Answer:
The first term is 3 and the common difference is 2
Step-by-step explanation:
The formula of the sum of the nth term of the arithmetic sequence is
[tex]S_{n}=\frac{n}{2}[2a+(n-1)d][/tex], where
a is the first termd is the common differencen is the position of the term∵ The sum of the first five terms of an arithmetic sequence is 35
∴ [tex]S_{5}[/tex] = 35
→ Substitute The values of n and S in the rule above
∵ 35 = [tex]\frac{5}{2}[2a+(5-1)d][/tex]
∴ 35 = [tex]\frac{5}{2}[2a+4d][/tex]
→ Simplify the right side
∴ 35 = 5a + 10d
→ Switch the two sides
∴ 5a + 10d = 35 ⇒ (1)
∵ The sum of the next five terms is 85
→ To find the sum of the first 10 terms add 85 to [tex]S_{5}[/tex]
∴ [tex]S_{10}[/tex] = 35 + 85 = 120
→ Substitute The values of n and S in the rule above
∵ 120 = [tex]\frac{10}{2}[2a+(10-1)d][/tex]
∴ 120 = 5[2a + 9d]
→ Simplify the right side
∴ 120 = 10a + 45d
→ Switch the two sides
∴ 10a + 45d = 120 ⇒ (2)
Now we have a system of equations to solve it and find a and d
→ Multiply equation (1) by -2
∵ -2(5a) + -2(10d) = -2(35)
∴ -10a + -20d = -70 ⇒ (3)
→ Add equations (2) and (3)
∵ (10a + -10a) + (45d + -20d) = (120 + -70)
∴ 25d = 50
→ Divide both sides by 25 to find d
∴ d = 2
→ To find a substitute d in equation (1) by 2
∵ 5a + 10(2) = 35
∴ 5a + 20 = 35
→ Subtract 20 from both sides
∵ 5a + 20 - 20 = 35 - 20
∴ 5a = 15
→ Divide both sides by 5
∴ a = 3
∴ The first term is 3 and the common difference is 2
Wayne placed an order for 1 2/3 sacks of brown lentils and 1/2 of a sack of green lentils. How much more brown lentils did Wayne order?
Answer:
1 1/6
Step-by-step explanation:
1 2/3 - 1/2 =
1 2/3 = 1 4/6
1/2 = 3/6
1 4/6 - 3/6 =
1 1/6
A 1971 Indian Motorcycle is worth 30 times its original cost. Today it is worth $3000. How much did it originally cost in 1971?
Answer: $100
Step-by-step explanation:
3,000 divided by 30 is 100
Answer: 100
Step-by-step explanation: divide 3,000 by 30
need help i dont know how to solv
Answer:
It's learn proper English. I'll rewrite your statement. I need help, I do not understand how to solve this. Thank you!
A snack recipe calls for 1 1/4 cups of dip and 1/5 cup of chips. charlie wants to make the same recipe using 1 cup of chips. how many cups of dip will charlie need?
Using the concept of ratio the number of cups of chips Charlie needs can be found out.
What is ratio?A ratio in mathematics shows how many times one number is contained in another. The ratio symbol is represented by a colon (:).A ratio is still valid if all of the quantities are multiplied by the same number. By dividing each quantity by the sum of all the numbers' common factors, ratios can be lowered (much like fractions are). The simplest version of a fraction is one in which the ratio's numbers are the smallest feasible integers.
Amount of dip required by the recipe be 'a' =[tex]1\frac{1}{4}[/tex] cups=[tex]\frac{5}{4}[/tex]cups
Amount of chips required by the recipe be 'b'= [tex]\frac{1}{5}[/tex]cups
Amount of chips to be used be 'c'= 1 cup
Number of cups of chips Charlie needs
=[tex]\frac{c*a}{b}[/tex]
=[tex]\frac{1*\frac{5}{4} }{\frac{1}{5} }[/tex]
=[tex]\frac{5*5}{4}[/tex]
=[tex]\frac{25}{4}[/tex] cups
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There was a country concert held at the park. For every 5 men there were 7 women that went to the concert. If 40 more women attended the concert than men, how many men and how many women attended the concert? Use the following diagram to help solve the ratio problem.
Step-by-step explanation:
i think it is 35 but im probaly wrong
What is the greatest common factor of 27 and 36?
Answer:
9!
