
When x = 1, y = 7, hence, considering the slope, when x = 0, y = 5, and:
The equation is f(x) = 2x + 5.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x). Examples are shift left, shift right, shift down, shift up, vertical stretching, horizontal stretching, vertical compression, horizontal compression, reflection over the x-axis, reflection over the y-axis, and rotations by a determined amount(in degrees). All these translations have predetermined rules that we apply to the figures.
For this problem, the rule is given by:
y = f(x - 9).
The translation is x -> x - 9, hence:
The graph of y = f(x) will shift right 9 units.
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Answer:
(For number 9) Range {y/0<y<infinity} Vertex (2,0)
Step-by-step explanation:
I took test
I hope I helped for that part of it.
Find the distance between pair of parallel lines with the given equations.
x=-2 x=5
The distance between pair of parallel lines with the given equations
x=-2 x=5 is 7 units
Definition of parallel linesParallel lines are any two or more lines that lie in the same plane but never cross one another. Both have the same slope and are equally distant from one another. No matter how far we extend a parallel line, it will always remain straight.
The fundamental characteristics listed below make it simple to recognize parallel lines.
Straight lines which are always the same distance apart from one another are known as parallel lines.No matter how far apart they are from one another, the parallel lines can never intersect.The distance between parallel lines on a graph can be given as x1 - x2 as both are equidistance from y for which y has been cancelled.
here x1 =5 and x2 = -2
So, x1 - x2 = 5 -(-2)
= 5 + 2
= 7
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Pleas help I need to pass
Answer:
?
Step-by-step explanation:
(7,-4); m = -6 pls help this is so confusing
Answer:
3;m=-6
Step-by-step explanation:
3;m=-6
7. (3pts) Amazon delivery boxes are launched from a horizontal conveyor belt moving at a rate of 3 m/s into bins for
shipping. If the surface of the conveyor belt is 1.4 m off the ground, what is the range of each Amazon box? (NOTE:
Only 1 point if no work is shown)
Show some work:
The range of each amazon box is 1.6035m
According to the question we have been given that
height of the conveyer belt = 1.4m
Speed of the belt = 3m/s
We need to find the range of the amazon box, that is we have to find the distance.
Formula for distance is , d = speed * time
We have been given the value of speed we need to find the value of time. For that we will use the formula,
h = [tex]\frac{1}{2} g t^{2}[/tex]
where, h = height
g = acceleration due to gravity = 9.8m/s²
t = time
Putting the required value for t we get,
t = [tex]\sqrt{\frac{2h}{g} } \\[/tex]
= [tex]\sqrt{\frac{2(1.4)}{9.8} } \\[/tex]
= √0.286
= 0.5435 s
Putting the value of time in distance formula we get,
d = 3 * 0.5435 m
= 1.6035 m
Hence the range of each amazon box is 1.6035m
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Given two terms of each arithmetic sequence, find a₁ and d . a₃=32 and a₇ =-8
The common difference d is 6 and the first term a1 is 20.
How to find the a1 and d?The difference between any two consecutive integers in an arithmetic progression (AP) sequence of numbers is always the same value.
The formula of Arithmetic progression is
a(n) = a1 + (n - 1)d
given that the two terms of arithmetic sequence,
a3 = 32 and a7 = -8.
now, find the common difference d.
a(n) = a1 + (n - 1)d
Let take a(n) = a7 and a1 = a3.
a7 = a3 + (7 - 3)d
a7 = a3 + 4d
now substitute the values of a6 and a4
-8 = 32 + 4d
-8 + 32 = 4d
d = 24/4
d = 6
so, the common difference d is 6.
then, find the term a1.
take the formula
a(n) = a1 + (n - 1)d
now, substitute a(n) = a3 and d = 6.
32 = a1 + (3-1)d
32 = a1 + 2d
32 = a1 + 2(6)
32 = a1 + 12
a1 = -12+32
a1 = 20.
so, the first term a1 is 20.
Hence, the common difference d is 6 and the first term a1 is 20.
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Can someone help me out? I need a number less than one. It can be any fun fact
Answer:
-7
Assuming that "It can be any"
Determine whether following set of numbers can be the measures of the sides of a triangle. If so, classify the triangle as acute, obtuse, or right. Justify your answer.
8,15,17
The following set of numbers, 8, 15, and 17, can be the measures of the sides of a triangle, specifically a right triangle.
To know if a set of number is a valid measure of the sides of a triangle, it must follow the Triangle Inequality Theorem which states that the sum of any two sides must be greater than the third side, such that a + b > c, a + c > b, and b + c > a.
let a = 8, b = 15, and c = 17
a + b > c 8 + 15 > 17 23 > 17 True
a + c > b 8 + 17 > 15 25 > 15 True
b + c > a 15 + 17 > 8 32 > 8 True
To know what type of triangle based on the length of its side:
1. Take the sum of the squares of the two smaller sides.
8^2 + 15^2 = 289
2. Compare it to the square of the largest side.
17^2 = 289
289 = 289
If the sum of the squares of the 2 is larger than the square of the 3rd, it is an acute triangle.
if they are equal, it is a right triangle
if they are smaller, then it is an obtuse triangle.
