By SSS (Side, side, side) congruency;
⇒ Δ T J D ≅ ΔS E K
Given that;
The vertices of ΔT J D are;
T (-4, -2) , J (0, 5), and D (1, -1),
The vertices of ΔS E K are;
S (-1, 3), E (3, 10) , and K (4, 4)
We have to prove that Δ T J D ≅ΔS E K.
What is congruency in triangle?
If all three corresponding sides are equal and all the three corresponding angles are equal in measure, then Two triangles are said to be congruent.
Now,
The vertices of ΔT J D are;
T (-4, -2) , J (0, 5), and D (1, -1),
The vertices of ΔS E K are;
S (-1, 3), E (3, 10) , and K (4, 4)
To prove Δ T J D ≅ΔS E K we use distance formula and prove all sides are equal.
In ΔT J D;
Distance between T and J;
[tex]D_{TJ} = \sqrt{(0-(-4))^2 + (5 -(-2))^2} = \sqrt{65}[/tex]
Distance between J and D;
[tex]D_{JD} = \sqrt{(1-0)^2 + (-1 -5)^2} = \sqrt{37}[/tex]
Distance between D and T;
[tex]D_{DT} = \sqrt{(1-(-4))^2 + (-1 -(-2))^2} = \sqrt{26}[/tex]
In ΔS E K;
Distance between S and E;
[tex]D_{SE} = \sqrt{(3-(-1))^2 + (10-3)^2} = \sqrt{65}[/tex]
Distance between E and K;
[tex]D_{EK} = \sqrt{(4-3)^2 + (4 -10)^2} = \sqrt{37}[/tex]
Distance between K and S;
[tex]D_{KS} = \sqrt{(4-(-1))^2 + (4 -3)^2} = \sqrt{26}[/tex]Clearly, Distance between sides of Δ T J D and ΔS E K are equal as;
[tex]D_{SE} = D_{TJ} \\\\D_{EK} = D_{JD}\\\\D_{KS} = D_{DT}[/tex]
Hence, By SSS congruency;
⇒ Δ T J D ≅ ΔS E K
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Refer to ®N . If CN = 8 centimeters, find D N .
CN and DN are radii of the same circle. So, they are equal in length then the value of DN = 8 cm.
What is a circle?A circle is defined as the collection of all points in the plane that are a fixed distance (the radius) from a fixed point (the center). A radius is any interval that connects a point on a circle to its center. Any two radii have the same length according to the definition of a circle.
A circle is a two-dimensional closed figure in which the set of all points in the plane is equidistant from a given point known as the "center."
A circle is a shape formed by all points in a plane that are at a given distance from the center. It is the curve traced out by a point moving in a plane so that its distance from a given point remains constant.
Here, CN and DN are radii of the same circle. So, they are equal in length then the value of DN = 8 cm.
The complete question is:
If CN = 8 centimeters, find DN.
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Compare the two numbers. Use > or < .
12,-√150
Compare the two numbers 12,-√150
[tex]-\sqrt{150} =-12.24[/tex]
So,12 > -√150
What is a square root?
A square root is a factor of a number in mathematics that, when multiplied by itself, equals the original value.Square roots can be taken into account more broadly in any situation where the concept of an object's square is specified.Among other mathematical structures, these include function spaces and square matrices.The term square root is sometimes used to refer to the major square root of a positive number, even though it is merely one of the two square roots of that number.To learn more about square roots, refer:
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Simplify (3^2)^4 i’ve needed to be pacifically about that
Answer:
Step-by-step explanation:
Hey there!
(3^2)^4
= (3 * 3)^4
= (9)^4
= 9^4
= 9 * 9 * 9 * 9
= 81 * 81
= 6,561
Therefore, your answer should be:
6,561
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Find the volume of a cone that has a radius of 1cm and a height of 3.4cm.
The volume of a cone that has a radius of 1 cm and a height of 3.4 cm is 3.56 cm³.
Volume of a cone is the space occupied by it in a three - dimensional space.
Volume of a cone is calculated using the formula:
[tex]V = \frac{1}{3} \pi r^{2} h[/tex]
where r is the radius of the base of the cone
[tex]\pi[/tex] is a constant having value 3.14
h is the height of the cone. It is the perpendicular height from the base.
According to the given condition,
r = 1 cm and h = 3.4 cm
Substituting these values in the equation above,
[tex]V = \frac{1}{3} \pi (1^{2}) (3.4)[/tex]
∴ V = 3.56 cm³.
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please help i'm stuck
Answer:
- 1 [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
substitute x = - 5 into f(x)
f(- 5) = [tex]\frac{1}{4}[/tex] × - 5 = - [tex]\frac{5}{4}[/tex] = - 1 [tex]\frac{1}{4}[/tex]
Solve the equation
W^2+2w-15=0?
Answer:
w = 3,−5
Step-by-step explanation:
If ur solving for w then that i presume.
Find an equation for the line parallel to y = 7 x + 3 and goes through the point ( − 4 , − 2 ) .
The equation of line parallel to the given equation and goes through the given point is y = 7x - 26.
What is the equation of line parallel to the given equation and goes through the given point?Given the data in the question;
Equation: y = 7x + 3Point: (-4,-2)First, we determine the slope by comparing the equation with the slope intercept formula ( y = mx + b )
y = 7x + 3
Hence,
Slope m = 7
Next, we use the point-slope formula y-y₁ = m( x-x₁ ) to determine the equation of the line parallel.
Note that, the slopes must equal.
Given that; slope m = 7, Point: (-4,-2)
Plug into the point-slope formula and simplify.
y-y₁ = m( x-x₁ )
y - (-2) = 7( x - (-4) )
y + 2 = 7( x + 4 )
y + 2 = 7x + 28
y = 7x + 28 - 2
y = 7x - 26
Therefore, the equation of line parallel to the given equation and goes through the given point is y = 7x - 26.
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Multiple the question bellow
Answer:
1
Step-by-step explanation:
We have to convert the whole number into an improper fraction :
4 = 4/1
Now we multiply the numerators together and the denominators together :
4 × 1 = 4
1 × 4 = 4
Our new fraction is 4/4 = 1
Hope this helped and have a good day
Evaluate each logarithm. log₃ 1/27
In mathematics, the logarithm is the reciprocal of a power. This means that the logarithm of a given number x is the exponent by which another fixed number (the base b) must be increased to get that number x. The simplest logarithm counts the number of times the same element occurs when multiplying repeatedly. The logarithm of x to base b is denoted by log b (x), or log b x without parentheses. Also, if confusion is impossible or the base doesn't matter, log x shows that even without an explicit base: B. In big O notation.
Solution:
Your problem → log (3,1/27)
log (3, (127)) =-3
Solution steps:
=log (3,127)
=log (3,0.037037)
=log3(0.037037)
=-3
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At a daycare, 74% of the kids were absent due to the chickenpox. If 37 kids stayed home, how many kids does the daycare normally have?
If 37 kids stayed home, the daycare normally has 143 kids.
Calculating number of childrenWe can use algebra to solve the problem.
Let's call the total number of kids in the daycare "x".
We know that 74% of the kids were absent, which means that 26% (100% - 74%) of the kids came to the daycare.
Note: 37 kids stayed home.
Set up the following equation:
0.26x = 37
To solve for x, divide both sides by 0.26:
x = 37 / 0.26
x ≈ 142.31
Therefore, the daycare normally has approximately 143 kids.
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Find the volume of the candle in Exercise 4 . Round to the nearest tenth if necessary.
The volume of the candle is 36.9 cubic inches.
Given that the candle is in a circular pillar shape. That is it is in cylindrical shape.
Height of the candle, h = 6 inches
Width of the candle = Diameter of the base circle = 2.8 inches
Radius of the circle, r = 2.8/2 = 1.4 inches
We need to calculate the volume of the cylindrical candle.
Volume of a cylinder = Area of the base circle x height of the cylinder
Therefore, volume of the candle, V = [tex]\pi r^2 h[/tex]
= 3.14 x 1.4 x 1.4 x 6
= 36.9264
= 36.9 cubic inches
The question is incomplete. Find the complete question below:
A circular pillar candle is 2.8 inches wide and 6 inches tall. Find the volume of the candle. Round to the nearest tenth if necessary.
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What is summation notation for the series?
b. 500+490+480+ . . . . . . . +20+10
The summation notation for the series 500+490+480+ . . . . . . . +20+10 is
[tex]25500-10\sum\limits^{50}_{n=1} {n}[/tex]
A summation notation is used to express a long summation into a single notation.
