Answer: 8.2 weeks.
Step-by-step explanation: If y = 4*3^t, then 600 = 4*3^t. Therefore, t = log3 (600/4), which is approximately 8.2 weeks.
3. If circle 2 were a glide reflection of circle 1, what transformations would be involved?
dilation and reflection
rotation and translation
translation and reflection
reflection and rotation
According to the Cartesian plane graph, it can be inferred that the circle was rotated and translated (option B).
How to identify the movements that were made to circle 1 to become 2?To identify the movements that were made to circle 1 to become 2 we must carefully observe the graph. Once we have analyzed this graph we can infer the movements that were made to the circle. In this case, the rotation was performed because it can be seen that it was rotated having the coordinate (-1.5, 0.5) as a reference or point of rotation.
However, it was also translated because it was shifted a bit down and to the left. So the correct answer would be option B.
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Answer: rotation and translation
Step-by-step explanation: I took the quiz
The table at right shows speed limits in some foreign countries in kilometers per hour. One kilometer is equal to 0.6 miles. What are these speed limits in miles per hour?
As an example, the 78-mph speed limit in the United States is equivalent to the 130 km/h restriction in Germany.
How quick is that speed?
A connection with a speed of 100 Mbps or higher is considered fast internet. Broadband internet speed is defined by the federal communications regulator (FCC) as 25 Mbps for downloading and 3 Mbps for upload.
We can increase each number by 0.6 to convert overall speed limitations from kilometers per hour into miles per hour. Here is the revised table:
Country Speed Limit (km/h) Speed Limit (mph)
Germany 130 78
France 110 66
Italy 150 90
Japan 100 60
Australia 110 66
United Kingdom 113 67.8
Hence, Because one kilometer is equivalent to 0.6 miles, it is evident that speed limits in the form of miles per hour were lower than those in kilometers per hour.
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3. A prop for the theater club’s play is constructed as a cone topped with a half-sphere. What is the volume of the prop? Round your answer to the nearest tenth of a cubic inch. Use 3.14 to approximate pi.
Given:-
A prop for threatre is constructed using a cone and a hemisphere.Use π = 3.14To find:-
The volume of the prop .Answer:-
The given figure is made up of a cone and a hemisphere , so to find the total volume , we would find the volume of cone and hemisphere individually and add them up to find the net volume.
Finding volume of cone:
The data we have is ,
Height = 14inches Radius = 9inches .As we know that the volume of cone is given by,
[tex]\implies V =\dfrac{1}{3}\pi r^2 h \\[/tex]
on substituting the respective values,we have;
[tex]\implies V =\dfrac{1}{3}\times 3.14 \times (9in.)^2 \times 14in .\\[/tex]
[tex]\implies V = \dfrac{1}{3}\times 3.14 \times 81in.^2\times 14in. \\[/tex]
[tex]\implies V = 1186.92 \ in.^3 \\[/tex]
Finding the volume of hemisphere:
As we know that the volume of hemisphere is given by;
[tex]\implies V =\dfrac{2}{3}\pi r^3 \\[/tex]
And here ,
r = 9 inches .So that;
[tex]\implies V =\dfrac{2}{3}\times 3.14\times (9\ in.)^3 \\[/tex]
[tex]\implies V =\dfrac{2}{3}\times 3.14\times 729\ in.^3 \\[/tex]
[tex]\implies V = 1526.04 \ in.^3 \\[/tex]
Hence the total volume will be ,
[tex]\implies V_{prop} = (1526.04 + 1186.92 )in.^3\\[/tex]
[tex]\implies V = 2712.96 \ in.^3 \\[/tex]
[tex]\implies \underline{\underline{ V_{prop}= 2713\ in.^3 }} \\[/tex]
Hence the volume of prop is 2713 in.³
and we are done!
Answer:
2713.0 in³ (nearest tenth)
Step-by-step explanation:
To calculate the volume of the prop, sum the volume of the cone and the volume of the half-sphere.
