An object is launched from a platform.
Its height (in meters), xxx seconds after the launch, is modeled by:
h(x)=-5(x-4)^2+180h(x)=−5(x−4)
2
+180h, left parenthesis, x, right parenthesis, equals, minus, 5, left parenthesis, x, minus, 4, right parenthesis, squared, plus, 180
How many seconds after being launched will the object hit the ground?
Answers
Answer:
10
Step-by-step explanation:
Ground level is where h = 0, so solve the equation ...
h(x) = 0
-5(x -4)^2 +180 = 0 . . . . substitute for h(x)
(x -4)^2 = 36 . . . . . . . . . . divide by -5, add 36
x -4 = 6 . . . . . . . . . . . . . . positive square root*
x = 10 . . . . . . add 4
The object will hit the ground 10 seconds after launch.
_____
* The negative square root also gives an answer that satisfies the equation, but is not in the practical domain. That answer would be x = -2. The equation is only useful for time at and after the launch time: x ≥ 0.
The object modeled by the quadratic equation h(x)=-5(x-4)²+180 will hit the ground 10 seconds after being launched.
The equation given is a quadratic equation which models the height of an object after being launched from a platform. To find out when the object will hit the ground, we need to determine when the height h(x) is equal to zero. The equation can be written as h(x) = -5(x - 4)² + 180.
To find the time when the object hits the ground, we set the height equal to zero and solve for x:
0 = -5(x - 4)² + 180
Solving the quadratic equation, we divide both sides by -5:
(x - 4)² = 36
Taking the square root of both sides gives two solutions: x - 4 = [tex]\pm6[/tex]. The positive root gives us the time after launch when the object hits the ground:
x - 4 = 6
x = 10
Therefore, the object will hit the ground 10 seconds after being launched.
Related Questions
Madison and Franklin are 6 in apart on a
map that has a scale of 1 in: 7 mi. How
far apart are the real cities?
Answers
Another way to think about it is as 7mil + 7mil + 7mil + 7mil + 7mil + 7mil=42 miles (You add the 7 six times since it is 6in and each inch is 7miles)
Final answer:
The actual distance between Madison and Franklin is 42 miles.
Explanation:
To find the actual distance between Madison and Franklin, we can use the given scale of 1 in: 7 mi. Since Madison and Franklin are 6 inches apart on the map, we can multiply the scale by the number of inches to find the distance in miles.
Distance in miles = Scale x Number of inches apart = 7 mi/in x 6 in = 42 miles
Therefore, the actual distance between Madison and Franklin is 42 miles.
Purse A which contains $1,000 today. If you leave it alone, it will contain $1,200 tomorrow (by magic). The next day, it will have $1,400. This pattern of $200 additional dollars per day will continue. Purse B which contains 1 penny today. Leave that penny in there, because tomorrow it will (magically) turn into 2 pennies. The next day, there will be 4 pennies. The amount in the purse will continue to double each day. How much money will be in each purse after a week? After two weeks? The genie later added that he will let the money in each purse grow for three weeks. How much money will be in each purse then? Which purse contains more money after 30 days?
Answers
Answer:
Purse A will contain 2400 (by magic) and Purse B will have 64 pennies
Step-by-step explanation:
how this happened is, by magic Purse A went up by 200 every day for 7 days a week. 7*200 would be 1400 so you add that to the money from today and get 2400. Purse B somehow got from 1 penny to 64 in 7 days. The rule on this is to multiply by 2 every day. 1,2,4,8,16,32 and 64. have fun with your magic :3
Which function has a constant rate of change -1/4?
Answers
Mansah earns a salary of GH¢ 10,000.00 per month, as a sales girl. In addition to the salary , she is given a commission of 15 percent of what ever sales that she makes in a month. In January this year, she made sales of GH¢ 1,500,00.00. What was the total Mansah earned at the end of January?
