Finding the value of any term in a given sequence is known as an arithmetic sequence if each term in the sequence is equidistant from the terms before and after. To find any term in a sequence, we first have to find the pattern of the sequence. Then we can multiply the distance between any two terms by one less than the number of terms we are looking for. Adding this to the first term gives you the term you want.
Here the first term a=2,
Common difference d=4-2=2
We know that,
f(n)=a+(n-1) d
f (10) =2+(10-1) (2)
=2+(18)
=20
We know that,
Sn=n2[2a+(n-1) d]
∴S10=102⋅ [2(2) +(10-1) (2)]
=5⋅ [4+(18)]
=5⋅ [22]
=110
Hence, the 10th term of the given series is 20, and the sum of the first 10th term is 110.
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WHAT DOES C=???
QUESTION BELOW
================================================
Work Shown:
M = number of miles
L = cost to rent a luxury car = 1.15M + 16.40
E = cost to rent an economy car = 0.80M+10.95
C = difference in price
C = L - E
C = (1.15M + 16.40) - (0.80M+10.95)
C = 1.15M + 16.40 - 0.80M-10.95
C = 0.35M + 5.45
Don't forget to distribute the negative to each term in the second parenthesis.
-------------------
Optional Section:
Let's say you drove M = 100 miles as an example.
The luxury car would cost L = 1.15M+16.40 = 1.15*100+16.40 = 131.40 dollars to rent.
The economy car would cost E = 0.80M+10.95 = 0.80*100+10.95 = 90.95 dollars to rent.
The difference in rental costs is L-E = 131.40-90.95 = 40.45 dollars.
Or you could say C = 0.35M+5.45 = 0.35*100+5.45 = 40.45
This means you pay $40.45 more if you go for a luxury car instead of an economy car.
Kevin is 6 years older than Timothy. 4 years ago, Kevin was twice as old as Timothy. Find their present ages.
Answer:
k=12
t=8
Step-by-step explanation:
two equations from the question
1 k=t+6
2 (k-4)=(t-4)×2
develop these
3. k-4=2t-8
4. 2 times first equation
2k=2t+12
subtract 4 from 3
-k-4=-20
k=16
sub back in
t=10
There are 130 people in a sport centre. 73 people use the gym. 62 people use the swimming pool. 58 people use the track. 22 people use the gym and the pool. 29 people use the pool and the track. 25 people use the gym and the track. 11 people use all three facilities. how many people use at least two facilities? check skip do not use a calculator get help report a mistake to hegartymaths on-screen keypad on off 789qwertyui
Using Venn diagram, out of the 130 people in the sport center, 54 people use at least two facilities.
Venn diagram is a diagram used to present the relationship between sets in a logical form. (See attached image)
Let n = number of people who use at least two facilities
A = people who use the gym = 73
B = people who use the swimming pool = 62
C = people who use the track = 58
A ∩ B = 22
B ∩ C = 29
A ∩ C = 25
A ∩ B ∩ C = 11
n = (A ∩ B - A ∩ B ∩ C) + (B ∩ C - A ∩ B ∩ C) + (A ∩ C - A ∩ B ∩ C) + A ∩ B ∩ C
n = (22 - 11) + (29 - 11) + (25 - 11) + 11
n = 11 + 18 + 14 + 11
number of people who use at least two facilities = 54
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What is the length of one leg of the triangle?
11 units
O 11√2 units
0 22 units
O 22√2 units
ww
Answer:
22
Step-by-step explanation:
45°
leg a = 1k
leg b = 1k
and leg c = hypotenuse = k * square root 2
k [tex]\sqrt{2}[/tex] = 22[tex]\sqrt{2}[/tex]
k = 22
-----------------------
leg a or b = k = 22
Evaluate the following expression. 8+[(84/12)-4]^2-7+3
Answer:
10 + 204 y
Step-by-step explanation:
Answer:
13.
Step-by-step explanation:
8+[(84/12)-4]^2-7+3
= 8 + (7 - 4)^2 - 7 + 3
= 8 + 3^2 - 7 + 3
= 8 + 9 - 7 + 3
= 17 - 7 + 3
= 10 + 3
= 13.
Find the magnitude and direction of the following vector.