[tex]\boxed{\begin{minipage}{4 cm}\underline{Volume of a cone}\\\\$V=\dfrac{1}{3} \pi r^2 h$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}[/tex] [tex]\boxed{\begin{minipage}{4 cm}\underline{Volume of a half-sphere}\\\\$V=\dfrac{2}{3} \pi r^3$ \\\\ where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\\end{minipage}}[/tex]
Therefore, the equation for the volume of the prop is:
[tex]V_{\sf prop}=\dfrac{1}{3} \pi r^2 h+\dfrac{2}{3} \pi r^3[/tex]
From inspection of the given diagram:
r = 9 inh = 14 inπ ≈ 3.14Substitute the values of r, h and π into the equation and solve for V:
[tex]\begin{aligned}\implies V_{\sf prop}&=\dfrac{1}{3} \pi r^2 h+\dfrac{2}{3} \pi r^3\\\\&=\dfrac{1}{3} (9)^2 (14)+\dfrac{2}{3} \pi (9)^3\\\\ &=\dfrac{1}{3} \pi (81) (14)+\dfrac{2}{3} \pi (729)\\\\ &=378 \pi+486 \pi\\\\ &=864 \pi\\\\&=864 \cdot 3.14\\\\&=2712.96\\\\&=2713.0\;\sf in^3\;\;(nearest\;tenth)\end{aligned}[/tex]
Therefore, the volume of the prop is 2,713.0 in³ to the nearest tenth.
$5 dollar less on dinner than James.
Answer:
x - 5
Step-by-step explanation:
Okay to write this problem as an expression it would be x -5. x represents James and -5 represents less than.
Answer:
x-5
Step-by-step explanation:
we don't know how much James has but we know it is $5 less so what ever the original amount is we are putting as x for now and we will subtract 5 because it is $5 less making our x-5.
you need to think about which __________ __________ you need to use
According to the information we can infer that sentence is completed with the words mathematical procedure.
How to complete the sentence?To complete the sentence we must identify the central idea and establish the right words to complete it. In this case, it is referring to a mathematical procedure then we could infer that these are the words that complete the sentence. Then the complete sentence would be like this:
You need to think about which Mathematical Procedure you need to use.Note: This question is incomplete. Here is the complete information:
Complementary information:
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You own a hamburger franchise and are planning to shut down operations for the day, but you are left with 12 buns, 18
defrosted beef patties, and 16 opened cheese slices. Rather than throw them out, you decide to use them to make burgers
that you will sell at a discount. Plain burgers each require 1 beef patty and 1 bun, double cheeseburgers each require 2
beef patties, 1 bun, and 2 slices of cheese, while regular cheeseburgers each require 1 beef patty, 1 bun, and 1 slice of
cheese. How many of each should you make?
plain burgers
double cheeseburgers
regular cheeseburgers
Answer:
Plain burgers: 12
Double cheeseburgers: 9
Regular cheeseburgers: 12
Step-by-step explanation:
Let's use P, D, and R to represent the number of plain burgers, double cheeseburgers, and regular cheeseburgers, respectively.
Each plain burger requires 1 patty and 1 bun, so we can make a maximum of 12 plain burgers (since we have 12 buns).
Each double cheeseburger requires 2 patties, 1 bun, and 2 slices of cheese, so we can make a maximum of 9 double cheeseburgers with the available patties, buns, and cheese. (We have enough patties and buns for 18 burgers, but each double cheeseburger uses twice as many patties, so we divide the total number of patties by 2 to get the maximum number of double cheeseburgers we can make.)
Each regular cheeseburger requires 1 patty, 1 bun, and 1 slice of cheese, so we can make a maximum of 16 regular cheeseburgers with the available patties, buns, and cheese (since we have 16 slices of cheese).
To maximize our sales, we want to make as many of each type of burger as we can. Since we can only make 12 plain burgers, we should make all 12 of those. We can then make 9 double cheeseburgers (using 18 patties, 9 buns, and 18 slices of cheese), and 12 regular cheeseburgers (using 12 patties, 12 buns, and 12 slices of cheese).
So the final answer is:
Plain burgers: 12
Double cheeseburgers: 9
Regular cheeseburgers: 12
The graph shows the total cost c of buying one large bucket of popcorn and d large drinks. Write an equation from the graph that could be used to find the total cost c if you buy one large bucket of popcorn and d large drinks.
Answer:
[tex]y = 4d + 8\\[/tex]
Step-by-step explanation:
Since d is the number of large drinks, and there is always a constant of 1 large popcorn, we go to (0, 8). This concludes that since we start off with the cost of 8 dollars with no large drink but a large popcorn, the popcorn will stay a constant cost of $8. (the equation for this scenario is as shown):
y = md + 8
y (total cost)
m (coefficient - in this sense the cost of the drinks.)
d (amount of drinks)
8 (the constant of 8 represents the cost of one large popcorn consistently)
Now, lets find the cost of the dink.
Go to (1, 12).
$12 dollars is the total cost, with one drink and one large popcorn bought.
