Answer:
Therefore the equation dor nth term is,
[tex]a_{n} =a_{1} + (n-1)\times d[/tex] and
[tex]a_{30} =-18[/tex]
Step-by-step explanation:
Given:
Arithmetic Sequence as
11 , 10 , 9 , 8 , ..........
∴ First term = a₁ = 11
Second term = a₂ = 10
∴ Common Difference = d = a₂ - a₁ = 10 - 11 = -1
∴ d = -1
To Find:
[tex]a_{n} = ?\\and\\a_{30} = ?[/tex]
Solution:
An equation for the nth term of the arithmetic sequence is given by
[tex]a_{n} =a_{1} + (n-1)\times d[/tex]
Substitute n= 30 for [tex]a_{30}[/tex] and a₁ and d we get
[tex]a_{30} =11 + (30-1)\times -1\\\\a_{30} =11+29\times -1\\\\a_{30} =11-29\\\\a_{30} =-18\\\\\therefore a_{30} =-18\ \textrm{as required}[/tex]
Therefore,
[tex]a_{30} =-18[/tex]
The nth term of the given arithmetic sequence can be represented by the equation an = 12 - n. The 30th term of this sequence is -18.
Explanation:In order to write an equation for the nth term of an arithmetic sequence, we need to know the first term (a1) and the common difference (d). In the given arithmetic sequence 11, 10, 9, 8, ..., the first term a1 is 11 and the common difference d is -1 (because each term reduces by 1).
The general formula for the nth term (an) of an arithmetic sequence is: an = a1 + (n-1) * d. Substituting the values of a1 and d in the equation, we get: an = 11 + (n-1) * -1 = 12 - n.
To find a30, substitute n = 30 in the equation, we get a30 = 12 - 30 = -18.
Learn more about Arithmetic Sequence here:https://brainly.com/question/35880655
#SPJ11
How many triangles will there be in the 7th term of the following
sequence?
Δ, ΔΔΔ, ΔΔΔΔΔ..
Ο
Α. 19
Ο
Β. 22
Ο
C 16
D. 8
There are 13 triangles will be in the 7th term.
What is mean by Triangle?
A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
The sequence is,
Δ, ΔΔΔ, ΔΔΔΔΔ..
Now,
Number of triangles in sequence are;
⇒ 1 , 3 , 5, ...
Clearly, The sequence is in arithmetic sequence, with common difference = 3 - 1 = 2 and first term is 1.
Hence, The 7th term is find as;
⇒ T ₇ = a + (n - 1) d
⇒ T ₇ = 1 + (7 - 1) (2)
⇒ T ₇ = 1 + 6 x 2
⇒ T ₇ = 1 + 12
⇒ T ₇ = 13
Thus, There are 13 triangles will be in the 7th term.
Learn more about the triangle visit:
https://brainly.com/question/1058720
#SPJ2
Ed’s birthday is less than 16 days away.
(NEED HELP!!!! WILL GIVE BRAINLY)
Answer:
it is less than and equal to
Step-by-step explanation:
its > with a line under it
If the balance at the end of eight years on an investment of $230 that has been invested at a rate of 3% is $285.20, how much was the interest
Answer:
The interest that is obtained from that investment is $55.2
Step-by-step explanation:
If the balance at the end of eight years on an investment of $230 that has been invested at a rate of 3% is $285.20, so the principal of investment is $230 and the matured sum is $285.20.
Now, we know that Principal + Interest = Matured sum.