-RS : R<-3,3> and S(-9,9)
The magnitude of the vector RS is found to be - 6√2.
The direction of the given vector RS is - Ф = 45° in the fourth quadrant clockwise
What exactly is a distance formula?The algebraic representation of the distances among two points based on their coordinates (in coordinate system). The Pythagorean theorem is used to calculate distances between points in 2- and 3-dimensional Euclidean space using rectangular coordinates.
Now, in response to the question;
The coordinates of points R and S are (-3,3) and (-9,9), respectively.
The distance formula is described as follows for the points R and S:
RS² = (x₂ - x₁)² + (y₂ - y₁)²
RS = √[(x₂ - x₁)² + (y₂ - y₁)²]
R and S's coordinates are-
(x₁,y₁) = (-3,3) and (x₂,y₂) = (-9,9).
Changing the values with in formula;
RS = √[(-9 + 3)² + (9 - 3)²]
RS = √[(-6)² + (6)²]
RS = √[36 + 36]
RS = 6√2 (magnitude of the vector RS)
Now, estimate the direction of the vector RS.
A vector's direction is described by the angle it makes with such a horizontal line.
To determine the direction of a vector, use one of the following equations:
tan Ф = Δy/Δx
Where, x = horizontal change
and, y = vertical change
tan Ф = (y₂ - y₁)/(x₂ - x₁)
= (-9 + 3)/(9 - 3)
tan Ф = -1
Ф = 45° angle of direction in the fourth quadrant clockwise.
As a result, the distance between coordinates R and s is observed to be 6√2, which is same as the magnitude of the given vector RS,
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By rounding to 1 significant figure, estimate
174.2 x 23.46
162.9 x 10.73
By rounding to 1 significant figure is 2.
What is significant figures ?Significant figures are the number of digits in a value, often a measurement, that contribute to the degree of accuracy of the value The first non-zero digit is where we start counting significant figures. The first non-zero digit of a number is considered the first significant figure when counting significant figures. The second digit is considered the second significant figure, and so on. The decimal point may be followed by a significant figure to the left or right of it.
Given: ([tex]\frac{(174.2 × 23.46)}{162.9 × 10.73}[/tex])
174.2 × 23.46 = 4086.732
162.9 × 10.73 = 1747.917
[tex]\frac{4086.732}{1747.917}[/tex] = 2.338 (approx)
= 2 ( rounding to 1 significant figure )
Hence the rounding to 1 significant figure is 2.
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Which inequality is equivalent to I x-4 I <9
(B) –9 < x – 4 < 9 inequality is equivalent to Ix-4I <9.
What is inequality?Inequality is a statement of an order relationship between two numbers or algebraic expressions (greater than, greater than, or equal to, less than, or less than or equal to). Inequality is defined as a difference in size, amount, quality, social position, or another factor. Inequality occurs when you have ten of something and someone else has none. (mathematics) A statement stating that one quantity is less than (greater than) another.So, Ix-4I <9:
|x-4|<9 ⇒ -9 < x-4 < 9-5 < x < 13Therefore, (B) –9 < x – 4 < 9 inequality is equivalent.
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The complete question is given below:
Which inequality is equivalent to I x-4 I <9?
A –9 > x – 4 < 9
B –9 < x – 4 < 9
C x – 4 < –9 or x – 4 < 9
D x – 4 > –9 or x – 4 < 9
What is the slope of the line determined by the equation 2 x+y=5 ?
A. -5/2
B. -2
C. -1
D. 2
E. 5/2
The slope of the line determined by the equation 2 x+y=5 is -2
What is a slope of an equation?A line's inclination or steepness can be determined using the slope formula. Finding the proportion of the change in the y-axis to the change in the x-axis allows it to be used to calculate the slope of any line.
The change in a line's "y" coordinate relative to its "x" coordinate is known as the line's slope.
The given equation = 2x + y = 5
It can be rewritten as: y = -2x + 5 (subtracted 2x from both the sides)
This is the slope-intercept form: y = mx + c
where m is the slope
If we check our equation, here m = -2
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C. what does it mean when an element is written inside a circle? at the intersection of two circles? outside the circles
D. do the elements written at the intersection of both circles from a subset of the two sets? Why?
Answer:
c ) it either shows diameter or radius
d) I am not sure
C. When elements are represented in a Venn diagram (using circles), the placement of elements inside or outside the circles indicates their relationship to the sets being represented.
D. Yes, the elements written at the intersection of both circles form a subset of the two sets.
C. Place an element inside a circle to indicate that it is a member of the set indicated by the circle.
An element that is positioned at the intersection of two circles denotes an element that is a part of both sets that are symbolized by those circles.
Outside the circles: In a Venn diagram, an element that is positioned outside every circle does not belong to any of the sets being represented.
D. This is so because these components are a part of the intersection of the two sets and as such, they are a part of both sets. In set theory, all of the components that are shared by two sets are contained in their intersection. Due to their simultaneous membership in both sets, the elements at the intersection are a subset of both sets.
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Find the sum of pair of vectors. < 13,-4 > + <-11,9>
The given statement states that the sum of two vectors is = (2 , 5).
What specifically is vector addition?Vector addition is the process of joining two or maybe more vectors to get a vector sum. The parallelogram law specifies the rules for adding and multiplying two or more vectors. When eigenvectors are aligned head to tail, this same vector total is calculated by drawing the same vector from the free tail to the free head.
According to the given data:Given two vectors are:
a =(13,-4 )
b = (-11,9)
The vector sum is,
M = [a1 + b1, a2 + b2]
= (Mx, My).
Substitution of the value we get:
M = (13 + (-11), (-4) + (9))
= (2 , 5)
The given statement states that the sum of two vectors is = (2 , 5).
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Find the slope of the line that passes through the two points. (1,3) and (4,9)
The slope passing through the two given two points (1,3) and (4,9) is 2.
What is meant by the slope of the line?The slope of a line is a measurement of its steepness and direction.
A line's slope is defined like a change in y coordinate with respect to a change in x coordinate.
The net y coordinate change is Δy, whereas the net x coordinate change is Δx. As a result, the change in y coordinate in relation to the change in x coordinate could be written as,m = Δy/Δx
where,m is the slope
Where, tan θ = Δy/Δx
This tanθ is also known as the line's slope.
A line's slope can be determined by calculating using two points just on straight line. We can use the slope of line formula with the coordinates of a two points.
Consider the coordinates of those 2 points,
P1 = (x₁, y₁)
P2 = (x₂, y₂)
Then slope will become;
Slope = m = tan θ = (y₂ - y₁)/(x₂ - x₁)
Now, as per the given question;
(x₁, y₁) = (1,3) and,
(x₂, y₂) = (4,9)
Substitute the values in the formula of the slope;
m = (9 - 3)/(4 - 1)
m = 6/3
m = 2.
Therefore, the slope of the line passing through the stated points is found to be 2.
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what value of X makes this equation true? -9x+15=3(2-x)
Answer:
3/2
Hope this helps <3
Answer:
Step-by-step explanation:
Equation
-9x+15=3(2-x) Remove the brackets.
Solution
-9x + 15 = 6 - 3x Add 9x to both sides
-9x+9x + 15 = 6 - 3x + 9x Combine
15 = 6 + 6x Subtract 6 from both sides
15 - 5 = 6 -6 + 6x Combine
10 = 6x Divide by 6
10/6 = 6x/6
Answer
x = 1 2/3 or 1.66666 ...
Which expression is equivalent to sum of quantity negative three and one third times n plus one sixth end quantity plus quantity one and three sixths times n minus three twelfths end quantity?
negative twenty nine sixths times n minus one twelfth
negative twenty nine sixths times n plus one twelfth
negative eleven sixths times n minus one twelfth
negative eleven sixths times n plus five twelfths
The equivalent expression is negative eleven sixths times n minus one twelfth. Option C
What are equivalent expressions?Equivalent expressions are simply defined as expressions that have same solution but differ in the arrangement of their variables, terms, constants and coefficients.