Answers
Answer:
66,000
Step-by-step explanation:
Answer:
GH¢32,500
Step-by-step explanation:
Monthly salary of Mensah=GH¢10,000.00
Commission=15%
15/100×GH¢ 1,500,00.00=GH¢22,500
Total amount earned=
Monthly salary+ Commission
GH¢10,000+GH¢22,500=GH¢32,500
Answer:
GH¢32,500
Step-by-step explanation:
Monthly salary of Mensah=GH¢10,000.00
Commission=15%
15/100×GH¢ 1,500,00.00=GH¢22,500
Total amount earned=
Monthly salary+ Commission
GH¢10,000+GH¢22,500=GH¢32,500
2x(x)=5
I need help
Answers
Step-by-step explanation:
X interprets (0,0), (-5, 0) all you must do is divide 5 by 2 so 5÷2=2.5 that is your answer
What is the volume of a cone with a radius of 4 centimeters and a height of 10 centimeters?
Cone V= 3Bh
1. Rewrite the formula for the base area: = 1 / 22h
2. Substitute the values into the formula V= (42)(10)
3. Evaluate the power
V = ŽA(16)(10)
4. Simplify to find the volume of the cone to be
a cm
Answers
Answer:
160/3 got it on the ed thing
The volume of the cone is 167.5 cubic centimeters
How to determine the volume of the cone?The given parameters are:
Radius, r = 4 cm
Height, h = 10 cm
The volume is calculated using:
[tex]V = \frac 13 * \pi r^2h[/tex]
So, we have:
[tex]V = \frac 13 * 3.14 * 4^2 *10[/tex]
Evaluate
[tex]V = 167.5[/tex]
Hence, the volume of the cone is 167.5 cubic centimeters
Read more about volume at:
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If f(1) =7 and f(n)=-5f(n-1)-n
then find the value of
f(4)
Answers
Final answer:
Using the recursive relationship f(n) = -5f(n-1) - n, we calculated the values step by step to find that f(4) is -914.
Explanation:
The question asks us to find the value of f(4) given that f(1) = 7 and the recursive relationship f(n) = -5f(n-1) - n.
To find f(4), we need to compute it in a step-by-step manner by first finding f(2) and f(3), and using those results to finally compute f(4).
Starting with f(1) = 7, we calculate f(2):
f(2) = -5f(1) - 2 = -5*7 - 2 = -35 - 2 = -37.
Next, calculate f(3):
f(3) = -5f(2) - 3 = -5*(-37) - 3 = 185 - 3 = 182.
Finally, calculate f(4):
f(4) = -5f(3) - 4 = -5*182 - 4 = -910 - 4 = -914.
Therefore, the value of f(4) is -914.
Final answer:
Using the recursive function given, by computing step by step from f(1) up to f(4), we find that f(4) equals -914.
Explanation:
To find the value of f(4), we must use the given recursive relation f(n) = -5f(n-1) - n, starting with the base case f(1) = 7.
Find f(2):f(2) = -5f(2-1) - 2 = -5f(1) - 2 = -5(7) - 2 = -35 - 2 = -37Find f(3):
f(3) = -5f(3-1) - 3 = -5f(2) - 3 = -5(-37) - 3 = 185 - 3 = 182Find f(4):
f(4) = -5f(4-1) - 4 = -5f(3) - 4 = -5(182) - 4 = -910 - 4 = -914
Therefore, f(4) = -914.
Mr. Tesoro drew this quadrilateral with two equal sides that meet at a right angle and a pair of equal opposite angles that are not right angles. What type of quadrilateral did he draw?
Answers
Answer:
The answer is kite.
Step-by-step explanation:
Well, just looking at the definition of a kite, we can see that it lines up with Mr. Tesoro's description and drawing of the quadrilateral. A kite has one right angle that meets up witht two equal lines. The opposite pair of lines, that are much longer, don't meet up to be a right angle. The definitions line up, so there's your match; the anser is kite.
a data set includes the following test scores:75,82,62,78.The score on a retake is 96.it the retake score replaces the lowest test grade, how is the mean affected
Answers
Answer:
Increase by 8.75
Step-by-step explanation:
75+82+67+72=296
296/4= 74
74 = Original Mean
75+82+96+78=331
New mean 82.75
82.75-74=8.75
Answer:
The mean increased by 6.8
Step-by-step explanation:
If a = 4, Evaluate 35 - 3a
Answers
Answer:
23
Step-by-step explanation:
3 times 4 equals 12
then do
35 minus 12
Answer:
a=4
35-3a=
35-3(4)=
35- 12=23
Step-by-step explanation:
The average number of hours of sleep per night was 9.46 hours for a sample of 104 five to seven year-old children. The number 9.46 is a __________, because it is a number that can be computed from the sample of 104 children.
