Find the missing term of each arithmetic sequence.14,..., 28, ...........
The missing terms of the given arithmetic sequence AP are 14, 21, 28, 35.
What exactly is arithmetic progression?An arithmetic progression (AP) is a sequence with the same distinctions between each successive term.
Each term (apart from the first) in an arithmetic progression is derived by adding a specific number to the term before the first one.For the initial term 'a' of an AP as well as the common difference 'd,' the very next arithmetic progression equations are frequently used to solve different AP problems.An AP's most common difference 'd': d = a2 - a1 = a3 - a2 = a4 - a3 =...... = a - an-1. nth term of an AP: an = a + (n - 1) dThe sum of an AP's n terms is: Sn = n/2(2a+(n-1)d) = n/2(a + l), where l is the AP's final term.Now, in response to the question;
The arithmetic sequence.14,..., 28, ............
There are total 4 terms in the series.
Let the initial term is 'a₁' is given as 14.
Let the second term is 'a₂'.
Let the third term be 'a₃' which is given as 28.
Ans, the let the fourth term is represented as 'a₄'.
As, we know that in the AP, the difference of the two consecutive terms is equal and called as common difference.
Thus,
d = a₂ - a₁ ........(equation 1)
d = a₃ - a₂ .......(equation 2)
Thus, equating the two equation;
a₂ - a₁ = a₃ - a₂
Substituting the values;
a₂ - 14 = 28 - a₂
Simplifying the equation;
2a₂ = 28 + 14
2a₂ = 42
a₂ = 21.
Put the obtained value in equation 1 and find d.
d = a₂ - a₁
d = 21 - 14
d = 7
Now, estimate a₄.
a₄ = a₃ + d
a₄ = 28 + 7
a₄ = 35
Therefore, the complete arithmetic sequence is 14, 21, 28, 35.
To know more about the arithmetic sequence, here
https://brainly.com/question/6561461
#SPJ4
Given the original statement "If a number is negative, the additive inverse is positive,” which are true? Select three options.
If p = a number is negative and q = the additive inverse is positive, the original statement is p → q.
If p = a number is negative and q = the additive inverse is positive, the inverse of the original statement is ~p → ~q.
If p = a number is negative and q = the additive inverse is positive, the converse of the original statement is ~q → ~p.
If q = a number is negative and p = the additive inverse is positive, the contrapositive of the original statement is ~p → ~q.
If q = a number is negative and p = the additive inverse is positive, the converse of the original statement is q →
The true statements are
If p = a number is negative and q = the additive inverse is positive, the original statement is p → q.If p = a number is negative and q = the additive inverse is positive, the inverse of the original statement is ~p → ~q.If q = a number is negative and p = the additive inverse is positive, the converse of the original statement is q → qHow to determine the true statement?The original statement is given as:
If a number is negative, the additive inverse is positive
This can be represented as
If p, then q
i.e. if p → q
So, (a) is correct
For the inverse, we simply negate the hypothesis and the conclusion
i.e. if ¬p → ¬q ----(b) is correct
For the converse, we simply switch the hypothesis and the conclusion
i.e. if q → p ----(e) is correct
Hence, the true statements are (a), (b) and (e)
Read more about conditional statements at:
https://brainly.com/question/4421013
#SPJ1
HELP PLEASEEEE
Jerald is having drain issues at his home and decides to call a plumber. The plumber charges $45 to come to his house and $50 for every hour they work. If the plumber charges Jerald a total of $250, how many hours did the plumber work?
Write and solve an equation to determine the number of hours worked by the plumber.
45x + 50 = 250; x = 4.4 hours
45x − 50 = 250; x = 6.7 hours
50x + 45 = 250; x = 4.1 hours
50x − 45 = 250; x = 5.9 hours
Answer: The answer would be D. I hope this is helpful :))
Can someone help me! I have turned this is twice already and I am still getting it wrong. Write the numbers in decreasing order. 1.¯3, − 8/5, √13, π, −0.7
I keep saying the correct answer is √13, π, - 8/5, 1.¯3, -0.7
HOW IS THIS WRONG?!
The answer in ascending order is -8/5, -0.7, 1.⁻3, [tex]\pi[/tex], [tex]\sqrt{13}[/tex]
What is ascending order?
