The time when the ball hit the ground, which is thrown from a height of 70 meters with an initial downward velocity of 10 m/s is 2.87.
What is a quadratic equation?A quadratic equation is the equation in which the unknown variable is one and the highest power of the unknown variable is two.
The standard form of the quadratic equation is,
[tex]ax^2+bx+c=0[/tex]
Here,(a,b, c) is the real numbers and (x) is the variable. To solve the equation for x, use the following formula,
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
The ball's height h (in meters) after t seconds is given by the following.
[tex]h=70-10t-5t^2[/tex]
The ball is thrown from a height of 70 meters with an initial downward velocity of 10 m/s. In this case,
Height h=70 metersVelocity v=10 m/s.The time when the ball hit the ground has to be find out. The value of the height when it hit the group is zero. Put the value of h=0 in the above equation,
[tex]h=70-10t-5t^2\\0=70-10t-5t^2\\5t^2+10t-70=0\\5t^2+10t-70=0\\[/tex]
Solve the quadratic equation using the following formula,
[tex]t=\dfrac{-10\pm \sqrt{10^2-4(10)(-70)}}{2\times5}\\t=-4.87, t=2.87[/tex]
Consider positive value. Thus, the time when the ball hit the ground, which is thrown from a height of 70 meters with an initial downward velocity of 10 m/s is 2.87.
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A farmer wants to set up a pigpen using 40ft of fence to enclose a rectangular area of 51 square feet. Find the dimensions of the pigpen.
Answer:
The sides of the pigpen are 3 by 17
Step-by-step explanation:
Perimeter of pigpen => 2x + 2y = 40
Area of pigpen => xy = 51 (this is assuming x = length, and y = width)
Let's isolate "y" for the first equation;
2x + 2y = 40
2(x + y) = 40
x + y = 20
y = 20 - x
xy = x(20 - x) = 51 = 51
20x - x^2 = 51
x^2 - 20x + 51 = 0
According to the quadratic equation =>
x = ( - (- 20) + √(- 20)^2 - 4 * 1 * 50 ) / 2 * 1 = 17
x = ( - (- 20) - √(- 20)^2 - 4 * 1 * 50 ) / 2 * 1 = 3
The dimensions of the pigpen are actually 17 by 3
Proof: 17(3)= 51, 2(17) + 2(3) = 40
If f(x)=×^2+7x-5 and you divide by x-2, What is the quotient and remainder?
Answer:
The quotient is : x+9
The remainder is : 13
Step-by-step explanation:
The question requires you to perform the long division method;
This will be;
[tex]x-2\sqrt{x^2+7x-5}[/tex]
start with the x term in x-2 and the first term in the function, x², to get x then multiply the x with x-2 to get x²-2x and perform the operation below;
x-2√x²+7x-5 -----------to first get x and then multiply x*[x-2]⇒x²-2x
- x²-2x+0 ------------perform subtraction of like terms
---------------------
9x-5 ----now divide this answer by x-2 ,starting with x and 9x
----------------------This will give , 9 then multiply 9 by x-2 to get 9x-18 and perform the subtraction operation as;
9x-5
- 9x-18
------------------------
13
So the answer will be; x+9 remainder 13
the square with a side length (x + 3) and an equilateral triangle with side lengths (3x-1) have the same perimeter what is the value of x?
Help please
Answer: x = 9/5 or [tex]1\frac{4}{5}[/tex]
35 1/5 is the perimeter of the square and the triangle.
Step-by-step explanation:
The square has 4 sides, so the perimeter of the square is 4(x+3)
The triangle has 3 sides so the perimeter is 3(3x-1)
The perimeters are equal, so 4(x+3) = 3(3x-1)
Solve by distributing and then
4x +12 = 9x - 3 subtract 4x from both sides and add 3 to both sides
4x-4x +12 -3 = 9x-4x -3 +3 cancel the zero sums and combine similar terms.
9 = 5x divide both sides by 5
x = 9/5
Check: 4(9/5 +3) = 3[3(9/5) -1]
36/5 + 3 = [3( 27/5 -1 ] 27/5 -3 -3 equivalent -15/5 27/5 -15/5 = 12/5
36/5 = 3(12/5) = 36/5 TRUE! simplify to mixed numbers
35 1/5 is the perimeter of the square and the triangle.
Answer:
u,
Step-by-step explanation:
During a soccer game, Erin scored 1 of 2 goals attempted. Lauren scored 6 of 8 goals attempted. Write the fraction that represents each and compare. Who was the most successful? SHOW YOUR WORK AND EXPLAIN YOUR ANSWER.
(I KNOW THAT ERIN IS 1/2 AND LAUREN IS 6/8 BUT IM NOT SURE HOW TO COMPARE THEM)
Answer:
Lauren.
Work:
1/2 vs. 6/8
1/2 * 4/4 = 4/8
6/8 > 4/8
Answer:
One half as a percentage is 50%.
Six eighths as a percentage is 75%.
So Lauren scored 75 percent of her attempts.
Erin only scored 50% of her attempts.
Therefore, Lauren was the most successful during the game.
Work:
1/2 equals 50%.
6/8 equals 75%.
Hope this helps!
Try factoring this before moving on: 25+10x+x^2
Answer:
Step-by-step explanation:
x2 + 10x + 25
x2 + 5x + 5x + 25
x (x + 5) + 5(x + 5)
(x + 5) (x + 5)
Which polynomial is in standard form?
2x-3x+ 10x
-16x2-9x+12
15x-6x2+3
-7x?+ 9x9 - 11x
Answer:
[tex]-16x^2-9x+12[/tex]
Step-by-step explanation:
[tex]2x-3x+ 10x[/tex]
[tex]-16x^2-9x+12[/tex]
[tex]15x-6x^2+3[/tex]
[tex]-7x+ 9x^9 - 11x[/tex]
Standard form is when the polynomial's terms's degrees go down so the highest power is the first and the lowest is the last.
We see that the first expression can be more simplified so that isn't right.
We see that the second expression is in standard form so that might be right.
We see that the third expression has the highest power as the second term so that is wrong
We see that last expression is the same as the third one so that is also wrong.
We can conclude that [tex]-16x^2-9x+12[/tex] is the correct one or in standard form.
I really need help please
Factor the expression 1/4x + 11/4
Answer:
1 /4 ( x+11 )
Step-by-step explanation:
Factor 1 /4 out of each term.
Which property of addition is shown in the equation below?
a + bi + 0 + Oi = a + bi
A.commutative property
B.inverse property
C.identity property
D.associative property
Answer:
This is the identity property. It means that any number added by zero would be the same number. In the second expression the zeroes were taken away.
Step-by-step explanation:
like and 5 start luv u
The gym charges a membership fee of $75 and a
monthly fee of $25. If you have budgeted $325 for a
membership, how many months are you able to
afford?
Answers:
: 10
:: 3
:: 15
:: 6
we be bakos thoes LOOK ET EM TOES
Can you help me please
Answer
3
Step-by-step explanation:
(4-1)^2+(8-8)^2=9
square root of 9 is 3
What is the slope of the line on the graph below
o1/5
o1/3
o3
o5
Hurry ASAP
The function T(d)=10d + 20 gives the temperature in deegrees celcius inside the earth as a function if d, the depth in kilometers ,Find the temperature at.
Answer:
Step-by-step explanation:
The question is incomoplete. Here is the complete question.
The function T(d)=10d + 20 gives the temperature in deegrees celcius inside the earth as a function if d, the depth in kilometers ,Find the temperature at 5km, 20km and 100km
T(d)=10d + 20
T(5)=10(5) + 20
T(5)= 50+ 20
T(5) = 70
Hence the temperature is 70 when d = 5km
when d = 20km
T(20)=10(20) + 20
T(20)= 200+ 20
T(20) = 220
Hence the temperature is 220 when d = 20km
when T = 100km
T(100)=10(100) + 20
T(100)= 1000+ 20
T(100) = 1020
Hence the temperature is 1020 when d = 100km
The temperatures at 5km, 20km and 100km are; 70°C, 220°C, and 1020°C respectively.
The complete question requires that we find the temperature at 5km, 20km and 100km.
The temperature function is; T(d)=10d + 20
For 5km;
T(5)=10(5) + 20T(5) = 70°CFor 20km;
T(20) = 10(20) + 20T(20) = 220°CFor 100km;
T(100)=10(100) + 20T(100) = 1020°CRead more;
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HELPPPP!!!! PLEASEEE!!!
Which statement below is true?
