The arithmetic sequence AP's 32nd term is calculated to be 225.
What is the definition of an AP arithmetic sequence?An arithmetic progression (AP) in mathematics is a list and maybe sequence of numbers with each term is obtained by adding a sequence to the term before it.
With the exception of arithmetic progression, the fixed number is denoted by the letter 'd.'Common difference => d = a2 - a1 = a3 - a2 = a4 - a3 =...... = a - an-1.nth term of an AP: an = a + (n - 1) dThe sum of n terms of an AP's => Sn = n/2(2a+(n-1)d) = n/2(a + l), where l = last term of the AP.Finally, the solution to the question is as follows:
The numbers in the displayed sequence are as follows:
101,105,109,113, ...........
We must explore the 32nd number in the series because it contains 32 terms.
The common difference with both two consecutive terms of an AP which are equal is denoted by 'd.'
Let's assume the first term is'a₁' = 101.
Let's assume 'a₂' = 105 is the second term.
Let's assume the third term is 'a₃' = 109
Substitute the values the preceding equation; the 32nd term is-
d = a₂ - a₁
Obtain the common difference;
d = 105 - 101
d = 4
Put the values in the preceding formula; the 32nd term is
The formula finds the nth term equation;
nth term of an AP: an = a + (n - 1) dTotal number of terms is; n = 32Initial term is a = 101Common difference d = 4Put the given values in nth term formula;
a₃₂ = a + (n - 1) d
a₃₂ = 101 + (32 - 1)(4)
a₃₂ = 101 + 128 - 4
a₃₂ = 225
Thus, the 32nd term value of the arithmetic sequence is calculated to be 225.
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Seeta did a puzzle in 3 minutes 45 seconds.
Ninal did the same puzzle in 7 minutes 28 seconds.
Seeta says,
'I did the puzzle in less than half the time Ninal did the puzzle.
(b) Is Seeta right?
You must show all your working.
Yes, Seeta is right a takes puzzle in 3 minutes 45 seconds time
3 x 60 = 180 + 45 = 225 seconds.
Seeta's time. 7 x 60 = 420 + 28 = 448 seconds. Nina's time.
if you times the 448 by 2 it =224.
Yes, Seeta is right.
Time is the ongoing progression of existence and things that happen in what seems to be an irrevocable order from the past, present, and forward into the longer term.
Time is a quantity that is a part of several measurements that are used to compare the length of events or the gaps between them, to match how long they last, to order events, and to live how quickly things change in the real world or in our conscious experience. together with the three spatial dimensions, time is usually referred to as a fourth dimension.
Time has long been an important topic of study in philosophy, theology, and science, but scholars haven't been able to define it in a way that is applicable to all of these disciplines without becoming circular. Nevertheless, numerous industries and business domains.
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In the figure below, =m∠JKM 98°, =m∠LKM 70°, and KN bisects ∠LKM. Find m∠JKN.
In the given question angle ∠JKN is 63°.
What are angles?An angle is a figure in Plane Geometry formed by two rays or lines that share a common endpoint. "Angle" comes from the Latin word "angulus," which means "corner." The two rays are referred to as the sides of an angle, and the common endpoint is referred to as the vertex.So,
Since KN bisects ∠LKM which is 70°.
Then, ∠NKM will automatically be 35°.Now, we know that: (refer to the diagram below)
∠JKN = ∠JKM - ∠NKM∠JKN = 98° - 35°∠JKN = 63°Therefore, in the given question angle ∠JKN is 63°.
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Karen is planning a graduation party for the senior class. She plans to rent a meeting room at the convention center that costs 400 . There is an additional fee of 5.50 for each person who attends the party.
c. There are 285 people in Karen's class. If 2/3 of these people attend, how much will the party cost?
The party costs a total of 1445.
Given,
The rent of meeting room at the convention center = 400
Additional fee for each person attends the party = 5.50
Number of people in Karen’s class = 285
The number of people attended the graduation party:
2/3 of 285
= (2/3)285
= 95 x 2
= 190
Therefore the additional fee collected from 190 people,
190 x 5.50 = 1045
Now the total cost of the party = rent of room + total additional fees
= 400 + 1045
= 1445
That is, the party costs a total of 1445.
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An equilateral triangle has
sides of 4x + 10. Write an
expression for the perimeter of
the triangle.
Determine the value of x when the perimeter is 42.
Answer:
x = 1 if the perimeter is 42
Step-by-step explanation:
Given
s = 4x + 10
when Perimeter = 42, what is x?
Solution
Perimeter = 3s
Perimeter = 3(4x +10) Remove the brackets
Perimeter = 12x + 30
Let the Perimeter = 42
42 = 12x + 30 Subtract 30 from both sides
42-30 = 12x + 30-30 Combine
12 = 12x Divide by 12
12/12 = 12x/12
x = 1
Use the graphs of f and g to graph h(x)=(f+g)(x). I need help with #4.
Answer:
My teacher helped
Step-by-step explanation:
Which graph shows a set of ordered pairs that represent a function?
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The second graph shows a set of ordered pairs that represent a function.
What is function?Functions are an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
here, we have,
A relation is a function in which every x value will have different y values, this represents "every input will have unique output" part of the definition of the function,
When we observe the graphs (attached), we will notice in graph 1) there are two ordered pairs with same x value and different y values, (2, -1) and (2, -3), which is making them out of the list of being a function,
In graph 2) we have, (-2, 2), (1, 1), (5, 4), (-4, -4), (2, -5) and (4, -3), in this all the order pairs have different x-y values, therefore, this set of ordered pairs that represent a function.
Hence, the second graph shows a set of ordered pairs that represent a function.
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The question do not have graph, so, the question is solved for the graph attached.
An athlete preparing for a marathon runs 21.3miles .how many kilometers did they run?
An athlete preparing for a marathon runs 21.3 miles then the athlete will run 34.27903 kilometer.
What is kilometer?The kilometer (spelled kilometer in American English) is just a metric unit of length equivalent to one thousand meters.
Since there are 1.6 kilometers in a mile, multiply the number of miles by 1.6 to convert them to kilometers. Because 20 × 1.6 = 32 kilometers, 20 miles is equivalent to 32 kilometers. The more precise method would yield a conversion of 20 miles to kilometers of 32.1868.
Conversion of mile into kilometer.
It is known that, 1 mile = 1.60 kilometer.
Then, 21.3 mile = 1.60 × 21.3 = 34.08 kilometer.
An athlete training for a marathon will cover 34.27903 kilometers if they run 21.3 miles.
Therefore, the athlete will run 34.27903 kilometer.
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Solve for x.
33 ÷ x = 3
Will mark brainlest
=================================
[tex]\\[/tex]
[tex]33\div x=3\\[/tex]
multiplying both sides by x
[tex]33=3x\\3x=33[/tex]
dividing by 3 both sides
[tex]x=11[/tex] {SOLUTION}===================================
#Carryonlearning
[tex]\textcopyright ELIZA[/tex]
Answer:
x = 11
Step-by-step explanation:
33/x = 3
33 = 3x
x = 33/3
x = 11
Hope it helps!!!
By first rounding each number to 1 significant figure, estimate the answer to 527 +389
Answer:
900
Step-by-step explanation:
527 to 1sf is 500
389 to 1sf is 400
400+500=900
Answer:
900
Step-by-step explanation:
527 to 500
389 to 400
500+400=900
What is the probability of drawing a red marble?
Answer:
[tex] \sf \: \frac{1}{4} [/tex]
Step-by-step explanation:
since the total of red marbles is 5 and the total of all the colours of marble is 20
therefore we write it like this;
[tex] \sf \frac{Total \: of \: red \: marbles}{Total \: of \: all \: the \: marbles}[/tex]
[tex] \rightarrow \sf \: \frac{5}{20} = \frac{1}{4}[/tex]
=
A
C
F
xº
E
G
80°
160°
D
B
The value of angle ∠AEF or ∠x is 80°.
What are angles?When two straight lines or rays intersect at a common endpoint, an angle is formed. An angle's vertex is the common point of contact. The term angle is derived from the Latin word angulus, which means "corner." The basic angles are Acute angle, Obtuse angle, Right angle, Straight angle, reflex angle, and full rotation.So,
∠CEB is 160° with EG being an angle bisector leaving ∠CEG = 80° and ∠BEG = 80°FEG is a straight line with ∠FEG being 180°.∠FED + ∠DEB + ∠BEG = ∠FEG80° + ∠DEB + 80° = 180°160° + ∠DEB = 180°∠DEB = 180° - 160°∠DEB = 20°Then,
∠AEC = 20° = ∠DEB (Inversely opposite angles)Now,
FEG is a straight line with ∠FEG being 180°.∠CEG + ∠AEC + ∠AEF = ∠FEG80° + 20° + ∠AEF = 180°100° + x = 180°x = 180° - 100°x = 80°∠AEF = 80°Therefore, the value of angle ∠AEF or ∠x is 80°.
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Write in simplest form.
x³ = 686
Due today
Answer:
[tex]x = 7 \sqrt[3]{2} [/tex]
What can we use to represent repeated multiplication
Answer:
This expression can be written in a shorter way using something called exponents. An expression that represents repeated multiplication of the same factor is called a power.
Answer:
Step-by-step explanation:
This formula can be written shorter using so-called exponents. Expressions representing repeated multiplications of the same factor are called exponentiations. 5 is called the base and 2 is called the exponent.
If a student picked is 10 years old, what
are the chances that they skip breakfast?
Answer:
There are 29% chance that they will skip their breakfast
Step-by-step explanation:
40 / 14 x 10 = the percentage of the kid skipping his breakfast
40 / 14 x 10 = 28.5%
28.5 = (rounded off) = 29%
The kid has a 29% chance of skipping the breakfast
Write an equation of the line through the pair of points in slope-intercept form. (Lesson 3-4 )
(-1,8) and (5,-4)
y = -2x + 6 is the equation of the line in slope-intercept form passing through points (-1 , 8) and (5 , -4).
An equation of a line in slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept.
Given two points passed through by the line, you can use them to write the equation of the line in slope-intercept form.
1. Find the slope of the line using the two given points.
let Point 1(-1 , 8) and Point 2(5 , -4)
slope = m = (y2 - y1) / (x2 -x1)
m = (-4 - 8) / (5 - -1)
m = -12 / 6
m = -2
2. Use the value of the slope and one of the points to find the value of the y-intercept, b. Plug in these values in the formula for slope-intercept form.
y = mx+ b
y = -2x + b
Using Point 1,
8 = -2(-1) + b
8 = 2 + b
b = 6
3. Write the equation of the line in slope-intercept form.
y = mx+ b
where m = -2 and b = 6
y = -2x + 6
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Which of the following domain restrictions would allow the inverse of f(x) = (x + 4)^2 - 1 graphed below to also be a function? Select the THREE (3) that apply!
The domain restrictions that would allow the inverse of f(x) to also be a function are given as follows:
x ≤ -4.x ≥ 1.x > -3.When does a graph represents an one to one function?The function is one to one if there are no horizontally aligned points, that is, each value of y is also related to only one value of x. A function will have an inverse in the part of the domain of the function that is one to one.
For this problem, the relation is symmetric at x = -4, hence the domains x <= -4 and x >= -4 must not intersect for the inverse to be a function, and the restrictions are given by:
x ≤ -4. (no horizontally aligned points considering only x ≤ -4).x ≥ 1. (same).x > -3(same).More can be learned about one to one functions at brainly.com/question/10853542
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Simplify the expression. (7)³- ((7)4)² = (7)
Step-by-step explanation:
7³−((7)(4))² =7
−441≠7
False
Determine whether each series is arithmetic or geometric. Then evaluate the finite series for the specified term number. 5000+1000+200+. . . . . . ; n=5
The given series is geometric series. The sum of its first 5 terms is 6248.
To determine whether the series is an arithmetic or geometric one, we need to check how the consecutive terms relate to each other.
If it is an arithmetic series, then:
a(n) = a(n-1) + d
where d is the common difference.
If it is a geometric series, then:
a(n) = a(n-1) . r
where r is the common ratio.
The given series is:
5000 + 1000 + 200 +. . . .
and the number of terms is 5.
In the given series:
a(1) = 5000
a(2) = 1000
a(3) = 200
Notice that
a(2)/a(1) = 1000/5000 = 0.2
a(3)/a(2) = 200/1000 = 0.2
Since the ratio of consecutive terms are constant, then the given series is a geometric series. Furthermore, its ratio, r = 0.2
Sum formula for the first n term of a geometric series is:
S(n) = a(1) . (1 - rⁿ)/(1 -r)
Substitute n = 5, a(1) = 5000, and r = 0.2
S(5) = 5000 . (1 - (0.2)⁵)/(1 - 0.2)
S(5) = 5000. (0.99968) / 0.8
= 6248
Since the number of terms is not much we can also evaluate the sum directly. Write all the terms until n = 5.
a(4) = 200 . (0.2) = 40
a(5) = 40 . (0.2) = 8
Hence, the series is:
5000+1000+200+40+8 = 6248.
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What is 50+50 and explain how you got the anwer
Answer:
50+50=100
How I got answer there are two 50 so if I multiply 50×2 I will get 100
and answer will come
Answer:
100
Step-by-step explanation:
Columnar addition
50
+50
____
100
Expand and simplify (2x+5) (2x-5) (3x+7)
Answer:
yall i tried
Step-by-step explanation:
bring it to the formula first then gotta multiply
Write the function rule for each function reflected in the given axis.
f(x)=4+x ; x -axis
Functions can be reflected on the x-axis, the y-axis, or both axes. For example, function reflection y= f(x) can be written as y= -f(x) or y= f(-x) even y= -f(-x). There are four types of function or graph transformations: reflection, rotation, translation, and dilation. In mathematics, especially geometry, mirror or mirroring means flipping, so basically, the mirroring of a function is the mirror image of a given function or graph. Hence the reflection function is commonly known as the reflection function.
The reflection of the given function should be similar in size and shape to the original function.
f(x)=4+x; x -axis
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Determine whether the quadrilateral can always, sometimes, or never be inscribed in a circle. Explain your reasoning.kite
A pair of opposite angles is supplementary, a quadrilateral ABCD can be inscribed in a circle.
What can be inscribed in a circle?
Every circle has an inscribed triangle with any three given angle measurements (summing to 180°, of course), and every triangle can be inscribed in any circle (which is called its circumscribed circle or circumcircle). Every triangle has an incircle, which is a circle that has been inscribed.
A cyclic quadrilateral is one that can be encircled by a circle. If and only if a pair of opposite angles is supplementary, a quadrilateral ABCD can be inscribed in a circle. Because the sum of all the angles is 360 degrees, it is true that one pair of supplementary angles is supplementary if and only if both pairs are supplementary.
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What is the mean of the temperatures shown
on the map below? Give your answer in °C.
-7
-1
-4
0
2
Temperatures given in °C
Answer:
the mean is -2 degrees celsius
Step-by-step explanation:
-7 + -1 + -4 + 0 + 2 = -10
-10 / 5 = -2
LCM of 21, 56
I really need help it’s due today
Answer: the answer is 168
In this problem, you will investigate the relationships among three points of concurrency in a triangle.
c. Draw a right triangle and find the circumcenter, centroid, and orthocenter.
Construct the centroid (medians), circumcenter (perpendicular bisectors), and orthocenter of a right triangle (altitudes).
What points of concurrency are always inside the triangle?The three angle bisectors of a triangle are concurrent in a point equidistant from its sides. The incenter of a triangle is the point at which the triangle's angle bisectors intersect. The incenter is always inside the triangle.
The point where the three perpendicular bisectors meet is the circumcenter of a triangle. It is the circumcenter of the circle encircling the triangle, equidistant from the triangle's three vertices.
The incenter exists crucial for angle bisectors; the orthocenter is important for perpendicular bisectors; the circumcenter is important for altitudes; and the centroid is important for medians.
Construct a right triangle's centroid (medians), circumcenter (perpendicular bisectors), and orthocenter (altitudes).
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PQ is a building of height 70 m. The angle of depression of a car R from the top is 40 degrees. The distance between R nd Q is?
Given the height of building PQ and the angle of depression of a car R from the top of the building, the distance between R nd Q is approximately 58.7 meters.
What is the distance between R nd Q?Given the data in the question;
PQ is a building of height 70 mThe angle of depression of a car R from the top is 40 degrees Distance between R nd Q = ?This forms a right triangle as drawn in the image below and to determine the distance between R and Q,
We use one of the six function of angle used in trigonometry.
tanθ = Adjacent / Opposite
We plug in the values from the diagram and solve for RQ.
tanθ = Adjacent / Opposite
tan( 40° ) = RQ/70m
RQ = tan( 40° ) × 70m
RQ = 0.83909963 × 70m
RQ = 58.7m
Given the height of building PQ and the angle of depression of a car R from the top of the building, the distance between R nd Q is approximately 58.7 meters.
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Enlarge the triangle by scale factor - with centre (-1,2).
YA
5
4
43WA
2
1
OT N 345
-5-4-3-2-1 1 2 3 4 5 x
-2
-3
-4
-5
Extend the triangle's size by -1/3 with the center point (-1,2).
The triangle's vertices of new location point are (-2,1),(0,1) and (-3,4).
The triangle's vertices' coordinates are not specified. Assume that the triangle's vertices are located at points A(2, 5), B(-4, 5) and C. (5, -4).
A point is transformed when it is moved from its original location to a new one. Reflection, rotation, translation, and dilation are examples of Dilation is the growth or contraction of an object's size. A point A(x, y) is displaced from a point (a, b) by a factor k as follows:
[tex]A^{'}= (k(x-a)+a,k(y-b)+b)[/tex]
Where, (a,b)=(-1,2) and k=[tex]\frac{-1}{3}[/tex].
The triangle's vertices are located at points A(2, 5), B(-4, 5), and C. (5, -4). The new address is:
[tex]A^{'}= (\frac{-1}{3} (2-(-1))-1,\frac{-1}{3}(5-2)+2)=(-2,1)\\B^{'}= (\frac{-1}{3} (-4-(-1))-1,\frac{-1}{3}(5-2)+2)=(0,1)\\C^{'}= (\frac{-1}{3} (5-(-1))-1,\frac{-1}{3}(-4-2)+2)=(-3,4).[/tex]
Therefore, The triangle's vertices of new location points are (-2,1),(0,1) and (-3,4).
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Of the 240 seniors at Central High School, 194 attended
the prom. How many seniors at Central High School, to
the nearest percent, did NOT attend the prom?
5 more than one eighth of a number equals 13
Answer:
Step-by-step explanation:
Ten more than x x + 10
A number added to 5 5 + x
A number increased by 13 x + 13
5 less than 10 10 - 5
A number decreased by 7 x - 7
Difference between x and 3 x - 3
Difference between 3 and x 3 - x
Twice a number 2x
Ten percent of x 0.10x
Ten times x 10x
Quotient of x and 3 x/3
Quotient of 3 and x 3/x
Five is three more than a
number
5 = x + 3
The product of 2 times a
number is 10
2x = 10
One half a number is 10 x/2 = 10
Five times the sum of x and 2 5(x + 2)
Seven is greater than x 7 > x
Five times the difference of a
number and 4
5(x - 4)
Ten subtracted from 10 times a
number is
that number plus 5
10x - 10 = x
+ 5
The sum of 5x and 10 is equal
to the product of x and 15
5x + 10 =
15x
The sum of two consecutive
integers
(x) + (x + 1)
The sum of two consecutive
even integers
(x) + (x + 2)
The sum of two consecutive odd
integers
(x) + (x + 2)
Answer:
x=64
Step-by-step explanation:
5+(1/8)x=13
Subtract 5 to both sides to get (1/8)x=8
Multiply by the reciprocal of 1/8 (8) on both sides. The 1/8 and 8 cancel and the answer should be x=64
Use the table below to complete the following statements.
The value of m • n (8) is
The value of n • m (-4) is
Answer:
Step-by-step explanation:
