It's geometric sequence:
[tex]a_1=1.2,\ a_2=3,\ a_3=7.5,\ a_4=18.75,\ ....[/tex]
Calculate the common ratio:
[tex]r=\dfrac{a_{n+1}}{a_n}\to r=\dfrac{3}{1.2}=2.5[/tex]
The explicit formula of geometric sequence:
[tex]a_n=a_1r^{n-1}\to f(x)=a_1r^{x-1}[/tex]
Substitute:
[tex]a_1=1.2,\ r=2.5\\\\f(x)=1.2\left(2.5)^{x-1}[/tex]
Answer: "f(x) = 1.2(2.5)x-1"
Answer:
AStep-by-step explanation:
100% righttt
Need help asap with number 4
Determine the equation of the line through (-1,2) and perpendicular to the line 2x-3y+5=0
Which expression is the result of the perimeter of rectangle b minus the perimeter of rectangle a
Consider the equation 22+3x/3x+7=2 How do you begin isolating the variable x to one side of the equation?
You have 22+3x/3x+7=2. That 3x/3x raises eyebrows; is this what you meant, with the result that 3x/3x = 1? or did you mean
3x
22 + ------------- + 7 = 2?
3x+7
If you meant the latter, then simplify the equation by subtracting 2 from both sides:
3x
27 + ---------- = 0
3x+7
Multiply all three terms by (3x+7), obtaining
27(3x+7) + 3x = 0
Then 21x + 3x + 189 = 0, so that 24x = -189, or x = -189/24 = -7 7/8
Reflection across the x-asis?
Which point represents a solution to the system y ≤ (1)/(5)x y > 4x-3 select all that apply
(5,1)
(0,0)
(-2,-3)
(2,5)
can you help me with this question and explain how you got the answer please and thank you ! this is very important !!!!!!!!!
What is an equation that equals 58 explain!
Some equations that equal 58 include: 58x, 29 + 29, and y + 58x.
For example, 58x is equal to 58 because you can change x to 1, and 58 times 1 is 58. Therefore, it is equal to 58.
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Quadrilateral ABCD is a rhombus. Suppose measure of angle A decreases. Which of the following changes would also need to happen in order for ABCD to still be a rhombus?
If angle A of a rhombus decreases, angle C must also decrease and the side length of the rhombus must remain the same for it to still be a rhombus.
Explanation:When angle A of a rhombus decreases, there are two changes that need to happen in order for the rhombus to still be a rhombus.
The opposite angle, angle C, must also decrease by the same amount in order to maintain the opposite angles of a rhombus being equal. The side length of the rhombus must remain the same, as all sides of a rhombus are congruent.
Therefore, if angle A decreases, angle C must also decrease by the same amount, and the side length of the rhombus must remain the same in order for ABCD to still be a rhombus.
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IS THE SQUARE ROUTE OF 7 OR 14/5 BIGGER
Waylon played defense in 12 soccer games. This was 60% of the total number of games he played. How many games did Waylon play?
Tanisha opened a bank account. She deposited $74.50 into her account every month for 10 months. She used $32.50 every month to pay for painting classes. After 10 months, she used 1 over 2 of the total money left in her account to go to a summer camp for painters. What is the total amount of money Tanisha spent to go to the summer camp?
Answer:
A
Step-by-step explanation:
If a Rubik’s Cube has a volume of 384 cubic centimeters, how long is one side of the cube?
PLEASE HELP!!!! Show steps and explain how to get the answer please
Solve 5x-16=4(x-8)-3x
5x-16 = 4(x-8)-3x
first expand what is in parenthesis
4(x-8) = 4x-32
so now you have 5x-16 = 4x-32-3x
subtract 3x from 4x on the right side of equation 4x-3x = x
5x-16 = x -32
subtract 1x from each side to get
4x-16 = -32
add 16 to both sides to get 4x=-16
x = -16/4 = -4
x=-4
If angle DAB measures 34 degrees, what is the measure of arc DB
Which statement is true for the equation 3x − 3x − 2 = −2?