We have already discussed that we will have a constant of 8 because no matter the amount of drinks we will get, we would have bought 1 large popcorn at $8.
Therefore, we must subtract 8 dollars from 12.
12 - 8 = 4
From the total cost of everything we bought (2 things) and subtracting it with the cost one of the things we bought, we get the cost of the other thing.
each drink will cost $4.
Therefore, with all the variables and their listed meanings, this will be our given equation:
y = 4d + 8
9 inches of ribbon is needed for wrapping one present. How many presents can be wrapped with 8 yards of ribbon?
Answer: 32 presents can be wrapped with 8 yards of ribbon
Step-by-step explanation:
Convert yards to inches
1 yard = 36 inches
8 yards = 288 inches
Divide 288 inches by 9 inches
288/9 = 32
Answer: You can wrap 32 presents with 8 yards.
Step-by-step explanation:
So, first, you need to know how many inches are in a yard. There are 36 inches in 1 yard.
Then, do 36 inches times 8 yards to figure out how many yards are in 8 yards. So in 8 yards, there are 288 inches.
Finally, do 288 divided by 9 to figure out how many present you can wrap with 8 yards (288 inches).
You can wrap 32 presents with 8 yards.
I hope this helped!
Question In the coordinate plane, what is the length of the line segment that connects points at (5, 4) and (−3, −1)? Enter your answer in the box. Round to the nearest hundredth. units?
The length of the line segment that connects points at (5, 4) and (−3, −1) is found to be 9.43 units.
Explain about the distance formula?The distance formula is still a formula used to determine how far apart two places are from one another. The dimensions of these points are unlimited. For instance, you could need to determine the separation between two points in space, a plane, or a line (1, 2, or 3 dimensions) .Using the formula obtained from Pythagoras' theorem, distance can be computed.
The distance formula in coordinate geometry is:
(P, Q) = √ (x2 – x1)² + (y2 – y1)².
Given points: (5, 4) and (−3, −1)
d = √ (-3 - 5)² + (4 + 1)²
d = √ 64 + 25
d = √ 89
d = 9.43
Thus, the length of the line segment that connects points at (5, 4) and (−3, −1) is found to be 9.43 units.
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Find the discriminant for each Quadratic and state the types of roots.
2x² + 3x - 3=0
4x²-6x+2=y
0=x²-3x+8
y=5x²+4x+1
9. The discriminant is 33. And the roots are real and distinct.
10. The discriminant is 4. And the roots are real and distinct.
11. The discriminant is -23. And the roots are imaginary roots.
12. The discriminant is -4. And the roots are imaginary roots.
What is the discriminant?
The quadratic equation is ax² + bx + c = 0. Then the discriminant is given as,
D = b² - 4ac
If D > 0, then the roots are real and distinct root.If D = 0, then the roots are real and equal roots.If D < 0, then the roots are imaginary roots.9. 2x² + 3x - 3 = 0, the discriminant is given as,
D = 3² - 4 × 2 × (-3)
D = 33
Roots are real and distinct.
10. 4x² - 6x + 2 = y, the discriminant is given as,
D = (-6)² - 4 × 4 × (2)
D = 4
Roots are real and distinct.
11. 0 = x² - 3x + 8, the discriminant is given as,
D = (-3)² - 4 × 1 × (8)
D = - 23
Roots are imaginary.
12. y = 5x² + 4x + 1, the discriminant is given as,
D = (4)² - 4 × 5 × (1)
D = -4
Roots are imaginary.
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Area = 2,800 square meters
2,800
Square meters Find the unknown measure of the rectangle
When given the area of a rectangle, and one of the sides, the unknown measure of the rectangle would be 40 meters
How to find the area of a rectangle ?To find the area of a rectangle, you can use the formula:
A = l x w
where A is the area of the rectangle, l is the length of the rectangle, and w is the width of the rectangle.
Seeing as you were given the area to be 2, 800 square meters and one of the sides measures 70 meters, the unknown measure of the rectangle would be:
70x Unknown = 2, 800
Unknown = 2, 800 / 70
Unknown measure = 40 meters
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Full question is:
Area = 2,800 square meters
Side A = 70 meters
Find the unknown measure of the rectangle
Translate the sentence into an equation using n as the unknown number. Then solve the equation for n. Two times a number increased by 5 is 15. a. 2n(5) = 15 n = 1.5 c. 2n + 5 = 15 n = 20 b. 2n + 5=15 n = 5 d. n + 5 = 15 n = 10 Please select the best answer from the choices provided
9. At a scouts' camp. there is sufficient food to last 72 scouts for 6 days. If 18 scouts do not turn up for the camp, how much longer can the food last for the other scouts?