From the information given, we can represent the expression as;
{ - 3 1/ 3n + 1/ 6 } + { 1 3/ 6n - 3/ 12 }
Convert mixed fraction to improper fractions and expand the bracket
{ -10/3n + 1/ 6 } + { 9/6n - 3/ 12}
-10/3n + 1/ 6 + 9/6n - 3/ 12
Now, collect like terms
-10/3n + 9/ 6n + 1/ 6 - 3/ 12
Find the lowest common multiple
-20+ 9n/6 + 2 - 3 /12
-11n/ 6 - 1/ 12
Thus, the equivalent expression is negative eleven sixths times n minus one twelfth. Option C
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Answer:
C
Step-by-step explanation:
i had this and got it right
how do i solve this angle problem?
Answer:
x = 12
Step-by-step explanation:
NB. Supplementary angles / Angles of a straight line add up to 180°
180° - 124° (the given angle)
= 56°
This means that the other part of the angle must be equal to 56° ...in other words (4x + 8)° = 56°
(4x + 8)° = 56°
56° - 8°
= 48°
So 4x = 48°
-Divide both sides by 4 in order to get rid of the 4 infront of the x so that you're able to get x alone to solve.
4x ÷4 = 48° ÷4
x = 12
You can substitute 12 in the place of x to see if this is correct.
(4(12) +8)° = 56°
56° + 124° = 180°
....therefore x = 12
In one hour a machine can make
300 paper clips
or
360 springs.
At 1 pm the machine starts working.
It makes 450 paper clips and then changes to making springs.
How many springs will the machine make by 6 pm?
The amount of springs the machine will make by 6 pm is; 96 strings
How to solve Algebra Word problems?We are given that;
Amount of paper clips machine can make in an hour = 300 paper clips
Amount of strings the machine can make in an hour = 360 strings
Now, the machine starts working at 1pm and makes 450 paper clips.
Thus, time taken = 450/360 = 1.25 hours
This is at 2:15 pm
By 6pm, time taken would be 6:00 - 2:15 = 3:45 or 3.75 hours
Thus, number of springs made = 360/3.75 = 96 springs
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Answer:
1260 springs
SBS answer:
(pc = paper clips)
(s = springs)
300 pc = 1 hour
therfore
450 pc = 1.5 hours
1 pm + 1.5 hours will take us to 2:30 pm
2:30pm to 6:00pm will take 3.5 hours
360 c = 1 hour
so
1080 c = 3 hours
so
1260 = 3.5 hours
taking us to 6pm
Simplify each expression.
(9/-3) - 2
(9/-3) - 2
= (-3)(-2)
= -6
What is algebraic equation?
An algebraic equation or polynomial equation is an equation of the frame P=0 where P could be a polynomial with coefficients in a few fields, regularly the field of the rational numbers.
algebraic equation, a statement of the equality of two expressions defined by applying to a set of factors the algebraic operations, namely, expansion, subtraction, increase, division, raising to a control, and extraction of a root.
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Homework Yelp please
Answer:
I might be able to help. :))
Chemistry The time required for a certain chemical reaction is related to the amount of catalyst present during the reaction. The domain of the relation is the number of grains of catalyst, and the range is the number of seconds required for a fixed amount of the chemical to react. The table shows the data from several reactions.
a. Is the relation a function?
If the x values do repeat, quickly determine whether the y values match (y values are the second ones in the parenthesis). if, given the identical x values, the y values diverge.
What is a domain in math?
The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.The most crucial aspect of a function to keep in mind is that there is ONLY ONE Y value for EVERY X value.
The x values shouldn't repeat if you look at your set of points, according to this (x is the first value in the parenthesis).
If the x values do repeat, quickly determine whether the y values match (y values are the second ones in the parenthesis).
if, given the identical x values, the y values diverge.
Example: Because the second and third points both have the same x value (in this case 3, in this case), but different y values, (2,8)(3,5)(3,7)(5,8) is not a function (in this case 5 and 7).
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4 1/5 divided 2 3/5
7 1/2 divded 6 2/3
6 1/2 divded by 1/2
1 1/5 divded 1 2/5
1 2/3 divded 5
6 divded by 1 1/5
5 2/5 divded 1 1/5
HELP ME PLEASE THNX THNXIREFJJFOEEO
A fraction represents a part by whole.4 1/5 divided 2 3/5 is 21/13,7 1/2 divded 6 2/3 is 9/8,6 1/2 divded 1/2 is 13, 1 1/5 divded 1 2/5 is 6/7,1 2/3 divded 5 is 1/3,6 divded by 1 1/5 is 5,5 2/5 divded 1 1/5 is 27/6.