Hence, the interest that is obtained from that investment is $(285.2 - 230) = $55.2 (Answer)
Answer:
The interest credited after investment is $55.2
Step-by-step explanation:
Given as :
The investment principal amount = p = $230
The Amount after 8 years of investment = A = $285.20
The Time period for investment = 8 years
The rate of interest applied = r = 3%
Let The interest credited after investment = I
Now, According to question
From Compound Interest
Amount = Principal × [tex](1+\dfrac{\textrm rate}{100})^{\textrm time}[/tex]
And Interest = Amount - Principal
Or, I = A - p
Or, I = $285.20 - $230
∴ I = $55.2
So, The interest credited after investment = I = $55.2
Hence, The interest credited after investment is $55.2 Answer
capacity measures how much a liquid weighs
Answer: Im assuming this is a true or false question anyways the answer would be false if it is
Step-by-step explanation:
Find the number of pancakes Sandra can make in 20 minutes if she takes half an hour to prepare six pancakes at a constant rate
Answer: 4 pancakes
Step-by-step explanation: because 30min÷6pancakes=5
So, 20min÷5=4
Each lapel on a suit jacket is in the shape of a triangle two of the three angles of each triangle measures 47 and 68 what is the measure of the third angle
The measure of the third angle is 65°
Step-by-step explanation:
Each lapel on a suit jacket is in the shape of a triangle
Two of the three angles of each triangle measures 47 and 68We need to find the measure of the third angleIn a triangle:
∵ The sum of the measures of the interior angles = 180°
∵ The measure of one angle = 47°
∵ The measure of other angle = 68°
- Substitute the measures of the two angles in the rule above
∴ 47 + 68 + measure 3rd angle = 180°
- Add the like terms
∴ 115 + measure 3rd angle = 180°
- Subtract 115 from both sides
∴ measure 3rd angle = 65°
The measure of the third angle is 65°
Learn more:
You can learn more about the triangles in brainly.com/question/13013931
#LearnwithBrainly
Can anybody answer this for me please?
Answer:
1. f(2) = 6
2. Slope, m = [tex]$ \frac{7}{2} $[/tex]
Step-by-step explanation:
Problem 1:
Given f(x) = |3x|
To find f(2), substitute x = 2.
⇒ f(2) = |3(2)|
= |6|
= 6
Problem 2:
The given equation is: 2y = 7x + 8
The general equation of the line is: y = mx + c, where m is the slope of the line.
Therefore, we reduce the given equation to the general form of the line.
Dividing the given equation by 2, we get:
y = [tex]$ \frac{7}{2}x + \frac{8}{2} $[/tex]
[tex]$ \implies y = \frac{7}{2}x + 4 $[/tex]
Thus, slope, m = [tex]$ \frac{7}{2} $[/tex] which is the answer.
Problem 3:
Given with 14 gallons of gas, we can drive 392 miles.
The capacity of the tank if 14 gallons.
If 14 gallons can take us 392 miles, then 1 gallon of gas should take us: [tex]$ \frac{392}{14} $[/tex] miles.
= 28 miles/gallon of gas
Therefore, with 3.7 gallons of gas, we can travel 3.7 X 28 miles
= 103. 6 miles
Raji has 5/7 as many CDs as Megan. If Raji gives 1/10 of her CDs to Megan, what will be the ratio of the number of Raji’s CDs to Megan’s
Answer:
3:5
Step-by-step explanation:
Please see attached picture for full solution. ( Unit method)
Read the question and answer it below the question
Answer:
G
Step-by-step explanation:
G = -2
-2 is greater than -4, yet, less than 0
An arithmetic sequence has a first term of 3 and a fifth term of 31 what is it’s second term
Answer:10
Step-by-step explanation:
Adds 7 each time
31 - 3 = 28
Going from first term to fifth term is 4 increases.
28 ÷ 4 = 7
This means we have a common difference of 7.
Sequence is 3, 10, 17, 24, 31
plz help me fast thanks
Answer:
E
Step-by-step explanation:
There are 48 cards numbered from 1 to 48.
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48
Multiples of 8: 8, 16, 24, 32, 40, 48
Multiples of 6 and 8: 24, 48.
Hence,
Total number of cards = 48,
Number of cards which are multiples of 6 and 8 = 2
The probability that the number card is a multiple of both 6 and 8 is
[tex]P=\dfrac{2}{48}=\dfrac{1}{24}[/tex]
What is the maximum value of 4(x + 7)(2 - x), over all real numbers x?
