Answer:
The equation for the nth term of the given arithmetic sequence is: [tex]\mathbf{a_n=13n+22}[/tex]
Step-by-step explanation:
We need to write an equation for the nth term of the arithmetic sequence:
15,28,41 ....
The equation for arithmetic sequence is: [tex]a_n=a_1+(n-1)d[/tex]
Where [tex]a_n[/tex] is the nth term, [tex]a_1[/tex] is first term and d is common difference
In the given sequence we have:
a₁ = 15
a₂ = 28
We can find common difference using the formula:
[tex]a_n=a_1+(n-1)d\\Put\: n=2, a_2=28\: and\: a_1=15\\a_2=a_1+(2-1)d\\28=15+d\\d=28-15\\d=13[/tex]
So, the common difference d is 13
Now, equation for nth term will be:
[tex]a_n=a_1+(n-1)d\\Put\:a_1=15, d=13\\a_n=15+(n-1)13\\Solving:\\a_n=15+13n-13\\a_n=13n+2[/tex]
So, the equation for the nth term of the given arithmetic sequence is: [tex]\mathbf{a_n=13n+22}[/tex]
where n=1,2,3..
i am thinking of a number x. What algebraic expression represents "eight less than three times this number "?
Answer:
3x-8
Step-by-step explanation:
3x is three times the number, -8 is 8 less.
3x+8=35 Show your work
Answer:
x=9
Step-by-step explanation:
So first subtract 8 on both Sides
3x+8-8=35-8
3x=27
Now divide 3 on both sides to isolate the variable x
x=9
So x=9
Answer:
so to do this you need to subtract 8 from 35 to get 27 now do 27 divide by 3 to get 9
3x+8=35
3x=35 - 8 = 27
3x = 27
3x divided by 27 = 9
Step-by-step explanation:
Compote table please help me please?
A certain ride at an amusement park requires that children be at least 50 inches tall but no more that 65 inches tall. Which of the following absolute values best represents this restriction, where h represents height?
Answer:
|h-57.5| less than or equal to 7.5
Step-by-step explanation:
Since the question states that a child must be 50 and 65 inches, plug in values that are within this range and determine which answer choice gives a TRUE relationship. Choose 60 for h.
Also, I just did it.
Simplify: [-5]+2 answer please
Answer:
I think it's -3
hope it's right:)
Step-by-step explanation:
[tex] \sf{ \huge{( - 5) + 2}}[/tex]
While adding or subtracting integers with unlike signs , subtract and keep the sign of the higher integer. In our case , subtract 2 from 5 and keep the sign of higher integer i.e ( - )
⟿ [tex] \sf{ \huge{ \boxed{ { - 3}}}}[/tex]
Hope I helped ! ♡
Have a wonderful day / night ! ツ
▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁
the height of a shed is 6cm. a ladder leans agaisnt the shed with its base 4.5 m away, and its top just reaching the roof. what is the length of the ladder?
Answer:
4.5m
Step-by-step explanation:
The set up is a right angles triangle
Height of the shed = opposite side = 6cm
Distance of the ladder from the shed = adjacent = 4.5m
Lenght of the ladder = Hypotenuse = x
Using pythegoras theorem to find the length of the ladder
hyp² = opp²+adj²
hyp² = 0.06² + 4.5²
hyp²= 0.0036+20.25
hyp² = 20.2536
hyp = √20.2536
hyp = 4.50m
Hence the length of the ladder is 4.5m
which expression is equivalent to 3(7v)
The Corner Cafe recently served 8 pastries, including 4 blueberry scones. Considering this data, how many of the next 18 pastries served should you expect to be blueberry scones? blueberry scones
Answer:
9
Step-by-step explanation:
because half of the 8 pastries served were blueberry. so you would divide 18 by 2
The graph of a system of linear equations with the same slope and the same y-intercepts will have no solutions.
Always
Sometimes
Never
Answer:
Never
Step-by-step explanation:
If two equations have the same slopes and the same y-intercepts they are equivalent to each other
Here's why:
The formula for a linear equation is y= mx +b
b= y- intercept
m= slope
m and b are only variable that have to be replaced by a number for the equation to be complete
Therefore, when m and b (or the slope and the y-intercept) of both equations are the same, the two equations are the same
The answer would be allrealnumbers, not nosolutions
Hope this helps!!!
Charles is planning on driving his car to the family reunion. The distance to
the meeting place is 1243 miles. If his car gets 30 mpg, how many gallons of
gas will he need?
A. 41.4
B. 51.4
C. 31.4
D. 21.4
Answer: 41.4
Step-by-step explanation:
1243/30=41.4
plz help need this! pic in bottom!
Answer:
Step-by-step explanation:
13d + 8 = -1
subtract 8 from both sides
13d = -9
d = -9/13
either keep it in fraction form or if you divide it out it is -0.6923
Potato salad can be purchased at the grocery store for $2.58 per pound. If Michael wants to buy 2.5 pounds of potato salad, how much will it cost?
Answer: $6.45
Step-by-step explanation: Since 1 pound is $2.58, and we need to find out how much is 2.5 pounds, we can just multiply 2.58 by 2.5. Should be simple for you. Hope this helps. :)
Explain how you can use multiplication to solve a division problem.
Answer:Inverse operation
Step-by-step explanation: an example is 5 x 5. That equals 25 so take 5 and divide that by 5. Inverse operation is important.
For example, Emily received a 67 on her first economics exam, which counts for 20% of her grade; an 84 on her second exam, which counts for 30% of her grade; and a 78 on her third exam, which counts for 50% of her grade. What is her weighted average in the class
Answer:
77.6
Step-by-step explanation:
Given the data:
Weighting :
First exam = 20% ; second exam = 30% ; third exam = 50%
Scores :
First exam = 67 ; second exam = 84 ; third exam = 78
Weighted Average :
Σ(Weight * Score)
Σ[(0.2 * 67) + (0.3 * 84) + (0.5 * 78)]
13.4 + 25.2 + 39
= 77.6
Based on the weights assigned to these grades, Emily's weighted average in the class would be 77.6 marks.
Emily's weighted average= ∑ (Percentage of grade x Score in exam)
Solving gives:
= (20% x 67) + ( 30 % x 84) + (50% x 78)
= 13.4 + 25.2 + 39
= 77.6
Emily's weighted average is 77.6 marks.
Find out more on weighted average at https://brainly.com/question/14432034.
Add the two expressions.
−4.2x+3 and 2.5x−6
The rectangle shown has a perimeter of 84 cm and the given area. Its length is 6 more than 5 times its width. Write and solve a system of equations to find the dimensions of the rectangle.
Is the graph proportional or nonproportional number of chores and age
Answer:
where is the graph??
Step-by-step explanation:
1. A family eats at a restaurant. The bill is $42. They have a coupon that gives them 15% off
their meal. The family then leaves a 20% tip.
a. How much did the family spend on the meal after the coupon?
b. How much did the family spend on the meal in total?
[tex]42 - 42 \times 15\%[/tex]
[tex] =42 - 42 \times \frac{15}{100} [/tex]
[tex] =42 - 21 \times \frac{15}{50} [/tex]
[tex] =42 - \frac{315}{50} [/tex]
[tex] = 42 - 6 \: \frac{15}{50} [/tex]
[tex] = 41 \: \frac{50}{50} - 6 \: \frac{15}{50} [/tex]
[tex] = 35 \: \frac{35}{50} [/tex]
[tex] = 35.70[/tex]
Answer:The family did spend $35.70 on the meal after the coupon
b.Solution:[tex]35.70 + 42 \times 20\%[/tex]
[tex] = 35.70 + 42 \times 0.2[/tex]
[tex] = 35.70 + 8.4[/tex]
[tex] = 44.10[/tex]
Answer:The family did spend $44.10 on the meal in total.
#CarryOnLearning
#AnswerForTrees
#BrainlyBookSmart
First person to answer will get 100 points & Brainliest!
Answer:
heyyyyyy
Step-by-step explanation:
Find the slope and the y-intercept of the line.
y=-2
5
Ex+6
slope:
.
08
Х
$
y-intercept: 0
Answer:
Slope = -⁵/2
y-intercept = 6
Step-by-step explanation:
The equation, [tex] y = -\frac{5}{2}x + 6 [/tex], is given in the slope-intercept form, y = mx + b
Where:
m = slope
b = y-intercept
Therefore:
Slope of the equation = -⁵/2
y-intercept if the equation = 6
what is different of the four shapes?
Answer:
It has only 1 pair of parallel sides.
Step-by-step explanation:
Answer:
It has only 1 pair of parallel sides
Step-by-step explanation:
What is the x-intercept of the following equation? 4x + 2y = 12
Answer:
3
Step-by-step explanation:
Carol had a previous balance of $557.83 in her checking account. She deposited checks
totaling $882.84, made cash withdrawals of $325.00, and wrote checks totaling
$617.77 that were paid by the bank. She also earned interest of $1.15. What is her
present balance?
(Present Balance = Previous Balance + Deposits - Withdrawals - Service Charges/Fees
+ Interest)
c) $496.75
b) $499.05
a) $2.384.59
d) $1.149.05
Answer:
x^2-4/7x-12/49=0
x= 6/7 and -2/7
Step-by-step explanation:
Jodie bought a refrigerator on sale for 35% off the original price, for $97. What was the price of the refrigerator before the sale?
$97 = (Original Price) - (35% of Original Price)
$97 = (Original Price) - (0.35 of Original Price)
$97 = (1 - 0.35) of (Original Price)
$97 = (0.65) of (Original Price)
$97 = 0.65 · (Original Price)
Divide each side by 0.65 .
$97/0.65 = Original Price
$149.23 = Original Price
What word describes the slopes of the line
Answer:
Positive
Step-by-step explanation:
There are a couple ways we can go about this.
First, we can see that as x increases, so does y, so that means its positive
For perspective, if x is the amount of time and y is the number of sales, we can see that the sales are going up and not going down or staying at the same place
If you wanna check your work on that, you can plot two points and find the slope using y1-y1/x1-x2 and the slope will be positive.
We can also use the process of elimination, we know it can't be zero because it's not a straight, horizontal line and we know its not undefined because it isn't a straight vertical line, so it's between negative and positive, and since the line is going up, that means that it's positive.
The coordinates of the vertices of △XYZ are X(−5, 5), Y(−3, −2), and Z(4, 0). The slope of XZ is __, the slope of YZ is __, and the slope of XY is __. △XYZ __ a right triangle because ____________.
-7/2 -5/9 -2/7 2/7 9/5 is is not no two of these slopes have a product of -1 two of these problems have a product of -1
Answer:
Slope of XZ = -5/9
Slope of YZ = 2/7
Slope of XY = -7/2
Step-by-step explanation:
Slope is expressed as;
m = y2-y1/x2-x1
For XZ
X(−5, 5), and Z(4, 0)
Slope of XZ = 0-5/4-(-5)
Slope of XZ = -5/4+5
Slope of XZ = -5/9
For YZ
Y(−3, −2), and Z(4, 0).
Slope of YZ = 0-(-2)/4-(-3)
Slope of YZ = 2/4+3
Slope of YZ = 2/7
For XY
X(−5, 5), Y(−3, −2)
Slope of XY = -2-5/-3-(-5)
Slope of XY = -7/-3+5
Slope of XY = -7/2
For two lines to be perpendicular, the product of their slope must be -1
Taking the product of XY and YZ
mXY * mYZ = -7/2 * 2/7
mXY * mYZ = -1
since the product of mXY and mYZ is -1. this shows that line XY is perpendicular to YZ and showing that the triangle XYZ is right triangle
Oceanside Bike Rental Shop charges a 15 dollar fixed fee plus 9 dollars an hour for renting a bike. Dan paid 69 dollars to rent a bike. Which equation when solved would show how many hours the bike was rentented? Let h = hours
Answer:
Step-by-step explanation:
Dan paid 69 divided by 9 = H - 15
2.
The PE teacher is ordering equipment for the next school year. There are 156 students. She needs enough basketballs so that there is 1 basketball for every 12 students. How many basketballs does she need to order?
a.
312 basketballs
c. HELP PLSSSS
13 basketballs
b.
12 basketballs
d.
11
Answer:
13 basketballs
Step-by-step explanation:
Probability Questions Help is needed plzzzzzzzzzz
Answer: 0.0049 hope this is right
Melanie is looking for a loan. She is willing to pay no more than an effective rate of 9.955% annually. Which, if any, of the following loans meet Melanie’s criteria?
Loan A: 9.265% nominal rate, compounded weekly
Loan B: 9.442% nominal rate, compounded monthly
Loan C: 9.719% nominal rate, compounded quarterly
a.
B only
b.
A and C
c.
A and B
d.
None of these fit Melanie’s criteria.
Answer:
The correct answer is C.
Step-by-step explanation:
Giving the following information:
Loan A: 9.265% nominal rate, compounded weekly
Loan B: 9.442% nominal rate, compounded monthly
Loan C: 9.719% nominal rate, compounded quarterly
To calculate the effective annual rate, we need to use the following formula:
Effective annual rate= [(1+i)^n] - 1
Loan A:
i= 0.09265/52= 0.001782
Effective annual rate= [(1.001782^52) - 1]
Effective annual rate= 0.097 = 9.7%
Loan B:
i= 0.09442/12= 0.007868
Effective annual rate= [(1.007868^12) - 1]
Effective annual rate= 0.0986 = 9.86%
Loan C:
i= 0.09719/4= 0.02439
Effective annual rate= [(1.02439^4) - 1]
Effective annual rate= 10.11%
Answer:
c
Step-by-step explanation: