Answer:
The first term of the sequence is -8.95 with a common difference of 2.1.
The sequence is:
-8.95, -6.85, -4.75, -2.65...
Step-by-step explanation:
We are given that the sum of the first ten terms of a linear sequence is 5, and the sum of the next ten terms is 215.
And we want to find the sequence.
Recall that the sum of an A.P. is given by:
S = k / 2 ( a + xk)
Where a is the first term, k is the number of terms, and x_k is the last term.
We can represent our term values with the direct formula:
Xn = a + d (n-1)
Where the first term, x₁ = a.
The sum of the first ten terms is 5. Hence, S = 5, k = 10, a = x₁ and x_k = x₁₀:
(5) = 10/2 (a+xk)
5 = 5(a+(a+9d))
2a + 9d = 1
The sum of the next ten terms (that is, from x₁₁ to x₂₀) is 215. Hence, S = 215 when k = 10, a = x₁₁, and x_k = x₂₀:
(215) = (10)/2 (a + xk)
215 = 5((a+d(11-1))+(a+d(20-1)))
2a + 29d = 43
This yields a system of equations:
[tex]\left \{ {{2a+9d=1} \atop {2a+29d=43}} \right.[/tex]
Solve:
(2a + 9d) + (-2a - 29d) = (1) + (-43)
-20d = -42
d = 2.1
Consequently:
a = 1/2(1-9d)
= 1/2(1-9(2.1))
= -8.95
In conclusion, the first term of the sequence is -8.95 with a common difference of 2.1.
The sequence is:
-8.95, -6.85, -4.75, -2.65...
need helps plsssssssssssssss
Answer:
64
Step-by-step explanation:
4^3 is just 4*4*4
so 4*4=16
and 16*4=64
TADAAAAAAAAAA
Find the quotient. Write the answer in the simplest form.
58÷34
Answer:
1.70588235294
Step-by-step explanation:
i think
Answer:
1.70
Step-by-step explanation:
Evaluate [tex]\frac{bd}{a}[/tex] + c if a=−2a=-2 , b=3b=3 , c=−12c=-12 , and d=−4
Answer:
{a,c,d,b} = {49/16,29/16,2,-31/48}
Step-by-step explanation:
[1] 3a + c - 4d = 3
[2] -4a + 4c + d = -3
[3] -a - 2d + 3b = -9
[4] - d = -2
// Solve equation [4] for the variable d
[4] d = 2
// Plug this in for variable d in equation [1]
[1] 3a + c - 4•(2) = 3
[1] 3a + c = 11
// Plug this in for variable d in equation [2]
[2] -4a + 4c + (2) = -3
[2] -4a + 4c = -5
// Plug this in for variable d in equation [3]
[3] -a - 2•(2) + 3b = -9
[3] -a + 3b = -5
// Solve equation [1] for the variable c
[1] c = -3a + 11
// Plug this in for variable c in equation [2]
[2] -4a + 4•(-3a+11) = -5
[2] -16a = -49
// Solve equation [2] for the variable a
[2] 16a = 49
[2] a = 49/16
// Plug this in for variable a in equation [3]
[3] -(49/16) + 3b = -5
[3] 3b = -31/16
[3] 48b = -31
// Solve equation [3] for the variable b
[3] 48b = - 31
[3] b = - 31/48
// By now we know this much :
a = 49/16
c = -3a+11
d = 2
b = -31/48
// Use the a value to solve for c
c = -3(49/16)+11 = 29/16
Step-by-step explanation:
so bd/a+c= 3×(-4)/-2 +(-12)= -12/-2+(-12)=6+(-12)=6-12=-6
so the answer is -6
Select the values that make the inequality n > 1 true.
(Numbers written in order from least to greatest going across.)
what is the eqausion for 45 to 78
Answer:
23?
Step-by-step explanation:
78 minus 45 equals 23
This is the only reasonable answer I can decipher from your question.
make v the subject of the formula
[tex]T =\dfrac 5{V+1}\\\\\\\implies VT+T = 5\\\\\implies VT = 5-T\\\\\implies V =\dfrac{5-T}T[/tex]
Step-by-step explanation:
One way we can make V the subject of the formulas by rearranging the terms mathematically to get V on one side of the equation and the other terms on the other side:
since T = 5 ÷ (V + 1) [multiply both sides by (V+1)]
T (V + 1) = 5 [divide both sides by T]
(V + 1) = 5 ÷ T [subtract 1 from both sides]
V = (5 ÷ T) - 1 OR [tex]V = \frac{5}{T} - 1[/tex]
If we want the RHS with over a single denominator we can write it as
V = (5 ÷ T) - (T ÷ T) [rewrite 1 in terms of T (T/T)]
V = (5 - T) ÷ T OR [tex]V = \frac{5 - T}{T}[/tex]
What is the slope of the line shown on the graph to the right?
Vanessa walks her puppy 12 of a miles in 20 minutes. How far does she walk her puppy in 1 hour?
Show work. (Type answer in word form)
Answer:
thirty-six of a miles or [tex]36[/tex] miles of a miles <--- I didn't know if you meant regular miles
Step-by-step explanation:
We can convert 1 hour to 60 minutes
[tex]60\div20=3[/tex]
Since it is [tex]3[/tex] [tex]times[/tex] the time and we assume her rate is consistent we multiply 3 by 12
[tex]3\cdot12=36[/tex] of a miles
thirty-six of a miles
Brainliest please :)
Answer:
Vanessa walks her puppy for 36 miles in 1 hour.
Step-by-step explanation:
She walks 12 miles in 20 minutes
1 hour = 60 minutes
There are 3 - 20 minute periods so she walks her puppy 12(3) miles, or 36 miles
-Chetan K
How many students read in 15 minutes between 8am and 9am
Find the slope of the line y=5x+4
=
5
x
+
4
Answer:
5 is the slope of the line
Answer:
slope = 5
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 5x + 4 ← is in slope- intercept form
with slope m = 5
a touch of italy has a special offer on lunch pizza:$4.00 for each slide and they charge $2.00 to deliver.write an expression to determine how much it would cost to buy s slices of pizza
Answer:
Step-by-step explanation:
4 x 2 = 8
there fore, it would take 8 $ to buy 5 slices excluding the delvry.
so, 8 x 2 = 16
16$ total
pls give me brainliest
The scale factor from A DEF to A ABC is
6
5
ООО
4.5
Answer:
Between the edges of the first two triangles there is a ratio. To find this ratio, you need to ratio one edge of a small triangle to one edge of a large triangle. So 5/30=6/36=8/48=1/5. The ratio we want to find is 1/5 or 5.
Evaluate. (4/5)^3this is a fraction, and an exponent, not 4 divided by 5, please get answer in quickly.
Answer:
[tex]\frac{64}{125}[/tex]
Step-by-step explanation:
[tex]\frac{4}{5} ^{3}[/tex]
To solve this you would cube the numerator and then the denominator:
4³ = 645³ = 125The answer is [tex]\frac{64}{125}[/tex]
Hope this helps!
arrange the cards into three pairs of the same total.
-7,-5,-3,3,1,-1
the answer is ( -7; 3) (-5; 1) ( -3;-1)
ok done. Thank to me :>
Mitchell solves the following system of equations using the elimination method.
−2x+3y=6
4x−6y=−6
He chooses to eliminate the variable x.
Which statement correctly describes his process and solution?
Answer:
Mitchell multiplies −2x+3y=6 by 2 and then adds the equations. He finds the result is a contradiction, so there is no solution.
Step-by-step explanation:
HELP ME!! Move the terms to their corresponding categories. Either Domain or Range.
Step-by-step explanation and answer:
To understand this problem, you must first understand the definition of domain and range. Domain is all possible x values (possible input), and range is all possible y values (possible output). Based on this, we can now sort the terms as the following:
Domain
Independent variableInput valueX-valueRange
Dependent variableY-valueOutput valueHope this helps!!
a Members of a soccer team raised $1530.50 to go to a tournament. They rented a bus for $1164.50 and budgeted $30.50 per player for meals. Write and solve an equation which can be used to determine x, the number of players the team can bring to the tournament.
The number of players that can be taken to the tournament is 12 players.
The equation that can be used to represent the total amount spent by the soccer team is:
Total amount spent = cost of rented bus + (cost per meal x total number of players)
$1530.50 = $1164.50 + $30.50x
Where: x = total number of player
In order to determine the value of x, the following steps would be taken:
Combine similar terms
$1530.50 - $1164.50 = $30.50x
$366 = $30.50x
Divide both sides of the equation by 30.50
x = $366 / $30.50
x = 12 players
A similar question was answered here: https://brainly.com/question/22358515
identify if the graph represents quadratic function
Answer:
Graph #2 for sure, both axis are linear and the curve is a parabola all right.
On graph #1: I can't for the life of me read the units on the Y axis, so you have to check: if they're going 2000 4000 6000, then that is a parabola as wel. If they're increasing esponentially, ie 2000 4000 8000, then one of the two axis is logarithmical and the curve is no longer quadratic.
Sketch the graph of each line by identifying the x-and y-intercepts.
Answer:
Slope: 5/3, Y-intercept: (0,-3)
Step-by-step explanation:
`
60x4= blank tens x 4 = blank tens = blank
Answer:6 tens
Step-by-step explanation:
Simple. 60 equals 6 tens so blank equals 6 tens
Blank tens = 6
Hope this helps :)
what multiplication fact can you double to find 4 x 7?
Answer:
2 x 7
Step-by-step explanation:
4 x 7 = 28
Since you want doubled, we have to half to find start.
28/2 = 14
Only solid equation that equals 14 is 2 x 7
And since 4 is a double of 2, the answer checks out
The multiplication fact that can be doubled to find 4 x 7 is
2 x 7.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
4 x 7 = 28
Now,
The multiplication of 2 x 7 = 14.
If 2 x 7 is double we get,
2 x (2 x 7) = 2 x 14 = 28
Thus,
The multiplication fact is 2 x 7.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ5
what is the value of H in the diagram below?
Answer:
the value of h in the diagram is I hope hight
Can someone pleaseeee help me :(
Answer: x-5 / x
Step-by-step explanation:
because…
Answer:
[tex]\frac{x - 5}{x}[/tex]
Step-by-step explanation:
[tex]\frac{\frac{x - 5}{x + 4} }{\frac{x}{x + 4} }[/tex]
It can also be written as :-
[tex]=> \frac{x - 5}{x + 4} \div \frac{x}{x + 4}[/tex]
[tex]=> \frac{x - 5}{x + 4} \times \frac{x + 4}{x}[/tex]
Cancel x + 4 from numerator and denominator.
[tex]=> \frac{x - 5}{x}[/tex]
Write an equation in slope intercept form of the line
Answer: y=-1/4x+4
Step-by-step explanation:
slope goes down 1, and right 4 so it's -1/4. Y-intercept is positive 4 so it will be +4
Find the number that makes the ratio equivalent to 1:2.
6:
What is it
Each train car holds 71 passengers. About how many train cars
would be needed to carry 567 people?
567/71 because passengers/(train cars/passengers) = train cars
71 x 7 = 497 (not enough)
71 x 8 = 568 (enough)
Answer: 8 train cars
How to find standard deviation khan academy.
Answer:
I cant even see anything can you reupload your answer, please?
Step-by-step explanation:
50 points and brainliest to first correct answer. And NO LINKS. Ty :)
If ABCD is dilated by a scale factor of 2 about point E, which of the following is true about line E prime F prime?
Square ABCD is shown with line EF running horizontally through the center of the figure.
Question 2 options:
line E prime F prime is perpendicular to line EF.
line E prime F prime is parallel to line EF.
line E prime F prime intersects with point B′.
line E prime F prime passes through the center of dilation.
Go here to see the image (it wouldnt let me attach it). The answer on this one doesnt seem right so someone pls give correct answer :)
https://brainly.com/question/24244927
Is this the question below if it is the answer is..
Answer/Step-by-step explanation:
line E prime F prime passes through the center of dilation.
Jon bought a car that costs $2150. He paid $750 down and made a payment of $95 at the end of the first month. How much did he still owe?
Answer:
$1,305
Step-by-step explanation:
subtract how much he paid for the car with how much he paid down
2150-750=1400
then subtract that by the 95 dollars he paid off in the first month
1400-95=1,305
He still needs to pay off $1,305.
Hope this helps!!
Area of the figure 4cm 4cm 12cm and 8cm