The 12th term of the geometric sequence is a₁₂ = -244140625.
Define Geometric Progression
A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value. Its general term is,
aₙ = a₁ · rⁿ⁻¹.
The geometric sequence,
5, -25, 125 ....
from here,we know
a₁ = 5
Calculate the ratios of all the adjacent terms ,
r = aₙ₊₁ / aₙ
r = -25/5 = -5
r = 125/-25 = -5
We know, the formula for geometric sequence is
aₙ = a₁ · rⁿ⁻¹
Where, a₁ = initial term
r = common ratio
Now, we need to find 12th term so for that n = 12
Now, plug in the values
aₙ = a₁ · rⁿ⁻¹
a₁₂ = 5 * (-5) ¹²⁻¹
= 5 * -5¹¹
After calculation we get,
a₁₂ = -244140625
Hence, the 12th term of the geometric sequence is a₁₂ = -244140625.
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what is the nth term of the following quadratic sequence :
-1, 4, 15, 32, 55
The nth term of the following quadratic sequence -1, 4, 15, 32, 55 is 119.
What is meant by quadratic sequence?Any number sequence in which the second difference between any two successive terms is constant is referred to as a quadratic sequence. Think about the example below: 1;2;4;7;11;… We observe that all of the second differences equal one.
When the nth term rule includes a n2, the sequence is said to be quadratic (remember, a term is the word for a number in a sequence). A quadratic sequence's terms do not share a difference, in contrast to a linear sequence. The nth term of an arithmetic series can be calculated using our understanding of finding the nth term to be 2 n 2n 2n.
Let us assume that n=6,
aₙ=(n+1)(3n-1)
a₆=(6+1)(3(6)-1)
a₆=7(17)
a₆=119
Therefore, the nth term of the following quadratic sequence -1, 4, 15, 32, 55 is 119.
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Find the area of this below, giving your answer to 1 decimal place.
The total surface area of the shape is 198.6cm²
What is mensuration?Mensuration is the branch of mathematics that studies the measurement of geometric figures and their parameters like length, volume, shape, surface area, lateral surface area, etc.
From the given figure the two semi circles left and right can be resolved as a whole (a complete circle) with diameter d 10cm
Radius r = 10/2= 5cm
Area of circle A= πr²A= 3.142*5²
A= 3.142*25
A= 78.55
A= 78.6cm²
The remaining part of the shape is a rectangle with length (22-10)= 12cm
I.e the 10 is as a result of the radius of the two semi circles = r+r= 5+5=10
The rectangle has a width of 10cm
Area of rectangle A=12*10= 120cm²
Hence the total surface area of the shape
Total area = 120+78.6 = 198.6cm²
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A group spends $277. 50 to rent 15 tubes for a float down the ichetucknee river. How many of each type of tube does the group rent?.
The group rents 11 person tubes and 4 cooler tubes.
Let the no. of person tubes = x
Let the no. of cooler tubes = y
According to question,
Total no. of tubes = 15
Therefore, x + y = 15 ......... (I)
Cost of one person tube = $ 20
Cost of x person tube = 20x
Cost of one cooler tube = $ 12.50
Cost of y cooler tube = 12.5y
According to question,
Total cost = $ 270
Therefore, 20x + 12.5y = 270 .......... (II)
By solving equation (I) and (II), we get
x = 11
y = 4
Hence, The group rents 11 person tubes and 4 cooler tubes.
Correct Question :
A company that offers tubing trips down a river rents tubes for a person to use and "cooler" tubes to carry food and water. A group spends $270 to rent a total of 15 tubes. Write a system of linear equations that represents this situation. How many of each type of tube does the group rent? Person tube $20 Cooler tube $12.50.
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Find the area of the triangle. All help is appreciated
The area of the triangle with two sides of 8 and 11 units and an angle of 75°
is 85 units².
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
We know in a ΔABC area of the triangle is (a×b×sinC).
The given triangle has two sides 8 units and 11 units and the angle to the unknown side is 75°.
∴ The area of the triangle is (8×11×sin75°) units².
= 88sin75° units².
= 85 units².
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4-5: MathXL for School: Practice & Problem Solving
4.5.PS-15
Question Help
Reasoning Kareem cannot decide which of two washing machines to buy. The selling price of each is $520. The first is
marked down by 40%. The second is marked down by 10% with an additional 30% off. Find the sale price of each
washing machine. Use pencil and paper. Explain why Kareem should buy the first washing machine rather than the
second if the machines are the same except for the selling price.
The sale price of the first washing machine is $
(Round to the nearest dollar as needed.)
Enter your answer in the answer box and then click Check Answer.
1
part
remaining
GITTE
Due 12/05/2
Clear All
Check Answer
The sale price of the 2nd Washing machine is more expensive and profitable than the first Washing machine, So Kareem should choose the 2nd Washing machine to get profit.
Selling price and Marked price:The price a buyer pays for a good or service is known as the selling price. When the selling price is greater than the cost price, then we will get a Profit. Marked price, is the amount that a seller actually receives from a customer after negotiating a price or striking a deal.
Here we have
The selling price of washing machines is $520
The first one is marked down by 40%.
The second is marked down by 10% with an additional 30% off.
For the first Washing machine,
Let x be the sale price of the machine
Given that the price is 40% marked down
=> the selling price of Washing machine = x - 40% of x
= [tex]x - \frac{40x}{100}[/tex]
= x - 0.4x = 0.8x
As we know the selling price of the washing machine = $ 520
=> 0.8x = 520
=> x = 520/0.8
=> x = 650
The sale price of the first washing machine = $ 650.
For the 2nd Washing machine,
Let y be the sale price of the machine
Given that the price is 10% marked down
=> the selling price of Washing machine = y - 10% of y
= [tex]y - \frac{10y}{100}[/tex]
= x - 0.1x = 0.9x
And given 30% off
30% off on 0.9x = 30% of 0.9x
The selling price will be = 0.9x - 30% of 0.9x
=> 0.9x - 0.27x = 0.63x
As we know the selling price of a washing machine = $ 520
=> 0.63x = 520
=> x = 520/0.63
=> x = 825.39
The sale price of the 2nd washing machine = $ 825.39.
By the above calculations
The sale price of the 2nd Washing machine is more expensive and profitable than the first Washing machine, So Kareem should choose the 2nd Washing machine to get profit.
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Solve for x ?????????????????
Answer:
x = 7
Step-by-step explanation:
Compare the ratios of the longer side length to the shorter side length:
8 : 10 = (3x - 9) : 15
8*(3/2) : 15 = (3x - 9) : 15
Then, form an equation.
8 * (3/2) = 3x - 9
12 = 3x - 9
21 = 3x
7 = x
You need enough carpet to cover the floor in a triangular room. How much carpet will you need? if necessary, round to the nearest tenth. A right triangle with side 15 feet and hypotenuse 20 feet. A. 175 square ft b. 13. 2 square ft c. 99 square ft d. 48. 2 square ft.
13.2 square ft area of carpet will you need .
What is a right-angle triangle, exactly?
A right-angled triangle is a particular kind of triangle in which one of the angles is 90 degrees. The sum of the other two angles is 90 degrees.
The triangle's base and perpendicular sides both include the right angle. The hypotenuse, or third side, is the longest of the three. It is also known as the hypotenuse.
the area of rigth triangle
20² = 15² + x
400 = 225 + x²
x² = 400 - 225
x = 13.2
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A city has 3 new houses for every 7 old houses. If there are 21 new houses in the city, how many old houses are there?
A.
52
B.
49
C.
51
D.
47
Answer:
B. 49
Step-by-step explanation:
21/3 = 7 new houses
7*7 = 49 old houses
Answer:
Answer to the question is B: 49
There are 11 paper clips in the drawer. 3 are gold. 8 are silver.