Hence, 8, 15, and 17 can be the measure of the sides of a right triangle.
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Example 1 Position and label each triangle on the coordinate plane.isosceles ΔF G H with base FG that is 2 a units long
The Δ FGH with base FG that is 2a unit long has been drawn below.
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.
The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.
Δ FGH is a isosceles triangle.
Now isosceles triangle is a triangle whose two sides are equal.
In the ΔFGH, HF = HG
Hence "The Δ FGH with base FG that is 2a unit long has been drawn below".
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Can someone help me find the value of x
Each team can have 3, 4 or 5 people 21 people take part. How many different possible arrangements of teams are there?
Step-by-step explanation:
Lets understand the situation,
This means Each team can have 3, 4 or 5 people.And 21 people take part.
we have to find How many different possible arrangements of teams are there.
Solution:-Situation 1.
if 7 groups of people 3 Team7×3=21.situation 2.
if 4 groups of people 4 teams and 1 group of people 5 Team.(4×4)+(1×5)=21.Situation 3.
if 2 groups of people 3 Team and 3 group of people 5 Team.(2×3)+(3×5)=21.situation 4.
if 4 groups of people 3 Team and 1 group of people 4 Team And 1 group of people 5 team.(4×3)+(1×4)+(1×5)=21.compete each table. use the table to determine the unit rate. Lorenzo can read 12 pages of his book in 3 minutes
Answer:
1 is 6 pages, 7 minutes is 24 pages, 14 minutes is 45 pages
Step-by-step explanation:
the unite rate is 3
solve for y 2x + 4y = -1
Answer:
y = -1/4 -x/2
Step-by-step explanation:
The solution is attached.
The history book cause 850
Find the sum of the first 25 terms of the series:
215 + 200 + 185 +...
Answer:
875
Step-by-step explanation:
215+200+185+170+155+140+125+110+95+80+65+50+35+20+5+(-10)+(-25)+(-40)+(-55)+(-70)+(-85)+(-100)+(-115)+(-130)+(-145) =875
I'm sure there's an easier way to do this, but if you want a correct answer, here you go. Have a good day!
Answer:
875
Step-by-step explanation:
I think hope it right
the larger of two numbers is six more than three times the smaller number. If the sum of the two numbers is 34, what are the two numbers?
Answer:
7 and 27
Step-by-step explanation:
We can make an equation for this, it looks like this:
6+3x+x=34
Simple algebra can be used to solve this (x is the smaller number)
1. 6+3x+x=34
2. 6+4x=34 Combine like terms
3. 4x=28 Simplify
4. x=7 simplify
Now that we have the smaller number we can use a portion of the original equation to solve with x=7.
1. 6+3x
2. 6+3(7)
3. 6+21
4. 27
So the smaller number is 7, and the larger number is 27.
Helpppp it is due at 11:59
Answer: x<1
Step-by-step explanation:
add 12 to both sides, divide by 2 on both sides.
Write each arithmetic series in summation notation. 1+5+9+. . . . . +41+45
The arithmetic series 1+5+9+. . . . . +41+45 can be expressed in summation notation as [tex]\sum\limits^{12}_{n=1} {(4n-3)}[/tex]
The given arithmetic series:
1+5+9+. . . . . +41+45
To write the series in summation notation:
Find the common difference (d) of the series.
d = 5 - 1 = 4
Recall the formula for the nth term in an arithmetic sequence:
a(n) = a(1) + (n-1) . d
Substitute a(1) = 1 and d = 4:
a(n) = 1 + (n-1) . 4
a(n) = 4n - 3
Find n that leads to a(n) = 45
a(n) = 4n - 3
45 = 4n - 3
4n = 48
n = 12
Thus, the lower limit of the summation is n =1, and the upper limit is n = 12
Now write in summation notation as:
[tex]\sum\limits^{12}_{n=1} {a(n)}= \sum\limits^{12}_{n=1} {(4n-3)}[/tex]
This summation notation can be further simplified using the properties of summation operator:
[tex]\sum\limits^{12}_{n=1} {(4n-3)}=\sum\limits^{12}_{n=1} {4n}-\sum\limits^{12}_{n=1} {3}[/tex]
[tex]=\sum\limits^{12}_{n=1} {4n}-12\times3[/tex]
[tex]=\sum\limits^{12}_{n=1} {4n}-36[/tex]
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HELP
Joseph buys a subway pass for $55. Every time he rides the subway, money is deducted from the value of the pass. He rode the subway 5 times and $40 was deducted from the value of the pass. How much was deducted from Joseph's account for each ticket? Write a mathematical expression to represent this situation; then find the answer.
1) The mathematical expression that represents this scenario is T = 40/5.