The given series is:
500+490+480+ . . . . . . . +20+10
This is an arithmetic series with:
a(1) = 500, and
d = 490 - 500 = -10
The last term is a(n) = 10. Find n first by using the nth term formula of an arithmetic sequence:
a(n) = a(1) + (n-1) . d
10 = 500 + (n-1) . (-10)
10 = 500 -10n + 10
10 n = 500
n = 50
Write the explicit formula for the nth term:
a(n) = a(1) + (n-1) . d
a(n) = 500 + (n-1) . (-10)
a(n) = 500 -10n + 10
a(n) = 510 - 10n
The series is the summation notation from n=1 to n = 50
[tex]=\sum\limits^{50}_{n=1} {a(n)}[/tex]
[tex]=\sum\limits^{50}_{n=1} {(510-10n)}[/tex]
[tex]=\sum\limits^{50}_{n=1} {510} -\sum\limits^{50}_{n=1} {10n}[/tex]
[tex]=510\times50-10\sum\limits^{50}_{n=1} {n}[/tex]
[tex]=25500-10\sum\limits^{50}_{n=1} {n}[/tex]
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Write in point-slope form an equation of the line through each pair of points. (-10,3) and (-2,-5)
The equation of the line in point-slope form, which passes through the pair of points located at (-10 , 3) and (-2 , -5), is y - 3 = -(x + 10).
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, 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. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).
Getting the slope of the two points: (-10 , 3) and (-2 , -5).
m = (y2 - y1)/(x2 - x1)
m = (-5 - 3)/(-2 - -10)
m = -8/8
m = -1
Using the point slope form, plug in the values of the slope and one point to set up the equation.
(y - y1) = m(x - x1)
where m = -1 and (x1 , y1) = (-10 , 3)
(y - 3) = -1(x - -10)
y - 3 = -(x + 10)
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Solve the equation x - 23 = 72
Answer:
Step-by-step explanation:
x=72+23
x=95
Answer: x = 95
Step-by-step explanation:
Add 23 to both sides to isolate x
x - 23 + 23 = 72 + 23
x = 95
Skylar is a lifeguard at a swimming pool. Last week, they worked 3 3/4 equal-length shifts, because rain closed the pool early one day. Those shifts totaled 11 1/4 hours of work. How long is a single shift?
Answer:
3 hours i believe
Step-by-step explanation:
i did 11.25 (11 1/4) divided by 3.75 (3 3/4)
The total number of hours in a single shift is 3 hours
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the total number of hours in a single shift be = A
Now , The total length of equal shifts Skylar worked last week = 3 3/4 shifts
The total length of equal shifts Skylar worked last week = 15 / 4 shifts
The total number of hours Skylar worked in the week = 11 1/4 hours
The total number of hours Skylar worked in the week = 45 / 4
Now , the equation will be
Total length of equal shifts Skylar worked last week = total number of hours Skylar worked in the week
So ,
Total length of one shift of Skylar = total number of hours Skylar worked in the week / Total length of equal shifts Skylar worked last week
On substituting the values in the equation , we get
Total length of one shift of Skylar A = ( 45/4 ) / ( 15/4 )
On simplifying the equation , we get
A = ( 45/4 ) / ( 15/4 )
A = 45 / 15
A = 3 hours
Therefore , the value of A is 3 hours
Hence , The total number of hours in a single shift is 3 hours
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Drag and drop the correct values to complete the table of values for the equation y=-2x+3.
Answer:
Step-by-step explanation:
So it gives us the equation y=2x+3
Thinking process
1. What you want to do is remove the 3 from the equation so you just get y=2x
How to solve(example)
For the first row to find x first minus 3 from 9 which is 6
9-3=6
Then six divided by two so you can find x.
2x=6
x=3
Solve the equation [tex]\sqrt{x} -6+2=6[/tex] for the variable. Can someone help me with this?
Answer:
x=100
Step-by-step explanation:
√x-6+2=6
√x -4 =6
√x =6+4
√x = 10
squere both sides of the equation
x =100
Asher's sister is eight years older than Asher. Their combined ages add up fo 20.
How old is Asher?
Answer:14
Step-by-step explanation:X+8=asher's age X=Asher's sisters age
x+x+8 =20
2x+8=20
2x+8-8=20-8
2x=12
2x/2=12/2
x=6
x+8=asher's age
6+8=14
What is the value of 4x² + 2x - 1 when x = 3/4 ? Express the answer as a decimal.
The answer is an decimal form is 2.75
In the given Statement is:
What is the value of 4x² + 2x - 1 when x = 3/4 ?
Express the answer as a decimal.
Let's Come to the solution:
4x² + 2x - 1 __(1)
Now put the value of x = 3/4 in above equation:
4 (3/4)² + 2 (3/4) - 1
Solve the equation, and get the answer
4 x (9/16) + 3/2 - 1
9/4 + 3/2 - 1
Taking the L.C.M
= [tex]\frac{9+6-4}{4}[/tex]
= 11/4
= 2.75 is the answer
Hence, The answer is an decimal form is 2.75
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1/3a = -5
please help ! ):
The value of a in the expression is 15.
How to illustrate the expression?It should be noted that an expression shows that relationship that exists between variables.