Answer:
9 54 divided by 9 = 6 72 - 18 = 54
Step-by-step explanation:
please answer this is
Answer:
Its answer number 4
Step-by-step explanation:
Working 8 hours a day, 48 men can complete a job in 1 week. How many men working 6 hours a day will complete the same job in 16 days?
The number of men needed to complete the same job in 16 days working 6 hours a day is given as follows:
28 men.
How to obtain the number of men?The number of men is obtained applying the proportions in the context of the problem.
The rule of three is given as follows:
n/48 = 8/6 x 7/16.
(the time is inverse proportional to the number of men, hence the fractions are inverted).
Thus:
n/48 = 56/96
Applying cross multiplication, the number of men is obtained as follows:
96n = 48 x 56
n = 48 x 56/96
n = 28 men.
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Dividing integers, please help
Answer:
The percent of Dan's average did he score during this game is 11.11%
What percent of Dan's average did he score during this game?
Dan's score in the high school basketball team during last game= 18 points
Dan's score in the high school basketball team during this season = 20 points
Percent of Dan's score during this game = (20 - 18) / 18 × 100
= 2/18 × 100
= 11.11%
In conclusion, Dan scored an average percentage of 11.11% during this game.
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(2x+3)(xexponent2 - 6x - 2)
Answer:
Step-by-step explanation:
We can use the distributive property and basic algebraic operations to multiply the given expression:
(2x+3)(x^2 - 6x - 2)
= 2x(x^2 - 6x - 2) + 3(x^2 - 6x - 2) // Distribute 2x and 3
= 2x^3 - 12x^2 - 4x + 3x^2 - 18x - 6 // Multiply each term
= 2x^3 - 9x^2 - 22x - 6 // Combine like terms
Therefore, (2x+3)(x^2 - 6x - 2) simplifies to 2x^3 - 9x^2 - 22x - 6.
m Arch ML = 76 Degrees ; m
Answer:
A part of basic arithmetic, long division is a method of solving and finding the answer and remainder for division problems that involve numbers with at least two digits. Learning the basic steps of long division will allow you to divide numbers of any length, including both integers (positive,negative and zero) and decimals. This process is an easy one to learn, and the ability to do long division will help you sharpen and have more understanding of mathematics in ways that will be beneficial both in school and in other parts of your life.[1]
Step-by-step explanation:
A part of basic arithmetic, long division is a method of solving and finding the answer and remainder for division problems that involve numbers with at least two digits. Learning the basic steps of long division will allow you to divide numbers of any length, including both integers (positive,negative and zero) and decimals. This process is an easy one to learn, and the ability to do long division will help you sharpen and have more understanding of mathematics in ways that will be beneficial both in school and in other parts of your life.[1]
Julian is training to make his school's track team. Each week he runs a 400-meter dash and keeps track of his weekly change to monitor his improvement. If Julian's 400-meter dash time was 59 7/10 seconds when he began his training, what was his timed lap after 4 weeks of training? Write your answer as a mixed number in simplest form.
Please helppppppp!!!!
Julian's timed lap after 4 weeks of training written in mixed fraction form is 58 1/10 seconds.
What are fractions?
Every number of equal parts is represented by a fraction, which also represents a portion of a whole. A single object or a collection of objects might be whole. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object. The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves. The number of parts into which the whole has been divided is shown by the denominator. How many sections of the fraction are displayed or chosen is shown in the numerator.
Given,
Number of metres run Julia runs each week = 400
Time taken to run 400m dash in the beginning = 59 7/10 seconds
= 597/10 seconds
Since the time is given in fractions, we have to do fraction subtraction for the following weeks.
Time taken in week 1 = 597/10 - 0.6 seconds = 597/10 - 6/10 = 591/10 seconds
Time taken in week 2 = 591/10 - 1/4 = 2364 - 10 / 40 = 2354/40 seconds
Time taken in week 3 = 2354/40 + 0.1 = 2354/40 + 1/10 = 2358/40
Time taken in week 4 = 2358/40 - 17/20 = 2358-34 / 40 = 2324/40
= 581/10= 58 1/10 seconds.
Therefore Julian's timed lap after 4 weeks of training written in mixed fraction form is 58 1/10 seconds.