What is fraction?
A fraction represents a part by whole.
4 1/5 divided 2 3/5
=(21/5)/(13/5)=21/13
7 1/2 divded 6 2/3
=(15/2)/(20/3)=15/2*3/20=9/8
6 1/2 divded 1/2
=(13/2)/(1/2)=13
1 1/5 divded 1 2/5
=(6/5)/(7/5)
=6/7
1 2/3 divded 5
(5/3)/5/1
=5/3*1/5=5/15=1/3
6 divided by 1 1/5
6/(6/5)=6/1*5/6
=5
5 2/5 divded 1 1/5
=27/5/6/5
=27/6
Therefore 4 1/5 divided 2 3/5 is 21/13,7 1/2 divded 6 2/3 is 9/8,6 1/2 divded 1/2 is 13, 1 1/5 divded 1 2/5 is 6/7,1 2/3 divded 5 is 1/3,6 divded by 1 1/5 is 5,5 2/5 divded 1 1/5 is 27/6.
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Determine whether each list is a sequence or a series and finite or infinite. 4/3, 7/3, 10/3, 13/3,16/3, . . . . . .
From the list of numbers presented:
4/37/310/313/316/3we can determine that this is a infinite serie.
What are sequences?A sequence is an order of elements that are governed by a pattern, that is, it has variations between each element that remain constant and allow us to determine values before or after the known elements.
A sequence maintains an order, and this numerical order can be finite or infinite, in the given case we have the following list:
4/3, 7/3, 10/3, 13/3, 16/3
(4 + 3(x - 1))/3 = (4 + 3x - 3)/3 = (1 + 3x)/3(1 + 3*1)/3 = 4/3(1 + 3*2)/3 = 7/3(1 + 3*3)/3 = 10/3(1 + 3*4)/3 = 13/3(1 + 3*5)/3 = 16/3(1 + 3x)/3
In this series we have the initial value of the same, but we do not know the final value, although we know its behavior, we can say that this series has no end, it is an infinite serie.
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Solve y3 = −8.
please helpp
Answer:
-2
Step-by-step explanation:
Cube root of eight is 2
y= -2
does someone mind helping me with this? Thank you!
=======================================================
Work Shown:
A = area of the triangle on top, aka ceiling
A = 0.5*base*height = 0.5*6*8 = 24
B = area of the triangle on the bottom, aka floor
B = A = 24
C = area of the front rectangular face
C = length*width = 10*7 = 70
D = area of the face in back on the left
D = length*width = 6*7 = 42
E = area of the face in back on the right
E = length*width = 8*7 = 56
Total surface area = A+B+C+D+E = 24+24+70+42+56 = 216 square meters
------------------------
Alternative Method:
A = area of the triangle on top, aka ceiling
A = 0.5*base*height = 0.5*6*8 = 24
B = area of the triangle on the bottom, aka floor
B = A = 24
LA = lateral area = wall area
LA = (perimeter of the base)*(height)
LA = (6+8+10)*(7)
LA = 24*7
LA = 168
Total surface area = A+B+LA = 24+24+168 = 216 square meters
Draw ΔX Y Z and find the slope of each side of the triangle. Determine whether the triangle is a right triangle. Explain. X(0,0), Y(1, h), Z(2 h, 0)
A right-angled triangle is a triangle whose two adjacent sides form a right-angle triangle between them. The given triangle is a right-angled triangle.
What is a right-angle triangle?A right-angled triangle is a triangle whose two adjacent sides form a right-angle triangle between them.
The slope of the sides of the triangle can be written as,
The slope of XY = (2h - 0)/(2h - 0) = 1The slope of YZ = (0-2h)/(4h - 2h) = -2h/2h = -1The slope of XZ = (0 - 0)/(4h - 0) = undefined, therefore, the line will be horizontalThe given triangle is a right-angle triangle because the slope of the two lines is 1 and -1, whose product is -1. Therefore, the two lines are perpendicular to each other.
Hence, the given triangle is a right-angled triangle.
