The quadratic function f(x) = 2x² - 16x + 24 can be rewritten in the vertex form f(x) = 2(x - 4)² + 4.
What is the vertex form of the given function?Given the function in the question:
f(x) = 2x² - 16x + 24
To determine the vertex form f(x) = a(x-h)² + k, we need to complete the square.
Factor out the leading coefficient of 2:
f(x) = 2x² - 16x + 24
f(x) = 2(x² - 8x + 12)
To complete the square, we need to add and subtract the square of half of the coefficient of x:
f(x) = 2[(x² - 8x + 16) - 4] + 8
Since (x² - 8x + 16) is a perfect square trinomial, we factored as (x - 4)².
f(x) = 2[(x - 4)² - 4] + 8
Now we can simplify and rewrite in the desired form:
f(x) = 2(x - 4)² - 4 + 8
f(x) = 2(x - 4)² + 4
Therefore, the vertex form is f(x) = 2(x - 4)² + 4.
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Rachel works at a lemonade stand at the park on Monday she used 1 2/5 bags of lemons on Tuesday she use 1 1/4 times as many lemons as on Monday how many bags of lemons does Rachel have use on Tuesday
Answer:
1.75 Bags of Lemons
Step-by-step explanation:
1 2/5 = 1.4
1 1/4 = 1.25
1.4 * 1.25 = 1.75 Bags of Lemons
What is the solid formed when rotated around the side length of 4?
O cylinder with a height of 3 units and a radius of 4 units
O cone with a height of 4 units and a radius of 3 units
cylinder with a height of 3 units and a radius of 5 units
O cone with a height of 5 units and a radius of 4 units
Find the volumes and surface areas of the solids. Give your answers in terms of .
Surface Area: square units
Volume: cubic units
Answer: B: cone with a height of 4 units and a radius of 3 units
Step-by-step explanation:
Surface Area: 9pi + 15pi = 24pi square units
Volume: 9pi x 4 x 1/3 = 12pi cubic units
if det [a 10 e b d 0] = [2 10 3 6 -1 0],find a,d and e
Answer:
The given equation is:
det [a 10 e b d 0] = [2 10 3 6 -1 0]
The determinant of a 3x3 matrix is calculated as follows:
|a b c|
|d e f| = a(ei - fh) - b(di - fg) + c(dh - eg)
Applying this formula to the given matrix, we get:
det [a 10 e b d 0] = a(d0 - b-1) - 10(ed - b0) + e(10*-1 - d*3)
= ab + 10b - 10ed - 3e
Substituting the given values, we get:
ab + 10b - 10ed - 3e = 2(6-0) - 10(3-(-1)) + 3(10-(-1))
ab + 10b - 10ed - 3e = 12 + 40 + 33
ab + 10b - 10ed - 3e = 85
We can simplify this equation by factoring out b and e:
b(a + 10) - e(10d + 3) = 85 - 10b
We can solve for a, d, and e by setting up a system of equations using the given values of the determinant:
ab + 10b - 10ed - 3e = 85
From this equation, we can solve for b:
b(a + 10) - e(10d + 3) = 85 - 10b
Substituting the value of b from the determinant equation, we get:
(a+10)(-1) - e(10d+3) = -8.5
Simplifying, we get:
-a - 10e - 3.3d = -8.5 ...(1)
Also, from the determinant equation, we have:
6a + 10d + 3e = 29
Solving for e in terms of a and d, we get:
e = (29 - 6a - 10d)/3 ...(2)
Substituting equation (2) into equation (1), we get:
-a - 10[(29 - 6a - 10d)/3] - 3.3d = -8.5
Simplifying and multiplying both sides by -3, we get:
3a + 20d - 29e = 25.5
Substituting equation (2) into this equation, we get:
3a + 20d - 29[(29 - 6a - 10d)/3] = 25.5
Simplifying, we get:
a + 6d - 29 = 1.5
a + 6d = 30.5
We have two equations in two variables:
-a - 10e - 3.3d = -8.5
a + 6d = 30.5
Solving for a and d using any method (substitution, elimination, etc.), we get:
a = 7
d = 4
Substituting these values into equation (2), we get:
e = (29 - 6a - 10d)/3 = (29 - 6(7) - 10(4))/3 = -3
Therefore, a = 7, d = 4, and e = -3.
Step-by-step explanation:
I am unsure about how to do this problem, pictured below.
The time taken to reach a population of 500 is gotten from 500=50e^0.55t
What is the exponential growth?
Exponential growth is a process that increases quantity over time as in the bacterial culture here.
We know that from the question, we have;
P(t)=Poe^rt
P(t) = population at time t
Po= Initial population
r = growth rate
t = time taken
Then we have that;
150 = 50e^2r
3=e^2r
ln3 = 2r
r = ln3/2
r = 0.55
If the rate of growth is 0.55, then to reach a population of 500;
500=50e^0.55t
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8[tex]\sqrt{x} -80[/tex]
Answer: [tex]8(\sqrt{x} -10)[/tex]
Step-by-step explanation:
[tex]8\sqrt{x} - 80[/tex]
[tex]8(\sqrt{x} -10)[/tex]
Please help asap need it please
Answer:
Step-by-step explanation:
i think that you times the numbers
Round to the nearest tenth, then find the difference. 13.56 − 10.02 = ___ pleas help in test and am about to leave soon.
The difference between 13.56 and 10.02 is 3.54.
What is subtraction?Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.
The difference between 13.56 and 10.02 can be calculated by doing the subtraction. As,
(13 + 0.56) - (10 + 0.02)
= (13 - 10) + (0.56 - 0.02)
= 3 + 0.54
= 3.54
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What function is represented in the table?
Select one:
y = .5(4^x)
y = 2(.5^x)
y = .5(2^x)
y = 4(.5^x)
The function that represents in the table is y = 0.5(2^x)
Option C is the correct answer.
We have,
Looking at the table,
We can observe that as the value of x increases, the value of f(x) doubles.
This doubling of f(x) indicates that the base of the exponential function is 2.
Also, when x = 0, the value of f(x) is 0.5, which means that the y-intercept of the exponential function is 0.5.
Thus,
The function can be represented as y = 0.5(2^x).
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Use the drawing tool(s) to form the correct answers on the provided graph.
Graph the system of equations given below on the provided graph.
32+y
Then, use the Mark Feature tool to plot the solution to the system.
Drawing Tools
Select
Mark Feature
Line
Click on a tool to begin drawing.
=
-5
10-
80
92
3 Delete
The solution of the given system of equations is (-3, 4).
Given two linear equations.
2x - 3y = -18
3x + y = -5
Multiplying the first equation by 3 and the second equation by 2,
6x - 9y = -54
6x + 2y = -10
Subtracting the equations,
-11y = -44
y = 4
Substituting,
x = -3
The graph of the system of equations is given below.
Hence the solution is (-3, 4).
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Exponential model (10,160) (11,250)
The Exponential model is y = 0.74 (1.79)ˣ
We have,
(10, 160) and (11, 250)
Using the Exponential model
y = abˣ
where a is the initial amount and be is the constant.
Now, the value of b is
= 250/ 140
= 1.79
Now, y = abˣ
140 = a (1.79)⁹
a = 0.74
So, the Exponential model is y = 0.74 (1.79)ˣ
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3.
You have two credit cards. If you budget $375 to pay off your credit card debt and you payoff the highest interest card first while maintaining the interest accrued on the other card, how many months does it take you to pay it off?
Card Name (APR %) Existing Balance Credit Limit
Murk (5.6%) $675.49 $1,500.00
Mini (9.85%) $902.43 $1,000.00
5 months
2 months
4 months
3 months
It takes A. 5 months to pay off (Mini) the highest interest card.
How many months to pay off the highest interest card debt?To determine the number of months it takes to pay off the credit card debt, we shall calculate the monthly payment to pay off the highest interest card first.
First, calculate interest accrued on each card per month:
Murk: (5.6/100)/12 * $675.49 = $2.98 per month
Mini: (9.85/100)/12 * $902.43 = $7.42 per month
Next, we determine the order in which to pay off the cards, which is highest interest card first, we can allocate the entire $375 to Mini and leave a minimum for interest accrued on Murk.
This should be a percentage of the balance.
Assuming it's 2% of the balance, which is $13.51.