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The total cost of a belt and a jacket was $91.85, If the price of the belt was 8.61
less than the jacket, what was the price of the belt
Answer: $41.62
Step-by-step explanation:
let the price of the jacket be X
then the price of belt will be X-8.61
according to question
X + X-8.61 = 91.85
2X - 8.61 = 91.85
2X = 91.85 + 8.61
2X = 100.46
X = $50.23
cost of jacket = $ 50.23
cost of belt = $ 41.62
Hope this helps!!!
Answer: $41.62
Step-by-step explanation:
*j = jacket* *b = belt*
belt + jacket = 91.85 (the total cost of the belt and jacket)
belt = jacket - 8.61 (the price of the belt is $8.61 less than the jacket)
We can use substitution to solve for the value of b.
Substitute the second equation into the first equation:
(j - 8.61) + j = 91.85
Simplify by combining like terms:
2j - 8.61 = 91.85
Add 8.61 to both sides:
2j = 100.46
Divide both sides by 2:
jacket = 50.23
b = j - 8.61
b = 50.23 - 8.61
b = 41.62
I need help in this please
The x-intercepts and y-intercepts of the graph include the following:
x-intercept: B. -1.
y-intercept: D. none.
The equations for all vertical and horizontal asymptotes are as follows;
Vertical asymptote: x = 1.
Horizontal asymptote: y = 4.
What is the x-intercept?In Mathematics, the x-intercept can be defined as the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" or y-value is equal to zero (0).
What is an asymptote?In Mathematics, an asymptote can be defined as a line which the graph of a given function approaches but would never touch. Additionally, the vertical asymptote of a function simply refers to the value of x which makes its denominator equal to zero (0).
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true or false, a trapezoid is a quadrilateral with one or more parallel side
Answer:
A trapezoid is a quadrilateral with one pair of opposite sides parallel. It can have right angles (a right trapezoid), and it can have congruent sides (isosceles), but those are not required.
The graph shows g(x), which is a translation of f(x)=x2. Write the function rule for g(x).
The function g(x) is translation of f(x) 9 units up. The solution has been obtained by using transformation.
What is transformation?An operation known as a transformation involves moving a polygon or other two-dimensional object on a plane or coordinate system.
We are given that the function g(x) is a translation of the function
f(x) = x².
In the graph, we can see that the vertex of the parabola is at (0, 9).
This means that the function g(x) is 9 units up from the function f(x).
So, g(x) = x² + 9
Hence, the function g(x) is translation of f(x) 9 units up.
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During a lab experiment, the temperature of a liquid changes from 6.4°F to 10.75°F.
What is the percent of increase in the temperature of the liquid?
Enter your answer in the box as a percent rounded to the nearest hundredth. Help pls
Answer:
67.97%
Step-by-step explanation:
Answer:
67.97%
Step-by-step explanation:
Confused on what it is asking me to solve. Squared numbers are the answers
Answer:
↓ ↓ ↓
Step-by-step explanation:
Given: f(x)= x² -4x + 3
Find :-
a) f(1)
f(x)= x² -4x + 3
→ Substitute x with with 1:-
[tex]\tt f(1)=\left(1\right)^2-4\left(1\right)+3[/tex]
[tex]\tt f(1)=1-4\cdot \:1+3[/tex]
[tex]\tt f(1)=1-4+3[/tex]
[tex]\boxed{\tt f(1)=0}[/tex]
_______________________
b) f(3)
f(x)= x² -4x + 3
→ Substitute x with with 3:-
[tex]\tt f(3)=\left(3\right)^2-4\left(3\right)+3[/tex]
[tex]\tt f(3)=\left(3\right)^2-4\left(3\right)+3[/tex]
[tex]\tt f(3)=3^2-4\cdot \:3+3[/tex]
[tex]\tt f(3)=3^2-12+3[/tex]
[tex]\tt f(3)=3^2-9[/tex]
[tex]\tt f(3)=9-9[/tex]
[tex]\boxed{\tt f(3)=0}[/tex]
_______________________
c) f(-1)
f(x)= x² -4x + 3
→ Substitute x with with -1:-
[tex]\tt f(-1)=\left(-1\right)^2-4\left(-1\right)+3[/tex]
[tex]\tt f(-1)=\left(-1\right)^2+4\cdot \:1+3[/tex]
[tex]\tt f(-1)=1+4+3[/tex]
[tex]\boxed{\tt f(-1)=8}[/tex]
_______________________
d) -f(1)
f(x)= x² -4x + 3
→ -f(1)
[tex]\tt -f(1)=\left(1\right)^2-4\left(1\right)+3[/tex]
[tex]\tt -f(1)=1-4\cdot \:1+3[/tex]
[tex]\tt -f(1)=1-4+3[/tex]
[tex]\boxed{\tt -f(1)=0}[/tex]
_____________________
Hope this helps! :)
This question is for Geometry. If you know the answer, please send.