Answers
Answer:
Statistic
Step-by-step explanation:
-In statistics, a statistic is a characteristic or an attribute of a sample used to estimate or calculate the true values/characteristics of an entire population.
-The value 9.6 is only representative of the small sample size of 104 children.
-If the sample size is sufficient enough it can be used to calculate the population's mean, standard deviation and other Central Limit Theorem measures.
The number 9.46 is referred to as a statistic in this context. A statistic is a characteristic that can be computed from the data in a sample, like the average sleep time of 104 children in this case.
Explanation:The average number of hours of sleep per night was 9.46 hours for a sample of 104 five to seven year-old children. In this context, the number 9.46 is referred to as a statistic.
A statistic is a characteristic that can be computed from the data in a sample. For example, in this case, the data was collected from a group (or sample) of 104 children, and the average hours of sleep they got per night was calculated. The resultant number, 9.46 hours, serves as an estimation of the parameter we are interested in: the average sleep time of all 5 to 7 year-olds.
The term is frequently used in
statistics
, a branch of math that refers to the collection, analysis, interpretation, presentation, and organization of data.
Learn more about Statistic here:https://brainly.com/question/31538429
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Zach use the steps to solve this equation when Zack check the solution, it didn’t work. What was his mistake
Answers
Answer:C
Step-by-step explanation:
The area of the window is
Answers
Jess made 3 different stacks of wooden blocks The first stack was 7 blocks high the second stack was 3 blocks higher than the first and the the final stack was 7 blocks higher than the second In the total how many blocks did Jess use for all 3 stacks
Answers
Answer:
Jess used 34 blocks
Step-by-step explanation:
the first stack =7
second stack =7+3=10
third stack =10+7=17
total: 7+10+17=34
A wheel completes 2.4 revolutions in 3 seconds.
What is the angular velocity of the wheel in radians per minute?
State your answer in exact form as a simplified fraction.
Answers
Answer:
The angular velocity of the wheel in radians per minute is 96·π·rad/min
Where π = 22/7 then the angular velocity is [tex]301\frac{5}{7} \ rad/min[/tex]
Step-by-step explanation:
The number of revolutions completed per 3 seconds = 2.4 revolutions
∴ The number of revolutions completed per second = 2.4/3 = 0.8 = 4/5 revolutions
The angle per revolution = 2π radians
∴ Angular velocity per second = 0.8×2×π rad/sec
The angular velocity of the wheel in radian per second = 1.6·π·rad/sec
1 minute = 60 Seconds
∴The angular velocity of the wheel in radians per minute = 96·π·rad/minute
Where π = 22/7 then the angular velocity = [tex]301\frac{5}{7} \ rad/min[/tex].
Answer:96pi
Step-by-step explanation:
A television network, Network A, is scheduling its fall lineup of shows. For the Tuesday night 8 p.m. slot, Network A has selected its top show. If its rival network, Network B, schedules its top show during the same time slot, Network A estimates that it will get 1.1 million viewers. However, if Network B schedules a different show during that time slot, Network A estimates that it will get 1.6 million viewers. Network A believes that the probability that Network B will air their top show is 0.4 and the probability that Network B will air another show is 0.6.
Determine the expected number of viewers (in millions) for Network A's top show.
Network A expects that how many million people will watch their show (type an integer or decimal).
Answers
Answer:
The number of viewers Network A expects will watch their show is 1.4 million viewers.
Step-by-step explanation:
The expected value is calculated by multiplying the possible outcomes by the probability of their occurrence and adding the results
Therefore, we have the expected value given by the following expression;
Estimated network A viewers where network B schedule top show = 1.1 million viewers
Estimated network A viewers where network B schedule a different show = 1.6 million viewers
Probability that Network B will air its top show = 0.4
Probability that Network B will air another show = 0.6
We therefore have;
Expected value, E of Network A viewers is therefore;
E = 1.1 × 0.4 + 1.6 × 0.6 = 0.44 + 0.96 = 1.4 million viewers.
Network A expects 1.4 million viewers will watch their show.
On Martin's first stroke, his golf ball traveled 4/5 of the distance to the hole. On his second stroke, the ball traveled 79 meters and went into the hole. How many kilometers from the hole was Martin when he started?
Answers
Answer:
0.395 kilometre
Step-by-step explanation:
Given:
On Martin's first stroke, his golf ball traveled 4/5 of the distance to the hole.
On his second stroke, the ball traveled 79 meters and went into the hole.
Question asked:
How many kilometres from the hole was Martin when he started?
Solution:
Let distance from Martin starting point to the hole in meters = [tex]x[/tex]
On Martin's first stroke, ball traveled = [tex]\frac{4}{5} \ of \ total \ distance\ to\ the\ hole[/tex]
[tex]=\frac{4}{5} \times x=\frac{4x}{5}[/tex]
On his second stroke, the ball traveled and went to the hole = 79 meters
Total distance from starting point to the hole = Ball traveled from first stroke + Ball traveled from second stroke
[tex]x=\frac{4x}{5} +79\\ \\ Subtracting\ both\ sides\ by \ \frac{4x}{5}\\ \\ x- \frac{4x}{5}= \frac{4x}{5}- \frac{4x}{5}+79\\ \\ \frac{5x-4x}{5} =79\\ \\ By \ cross\ multiplication\\ \\ x=79\times5\\ \\ x=395\ meters[/tex]
Now, convert it into kilometre:
1000 meter = 1 km
1 meter = [tex]\frac{1}{1000}[/tex]
395 meters = [tex]\frac{1}{1000}\times395=0.395\ kilometre[/tex]
Thus, there are 0.395 kilometre distance from Martin starting point to the hole.
what type of graph does not have scale and aces defined on it?
Answers
Answer:
C
Step-by-step explanation:
working together it takes two computers 10 minutes to send out a company's email. If it takes the slower computer 30 minutes to do the job on its own, how long will it take the faster computer to do the job on its own?
Answers
Answer: it will take the faster computer 15 minutes to do the job on its own.
Step-by-step explanation:
Let t represent the number of minutes it will take the faster computer to do the job on its own. It means that the rate at which it does the job per minute is 1/t
If it takes the slower computer 30 minutes to do the job on its own. It means that the rate at which it does the job on its own per minute is 1/30
By working together, they would work simultaneously and their individual rates are additive. Working together it takes two computers 10 minutes to send out a company's email. It means that the rate at which both computers work together per minute is 1/10 Therefore,
1/t + 1/30 = 1/10
Cross multiplying by 30x, it becomes
3x = x + 30
3x - x = 30
2x = 30
x = 30/2
x = 15 minutes
Line segment QP is tangent to the circle. A circle is shown. Secant M P and tangent Q P intersect at point P outside of the circle. Secant M P intersects the circle at point N. The length of Q P is n, the length of N P is 11.5, and the length of M N is 24. What is the length of line segment QP? Round to the nearest unit. 13 units 17 units 18 units 20 units
Answers
Answer:
The length of line segment QP is 20 units ⇒ 4th answer
Step-by-step explanation:
If a secant and a tangent are drawn from a point outside the circle, then the product of the lengths of the secant and its external segment equals the square of the length of the tangent segment
Look to the attached figure
∵ PQ is a tangent to the circle
∵ PM is a secant intersects the circle at points N and M
- That means the product of the lengths of PM and PN is
equal to the square of the length of PQ
∴ (PQ)² = (PN). (PM)
∵ The length of Q P is n units
∴ PQ = n
∵ The length of N P is 11.5 units
∴ NP 11.5
∵ The length of M N is 24 units
∴ MN = 24
- The length of the secant PM is the sum of the lengths of PN
and MN
∵ PM = PN+ NM
∴ PM = 11.5 + 24 = 35.5
Substitute the values of PQ, PN, and PM in the formula above
∵ n² = 11.5 × 35.5
∴ n² = 408.25
- Take √ for both sides
∴ n = 20.205197
- Round it to the nearest unit
∴ n = 20
∵ n is the length of PQ
∴ The length of line segment QP is 20 units
Answer:
D. 20 units
Step-by-step explanation:
A line has the points (3,7) and (5,19) on it. What is the slope of that line?
