The value of t at a height of 11 feet is 0.36 sec when the ball is going upwards and 1.39 seconds when the ball is coming downwards.
What is a quadratic equation?A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers.
It is written in the form of ax²+bx+c.
Given that the height of the ball at time t is given by the function,
[tex]h(t) = 3+ 28t -16t^2[/tex]
where t is in seconds and h is in feet.
Now, the height of the ball is given to be 11 feet, therefore, substituting the value of h in the function as 11,
[tex]h(t) = 3+ 28t -16t^2\\\\11 = 3+ 28t -16t^2\\\\-16t^2 + 28t +3 -11 = 0\\\\-16t^2 + 28t -8 = 0[/tex]
Now, solving the given quadratic equation, we will get,
[tex]x= \dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\t = \dfrac{-(28)\pm \sqrt{(28)^2-4(-16)(-8)}}{2(-16)}\\\\t= 0.36\ or\ 1.39[/tex]
Hence, the value of t at a height of 11 feet is 0.36 sec when the ball is going upwards and 1.39 seconds when the ball is coming downwards.
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|x-20| if x<-20
I need help with the opposite equation
A store is currently offering a 60% discount on all items purchased. Your cashier is trying to convince you to open a store credit card and says to you, “ In addition to the 60% discount you are receiving for purchasing these items on sale today you will get an additional 20% off for opening a credit card account. That means you are getting 80% off!
If we were getting 60% discount early and then again we are receiving 20% discount for using credit card then it means that we are getting 80% discount.
What is discount?Discount means the amount which is deducted by sellers from the amount to be payable by buyers.
How to calculate discount?Let the total price to be paid by us to store is $100.
Discount received because on purchase on sale day=100*60%
=60
Discount received due to use of credit card=100*20%
=20
Total discount received from store=60+20
=80
Percentage=80/100*100
=80%
Hence the total discount received by us from store is 80%.
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The difference between two consecutive cube numbers is always odd or even?
Answer:
odd
Step-by-step explanation:
take example of 2^3 +3^3 it's odd
now others try yourself
Watch help vide
Anna took a taxi from her house to the airport. The taxi company charged a pick-up
fee of $3 plus $2.25 per mile. The total fare was $48, not including the tip. How many
miles was the taxi ride?
Anna has traveled 20 miles in the taxi.
What is equation?An equation is a relationship between the variables and constants representing how they are related to each other. It includes equal to "=" sign.
The total amount paid is $48. So, the right side of the equation will be 48.
The cost of 1 mile is $2.25 so, the cost of x miles will be 2.25x.
Determine the total cost in terms of x.
Total cost = Fixed Cost+ Variable cost
= 3+2.25x
Determine the equation and solve it.
3+2.25x=48
2.25x=45
x=20
Thus, the taxi has traveled 20 miles.
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Pls help me
Pls show your answer pls and thank you
Answer:
Step-by-step explanation:
Beth's position over time is constant, which makes the problem a lot easier. You are asked for the rate of position versus time, so begin by doing that. Since the rate is constant, clearly from the table, you can take any two data points and take their ratio. Her rate would be 11 feet every 5 seconds, or equivalently 2.2 feet every second. To graph the data, put position on the x-axis and time on the y-axis. The slope will be 2.2 at every point along her bike ride.
Moving on to the third part. If Amy traveled at a rate of 75 feet every 30 seconds, then she would be traveling 2.5 feet every second. Amy's rate is larger than Beth's rate. Since the rate corresponds to the slope of the postion vs. time graph, Amy's graph will have a steeper incline since the slope is 2.5
A regular hexagon has an area of approximately
20 square centimeters. If the apothem measures
2.4 centimeters, find the approximate length of
each side.
Answer:
The side is approx 2.78cm
Step-by-step explanation:
There is an area formula for regular polygons that uses the apothem:
A = 1/2•a•s•n
a is the apothem.
s is the side length.
n is the number of sides.
The area, A is given and also the apothem is given, as well as the number of sides.
The shape in your problem is a hexagon, so it has 6 sides.
A = 1/2 asn
20 = 1/2(2.4)s(6)
Multiply.
20 = 7.2s
Divide.
20/7.2 = s
2.78 = s
s = 2.78
what is this its to hard :|
Answer:
25
Step-by-step explanation:
We take both medians and subtract.
53-28=25
if X varies inversely as the cube root of y and X=1 when y=8. find y when X =3
Answer:
The work is straight forward once you know the formular
6) Kate wants to buy some daisies for $6.99, some potting soil for $3.98, and a ceramic pot for $7.95. She has $20.00. Which number sentence represents the amount of change Kate receives back?
By taking a subtraction, we will see that the change that Kate receives is $1.08
How to get the change?The change will be given by the difference between what Kate has, and the cost of all the items she buys.
She has $20.00, and the costs are: $6.99, $3.98, and $7.95.
Then the change will be:
C = $20.00 - $6.99 - $3.98 - $7.95 = $1.08
We conclude that the change is $1.08
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According to the rules of NCAA volleyball, there must be exactly 6 players on the court at all times and each player has a unique designated position on the court. How many different starting position configurations are possible for the 6 starting players of an 8-member volleyball team that follows this rule? Please answer quick.
Answer:
20160Step-by-step explanation:
This is a permutation of 6 out of 8
Use formula
P(n, r) = n!/(n-r)!Find the number of starting positions
P(8,)6 = 8!/(8 - 6)! = 8!/2! = 1*2*3*4*5*6*7*8/1*2 = 20160
The point-slope form of the equation of the line that passes through (-5, -1) and (10,-7) is y+7= -5/2(x-10)What
is the standard form of the equation for this line ?
One way we can organize a linear equation is in standard form:
[tex]Ax+By=C[/tex]
A, B and C are typically integersAnother way we can organize a linear equation is in point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
m is the slope[tex](x_1,y_1)[/tex] is a point that falls on the lineSolving the QuestionWe're given:
Line passes through (-5,-1) and (10,-7)Point-slope form is [tex]y+7=-\dfrac{5}{2}(x-10)[/tex]We only need the point-slope form equation to find the stand form of the equation for this line. All we have to do is rearrange the numbers to get them in the right places.
[tex]y+7=-\dfrac{5}{2}(x-10)[/tex]
⇒ First, multiply both sides by 2 to get rid of the fraction:
[tex]2y+14=-5(x-10)[/tex]
⇒ Now, open up the parentheses:
[tex]2y+14=-5x+50[/tex]
⇒ Move -5x to the other side:
[tex]5x+2y+14=50[/tex]
⇒ Move 14 to the other side:
[tex]5x+2y=50-14[/tex]
⇒ Combine like terms:
[tex]5x+2y=36[/tex]
Answer[tex]5x+2y=36[/tex]
solve
-2(x + 2)(x - 1)
Answer:
-2x^2 -2x + 4
Step-by-step explanation:
Distributive prop.
(-2x-4)(x-1)
-2x^2 + 2x - 4x + 4
-2x^2 -2x + 4
What is the square root of a number if it is in ratio form
The square root of 25 is 5. It is the positive solution of the equation x2 = 25. The number 25 is a perfect square.
...
Square Root of 25 in radical form: √25.
Really need help anybody!?!
Answer:
it's got to be 3........
Is 10, 20, 40, 80... an arithmetic sequence?
Answer:
No.
Step-by-step explanation:
A arithmetic sequence is a sequence of numbers that go up by the same value each time. We can clearly see that this set of numbers does not go up by the same value each time, therefore ruling it out as an arithmetic sequence. This sequence is a geometric sequence in case you're wondering.
Evaluate the expression for the given values.
(a) The expression 5p − 7d evaluated for p = 8 and d = 1/7
(b) The expression 5p − 7d evaluated for p = 3 and d = −6
(a) The expression 5p−7d evaluated for p=8 and d= 1/7 is______ .
Part 2 Of Question
b) The expression 5p − 7d evaluated for p = 3 and d = −6 is ______
Answer:
a is 39
b is 57
Step-by-step explanation:
you were given two different expressions to substitute.
the first one is p = 8 and d = 1/7
so we substitute into 5p - 7d
that is 5(8) - 7(1/7)
we get 40 - 1
which if we go ahead to evaluate we get 39
The second one p = 3 and d = -6
so we get 5(3) - 7(-6)
we get 15 - (-42)
if we go ahead to evaluate we get 15 + 42
two negative meeting each other gives you positive.
then it going too be 57
A standard deck of cards has 13 cards (2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king, ace) in each
of 4 suits (hearts, clubs, diamonds, spades). The hearts and diamonds cards are red. The
clubs and spades cards are black. You choose a card from a standard deck of cards at
random. What is the probability that you do not choose a club?
The probability that you do not choose a club is
Answer:
3/4
Step-by-step explanation:
Prob to pick a club is 13/52
Prob not to pick a club is 1 - 13/52
1 - 13/52 = 3/4
The prism below is made of cubes which measure 1/2 of an inch on one side. What is the volume?
Note: Figure is not drawn to scale.
OA. 15/2 cubic in
OB. 6 cubic in
OC. 30 cubic in
OD. 60 cubic in
the answer is B. 6 cubic in
Can yall help me with this pls
Help! This one step for solving standard deviation I don't understand...
When I got it wrong it tells me what to do but I don't get it? (2nd image)
x = 10
hope it helps...!!!
I need help it's due tomorrow!!!!
Answer:
56
Step-by-step explanation:
All You Need To Do Is Count intill You Reach That Point
solve for x ~
[tex]x {}^{2} - 16x = 0[/tex]
thankyou ~
Step-by-step explanation:
Mark me brainliest please[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Here we go ~
[tex]\qquad \tt \dashrightarrow \: {x}^{2} - 16x = 0[/tex]
[tex]\qquad \tt \dashrightarrow \: x(x - 16) = 0[/tex]
Now, there are two possibilities ~
[tex]\qquad \tt \dashrightarrow \:x = 0[/tex]
or
[tex]\qquad \tt \dashrightarrow \:x - 16 = 0[/tex]
[tex]\qquad \tt \dashrightarrow \:x = 16[/tex]
50 points each question. Please help. How do I solve?
[tex]~~~~~7e^{xy} +2x^2 -4y^2 =13\\\\\\\implies \dfrac{d}{dx}\left(7e^{xy} +2x^2 -4y^2\right) =\dfrac d{dx} (13)\\\\\\\implies 7\left[e^{xy} \dfrac{d}{dx} ( xy)\right] +2 \cdot 2x -4\cdot 2y \dfrac{dy}{dx} = 0\\\\\\\implies 7e^{xy} \left( x \dfrac{dy}{dx} +y\right) +4x -8y \dfrac{dy}{dx} =0\\\\\\\implies 7xe^{xy}\dfrac{dy}{dx} + 7ye^{xy} +4x -8y\dfrac{dy}{dx} = 0\\\\\\\implies \left(7xe^{xy} -8y \right) \dfrac{dy}{dx}=-7ye^{xy} -4x\\\\\\[/tex]
[tex]\implies \dfrac{dy}{dx} = \dfrac{-7ye^{xy} -4x}{7xe^{xy} -8y }[/tex]
Change the following fraction to a mixed number with the fraction part reduced to lowest terms. 84/42
Answer:
2
Step-by-step explanation:
since you have 84/42, and you are supposed to convert the improper fraction to a mixed number, the easiest place to start is to divide the two numbers and find the remainder. In this case, however, there is no remainder, as 84 divided by 42 is exactly 2. Therefore, the most simplified fraction would be 2 (although it does not look like a fraction the most simplified form of the fraction is 2/1 --> which is just 2). Hope this helps!
2. The value of C when y= 2x+C is tangent to the parabola y²=8x is: (a)-1 (b) 1 (c) 2 (d)-2
Answer:
B. The value of C is 1
Step-by-step explanation:
Given:
[tex]\displaystyle \large{y=2x+C}\\\displaystyle \large{y^2=8x}[/tex]
y = 2x + C is a tangent to parabola y² = 8xTo find:
value of CA line being a tangent to curve means both equations are equal but there has to be only one interception between both graphs.
Therefore, substitute y = 2x+C in y² = 8x:
[tex]\displaystyle \large{(2x+C)^2 =8x}[/tex]
Expand the expression (2x+C)² using perfect square:
[tex]\displaystyle \large{4x^2+4xC+C^2=8x}[/tex]
Simplify the equation:
[tex]\displaystyle \large{4x^2+4xC-8x+C^2=0}\\\displaystyle \large{4x^2+(4C-8)x+C^2=0}[/tex]
The discriminant says:
If b²-4ac > 0 then there are two real rootsIf b²-4ac = 0 then there is only one real rootIf b²-4ac < 0 then the are no real rootsFor this, we choose b²-4ac = 0 since tangents only have one intersection.
[tex]\displaystyle \large{b^2-4ac = (4C-8)^2-4(4)C^2 = 0}\\\displaystyle \large{16C^2-64C+64-16C^2=0}\\\displaystyle \large{-64C+64=0}[/tex]
Solve the equation for C:
[tex]\displaystyle \large{-64C=-64}\\\displaystyle \large{C=1}[/tex]
Therefore, the value of C is 1
Use log 2=a, log 3=b to evaluate log 216
Answer:
answer = 3(a +b)
Step-by-step explanation:
[tex] log(2) = a \: log(3) = b \: \: \\ log(216) = log(2 \times 2 \times 2 \times 3 \times 3 \times 3) \\ = log( {2}^{3} \times {3}^{3} ) \\ = log(2^{3} ) + log( {3}^{3} ) \\ = 3 log(2) + 3 log(3) \\ = 3(a) + 3(b) \\ = 3(a + b) \\ \\ log(216) = 3(a + b)[/tex]
[-32] <,>,= [15] what is the answer
Answer:
-32 < 15
Step-by-step explanation:
Whenever in the negatives, it's always less than zero. Because 15 is positive, it would be greater than -32.
A rectangular tabletop will be made of maple
wood that weighs 43 pounds per cubic foot. The
tabletop will have a length of eight feet, a width
of three feet, and a thickness of one inch.
Determine and state the weight of the tabletop,
in pounds.
A rectangular tabletop will be made of maple wood that weighs 43 pounds per cubic foot. The weight of the tabletop, in pounds, is 1032.
What is the volume of the rectangular tabletop?The volume of the rectangular tabletop is the product of the length, breadth, and height of the given tabletop.
Volume of rectangular tabletop= (length x width x height)
The tabletop will have a length of eight feet, a width of three feet, and a thickness of one inch.
Volume of rectangular tabletop= (length x width x height)
= [tex]8 \times 3 \times 1\\\\24[/tex]
A rectangular tabletop will be made of maple wood that weighs 43 pounds per cubic foot.
The weight of the tabletop, in pounds = 43 x 24
= 1032 pounds
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Find the value of X.
Answer:
Step-by-step explanation:
Vertically opposite angles are congruent.
-2x - 6 = 40
Add 6 to both sides
-2x = 40 + 6
-2x = 46
Divde both sides by (-2)
x = 46/(-2)
x = -23
Here are the test scores for 15 students in Mr. M's class.
96, 85, 59, 63, 76, 68, 94, 97, 89, 100, 93, 96, 72, 46, 78
What is the percentage of these test scores that are less than 90?
Answer:
60%
Step-by-step explanation:
If you look through the data, it is clear that 46, 59, 63, 68, 72, 76, 78, 85, and 89 are all less than 90. There are 9 elements total that are less than 90.
For percentages, you take the number you have and divide by the total. Since we know that there are 15 students, we can do 9 / 15. This gives us 0.6 which is 60%