Step-by-step explanation:
Answer: 9
Step-by-step explanation:So you look at whatever can be multiplied to get 27 or 36. When you do that 9 is your biggest number
HELP!!
What is the volume of this solid?
A. 39
B. 108
C. 27
D. 63
Answer: B
Step-by-step explanation:
4 times 3 times 3 times 3 times 3=108
Answer:
A. 39
Step-by-step explanation:
Given:
Length of a pyramid (lpy ) = 4 cm
Width of a pyramid (wpy ) = 3 cm
Height of a pyramid (hpy ) = 3 cm
It is given that the rectangular pyramid fits exactly on top of the prism, the length and width of the prism are the same for the base of the pyramid.
So, Length of a prism (lpr) =3 cm, width of a prism (wpr) = 3cm and height of a prism (hpr) = 3 cm
Volume of Prism (Vpr) = lpr × wpr × hpr
⇒ Vpr = 3 cm × 3 cm × 3 cm
⇒ Vpr = 27 cm³ ....(eq 1)
Volume of Rectangular Pyramid Vpy
= (lpy × wpy × hpy ) / 3
⇒ Vpy = (4 × 3 × 3) ÷ 3
⇒ Vpy = 12 cm³ ....(eq 2)
From 1 and 2, Volume of composite space,
Volume of composite space = Volume of prism + Volume of Pyramid
⇒ V = 27 cm³ + 12 cm³ = 39 cm³
⇒ V = 39cm³
Dendra's boat uses 3 gallons of gas in 4 hours. How many gallons of gas will she use in 15 hours?
Answer:11.25
Step-by-step explanation:because we have to find out how many gallons we have in one hour so you divide both sides by 4
4/4 is 1 hour
3/4 is 0.75 gallons then you have to multiply both sides by 15
1 hour times 15 is 15 hours
the 0.75 x 15 is 11.25
so the answer is 11.25 gallons that she uses in 15 hours
hope this helps
Find the least common denominator for these fractions. Enter your answer in the space provided. 1/2 and 2/9
Answer:
18.
Step-by-step explanation:
2 = 2
9 = 3*3
So, the LCD = 2*3*3 (no duplicates in the 2 lists).
= 18.
Glen rolls a biased dice 400 times.
The results are shown below in the table.
Score Frequency
1 95
2 134
3 45
4 26
5 75
6 25
Jake rolls the same dice 720 times.
Estimate how many 5's he can expect to get. Answer
When Jake rolls the same dice 720 times, the number of 5s will be 135.
How to illustrate the information?It should be noted that the frequency for 5 is 75 out of 400. This will be:
= 75 / 400
= 3/ 16
Therefore, when Jake rolls the same dice 720 times, the number of 5s will be:
= 3/16 × 720
= 135
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Singing star bitsy carlyle isnt as popular as she used to be at her latest concert she was only able to sell 910 tickets for a total of 15620 barely enough to pay her agent if regular seats cost 18.50 and mezzanine seats the only other option cost 16.25 how many mezzanine tickest were sold
The number of mezzanine tickets sold = 540
Total number of tickets sold = 910
Total number of tickets sold is the sum of the number of regular seats and the number of the mezzanine seats sold.
Let 'x' be the number of regular seats and 'y' be the number of mezzanine seats.
Then x + y = 910 ----------(1)
Cost of a regular seat = $ 18.50
So cost of x regular seats = 18.50x dollars
Cost of a mezzanine seat = $ 16.25
So cost of y mezzanine seats = 16.25y
Total amount of money she got by selling tickets = $ 15620
Therefore, 18.5x + 16.25y = 15620 ----------------(2)
Solve equations (1) and (2) for x and y.
Multiplying (1) with 18.5 throughout,
18.5x + 18.5y = 16835 ---------------(3)
Subtracting (2) from above equation (3), we get,
(18.5 - 16.25)y = 16835 - 15620
⇒ 2.25y = 1215
⇒ y = 1215/2.25
⇒ y = 540
Hence 540 mezzanine tickets were sold.
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Amir has 2 checking accounts. The first has a balance of -$20 and the
second has a balance of $160. What is the sum of the two sum balances
Answer:
D. 140. ....,.....
Step-by-step explanation:
160-20=140
The points L, M, N and O all lie on the same line segment, in that order, such that the ratio of LM:MN:NOLM:MN:NO is equal to 5:1:2.5:1:2. If LO=48,LO=48, find NO.NO.
The length of the line segment NO is 12 units
How to determine the length of NO?The ratios of the line segments are given as:
LM : MN : NO = 5 : 1 : 2
The length of LO is given as:
LO = 48
The above means that
NO = (NO Ratio)/(Total Ratio) * LO
So, we have
NO = 2/(5 + 1 + 2) * 48
Evaluate the product
NO = 12
Hence, the length of NO is 12 units
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Factor. x^2-x=20
HUGE POINTS WOWZIE WOOZA
Answer:
(x-5)(x+4) = 0
Step-by-step explanation:
Pre-SolvingGivenWe are given the quadratic equation x²-x=20
And we want to factor it, meaning that we want to split it apart, usually to make it easier to solve.
SolvingFirst, let's subtract 20 from both sides, as when all 3 terms of a quadratic equation are on the same side, it makes it a lot easier to solve.
x² - x = 20
-20 -20
_______________
x² - x - 20 = 0
Now, we can get on to factoring.
In a quadratic equation, written as ax² + bx + c = 0 (like in here), b (the coefficient in front of just x, not x²) is equal to the sum of two numbers, while c is the product of the same two numbers.
The coefficient in front of x (b) is -1, and c is equal to -20.
Now think: which two numbers add up to -1, and multiply to equal -20?
Those numbers are -5 and 4.
Now, to factor a quadratic, we split it up into 2 binomials multiplied by each other, and each binomial is x + one of the numbers we found above. It looks like this: (x+1)(x+2). Remember that this only affects the left side; the right side stays the same.
In this case, we have -5 and 4, which will take the place of 1 and 2 in the example above.
Therefore, the factored form of x² - x - 20 = 0 is (x-5)(x+4) = 0.
The triangles are congruent by SSS and HL.
Triangles R S T and V W X are shown. Triangle R S T can be rotated about point S and then shifted down and to the left to form triangle V W X.
Which transformation(s) can be used to map △RST onto
△VWX?
Using translation concepts, the transformations that are used to map △RST onto △VWX are:
Rotation, then a translation.
What is the missing information?The two triangles are given at the end of the answer.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
Looking at the image, we have that:
The orientation of the triangle changed, hence it underwent a rotation.After the function underwent the rotation, it was moved up and right, then it underwent a translation.More can be learned about translation concepts at https://brainly.com/question/4521517
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A kite of area 252 m² has one diagonal of length 9 m. Find the length of the other diagonal
Answer:
The other diagonal of the kite is 56 meters
Step-by-step explanation:
To find the length of the other diagonal you find to know the formula for finding the area of a kite which is A = (p×q)/2. It is given that the area is 252m² and one diagonal is 9m.
Place your given numbers in the formula for the area of the kite. With your numbers given the formula is 252 = (9q)/2 or alternatively 252 = (9p)/2Multiply both sides by 2 the reason being is that we are trying to islolate the unknown variable (weather it is p or q) so we are doing the inverse operation. So you will have 252 × 2 = (9p)/2×2 or (9q)/2×2. At the end of this step it is 504 = 9q or 504 = 9pDivide by 9 on both sides remember that the point is to islolate the variable. 504/9 = 9q/9 or 504/9 = 9p/9. The final answer is that your unknown diagonal (whether it was q or p) is 56 mWrite a numerical expression for the verbal expression. eighteen divided by the sum of two and seven
The numerical expression for the verbal expression is 18 ÷ (2+7).
Given,
Verbal expression = Eighteen divide by the sum of two and seven
we know that ,
We can write any verbal expression to numerical expression by using playing with numbers.
Playing with numbers:
Playing with numbers involves activities like arranging the numbers, understanding , finding out whether a given number is a factor of another number or a multiple of another number, and understanding the properties of factors and multiples
Now, According to question
Eighteen divided by the sum of two and seven
18÷(2+7)
Therefore,
The numerical expression is 18÷(2+7).
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The Shah family's pancake recipe uses 2 teaspoons of baking powder for every
1
3
of a teaspoon of salt. How much baking powder would they need if they used 1 teaspoon of salt?
The baking powder that they would need if they used 1 teaspoon of salt will be illustrated will be 6 baking Powder.
How to illustrate the information?It should be noted that from the information given, the Shah family's pancake recipe uses 2 teaspoons of baking powder for every 1/3 of a teaspoon of salt.
Therefore, the baking powder that they would need if they used 1 teaspoon of salt will be illustrated thus:
= Pancake recipe ÷ Teaspoon
= 2 ÷ 1/3
= 2 × 3
= 6
Therefore, the baking powder that they would need if they used 1 teaspoon of salt will be illustrated will be 6 baking Powder.
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The difference of 7 and the product of 2 and a number.
which of these expressions are equal?
I. 4.86x0.01
II.48. 6x 0.1
III. 0.0486x100
IV.48.6x10
Answer:
II. 48.6×0.1
III. 0.0486×100
Step-by-step explanation:
48.6×0.1 = 4.86
0.0486×100 = 4.86
Answer:
ll and lll are equal.
Step-by-step explanation:
4.86x0.01 = 0.0486
48.6 x 0.1 = 4.86
0.0485 x 100 = 4.86
48.6 x 10 = 486
HELP...................................! !
Answer:
Your answer would be 3.075.
Step-by-step explanation:
15 - 6.8 = 8.2
8.2 - 5 1/8 = 3.075
--------------------------------
Hope this helps!
Have a great day and God bless! :)
Express this number in scientific notation.
0.00067
How do you regular divide
Answer:
These are dividend, divisor, quotient and remainder.
Step-by-step explanation:
Determine the first digit or set of digits your divisor will go into at least once.
Determine the maximum number of times your divisor will go into the said digit or digits.
Place the answer over the corresponding digit. For multiple digits, place it over the last digit.
Multiply the answer from above by your dividend.
Place the result under your dividend starting from the left most digit.
Subtract the result from your dividend. Only subtract the digits that line up. For instance, if you have a five digit dividend, but the result is only two digits, only subtract using the first two digits of your dividend.
Bring down the next digit of your dividend beside the result.
Repeat the process using the new set of digits. Each time, bring down the next digit of your dividend.
Write the equation of a line that passes through point (16,7) with slope 5/4 in point slope form
Answer: y = 5x/4 - 13
Step-by-step explanation:
y=mx+b
7=5/4 *16+b
7=5*16/4 +b
7=80/4+b
7=20+b
b=-13
y = 5x/4 - 13
A company designs a new water pitcher. They take a picture of the pitcher for their promotional materials. What is the approximate area filled by the water in the picture on the flyers? The picture shows the outline of a pitcher. The height of a pitcher's body is 12 in, and the height from neck to top is 4 in. The width of the bottom is 8 in, the neck is 3 in, and the top open is 5 in.
Answer:
32in2
Step-by-step explanation:
I cant find my answer help needed
Step-by-step explanation:
the domain is the interval or set of all valid x (input) values.
the range is the interval or set of all valid y (function result) values.
so, we see here, x goes from -2 to +2.
and y stays between -5 and -1.
the hole point at (-2, -1) means the point itself is not included. the full point (2, -1) means the point itself is included.
the domain is
-2 < x <= +2
"-2 < x" because (-2, -1) is not included.
"x <= +2" because (2, -1) is included.
the range is
-5 <= y <= -1
"y <= -1" because for the included point (2, -1) y can reach -1, even though (-2, -1) is excluded.
can someone answer 2 1/2 x 1 3/5 =
Answer both questions please [ brainliest ]
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1. The measure of an angle is 84°. The measure of its complementary angle is ___
degrees.
2. The measure of an angle is 29°. The measure of its supplementary angle is ___ degrees.
Elliot uses 3/8
pound of clay to make a charm for a necklace. How much clay does he use to make
Answer:
five thousand clay to school
write a function g whose graph is a reflection in the x axis of the graph of f(x)=|x|-5
please help
A function g whose graph is a reflection in the x axis of the graph of f(x) = |x| - 5 is g(x) = 5 - |x|
The question asks to find a function g, that is, g(x)
The graph of g(x) is a reflection in the x axis of the graph of f(x) = |x| - 5
Reflection of a function in the x-axis gives us
y = g(x) = - f(x)
=> g(x) = - ( |x| - 5 )
=> g(x) = - |x| + 5
=> g(x) = 5 - |x|
Therefore, using the concept of reflection of a function in x axis of the graph of the given function, we get a function g whose graph is a reflection in the x axis of the graph of f(x) = |x| - 5 as g(x) = 5 - |x|
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