A) 3
B) (8,26)
C) 6
D) -6
Answers
Answer:
C) 6
Step-by-step explanation:
19 - 7 = 12
5 - 3 = 2
12/2 = 6
hope this helps :) please mark brainliest if you see fit :)
Write each set of fractions with the lowest common denominator and then find which fraction is greater. 4/7 and 5/8 3/8 and 4/9 5/6 and 7/8 3/10 and 4/15
Answers
Answer:
[tex]\frac{32}{56}\ < \frac{35}{56}[/tex]
[tex]\frac{27}{72} \ < \frac{32}{72}[/tex]
[tex]\frac{20}{24}\ < \frac{21}{24}[/tex]
[tex]\frac{9}{30}\ >\frac{8}{30}[/tex]
Step-by-step explanation:
Given that,
First set of fraction is [tex]\frac{4}{7}\ and \ \frac{5}{8}[/tex].
Second set of fraction is [tex]\frac{3}{8}\ and \ \frac{4}{9}[/tex].
Third set of fraction is [tex]\frac{5}{6}\ and \ \frac{7}{8}[/tex].
Fourth set of fraction is [tex]\frac{3}{10}\ and \ \frac{4}{15}[/tex].
Now,
Considering the first set of fraction:
LCM of 7 and 8 is 56. Now, multiply by 8 to both numerator and denominator to [tex]\frac{4}{7}[/tex]. and multiply by 7 to both the numerator and denominator to [tex]\frac{5}{8}[/tex]. We get new set of fraction as [tex]\frac{32}{56}\ and\ \frac{35}{56}[/tex].
∴[tex]\frac{32}{56}\ < \frac{35}{56}[/tex]
Again considering the second set of fraction:
LCM of 8 and 9 is 72. Now, multiply by 9 to both the numerator and denominator to [tex]\frac{3}{8}[/tex]. and multiply by 8 to both the numerator and denominator to [tex]\frac{4}{9}[/tex]. We get new set of fraction as [tex]\frac{27}{72} \ and \ \frac{32}{72}[/tex].
∴[tex]\frac{27}{72} \ < \frac{32}{72}[/tex].
Again considering the third set of fraction:
LCM of 6 and 8 is 24. Now, multiply by 4 to both the numerator and denominator to [tex]\frac{5}{6}[/tex]. and multiply by 3 to both the numerator and denominator to [tex]\frac{7}{8}[/tex]. We get the new set of fraction as [tex]\frac{20}{24}\ and \ \frac{21}{24}[/tex].
∴[tex]\frac{20}{24}\ < \frac{21}{24}[/tex].
Again considering the fourth set of fraction:
LCM of 10 and 15 is 30.Now, multiply by 3 to both the numerator and denominator to [tex]\frac{3}{10}[/tex]. and multiply by 2 to both the numerator and denominator to [tex]\frac{4}{15}[/tex].We, get the new set of fraction as [tex]\frac{9}{30}\ and \ \frac{8}{30}[/tex].
∴ [tex]\frac{9}{30}\ >\frac{8}{30}[/tex]
Someone help please ?
Answers
Answer:
16
Step-by-step explanation:
(-3r ^-4) ^-4
(-3) ^-4 * (r^-4) ^-4
We know a^-b = 1/a^b and c^d^f = c^(d*f)
1/(-3)^4 * (r)^((-4*-4)
1/81 * r^16
The value of m is 16
A family went to a baseball game. They parked the car in a parking lot which charged $20. The cost per ticket was $27. Write an equation for the total cost of going to the baseball game, where y is the total cost and x is the total number of people. If the family spent $236, how many people went to the game?
Answers
Answer:
[tex]y=27x+20[/tex]
8 people went to the game.
Step-by-step explanation:
Let x represent number of tickets.
We have been given that the family parked the car in a parking lot which charged $20. The cost per ticket was $27.
The cost of x tickets would be [tex]27x[/tex].
The total cost of going to baseball game would be equal to cost x tickets plus parking cost that is [tex]27x+20[/tex].
Therefore, the equation [tex]y=27x+20[/tex] represents the total cost (y) of going to the baseball game.