2) The value of T in the equation is $8.
What is a mathematical expression?A mathematical expression is a mathematical statement that has two different numbers (known or unknown) and at least one operation.
For instance, an equation is a mathematical equation showing that two variables are equal.
Data and Calculations:The payment for a subway pass = $55
The number of subway rides = 5
The total amount deducted from the value of the pass = $40
This implies that each subway ride costs = $8 ($40/5)
If T is the cost of a ticket and the total cost incurred for 5 subway rides is $40, therefore T = 40/5.
Thus, the mathematical expression that represents this scenario is T = 40/5.
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Over the next four days, Amanda plans to drive 160 miles, 235 miles, 185 miles, and 220 miles. If her car gets an average of 32 miles per gallon of gas, how many gallons of gas should she expect to use in all?
F. 25
G. 30
H. 35
J. 40
The correct option is F. 25.
The total number of gallons of gas Amanda will use to travel all the distances is 25.
What is defined as distance?The amount of between two things, or the state of being far apart, is defined as distance. A five-foot distance between two tables is an example of distance. The difference of the two sides of an issue is an example of distance.
Now, as per the given question;
Amanda plans to drive 160 miles, 235 miles, 185 miles, and 220 miles.
Thus, the total distance ravelled by Amanada is;
= 160 miles + 235 miles + 185 miles + 220 miles
= 800 miles
Amanada's car has the average of 32 miles per gallon of gas.
Thus, the car will cover a total of 32 miles for each gallon of gas.
Thus,
The number of gallon of gas requires = Total distance/(distance travelled for one gallon of gas)
The number of gallon of gas requires = 800/32
The number of gallon of gas requires = 25
Therefore, the gas required to travel a total distance of 800 miles is 25 gallons.
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0.1 = -10c
please help !
Answer: c=-0.01
Step-by-step explanation:
Can someone please help me I don’t understand and it’s a really important homework
Answer:
The large box weighs 18.75 and the small box weights 15.75
Step-by-step explanation:
We are looking to find 2 variables so we will need two equations.
Let l = the large box weight
Let s = the small box weight
7l + 9s + 273 5l +3s = 141
I want to add these two equations together and have one of the variables be eliminated. The way both equations are written now, neither variable will drop out. I see that 9 is a multiple of 3. If I multiply the second equation all the way through by - 3, the s variable will be eliminated.
-3(5l +3s) -3(141) Multiple everything by -3
-15l -9s = -423 Now I will add this to the original equation 7l + 9s = 273
7l + 9s = 273
-8l = -150 Divide both sides by -8
l = 18.75 This is the weight of the large box.
Plug in 18.75 to either of the ordinal equations to find the weight of the small box.
5l + 3s = 141
5(18.75) + 3s = 141 Distribute the 5
93.75 + 3s = 141 Subtract 93.75 from both sides
3s = 47.25 Divide both sides by 3
s = 15.75
Check:
Plug in 15.75 for s and 18.75 for l into both of the original equation to see if they equal.
7l + 9s = 273
7(18.75) + 9(15.75) =273
131.25 + 141.75 = 273 Checks
5l + 3s = 141
5(18.75) + 3(15.75) = 141
93.75 + 47.25 = 141
141 = 141 Checks
find the values of C for which C(x+2)—(x+2)(x–2)=0 has just one solution. please help me ASAP
==================================================
Work Shown:
C(x+2) - (x+2)(x-2) = 0
(x+2)(C-(x-2)) = 0
(x+2)(C-x+2) = 0
x+2 = 0 or C-x+2 = 0
x = -2 or x = C+2
If we want one solution only, then we must make C+2 = -2 which solves to C = -4
If C = -4, then x = C+2 = -4+2 = -2 which matches with the first solution mentioned. If C is anything else but -4, then we'd have two different solutions (eg: C = 10 leads to x = C+2 = 12 as the other solution)
The height of a triangle is three feet less than its base. If the area of the triangle is 275 square feet, find its base and height.
The base and height of triangle are 25 and 22 feet.
We are given the relation between base and height of triangle. Let us represent height with h and base with b. The equation relating the two quantities is as follows -
h = b - 3
Now, the area of triangle is given by the formula -
Area = 1/2 × base × height
Keep the values in formula to find the base of triangle
275 = 1/2 × b × (b-3)
550 = b × (b-3)
b² - 3b - 550 = 0
b² + 22b - 25b - 550 = 0
b (b + 22) -25 (b + 22) = 0
(b + 22) (b - 25) = 0
b = -22 and 25
As the value of base can not be negative, so, the base of triangle is 25 feet.
Calculating height of triangle-
Height = Base - 3
Height = 25 - 3
Height = 22 feet
Hence, the base and height of triangle are 25 and 22 feet.
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Would like the answer and an explanation.
Answer:
Step-by-step explanation:
triangles are similar so:
[tex]\frac{10}{10+14} = \frac{x}{36}[/tex]
24x=360
x=15
