Answer:
12 (-0.25)ⁿ
Step-by-step explanation:
recall that the general form for each term in the geometric progression is
arⁿ
such that the geometric progression looks something like.
ar⁰, ar¹, ar², ar³, ....., arⁿ, ......
also note that r⁰ = 1, hence ar⁰ is simply a
hence the G.P can be written
a, ar, ar², ar³, ....., arⁿ, ......
also note that r can be obtained by simply dividing the 2nd term with the 1stterm. i.e
r = ar ÷ a
now we are given the first 3 terms in the GP as
12, -3, 3/4, ....
comparing with the GP in the previous paragraph, we can see that ,
a = first term = 12
also
r = 2nd term ÷ 1st term
= -3 ÷ 12
= -0.25
hence the nth term
= arⁿ
= 12 (-0.25)ⁿ
Find the volume of the program. Round to the nearest tenth if necessary
This is pretty much half the volume of a rectangular prism, so we multiply 4.8*2.5*3.4 to get 40.8 mm^3
Then we take half of that to get 20.4 mm^3
Hope that helped you to understand!
estimate the sum 7.234 + 3.9 + 6.56
7.234 + 3.9 + 6.56
7.234 + 10.46
17.694 (actual)
17.69 (rounded to the hundredths place)
17.7 (rounded to the tenths place)
18 (rounded to the ones place)
Hope this helps! ;)
The diagram represents the factorization of x2 – 9x + 18. It is partially completed.
A 2-column table with 2 rows. First column is labeled x with entries x squared, question mark. Second column is labeled negative 3 with entries question mark, 18. First row is labeled x with entries x squared, question mark. Second row is labeled negative 6 with entries question mark, 18.
Which two terms are missing from the diagram?
–x and –8x
–2x and –7x
–3x and –6x
–4x and –5x
Answer:
The missing terms are - 3x and - 6x.
Step-by-step explanation:
The table represents the factorization of x2 – 9x + 18. It is partially completed.
So, the unknown term in the first row and second column will be the product of -3 and x i.e. -3x.
And the unknown term in the second row and first column will be the product of -6 and x i.e. -6x.
Therefore, the missing terms are - 3x and - 6x. (Answer)
The two terms that are missing in the diagram are –3x and –6x
How to determine the missing term Method 1The two missing term can be obtained as follow:
Multiply –3 and x together. The result is –3xMultiply –6 and x together. The result is –6xThus, the two missing term are –3x and –6x
Method 2The missing term can be obtained by doing a partial factorisation of the expression. This can be obtained as follow:
x² – 9x + 18
Multiply the 1st term (i.e x²) and the last term (i.e 18) together. The result is 18x².Find the two factors of 18x² such that the sum of the factors is equal to –9xThe factors are –3x and –6xSubstitute –3x and –6x in place of –9x in the equation above. We havex² – 9x + 18
x² – 3x – 6x + 18
Thus, the missing terms are –3x and –6x
Complete question:
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Which statement describes the graph of f(x) = x² - 6x + 9?
a line with an x-intercept of (-3, 0)
a parabola with an x-intercept of (-3, 0)
a line with an x-intercept of (3, 0)
a parabola with an x-intercept of (3, 0)
Answer:
A parabola with an x-intercept of (3, 0)
Step-by-step explanation:
We can immediately rule out the first and third options, because the equation of a second degree function is a parabola.
Your equation is
ƒ(x) = x² - 6x + 9 = 0
We can factor this equation as
ƒ(x) = (x - 3)²
The parent parabola, y = x², has its x-intercept at (0,0).
Your function subtracts three from x, so the intercept is shifted three units to the right.
The graph of your function is a parabola with an x-intercept of (3, 0).
The figure below shows the graph of your function shifted three units by subtracting three from x.