Answer:
The maximum value of function is 81 .
Step-by-step explanation:
Given function as :
y = 4 (x + 7) (2 - x)
Now, The function can be written as
y = 4 (2 x - x² + 14 - 7 x)
y = 4 ( - x² - 5 x + 14)
y = - 4 x² - 20 x + 56
Now, For maximum value of function , differentiation of y with respect to x
[tex]\frac{\partial y}{\partial x}[/tex] = 0
Or, [tex]\frac{\partial ( - 4x^{2} - 20 x +56)}{\partial x}[/tex] = 0
Or, - 8 x - 20 = 0
Or, - 8 x = 20
∴ x = [tex]\dfrac{-20}{8}[/tex]
i.e x = [tex]\dfrac{-5}{2}[/tex]
Now, Putting the value of x in the given equation
y = - 4 ( [tex]\dfrac{-5}{2}[/tex])² - 20 ( [tex]\dfrac{-5}{2}[/tex]) + 56
Or, y = - 4 ([tex]\dfrac{25}{4}[/tex]) + 50 + 56
Or, y = - 25 + 50 + 56
∴ y = 81
So, The maximum value of function is 81
Hence,The maximum value of function is 81 . Answer
Ivan buys candy that costs $7 per pound. He will buy at most 9 pounds of candy. What are the possible amounts he will spend on candy?
Use c for the amount (in dollars) Ivan will spend on candy.
Write your answer as an inequality solved for c.
Answer: 7c ≤ 63
Ivan will buy at most 9 pounds of candy, which means that multiplying 9 by 7, the cost of the candy, will get your answer: 63. Plug these values into an inequality with a less than or equal to sign (≤) facing away from 63 and you're done!
The possible amounts Ivan will spend on candy can be represented as c ≤ 7.
Explanation:Let's denote the amount Ivan will spend on candy as c. The cost of candy is $7 per pound, and Ivan will buy at most 9 pounds of candy. Therefore, the maximum amount he could spend on candy is 9 pounds multiplied by $7 per pound, which is 9c ≤ 63.
Since we are looking for possible amounts, we can rewrite this inequality as c ≤ 63/9, which simplifies to c ≤ 7.
So, the possible amounts Ivan will spend on candy are values less than or equal to $7.
Learn more about Inequality here:https://brainly.com/question/40505701
#SPJ3
Solve for x: 2/3 = 8/x+6
A)-6
B)6
C)9
D)12
Answer:
Step-by-step explanation:
2/3 = 8/x+6
2 * ( x+6) = 8 * 3
2x + 2 * 6 = 24
2x + 12 = 24
2x = 24 -12
2x = 12
x = 12/2
x = 6
Answer:
I took the test and its B
Step-by-step explanation:
Also the person above me has got it covered so im gonna avoid confusion and not explain
2/7 with an exponent of 3
Answer:
Step-by-step explanation:
(2/7)^3=8/343
Answer:
(2/7)^3
8/343
Step-by-step explanation:
(2/7)^3=2^3/7^3
=8/343
Write the equation of the line 3x - 4y = 20 in slope-intercept form.
Answer:
y=3/4x-5
Step-by-step explanation:
3x-4y=20
4y=3x-20
y=3/4x-20/4
y=3/4x-5
9x + 2(3x + 7) = -31
x=-3
Step-by-step explanation:Solve:9x+2(3x+7)= -31
multiply the "3x" and the "7" by two (distributive property)
[="6x" and "7"]
add the "9x" and the "6x" [="15x"]
subtract "14" from"-31" [= "-45"]
divide "15x" from "-45"
="-3"
Check:put the "-3" in for "x"
multiply 9(-3) [=-27]
multiply 3(-3) [=-9]
distribute the 2 to the "-9" and the "7" [="-18" and "14"]
add the "-18" and "14" [=-4]
add the "-27" and the "-4"
=-31 ✓
What it looks like:Solve:9x+2(3x)+2(7)= -31
9x+6x+14= -31
15x+14= -31
-14 -14
15x= -45
/15= /15
x= -3
Check:9x+2(3x+7)= -31
9(-3)+2(3(-3)+7= -31
-27+2(-9+7)= -31
-27+(2(-9)+2(7))= -31
-27+(-18+14)= -31
-27+ (-4)= -31
-31= -31✓
5x-2 \ 3 = 6 what does x equal
If you're talking the equation [tex]\frac{5x-2}{3} =6[/tex], then:
[tex]\frac{5x-2}{3} =6[/tex]
multiply [tex]3[/tex] onto both sides.[tex]5x-2=18[/tex]
add [tex]2[/tex] to both sides.[tex]5x=20[/tex]
divide both sides by 5[tex]x=4[/tex]
If you're talking about the equation [tex]5x-\frac{2}{3} =6[/tex], then:
[tex]5x-\frac{2}{3} =6[/tex]
add [tex]\frac{2}{3}[/tex] to each side[tex]5x = 6+\frac{2}{3}[/tex]
divide both sides by [tex]5[/tex].[tex]x=\frac{6}{5} +\frac{2}{15}[/tex]
find the common denominator of [tex]\frac{6}{5}[/tex] and [tex]\frac{2}{15}[/tex]. In this case its [tex]15[/tex], so multiply both the numerator and denominator of [tex]\frac{6}{5}[/tex] by [tex]3[/tex].[tex]x=\frac{18}{15} +\frac{2}{15}[/tex]
Now that there is a common denominator, add the two terms together.[tex]x=\frac{20}{15} = \frac{4}{3} = 1\frac{1}{3}[/tex]
7. The startup cost for a boutique is $15,000, and each floral arrangement costs $17 for the boutique to make. If each arrangement is then sold for $25, after how many arrangements does the boutique break even?
Answer:
1875 arrangements
Step-by-step explanation:
Break-Even is the point when costs are equal to profit.
The cost is 15,000
We need to cover this up with the profit we get from sales.
Each arrangement is 17 (cost) and is sold for 25, so the profit from each arrangement is:
25 - 17 = 8
So, with each arrangement sale, we make profit of $8. How many of these we need to sell in order to break even (in order to make 15,000)??
We simply divide this amount (15,000) by the profit we make from each arrangement ($8), so that would be:
Number of Arrangements Needed to Break-Even = 15,000/8 = 1875
After 1875 arrangements, the boutique breaks even.
ABCD is a parallelogram if side ab=4x+7 and bc=8x-12 and side cd=7x-14 find the value of x
Answer:
Therefore the value of 'x' is 7.
Step-by-step explanation:
Given:
[] ABCD is a Parallelogram
AB = 4x+ 7
BC = 8x - 12
CD = 7x - 14
To Find:
x = ?
Solution:
[] ABCD is a Parallelogram ..............Given:
Opposite sides of a Parallelogram are Equal
side AB and CD are the opposite sides of the parallelogram.
∴ AB = CD
On substituting the values we get
[tex]4x+7=7x-14\\\\7x-4x=7+14\\\\3x=21\\\\x=\dfrac{21}{3} =7\\\\\therefore x =7[/tex]
Therefore the value of 'x' is 7.
the difference of 2 2/3 and a number n divided by -2 1/5 equal to -13 / 33 find the value of n.
The value of n is [tex]1\frac{4}{5}[/tex].
