Answers
Answer:
t = 4 s
Step-by-step explanation:
Given function:
[tex]h(t)=-16t^2+48t+64[/tex]
where:
h = height of the ball (in feet)t = time (in seconds)When the ball hits the ground, its height will be 0 ft.
Therefore, set the function to zero and solve for t:
[tex]\begin{aligned}h(t) &=0\\ \implies -16t^2+48t+64 & =0\\ -16(t^2-3t-4)& =0\\ t^2-3t-4 &=0\\ t^2+t-4t-4&=0\\ t(t+1)-4(t+1)&=0\\(t-4)(t+1)&=0\\ \implies t&=4, -1\end{aligned}[/tex]
As time is positive, t = 4 s (only).
Given
[tex]h = - 16 {t}^{2} + 48t + 64[/tex]
Where:- h= Height of ball (given in feet[ft]) and,
t= time (in seconds [s])
To find:-Time = (t)
SolutionWe know,
[tex] \text{When the ball hits the ground its height will be 0}[/tex]
[tex] \therefore h(t) = 0[/tex]
[tex] \implies - 16 t^{2} + 48t + 64 = 0 \\ \\ \fbox{taking - 16 as common multiple} \\ \\ \implies - 16(t {}^{2} - 3t - 4) = 0 \\ \\ \implies t {}^{2} - 3t - 4 = 0 \\ \\ \fbox {factorising the \: equation} \\ \\ \implies t {}^{2} - t - 4t - 4 = 0 \\ \\ \implies t(t + 1) - 4(t + 1) = 0 \\ \\ \implies(t - 4)(t + 1) = 0[/tex]
[tex] \tt{Either} \\ t - 4 = 0 \\ t = \red{ 4 } \\ \\ \tt{Or} \\ t + 1 = 0 \\ t = \red{ - 1}[/tex]
We know, Time cannot be negative.
So, Time (t) = 4 seconds
Related Questions
find the measures of
Find the measure of
Find the measure of
Find the measure of
Answers
Answer:
15.
If we look at angle BOD, that would form a right angle (90°), given that one part of that whole angle is 30°, the other would be;
30° + x = 90°
-30 -30
x = 60°, therefore ∠BOC = 60°.
If we take a look at angle EOC, we can see that that angle is a straight angle (180°), we can also see that a right angle (90°) is a part of that angle alongside the angle we just previously found (60°). So all of those angles plus the unknown angle (AOE) which we will consider 'x' summed up would result in 180 degrees.
Now we set up the equation;
90° + 60° + x = 180°
150 + x = 180
-150 -150
x = 30°, therefore ∠AOE = 30°.
16.
The sum of the interior angles in a triangle will always equal 180°. (We can also confirm this using the formula (n - 2) x 180.)
Given two of the angles, we must add them and the unknown angle(D) which we will consider 'x' to make it result in 180°.
Now we set up the equation;
55° + 18° + x = 180°
73 + x = 180
-73 -73
x = 107°, therefore ∠EDF = 107°.
17.
To find angle P, we must first find the supplement of 34° because 34° and the angle beside forms a straight angle (180°).
Set up an equation;
34 + x = 180
-34 -34
x = 146°, now that we've found the supplement, we add this supplement with the other given angle (23°) because all three angles (unknown angle which we will consider x + 23 + 146) will equal 180°(sum of interior angles of triangle).
146° + 23° + x = 180°
169 + x = 180
-169 -169
x = 11°, therefore ∠QPR = 11°.
18.
Seeing that the bigger triangle has a 90° angle (indicated with a square), and two other equal angles(indicated with the two lines on both legs of the big triangle), we solve for those two missing equal angles in the bigger triangle which we will then use to solve for the smaller triangle's angle.
2x + 90° = 180°
-90 -90
2x = 90
/2 /2
x = 45°, so now we know the two angles in the bigger triangle excluding the right angle.
One of those equal angles is vertical to the smaller triangle, and vertical angles are congruent.
Hence, the angle vertical to the bigger triangle in the smaller triangle will be 45°.
Now we solve for ∠CDE.
Add the two angles and the missing angle to equal 180°.
Set up the equation;
86° + 45° + x = 180°
131 + x = 180
-131 -131
x = 49°, so ∠CDE = 49°.
The first three steps in writing f(x) = 40x 5x2 in vertex form are shown. write the function in standard form. f(x) = 5x2 40x factor a out of the first two terms. f(x) = 5(x2 8x) form a perfect square trinomial. (eight-halves) squared = 16 f(x) = 5(x2 8x 16) – 5(16) what is the function written in vertex form?