It has no solution.
It has one solution.
It has two solutions.
It has infinitely many solutions.
The equation will have infinitely many solutions.
What is an equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
This equation has infinitely many solutions.
3x - 3x - 2 = - 2
3x - 3x = 0
3x = 3x
This equals each other meaning infinite solutions.
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A barrel shaped like a cylinder is laid on its side and rolled up a ramp that is 92m long. The barrel has a circular base that turns 46 times in being rolled up the ramp. What is the diameter of the circular base?
A ball is dropped from a height of 5 ft and bounces to 60% of its previous height on each subsequent bounce. Which statement is true regarding the vertical distance the ball has traveled when it hits the ground for the fourth time?
A) 10.88 ft vertical distance traveled total
B) 16.76 ft vertical distance traveled total
C) 18.06 ft vertical distance traveled total
D) 21.76 ft vertical distance traveled total
Answer:
the answer is 16.76 ft option B
Step-by-step explanation:
The vertical distance the ball has traveled when it hits the ground for the fourth time is 16.76m.
What is the percentage?The Percentage is the value per hundred.
Distance traveled by the ball when it hits the ground first time =5m
After the first hit, it bounces to 60% of its previous height
60% of 5m =3m
This means ball goes 3m up and then 3m down before hitting for the second time.
So, the vertical distance traveled by the ball till the second hit=5+3+3 =11m
After the second hit, it bounces to 60% of its previous height
60% of 3m =1.8m
This means ball goes 1.8m up and then 1.8m down before hitting for the third time.
So, the vertical distance traveled by the ball till the third hit=11+1.8+1.8 = 14.6m
After the third hit, it bounces to 60% of its previous height
60% of 1.8m =1.08m
This means ball goes 1.08m up and then 1.08m down.
So, the vertical distance traveled by the ball till the fourth hit=14.6+1.08+1.08 = 16.76m
Hence, the vertical distance the ball has traveled when it hits the ground for the fourth time is 16.76m.
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Jose made 33 of the 88 baskets for basketball team.What percent did he no make?
Raul has $640 saved, and jaime has $320 saved. They each begin a new job on the same day and save all of their money. Raul earns $180 per day and jaime earns $200 per day. In how many days will they have an equal amount of money
In 16 days will they have an equal amount of money.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Raul has $640 saved, and jaime has $320 saved.
Raul earns $180 per day and jaime earns $200 per day.
let the be number of days they both have same amount
640 + 180x = 320 + 200x
320 = 20x
x= 16
Hence, 16 days will they have an equal amount of money.
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The top base of a trapezoid is 18 inches and the bottom base is 22 inches. The height of the trapezoid is 8.5 inches. What is the area of the trapezoid
Final answer:
The area of the trapezoid with top base 18 inches, bottom base 22 inches, and height 8.5 inches is calculated using the formula (1/2) × (base1 + base2) × height, resulting in an area of 170 square inches.
Explanation:
To calculate the area of the trapezoid, you can use the formula for the area of a trapezoid, which is A = (1/2) × (base1 + base2) × height. In this case, the top base (base1) is 18 inches, the bottom base (base2) is 22 inches, and the height is 8.5 inches.
Using the formula, we get:
A = (1/2) × (18 inches + 22 inches) × 8.5 inches
A = (1/2) × 40 inches × 8.5 inches
A = 20 inches × 8.5 inches
A = 170 square inches
So, the area of the trapezoid is 170 square inches.
Find the sum of the three expressions and choose the correct answer.
-2u 3 v + 5uv - 1
7u 3 v - 2u 2 v 2
5u 2 v 2 - uv + 6
The answer choices are.....
A. 5u3v + 3u2v2 + 4uv + 5
B. -5u3v - 3u2v2 + 4uv + 7
C. 5u3v - 3u2v2 + 4uv - 5
which of the following best explains why cos 2pi/3 is not equal to cos 5pi/3
A.The angles do not have the same reference angle.
B.Cosine is negative in the second quadrant and positive in the fourth quadrant.
C.Cosine is positive in the second quadrant and negative in the fourth quadrant.
D.The angles do not have the same reference angle or the same sign.
In this exercise we have to use the knowledge of cosine quadrants, like this:
Letter B
We have that the quadrant of the cosine is given by:
The two quadrants on the right are positive.The two quadrants on the left are negative.So we know that:
[tex]cos (2\pi/3)[/tex] If it's in quadrant three, that's negative.
[tex]cos(5\pi/3)[/tex] If you're in quadrant four, that's positive.
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The correct answer is option B. Cosine is negative in the second quadrant and positive in the fourth quadrant.
To determine why [tex]cos(\frac{2\pi }{3})[/tex] is not equal to [tex]cos(\frac{5\pi }{3})[/tex], we can analyze the properties of cosine in different quadrants.
Reference Angles: The reference angle for both [tex]\frac{2\pi }{3}[/tex] and [tex]\frac{5\pi }{3}[/tex] is [tex]\frac{\pi }{3}[/tex].Quadrants: [tex]\frac{2\pi }{3}[/tex] is in the second quadrant, while [tex]\frac{5\pi }{3}[/tex] is in the fourth quadrant.Sign of Cosine: In the second quadrant, cosine is negative. In the fourth quadrant, cosine is positive.Thus, because cosine is negative in the second quadrant and positive in the fourth quadrant, [tex]cos(\frac{2\pi }{3})[/tex] is not equal to [tex]cos(\frac{5\pi }{3})[/tex]. Therefore, the best explanation is: Cosine is negative in the second quadrant and positive in the fourth quadrant.
If a 12-student class averaged 90 on a test, and a 20-student class averaged 80 on the test, then all 32 students averaged
Find the area of a circle, in terms of pi, if the radius is 20 ft.
10 times the sum of half a number and 6 is 8
help please thank you
An architectural drawing lists the scale as 1/4" = 1'. If a bedroom measures 1.5" by 2.25" on the drawing, how large is the bedroom?
The scale of the architectural drawing is such that 1/4" represents 1'. This means, if the room measures 1.5" by 2.25" on the drawing, it measures 6 feet by 9 feet in real life.
Explanation:In this scenario, the unit scale indicates that 1/4" on the drawing represents 1' in real life. So, to find the real-life dimensions of the room, you would need to convert the drawing dimensions to real-life dimensions.
For the length, 1.5" on the drawing would equate to 1.5 * 4 feet because every 1/4" equals 1 foot. Therefore, the length of the room is 6 feet.
The width of the room is similarly calculated. 2.25" on the drawing would equate to 2.25 * 4 feet which gives us a width of 9 feet.
So, the bedroom in real life is 6 feet by 9 feet.
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The bedroom is 6 feet by 9 feet in real life.
Explanation:To determine the actual size of the bedroom, we can use the scale given in the architectural drawing. The scale 1/4" = 1' means that every 1/4 inch on the drawing represents 1 foot in real life. In this case, the bedroom measures 1.5 inches by 2.25 inches on the drawing. To find the actual size, we can multiply these dimensions by the scale factor: 1.5 inches * (1 foot / 1/4 inch) = 6 feet, and 2.25 inches * (1 foot / 1/4 inch) = 9 feet. Therefore, the bedroom is 6 feet by 9 feet in real life.
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19. if a vechicle was purchased for $32345. there's a 6% sales tax on automobile sales, how much tax will be added to the price of the car
What is the degree of 6x5 - 4x2 + 2x3 - 3 + x?
Answer:
55555555555555555555
Step-by-step explanation:
The degree is 5.
what is degree of polynomial?The degree of a polynomial is the highest power of the variable in a polynomial expression.
Given function:
6x5 - 4x2 + 2x3 - 3 + x
as, the function have powers 2, 3 and 5.
Among which the highest power is 5.
So, degree of the polynomial is highest power of the variable present in an equation.
Hence, the degree of polynomial is 5.
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Write an equation of the line that has a slope of 5 and y-intercepts 3 in slope-intercept form.