Step-by-step explanation:
Given,
[tex](2\frac{2}{3}-n)/-2\frac{1}{5}=\frac{-13}{33}[/tex]
Writing the fractions in simplified form;
[tex](\frac{8}{3}-n)/\frac{-11}{5}=\frac{-13}{33}[/tex]
Taking LCM on left hand side;
[tex](\frac{8-3n}{3})/\frac{-11}{5}=\frac{-13}{33}\\[/tex]
[tex]\frac{8-3n}{3}*\frac{-5}{11}=\frac{-13}{33}\\\\\frac{-40+15n}{33}=\frac{-13}{33}\\\\[/tex]
Multiplying both sides by 33
[tex]33*(\frac{-40+15n}{33})=\frac{-13}{33}*33\\-40+15n=-13\\15n=-13+40\\15n=27[/tex]
Dividing both sides by 15
[tex]\frac{15n}{15}=\frac{27}{15}\\n=\frac{9}{5}\\n=1\frac{4}{5}[/tex]
The value of n is [tex]1\frac{4}{5}[/tex].
Keywords: fraction, division
Learn more about fractions at:
brainly.com/question/10541435brainly.com/question/10666510#LearnwithBrainly
2) Brian purchased pens for 75 cents each and pencils for 40 cents each he bought total of 22 writing utensils for $11.95. How many pencils did he buy?
This is due this Wednesday it’s needs to be done ASAP!! It needs to be shown full work help me!!!
Answer:
13 pencils.
Step-by-step explanation:
Let x be the pens and y be the pencils
Given:
Brian purchased pens for 75 cents each and pencils for 40 cents each he bought total of 22 writing utensils for $11.95.
Total pens and pencils is 22
So, [tex]x+y=22[/tex]----------------(1)
And he bought all utensils for $11.95. and each pen for 75 cents and pencils for 40 cents.
[tex]0.75x+0.40y=11.95[/tex]------------(2)
solve equation 1 and equation 2 for x and y.
From equation 1.
[tex]x+y=22[/tex]
[tex]y=22-x[/tex]----------------(3)
put y value in equation 2.
[tex]0.75x+0.4(22-x)=11.95[/tex]
[tex]0.75x+0.4\times 22-0.4x=11.95[/tex]
[tex]0.75x+8.8-0.4x=11.95[/tex]
[tex]0.75x-0.4x=11.95-8.8[/tex]
[tex]0.35x=3.15[/tex]
[tex]x=\frac{3.15}{0.35}[/tex]
[tex]x=9[/tex]
Now substitute x value in equation 3.
[tex]y=22-9[/tex]
[tex]y=13[/tex]
So, he buy 13 pencils.
Which graph represents y=^3 square x+2?
Answer:
File is given in attachements .
Step-by-step explanation:
[tex]y = \sqrt[3]{x} + 2[/tex] will pass through (0,2) and (-8,0) . Its shape will be as shown in the graph.
Answer:
Graph C
Step-by-step explanation:
Find the product for 2(2n + 3)
To find the product for 2(2n + 3), use the distributive property to multiply 2 with each term inside the parentheses, resulting in 4n + 6.
Explanation:The question asks to find the product for 2(2n + 3). To solve this, we need to use the distributive property of multiplication over addition, which states that a(b + c) = ab + ac. Applying this rule to the given expression, we multiply 2 with each term inside the parentheses.
First, multiply 2 by 2n to get 4n. Next, multiply 2 by 3 to get 6. Therefore, the expression simplifies to 4n + 6.
We have successfully used the distributive property to find that the product of 2(2n + 3) is 4n + 6.
In ordered pair a solution [tex]y\geq x-5?[/tex]
Answer:
The graph is plotted below.
One ordered pair as solution is (0, 0).
Step-by-step explanation:
Given:
The inequality is given as:
[tex]y\geq x-5[/tex]
In order to plot it, we first replace '≥' by '=' sign. This gives,
[tex]y = x-5[/tex]
Now, we plot the above line. For that, we need the x and y intercepts.
At x-intercept, y = 0. So,
[tex]0=x-5\\x=5[/tex]
The point is (5, 0)
At y-intercept, x = 0. So,
[tex]y=0-5\\y=-5[/tex]
The point is (0, -5)
Now, plot these two points and draw a line passing through these two points. The graph is shown below.
Now, replace '=' by '≥' sign. Since, 'y' is greater than equal to 'x - 5'. So, the solution region is above the given including the values on the line.