So, in month 1, we will pay:
Mini: $375
Murk: $13.51
Leaving these balances:
Murk: $675.49 + $2.98 - $13.51 = $664.96
Mini: $902.43 - $375 + $7.42 = $534.85
In month 2:
Mini: $534.85 + $7.42 = $542.27
Murk: $13.51 + $2.98 = $16.49
Balances:
Murk: $664.96 + $2.98 - $16.49 = $651.45
Mini: $542.27 - $375 + $7.42 = $174.69
month 3:
Mini: $174.69 + $7.42 = $182.11
Murk: $13.51 + $2.98 = $16.49
Balances:
Murk: $651.45 + $2.98 - $16.49 = $638.94
Mini: $182.11 - $174.69 + $5.52 = $12.94
month4:
Mini: $12.94 + $7.42 = $20.36
Murk: $13.51 + $2.98 = $16.49
Balances:
Murk: $638.94 + $2.98 - $16.49 = $625.43
Mini: $20.36 - $12.94 + $0.54 = $8.96
month 5:
Mini: $8.96 + $7.42 = $16.38
Murk: $13.51 + $2.98 = $16.49
Balances:
Murk: $625.43 + $2.98 - $16.49 = $612.92
Mini: $16.38 - $8.96 = $7.42
So, Mini's balance is paid off here.
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Note:
And we can allocate the entire $375 budget to Murk.
This means we will pay off Murk in month 6:
Murk: $612.92 + $2.98 + $375 - $13.51 = $977.39
At Dela's Deli, Dela fills containers with homemade vinaigrette salad dressing. The table shows the amount of vinegar and olive oil used for the dressing.
Number of containers Vinegar (tsp) Olive Oil (tsp)
1 4 12.5
6
At this rate, how much vinegar and olive oil will be used to make 6 containers of salad dressing?
Dela will use 10 teaspoons of vinegar and 75 teaspoons of olive oil to make 6 containers of salad dressing.
Dela will use 10 teaspoons of vinegar and 18.5 teaspoons of olive oil to make 6 containers of salad dressing.
Dela will use 24 teaspoons of vinegar and 75 teaspoons of olive oil to make 6 containers of salad dressing.
Dela will use 24 teaspoons of vinegar and 18.5 teaspoons of olive oil to make 6 containers of salad dressing.
Dela will use 24 teaspoons of vinegar and 75 teaspoons of olive oil to make 6 containers of salad dressing.
We have,
Dela uses a ratio of 4 teaspoons of vinegar to 12.5 teaspoons of olive oil.
So, for 6 containers
= 4 x 6
= 24 teaspoons of vinegar
and, = 12.5 x 6
= 75 teaspoons of olive oil
Thus, Dela will use 24 teaspoons of vinegar and 75 teaspoons of olive oil to make 6 containers of salad dressing.
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The Sugar Sweet Company will choose from two companies to transport its sugar to market. The first company charges $5500 to rent trucks plus an additional
fee of $200.25 for each ton of sugar.
The second company charges $4995 to rent trucks plus an additional fee of $225.50 for each ton of sugar.
For what amount of sugar do the two companies charge
the same?
What is the cost when the two companies charge the
same?
$
Let’s solve this problem by setting the cost of the two companies equal to each other and solving for the amount of sugar. Let x be the amount of sugar in tons.
The cost for the first company is 5500 + 200.25x and the cost for the second company is 4995 + 225.50x.
Setting these two expressions equal to each other, we get:
5500 + 200.25x = 4995 + 225.50x
Solving for x, we get:
25.25x = 505
x = 20
So, the two companies charge the same when the amount of sugar is 20 tons.
The cost when the two companies charge the same is:
5500 + 200.25 * 20 = $9505
So, when the two companies charge the same, the cost is $9505.
Received message. Let's solve this problem by setting the cost of the two companies equal to each other and solving for the amount of sugar. Let x be the amount of sugar in tons. The cost for the first company is 5500 + 200.25x and the cost for the second company is 4995 + 225.50x. Setting these two expressions equal to each other, we get: 5500 + 200.25x = 4995 + 225.50x Solving for x, we get: 25.25x = 505 x = 20 So, the two companies charge the same when the amount of sugar is **20 tons**. The cost when the two companies charge the same is: 5500 + 200.25 * 20 = $9505 So, when the two companies charge the same, the cost is **$9505**.
MARK ME BRAINLEISTIf the diameter of a circle is 8.4 in.. find the area and the circumference of the circle. Use 3.14 for pl. Round your answers to the nearest
hundredth.
Given that the diameter of a circle is 8.4 inches.
The radius (r) of the circle can be found by dividing the diameter by 2:
r = d/2 = 8.4/2 = 4.2 inches
The area (A) of a circle can be found using the formula:
A = πr^2
Substituting the value of r, we get:
A = 3.14 x 4.2^2 = 55.3896 ≈ 55.39 square inches
The circumference (C) of a circle can be found using the formula:
C = 2πr
Substituting the value of r, we get:
C = 2 x 3.14 x 4.2 = 26.3896 ≈ 26.39 inches
Therefore, the area of the circle is approximately 55.39 square inches and the circumference of the circle is approximately 26.39 inches.