Ascending order refers to the arrangement of numbers in ascending order, from least to greatest. We must first compare numbers before we may arrange them in any order. Count how many digits are in each number. The number with the fewest digits is the smallest.
The numbers arranged in ascending order are
-8/5, -0.7, 1.⁻3, [tex]\pi[/tex], [tex]\sqrt{13}[/tex]
To know more about ascending order arrangements, click on the link
https://brainly.com/question/20681445
#SPJ1
I NEED HELP WITH THIS MATH PROBLEM !!
An equation that relates T to N can be written as T = 750 + 560N.
What is an equation?An equation can be defined as a mathematical expression which shows that two (2) or more thing are equal.
What is a function?A function can be defined as a mathematical expression which can be used to define and represent the relationship that exist between two or more variables in a population (data set).
How to write an equation relating T to N.Since the total amount saved by using both plans (functions A and B) is represented by T, an equation that relates T to N can be written as follows:
T = A + B
Substituting the given parameters into the formula, we have;
T = (750 + 165N) + 395N
T = 750 + 165N + 395N
T = 750 + 560N.
Read more on function here: https://brainly.com/question/19537858
#SPJ1
Complete Question:
Ann and her husband are each starting a saving plan. Ann will initially set aside $750 and then add $165 every month to the savings. The amount A (in dollars) saved this way is given by the function A=750+165N , where N is the number of months he has been saving. Her husband will not set an initial amount aside but will add $395 to the savings every month. The amount B (in dollars) saved using this plan is given by the function B=395N. Let T be total amount (in dollars) saved using both plans combined. Write an equation relating T to N.
Simplify your answer as much as possible.
I need this answered please
y=mx+c, where m is slope. Here x=-2, x-intercept at (x,y)=(-2,0)
and there is no y intercept.
What is slope intercept form?y=mx+c, where m is slope.
The x-intercept is the value of x when y=0.
Since x=-2 for all values of y
it follows that x=-2 when y=0.
The y-intercept is the value of y when x=0 (or alternately the solution point of the form 90,y)). since x neq 0 not matter what value is assigned to y, no such point exists (graphically x=-2 is a vertical line parallel to, and therefore never intersecting, the Y-axis).
Therefore x-intercept at (x,y) is (-2,0) and there is no y intercept.
To learn more on Slope intercept form visit:
https://brainly.com/question/20786109
#SPJ1
HELPPPP PLEASE I GOT 5 mins before it’s dueee .
Answer:
Jajajjajjajj
Step-by-step explanation:
can someone help me im really stuck -57=y-2
Answer: y = -55
Step-by-step explanation:
-57 = y -2
-57 + 2 = y
-55 = y
(2x -1){2} = (x+1){2}
Answer:
X = 2
Step-by-step explanation:
4x-2 = 2x+2 multiply the brackets on both sides
4x-2x = 2+2 bring thes x's to one side & the constants to another side
2x = 4 simplify
X = 4÷2 divide
x = 2
A quadrilateral has a perimeter of 12 and all of the side lengths are odd integers. What is the probability that the quadrilateral is a rhombus?
A quadrilateral has a perimeter of 12 and all of the side lengths are odd integer then the probability that the quadrilateral is a rhombus is 1/4.
What is perimeter ?If the midpoints of a rhombus with 12-inch sides are connected, a quadrilateral is created. A square with a 12-inch diagonal would be the quadrilateral that is constructed.
A perimeter is a closed path that encloses, surrounds, or delimits a one-dimensional length, a two-dimensional shape, or both. The circumference of a circle or an ellipse is its perimeter. There are numerous practical uses for calculating the perimeter.
All four side lengths must be added up in order to determine the perimeter, or the distance around the rectangle. Since there are two of each side length, it is simple to multiply the total of the length and the breadth by two in order to accomplish this task efficiently.
To learn more about perimeter from the given link:
brainly.com/question/6465134
#SPJ4
-9(1 - 10n) -2(3n + 9)
Answer:
[tex]84n-27[/tex]
Step-by-step explanation:
[tex]-9(1-10n) -2(3n+9)[/tex]
[tex]-9+90n-6n-18[/tex]
[tex]{84n-27}[/tex]
Given that the zeros of a quadratic function are -2 and 8, what is the standard form of the quadratic function?
Using quadratic equation, The equation for given value of zeros is equation is x² - 6x - 16 = 0.
What is a quadratic equation?f(x) = ax2 + bx + c, where a, b, and c are integers and an is not equal to zero, is a quadratic function.
A parabola is the shape of a quadratic function's graph. Although the "width" or "steepness" of a parabola can vary as well as its direction of opening, they always have the same fundamental "U" form. The three graphs in the image below are all parabolas.
The following must be true if those are the 0s:
-2 + 2 = 0
8 - 8 = 0
We would thus get the following equation if we were to include them in a quadratic-based one:
(x + 2)(x - 8) = 0
x² - 8x + 2x - 16 = 0
FOIL
Roughly speaking, x² - 6x - 16 = 0
To learn more about quadratic equation from given link
https://brainly.com/question/1214333
#SPJ1
Answer:
f(x) = x2 − 6x − 16
Step-by-step explanation:
Write the zeros as solutions of two equations.
x = −2 x = 8
x + 2 = 0 x − 8 = 0 Rewrite each equation so that it equals 0.
Find the product of the two binomials.
(x + 2)(x − 8) = x2 − 8x + 2x − 16 Multiply.
= x2 − 6x − 16 Simplify.
Rewrite the equation in function notation.
f(x) = x2 − 6x − 16
Therefore, the quadratic function with zeros of −2 and 8 is f(x) = x2 − 6x − 16.
Identify all the correct names for the given angle.
The correct names for the given angle is ∠PHV.
What is termed as the angle?An angle is formed in geometry when two rays have been merged at their endpoints. These rays are known as the angle's sides or arms.The arms as well as the vertex are the two main components of an angle.The Angle's Arms: The arms of the angle are the two rays that meet at a center element to form the angle.The angle's vertex: A vertex is a main endpoint shared by both rays.How to name the any angle?
For naming any angle, the common vertex must come in the middle of the name.
But it could start with any of the end point.
Thus, the angle given can be named either ∠PHV or ∠VHP.
To know more about the angle, here
https://brainly.com/question/24775470
#SPJ9
The scale on a map is 1 : 25 000
How many kilometres on the ground is represented by 9 cm on the map?
2.25 kilometers on the ground is represented by 9cm on the map
According to the question, the scale on the map is in the ratio 1 : 25000
That is the length on the map = length of the ground
1cm = 25000 cm
1 cm = 25000/100000 km
1 cm = 0.25 km
Now we have to find the length of the ground in kilometres which is represented by 9cm on the map
That is we have to find the ratio, 9cm : x km
As from above, we know that,
1cm = 0.25 km
9 cm = 0.25*9 km
= 2.25 km
Hence 2.25 km on the ground is represented by 9 cm on the map
Learn more about ratio here : https://brainly.com/question/25927869
#SPJ9
What is the expression and value of "six less than nine times the sum of a number and eight" when n = 5? 9 (n 8) minus 6; when n = 5, the value is 111. 6 minus 9 (n 8); when n = 5, the value is 111. 9 (n) 8 minus 6; when n = 5, the value is 47. 6 minus 9 (n) 8; when n = 5, the value is 47.
The correct expression and value is A. 9(n+8)-6, when n=5, the value is 111.
Firstly forming the expression using given information, starting the end of sentence. Breaking sentence into parts as follows -
1. the sum of a number and eight
2. nine times the sum of a number and eight
3. six less than nine times the sum of a number and eight
Let the number be n.
So, equation according to 1. Sum = (n + 8)
Equation according to 2. 9(n + 8)
Equation according to 3. 9(n + 8) - 6
So, the expression is 9(n + 8) - 6
Now, keeping the value of n as 5 and finding the value of expression.
Value = 9(5 + 8 ) - 6
Firstly solving the bracket
Value = 9 × 13 - 6
Performing multiplication
Value = 117 - 6
Performing subtraction
Value = 111
Hence, the expression and value is A. 9(n+8)-6, when n=5, the value is 111
Learn more about solving expression -
brainly.com/question/29114
#SPJ4
The complete question is -
What is the expression and value of “six less than nine times the sum of a number and eight” when n = 5
A.9(n+8)-6, when n=5, the value is 111
B. 6-9(n+8), when n = 5, the value is 111
C. 9(n)+8-6, when n = 5 the value is 47
D.6-9(n), when n = 5, the value is 47
Answer:
The correct expression and value is A. 9(n+8)-6, when n=5, the value is 111.
Step-by-step explanation:
What does it mean to have a measure of center?
Answer:
It's a single number used to describe a set of numeric data.
Simplify:
PLEASE HELP
(3^2 x 3^3) 5
a
3^10
b
3^30
c
3^25
d
9^10
Answer:
1215
Step-by-step explanation:
What does the point (6,2) represent?
Find the geometric mean between each pair of numbers.
18 and 1.5
The geometric mean between the pair of numbers, 18 and 1.5, is 3√3.
Geometric mean, like arithmetic mean, is a kind of average and a measure of central tendency.
To solve for the geometric mean, we multiply the numbers together and then take a square root (for two numbers), cube root (for three numbers) etc. In other words, geometric mean is the nth root of the product of n values.
The formula for the geometric mean is given by:
GM = n√x1 x2 . . . xn
Solving for the geometric mean between 18 and 1.5 using the formula:
GM = n√x1 x2 . . . xn
where n = 2, x1 = 18, and x2 = 1.5
GM = √(18)(1.5)
GM = √27
GM = 3√3
To learn more about geometric mean: https://brainly.com/question/2292573
#SPJ4
Find each difference.
(5/2) - (13/4)
The difference is -3/4.
How to calculate the difference?Given,
(5/2) - (13/4)
Solution:
Taking L.C.M,
(5/2) - (13/4) = 10/4 - 13/4
= -3/4
The difference is -3/4.
To learn more about differences, refer
brainly.com/question/946189
#SPJ4
What is the value of f(−1) when f(x)= 2 x + 2?
if f(x)=2x+2
and f(x)= -1
2(-1) +2
-2 + 2 =0
the value would be 0
y varies directly with x . Explain your answer.If x is divided by 7 , what happens to y ?
The required value of y also gets divided by 7.
What is the constant of proportion?
A constant of proportion is illustrated as the ratio which relates two given quantities with each other in the relationship of proportion. Constant of proportion is also called constant variation, rate of change, and constant ratio.
Solving for the value of y
let k be the constant of proportion
When a quantity varies directly with other quantity, then we have a relation, y = kx
Now, find k for, some fixed value of x and y
Further, calculate y when x is divided by 7. In a general case, y will also be divided by 7 as both x and y varies directly.
Hence, the value of y also gets divided by 7.
To learn more about the constant of proportion, visit the link:
https://brainly.com/question/24868934
#SPJ4
transposition of formulae
n=p+cr for r
Answer:
r = (n - p)/c
Step-by-step explanation:
n = p + cr
Subtract p from both sides
n - p = p + cr - p
n - p = cr
Divide both sides by c.
(n - p)/c = cr/c
r = (n - p)/c
Austin runs a farm stand that sells raspberries and apples. Each pound of raspberries sells for $4 and each pound of apples sells for $1.50. Austin made $267.50 from selling a total of 95 pounds of raspberries and apples. Determine the number of pounds of raspberries sold and the number of pounds of apples sold.
Answer:
50 pounds of raspberries and 45 pounds of apples is sold
Solution:
Let "a" be the number of pounds of raspberries sold
Let "b" be the number of pounds of apples sold
Cost of each pound of raspberry = $ 4
Cost of each pound of apple = $ 1.50
Austin made $267.50 from selling a total of 95 pounds of raspberries and apples
Therefore,
a + b = 95
b = 95 - a ------ eqn 1
Austin made $267.50. Therefore,
number of pounds of raspberries sold x Cost of each pound of raspberry + number of pounds of apples sold x Cost of each pound of apple = 267.50
4a + 1.50b = 267.50 --------- eqn 2
Substitute eqn 2 in eqn 1
4a + 1.5(95 - a) = 267.50
4a + 142.5 - 1.5a = 267.50
2.5a = 125
a = 50
Substitute a = 50 in eqn 1
b = 95 - 50
b = 45
Thus 50 pounds of raspberries and 45 pounds of apples is sold
Step-by-step explanation:
hope it helps u
Find all points having an x-coordinate of 3 whose distance from the point (-1,-4) is 5
Answer: (3, -7) and (3, -1)
Step-by-step explanation:
Distance formula: a^2 + b^2 = c^2
c is the distance between different points which is 5 in this case
a=3-(-1)
a=3+1
a=4 ==> distance between x-coordinates
4^2+b^2=5^2
16+b^2=25
b^2=9
b=3
Distance from -4 and y-coordinate of a different point is equaled to 3.
How to express this in the form of an equation?
|-4-y|=3 ==> where y is the y-coordinate of a different point
-4-y=3
-4+4-y=3+4
-y=7
y=-7 ==> (3, -7)
-4-y=-3
-4+4-y=-3+4
-y=1
y=-1 ==> (3, -1)
(3, -7) and (3, -1)
Use log₅ 2 ≈ 0.43 and log₅7 ≈ 1.21 and the properties of logarithms to approximate log₅ √14 without using a calculator.
[tex]log_{5} \sqrt{14}[/tex] ≈ 0.82
The property of logarithms log ab = log a + log b , log a/b = log a - log b
[tex]log_{5} 2[/tex] ≈ 0.43
[tex]log_{5} 7[/tex] ≈ 1.21
We need to find,
[tex]log_{5} \sqrt{14}[/tex]
= 1/2[tex]log_{5} 14[/tex]
= 1/2[tex]log_{5} 2*7[/tex] ( log ab = log a + log b)
= 1/2 ([tex]log_{5} 2[/tex] + [tex]log_{5} 7[/tex])
=1/2( 0.43 + 1.21)
= 1/2 × 1.64
= 0.82
Hence logarithms of [tex]log_{5} \sqrt{14}[/tex] = 0.82
To know more about the logarithms refer to the link given below:
https://brainly.com/question/12049968
#SPJ4
Solve each equation. Check each solution. 1/3x =-2
Find a₁ for each arithmetic series.Evaluate S₁₀ for the series x+(x+y)+(x+2 y)+ . . . . .
The sum of the first 10 terms of the arithmetic series x+(x+y)+(x+2 y)+ . . . . . is S(10) = 10x+45y
The given arithmetic series:
x+(x+y)+(x+2 y)+ . . . . .
Notice that:
a(1) = x
a(2) = x+y
a(3) = x+2y
We can find the common difference:
d = a(2) - a(1)
= (x+y) - x = y
Recall the formula for the nth term of an arithmetic series:
a(n) = a(1) + (n - 1) . d
Substitute n = 10, a(1) = x, and d = y into the formula:
a(10) = x + (10 - 1)y
a(10) = x+9y
Use the sum formula:
S(n) = n/2 [a(1) + a(n)]
S(10) = 10/2 [x + (x+9y)]
S(10) = 5 .(2x+9y)
S(10) = 10x+45y
Learn more about arithmetic series here:
https://brainly.com/question/11994891
#SPJ4
The volume of a cylinder is 770cm³. It has a height of 5cm. Find its radius.
The radius of a cylinder having height of 5cm and volume 770 cm³ is 7 cm.
Volume of a cylinder is the space occupied by it in a three - dimensional space.
Volume of a cylinder is calculated using the formula:
[tex]V = \pi r^{2} h[/tex]
[tex]r = \sqrt{\frac{V}{\pi h} }[/tex]
where r is the radius of the base of the cylinder.
is a constant having value 3.14
h is the height of the cylinder. It is the perpendicular height from the base.
According to the given condition,
V = 770 cm³ and h = 5 cm.
Substituting these values in the equation above,
∴ r = 7 cm
To learn more about volume of a cone, refer to this link:
brainly.com/question/1984638
#SPJ4
A number is divided by 6 and then the quotient is added to 12.The result is 4.Find the number
Answer:
So the number is -48
Step-by-step explanation:
Lets say that the number is x
(x /6)+12=4
x/6=-8
x=-48