A. If p → q is true, then q → p is true.
B. If p → q is true and p is true, then q is true.
C. If p → q and q → r are true, then q → p is true.
D. If p → q and q → r are true, then r → p is true.
Answer: i believe the answer is B
Step-by-step explanation: because if p to q is true, then that means p and q are both true!
70-21.45=?
I need a answer fast and it is worth 25 points
Answer:
48.55
Step-by-step explanation:
Answer:
48.55
Step-by-step explanation:
Convert 70 into 70.00 and then it will be easier to subtract.
3. A test consists of 30 true/false questions. To pass the test a student must answer at least 18 questions correctly. If a student guesses on each question, what is the probability that the student will pass the test?
Answer: the answer would be15%
Step-by-step explanation:
Please hurry need help
Answer:
-11
Step-by-step explanation:
q=you+have+50+blueberries+and+75+scone.+You+want+to+make+as+many+identtical+bags+as+possible.+Each+bag+should+have+an+equal+number+of+blueberry+scones+and+an+equal+number+of+cranberry+scones.+What+is+the+greatest+number+of+bags+you+can+fill&cvid=1ea9df65fe52425e9572dfee62446327&pglt=43&FORM=ANNTA1&PC=DCTS
Answer:
uhmmmmm... i no understand...
Step-by-step explanation:
Answer:
25 baggies; each bag has 2 blueberry scones, and three cranberry scones.
Step-by-step explanation:
The question format is a bit bugged, but I assume the question is asking "You have 50 blueberry scones and 75 cranberry scones. You want to make as many identical bags as possible. What is he greatest number of bags you can fill?"
The first thing to realize when solving this question is that whatever the answer is equal to, it must be able to be equally divided from both 50 and 75, otherwise it will have a remainder, and at least one bag will have too many or not enough scones.
This means that the answer must be a factor of both 50 and 75.
The factors of 50 includes {1, 2, 5, 10, 25, 50}
The factors of 75 includes {1, 3, 5, 15, 25, 75}
In the two sets, only 1, 5, and 25 are common factors. Of the three factors, 25 is the greatest number, and thus the greatest number of bags that can you can fill.
The Cooking Club made some pies to sell at a basketball game to raise money for the new math books. The cafeteria contributed four pies to the sale. Each pie was then cut into five pieces and sold. There was a total of 60 pieces to sell How many pies did the club make?
Answer:
the cooking club made 8 pies
Step-by-step explanation:
first do 60 divided by 5 to find the total number of pies you get 12
then since the cafetria donates four pies and the cooking club makes the rest, you do 12-4=8
There were 11 pies cooked in all by the club to earn money for the basketball game.
What is Function?
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.
Given, The Cooking Club made some pies to sell at a basketball game to raise money for the new math books. The cafeteria contributed four pies to the sale.
Each Pie cut into four pieces
Since there were 60 pieces of pie
The total number of pies sell at a basketball game = 60/4
The total number of pies sell at a basketball game = 15
Also, given there were four pies donated by Cafeteria
Thus,
Total pie basketball team made = 15 - 4
Total pie basketball team made = 11
Therefore, the Total number of pies made by the club to raise funds for the basketball game is 11.
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x is greater than or equal to -5 and less than 0
Answer:
-5 ≤ x < 0
Step-by-step explanation:
Step 1: Convert word signs to math
greater than or equal to: ≤ x
less than: x <
Step 2: Substitute in numbers
-5 ≤ x < 0
b. The 100th term of 60, 110, 160, ... is (Simplify your answer.) How to do this?
The 1st term is 60.
Add 50 to this to get the 2nd term, 60 + 50 = 110.
Add 50 to that to get the 3rd term, 110 + 50 = 160.
Add 50 to that to get the 4th term, 160 + 50 = 210.
And so on...
Notice that in the 2nd term, we added 1 copy of 50 to the 1st term.
In the 3rd, we ultimately added 2 copies of 50 to the 1st term.
In the 4th, we added 3 50s.
And so on... If the pattern continues, then the n-th term can be obtained by adding (n - 1) copies of 50 to the first term.
So, the 100th term is
60 + (100 - 1) * 50 = 5010
x to the 5 power times x to the 8 power time x to the 0 power
idk i am in 6th grade idk
helpp mee i’ll give you 20 points for it
Answer: Part A: Noah eats 10/8's. Or 1 and 2/8's if you have to simplify.
Part B: Draw the circles and cut them into 8 slices and color in two of each.
Part C: So if Jessica ate half of what Noah eats, she only ate 5/8's of pizza.
Part D: Noah and Jessica together ate 15/8's of pizza or if you want to simplify, 1 and 7/8's of pizza. There is 25/8's of pizza left, or 25 pieces left. And the remaining friends ate 1/5 of the remaining pizza which was 25 pieces. So, they ate 5 pieces. So they ate 5/8's of the remaining pizza.
Step-by-step explanation:
I think this might be your answer. Double check to make sure i am not wrong.
The pH of a solution is measured eight times by one operator using the same instrument. She obtains the following data: 7.15, 7.20, 7.18, 7.19, 7.21, 7.20, 7.17, and 7.18. (a) Calculate the sample mean. Round your answer to 3 decimal places. (b) Calculate the sample variance. Round your answer to 6 decimal places. (c) Calculate the sample standard deviation. Round your answer to 3 decimal places. (d) Which of the following are potential major sources of variability in the experiment
Answer:
(a)7.185
(b)0.000371
(c) 0.019
(d)Sample variance and Sample standard deviation
Step-by-step explanation:
We are given the following sample data.
7.15, 7.20, 7.18, 7.19, 7.21, 7.20, 7.17, 7.18.
(a) Calculate the sample mean. Round your answer to 3 decimal places.
The formula for sample mean =
Sum of terms/Number of terms
= 7.15 + 7.20+ 7.18+7.19+7.21+7.20+7.17+ 7.18/8
= 57.48/8
= 7.185
(b) Calculate the sample variance. Round your answer to 6 decimal places.
The formula for sample Variance =
(x - mean)²/n - 1
n = 8
Sample variance = (7.15 - 7.185)² + (7.20-
7.185)²+ (7.18 -7.185)² + (7.19 -7.185)² + (7.21 - 7.185)² + (7.20 - 7.185)² + (7.17 - 7.185)² + (7.18 - 7.185)² /8 - 1
= 0.001225 + 0.000225+ 0.000025+ 0.000025 + 0.000625 + 0.000225 + 0.000225 + 0.000025/7
= 0.0026/7
= 0.000371428571
Approximately to 6 decimal places = 0.000371
(c) Calculate the sample standard deviation. Round your answer to 3 decimal places.
The formula for Sample Standard Deviation = √Sample variance
= √0.000371428571
= 0.01927248223
To 3 decimal places = 0.019
(d) Which of the following are potential major sources of variability in the experiment
Sample variance
Sample standard deviation
Lillian read 2 books in 3 months. What was her rate of reading, in books per month? Give your answer as a whole number/ a fraction in simplest form
Answer: 2/3
Step-by-step explanation:
Books per month is books divided by months
she read 2 books in 3 months, so divide 2/3
2/3 is your answer
Fraction in simplest form is [tex]\frac{2}{3}[/tex] .
Given Lillian read 2 books in 3 months.
So, He read books in one month is [tex]\frac{2}{3}[/tex].
Hence Lillian reads [tex]\frac{2}{3}[/tex] books per month.
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k4 minus 7 k2 (if k =3)
Answer:
472k
Step-by-step explanation:
cause it was plus the number to the number
Answer:
11
Step-by-step explanation:
k4 -7 + k2
(3)4 -7 +(3)2
12-7+6
=11
Working simultaneously, four fudge machines complete a big order in 32 hours. All the machines at the fudge factory work at the same pace. If only half of the machines are working, in how many hours will the order be complete?
Answer:
64 hours
Step-by-step explanation:
Hope this helps :)
The school talent show is 92 minutes long. Acts in the talent show are each about 4 minutes long. How many acts should there be?
Estimate:
Tape Diagram:
Show your work:
Answer:
23 acts
Step-by-step explanation:
This is a division problem.
92/4 = 23
Answer: 23 acts
need help answering
Answer:
I haven't done this in a while but wouldn't it just be--
17. X=40
18. X=40
19. X=55
Step-by-step explanation:
write down the two irrational number
Answer:
Square root of 2
Pi
Step-by-step explanation:
Answer:
square root of 5 pi sq root of -11
Step-by-step explanation: