Leyla drops a penny from a height of 150m. How long will it take to hit the ground? Round to the nearest tenth of a second. use the formula h(t)=-4.9t²+v₀t+h₀, where v₀ is the initial velocity and h₀ is the initial height.
Answers
It will take approximately 5.5 seconds for the penny to hit the ground.
To determine the time it takes for the penny to hit the ground, we can use the given formula for the height as a function of time:
[tex]\[ h(t) = -4.9t^2 + v_0t + h_0 \][/tex]
Given that the penny is dropped and not thrown, the initial velocity [tex]\( v_0 \)[/tex] is 0. The initial height [tex]\( h_0 \)[/tex] is 150 meters. We want to find the time [tex]\( t \)[/tex] when the height [tex]\( h(t) \)[/tex] is 0, which is when the penny hits the ground.
Plugging in the known values, we get:
[tex]\[ 0 = -4.9t^2 + 0 \cdot t + 150 \][/tex] Simplifying, we have:
[tex]\[ 4.9t^2 = 150 \][/tex]
Now, we solve for [tex]\( t \)[/tex]:
[tex]\[ t^2 = \frac{150}{4.9} \][/tex]
[tex]\[ t^2 \approx 30.612244898 \][/tex]
Taking the square root of both sides to solve for [tex]\( t \)[/tex]:
[tex]\[ t \approx \sqrt{30.612244898} \][/tex]
[tex]\[ t \approx 5.532851414 \][/tex]
Rounding to the nearest tenth of a second, we get:
[tex]\[ t \approx 5.5 \][/tex]
Related Questions
Calculate the difference 12.0875 – 7.50 using significant digits.
A. 4.5
B. 4.587
C. 4.59
D. 4.6
Answers
Answer:
The answer should be C.4.59.
What is 22+6\3= because i have it in my homework i need do know
Answers
6 ÷ 3 =2 , so 22 + 2= 24
hopefully this helps
Which of the following pairs of organisms compete with each other for food?
A. squirrels and owls
B. mice and owls
C. rabbits and green plants
D. mice and rabbits
Answers
True or false the fraction 9/21 is in lowest terms
Answers
9/12 in it's lowest terms is 3/7.
3\7 in decimal is 0.42857142 or 0.43
3\7 in percent 42.857143% or 43 %
use math way . c o m
I need to write these description into the new function but I keep getting the wrong thing -.-
1.The function f(x)=(1/2)^x is translated 4 units right, reflected across the x-axis, and vertically stretched by a factor of 1.5
2.The function f(x)=ln x is translated 3 units left, horizontally compressed by a factor of 1/4 and translated 0.5 units down.
3. The function f(x)=e^x is horizontally stretched by a factor of 3, reflected across the y-axis, and translated 1 unit right.
Answers
.. translation right by k units: f(x) ⇒ f(x-k)
.. translation up by k units: f(x) ⇒ f(x) +k
.. horizontal stretch by a factor of k: f(x) ⇒ f(x/k) . . . . same as compressed by 1/k
.. vertical stretch by a factor of k: f(x) ⇒ k*f(x)
.. reflection across the x-axis: f(x) ⇒ -f(x)
.. reflection across the y-axis: f(x) ⇒ f(-x)
The sequence in which these are done is important.
1. f(x) = (1/2)^x
.. translated 4 units right: f(x) = (1/2)^(x -4)
.. reflected across the x-axis: f(x) = -(1/2)^(x -4)
.. vertically stretched by a factor of 1.5: f(x = -1.5(1/2)^(x -4)
2. f(x) = ln(x)
.. translated 3 units left: f(x) = ln(x +3)
.. horizontally compressed by a factor of 1/4: f(x) = ln(x/4 +3)
.. translated down 0.5 units: f(x) = -0.5 +ln(x/4 +3)
3. f(x) = e^x
.. horizontally stretched by a factor of 3: f(x) = e^(x/3)
.. reflected across the y-axis: f(x) = e^(-x/3)
.. translated 1 unit right: f(x) = e^(-(x -1)/3)
The transformed equations for each of your base functions according to given changes are f(x) = -1.5*(1/2)ˣ⁻⁴, f(x) = ln(4×(x+3))-0.5, and f(x)=e⁻³×(x-1) respectively.
Explanation:1. The transformed function for your first one, namely f(x)= (1/2)ˣ, after being translated 4 units right, reflected across the x-axis, and vertically stretched by a factor of 1.5 would be f(x) = -1.5×(1/2)⁽ˣ⁻⁴⁾.
2. Your second function, f(x) = ln(x), after being translated 3 units left, horizontally compressed by a factor of 1/4, and translated 0.5 units down becomes:
f(x) = ln(4×(x+3))-0.5.
3. Your final function, f(x)=e^x, when it's horizontally stretched by a factor of 3, reflected across the y-axis, and translated 1 unit right, would transform into: f(x)=e⁻³×(x-1).
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2(3x+4)-5(1-2x)=7(2x-3)+12 in stages
Answers
6x+8-5+10x = 14x - 21 + 12
Stage 2: COMBINE LIKE TERMS
16x + 3 = 14x - 9
Stage 3: SOLVE
2x = -12
x = -6
Hope this helps!
LHS= 2(3x+4)-5(1-2x) = 6x+8 -(5-10x)
= 6x+8+10x-5 =16x +3
RHS= 7(2x-3)+12 = 14x-21+12=14x -9
since LHS=RHS
16x+3=14x-9 (by subtracting 14x from both sides)
2x +3 = -9 (by subtracting 3 from both sides)
2x =-12 (divide both sides by 2)
x = -6
Note:
please describe your problem with adding comments on your requirements.
Find the greatest common factor : 32a^3b^2, 44ab^3 and 40a^2b
Find the greatest common factor : 25^2q^3, 15p^2q^2 and 35pq^4
Answers
1) 4ab
2) 5pq²
Explanation
Greatest common factor is sometimes known as GCD (greatest common divisor). It means the greatest number that can divide a set of numbers.
For example, the GCD of 12 and 18 is 6.
Question 1
Find the GCF of 32a^3 b^3,44ab^3,and 40a^2 b. To do this you can factor out the common term.
32a^3 b^3,44ab^3,and 40a^2 b
Dividing every term by ab we shall have,
ab(32a^2 b^2,44b^2,and 40a)
Dividing again by 4,
4ab(8a^2 b^2,11b^2,and 10a)
Have no other common factor, the GCF = 4ab
Question 2
Find the GCF of 25p²q³,15p² q² and 35pq^4 . To do this you can factor out the common term.
25p²q³,15p² q² and 35pq^4
Dividing each term by 5,
5(5p²q^3, 3p²q² and 7pq^4)
Dividing again by pq2,
5pq² (5pq, 3p and 7q² )
There no been any other common divisor, the GCF = 5pq²
Answer:
Part A. 4ab
Part B. 5pq²
Step-by-step explanation:
Part A). In this part the given expressions are 32a³b², 44ab³, 40a²b
We have to find the greatest common factor of these expressions.
Factors of 32a³b² = 2×2×2×2×2×a×a×a×b×b
Factors of 44ab³ = 2×2×11×a×b×b×b
Factors of 40a²b = 2×2×2×5×a×a×b
So for the the greatest common factor we will choose the common factors (bold letters) of three expressions
GCF = 2×2×a×b = 4ab
Part B). The given expressions are 25p²q³, 15p²q² and [tex]35pq^{4}[/tex]
Factors of 25p²q³ = 5×5×p×p×q×q×q
Factors of 15p²q² = 3×5×p×p×q×q
Factors of [tex]35pq^{4}[/tex] = 5×7×p×q×q×q×q
Therefore greatest common factor will be = 5pq²
helppppppppppppppppppppppppppppppppppppp
Answers
a < -2
Explanation:
To solve the inequality, we will need to isolate the a on one side of the inequality as follows:
3 - 2a > 7
1- subtract 3 from both sides:
3 - 2a - 3 > 7 - 3
-2a > 4
2- divide both sides by -2. Remember that when dividing by a negative number, we flip the inequality sign.
-2a / -2 > 4 / -2
a < -2
Hope this helps :)
jesse uses 19 beads to decorate each picture frame. In all, Jesse used 133 beads. How many picture frames did Jesse make?
Answers
Answer:
use division: 133/19 = 7 picutre frames
Step-by-step explanation:
Khan academy how to solve equations with fractions and mixed numbers
Answers
Alternatively, you can simply do the arithmetic using the numbers given. You learned a long time ago how to add, subtract, multiply, and divide mixed numbers and fractions. Do these operations as necessary to solve the equations.
Factor completely 2x3 + x2 - 18x - 9
A. (x2-9)(2x+1)
B. (x-3)(x+3)(2x-1)
C. (x-3)(x+3)(2x+1)
D. (2x-3)(2x+3)(x-1)
Answers
2 x^3 + x^2 - 18 x - 9
Factor terms by grouping. 2 x^3 + x^2 - 18 x - 9 = (2 x^3 + x^2) + (-18 x - 9) = x^2 (2 x + 1) - 9 (2 x + 1):
x^2 (2 x + 1) - 9 (2 x + 1)
Factor 2 x + 1 from x^2 (2 x + 1) - 9 (2 x + 1):
(2 x + 1) (x^2 - 9)
x^2 - 9 = x^2 - 3^2:
(2 x + 1) (x^2 - 3^2)
Factor the difference of two squares. x^2 - 3^2 = (x - 3) (x + 3):
Answer: (x - 3) (x + 3) (2 x + 1) thus the Answer is C.