We know that the area of a circle is given by the formula A = π×r²
Given the diameter of the circle = 8.4 in
Therefore radius of the circle = 8.4/2 = 4.2 in (diameter/2 = radius)
Now Area of the circle = π × 4.2²
= 3.14 × 17.64
= 55.3896
= 55.39 (round up to the nearest hundredth)
Circumference of the circle = 2 × π × r
= 2 × 3.14 × 4
= 26.376
= 26.38 (round up to the nearest hundredth)
Therefore the area of the circle is 55.39 in² and the circumference is 26.38 in.
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The gradient of every point on the curve C with equation y = f(x), satisfies
dy/dx = 3x2 – 4x + k, where k is a constant. The points P (0, -3) and Q (2,7) both lie on C. find the equation for C.
The equation for the gradient on the curve C is y = x³ - 2x² + 5x - 3
Given data ,
Let the gradient of every point on the curve C is given by the equation dy/dx = 3x² - 4x + k
Now , we can integrate this equation with respect to x to obtain the equation for C
∫(dy/dx)dx = ∫(3x² - 4x + k)dx
Integrating the right-hand side with respect to x, we get:
∫(3x² - 4x + k)dx = x^3 - 2x^2 + kx + C1
where C1 is the constant of integration
Now, on simplifying the points P(0, -3) and Q(2, 7) that lie on C to find the values of C1 and k
For point P(0, -3)
when x = 0, y = -3
Plugging these values into the equation x³ - 2x² + kx + C1 = y, we get:
0³ - 2(0)² + k(0) + C1 = -3
C1 = -3
For point Q(2, 7):
when x = 2, y = 7
Plugging these values into the equation x³ - 2x² + kx + C1 = y, we get:
2³ - 2(2)² + k(2) - 3 = 7
k = 5
On substituting the values of C1 and k back into the equation , we get
y = x³ - 2x² + 5x - 3
Hence , the equation is y = x³ - 2x² + 5x - 3
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Use this table of values to draw the graph of y=2x+3 for values of x from -3 to 3
A graph of y = 2x + 3 for values of x from -3 to 3 is shown in the image attached below.
How to develop the table by using the linear function?Based on the information provided above, the required table can be constructed or developed as follows;
x y = 2x + 3 y___
-3 y = 2(-3) + 3 -3
-2 y = 2(-2) + 3 -1
-1 y = 2(-1) + 3 1
0 y = 2(0) + 3 3
1 y = 2(1) + 3 5
2 y = 2(2) + 3 7
3 y = 2(3) + 3 9
In this scenario and exercise, we would use an online graphing calculator to graphically represent the given data set in the table on a graph as shown in the image attached below.
In conclusion, we can reasonably infer and logically deduce that the domain of this linear function y = 2x + 3 is [-3, 3] and the range is [-3, 9].
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Marcus surveys the students in his school about their favorite lunch.
Lunch
Grilled Cheese
Roast Beef
Chili
Frequency
80
40
50
20
60
Use the data to describe the favorite lunch of students at Marcus's school. Round to the nearest percent and the nearest 10 students.
% of students surveyed preferred grilled cheese, so in a group of 3500 students, about
Chicken & Rice
Other
students will prefer grilled cheese.
32% of the students surveyed preferred grilled cheese, so in a group of 3500 students, about 1120 students will prefer grilled cheese.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
The total number of people surveyed is given as follows:
80 + 40 + 50 + 20 + 60 = 250.
80 students preferred grilled cheese sandwich, hence the percentage is obtained as follows:
p = 80/250 x 100%
p = 32%.
Hence the expected amount of 3500 students is given as follows:
0.32 x 3500 = 1120 students.
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May someone please help me with this question i need the assistance asap
Answer:
144
Step-by-step explanation:A first add 98 + 46 keyword Sum for interior angles
Determine if triangle PQR is similar to triangle LMK. If they are similar enter the scale factor from triangle LMK to triangle PQR.
Triangles PQR and LMK are not similar. Thus none.
What are similar triangles?Two or more triangles are said to be similar if on comparing their corresponding properties, some common relations holds. One important relation is the scale factor that relates one triangle with the other.
In the diagram given, we have;
scale factor = LK/ PR
= 18/ 10
scale factor = 1.8
But this scale factor can not be used to determine the side LM correctly.
That is,
LM ≠ 1.8*8
LM ≠ 14.4
since LM = 13
Therefore, it can be deduced that triangles PQR and LMK are not similar. Thus none.
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A movie theater offers two containers which container is the better value use 3.14 as an approximation for pi 
Answer:
cylinder
Step-by-step explanation:
You want to know which of two popcorn containers is a better value:
cone: diameter 12 cm, height 19 cm, cost $6.75cylinder: diameter 8 cm, height 15 cm, cost $6.25VolumeThe volume formulas for the two shapes are ...
V = 1/3πr²h . . . . . cone
V = r²h . . . . . . . . . cylinder
RatioFor r = d/2, the ratio of these two volumes is ...
[tex]\dfrac{V_{con}}{V_{cyl}}=\dfrac{\dfrac{1}{3}\pi\left(\dfrac{d_{con}}{2}\right)^2h_{con}}{\pi\left(\dfrac{d_{cyl}}{2}\right)^2h_{cyl}}=\dfrac{d_{con}^2\cdot h_{con}}{3\cdot d_{cyl}^2\cdot h_{cyl}}=\dfrac{12^2\cdot19}{3\cdot 8^2\cdot 15}=\dfrac{2736}{2880}=0.95[/tex]
The cone has less volume and costs more, so the cylindrical container is the better value.
K
Let u = 4i-3j, and v= -2i+ 7j. Find u-v.
U-V= (Type your answer in terms of i and j.)
The value of u -v is 6i - 10j.
We have,
u = 4i-3j, and v= -2i+ 7j.
So, u - v
= (4i - 3j) - (-2i + 7j)
= 4i - 3j + 2i - 7j
= (4i + 2i) + (-3j - 7j)
= 6i - 10j
Thus, the resultant vector is 6i - 10j.
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In how many way can a committee of three democrats And two republicans be formed from a group of ten democrats and ten republicans
The number of ways in which a committee of four Democrats and three Republicans be formed from a group of ten Democrats and eleven Republicans is 34650 ways.
We have,
By choosing some items from a set and creating subsets, permutation and combination are two approaches to represent a group of objects. It outlines the numerous configurations for a particular set of data. Permutations are the selection of data or objects from a set, whereas combinations are the order in which they are represented. Both ideas are critical to mathematics.
Here, the differences between permutation and combination are described in detail.
The number of ways in which we can select a committee of 4 democrats from ten democrats is:
P = 10C 4 = 10! / (4)! (10 - 4)!
P = 210
The number of ways in which we can select a committee of 3 Republicans from 11 Republicans is:
P = 11C 3 = 11! / 3! (11 - 3)!
P = 165
The number of ways in which a committee of four Democrats and three Republicans be formed from a group of ten Democrats and eleven Republicans is:
P = (210) (165) = 34650
The number of ways in which a committee of four Democrats and three Republicans be formed from a group of ten Democrats and eleven Republicans is 34650 ways.
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An experiment is conducted with a coin. The results of the coin being flipped twice 200 times is shown in the table.
Outcome Frequency
Heads, Heads 40
Heads, Tails 75
Tails, Tails 50
Tails, Heads 35
What is the P(No Heads)?
85%
75%
50%
25%
The probability representing the no heads in the outcome of flipping a coin 200 times is given by 25%.
Total number of times coin flipped = 200
Number of times we get,
Heads, Heads = 40
Heads, Tails = 75
Tails, Tails = 50
Tails, Heads = 35
The probability of getting no heads that is two tails in a coin toss. Probability is frequency of the outcome 'Tails, Tails' divided by the total number of trials.
⇒P(No Heads) = Frequency of 'Tails, Tails' / Total number of trials
From the table, the frequency of 'Tails, Tails' is 50,
And the total number of trials is 200.
This implies,
P(No Heads)
= 50 / 200
= 0.25
= 25%
Therefore, the probability of the no heads is equal to 25%.
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Can someone please help me solve this simple question for high reward
Answer:
D
Step-by-step explanation:
The Percentages are as follows
History: 80%
English: 82%
Reading: 84%
Math: 85%
Science: 86%
Kava is a beverage or extract that is made from Piper methysticum, a plant native to the western Pacific islands. Suppose that, in
a randomized comparative experiment to determine if taking kava daily can reduce insomnia, a group of participants with
insomnia were randomly assigned to take kava (treatment group) or a placebo (control group). After six weeks, the participants
were interviewed to see if they experienced a decrease in insomnia. The table shows the results from the sample. The counts are
the number of people in each group who experienced a decrease in insomnia.
