The given geometric series, the first term is a₁ = 2 and the common ratio is r = -1
What are some examples of geometric series?
In mathematics, a geometric series is an infinite series with the formula a + ar + ar2 + ar3 +, where r is referred to as the common ratio. The geometric series for a = 1 and r = 1/2, or 1 + 1/2 + 1/4 + 1/8 +, is a straightforward illustration and converges to a sum of 2. (or 1 if the first term is excluded).We are given to find the values of a₁ and r of the following geometric series
2 - 2 + 2 - 2 + 2 - ........
We know that
a₁ is the first term and r is the common ratio of the given geometric series.
We can see that the first term of the given geometric series is 2.
So. we must have
a₁ = 2
Also, common ratio is found by dividing a term by its preceding term.
Therefore, the common ratio r of the given geometric series is
r = -2/2 = 2 / -2 = ...... = -1
Thus, for the given geometric series, the first term is a₁ = 2 and the common ratio is r = -1.
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Find the intersection of the two lines by solving the system of equations.
x + y = -8
-x + y = -2
Answer:
(-3, -5)
Step-by-step explanation:
Adding the equations, we get 2y = -10, and thus y = -5.
Substituting this back into the first equation gives us that x = -3.
So, the point of intersection is (-3, -5).
A shopper bought 15 apples and 5 oranges. Which statement describes the ratio of apples to oranges?
The statement which describes the ratio of apples to oranges is; Choice D; 3:1 because the shopper bought 3 apples for every orange.
What is the ratio of apples to oranges?It follows from the task content that the shopper in discuss bought; 15 apples and 5 oranges.
On this note, by dividing both numbers by their greatest common factor, it follows that the resulting ratio is;
(15/5) : (5/5)
= 3 : 1.
Hence, Choice D is correct; 3:1 because the shopper bought 3 apples for every orange.
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Two students start a club the first week of school. Each member invites three new members the second week of school. Each of these new members then invites three additional members the following week. If the pattern of each new member inviting three new members each week continues, how many members will be in the club after five weeks?
80 students
121 students
242 students
363 students
In linear equation ,242 total number of members within 5 weeks.
What is linear equation ?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."a manual computation on how 1 member recruits his members until week 5. Then multiply the sum by 2.
old new
1: 1
2: 1 x 3 = 3 ⇒ 1 3 *only new members recruit 3 more
3: 3 x 3 = 9 ⇒ 4 9
4: 9 x 3 = 27⇒ 13 27
5: 27 x 3 = 81 ⇒ 40 81
40 + 81 = 121. Total number of members under 1 founding member.
121 x 2 founding members = 242 total number of members within 5 weeks.
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Answer: Option C
Step-by-step explanation:
Piano lessons with Ms. Bell cost $30 for
3/4
of an hour. What is Ms. Bell's hourly rate?
Answer:
$40
Step-By-Step Explanation:
Do someone have the answers
1. y = 5x + 15.
2. y = total cost
x = number of calendar
m = cost per calendar = slope = 5
b = initial value/y-intercept = 15
3. $1,015.
4. The equation in slope-intercept form is: y = 5x + 15
5. Slope (m) = 5
6. y-intercept (b) = 15; x-intercept = -3.
7. See attachment below for the graph.
How to Write an Equation that Models a Situation?Using the information given, we can create an equation in slope-intercept form y = mx + b, where m would be the slope and b would be the y-intercept of the linear equation.
Let,
y = total costx = number of calendarm = cost per calendar = slope = 5b = initial value/y-intercept = 151. To create an equation that models the situation, substitute m = 5 and b = 15 into y = mx + b:
y = 5x + 15.
2. The variables and numbers in the equation are:
y = total cost
x = number of calendar
m = cost per calendar = slope = 5
b = initial value/y-intercept = 15
3. Substitute x = 200 into y = 5x + 15
y = 5(200) + 15
y = 1,015
Total cost = $1,015.
4. The equation in slope-intercept form is: y = 5x + 15
5. The slope (m) = 5
6. The y-intercept (b) = 15
To find the x-intercept, substitute y = 0 into y = 5x + 15
0 = 5x + 15
-5x = 15
x = 15/-5
x = -3
The x-intercept = -3.
7. See attachment below for the graph.
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Rewrite (132 + 228) using factoring.
4(32 + 57)
6(22 + 222)
4(33 + 57)
16(116 + 14)
Answer:
can u help me with my homework
Answer:
Farmers are the backbone of our society. They are the ones who provide us all the food that we eat. As a result, the entire population of the country depends upon farmers. Be it the smallest or the largest country. Because of them only we are able to live on the planet. Thus Farmers are the most important people in the world. Though farmers have so much importance still they do not have proper living.
Students planted 360 tree saplings. which is 12% of the planned amount. How many seedlings are planned to be planted?
Y=(X-3)^2 from the parent function y=x^2
The parent function will shift the right side by 3 units after applying the transformation x → (x - 3).
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that:
The parent function is:
y = x²
After applying the transformation:
x → (x - 3)
The function will shift the right side by 3 units.
The equation of the function will be:
y = (x - 3)²
Thus, the parent function will shift the right side by 3 units after applying the transformation x → (x - 3).
The complete question is:
Describe the Transformation y=(x - 3)² if the parent function is y = x²
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Tell me did I choose all of the right equations
The square in the middle has an area of 1 square unit. What is the area of the entire
rectangle in square units? Explain your reasoning.
Prove that:
A-(A-B)⊆B
Help am i correct? I need help please give explanation
====================================================
Reason:
Focus on the numerator for now. The [tex](11^8)^2[/tex] is the same as [tex]11^{16}[/tex] because we multiply the exponents. The general rule is [tex](a^b)^c = a^{bc}[/tex]
Alternatively we can think of it like this
[tex](11^8)^2 = (11^8)(11^8) = 11^{8+8} = 11^{16}[/tex]
So far we have [tex]\frac{(11^8)^2}{11^3} = \frac{11^{16}}{11^3}[/tex]
------------
The last step is to subtract exponents due to the rule [tex]\frac{a^b}{a^c} = a^{b-c}[/tex] and the order of subtraction is important.
Therefore, [tex]\frac{(11^8)^2}{11^3} = \frac{11^{16}}{11^3} = 11^{16-3} = 11^{13}[/tex]
Round this number to the
nearest tenth.
6.3579
Answer: 6.4 :)
Step-by-step explanation:
6.358
Step-by-step explanation:
To round a number to the nearest tenth, look at the hundredth number .If that number is greater than 5,add 1 to the tenth value.If is less than 5 , leave the tenth place value as it is, and remove all the numbers present after the tenth's place.
Mrs Peh paid $1438 for 1 drum set and 1 keyboard. Tim paid $690 for 1 flute
and 1 keyboard. The drum set cost thrice as much as the flute. How much would
1 drum set and 1 flute cost?
Answer:
flute=374, drum=1122, keyboard=316
Find the measurement of the angle indicated for each trapezoid.
Answer:
∠ C = 50°
Step-by-step explanation:
• each lower base angle is supplementary to the upper base angle on the same side.
then
∠ C + ∠ D = 180°
∠ C + 130° = 180° ( subtract 130° from both sides )
∠ C = 50°
BROS HELPPP Oh my god I NEED HELPP
Answer:
Ok, so all you have to do, is substitute the numbers in for x.
Step-by-step explanation:
For example substitute -3 in for x and solve. I hope this helps some!
Which of the following is true of the composition G(F(y))?
The correct option is D.The function F(G(H(y))) depends on G(H(y)).
What is defined as the composite functions?The method by which two or even more functions into one function is identified as function composition.f(g(x)) or (f °g) represents this same composition of functions f(x) as well as g(x), where g(x) acts first (x). It integrates a number of functions to produce another. The output of one function inside the parenthesis is becoming the input of the other function in a function composition.For the given question-
A function is defined by its argument (values in parentheses after a function name). G(H(x)) is the argument of function F in F(G(H(x))).
F(G(H(x)) is dependent on G(H(x)).
Answers A and C make no statements about the particular composition. Answer option B depicts a composition (H(G(x)) that is unrelated to the argument of function F.
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The complete question is-
Which of the following is true of the composition F(G(HyX)))?
A. The function G(F(H(y))) depends on G(H(y)).
B. The function F(G(H(y))) depends on H(G(y)).
C. The function H(G(F(y))) depends on G(F(y)).
D.The function F(G(H(y))) depends on G(H(y)).
six million, ninety-six thousand, sixty-one
in standard notation
In two or more complete sentences, explain how to use ordered pairs of points in f(x)=2x+5 and g(x)= x-5/2 to determine if f(x) and g(x) are inverses of each other.
The ordered pair given are not inverse to each other because:
Substituting a value say 5/2 into f(x)=2x+5 gives 10Substituting 10 into g(x)= x-5/2 does not return 5/2How to know inverse functionsWhen two functions are inverse to each other substituting a value A in function say AA will give answer say X, substituting the answer X to the the other function say BB returns the value A.
Instance
say function AA, plug in A gives X
the inverse will be:
say function BB plug in X gives A
So, we have f(x)=2x+5 and g(x)= x-5/2
plugging in say 5/2 in f(x) will give
f(x) = 2 * 5/2 + 5
f(x) = 5 + 5
f(x) = 10
We plug in 10 to g(x)= x-5/2
g(x) = 10 - 5/2
g(x)= 7/2
since 7/2 ≠ 5/2 the pair of functions are not inverse to each other
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help pleaseeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee !!
Answer:
21, -4, 5
Step-by-step explanation:
In the function we are changing x into -5 :
So :
(-5)² - 4
25 - 4 = 21
f(0) will be :
0² - 4
0 - 4 = -4
f(3) will be :
(3)² - 4
9 - 4 = 5
Hope this helped and have a good day
How much 8% saline solution should Kent mix with 60 cubic centimeters (cc) of an 18% saline solution to produce an 11% saline solution?
cubic centimeters of an 8% saline solution is needed.
X
5
Based on the concentration of the saline solution and the cubic centimeters of the saline solution, the amount that should be mixed is 140 cubic centimeters
How to find out the cubic centimeters for mixing?Assuming that the quantity of the saline solution that Kent should mix is denoted by x, the formula would be:
0.08x + (0.18 x 60) = 0.11 (x + 60)
Solving gives:
0.08x + 10.8 = 0.11x + 6.6
10.8 - 6.6 = 0.11x - 0.08x
4.2 = 0.03x
x = 4.2 / 0.03
x = 140 cubic centimeters
In conclusion, 140 cubic centimeters of the saline solution is needed.
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3. What is this number in standard form? (1 point)
5.75 x 109
O5,750,000,000
O 575,000,000,000
O
0.00000000575
O 0.575000000000
4
HELP PLSSSSSSSS
Answer:
5,750,000,000
Step-by-step explanation:
What is the slope of the line that passes through the points (6,2) and (-18,2)
Answer:
0
Step-by-step explanation:
Since the Y coordinate does not change the slope is 0
Can anyone help me with this?
Answer: y=40x
Step-by-step explanation:
help me asap im in a dba back to basics exam and didnt study
Answer:
is this flvs full flex? I'm in this as well, whats your grade?
also im doing 12th grade math if you havent gotten to that point yet you will be working in Aleks for math and phewww, good luck i hate this
Step-by-step explanation:
how can we multiply 2 equations
Answer:
Given equations:
a = x + yb = x - yTo multiply 1 and 2;
[tex]{ \tt{a \times b = (x + y)(x - y)}} \\ = { \tt{(x.x) + (x. - y) + (y.x) + (y. - y)}} \\ = { \tt{ {x}^{2} - xy + xy - {y}^{2} }} \\ = { \tt{ {x}^{2} - {y}^{2} }}[/tex]
Is 0.6294 terminating or repeating
Answer:
This is terminating. As a fraction it would be: [tex]\frac{6294}{10000}[/tex] not simplified
Step-by-step explanation:
If it was repeating you would see a repeat bar over part of the number. Or 3 .... showing that the number goes on.
Jack works in a bookstore. He has 300 books to stock on the shelves. So far, he has stocked 120 books today. What percent of the books does he have left to stock?
A. 30%
B. 40%
C. 50%
D. 60%
Answer:Jack has 60% of the books left to stack.
Step-by-step explanation:
Answer:
Step-by-step explanation:
60% (300-120) 180/300*100=60. 60%
May I get help with my math?
Answer:
I don't know and your read in which class
HELP IM TIMED ILL MAKE AS BRAINLIEST
Answer: 26
Step-by-step explanation: 208/8=26