Mr. Slater invested $100,000 in a portfolio that is contains 60% stocks and 40% bonds. Over the course of a year, the value of the stocks
increased to 67%, and the value of the bonds decreased to 33%. The current value of his investment is $118,400. How much should Mr. Slater
move from stocks to bonds to rebalance his portfolio to 60% stocks and 40% bonds?
A.
$8,900
OB. $8,500
C.
$8.288
D.
$8,100
Answer:
c.8288
Step-by-step explanation:
Answer:
Mr. Slater invested $100,000 in a portfolio that is contains 60% stocks and 40% bonds. Over the course of a year, the value of the stocks increased to 67%, and the value of the bonds decreased to 33%. The current value of his investment is $118,400. How much should Mr. Slater move from stocks to bonds to rebalance his portfolio to 60% stocks and 40% bonds?
A.
$8,900
B.
$8,500
C.
$8,288
D.
$8,100
Step-by-step explanation:
#platofam
The larger of two numbers is 15 more than the smaller number. Five times the larger number is 40 more than twelve times the smaller number. Find the num
Answer:
The numbers are 20 and 5.
Step-by-step explanation:
x = y + 15
5x = 12y + 40
5(y + 15) = 12y + 40
5y + 75 = 12y + 40
-7y = -35
y = 5
x = 5 + 15 = 20
The numbers are 20 and 5.
other dude correct
Step-by-step explanation:minecraft IGN Toothpaste123 and use code gki in the fortnite item shop. i play hypixel skyblock btw!
jeffery plans to rent a beach house for his sister's birthday and will use his savings pay for it. The company charges a $25.00 cleaning fee plus $10.00 per hour for the house . if he rents the house for 6 hours, what will be the change in jeffery's saving?
Answer:
-$85
Step-by-step explanation:
The charge will be $25 + ($10/h)(6 h) = $25 +60 = $85.
Jeffrey's savings will decrease by $85, so the net change is -$85.
2/3 year is how many months
Answer:
2/3 of a year is 8 months.
Step-by-step explanation:
Since there is 12 months in a year, divide 12 by 3.
12÷3= 4
Now, multiply 4 by 2.
4×2= 8
This gives you the answer of 8 months.
Answer: 8 months
Step-by-step explanation: multiply denominator and numerator by 4 so it can be equivalent to 12 months.
Round 6.677 to the nearest tenth,
Answer:
6.7
Step-by-step explanation:
the tenths place is one spot after the decimal
Why wouldn’t you use a division to find an equivalent fraction for 7/15
To simplify a fraction by division you must have common factors between the denominator and the neominator to divide (or cancel) them
What is 20 = f - 27.
Answer: 47
Step-by-step explanation:
Just add 27 and 20 then you get f
Just use inverse operations
Aaron runs a distance of 7.2km in the SE direction. How Far East has Aaron run?
when factoring, what is the first thing you need to do?
Answer:
1st step would be to check to see if you can factor anything out:
Greatest Common Factor. This means the greatest number that you can divide EVERY term by.
Suppose f(x) = x+1. Find the graph of f(1/4x)
The graph of the equation [tex]f(\dfrac{1}{4}x)=\dfrac{1}{4}x+1[/tex] has a slope of 1/4 and y-intercept of 1.
What is the graph of a linear equation.
The graph of a linear equation is a straight line graph. It can be expressed as function of x i.e. f(x) = y = mx + b.
Given that: f(x) = x + 1, we are to graph the function of f(1/4x). We will have to replace (1/4x) into the original equation.
[tex]f(\dfrac{1}{4}x)=\dfrac{1}{4}x+1[/tex]
It implies that the graph of f(1/4x) has a slope of 1/4 and the y-intercept is 1. So it will be less steeper than the equation f(x) = x + 1.