The measure of side AC of the right triangle is 7.2 units.
What is the measure of side AC?The figure in the image is the of a right triangle.
Angle A = 51 degreeOpposite to angle A = BC = 8.9Adjacent to angle A = ACTo solve for the measure of side AC, we use trigonometric ratio.
The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).
Tangent = Opposite / Adjacent
tan( A ) = BC / AC
Plug in the values and solve for side AC.
tan( 51° ) = 8.9 / AC
AC = 8.9 / tan( 51° )
AC = 8.9 / 1.234897
AC = 7.2
Therefore, side AC has a value of 7.2 units.
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The answer should be 3278 ft I just need help with how to get it and the work.
The Panther I traveled approximately 2413 miles before reaching a speed of 130 mph.
What is a trapezoid?A trapezoid is a quadrilateral having two parallel bases and one set of other sides called legs.
To estimate the distance traveled by the Panther I, we need to approximate the area under the velocity curve between 0 and 25.7 seconds. We can divide the area into trapezoids using the data given in the table.
The first trapezoid has a height of 30 mph and a base of 1.8 seconds. The second trapezoid has a height of 40 mph and a base of 1.3 seconds (the difference between 3.1 and 1.8).
Continuing in this way, we get the following table:
Speed Height
Range (mph) Base (s) Area (mph * s)
0-30 30 1.8 54
30-40 40 1.3 52
40-50 50 1.1 55
50-60 60 1.3 78
60-70 70 1.9 133
70-80 80 1.8 144
80-90 90 2.3 207
90-100 100 3.1 310
100-120 120 6.3 756
120-130 130 4.8 624
To find the total area, we add up the areas of all the trapezoids:
54 + 52 + 55 + 78 + 133 + 144 + 207 + 310 + 756 + 624 = 2413
Therefore, the Panther I traveled approximately 2413 miles before reaching a speed of 130 mph.
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The table below shows a relationship between hours and miles traveled:
After reading the table, a student writes this equation to show the proportional relationship between hours and miles traveled. The constant of proportionality is 30.
m = 30h
Based on the table and the equation, how many miles would they travel after 12 hours?
A: 360 miles
B: 600 miles
C: 240 miles
D: 42 miles
Answer:360
Step-by-step explanation:
A ball is thrown upward with an initial velocity of 75 feet per second and an initial height of 4 feet. Given h(t) = −16t2 + v0t + h0, complete function h to model the vertical motion of the ball. Then find the ball’s maximum height, to the nearest foot.
The maximum height of the ball is given as follows:
92 feet.
How to model the height of the ball?The quadratic function modelling the height of the ball is given as follows:
h(t) = -16t² + v(0)t + h(0).
In which:
v(0) is the initial velocity.h(0) is the initial height.The parameters for this problem are given as follows:
v(0) = 75, h(0) = 4.
Hence the equation is:
h(t) = -16t² + 75t + 4.
The coefficients are given as follows:
a = -16, b = 75, c = 4.
As the quadratic equation is concave down, the maximum height is at the vertex.
The t-coordinate of the vertex is given as follows:
t = -b/2a
b = -75/-32
b = 2.34375s.
Hence the maximum height is of:
h(2.34375) = -16(2.34375)² + 75(2.34375) + 4.
h(2.34375) = 92 feet.
More can be learned about quadratic functions involving the height of a ball at https://brainly.com/question/12446886
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Consider the expressions 3x(x − 2) + 2 and 2x2 + 3x − 18.
Part 1
Evaluate each expression for x = 4 and for x = 5. Based on your results, do you know whether the two expressions are equivalent? Complete the explanation.
For x = 4, each expression has a value of
26
. For x = 5, each expression has a value of
47
. These results suggest that the expressions
may be
equivalent, but
do not prove that
the expressions are equivalent.
Part 2 out of 2
Evaluate each expression for x = 3. Based on your results, do you know whether the two expressions are equivalent? Complete the explanation.
For x = 3, the first expression has a value of
, and the second expression has a value of
. Since these values are
(select)
, the expressions
(select)
equivalent.