Given:
The sum of third and seventh terms of an AP is 20.
To find:
The sum of the first nine terms.
Solution:
We have, the sum of third and seventh terms of an AP is 20.
[tex]a_3+a_7=20[/tex] ...(i)
nth term of an AP is
[tex]a_n=a+(n-1)d[/tex]
where, a is first term and d is common difference.
[tex]a_3=a+(3-1)d[/tex]
[tex]a_3=a+2d[/tex] ...(ii)
[tex]a_7=a+(7-1)d[/tex]
[tex]a_7=a+6d[/tex] ...(iii)
Using (i), (ii) and (iii), we get
[tex](a+2d)+(a+6d)=20[/tex]
[tex]2a+8d=20[/tex] ...(iv)
Now, the sum of first n terms of an AP is
[tex]S_n=\dfrac{n}{2}[2a+(n-1)d][/tex]
Put n=9 to find the sum of first 9 terms of an AP.
[tex]S_n=\dfrac{9}{2}[2a+(9-1)d][/tex]
[tex]S_n=\dfrac{9}{2}[2a+8d][/tex]
[tex]S_n=\dfrac{9}{2}[20][/tex] [Using (iv)]
[tex]S_n=\dfrac{180}{2}[/tex]
[tex]S_n=90[/tex]
Therefore, the sum of the first 9 terms is 90.
3/4 divided by 1/5
Please answer soon
Answer:
15
Step-by-step explanation:
im in algebra two so you can trust my answer. happy holidays and stay safe!
What does x equal I this problem
Answer: The answer is X= 9 Hope this helps :) Please mark Brainliest
Step-by-step explanation:
Help please
How are the properties of exponents used to rewrite expressions?
Answer: The five exponent properties are
Product of Powers: When you are multiplying like terms with exponents, use the product of powers rule as a shortcut to finding the answer. It states that when you are multiplying two terms that have the same base, just add their exponents to find your answer.
Power to a Power: When raising a power to a power in an exponential expression, you find the new power by multiplying the two powers together. ... Then multiply the two expressions together. You get to see multiplying exponents (raising a power to a power) and adding exponents (multiplying same bases).
Quotient of Powers: When you are dividing like terms with exponents, use the Quotient of Powers Rule to simplify the problem. This rule states that when you are dividing terms that have the same base, just subtract their exponents to find your answer. The key is to only subtract those exponents whose bases are the same.
Power of a Product: The Power of a Product rule is another way to simplify exponents. When you have a number or variable raised to a power, it is called the base, while the superscript number, or the number after the '^' mark, is called the exponent or power.
Power of a Quotient: The Power of a Quotient rule is another way you can simplify an algebraic expression with exponents. When you have a number or variable raised to a power, the number (or variable) is called the base, while the superscript number is called the exponent or power
You can use these any way you want to rewrite an equation.
Hope this helped
Step-by-step explanation:
You have 3/5gallon of juice and drink 1/3 gallons how much is left
Answer:
4/15 gallons of juice
Step-by-step explanation:
Total gallon you have = 3/5gallons
Amount consumed = 1/3 gallons
Amount left = Total gallons + Amount consumed
Amount left = 3/5-1/3
Find the LCM
amount left = (3)(3)-5(1)/15
Amount left = (9-5)/15
Amount left = 4/15
Hence 4/15 gallons of juice is left
help please I beg you
Answer:
a. x= 5
b. x=9
Step-by-step explanation:
a.
2x=10
10/2=5
x=5
b. 3x=27
27/3=9
x=9
Please mark me brainliest
:)
Answer:
a) x=5
b) x=9
Step-by-step explanation:
a) 2x=10
x=10/2
x=5
b)3x=27
x=27/3
x=9
I need help with this please
Answer:
b
Step-by-step explanation:
there's a property for Alternate Interior Angles
Answer:
Choice B
Step-by-step explanation:
The reason why < 3 is equal to < 6 is because they are alternate interior angles.
The first choice are supplementary angles they add up to 180 so they can't be equal.
The third one is false because we don't actually know the measurements of the angles but they both need to be 45° to add up to 90 since they are equal to each other.
The last one is also incorrect because they are vertical angles just like the third choice and they aren't on a line so they can't add up to 180.
when a three-dimensional figure is exended infinitely in all directions,which of the following best describes what is formed?
Answer:
2
Step-by-step explanation:
What is 70% of 40??????
Answer:
28
Step-by-step explanation:
hope this helps
Answer:
28
Step-by-step explanation:
70% is equal to 70/100. "of" when used in math means multiplaication.
so we do 70/100 x 40
we can simplify 70/100 to get 7/10.
now we multiply:
7/10 x 40 = 28
What is the exact value of tan ( 5 pi/8 )
===================================================
Explanation:
Make sure your calculator is in radian mode. Use your calculator to find that tan(5pi/8) = -2.41421 which is approximate.
Since the value is negative, this means the answer is between choices C and D. You can use your calculator to compute those expressions given and you should find it matches with choice D.
----------------------
Further explanation:
We can apply the half angle identity for tangent like so
[tex]\tan\left(\frac{x}{2}\right) = \pm \sqrt{\frac{1-\cos(x)}{1+\cos(x)}}\\\\\\\tan\left(\frac{5\pi/4}{2}\right) = -\sqrt{\frac{1-\cos(5\pi/4)}{1+\cos(5\pi/4)}}\\\\\\\tan\left(\frac{5\pi}{8}\right) = -\sqrt{\frac{1-\left(-\frac{\sqrt{2}}{2}\right)}{1+\left(-\frac{\sqrt{2}}{2}\right)}}\\\\\\[/tex]
Simplifying further, we get
[tex]\tan\left(\frac{5\pi}{8}\right) = -\sqrt{\frac{1+\frac{\sqrt{2}}{2}}{1-\frac{\sqrt{2}}{2}}}\\\\\\\tan\left(\frac{5\pi}{8}\right) = -\sqrt{\frac{2+\sqrt{2}}{2-\sqrt{2}}}\\\\\\[/tex]
In the last step, I multiplied top and bottom of the outer fraction by 2 to clear out the denominators of the inner fractions.
Answer:
Answer D
Step-by-step explanation:
on edge 2023
The graphs below have the same shape. What is the equation of the blue
graph?
A. g(x) = (x+4)^2
b. g(x) = x^2-4
c. g(x) = x^2+4
d. g(x) = (x-4)^2
(D) [tex]g(x)=(x-4)^{2}[/tex]
Graphs:The set of ordered pairings (display style [tex](x,y)[/tex]) of a function (display style [tex]f(x)=y[/tex]) in mathematics is known as the graph of that function. These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the typical case where "display style [tex]x[/tex]" and "display style [tex]f(x)[/tex]" are real values.Graph equations:Equations with graphs as the unknowns are known as graph equations in graph theory. The concept of isomorphism is one of the key issues in graph theory. Different graph equations may be used to express the aforementioned graphs.Therefore, the correct equation for the blue graph is [tex]g(x)=(x-4)^{2}[/tex].
Know more about the Graphs here:
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A restkaurant worker is able to clean 32 dishes in 8 minutes. How many minutes would it take to clean 58 dishes?
Answer:
14.5
Step-by-step explanation:
Find the unit rate
which one is greater 0.503 or 0.53
Answer:
0.53
Step-by-step explanation:
Hope this helps.
Reciprocal of 5/6=..............
Step-by-step explanation:
To find the reciprocal, divide 1 by the number given. Simplify. Multiply the numerator by the reciprocal of the denominator. Multiply 65 6 5 by 1 1 .
This table shows a proportional relationship between the number of cups of bananas and apples used for a smoothie.
Cups of
Bananas
Cups of Apples
1
6
2
12
4
24
Enter the number of cups of bananas used for 1 cup of apples.
cups
Answer:
For every 1 cup of banana you have to add 6 cups of apples. So it means there's six times as much apples as there is bananas. If there's 3 cups of apples, which is half of 6, it means the banana would now also have to be halved from 1 to half a cup.
Whatever you do to the bananas or the apples, you have to maintain the same ratio. Which is that apples is 6 times as much as bananas.
So 1 cup of apple would need to be divided by 6, to get banana. That would be approximately 1÷6= 0.167 cups
The graph below represents one function, and the table represents a different function. How are the functions similar? How are they different?
Answer:
Step-by-step explanation:
they both go thur the point (0,-4) so they both have the same b in the slope intercept from of y =mx +b
but.. they have a different slope... m , the graph has a slope m of 4/3 while the table has a slope of 1 , both positive.. :)
The equation given by the graph is y = (4/3)x - 4 while the table is y = x - 4. Both equation have a y intercept of -4.
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
From the graph, using the point (3, 0) and (0, -4):
y - 0 = [(-4 - 0)/ (0 - 3)](x - 3)
y = (4/3)x - 4
From the table using (0, -4) and (2, -2):
y - (-4) = [(-2-(-4))/(2-0)](x - 0)
y = x - 4
The equation given by the graph is y = (4/3)x - 4 while the table is y = x - 4. Both equation have a y intercept of -4.
Find out more on equation at: https://brainly.com/question/2972832
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I need that r d d d d d. D d d d d d d. D
Answer:
D is not a function.
Step-by-step explanation:
The first option is a function because it makes up a straight line. The second option is also a function because it is also known as y = -3/2x + 2 creating a slope function. The third option is also a function because there is no more than one point for each x value. The last option is not a function because the number 2 is going for 2 variables A and B and you can't have them with more than one so D is your answer.
Answer:
D is not a function.
Step-by-step explanation:
The first option is a function because it makes up a straight line. The second option is also a function because it is also known as y = -3/2x + 2 creating a slope function. The third option is also a function because there is no more than one point for each x value. The last option is not a function because the number 2 is going for 2 variables A and B and you can't have them with more than one so D is your answer.
Have no idea how to do this lok
Answer:
that hard
Step-by-step explanation:
plzzzzzzzzzzzzzzzzzzzzzzz
Option C. Please mark me as brainliest.
solve for y when x=4
-y+5x=2(y+7x)
A. y=18
B. y=7
C. y=4
D. y=-12
Answer:
D.) y=-12
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Hope this helped you!! :)
this months rainfall is 30% less than last months total of 3.5 inches.
PLZZZZ ANSWWERRR ASAPPP MARKING BRAINLIEST
Answer:
1.05
Step-by-step explanation:
3.5x.30=1.05
Answer:
1.05
Step-by-step explanation:
You will have to multiply if you are trying to find the amount of water in total. So, 0.30*3.5=1.05. So, that would be your answer for the amount of rainfall.
I need help, please solve this 2(x+5)^4=128
Question 7 of 25 Which of the binomials below is a factor of this trinomial? x - 6x-16 O A. X-1 O B. X-8 OC. X-16 O D. x-2
Answer:
(x-8) is the factor.
Step-by-step explanation:
The given trinomial is [tex]x^{2}-6x-16[/tex].
We need to find the factor of this trinomial.
[tex]x^{2}-6x-16=x^2-8x+2x-16\\\\=x(x-8)+2(x-8)\\\\=(x+2)(x-8)[/tex]
The factors of [tex]x^{2}-6x-16[/tex] is (x-2) and (x-8).
So, the factor of [tex]x^{2}-6x-16[/tex] is (x-8). Hence, the correct option is (B).
Jillian is making accessories for the soccer team. She uses 667.43 inches of fabric on headbands for 27 players and 4 coaches. She also uses 237.87 inches of fabric on wristbands for just the players. How much fabric was used on a headband and wristband for each player?
Answer:
21.53 in of fabric on headbands
7.67 in of fabric on wristbands.
Step-by-step explanation:
Step one:
given data
the total amount of person players plus coaches= 27+4= 31
for each person, she uses = 667.43/31= 21.53 in of fabric on headbands
She also uses 237.87inches of fabric on wristbands for just the players
For each player, she will use= 237.87/31= 7.67 in of fabric
Hence for each player, she used
21.53 in of fabric on headbands
7.67 in of fabric on wristbands
Find the value of x. Diagram is not to scale
Answer:
b: 70
Step-by-step explanation:
45+45=90
24+24=48
The scale of the triangle is 2
35*2=70
Mrs. Maxwell is teaching a 5th grade class. She is standing 9 meters in front of Bruce. Ruth is sitting to Bruce's right. If Ruth and Mrs. Maxwell are 15 meters apart, how far apart are Bruce and Ruth?
9514 1404 393
Answer:
12 m
Step-by-step explanation:
The distances of interest are the sides of a right triangle whose right angle is at Bruce. The hypotenuse of the triangle is the Teacher-Ruth distance. The unknown side (x) can be found using the Pythagorean theorem:
x² + 9² = 15²
x² = 225 -81 = 144
x = √144 = 12
Bruce and Ruth are 12 meters apart.
Can someone help me please
Answer: B
Step-by-step explanation:
It has to be B. None of the other answers make sense.
Solve the system please
Answer:
(2,-1,1) I believe
The Langleys spend 40% of their monthly income on rent. If their monthly income is $4,400, how much money do the Langleys spend on rent? Help please.
100%=$4400
40% $=?
40 ×4400/100
$1760
y=-4/7x-4
Can someone help me please
Find the slope using points: (2,5) and (8,9)
Answer: The slope is 2/3:)
Step-by-step explanation: (2,5) and (8,9)
9-5 =4 /2=2
8-2 =6 /2= 3
Answer: 2/3 or 4/6.
Step-by-step explanation:
Slope = (y2-y1) / (x2-x1)
(9 - 5) / (8-2)
= 4/6, which reduces to 2/3.
The slope of the line between the two given points is 4/6, or 2/3 in simplest terms.