What fraction of the paper clips are gold?
Answer: 3/8
Step-by-step explanation:
The total number is 11 paper clips
We know that three are gold
And the question ask what fraction of the paper clips are gold
So take 3 divided by the total
So the fraction is 3/8
1. Find the area of the given shape:
65m
6m
Answer:
195
Step-by-step explanation:
Formula: A=1/2*b*h
6*65=390
390/2=195
So I multiplied those numbers together and decided to divide them by two, just like the formula wanted.
I hope this helps!!!
y is greater than negative 4 over 3x plus 2
In Standard Form , [tex]y = -\frac{4x}{3} + 2[/tex] can be written as 4x+3y =6 .
What is Standard Form of a Equation ?
Ax+By=C
The standard form for linear equations in two variables is Ax+By=C. For example, 2x+3y=5 is a linear equation in standard form. When an equation is given in this form, it's pretty easy to find both intercepts (x and y).
The standard form of a linear equation is helpful for determining the x and y-intercepts of a graphed equation. It also helps you understand the concept of least common denominators, which is finding the lowest number to multiply and thus convert two fractions into whole numbers.
Given Equation :[tex]y = -\frac{4x}{3} + 2\\[/tex]
To convert it into Standard form , Multiply both sides with 3
[tex]3y = 3(\frac{-4x}{3} +2)[/tex]
[tex]3y = -4x + 6\\4x + 3y = 6[/tex]
Hence , In Standard Form , [tex]y = -\frac{4x}{3} + 2[/tex] can be written as 4x+3y =6 .
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The graph of y = f(x) is shown below. Find all values of x where f(x) = 8.
The value of x when f(x) of 8 according to the graph is; 4.
How to calculate value of x?In order to determine a point's coordinates in a coordinate system, you must do the opposite. Start at the point and move in a vertical line in either an upwards or downwards direction to the x-axis. Here is the x-coordinate for you. Next, repeat the process while following a horizontal line to determine the y-coordinate.
According to the graph;
To determine the value of x when f(x) = 8.
We must plot a line of the equation; y = 8.
This y = 8 line produces a horizontal line.
The point at which the horizontal line, y = 8 intersects the given graph has an x coordinate.
Ultimately, this point has x coordinates of 4, making 4 the value of x when f(x) = 8.
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3. The graph of a function f consists of a semicircle
and two line segments as shown above. Let
g( x) =∫1
x
f (t)dt .
(a) Find g(1) , g(3) , and g(−1) .
Answer:
so the(g) semicircle should go up top with
The table shows y as a function of x. Suppose a point is added to this table. Which choice gives a point that preserves the function?
Responses
A (−3, −8)(−3, −8)
B (−6, 3)(−6, 3)
C (−5, −2)(−5, −2)
D (9, 8)
The point that preserves the function is option A(-3,-8).
What do you mean by function?
A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
According to the given question,
We have four option for the answer.
Note: if f is a function then each number of the domain has an unique image.
Since (regarding the table) the image of 9 is 6 then the answer D is wrong
The same apply on answers B and C .
Therefore, the right answer is A(-3,-8).
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Aaden has z quarters and y dimes. He has no more than 22 coins worth no less than $3.60 combined. Solve this system of inequalities graphically and determine one possible solution. Give each inequality in slope-intercept form.
By using linear inequation it can be calculated that-
One possible solution is Aiden has 8 quarters and 14 dimes
What is linear inequation?
Inequation shows the comparision between two algebraic expressions by connecting the two algebraic expressions by >, <, ≥, ≤
A one degree inequation is known as linear inequation
Aaden has z quarters and y dimes.
He has no more than 22 coins
z + y ≤ 22
z ≤ -y + 22 .... (1)
He has no less than $3.60 combined.
0.25z + 0.1y ≥ 3.60
5z + 2y ≥ 45
5z ≥ -2y + 45
z ≥ -0.4y + 9 .... (2)
This system of linear inequation is solved graphically
From the graph it is clear that
one solution is z = 8 and y = 14
One possible solution is Aiden has 8 quarters and 14 dimes.
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Aaron had $22 to spend on 4 beakers for his science class. After buying them, Aaron had $2 left. How much did each of the beakers cost?
Answer:
6.50
Step-by-step explanation:
Matt is filling containers of rice. Each container holds \dfrac{1}{4}
4
1
start fraction, 1, divided by, 4, end fraction of a kilogram of rice.
If Matt has 777 kilograms of rice, how many containers can he fill?
The number of containers that he can fill is 3108.
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,
The formula for the division of fractions is:
= a/b ÷ c/d
= a x d / b x c
Amount of rice in a container = 1/4 kg
The total amount of rice = 777 kg.
The number of containers.
= 777 ÷ (1/4)
= 777/(1/4)
= 777 x 4
= 3108
Thus,
The number of containers is 3108.
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2(a+c) =5(a-b) make c the subject
find the slope of a line that goes through the points ( -3,4) and (-3,1)
Please help me solve this
0
Step-by-step explanation:
The slope for this linear function would be 0.
It'd be a straight line, and slope tells you the steepness of a line, so it won't have slope.
Equation: x=-3
Image included to see line, and the two points.
Answer:
The slope is –3
Step-by-step explanation:
using the coordinate
(–3,4) and (–3,1)
x1 = –3,x2 = –3,y1 = 4, y2 = 1
using the formula for slope
m = y2 — y1/x2 — x1
m = 1 – 4/–3–(–3)
m = –3/–3+3
m = –3/0
m = –3
i hope this helps please rate the answer as brainliest so you can get some points
The population of the city of Peachwood is currently 12,000 and
increases every year at a rate of 5%. The function that describes the
model is g(f) = 12000 1.05* Which of the following choices would
be the number of people in the city after 1 year?
A.$12,000
B. $12,600
C.$14,100
D.None of the choices are correct.
Answer:
D.None of the above are correcr
Step-by-step explanation:
if the population of peachwood increases by 5% every year then after 1 year 5 percent of 12,000 would be added to 12,000 and 5 percent of 12,000 is 600 so the answer would be 12,600
Option B is the correct Answer and $12600 people are in the city after 1 year.
Given the population of peachwood=12000
The rate that increases per year is given as 5%
We are given the function that g(f) = 12000 * 1.05x is considered as equation(1)
Here x in f(x) defines the number of years that passed in the city of Peachwood
so x value is considered as 1
The f(x) is the total population of Peachwood these are two key elements in this function
Now substitute the x value in equation (1)
Therefore after 1 year, the equation would be
f(x)=12000*1.05x
f(1)=12000*1.05(1)
g(f)=$126000
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Scars for Question 2 of 5 points)
2. The line segment graphed on the coordinate plane represents a roof with several triangular supports. Each support is triangular, with a horizontal board that starts on the edge of the roof and connects with a vertical board that ends on the
+
Answer
(a) Does each support have the same starting coordinates? Explain
(b) Does each support have the same ending coordinates? Explain
(c) Does each support have the same change in x-values? E
2 Explain
(d) Does each support have the same change in y-values? Explain
(e) Does each support have the same ratio of change in y-values over change in x-values? Explain
If unit of a certain commodity are produced, then the marginal cot i dc/da = 9x^24x15x ^1/4 10. Suppoe the total cot of producing the 1t unit i 100. Calculate the total cot of producing the firt 16 unit. (calculu 1)
Therefore, the total cost of producing the first 16 units of a certain commodity is 28940.
What are linear equations?The mathematical formula for a straight line on a graph is called a linear equation. Y = mx + b, where m is the line's slope b seems to be the y-intercept, or the place where the line crosses the y-axis, is how it is expressed. Because they simply have one variable and no exponents, linear equations are comparatively easy to solve. They may be used to simulate a variety of real-world events, including population increase and the supply-demand connection in the economy. Generally speaking, linear equations are a fundamental algebraic tool produced and are used to represent and analyse a wide variety of data types.
How to solve?
dc/da = [tex]9x^{2} + 4x + 15x^(1/4) +10[/tex]
Differentiate with respect to x
dc/da = [tex]18x + 4 + 15/4 x^(-3/4)[/tex]
input the value 100 for the value of x,
dc/da = 1800 + 4.75
dc/da = 1808.75
To produce the first 16 units,
1808.75 × 16 = 28940
The cost of producing the first 16 units is 28940
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The reciprocal of x^3
Answer:
x^-3
Step-by-step explanation:
The reciprocal of x^3 is x to the power of negative 3 (aka [tex]\frac{1}{x^3}[/tex]).
can someone help me with these questions only five of them.
Answer:
Step-by-step explanation:
For number 1, It is $52.4
Divide the cost by the number f days to get your constant
for number 2, It is 2
Just format it to y=mx+b
I do not know the answer to the third one
And the fourth one it is true with a 1/25 fraction
The purpose of a interview
Answer:
To make sure who ever want the job is reliable and suitable for it.
Step-by-step explanation:
The product of two consecutive odd intergers is 143. What are the solutions
Answer:
11 and 13
(11x13)
solve the matrix equations
with full explanations and workings please
Answer:
Step-by-step explanation:
x<60
[tex]x^{2} +11x +24[/tex]
The factored form of the equation x² + 11x + 24 is (x + 3)(x + 8).
How to factor quadratic equation?A quadratic equation is an algebraic equation of the second degree in x. Quadratic equation can be represented in standard form as follows:
ax² + bx + c
where
a, b and c are constantFactoring a quadratic equation can be defined as the process of breaking the equation into the product of its factors.
Therefore, let's factor the equation x² + 11x + 24 as follows:
x² + 11x + 24
The two numbers we can add to get 11 and multiply to get 24 are 3 and 8.
Therefore,
x² + 3x + 8x + 24
x(x + 3) + 8(x + 3)
Hence, the factored form is (x + 3)(x + 8)
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Work out the value of (6. 31 * 10 ^ 5) + (2. 6 * 10 ^ 4) give your answer in standard form.
The standard form of (6.31×10⁵ ) + (2.6×10⁴) is 65.7 × 10⁴.
What is a simplification of an expression?
Usually, simplification involves proceeding with the pending operations in the expression.
Simplification usually involves making the expression simple and easy to use later.
As given,
(6.31×10⁵ ) + (2.6×10⁴) = ( 6.31× 10⁴ ×10 ) + (2.6 × 10⁴ )
= ( 6.31 × 10 + 2.6 )
= ( 63.1 + 2.6 )
= ( 65.7 )
= 65.7 × 10⁴
Hence, the standard form of ( 6.31× 10⁵) + (2.6 × 10⁴) = 65.7 × 10⁴.
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What is the equation of a line that is parallel to 3x + 4y = 15 and passes through the point (8, - 2)?
Enter your answer in slope-intercept form (y=mx+b) in the box.
Step-by-step explanation:
in the slope- intercept form
y = mx + b
m is the slope, b is the y-intercept (the y-value when x = 0).
a parallel line must have the same slope, but a different y- intercept.
as you can see, the slope is always the factor of x, when we have a "y = ..." form.
so, coming from
3x + 4y = 15
4y = -3x + 15
y = (-3/4)x + 15/4
the slope is therefore -3/4.
b we get by using the given point coordinates in the equation :
-2 = (-3/4)×8 + b = -24/4 + b
b = -2 + 24/4 = -2 + 6 = 4
so, the full equation is
y = (-3/4)x + 4