Therefore, any ordered pair in the solution region is a solution of the given inequality. From the graph, one such ordered pair is (0, 0).
This can be verified from the inequality also.
[tex]0\geq 0-5\\0\geq -5(True)[/tex]
So, one ordered pair is (0, 0).
What is the solution set of {x | x > -5} {x | x < 5}?
all numbers except -5 and 5
the numbers between -5 and 5
the empty set
all real numbers
What is the solution set of {x | x < -5} ∩ {x | x > 5}?
all numbers less than -5 and greater than 5
the numbers between -5 and 5
the empty set
all real numbers
Answer:
The numbers between -5 and 5
Step-by-step explanation:
Intersection of Intervals
Given the intervals A,B,C,etc. The intersection of them all is the set of all values that are common to all the intervals.
We must find
[tex]\{x | x > -5\} \bigcap \ \{x | x < 5\}[/tex]
which is the intersection between the intervals x > -5 and x < 5. The intersection represents all the numbers greater than -5 and less than 5. It can also be said The numbers between -5 and 5 (non inclusive), third option
Answer: The answer is D all real numbers
If Tian has 56 paper clips. He gives 3/4 of them to joe. Joe gives 2/7 of what he receives to Rahul. How many paper clips does Rahul get?
Rahul gets 12 paper clips.
Step-by-step explanation:
Given,
Paper clips Tian have = 56
He gives 3/4 of them to joe.
Joe gets = [tex]\frac{3}{4}*56=\frac{168}{4}[/tex]
Joe gets = 42 paper clips
He given 2/7 of received to Rahul.
Rahul gets = [tex]\frac{2}{7}*42=\frac{84}{7}[/tex]
Rahul gets = 12 paper clips
Rahul gets 12 paper clips.
Keywords: fraction, division
Learn more about fractions at:
brainly.com/question/1388658brainly.com/question/1414350#LearnwithBrainly
Space provided.
1. Find the equation of the line that is modeled by the values in the table shown below.
Part I: Determine the slope of the line. Show the work you did to find the slope. (6 points)
Answer:
1) The slope of the line is [tex]m=\frac{5}{2}[/tex] or [tex]m=2.5[/tex]
2) The equation of the line is [tex]y=2.5x-4[/tex]
Step-by-step explanation:
step 1
Find the slope
we know that
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
take any two points from the values in the table
(2,1) and (4,6)
substitute the values in the formula
[tex]m=\frac{6-1}{4-2}[/tex]
[tex]m=\frac{5}{2}[/tex]
[tex]m=2.5[/tex]
step 2
Find the equation of the line in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=2.5[/tex]
[tex]point\ (2,1)[/tex]
substitute
[tex]y-1=2.5(x-2)[/tex]
Convert to slope intercept form
isolate the variable y
[tex]y-1=2.5x-5[/tex]
[tex]y=2.5x-5+1[/tex]
[tex]y=2.5x-4[/tex]
Tamara has 14 red gel pens and 16 snap bracelets for goodie bags
Answer:
ok??? whats the question?
Step-by-step explanation:
Answer:
question???
Step-by-step explanation:
Which equation shows y=-1/2x +4 is in standard form?
The equation in standard form is x + 2y = 8
Solution:
Given that we have to write the given equation in standard form
The equation given is:
[tex]y = \frac{-1}{2}x + 4[/tex]
The standard form of an equation is Ax + By = C
In this kind of equation, x and y are variables and A, B, and C are integers. When we shift the variable terms to the left side of the equation and everything else to the right side, we get the standard form.
[tex]y = \frac{-1}{2}x + 4\\\\y = \frac{-x}{2} + 4\\\\y =\frac{-x + 8}{2}\\\\2y = -x + 8[/tex]
Keep the variables on one side and constant term on other side
x + 2y = 8
Thus the above equation is in standard form of Ax + By = C
Answer:
x+2y=8
Step-by-step explanation: