The first five terms of the sequence an =5 n-3 are 2, 7, 12, 17 and 22.
According to the question.
We have a formula or a rule for finding the terms of a sequence i.e.
an = 5n -3.
The first term of the sequnence an = 5n - 3 is given by
a(1) = 5(1) -3 = 5 -3 = 2
The second term of the sequence an = 5n - 3 is given by
a(2) = 5(2) - 3 = 10 - 3 = 7
The third term of the sequence an = 5n -3 is given by
a(3) = 5(3) - 3 = 15 - 3 = 12
The fourth term of the sequence an = 5n - 3 is given by
a(4) = 5(4) - 3 = 20 - 3 = 17
The fifth term of the sequence an = 5n - 3 is given by
a(5) = 5(5) - 3 = 25 - 3 = 22
Hence, the first five terms of the sequence an =5 n-3 are 2, 7, 12, 17 and 22.
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The radius of the circle is 5 centimeters line segment ab is a diameter of the circle what is the value of x to the nearest tenth
The value of x to the nearest tenth is 8.9 cm.
How to find the diameter of a circle?The radius of the circle is 5 centimetres. Line segment ab is a diameter of the circle.
The diameter of the circle is twice the length of the radius.
Hence, the value of x can be found as follows:
AB = 10 cm
Using Pythagoras theorem,
c² = a² + b²
where
c is the hypotenusea and b are the other legs.Therefore,
10² - 4.5² = x²
100 - 20.25 = x²
x² = 79.75
x = √79.75
x = 8.93028554975
x = 8.9
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Write in simplest form.
x³ = 686
Due today
Answer:
[tex]x = 7 \sqrt[3]{2} [/tex]
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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Points O, A, B lie on the same line. OA = 12 cm, OB = 9 cm. Find the distance between the midpoints of segments OA and OB if: Point O does not lie on the segment AB pls help ASAP with explnation
The distance between the midpoints of segments OA and OB is 1.5 cm.
Given that, points O, A, and B lie on the same line. OA = 12 cm, OB = 9 cm.
We need to find the distance between the midpoints of segments OA and OB.
What is the midpoint of the line segment?A midpoint of a line segment is the point on a segment that bisects the segment into two congruent segments. The midpoint of a line segment is the point on a segment that is at the same distance or halfway between the two ending points.
Let X be the midpoint of OA and Y be the midpoint of OB.
Now, the midpoint of OA is OX=AX=OA/2
=12/2=6 cm
Then, the midpoint of OB is OY=YB=OB/2
=9/2=4.5 cm
The distance = 6-4.5=1.5 cm
Therefore, the distance between the midpoints of segments OA and OB is 1.5 cm.
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HELPPP mathhhhhhh 20 pointsss
7^4.3^-6.y is equivalent to 7.7.7.7.y/3.3.3.3.3.3 which is option (B).
b^10/b^4 is b^6 and (p^2+p-8)-(-4p^2-p+3) is 5p^2+2p-5.
What is Equation?Two expressions with equal sign in between is called as equation.
4. 7^4.3^-6.y
In the given expression, 7 has 4 exponent and 3 has -6 exponent.
This can be written as 7.7.7.7.y/3.3.3.3.3.3.
5. b^10/b^4 is b^10-4=b^6.
6. (p^2+p-8)-(-4p^2-p+3)
=p^2+p-8+4p^2+p-3
=5p^2+2p-5.
Therefore 7^4.3^-6.y is equivalent to 7.7.7.7.y/3.3.3.3.3.3 which is option (B), b^10/b^4 is b^6 and (p^2+p-8)-(-4p^2-p+3) is 5p^2+2p-5.
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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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=
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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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
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
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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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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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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Simplify the expression. (7)³- ((7)4)² = (7)
Step-by-step explanation:
7³−((7)(4))² =7
−441≠7
False
Read the question. Then fill in the correct answer on the answer document provided by your teacher or on a sheet of paper.
Eddie conducted a random survey of 50 students and fund that 14 nf them spend more than 2 hours each night doing homework. If there are 421 students at Eddie's school, predict how many of them spend more than 2 hours each night doing homework.
F. 118 H. 125
G. 124 J. 131
The prediction of the number of students who spend more than 2 hours each night doing homework are 118.
It is given in the question that in a random survey of 50 students and fund that 14 of them spend more than 2 hours each night doing homework.
There are 421 students in the school.
We have to predict the number of students who spend more than 2 hours each night doing homework.
