Sketch a graph representing f(x), indicating all intercepts and min or max points.
Answers
Given the function below;
[tex]f(x)=4-\frac{x^2}{8}[/tex]The x-intercept is the point where f(x) = 0 as shown:
[tex]\begin{gathered} 0=4-\frac{x^2}{8} \\ 0=32-x^2 \\ x^2=32 \\ x=\pm\sqrt{32} \\ x=\pm5.66 \end{gathered}[/tex]The x-intercept of the graph will be at (5.66, 0) and (-5.66, 0)
The y-intercept occurs at the. point where x = 0 to have:
[tex]\begin{gathered} f(0)=4-\frac{0^2}{8} \\ f(0)=4 \end{gathered}[/tex]The y-intercept is (0, 4)
The equivalent graphis as shown below
The graph shows that the function has a maxmum point at (0, 4) with no minimum point.
Related Questions
In order for the data in the table to represent a liner function with a rate of change of -8, what must be the value of a
Answers
By definition, the Rate of change is also called "Slope".
The slope of a line can be found dividing the difference between the y-coordinates of two points, by the difference between the x-coordinate of those points:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]In this case you know that:
[tex]m=-8[/tex]Knowing the following point on the line:
[tex]\mleft(10,27\mright);(11,a)[/tex]You can set up the following (substituting the slope and the coordinates of those point into the formula)
[tex]-8=\frac{27-a}{10-11}[/tex]Now you can solve for "a":
[tex]\begin{gathered} (-8)(-1)=27-a \\ 8-27=a \\ -19=a \\ a=19 \end{gathered}[/tex]The answer is: Third option.
Consumer Economics Each family in a neighborhood is contributing $20 worth of food to the neighborhood picnic. The Harlin family is bringing 12 packages of buns. The hamburger buns cost $2.00 per package. The hot-dog buns cost $1.50 per package. How many packages of each type of bun did they buy?Choose the correct equation that represents the number of buns purchased. [ Select ]Choose the correct equation that represents the cost of the buns. [ Select ][ Select ] packages of hamburger buns were bought.[ Select ] packages of hot dog buns were bought.
Answers
Explanation
In the question, we are given some important details to work with. Here is a list of them.
1) First, we must note that each family is contributing $20 worth of food.
2) Harlin's family brought 12 packages to the party.
3) The 12 packages consist of two types of buns namely hamburgers and hot dogs. The hamburger buns cost $2 per package while the hot-dog buns cost $1.50
Part A
Let's assume that the number of hamburger packages represents x and the number of hot dogs packages represents y. We can conclude that the sum of bought packages should be equal to 12. We can then translate this information into the equation below.
[tex]x+y=12[/tex]Answer A: x+y = 12
Part B
Now, we can figure out the equation that represents the cost of the buns. Since we know the cost of each buns package, we can multiply the cost of each buns package by the number of packages that were brought to the party by the Harlin family.
Also, we will add the resulting expressions and equate it to the cost of the worth of food each family will bring to the party.
Therefore,
[tex]\begin{gathered} Total\text{ cost of hamburgers = }2\times x=2x \\ Total\text{ cost of Hot dogs = 1.50 x y =1.5y} \\ \therefore\text{Tota cost of buns }\Rightarrow\text{ }2x+1.5y=20 \\ \\ \end{gathered}[/tex]Answer B: 2x+1.5y = 20
Part C And Part D
The above sections can be gotten by solving the previous systems of equations simultaneously. Therfore,
[tex]\begin{gathered} x+y=12\text{ -----1} \\ 2x+1.5y\text{ =20 -----2} \end{gathered}[/tex]Let's create equation three from equation 1
[tex]x=12-y-----3[/tex]Then we will substitute equation three into the untouched equation 2
[tex]\begin{gathered} 2(12-y)+1.5y=20 \\ 24-2y+1.5y=20 \\ 24-0.5y=20 \\ -0.5y=20-24 \\ -0.5y=-4 \\ y=\frac{-4}{-0.5} \\ y=8 \end{gathered}[/tex]
it cost $54.50 to put 24,000 in your bathroom how much would you expect it to cost if you wanted 36 tiles
Answers
Given, the cost of 24 tiles $54.50
Step 1: Calculate how much a tile cost. To obtain the cost per tile
[tex]1\text{ tile cost= \$}\frac{54.50}{24}[/tex]Step 2: Calculate the cost to put 36 tiles (i.e the cost per tile multiply by 36)
[tex]\begin{gathered} =\frac{54.50}{24}\times36 \\ =54.50\times1.5 \\ =\text{ \$81.75} \end{gathered}[/tex]Hence, it will cost $81.75 to put 36 tiles
On your own paper, graph the system of equations and identify the solution.−+=−22+=10
Answers
The system of equations is given as
[tex]\begin{gathered} -x+y=-2 \\ 2x+y=10 \end{gathered}[/tex]To plot the graph for each equation, we can prepare a table of values taking
[tex]x=2,4,6,8,10[/tex]EQUATION 1: -x +y = -2
EQUATION 2: 2x + y = 10
The graph can then be drawn as shown below:
The solution to the system of equations is the point where the two graphs intersect.
This is seen in the graph above as (4, 2).
Hence, the correct option is the FOURTH OPTION.
Monica has a yearly salary of $29,700. Her employer withholds $2948 in state and federal taxes and $2573 in FICA taxes throughout the year. She has the following monthly costs: transportation is $140, cell phone bill is $65, student loans require $300 in repayment, and rent is $675. She is using the average monthly costs for each of the following in order to gain an idea of other monthly expenses: utilities are $130, internet is $55, health insurance is $278, and groceries are $220. What is Monica’s monthly net pay amount? Round your answer to the nearest cent, if necessary.
Answers
Step-by-step explanation:
your teacher is not very precise, I fear.
the yearly salary ($29,700) is the gross pay she gets.
the gross pay minus the taxes ($2,948 and $2,573) is then the net pay she receives.
in many cases the employer also withholds the health insurance premium (and then that has to be subtracted too before getting the net pay).
I just think your teacher means by "net pay" how much she will have left are all the monthly costs.
her annual net pay amount is
$29,700 - $2,948 - $2,573 = $24,179
the monthly net pay is $24,179/12 = $2,014.916666... ≈
≈ $2,014.92
she has to pay monthly
$140
$ 65
$300
$675
$130
$ 55
$278
$220
---------
$1,863
based on her monthly net pay she has left
2,014.916666...
- 1,863
---------------------------
151.9166667 ≈ $151.92
per month
please pick based on what you think your teacher means by net pay : the actual net pay by her employer, or how much money she has monthly left after paying all bills.
In 1991 the average family income was about 39000, and in 2011 it was about 66820.
Let
x
=
0
represent 1991,
x
=
1
represent 1992, and so on. Find values for
a
and
b
(rounded to one decimal place if necessary) so that
f
(
x
)
=
a
x
+
b
models the data
a
=
b
=
What was the average family income in 2006?
Answers
The average family income in 2006 is $59865.
What is the income?Based on the information illustrated, the required model is given as:
y = ax + b
y = average family income
x = years since 1991
The slope based on the information given is b = 39000.
Therefore, the family income in 2006 will be:
= (1391 × 15) + 39000
= 59865
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2x-5y = 10
x-intercept:
y -intercept:
Answers
Answer:
x-intercept: (−5, 0)
y-intercept: (0, 2)
Step-by-step explanation:
FOR X INTERCEPT WE KNOW THAT Y WILL BE A AT THE AXIS LINE WE CAN SUBSTITUTE THW VALUE O IN THE PLACE OF Y TO GET X-INTERCEPT
[tex]2x - 5(0) = 10 \\ 2x = 10 \\ \frac{2x}{2} = \frac{10}{2} \\ x = 5[/tex]
5 is the x-intercept
(5,0)
FOR Y INTERCEPT ON THE Y AXIS X IS EQUAL TO 0 WE CAN PLUG IN TO FIND THE VALUE OF THE Y -INTERCEPT IN THE EQUATION
[tex]2(0) - 5y = 10 \\ - 5y = 10 \\ \frac{ - 5y}{ - 5} = \frac{10}{ - 5} \\ y = - 2[/tex]
-2 is the Y-intercept
(0,-2)
Hope this helps
On the first day of summer break, Katie and her friends go to the theater to see the latest action movie, Dark Emperor: Fist of Vengeance. After Katie buys a ticket, she also buys a bucket of popcorn and a soda for $9.25. In all, Katie spends $23.25 at the movie theater. Which equation can you use to find the cost c of Katie's ticket?