In this case, we are given the expression that 1/3a = -5
To find the value of a will be:
a/3 = 5
Cross multiply
a = 3 × 5.
a = 15
Therefore, the value of a in the expression is 15.
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1/3a = -5. Find the value of a.
When placed in the box below, what expression will complete an example of the commutative property of addition 7(2+9)= ?
The expression for 7(2+9) IS A(B+C) which is distributive property of addition over multiplication.
Only two arithmetic procedures are subject to the commutative property: Multiplication and Addition
A + B = B + A Which is Commutative property of addition
A.B = B.A, which is a commutative property of multiplication.
Distributive property is A(B+C) =AB+AC
The operation on numbers that are available in brackets can be distributed for each number outside the bracket, according to the distributive property. It is one of the mathematical properties that is used the most. Commutative and associative qualities are the other two important features.
from the given data 7(2+9) =7*2+7*9
=14+63
=77
Now, we can clear that 7(2+9) =7(9+2)
Hence, the expression for commutative property of addition is A(B+C) = AB+AC.
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Write a flow proof.
Given: ΔQ R S /RT is isosceles with QR ≅ SR.
RT bisects QS at point T .
Prove: QRT ≅ ΔS R T
We came to the conclusion that ΔQRT ≅ ΔSRT is under the side-side-side (SSS) condition.
What accurately does "triangle congruency" mean?If all three corresponding sides are equal and all three corresponding angles are equal in measure, two triangles are said to be congruent.These triangles can be moved, rotated, flipped, and turned to look exactly the same.They will coincide if they are repositioned.Two triangles are congruent if they satisfy the five congruence conditions.They are the side-side-side (SSS), the side-angle-side (SAS), the angle-side-angle (ASA), the angle-angle-side (AAS), and the right angle-hypotenuse-side (RHS).So,
Given: ΔQRS/SRT is isosceles with QR ≅ SR; RT bisects QS at point T.
To prove: ΔQRT ≅ ΔSRT
QR = SR = GivenQT = QS = Given: (RT bisects QS at point T)RT = RT = Common baseSo, we can say that ΔQRT ≅ ΔSRT under SSS condition.
Therefore, ΔQRT ≅ ΔSRT is congruent under SSS condition.
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A bag contains 3 red chips, 5 green chips, 2 yellow chips, 4 brown chips, and 6 purple chips. One chip is chosen at random, the color noted, and the chip returned to the bag.
b. What is the probability that both chips are purple?
The probability of selecting that both chips are purple is 3/40
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
P(E) = Number of favorable outcomes / total number of outcomes
It is Given that A bag contains 3 red chips, 5 green chips, 2 yellow chips, 4 brown chips, and 6 purple chips. One chip is chosen at random, the color noted, and the chip returned to the bag.
The probability of selecting that both chips are purple
= 6/20 x 5/20
= 30/400
= 3/40
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A professor expects the education and health service industries to increase total employees by 14.8% from 2009 to 2016. Based on the employment graph below, approximately how many new jobs will the education and health service industries gain between 1/2009 and 1/2016?
Education and Health Services - All Employees, 2000-2009
A line graph titled Education and Health Services, All Employees, 2000 to 2009, where the x-axis shows years and the y-axis shows all employees, in thousands. Line starts at 15,000 on January 2000, and increases gradually to 16,000 on January 2002, 17,200 on January 2005, 18,100 on January 2007, and 19,200 on January 2009.
The number of new jobs gained is 2,842.
How many new jobs are gained?A graph can be described as a pictorial representation of data. A graph is made up of a x-axis and a y-axis.
Percentage can be described as a fraction of an amount expressed as a number out of hundred. The sign used to represent percentage is %.
Percentage increase from 2009 to 2016 = percentage increase x number of employees in 2009
14.8% x 19,200
0.148 x 19,200 = 2,842
Here is the complete question:
A professor expects the education and health service industries to increase total employees by 14.8% from 2009 to 2016. Based on the employment graph below, approximately how many new jobs will the education and health service industries gain between 1/2009 and 1/2016?
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Answer:
c. 16,273,200
Step-by-step explanation:
Edge 2022
State whether sentence is true or false. If false, replace the underlined word or phrase to make a true sentence.
The ₋component form of a vector describes the vector in terms of change in x and change in y .
Given statement 'The component form of a vector describes the vector in terms of change in x and change in y.' is True.
For a vector V whose initial point is (x1, y1) and the terminal point is (x2, y2), the component form of a vector V is given as: < x₂ – x₁, y₂ – y₁ >
The coordinates of the component form of vector are nothing but the ordered pair that describes the changes in the x-values and y-values.
Consider a vector v whose initial point is (1, 3) and the terminal point is (3, 6).
The component form of vector v is:
<3 - 1, 6 - 3>
= <2, 3>
Here, 2 is the change in the x-values from initial point to terminal point and 3 is the change in the y-values from the initial point to the terminal point.
Therefore, given statement 'The component form of a vector describes the vector in terms of change in x and change in y.' is True.
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Solve each system by elimination.
2x - 3y = -1 3x + 4y = 8
The solution of the given system of equations is (20/17, 19/17)
We can solve a system of equations using:
- graphical method
- elimination method
- substitution method
The given system of equations:
2x - 3y = -1 ...... (1)
3x + 4y = 8 ...... (2)
To be able to use the elimination method, multiply equation (1) by 3 and equation (2) by 2.
2x - 3y = -1 (⨉3)
⇔ 6x - 9y = -3 .........(3)
3x + 4y = 8 (⨉2)
⇔ 6x + 8y = 16 .........(4)
Substract equation (3) from (4)
6x + 8y = 16
6x - 9y = -3 –
17y = 19
y = 19/17
Substitute y = 19/17 into equation (1)
2x - 3y = -1
2x - 3(19/17) = -1
2x - 57/17 = -17/17
2x = (-17 + 57) / 17
2x = 40/17
x = 20/17
Thus, the solution is (20/17, 19/17)
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If 5 is lessened by 1/2 of a number the result is the same as subtracting 5/6 from 11.
Write an equation to represent the situation, use X as the variable.
The equation to represent the given situation is 1/2X-5=11-5/6 using X as the variable.
What is an equation and how it can be formed?
Mathematically, an equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”.
When we are given a mathematical problem that is or may be described using algebraic expressions, we form and solve equations. The information from the situation and the algebraic expressions can be used to create an equation. The equation can then be solved to obtain the answer.
Given the situation: If 5 is lessened by 1/2 of a number the result is the same as subtracting 5/6 from 11.
To write an equation for the given situation.
Let the number be X.
If 5 is lessened by 1/2 of the number, we get the expression 1/2X-5
Subtracting 5/6 from 11 gives the expression 11-5/6
Now, it is given that both the situations are same so equating both the expressions we get,
1/2X-5=11-5/6
⇒1/2X-5=61/6
Hence, the equation to represent the situation is 1/2X-5=11-5/6.
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7) in one week, you earned $75.00 at your afterschool tutoring job. after working 8 more hours the following week, you had a total of $195.00. a) how much do you make per hour as a tutor?
Solving for the rate, you make $15 per hour as a tutor.
Rate is defined as the ratio between two quantities of different units.
Let x = rate
n = total amount you've earned = $195.00
t = time you've worked = 8 hours
If in one week, you earned $75.00 at your afterschool tutoring job, and after working 8 more hours the following week, you had a total of $195.00, then we can express this as
n = xt + $75.00
Substitute the values to solve the rate, x.
n = xt + $75.00
$195.00 = x(8 hours) + $75.00
8hours (x) = $195.00 - $75.00
8hours (x) = $120.00
x = $15/hr
rate = $15 per hour
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please help me with this question! Thirty dollars is to be divided among three girls and two boys so that each of the girls receives twice as much as each of the boys. How much does each person receive?
Answer:
3.75 dollars for the boys and 7.5 for girls
Step-by-step explanation:
Boys get x amount.
Girls get 2x
6x+2x=8x
30/8=3.75
Each boy receive the amount of $3.75 and Each girl receive the amount of $7.5
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let consider that each boy gets $x
It is given that each of the girls receives twice as much each of the boys
So, each girl receive the amount of 2x
Since there are 3 girls .
So, Three girls received the amount = 3(2x)=6x
2 boys get amount of 2x
Therefore,
6x+2x=8x
30/8
=3.75
Hence Each boy receive the amount of $3.75 and Each girl receive the amount of $7.5
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Find the first five terms of each sequence. a n =-n²+2 n
The first five terms of the sequence. an=n2 +2 are 3, 6, 11, 18 and 27.
The sequence is given as n² + 2.
The first term will be:
= n² + 2 = 1² + 2 = 1 + 2 = 3
The second term will be:
= n² + 2 = 2² + 2 = 4 + 2 = 6
The third term will be:
= n² + 2 = 3² + 2 = 9 + 2 = 11
The fourth term will be:
= n² + 2 = 4² + 2 = 16 + 2 = 18
The fifth term will be:
= n² + 2 = 5² + 2 = 25 + 2 = 27
Therefore, the first five terms of the sequence. an=n2 +2 are 3, 6, 11, 18 and 27.
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