To find the number of people who went to game, we will equate total cost with 236 as:
[tex]236=27x+20[/tex]
[tex]236-20=27x+20-20[/tex]
[tex]216=27x[/tex]
[tex]\frac{216}{27}=\frac{27x}{27}[/tex]
[tex]8=x[/tex]
Therefore, 8 people went to the game.
A composite figure has a radius of 10 cm.
10 cm
What is the area of this composite figure? Use 3.14 for $.
23.55 cm
78.5 cm
© 235.5 cm?
314 cm?
Mark this and return
Save and Exit
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Next
Next
Answers
Answer: 314cm
Step-by-step explanation:
The area of a circle = πr^2
where π = 3.14
r = radius
From the question, we've been given the radius as 10cm. So, we plug the radius into the formula.
Area= πr^2
= 3.14 × (10 × 10)
= 3.14 × 100
= 314 cm
Answer:
Step-by-step explanation:
Given a composite figure,
A circle of radius r = 10cm
We want to find the area of the circle?
Area of a circle is calculated using
A = πr²
Where π is given to be 3.14
π = 3.14
And r is the radius of the circle
Then, area of the composite figure is
A = πr²
A = 3.14 × 10²
A = 3.14 × 100
A = 314 cm²
The last option is correct
What’s is 2+2 I really need help
Answers
Answer:
4
Step-by-step explanation:
What can readers best infer about Blackfeet culture from
this excerpt?
O
O
O
O
how sickness was cured
what people gathered to eat
how people farmed the land
what religious beliefs people held
Answers
Answer:
b
Step-by-step explanation:
Answer:The answer is B
Step-by-step explanation:
Have have a garden that is 9 feet by 12 feet and you want to buy a pathway around the garden that is x feet, write an expression for the area of the pathway
Answers
Answer:
An expression for the area of the pathway is [tex]4x^2+42x[/tex]
Step-by-step explanation:
Length of garden = 9 feet
Breadth of garden = 12 feet
Area of garden = [tex]Length \times Breadth = 9 \times 12 =108 ft^2[/tex]
We are given that you want to buy a pathway around the garden that is x feet
Width of pathway = x feet
Outer length = 9+x+x=9+2x
Outer breadth = 12+x+x=12+2x
Area of path including garden =[tex]Length \times Breadth = (9+2x)(12+2x)[/tex]
Area of path = Area of path including garden - Area of garden
Area of path =[tex](9+2x)(12+2x)-108[/tex]
Area of path =[tex]108+18x+24x+4x^2-108[/tex]
Area of path =[tex]4x^2+42x[/tex]
Hence an expression for the area of the pathway is [tex]4x^2+42x[/tex]
100 points!!! Simplify the bottom right so there are no radicals in the denominator.
Answers
Answer:
-
[tex] \frac{ - \sqrt{2} }{10} [/tex]
step by step:
[tex] \frac{ - 1}{5 \sqrt{2 } } \times \frac{ \sqrt{2} }{ \sqrt{2} } = \frac{ - \sqrt{2} }{5 \times 2} = \frac{ - \sqrt{2} }{10} [/tex]
multiply by the square root of 2 to get rid of the square root of 2 on the bottom, then simplify. hope this helped :)
[tex]\\ \sf{:}\longrightarrow \dfrac{-1}{5\sqrt{2}}[/tex]
Multiply 5√2 on both numerator and denominator[tex]\\ \sf{:}\longrightarrow \dfrac{-1(5√2)}{(5√2)^2}[/tex]
[tex]\\ \sf{:}\longrightarrow \dfrac{-5√2}{25(2)}[/tex]
[tex]\\ \sf{:}\longrightarrow \dfrac{-5√2}{50}[/tex]
[tex]\\ \sf{:}\longrightarrow \dfrac{-√2}{10}[/tex]
Solve the equation: 3(x - 4) = -21 *
Answers
Answer:
x = -3
Step-by-step explanation:
simplify
3(x - 4) = -21
3x - 12 = -21
3x = = -9
x = -3
-distribute-
3x-12=-21
-Move the -12 to the other side, separating the coefficient-
3x=-9
-Divide both sides by 3-
Answer: x=-3