Probability of number of students who spend more than 2 hours in doing homework = 14/50 = 7/25= 0.28
If there are 421 students, number of students who spend more than 2 hours in doing homework = 0.28*421 = 117.88 ≈ 118.
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2|4w-1|=3|4w+2| Solve for W, but it’s absolute value so 2 and 3 cannot be distributed
Answer:
w = -2, (-1/5)
Step-by-step explanation:
2|4w - 1| = 3|4w + 2|
8w - 2 = 12w + 6
-12w -12w
-------------------------
-4w - 2 = 6
+2 +2
---------------------
-4w = 8
÷-4 ÷-4
w = -2
2|4(-2) - 1| = 3|4(-2) + 2|
2|-8 - 1| = 3|-8 + 2|
2|-9| = 3|-6|
18 = 18
----------------------------------------------------------------------------------------------------------
2|4w - 1| = -(3|4w + 2|)
2|4w - 1| = -3|4w + 2|
8w - 2 = -12w - 6
+12w +12w
-------------------------
20w - 2 = -6
+2 +2
20w = -4
÷20 ÷20
------------------
w =(-1/5)
2|4(-1/5) - 1| = 3|4(-1/5) + 2|
2|(-4/5) - 1| = 3|(-4/5) + 2|
2|(-9/5)| = 3|(6/5)|
3.6 = 3.6
I hope this helps!
Question Add −1.5+1.75 Plot the first addend and the sum on the number.
Answer:
Step-by-step explanation:
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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b. What are the heights of the 6 th and 10 th bounces?
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?
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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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]
PLEASE HELP LE WITH THIS ANSWET
Answer: 5
Step-by-step explanation:
GH=GD+DH
GD=DH ==> indicated by the ticks on the two line segments GH and DH.
GH=DH+DH
4x-4=8+8
4x-4=16
4x=20
x=5
What is the slope of a line perpendicular to the line through the points (-1,6) and (3,-4) ?
A. m=-5/2
B. m=-1
C. m=-2/5
D. m=2/5
The slope of the line passing through two points (-1, 6) and (3, -4) is Option A ( m = [tex]\frac{-5}{2}[/tex] )
It is given that, the line is passing through two points (-1, 6) and (3, -4)
Slope is the measurement of the level of steepness of the line or it is a line's steepness determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).
The formula to find the slope of the line passing through two points is given by
m = [tex]\frac{y2 - y1}{x2 - x1}[/tex]
We need to find the slope of the line passing through both points
where y1 = 6, y2 = -4, x1 = -1, x2 = 3
Putting values in the formula to find the slope of the line
we get,
m = [tex]\frac{-4 - 6}{[3 -(-1)]}[/tex]
m = [tex]\frac{-10}{4}[/tex]
m = [tex]\frac{-5}{2}[/tex]
Hence The slope of the line passing through two points (-1, 6) and (3, -4) is m = [tex]\frac{-5}{2}[/tex]
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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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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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Review the graph. A student spends 16.5 hours studying and receives a mark of 61.4%. Which statement
describes this result?
A. The result is not an outlier and there is a gap in the data.
B. The result is not an outlier and there is no gap in the data.
C. The result is an outlier and there is a gap in the data.
D. The result is an outlier and there is no gap in the data.
Answer: D. The result is an outlier and there is no gap in the data.
The statement describes this result is; D. The result is an outlier and there is no gap in the data.
In statistics, an outlier is a data point that differs significantly from other observations. An outlier may be due to variability in the measurement or it may indicate experimental error; the latter are sometimes excluded from the data set.
From the graph, at 16.5 hours, the exam score is approximately 90%. Thus, we can conclude that if a student spends 16.5 hours studying and receives a mark of 61.4%, then the result is an outlier and there is no gap in the data.
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Find an equation of the line in the form y=f(x) that satisfies the given conditions. through (7, 1); slope 2
Answer:
y = 2x - 13.
Step-by-step explanation:
The point-slope form of a line is:
y - y1 = m(x - x1)
Substituting the given values:
y - 1 = 2(x - 7)
y = 2x - 14 + 1
y = 2x - 13.
LCM of 21, 56
I really need help it’s due today
Answer: the answer is 168
Samantha owes her father 21.21. She just got paid 13 for babysitting. If she gives that money to her dad, how much will she still owe him? No dollar sign needed. Write your answer as a negative integer, rounded to the nearest h
Answer:
she'll still owe him 8.21
Step-by-step explanation:
i dont know what you mean by write it as a negative integer ?
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:
