Answer:
78,732
Step-by-step explanation:
a_1 = 4
a_2 = 12
a_2/a_1 = 12/4 = 3
a_1 = 4
a_2 = 4 * 3 = 4 * 3^1 = 12
a_3 = 4 * 3 * 3 = 4 * 3^2 = 36
a_n = 4 * 3^(n - 1)
For n = 10:
a_10 = 4 * 3^(10 - 1) = 4 * 3^9 = 4 * 19,683 = 78,732
Final answer:
The formula for the nth term of a geometric sequence is a(n) = [tex]\[ a_n = a_1 \times r^{(n-1)} \][/tex], where a(n) is the nth term, a(1) is the first term, and r is the common ratio. In this case, the first term is 4 and the second term is 12. By using the formula, the calculated tenth term is 78,732. Therefore, the correct answer is C.
Explanation:
The formula for the nth term of a geometric sequence is given by:
[tex]\[ a_n = a_1 \times r^{(n-1)} \][/tex]
where:
- [tex]\( a_n \)[/tex] is the nth term,
- [tex]\( a_1 \)[/tex] is the first term,
- [tex]\( r \)[/tex] is the common ratio,
- [tex]\( n \)[/tex] is the term number.
In this case, the first two terms are given as 4 (which is [tex]\( a_1 \)[/tex]) and 12 (which is [tex]\( a_2 \)[/tex]).
The common ratio ([tex]\( r \)[/tex]) can be found by dividing the second term by the first term:
[tex]\[ r = \frac{a_2}{a_1} = \frac{12}{4} = 3 \][/tex]
Now, you can use this common ratio in the formula to find the 10th term [tex](\( a_{10} \))[/tex]):
[tex]\[ a_{10} = 4 \times 3^{(10-1)} \][/tex]
[tex]\[ a_{10} = 4 \times 3^9 \][/tex]
[tex]\[ a_{10} = 4 \times 19683 \][/tex]
[tex]\[ a_{10} = 78,732 \][/tex]
So, the correct answer is: C) 78,732
If x/9 is equivalent to 0.5 segment, what is the value of x?
Answer:
X=4.5
Step-by-step explanation:
9 x 0.5 = 4.5
You can even test it. 4.5/9 does in fact, equal 0.5
A board is leaning against a building so
that the top of the board reaches a
height of 18 feet. The bottom of the
board is on the ground 4 feet away from
the wall. What is the slope of the board
as a positive number?
The slope of a line is given by rise over run. The slope of the board leaning against the building is 4.5; given by the height it reaches (18 feet) divided by the distance from the base of the building to the base of the board (4 feet).
Explanation:The subject of your question is the slope of a line in a mathematical context, specifically when dealing with the Algebra of Straight Lines. First, let's recall what slope is. The slope of a line, commonly represented as m, is the measure of the vertical change (rise) for each unit of horizontal change (run).
To find the slope of the board leaning against the building, we can take the rise over the run. Here, the rise is the height of the building which the board reaches - 18 feet. The run is the distance from the building to the board's base on the ground - 4 feet. Hence, the slope m of the board would be calculated as follows: m = rise/run = 18/4 = 4.5.
A positive slope indicates that the line rises from left to right, like the board leaning against the building. So, the slope of the board as a positive number is 4.5.
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Solve 3x+k= c for x.
Answer:
x = [tex]\frac{c-k}{3}[/tex]
Step-by-step explanation:
Given
3x + k = c ( isolate the term 3x by subtracting k from both sides )
3x = c - k ( divide both sides by 3 )
x = [tex]\frac{c-k}{3}[/tex]
2/3x - 4 = 20
How do I solve this?
Answer:
x=20
Step-by-step explanation:
Answer is in the picture
PLEASE Give me BRAINLIEST
No explanation needed, A,B,C, or D?
Answer:
B I think
Step-by-step explanation:
Solve the system. 23x - 12y = 1 - 43x +y =-3
Answer:
The values are [tex]x=\frac{35}{493}[/tex] and
[tex]y=\frac{26}{493}[/tex]
The solution is ([tex]\frac{35}{493},\frac{26}{493}[/tex])
Step-by-step explanation:
Given equations are [tex]23x-12y=1\hfill (1)[/tex]
[tex]-43x+y=-3\hfill (2)[/tex]
To solve the given equations :
Multiply the equation (2) into 12 we get
[tex]-516x+12y=-36\hfill (3)[/tex]Now adding equations (1) and (3) we get
23x-12y=1
-516x+12y=-36
____________
-493x=-35
[tex]x=\frac{35}{493}[/tex]
Substitute the value of [tex]x=\frac{35}{493}[/tex] in equation (1) we get
[tex]23\times (\frac{35}{493})-12y=1[/tex]
[tex]\frac{805}{493}-12y=1[/tex]
[tex]-12y=1-\frac{805}{493}[/tex]
[tex]-12y=\frac{-312}{493}[/tex]
[tex]y=\frac{26}{493}[/tex]
Therefore the values are [tex]x=\frac{35}{493}[/tex] and
[tex]y=\frac{26}{493}[/tex]
The solution is ([tex]\frac{35}{493},\frac{26}{493}[/tex])
how can u use volume and surface area to solve real world problems
Answer:
You could use surface area to find the amount of wrap needed for a bale. You could use surface area to figure out how much frosting is needed to frost a cake. You could use surface area to find out how much paint is needed to paint a house.
Step-by-step explanation:
Surface area and volume have numerous real-world applications. They are employed in Biology to understand cell functioning, in Physics to calculate celestial volumes, and in Environmental Studies to assess pollution levels and treat diseases. Accurate measurements and unit consistency are crucial for these applications.
Explanation:Volume and surface area can be implemented in an array of real-world scenarios. For instance, in Biology, the calculation of surface area to volume ratios is essential in understanding how cells function. Larger cells have a smaller surface area to volume ratio, which can impact how efficiently they can transfer nutrients or remove waste. If the cell becomes too large, it might not be able to sustain itself sufficiently with the nutrients absorbed, or remove waste effectively. Thus, we see here that surface area to volume ratios can even be essential for life itself.
In Physics, we can extrapolate the volume of Earth's oceans or the galaxy by observing specific measurements. Volume calculations are also used in Engineering and Construction to estimate the quantity of material needed for a particular project. In Environmental Studies, we can evaluate the pollution affecting species habitat or resolve diseases impacting humans, using these geometric concepts.
In all these cases, a consistent usage of appropriate units (likes meters, kilograms, and others depending on the context) is key to getting accurate results. Also, bear in mind that the application of these mathematical concepts often requires creativity and insight to solve problems effectively.
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help pls thanks you
Each year Malcolm earns about 120 hours of vacation time at his job. There are 52 weeks in a year. What is the approximate number of hours of vacation time that malcolm earns each week?
Answer:
2.3
Step-by-step explanation:
.
By dividing the total vacation hours Malcolm earns in a year (120) by the total number of weeks in a year (52), we find that Malcolm earns approximately 2.31 hours of vacation time per week.
Explanation:The question is asking us to find out how many vacation hours Malcolm earns per week. To solve this, we can simply divide the total vacation hours Malcolm earns in a year (120) by the total number of weeks in a year (52).
Here's the step by step process:
Identify the total vacation hours Malcolm earns in a year, which is 120.Next, we divide that number by the number of weeks in a year, which is 52.Perform the calculation: 120 ÷ 52 ≈ 2.31.Therefore, Malcolm earns approximately 2.31 hours of vacation time per week.
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determine whether each pair of functions are inverse functions. 1) f(x)=10x+9/8, g(x)=25x-9/10 2) f(x)=x-9, g(x)=x+9
a. both 1 and 2 are inverse functions.
b. only 2 is an inverse function
c. brother 1 nor 2 is an inverse function.
d. only 1 is an inverse function
Final answer:
After analyzing both pairs, it is evident that only the second pair, f(x) = x - 9 and g(x) = x + 9, meet the requirements for inverse functions, as both compositions f(g(x)) and g(f(x)) return the original input x. Hence, option b: only 2 is an inverse function, is correct.
Explanation:
To determine whether each pair of functions are inverse functions, we must check if applying one function following the other returns the original input value. For two functions, f(x) and g(x), to be inverses of each other, the following must hold true:
f(g(x)) = x
g(f(x)) = x
Pair 1: f(x) = 10x + 9/8, g(x) = 25x - 9/10
Applying g to f:
g(f(x)) = g(10x + 9/8) = 25(10x + 9/8) - 9/10
After simplifying, this does not equal x, so f and g are not inverse functions.
Pair 2: f(x) = x - 9, g(x) = x + 9
Applying g to f:
g(f(x)) = g(x - 9) = (x - 9) + 9 = x
Applying f to g:
f(g(x)) = f(x + 9) = (x + 9) - 9 = x
In the second pair, both compositions return the input x, so f and g are inverse functions of each other. Therefore, the answer is option b: only 2 is an inverse function.
-4/5x - 20/7x = 663/56 - 1/2x
Answer:
I believe the answer to this question is: X= -3 3/4
Please help!!
What is the location of the point on the number line that is 4/9 of the way from
A= -8 to B = 10?
Ο Α. 0
OB. 2
O c. -2
O D. -1
Answer:
Α. 0
Step-by-step explanation:
Given A = -8 and B = 10
The distance between A and B
= B - A
= 10 - (-8)
= 10 + 8
= 18 units
4/9 of the way between A and B
= 4/9 of the distance between A and B
= 4/9 x 18 units
= 8 units.
Hence the location of the point that is 4/9 of the way from A to B
= value at point A + 8 units
= -8 + 8
= 0 (answer)
A. 0
Step-by-step explanation:
The answer is 0 (zero)
3(x+2)=−5−2(x−3)
x = ___
(type your answer as a number, "no solution" or "infinite solutions")
Answer:
x = -1
Step-by-step explanation:
3(x+2)=−5−2(x−3) multiply 3 and -2 with inside the parenthesis
3x + 6 = -5 -2x + 6 now add the like terms
3x + 2x = 1 - 6
5x = -5 simplify both sides
x = -1
1. Which equation represents a linear function?
a. 3y + x2 + x = 0
b. 4x + 2(y – 1) = 0
c. y = 12vx – 5
d. 2x3 + y = 9
Answer:
b.
Step-by-step explanation:
4x + 2(y – 1) = 0
The variables are all of unit degree so it is linear.
On a weather map,an isobar connects places with the same
Answer:
pressure
Step-by-step explanation:
the root words for isobar are
iso - same or equal
bar - pressure (from greek "baros")
Answer:
Pressure
Step-by-step explanation:
14. Find the value of the function:
If f(x) = 4x + 4x - 4, find f(0).
f(0) =
Answer:
f(0) = -4Step-by-step explanation:
[tex]f(x)=4x^2+4x-4\ or\ f^*(x)=4x+4x-4=8x-4\\\\f(0)-\text{put}\ x=0\ \text{to}\ f(x):\\\\f(0)=4(0)^2+4(0)-4=4(0)+0-4=0-4=-4\\\\f^*(0)=8(0)-4=0-4=-4[/tex]
The maximum value of y=√(x+2)-1 on the interval [-2 ,2]
Answer:
1
Step-by-step explanation:
The square root function is monotonically increasing, so will have a maximum at the right end of any interval. Here the maximum is at x=2. That value is ...
y = √(2+2) -1 = 2 -1 = 1
The maximum value on the interval is 1.
7y+3=4y−18
y = ___
(type your answer as a number)
Answer:
y = -7
Step-by-step explanation:
To solve for 'y', we need to isolate it, meaning to separate it from everything else. You move numbers in the equation around by canceling them out, which you do with opposite or reverse operations. (Addition and subtraction are opposites. Division and multiplication are opposites).
First, bring all of the numbers with 'y' to the left, and bring all of the numbers without 'y' to the right. Then isolate y.
7y + 3 = 4y - 18 Move 'y' to the left.
7y - 4y + 3 = 4y - 4y - 18 Subtract 4y from both sides.
7y - 4y + 3 = -18 Notice 4y - 4y cancelled out. Combine like terms on the left. 7y and -4y both have 'y'.
3y + 3 = -18 Move the numbers to the right.
3y + 3 - 3 = -18 - 3 Subtract 3 from both sides.
3y = -18 - 3 +3 and -3 cancelled out. Combine like terms on right.
3y = -21 Cancel out the '3' attached to 'y'.
3y/3 = -21/3 Divide both sides by 3.
y = -21/3 3y/3 becomes just 'y' because 3 ÷ 3 is 1.
y = -7 Answer for y.
The chart below shows one store's sales of computers, listed by model.
May
June
Quilren
Quilren
Dinztop
u Quilren 2
Juvanto
Dinztop
Quilren 2
Juvanto
If the changes in sales between May and June continue at the same rate, what will be the percent change in total computer
sales from June to July? (Round your answer to the nearest tenth.)
17.1%
20.7%
34.0%
43.2%
Answer:
17.1
Step-by-step explanation:
Final answer:
The percent change in total computer sales from June to July cannot be calculated without the specific numerical sales data for each model. We need the quantities sold in May and June to determine the rate of change and project this to July.
Explanation:
To determine the percent change in total computer sales from June to July, based on the provided sales chart data, we first need to calculate the change from May to June for each computer model separately. If we assume that the sales data numbers in the chart represent the quantity of computers sold, we can take the difference in sales of each model between the two months and then sum these differences to get the total change in sales. Afterward, we'll need to express this total change as a percentage of the total sales in June.
However, the actual sales data with quantity figures are not provided; hence, we cannot calculate the exact percent change. The question seemingly requires specific numerical data to calculate the change in percentage, which is not included in the text above. Without such data, it is impossible to provide a step-by-step solution to the question regarding calculating the percent change in total computer sales.
how many integers from 1 to 1 million dont have common factors with 2020
Is -3.5 greater than -1.5
Answer:
No.
Step-by-step explanation:
On the number line, a number is greater than a number to its left. For example, 3 is to the left of 5, so 5 is greater than 3.
On the number line, -3.5 is to the left of -1.5, so -1.5 is greater than -3.5.
After comparing the given two negative numbers we conclude that,
the number -3.5 is not greater than -1.5.
A negative number is one that always has a value lower than zero and is denoted by the minus (-) symbol.
The given numbers are,
-3.5 and -1.5
Subtract -1.5 from -3.5
-3.5 - (-1.5)
Remove bracket by multiplying signs,
-3.5 + 1.5
= -2.0
Now it can be written,
-3.5 = -1.5 - 2.0
Since,
-1.5 - 2.0 < -1.5
Therefore,
-3.5 < -1.5
Hence,
The number -3.5 is not greater than -1.5.
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Given the below sequence:
-1, -3, -5, -7, . . .
(a) What are the next 3 terms
(b) Is this an arithmetic or geometric sequence?
(c) Why?
(d) How would you find the 27th term? Find the 27th term. (show your work)
Answer:
a) The next three terms are -1,-3,-5,-7,-9,-11,-13
b) This is arithmetic sequence
C) The difference of second term and first term is -2 in given sequence so the given sequence is an arithmetic sequence.
d) The 27 th term is -53
Step-by-step explanation:
a) the given sequence is arithmetic sequence
the difference of second term and first term is -2
given sequence is -1,-3,-5,-7.....
the nth term in arithmetic sequence
[tex]t_{n} = a+(n-1)d[/tex]
First term is a = -1 and difference is d = -2
finding fifth term is
[tex]t_{5} = -1 +(5-1)(-2)[/tex]
[tex]t_{5} = -1-8 =-9[/tex]
finding sixth term is
[tex]t_{6} = -1 +(6-1)(-2)[/tex]
[tex]t_{6} = -1-10 =-11[/tex]
finding seventh term is
[tex]t_{7} = -1 + (7-1)(-2)[/tex]
[tex]t_{7} = -1 -12 =-13[/tex]
The next three terms are -9,-11,-13
The given sequence is -1,-3,-5,-7,-9,-11,-13
b) This is arithmetic sequence.
C) because the difference of second term and first term is -2 so the given sequence is arithmetic sequence.
d) by using nth term formula in arithmetic sequence
[tex]t_{n} = a+(n-1)d[/tex]
a= -1 and d =-2
find 27 t h term :-
[tex]t_{27} = -1 + (27-1)(-2) = -1-52=-53[/tex]
In Triangle F G H, what is the measure of Angle H?
Triangle F G H. Angle F is 43 degrees, angle G is x degrees, angle H is (x minus 1) degrees.
42 degrees
43 degrees
68 degrees
69 degrees
Answer: 68
Answer:
69°
Step-by-step explanation:
The three interior angles in a triangle will always add up to 180°, so we have:
43°+x+(x-1)=180°
43°+2x-1°=180°
2x=180°-43°+1°
2x=138°
x=69°
Answer:
69 degrees
Step-by-step explanation:
Which of the following shapes is a convex polygon?
Answer:
Therefore the correct option is B.
Step-by-step explanation:
i) A convex polygon is a polygon which has all its interior angles as less than 180°.
ii) From visual inspection of all four options only option B seems to fulfill the criteria mentioned in i)
Therefore the correct option is B.
Answer:the answer is b
Step-by-step explanation:
I got it corrrect trust me
What is 13.92 divided by 24 equal?
Answer:
0.58
Step-by-step explanation:
Using 6 as a denominator, what fraction completes the following equation: 1 − 1/3 = ? a. 3/6 c. 5/6 b. 4/6 d. 2/6
Answer:
the answer is c :)
In a different plan forarea codes the first digit is 1 through 6 the second digit is either 5 6 7 or 8 the third digit could be any number except 5 with this plan how many ways is area code possible
Answer:
216
Step-by-step explanation:
There are 6 options for the first digit.
There are 4 options for the second digit.
There are 9 options for the third digit.
The total number of combinations is 6 × 4 × 9 = 216.
Find the x-component of this vector:
Answer: -13.9
This value is approximate.
==================================================
Explanation:
This angle is in quadrant Q2, which is where x is negative and y is positive.
The angle shown of 65 degrees is added to the 90 degree angle to the right resulting in 65+90 = 155 degrees overall. See diagram below.
The x component of the vector is found by the formula
x = r*cos(theta)
we will plug in r = 15.3 as the magnitude of the vector and theta = 155 as the angle
x = 15.3*cos(155)
x = -13.8665 approximately
x = -13.9 rounding to one decimal place (as 15.3 and 65.0 are both rounded to one decimal place)
plz help i will mark brainliest
Answer:
x = 9.
Step-by-step explanation:
42 - 15 = 27
27 ÷ 3 = 9
what is -22 = -9 +n
Answer:
If you are looking for n then
N = -13
Step-by-step explanation:
-13+-9 is -22
Answer
n= -13
-22 = -9 + n
first flip the equation
n + -9 = -22
then add 9
so -22 + -9 = - 13
so n = -13