– 2(– 3х + 4) + 3x — 3 = — 29
Answer:
x = - 2
Step-by-step explanation:
– 2(– 3х + 4) + 3x — 3 = — 29
6x - 8 + 3x - 3 = - 29
9x = - 29 + 8 + 3
9x = - 18
x = - 18 : 9
x = - 2
Answer:
x = -2
Step-by-step explanation:
– 2(– 3х + 4) + 3x — 3 = — 29 multiply -2 with inside the parenthesis remember negative sign multiplied by negative sign is positive
6x - 8 + 3x - 3 = - 29 add the like terms
9x - 11 = -29
9x = -29 + 11
9x = -18
x = -2
a book store cost $80 a day to keep open, and it spends $15 for each book that it sells. if each book sells for $23, what is the break-even point for this booksotre?
The break even point for this book store is 10
Solution:
Given that, book store cost $80 a day to keep open, and it spends $15 for each book that it sells
Cost to open the book store = $ 80
The formula for solving the break even point (BEP) is:
[tex]BEP = \frac{\text{Fixed cost}}{\text{Selling price - variable cost}}[/tex]
Fixed Cost is the cost that remains constant whether the services provided or products sold increases or decreases
Variable Cost is the cost that varies or differs in proportion to the products or services produced, whether they increased or decreased
In this problem,
Fixed cost = $ 80
Selling price = $ 23
Variable cost = $ 15
Therefore,
[tex]BEP = \frac{80}{23-15}\\\\BEP = \frac{80}{8}\\\\BEP = 10[/tex]
Thus break even point for this book store is 10
In order for the bookstore to continue its business, it should sell at least 10 books to meet its $80 cost
Answer:p=10
Step-by-step explanation:
Can someone please answer this question please answer my question and answer it correctly and show work please
Answer:
Hours inequality (solution set): 0 ≤ x ≤ 7
Cost inequality: $2 ≤ y ≤ $100
Step-by-step explanation:
The babysitter charges $14 dollars per hour + bus fare
Price per hour = $14
Bus fare = $2
Mr. Tyler wants to spend no more than $100
Subtract the bus fare from the total amount, as that will not contribute to the babysitter's hours
$100 - $2 = $98
Divide by $14 per hour
$98 ÷ $14 = 7 hours
The maximum amount of time that Mr. Tyler could hire the babysitter for is 7 hours
This means that the hours cannot be greater than 7. It is given that x cannot be less than 0, because the babysitter cannot work negative hours.
0 ≤ x ≤ 7
This inequality shows that the Mr. Tyler will not have the babysitter work for less than 0 hours, or more than 7 hours. He will have to pay $2 minimum, or $100 max. Below is the inequality to represent this:
(y represents amount Mr. Tyler will pay)
$2 ≤ y ≤ $100
Hope this helps :)
Ty sells signs in a monthly craft fair,and he can make 7 signs every 2 hours. Harrison can sign 15 signs every 4 hours. Who has the greater rate?
Answer:
If Ty can make 7 signs in 2 hours that means in 4 hours he could double that output to make 14 signs. Harrison, on the other hand, makes 15 signs every 4 hours. Therefore, by default - Harrison makes 1 more sign every 4 hours than Ty. Harrison has the greater rate. You have to figure out how many signs Ty can make in 4 hours, by multiplying 2 x 7 = 14. Hope that helps.
Step-by-step explanation:
Suppose that y varies directly with x
and y = 10 when x = 20. What is y
when x = 15?
It’s a fraction
Answer:
15/2
Step-by-step explanation:
y varies directly as x can be written as:
y & x
y = Kx
K = y/x
But from the question, we were told that:
y = 10
X = 20
K = y/x
K = 10/20
K = 1/2
The formula for the expression is:
y = Kx
y = 1/2 x
Now let us solve for y, when:
x = 15
y = 1/2 x
y = 1/2 x 15
y = 15/2
Final answer:
To find the value of y when x = 15, we first determined the constant of proportionality (k) using the given y and x values, which was found to be 0.5. We then plugged x = 15 into the direct variation formula y = kx, resulting in y = 7.5.
Explanation:
If y varies directly with x and y = 10 when x = 20, then we can write this direct variation as y = kx, where k is the constant of proportionality. To find k, we substitute the known values of x and y and solve for k:
10 = k × 20
k = 10 / 20
k = 0.5
With k found, we can now determine what y is when x = 15:
y = k × x
y = 0.5 × 15
y = 7.5
a relation contains the points (-5,-10) (-2,-4) (-1,-2) (4,8) (5,10) is this a function?
Answer:
This is a function and there is no value of x for which we will get two or more different values of y.
Step-by-step explanation:
A relation contains the points (-5,-10), (-2,-4), (-1,-2), (4,8), and (5,10).
So, if we want to model the equation that includes those points then we will get the equation of a straight line passing through the origin {Since the rate of change of y with respect to x is uniform.
The equation is y = 2x
Now, this is a function and there is no value of x for which we will get two or more different values of y. (Answer)
HELP ME FOR A BRAINLIST AND 20 POINTS
Answer:
Area = [tex]\frac{5}{12}[/tex] x²
Step-by-step explanation:
The area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
Here b = [tex]\frac{5}{6}[/tex] x and h = x, thus
A = [tex]\frac{1}{2}[/tex] × [tex]\frac{5}{6}[/tex] x × x = [tex]\frac{5}{12}[/tex] x²
An equation is shown : 5x + 3x = 5x + 15/2 what value of 3x makes the equation true?
Answer:
15/2
Step-by-step explanation:
Subtract 5x from both sides of the equation to find out.
5x +3x -5x = 5x +15/2 -5x . . . . . . subtract 5x
3x = 15/2 . . . . . . . . . . . . . . . . . . . . collect terms
The required value of 3x is 15/2.
PLEASE ANSWER
The graphs shown are of two different functions.
A. Both Graph A and Graph B have multiple y-intercepts.
B. Both Graph A and Graph B have only one x-intercept.
C. Graph A is a linear function because it has a constant rate of change.
D. Graph B is not a linear function but also has a constant rate of change.
Answer:
C: Graph A is a linear function and Graph B is also a function but a low and high constant rate
A college student borrows $1500 for 9 months to pay for a semester of school . if the interest is $92.81 find the monthly payment
The monthly payment for the loan of $1500 with $92.81 interest over 9 months is $176.98.
To calculate the monthly payment for a $1500 loan with $92.81 in interest over 9 months, we must first find the total amount to be paid back, which includes both the principal and the interest. The total repayment amount will be $1500 (the original loan) plus $92.81 (the interest), making the total amount $1592.81.
We can then divide this total amount by the number of months the loan will be held to find the monthly payment:
Monthly Payment = Total Repayment Amount ÷ Total Months
Monthly Payment = $1592.81 ÷ 9
Monthly Payment = $176.98
Therefore, the student needs to pay $176.98 every month to pay off the loan in 9 months.
2. Standard form: 8x + y = 9
Slope-intercept form:
Answer:
y = - 8x + 9
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c
Given
8x + y = 9 ( subtract 8x from both sides )
y = - 8x + 9 ← in slope- intercept form
The required slope intercept of the given equation of the line is given as y = -8x + 9.
What is the slope of the line?The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.
What is the equation?The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
Here,
Given the equation of the line,
8x + y = 9,
Rearrange the equation in slope intercept form,
y = -8x + 9
Thus, the required slope intercept of the given equation of the line is given as y = -8x + 9.
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Evaluate \dfrac{e}{4}+2f-3
4
e
+2f−3start fraction, e, divided by, 4, end fraction, plus, 2, f, minus, 3 when e=12e=12e, equals, 12 and f=\dfrac12f=
2
1
f, equals, start fraction, 1, divided by, 2, end fraction.
Answer:
The value of given expression is 1.
Step-by-step explanation:
Consider the given expression is
[tex]\dfrac{e}{4}+2f-3[/tex]
When e=12 and [tex]f=\dfrac{1}{2}[/tex].
Substitute e=12 and [tex]f=\dfrac{1}{2}[/tex] in the given expression.
[tex]\dfrac{12}{4}+2(\dfrac{1}{2})-3[/tex]
On simplification we get
[tex]3+1-3[/tex]
[tex]1[/tex]
Therefore, the value of given expression is 1.
The evaluated result of the expression e/4 + 2f - 3, given specific values e = 12 and f = 5, is 13.
To evaluate the expression e/4 + 2f - 3, we need to follow a systematic procedure. First, we replace 'e' and 'f' with their respective values or expressions, if provided. Once these values are substituted, we perform the mathematical operations in the given order: division, multiplication, and subtraction.
Assuming we have specific values for 'e' and 'f', let's say e = 12 and f = 5. Substituting these values into the expression, we get:
e/4 + 2f - 3
= 12/4 + 2 * 5 - 3
Now, we simplify each part of the expression step by step:
12/4 = 3 (division)
2 * 5 = 10 (multiplication)
3 - 3 = 0 (subtraction)
Summing up the simplified components, we get:
3 + 10 - 0
Finally, performing the remaining additions and subtractions:
3 + 10 = 13
13 - 0 = 13
So, when e = 12 and f = 5, the evaluated result of the expression e/4 + 2f - 3 is 13.
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Complete Question:
Evaluate the equation: e/4 + 2f - 3 when e = 12 and f = 5
Find the solution of the system of equations.
- 8x - 3y = 46
- 8x + 9y = 22
Answer:
x=-5, y=-2. (-5, -2).
Step-by-step explanation:
-8x-3y=46
-8x+9y=22
----------------
3(-8x-3y)=3(46)
-8x+9y=22
--------------------------
-24x-9y=138
-8x+9y=22
-------------------
-32x=160
x=160/-32
x=-5
-8(-5)-3y=46
40-3y=46
3y=40-46
3y=-6
y=-6/3
y=-2
Answer:
(-5, -2)
Step-by-step explanation:
You can find the solution to the system by either doing substitution or elimination. Since it is already it standard form, the easier way that I am showing you is elimination.
- 8x - 3y = 46 First you subtract! not add because you must
- 8x + 9y = 22 cancel 8 them out.
---- 6y=24
6 6
y=-2
to find x, just plug into either equation!
Find the geometric mean of
6 and 24.
Answer:
15
Step-by-step explanation:
6+24=30
30÷2=15
the formula for calculating the mean is the total of the numbers ÷ the number of numbers
Sanchez applied 6 fluid Ounces of an herbicide per acre on 300 acres of com. How many gallons
did he apply
Click here to enter text.
Answer:
Sanchez applied 1,800 fluid ounces of herbicide to his 300 acres of corn.
Step-by-step explanation:
Let's identify what we already know:
1) Sanchez has 300 acres of corn
2) For every 1 acre, Sanchez applies 6 fluid ounces of an herbicide.
So, we need to figure out how many fluid ounces Sanchez used for the entire six acres. We can create a formula for this:
300 acres x 6 fluid ounces = x
x equals total number of fluid ounces. We multiple the number of acres by the fluid ounces, to get 1,800 fluid ounces for the entire 300 acres of corn.
Final answer:
Sanchez applied a total of 14.0625 gallons of herbicide on 300 acres of corn, after converting the total amount of herbicide from fluid ounces to gallons using the equivalence of 1 gallon equal to 128 fluid ounces.
Explanation:
Sanchez applied 6 fluid ounces of herbicide per acre on 300 acres of corn. To determine how many gallons he applied, we'll use the unit equivalence that 1 gallon = 128 fluid ounces. First, we'll calculate the total amount of herbicide in fluid ounces by multiplying the rate of application by the number of acres:
6 fluid ounces/acre imes 300 acres = 1800 fluid ounces total.
Next, we'll convert fluid ounces to gallons:
1800 fluid ounces imes (1 gallon / 128 fluid ounces) = 14.0625 gallons.
Therefore, Sanchez applied 14.0625 gallons of herbicide on the 300 acres of corn.
the arlington drama club is selling tickets to an upcoming play. They can sell at most 250 tickets. The adult tickets for $15 each and student tickets costs $5 each. They would like to raise at least $2000. It x represents the number of adult tickets and y represents the number of student tickets.
Number of adult tickets = 75
Number of student tickets = 175
Solution:
Let x represents the number of adult tickets and
y represents the number of student tickets.
Total number of tickets sold = 250
⇒ x + y = 250 – – – – (1)
Cost of adult ticket = $15
Cost of student ticket = $5
Total cost of collection = $2000
15x + 5y = 2000 – – – – (2)
Multiply equation (1) by 5
⇒ (1) × 5 5x + 5y = 1250 – – – – (3)
Subtract equation (3) from equation (2), we get
15x + 5y – 5x – 5y = 2000 – 1250
⇒ 10x = 750
⇒ x = 75
Substitute x = 75 in equation (1), we get
⇒ 75 + y = 250
⇒ y = 250 – 75
⇒ y = 175
Number of adult tickets = 75
Number of student tickets = 175
Test corner points for maximum revenue. The optimal solution is 250 adult tickets and 0 student tickets, yielding $3750.
To solve this problem, let's set up the equations based on the given information:
1. The total number of tickets sold cannot exceed 250:
[tex]\[ x + y \leq 250 \][/tex]
2. The total revenue must be at least $2000:
[tex]\[ 15x + 5y \geq 2000 \][/tex]
Now, let's solve this system of inequalities step by step:
Step 1: Graph the constraints:
Let's graph the lines corresponding to the equations:
x + y = 250 and 15x + 5y = 2000
Step 2: Find the feasible region:
The feasible region is the area that satisfies all the given constraints. In this case, it will be the region below or on the lines ( x + y = 250 ) and ( 15x + 5y = 2000 ), and within the boundaries of the axes.
Step 3: Identify the corner points:
The corner points of the feasible region are the points where the lines intersect or touch the boundary lines.
Step 4: Test the corner points:
Substitute the coordinates of each corner point into the objective function (the total revenue) to find which one yields the maximum revenue.
Let's start with the calculations:
1. **Graph the constraints:**
We'll need to find the intercepts of each line and draw them on the graph.
For ( x + y = 250 ):
When ( x = 0 ), ( y = 250 )
When ( y = 0 ), ( x = 250 )
For ( 15x + 5y = 2000 ):
When ( x = 0 ), ( y = 400 )
When ( y = 0 ),[tex]x = \frac{2000}{15} = \frac{400}{3} \)[/tex]
Now, let's plot these points and draw the lines.
2. **Find the feasible region:**
Shade the region below or on the lines ( x + y = 250 ) and ( 15x + 5y = 2000 ), and within the boundaries of the axes.
3. **Identify the corner points:**
The corner points of the feasible region are the points where the lines intersect or touch the boundary lines.
4. **Test the corner points:**
Substitute the coordinates of each corner point into the objective function ( R = 15x + 5y ) to find which one yields the maximum revenue.
Let's calculate the corner points:
Corner Point 1: (0, 0)
[ R = 15(0) + 5(0) = 0 ]
Corner Point 2: (250, 0)
[ R = 15(250) + 5(0) = 3750 ]
Corner Point 3: (0, 400)
[ R = 15(0) + 5(400) = 2000 ]
Now, let's compare the revenues:
- Corner Point 1: $0
- Corner Point 2: $3750
- Corner Point 3: $2000
The maximum revenue is $3750, which occurs at the corner point (250, 0).
Therefore, to maximize revenue while satisfying the given constraints, the Arlington Drama Club should sell 250 adult tickets and 0 student tickets.