Note that where the above is given, the Standard Error is: 0.0322; while
The Value of the two-sample z-statistics p1-p2 = 6.048
How did we get the above results?To get the standard error, we can say
SE = √((p1 x (1-p1)/ n1) + (p2 x (1-p2)/n2) )
Substituting....
SE = √((0.7122 x (1-0.7122)/403) + (0.4594 x (1-0.4594)/468))
SE = 0.03223785349
SE ≈ 0.0322
2) For the two-sample z-statistic formula:
z = (p1 - p2) / SE
Substituting values ..........
z = (0.7122 - 0.4594) / 0.042
z = 6.048
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How many 1/4 cups of water fit inside of a 2 1/2 cup water bottle?
Answer:
There are 10 1/4 cups of water that fit inside a 2 1/2 cup water bottle.
To see why, note that 2 1/2 cups is equivalent to 10 quarter cups (2 x 4 = 8 and 8 + 2 = 10). Therefore, you can fill the water bottle with 10 1/4 cups of water.
PLEASE HELP (WILL GIVE BRAINLIEST
Answer:
A. V = 81π(7.25) = 1,844.90 cubic inches
V = 81(3.14)(7.25) = 1,843.97 cubic inches
B. Let p be the number of cans of paint.
1,843.97p = 10,000, so p = 5.42
Jessie will need 6 cans of paint.
C. Area of each storage area = π(9.5^2) = 283.53 square inches. Using 3.14 for π, this area is (3.14)(9.5^2) = 283.385 square inches. The base area of each paint can is 81π = 254.46 square inches (254.34 square inches if we use 3.14 for π). Jessie can't use the carrier because the area of each storage area exceeds the base area of each paint can.
Ellie is going to see a movie and is taking her 2 kids. Each movie ticket costs $13 and there are an assortment of snacks available to purchase for $5 each. How much total money would Ellie have to pay for her family if she were to buy 4 snacks for everybody to share? How much would Ellie have to pay if she bought x snacks for everybody to share?
Total cost with 4 snacks:
Total cost with x snacks:
Answer:
The amount of money spent on tickets and snacks will be $39 and $20. And the total amount is $59.
Step-by-step explanation:
The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Ellie is going to see a movie and is taking her 2 kids. Each movie ticket costs $13 and there are an assortment of snacks available to purchase for $5 each.
The amount of tickets is given as,
Ticket's amount = 3 x $13
Ticket's amount = $39
Then the amount spent on snacks is given as,
Snack's amount = 4 x $5
Snack's amount = $20
Then the total amount is given as,
Total amount = $39 + $20
Total amount = $59
The amount of money spent on tickets and snacks will be $39 and $20. And the total amount is $59.
Given the function f(x) =3x^2-6x-9 is the point (1,-12) on the graph of f?
The equation x² + y - 36 = 0 is symmetry about the y - axis.
We have to given that;
The equation of graph is,
⇒ x² + y - 36 = 0
Now, We get;
⇒ x² + y - 36 = 0
⇒ y = - x² + 36
By plotting the equation in graph we get;
The equation x² + y - 36 = 0 is symmetry about the y - axis.
Thus, The equation x² + y - 36 = 0 is symmetry about the y - axis.
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The function f(x) = 1.85x2 models the cost of a square carpet, where x is the length in feet. Find the average rate of change for f, to the nearest tenth, over the interval 10 ≤ x ≤ 20.
The average rate of change for function f(x) = 1.85x² to the nearest tenth over the interval 10 ≤ x ≤ 20 is equal to 55.5 (Rounding to the nearest tenth).
Function models the cost of a square carpet
f(x) = 1.85x²
The average rate of change of a function f(x) over an interval [a, b] is,
Average rate of change = [f(b) - f(a)] / (b - a)
The average rate of change of f(x) over the interval 10 ≤ x ≤ 20.
Using the given function, we have,
f(10) = 1.85(10)²
= 185
f(20) = 1.85(20)²
= 740
Now calculate the average rate of change,
average rate of change
= [f(20) - f(10)] / (20 - 10)
= (740 - 185) / 10
= 55.5 (Rounding to the nearest tenth)
Therefore, the average rate of change of function f(x) over the interval 10 ≤ x ≤ 20 is approximately 55.5.
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