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Write an equation of the line with the given slope and y -intercept. Use slope-intercept form. Then rewrite the equation in standard form. m = -1/2, b=4
Equation of the line is y = mx + b , and the equation is x + 2y = 8
The equation of the line with the slope and y-intercept in the slope-intercept form is:
y = mx+b
Where m = slope of the line
b = y-intercept
x,y = variable
Now we have to find an equation of the line whose slope (m) is -1/2 and y-intercept(b) is 4.
From the equation we have:
y = (-1/2)x + 4
2y = -x + 8
x+2y = 8
Therefore the equation of the line is x + 2y =8 with slope m=-1/2 and y-intercept = 4.
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in the figure below, B is between A and C and C is between B and D. if BC=4, BD=12, and AD=15 and AC
For the given values, the value of line AC has a value of 7 units.
What kinds of lines are there?There are two subsets of lines: line segments with two end points and rays with one beginning point and an infinite length on the other side, each symbolized by an arrow.
A line with several segments is provided in accordance with the supplied figure.
Segment BC equals 4, Segment BD equals 12, Segment AD equals 15, and Segment AC must be located.
Since, AC = AB + BC.
(AD - BD) Plus BC Equals AC.
AC = ( 15 - 12 ) + 4.
AC = 3 + 4
AC = 7.
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Complete Question -
in the figure below, B is between A and C and C is between B and D. if BC=4, BD=12, and AD=15 and AC
f(x+h)-f(x)/h
compute the difference quotient of given function
(t)=(2t)(3-t)
The difference quotient of f(t) is: (6 - 2h - 4t)
And when h tends to zero is (6 - 4t)
How to get the difference quotient?
Here we have the function:
f(t) = (2t)(3 - t)
Expanding the function we get:
f(t) = 6t - 2t^2
Now we want to get the difference quotient, which is:
(f(t+h) - f(t))/h
Replacing our function there, we will get:
( 6*(t + h) - 2*(t + h)^2 - 6*t + 2*t^2)/h
Now we can simplify the numerator to get:
(6*t + 6*h - 2t^2 - 2h^2 - 4*t*h - 6t + 2t^2)/h
(6h - 2h^2 - 4th)/h
Now divide by h so we get:
(6 - 2h - 4t)
Now, remember that in the difference quotient we need to take the limit when h tends to zero, in that limit we will get:
(6 - 4t)
That is the difference quotient of the function f(t).
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if 0 < x < 90 degrees and sin sin x = 5/13, what is tan x?
Step-by-step explanation:
If cos x = 5/13 and x is between 0 and 90 degrees, since we know that tan2x = sin2x/cos2x = (2 sinxcosx)/(cos^2x - sin^2x) and we are dealing with a 5-12-13 right triangle,
tan (2x) = 2(12/13)(5/13)/((5/13)^2 - (12/13)^2) = (2*12*5/13^2) / (25/13^2) - (144/13^2)= 120/(-119)= -1.008403
need help solving please
Answer: a=√3 b=√6
Step-by-step explanation:
We have a right-angled isosceles triangle
Hence, a=√3
According to the sine theorem :
[tex]\displaystyle\\\frac{b}{sin90^0} =\frac{a}{sin45^0} \\\\\frac{b}{1} =\frac{\sqrt{3} }{\frac{\sqrt{2} }{2} } \\\\b=\frac{2\sqrt{3} }{\sqrt{2} } \\\\b=\frac{2\sqrt{3}(\sqrt{2)} }{\sqrt{2} (\sqrt{2}) } \\\\b=\frac{2\sqrt{6} }{2} \\\\b=\sqrt{6}[/tex]
On the Math SAT, men have a distinct edge. In 2005, for instance, the men averaged about 538, and the women averaged about 504. You may assume (i) the histograms followed the normal curve, and (ii) both SDs were about 120. Estimate the percentage of men getting over 700 on this test in 2005.
The percentage of men getting over 700 on this test in 2005 is 8.85%.
How to calculate the value?It should be noted that based on the information illustrated, the percentage will be calculated thus:
= P(X - 538/120) > (700 - 538/120)
= P(Z > 1.35)
= 1 - P(Z <= 1.35)
Using normal table
= 1 - 0.9115
= 0.0885
Therefore, the percentage of men getting over 700 on this test in 2005 is 8.85%.
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