The factorization of the given polynomial 2x3 + x2 - 18x - 9 is (x-3)(x+3)(2x+1) and we achieve this by factoring common terms and applying the formula for difference of squares.
Explanation:To factor the polynomial 2x3 + x2 - 18x - 9, you would first tie together similar terms (if any), then check for any common factors in all the terms. In this case, we can factor this expression in two steps:
First step: Looking for common factors, we can rewrite the expression as x2(2x) - 9(2x) + x2 - 9.Second step: Then, factor using the formula for the difference of squares and you will find that the fully factored expression is (x-3)(x+3)(2x+1).Learn more about Factoring Polynomials here:https://brainly.com/question/35418869
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PLEASE HELP ASAP!!!!!!!!!
Answers
Answer C)
By what percent will a fraction decrease if its numerator is decreased by 50% and its denominator is decreased by 25%?
AND NO, it is not 33, 33.3, 66, or 66.6 percent.
Answers
[tex] \frac{N}{D} [/tex]
if its numerator is decreased by 50%
[tex] N - \frac{50}{100}N [/tex] ==> (this will be the numerator part)
if its denominator is decreased by 25%
[tex] D - \frac{25}{100}D [/tex] ==> (this will be the denominator part)
I try to separate them out, so it's easier to see the problem.
[tex] N - \frac{50}{100}N = \frac{100N}{100} - \frac{50N}{100} = \frac{50N}{100} [/tex]
[tex] D - \frac{25}{100}D = \frac{100D}{100} - \frac{25D}{100} = \frac{75D}{100}[/tex]
[tex] \frac{\frac{50N}{100}}{\frac{75D}{100}} = \frac{50N}{100} * \frac{100}{75D}[/tex]
[tex] \frac{50N}{75D} = \frac{2}{3}(\frac{N}{D})[/tex] by this, you can understand that
[tex] \frac{2}{3}(\frac{N}{D})[/tex] as 66.6% of N/D because 2/3 is 0.666666.... The answer should be 66.7% if you round them up.
(Please help~! 20 Points~!)
The solution to 8x = 32 is x = ___.
3
4
5
6
Answers
x=
[tex] \frac{32}{8} [/tex]
=4
Brainliest please? I am trying to move up a rank!
what is the length of the 2nd base of a trapezoid if the length of one base is 27 and the length of the midsegment is 19
Answers
x=(a+b)/2
"x" is the midsegment (x=19).
"a" and "b" are the bases (a=27).
2. When you clear the second base "b" from the formula x=(a+b)/2 and you substitute the values, you obtain:
x=(a+b)/2
2x=a+b
b=2x-a
b=2(19)-27
b=38-27
b=11
What is the length of the 2nd base of a trapezoid?
The answer is: 11
Answer: 11
Step-by-step explanation:
X=(a+b)/2
2x=a+b
B=2+-a
B=2(19)-27
B=3-27
B=11
PLEASE HELP ME OUT PLEASE!!
EXPLAIN IT PLEASE SO I CAN UNDERSTAND IT BETTER
THX
Answers
Someone Please Help!!!
Find the radian measure of an angle of -280 degrees
Answers
Answer:-14pi/9
Step-by-step explanation:
Point D is on segment BC. Segment BC measures 8x units in length.What is the length of segment BC?units
Answers
Can someone help me?
Answers
make sure your calculator is in Degree mode.
Please help and show work. 15 points.
Answers
the x satys the same, the Y reverses positive/negative
4x^3+2x^2+3x+4 divided by x+4
Answers
= 4x^2 -14x +59 -232/(x+4)
The remainder is f(-4) = -232.
Simplify: 4x^4+2x^3+3x^2+4x+4/x
If PQRS is a parallelogram, what is the value of Y
Answers
RQ = SP
1/4 y = 13
Now you will multiply the reciprocal of 1/4 on both sides.
4(1/4 y) = (13)4
y = 52.
So the answer is option C.
The value of y is equal to 52. The correct option is C.
What is a parallelogram?A parallelogram is a quadrilateral having four sides and the two opposite sides are equal and parallel to each other.
To find the value of y all you have to do is set side RQ and SP equal to each other because opposite sides of a parallelogram are congruent.
RQ = SP
1/4 y = 13
Now you will multiply the reciprocal of 1/4 on both sides.
4(1/4 y) = (13)4
y = 52.
Hence, the answer is option C.
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Factor completely.
y^2+6y+8
Answers
(y + ____)(y + ______)
The blanks equal the factors of the last term. The last term may have multiple pairs of factors, but you need to look at the middle term to find the correct pair. The sum of the pair of factors should equal the middle term. For instance, in this example 8 + 1 does not equal 6, even though it is a factor pair of 8. It is easier to grasp the answer if you name all the factor pairs and work from them. With practice, factor pairs will come easier. In this case, the factor pair is 4 and 2.
4x2 = 8 and 4 + 2 = 8.
Therefore, (y + 2)(y + 4) = y^2 + 6y + 8
Final answer:
To factor the expression [tex]y^2+6y+8[/tex] completely, we use the method of factoring binomials. The expression can be factored as (y + 2)(y + 4).
Explanation:
To factor the expression y2 + 6y + 8 completely, we need to find two binomials that multiply together to give us the original expression. Since the coefficient of the y2 term is 1, we know that the binomials will take the form (y + a)(y + b). To find the values of a and b, we need to find two numbers that add up to 6 (the coefficient of the y term) and multiply to give 8 (the constant term).
The numbers that satisfy these conditions are 2 and 4, because 2 + 4 = 6 and 2 × 4 = 8. So, we can factor the expression as (y + 2)(y + 4).
Carlos has $690,000 he wants to save. If the FDIC insurance limit per depositor, per banks will guarantee that all of his money is insured?
Answers
Answer:
D. $230,000 in bank A, $240,000 in bank B, $220,000 in bank C
Step-by-step explanation:
Carlos has $690,000 he wants to save. If the FDIC insurance limit per depositor, per banks will guarantee that all of his money is insured?
A. $200,000 in bank A, $200,000 in bank B, $290,000 in bank C
B. $200,000 in bank A, $220,000 in bank B, $270,000 in bank C
C. $230,000 in bank A, $260,000 in bank B, $200,000 in bank C
D. $230,000 in bank A, $240,000 in bank B, $220,000 in bank C
Which step will get you closest to the solution of this equation? 5⋅(x−2)=7
Answers
The. system shown is ____.
consistent
equivalent
inconsistent
Answers
Answer:
inconsistant mi boii
Step-by-step explanation:
The given system of equations is inconsistent.
What is a function? What is equation modelling? What is a mathematical equation and expression?In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the functionEquation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions.Given is the graph of three lines as shown.
A system of equations is called an inconsistent system of equations if there is no solution. Since, the given lines do not intersect at one common point, hence the given system of equations is inconsistent.
Therefore, the given system of equations is inconsistent.
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The graph shows the cost for renting a post hole digger from a local hardware store. Determine the rate of change or cost per day.
A) $60 per day
B) $30 per day
C) $90 per day
D) $15 per day
Answers
The given graph shows the cost for renting a post hole digger from a local hardware store. We have to determine the rate of change or cost per day.
Let us consider any two points.
Let us consider (1,30) and (2,60)
We have to determine the rate of change which is basically termed as "slope".
Rate of change is expressed as a ratio between a change in one variable relative to a corresponding change in another variable.
Therefore, rate of change or cost per day =
Change in y [tex] \div [/tex] Change in x
= [tex] \frac{60-30}{2-1} [/tex]
= 30
Therefore, the rate of change or cost per day is $30 per day.
A coin is tossed and a number cube is rolled. What is the probability that the coin shows heads and the number cube shows 5? A. start fraction 1 over 6 end fraction B. start fraction 1 over 12 end fraction C. start fraction 2 over 3 end fraction D. one-fourth
Answers
Answer:
i got 1/4
Step-by-step explanation:
me sorry in wrong
please help I will mark brainlist if correct
Answers
The admission fee at a fair is $2.00 for children and $4.00 for adults.
On Saturday 2,500 people entered the fair and $7,000.00 were collected.
How many children and how many adults attended? Give your answer, using x for children, y for adults.
Form of: x =, and y =
Let K = no. of children
Let A = no. of adults
2500 people mean
Kids + Adults
K + A = 2500
K = 2500 – A
2K + 4A = 7000
K + 2A = 3500
(2500 – A) + 2A = 3500
A = 3500 – 2500
(A = 1000, adults)
K = 2500 – A
K = 2500 -1000
(K = 1500, Kids)
CHECK:
1500*2 = $3000
1000*4 = $4000
(Total = $7000, people.).
Hope this helps:
PLEASE HELP MATH WILL MARK BRAINLY ASAP PICTURE ATTACHED
Answers
So for x we have 540 - 83 - 89 - 119 - 90 = 159° left