Answers
We have the following information:
c is the cost of Katie's ticket; a bucket of popcorn and a soda cost $9.25, we determine c by using the following expression:
[tex]c=23.25-9.25\Rightarrow c=14[/tex](This assuming there is no additional information).
Answer:1234567890
Step-by-step explanation:
hguhouhujnkujnuhb uj kj bk
Convert 3.5 ⋅ 104 to standard form. (5 points)
3,500
35,000
0.000035
Answers
Hope this helps!!
A. A one-way train ticket in the city costs $1.65. A monthly pass costs $55. For what numbers of rides should you buy the monthly pass?
B. In February, there are exactly 4 weeks. You ride the train one time each weekday and two times on Saturdays and Sundays in February. About how much do you save by using the cheaper option?
Answers
A. you should buy pass for minimum 34 ride per month to get profit.
B. you save 4.4$ by using the monthly pass.
How to calculate profit?
if monthly pass cost you more than one way pass then you loss money. To calculate the minimum amount of rides to get profit from monthly pass. Divide the monthly pass cost by one-way ticket cost.
A. minimum rides= cost of monthly pass/cost of one way ticket
minimum rides=[tex]\frac{55}{1.65}[/tex]
minimum rides=33.33
you need to travel at least 34 times to purchase the pass
B. you have 9 rides per week. 5 on weekdays and 4 on weekends
total rides per month= 9×4
=36
cost of 36 rides=36×1.65
59.4
amount you save=59.4-55
=4.4$
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Write an equation for a line perpendicular to 3 y − 6 x = − 15 and passing through the point (6,-4) y =
Answers
The equation of the line perpendicular to 3y-6x = -15 and passing through the point (6,-4) is y = (-1/2)x - 1
The equation of the line is
3y-6x = -15
Convert the equation to the slope intercept form of the line
3y-6x = -15
3y = 6x-15
y = (6x-15)/3
y = 2x-5
The slope intercept form of the line
y = mx+b
By comparing the result with slope intercept form
slope of the line m = 2
The slope of the line perpendicular will be the negative reciprocal of 2
m = -1/2
Therefore the slope of the line will be
y = (-1/2)x+b
The line is passing through the point (6,-4)
Substitute the values in the equation
-4 = (-1/2)×6+b
-4 = -3+b
b = -4+3
b = -1
Substitute the values in the slope intercept form
The equation of the line perpendicular to 3y-6x = -15 and passing through the point (6,-4)
y = (-1/2)x - 1
Hence, the equation of the line perpendicular to 3y-6x = -15 and passing through the point (6,-4) is y = (-1/2)x - 1
The complete question is
Write an equation for a line perpendicular to 3y − 6x = −15 and passing through the point (6,-4).
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What is the distributive property for 3×546 how do you rewrite that
Answers
Answer:
1638
Step-by-step explanation:
3(500)+3(40)+3(6)=1500+120+18=1638
Enter an inequality that represents the graph in the box.
Answers
The inequality that represents the graph is (1/4)x - y + 3/2 ≤ 0.
What is inequality?An inequality compares two non-qual objects.
We know the general equation of a line is ax + by + c = 0.
From observation, we can conclude that the given line has points (0, -6) and (2, 2).
∴ The slope of the line is [tex]\frac{y_2 - y_1}{x_2- _ x_1}[/tex].
= (0 - 2)/(-6 - 2).
= -2/-8.
= 1/4.
∴ Equation of the line in slope intercept form y = mx + b.
2 = (1/4)(2) + b.
2 = 1/2 + b.
b = 3/2.
∴ Equation of the line is y = 1/4(x) + 3/2.
(1/4)x - y + 3/2 = 0 but the region will be (1/4)x - y + 3/2 ≤ 0.
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Customers of a phone company can choose between two service plans for long distance calls. The first plan has a $26 monthly fee and charges an additional0.09 for each minute of calls. The second plan has a $19 monthly fee and charges an additional $0.13 for each minute of calls. For how many minutes of callswill the costs of the two plans be equal?
Answers
First Plan
Monthly fee = $26
charge per min = $0.09
Second Plan
Monthly fee = $19
charge per min = $0.13
Solution
Let the number of minutes spent on calls in a specific month be x
The total cost spent using the first plan:
[tex]0.09x\text{ + 26}[/tex]The total cost spent using the second plan:
[tex]0.13x\text{ + 19}[/tex]If the cost from the first plan would be equal to that of the second plan:
[tex]\begin{gathered} 0.09x\text{ + 26 = 0.13x + 19} \\ \text{collect like terms} \\ 0.04x\text{ = 7} \\ x\text{ = 175} \end{gathered}[/tex]Hence, the number of minutes of calls for which both plans would be equal is 175mins
PLS HELP SOLVE THE ABSOLUTE VALUE EQUATION
Answers
Answer:
See below
Step-by-step explanation:
If the question is SUPPOSED to be
| 2x +3 | = 3 you have to solve for the left side being positive or negative
Positive 2x + 3 = 3
2x = 0
then x = 0
Negative - ( 2x+3) = 3
-2x -3 = 3
-2x = 6
x = -3
So answer A
A clock has a minute hand that is 11 inches long and an hour hand that is 9 inches long. What is the
distance between the end of the hands at 9 o'clock? Round your answer to the nearest inch.
10 inches
14 inches
O16 inches
20 inches
Answers
The Pythagorean Theorem is used to determine that the distance between the hands at 9 o'clock is 14 inches.
What exactly is the Pythagorean theorem?The Pythagorean theorem, also known as the Pythagoras' theorem, is a fundamental relationship in Euclidean geometry between the three sides of a right triangle. It states that the area of the hypotenuse square is equal to the sum of the areas of the squares on the other two sides.It is implied that a clock has an 11-inch-long minute hand and a 9-inch-long hour hand.
We need to find the distance between the end of the hands at 9 o'clock.
At 9 o'clock, the hands form a right angled triangle.
Let the length of minute hand = x , hour hand = y and the distance between the end of the hands at 9 o'clock = z
Therefore, by using Pythagorean theorem,
x² + y² = z²
11² + 9² = z²
z = [tex]\sqrt{11^{2}+9^{2} }[/tex]
z = [tex]\sqrt{202}[/tex]
z = 14.21 rounded to 14 inch
Using the Pythagorean theorem, the distance between the ends of the hands at 9 o'clock is calculated to be 14 inches.
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When solving an equation with one variable on both sides what are three types of solutions youcan obtain?
Answers
whenever you have an equation with one variable on both sides, you might end up with one of the following case:
1. You might end up with an inconsistent equation, therefore there is not solution. Example
x = x+3. If you subtract x on both sides, you get 0=3 which is impossible.
2. You might end up having infinite solutions. Example:
x+6 = x+6. If you subtract x on both sides you get 6 =6 which is true regardless of the value of x.
3. You might end up having only one solution. Example:
3x +2 = x +5
If you subtract x on both sides and subtract 2 on both sides, you get
2x = 3.
then if you divide by two on both sides, you find
x = 3/2. So this equation has one unique solution.
How do I draw the fourth diagram in a square? How do I know how many sticks in the sixth diagram? How many thumb tacks are in the seventh diagram?
Answers
First, we have to analyze how each number grows (the number of thumbs and the number of sticks for each diagram)
So we can build two equations that give us the number of thumbs and the number of sticks for each diagram, let be n for the number of the diagram, so :
Now we can know the number of thumbs and sticks for any diagram, and we can solve the questions provided, first, let's draw the 4th diagram:
Now
How do I know how many sticks are in the sixth diagram?
sticks= 4(6) = 24
There are 24 sticks in the sixth diagram.
How many thumb tacks are in the seventh diagram?
thumbs= 3(7)+1 = 22
There are 22 thumbs in the seventh diagram.
I need help writing the formula step by step please if anyone can help
Answers
f(x)=x ^2
Translate 8.5 units to the left
f(x)= (x + 8.5 )^2
vertical Stretch of a factor of 3
f(x)= 3 (x + 8.5 )^2
7 units down
f(x)= 3 (x + 8.5 )^2 - 7
6ft , 5ft , c. What is the length of the hypotenuse
Answers
The length of the hypotenuse of the triangle is √61 ft
How to determine the length of the hypotenuse?From the question, we have the following parameters that can be used in our computation:
Smaller sides = 6ft and 5 ft
Hypotenuse = c
The hypotenuse of a triangle is calculated using the following Pythagoras theorem
Hypotenuse^2 = Opposite^2 + Adjacent^2
Where Opposite and Adjacent are 6 and 5
So, we have
c^2 = 5^2 + 6^2
Evaluate
c^2 = 61
Take the square roots
c = √61
Hence, the hypotenuse is √61 ft
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Suppose r varies directly as the square of m, and inversely as s. If r equals 16when m equals 9 and s equals 9, find r when m equals 27 and s equals 9.
Answers
Answer:
144
Step-by-step explanation:
r = k m^2 / s <====given ( k is proportionality constant)
16 = k ( 9^2) / 9 shows k = 1 7/9
then:
r = 1 7/9 * 27^2 / 9 = 144
Simplify the expression to a + bi form:(12 – 6i)(3 – 10i)
Answers
Solution:
Given the expression:
[tex](12-6i)(3-10i)[/tex]To simplify in the form:
[tex]a+bi[/tex]step 1:
Multiply the terms in the second parenthesis by each term in the first parenthesis.
Thus,
[tex]\begin{gathered} 12(3-10i)-6i(3-10i) \\ \Rightarrow36-120i-18i+60i^2 \end{gathered}[/tex]step 2:
Collect like terms.
[tex]\begin{gathered} 36-120i-18i+60i^2 \\ \text{but } \\ i^2=-1 \\ \text{thus,} \\ 36+60(-1)-120i-18i \\ \Rightarrow36-60-120i-18i \\ =-24-138i \\ \Rightarrow-24+(-138)i \end{gathered}[/tex]Hence, the expression is simplified as
[tex]-24+(-138)i[/tex]Use the data shown to answer the questions that follow.
Person Minutes Shopping in the Store Amount Spent on Groceries at Checkout
1 56.5 177.5
2 84.4 260.2
3 66.3 197.9
4 47.3 82.9
5 48.7 147.1
6 47.1 148.3
7 60.7 182.1
8 76 228
Which graph is most appropriate for these data?
Bar Chart
Scatter Plot
Pie Chart
Time Series Plot
Copy and paste the above data into Excel and make the most appropriate graph for these data. Make sure the x-axis represents the "Minutes Shopping in the Store" and that the y-axis represents the "Amount Spent on Groceries at Checkout."
I have successfully created this graph in Excel as requested.
I have not graphed the data.
One of the values in the plot of this data does not fit the pattern of the other values. It would be called an outlier.
What is the x-value and y-value of the outlier?
(
Number
,
Number
)
Hint: If you hover your mouse over the points in your Excel graph it will show you the exact x-value and y-value of the point.
Answers
The one data point that does not fit in scatter plot to the pattern is (60.7 , 182.1)
What is a scatter plot meaning?
A scatter plot is a collection of dots that are plotted on a horizontal and vertical axis. In statistics, scatter plots are crucial because they can demonstrate the degree of correlation, if any, between the values of observed quantities or occurrences (called variables).Determine the link or correlation between two variables using a scatter plot. You may find out whether your data points might be related by plotting a scattergram with them.The best chart is Scatter Plot
The one data point that does not fit to the pattern is
(60.7 , 182.1)
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Use the graph of the exponential function to answer the following question.Which statements about the graph are TRUE? Select all that apply. A. The x-intercept is 2. B. The y-intercept is 3. C. The asymptote is y = -1D. The range is all real numbers E. The domain is all real numbers F. The function shows growth G. As x increases, y approaches, but never reaches, -1
Answers
The curve intersect the x axis at x = 1. So x-intercept is 1. Statement A is false.
The curve intersect the y-axis at y= 3. So y intercept is 3. Statement B is correct.
The curve tends toward infinity at y = -1. So y = -1 asysmptote of the function. Statement C is correct.
The range of function is y > -1. So range is not all real number. Thus statement D is incorrect.
The function is defined for x > -0.5. At x = 0.5 function tends toward infinity. Thus statement E is incorrect.
As we move from left to right on x-axis then function decreases. So function shows decay. The statement F is incorrect.
The value of function approaches -1 as value of x increase but does not cross -1 ot touch the value y = -1. So statement G is correct.
Thus correct statement are,
B, C and G.
PLEASE ANSWER)At the grocery store, on 8-ounce bottle of salad dressing costs $1.76 A 28 ounce bottle costs 5.88. How much cheaper is it per ounce bottle rather then the 8 ounce bottle
Answers
A 28 ounce bottle is $0.01 per ounce cheaper than 8-ounce bottle of salad dressing.
What is termed as the unitary method?The unitary method is a process that determines the value of a single unit from value of multiple units, as well as the value of multiple units from value of a single unit. "It is a method in which we discover the value of a single unit by subtracting the value of multiple units as well as the value of multiple units by subtracting the value of a single unit."For the given question;
The 8-ounce bottle of salad dressing costs $1.76
This can be written as-
8-ounce bottle -----> $1.76.
For finding the price of one ounce divide both side by 8.
1-ounce bottle -----> $0.22
Now, for 28 ounce bottle.
28 ounce bottle costs $5.88.
28 ounce bottle-----> $5.88.
For finding the price of one ounce divide both side by 28.
1-ounce bottle -----> $0.21
Difference = 1-ounce for 28 bottle - 1-ounce for 8 bottle
Difference = $0.22 - $0.21
Difference = $0.01
Thus, 28 ounce bottle is $0.01 per ounce cheaper than 8-ounce bottle of salad dressing.
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001 (part 1 of 2) 10.0 points
A bug walking on the circular rim of a flower
pot completes one lap around the planter in
12.25 s.
If the radius of the planter is 11.3 em, how
fast was it traveling?
Answer in units of cm/s.
Answers
10 decimeters = 1 meter (m) = 1,000 millimeters
10 meters = 1 dekameter (dam)
10 dekameters = 1 hectometer (hm) = 100 meters
10 hectometers = 1 kilometer (km) = 1,000 meters
Question 1 of 10
What is the slope of the line shown below?
A. 3
B. -1/3
C. -3
D. 1/3
Answers
The manager of a theater wants to know whether the majority of its patrons are adults or children. One day, 5400
tickets were sold and the receipts totaled $23,258. The adult admission is $5.50, and the children's admission is $3.50.
How many adult patrons were there?
There were adult patrons.
Answers
In linear equation, No of Adults = 2,179, No of Children = 3,221 .
What in mathematics is a linear equation?
An x-y linear relationship, or two variables in which the value of one of them (often y) relies on the value of the other one, is what is known as a linear equation in two variables (usually x).The dependent variable in this scenario is y since it depends on the independent variable, x.Let Number of Adult admission be x
Number of children's admission be y
Total tickets were sold = 5400
so x+y= 5400 ....... eq 1
One adult ticket costs $5.50 ,so total Adult ticket costs = 5.50x
One Child ticket costs $ 3.50, so total Children tickets cost= 3.50 y
receipt totaled = $23,258
so 5.50x+3.50y= $23,258....... eq 2
multiply 5.50 to the eq 1, we get,
5.50x +5.50y = 29,700...... eq 3
subtract eq 2 from eq 3, we get,
5.50y-3.50y = 29,700- 23,258
2y= 6,442
divide by 2 both sides ,we get, y= 3,221
substitute the value of y in eq 1, we get,
x+ 3,221 =5400
x= 5400- 3221
x= 2,179
No of Adults = 2,179, No of Children = 3,221
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I need to write an explicit formula for this problem but I have not idea what I'm doing.
Answers
Given data:
The given series is -32, -25, -18, -11,....
The commo difference of the given series is,
[tex]\begin{gathered} d=-25-(-32) \\ =-25+32 \\ =7 \end{gathered}[/tex]The expression for the explicit formula for the given series is,
[tex]\begin{gathered} a_n=a+(n-1)d \\ =\text{ -32+(n-1)}(7) \\ =-32+7n-7 \\ =-39+7n \end{gathered}[/tex]The expression for recursive formula is,
[tex]\begin{gathered} a_n=a_{n-1}+d \\ =\lbrack-39+7(n-1)\rbrack+7 \end{gathered}[/tex]Write an inequality that represents the situation.A certain swimming pool holds no more than 700,000 gallons. How many gallons might be in the pool?
Answers
Let x represent the number of gallons that might be in the pool. When we say 'no more than 700000 gallons', it means 'less than or equal to 700000'. The symbol for 'less than or equal' to is '≤ '
Thus, the inequality representing this situation is
x ≤ 700000