Answers
The function f(x) = 5x² + 40x is a parabola. Then the vertex of the parabola will be at (–4, –80).
What is the parabola?It is the locus of a point that moves so that it is always the same distance from a non-movable point and a given line. The non-movable point is called focus and the non-movable line is called the directrix.
The function f(x) = 5x² + 40x
Then add and subtract 80, then we have
f(x) = 5x² + 40x + 80 – 80
f(x) = 5(x² + 8x + 16) – 80
f(x) = 5(x + 4)² – 80
The vertex of the parabola will be at (–4, –80).
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Which phrase describes the linear relationship between the values of x and y shown in the table? A. y is 4 more than x B. y is 6 more than x C. y is 3 times x D. x is 3 times y
Answers
The linear relationship on the table has a constant slope
The linear relationship is (c) y is 3 times x
How to determine the linear relationship?The table of values is given as:
x l y
3 l 9
0 l 0
For both x and y values on the table, we have:
y = 3x
i.e.
3 * 3 = 9 and 3 * 0 = 0
This means that the linear relationship is (c) y is 3 times x
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Mr. Blue's first year salary is $30,000 and it doubles each year. What is the explicit
rule for the sequence in simplified form? what is the recursive rule?
Answers
The explicit rule for the sequence in simplified form is y = 30000(2)^n
How to write the exponential functionThe standard exponential equation is expressed as:
y = ab^n
Given the following parameters
a is the initial values = 30,000
If the amount doubles each year then b = 2
Substitute the parameters
y = 30000(2)^n
Hence the explicit rule for the sequence in simplified form is y = 30000(2)^n
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Answer: Explicit Rule: a_n=30,000 • 2^n-1 Recursive Rule: a_n = 2a_n-1; a_1 =30,000
Step-by-step explanation: the Explicit Rule for a geometric sequence is a_n = r • a_n -1 and the Recursive Rule is a_n = a_1 • a_n-1
a_1 is the first term and r is the common ration. In this case, the first term is 30,000 as stated in the question and the common ration is 2 since it doubles each time. So substitute those numbers into the formulas and that’s what you’ll get! Hope this helps! God bless you all!!
The linear function f(x)=ax+b is graphed in the coordinate plane. Two equal intervals are compared,[-3,3] and [9,15]. What conclusion can be drawn from each interval of 6?
Answers
The linear function f(x) = ax + b has a constant rate
The conclusion from the each interval is that the function values changes at a constant rate
How to determine the conclusion?
The linear function is given as:
f(x) = ax + b
The interval is given as:
[-3,3] and [9,15]
Since the function is a linear function, the conclusion from the each interval is that the function values changes at a constant rate
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if the price of small box is $20 and the price of large box is $45. what is the greatest amount of money he received when he sells all the boxes he has made? For this amount of money how many boxes of each size did he make
Answers
Answer:
in order to know the money that he receive first the type and amount of box must be described unless the question may not have answer.
Which two sets of events are most likely independent?
O A. Event A: A student makes the drama team.
Event B. The student likes macaroni and cheese.
B. Event A: A student gets enough sleep.
Event B. The student is alert in class.
C. Event A: A car is blue.
Event B. The car lasts over 20 years.
D. Event A: A woman buys cat toys.
Event B: The woman has a cat.
Answers
Answer:
A - Event A: A student makes the drama team. / Event B. The student likes macaroni and cheese.C - Event A: A car is blue. / Event B. The car lasts over 20 years.True or False
1. A solution to 8 = -x + 10 is 2
Answers
Answer:
TrueStep-by-step explanation:
So, Lets find out if the solution is true or not, So first let us find the value of x.
⇒ 8 = -x + 10
We can rewrite the equation as,
⇒ -x + 10 = 8
Subtracting 10 from both sides we get :
⇒ -x + 10 – 10 = 8 – 10
⇒ -x = -2
Multiplying both sides by (-1) :
⇒ -1(-x) = -1(-2)
⇒ x = 2
Therefore,
The statement "A solution to 8 = -x + 10 is 2" is trueHey ! there
Answer:
TrueStep-by-step explanation:
In this question we are given with an equation that is 8 = -x + 10 and we have also given its solution that is 2 .And We are asked to tell whether the solution of given equation is true or false .
For finding that we must have to solve the equation .
Solution : -
[tex]\longrightarrow \qquad \: 8 = -x + 10[/tex]
Step 1 : Flipping the equation so that there's ease in solving :
[tex] \longrightarrow \qquad \: - x + 10 = 8[/tex]
Step 2 : Subtracting with 10 on both sides :
[tex] \longrightarrow \qquad \: - x + \cancel{10 }- \cancel{ 10} =8 - 10[/tex]
On further calculations , We get :
[tex] \longrightarrow \qquad \: - x = - 2[/tex]
Step 3 : Multiplying with -1 on both sides :
[tex] \longrightarrow \qquad \: - x \times - 1 = - 2 \times - 1[/tex]
We get :
[tex] \longrightarrow \qquad \: \blue{\underline{\boxed{ \frak{x = 2}}}}[/tex]
Therefore , it's TRUE that 2 is the solution of given equation .Alternative Solution : -
There's another easy way to check whether 2 is solution of given equation or not . This is done by substituting value of x that is 2 in given equation that is 8 = -x + 10 . So substituting value of x ( solution ) in given equation :
8 = - ( 2 ) + 108 = -2 + 108 = 8L.H.S = R.H.SAs we can see that left side is equal to right side .
Therefore , it's TRUE that 2 is the solution of given equation .#Keep Learning4. A plumber charges $65 per hour to fix a leak. What is an equation that relates the total cost of a leak repair c to the number of hours, h, it takes the
plumber to fix the leak? Show work
Answers
Answer:
c = 65h.
Step-by-step explanation:
cost = rate per hour * hours worked:
c = 65 * h .
What is the midpoint of XY if X is located at (-12, 8) and Y is located at (10, 17)
A. (-2. 25)
B. (-1, 12 5)
C. (-2, 11.5)
D. (32, 26)
E. None of the above
Answers
Answer: B
Step-by-step explanation:
Esmeralda has a magnet in the shape of a square. Each side of the magnet is 3 inches long. What is the perimeter of her magnet?
Answers
Answer:
12 inches
Step-by-step explanation:
This is a square of sidee length 3 inches. As there are four (equal) sides, the perimeter of this square magnet is 4(3 inches), or 12 inches.
i do not know this answer
Answers
The value of the provided function 14g², at the point g equal to negative 1 is 14, when this value is put in the function.
How to evaluate the value of a function at a point?To find the value of a function at a particular point, the value of the point has to be put on the place of a variable in the function and simplify the equation.
To evaluate the value of a function at a particular point, follow the steps given below.
Write down the function.Put the value of point in place of variable. Simplify the equation to find the value.The function given in the problem is,
[tex]f(g)=14g^2[/tex]
Here, the value of the function has to evaluate at g=-1. Put the value of g in the above function as,
[tex]f(-1)=14(-1)^2\\[/tex]
The square of -1 is 1. Thus,
[tex]f(-1)=14\times1\\f(-1)=14[/tex]
Hence, the value of the provided function 14g², at the point g equal to negative 1 is 14, when this value is put in the function.
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it’s urgent please help
Answers
Answer:
x = 5.4
Step-by-step explanation:
The marked sides are the hypotenuse and the side adjacent to the marked angle. That suggests the appropriate trig function is the cosine:
Cos = Adjacent/Hypotenuse
cos(19°) = 5.1/x
x = 5.1/cos(19°) . . . . . multiply by x/cos(19°)
x ≈ 5.4
What is the y-intercept of the line shown? A. 2 B. -2 C. 4 D. -4
Answers
The y-intercept will be where it crosses the y-axis. The y-axis is the line that goes up and down also know a vertically.
what is f(x)25x2+9x+10
Answers
Pls help me !!
a sector of a circle has a central angle measure of 90°, and an area of 7 square inches. what is the area of the entire circle?
area of the circle = __ square inches
Answers
Explanation:
90° is 90/360 = 1/4 of a full 360° rotation. Meaning that if the central angle of the pizza slice is 90°, then we have four equal slices.
One slice is 7 square inches, so all four slices combine to 7*4 = 28 square inches
The blades of a windmill turn on an axis that is 35 feet above the ground. the blades are 10 feet long and complete two rotations every minute. which of the following equations can be used to model h, the height in feet of the end of one blade, as a function of time, t, in seconds? assume that the blade is pointing to the right, parallel to the ground at t = 0 seconds, and that the windmill turns counterclockwise at a constant rate. h = negative 10 sine (startfraction pi over 15 endfraction t) 35 h = negative 10 sine (pi t) 35 h = 10 sine (startfraction pi over 15 endfraction t) 35 h = 10 sine (pi t) 35
Answers
Answer:
it is c
Step-by-step explanation:
:)
The sine equation is [tex]\rm y = 10sin(\frac{\pi}{15} t)+35[/tex] an option (c) is correct.
It is given that the blades of a windmill turn on an axis that is 35 feet above the ground. the blades are 10 feet long and complete two rotations every minute.
It is required to model the sine equation.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
We know the standard equation for the sine equation:
[tex]\rm y = Asin(wx)+h[/tex]
Where [tex]\rm T=\frac{2\pi}{w}[/tex]
[tex]\rm w = \frac{2\pi}{30}[/tex] ( In one minute, they complete two rotations.)
[tex]\rm w = \frac{\pi}{15}[/tex] ( T = 30)
At time t=0, the blade is horizontal. Hence, at t = 0, h = 35
And A = 10
Put all the values in the sine equation:
[tex]\rm y = 10sin(\frac{\pi}{15} t)+35[/tex]
Thus, the sine equation is [tex]\rm y = 10sin(\frac{\pi}{15} t)+35[/tex] an option (c) is correct.
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find the equation of the line drawn in the coordinate system below
Answers
Answer:
y=-2/1+4
or y=-2+4
Step-by-step explanation:
to find the slope, you count from one point of intersection to the next and the way it works is y/x so the line from one point to the next goes down 2 (making it negative also) and over 1, so -2/1 is your slope, and for the b part.. its just where the line intersects on the y axis (the line that goes up and down) so it would be 4
Can someone please help me on this
Answers
Answer:
1. Colored men
2. Not really sure, but maybe on a wall ??
3. To notify colored men what the president proclaimed
Step-by-step explanation:
c = y + a solve for y
Answers
Answer:
[tex]\boxed{\sf{y=c-a}}[/tex]Step-by-step explanation:
To solve for y, isolate it on one side of the equation.
c=y+aFirst, switch sides.
c=y+a
y+a=c
Then, you subtract by a from both sides.
y+a-a=c-a
Solve.
[tex]\Longrightarrow:\boxed{\sf{y=c-a}}[/tex]
Therefore, the correct answer is y=c-a.I hope this helps you! Let me know if my answer is wrong or not.
What method would you choose to solve the equation 2x 2squared – 7 = 9? Explain why you chose this method.
Answers
Answer:
Step-by-step explanation:
(2x2squared-7)2squared=9 2squared
4x4squared-28x2squared+49=81
4x4squared-28x2squared=81-49
4x4squared-28x2squared=32
solve this 6(x+4)+1=x+5
Answers
6x-x+25-5=0
5x+20=0
5x=-20
x= -20/5= -4
[tex] \sf :\implies \quad {\pmb{x = - 4}}[/tex]
Solution:Let's solve the given equation step by step ;
[tex] \sf :\implies \quad 6(x + 4) + 1 = x + 5[/tex]
The first step is to distribute the equation:
[tex] \sf :\implies \quad (6 \times x ) + (6 \times 4) + 1 = x + 5[/tex]
[tex] \sf :\implies \quad 6x + 24 + 1 = x + 5[/tex]
[tex] \sf :\implies \quad 6x + 25 = x + 5[/tex]
Second step is to combine the like terms:
[tex] \sf :\implies \quad 6x + 25 - x = 5[/tex]
[tex] \sf :\implies \quad( 6x - x) + 25 = 5[/tex]
[tex] \sf :\implies \quad 5x + 25 = 5[/tex]
Now, subtract 25 from both sides :
[tex] \sf :\implies \quad 5x + 25 - 25 = 5 - 25[/tex]
[tex] \sf :\implies \quad 5x = - 20[/tex]
Divide both sides by 5:
[tex] \sf :\implies \quad \dfrac{5x}{5} = - \dfrac{20}{5} [/tex]
[tex] \sf :\implies \quad \boxed{ \pmb{\sf x = - 4}}[/tex]
Hence, your answer is ; x = -4
Which correctly shows this equation
solved for w?
Answers
The equation solved for w is:
w = A/l
The correct option is A.
What is an equation?A pair of algebraic equations with the equal symbol (=) in the center and the same value are referred to as an equation.
Starting with the equation:
A/l = lw/l
We can simplify it by multiplying both sides by l:
A = lw
To solve for w, we need to isolate it on one side of the equation.
We can do this by dividing both sides by l:
A/l = w
Therefore, the required equation is A/l = w.
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find the volume
6ft
4ft
3ft
(i know it’s not 72)
Answers
Answer:
[tex] \fbox{Volume \: of \: pyramid \: = 24 ft³}[/tex]
Step-by-step explanation:
Given:
shape of object = Pyramidal
length of base l= 4ft
width of base w = 3ft
height of pyramid h = 6 ft
To find:
volume of pyramid = ?
Solution:
[tex]Volume \: of \: pyramid= \frac{l \times w \times h}{3} \\ Volume \: of \: pyramid= \frac{6 \times 4 \times 3}{3} \\ Volume \: of \: pyramid= \frac{24 \times \not3}{ \not3} \\ Volume \: of \: pyramid= 24 \: {ft}^{3} [/tex]
[tex] \fbox{Volume \: of \: pyramid \: = 24 ft³}[/tex]
Thanks for joining brainly community!A wheel with the 31 in. diameter has 651 rotations. Reflect on how different wheel sizes would change your answer. What would happen to the number of rotations if the circumference of the wheels were increased by 20%? For the wheel with 31 in. diameter, multiply its circumference 97.4 in. by 1.2 =________.
Answers
The number of rotations is reduced to 542.501 when the diameter of wheel is increased by 20 %.
How to compare rotations between two wheels of different diameter
The quantity of rotations (n), no unit, done by a wheel is equal by total traveled distance (s), in inches, divided by its circumference (p), in inches:
[tex]n = \frac{s}{p}[/tex]
[tex]n = \frac{s}{\pi\cdot D}[/tex] (1)
Where D is the diameter of the wheel, in inches.
If we know that n = 651 and D = 31 in, then the travelled distance is:
s = (651) · π · (31 in) (2)
s ≈ 63400.481 in
The travelled distance of the 31-in diameter wheel with 651 rotations is approximately 63400.481 inches.
By (2) we understand that the travelled distance is directly proportional to the diameter. Hence, if the diameter of the wheel is increased by 20 %, then we must multiply the diameter by 1.2 and divide the travelled distance by this result:
s ≈ 1.2 · π · (31 in)
s ≈ 116.867 in
[tex]n = \frac{63400.481\,in}{116.867\,in}[/tex]
[tex]n = 542.501[/tex]
The number of rotations is reduced to 542.501 when the diameter of wheel is increased by 20 %. [tex]\blacksquare[/tex]
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What is the area of this triangle?
1375 ft
1500ft
3300ft
4500ft
Answers
Answer:
probably 20 man think about it
Step-by-step explanation:
1/5c= 2 (whole number) 1/2
what is it
you have to divide them
ill also give the smartest
PLEASE
Answers
The value of c in the equation, 1/5c = 2 1/2 when divided is 12 1/2.
What are fractions?Fractions are numbers that are non integers. They are ususally made up of numerators and denominators. The numerator is the number above and the denominator is the number below.
What is the value of c?In order to determine the value of c, divide 2 1/2 by 1/5
2 1/2 ÷ 1/5
Convert the mixed fraction to an improper fraction
5/2 x 5 = 25/2 = 12 1/2
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A machine is supposed to fill bags with an average of 19.2 ounces of candy. The manager of the candy factory wants to be sure that the machine does not consistently underfill or overfill the bags . So the manager plans to conduct a significance test at the alpha = 0.10 significance level of H_{0} / mu = 19.2; H a : mu ne19.2 where mu = the true mean amount of candy (in ounces) that the machine put in all bags filled that day. The manager takes a random sample of 75 bags of candy produced that day and weighs each bag. The sample mean weight for the bags of candy was 19.28 ounces and the sample standard deviation was 0.81 ounce.
Find the P-value.
Answers
Answer: c. Step-by-step explanation:
A betta fish tank is in the shape of a cube. The volume of the fish tank is 216
cubic inches. What is the edge length, in inches, of the fish tank?
6)
Type the number in the box.
inches
Answers
To find this answer, we need to understand how to get the Volume.
We get the volume by the formula: L x W x H
L = Length
W = Width
H = Height
So, we can see that there are 3 units required to know for getting the volume, if that's true, then, to do the inverse operation of finding the volume. That can be done by using thie formula:
[tex]V=a^3[/tex]
a= edge
Solving for a
a=V⅓=216⅓=6
So hence, each of the Cube shaped Fish Tank is 6in³now, let's look at how to find whether our answer is right or wrong
6x6=36
36x6=216
So hence, our answer is right!
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The length of a betta fish tank that has a shape of a cube and volume of 216 cubic inches is 6 inches.
Volume of a cube
A cube has all its sides equal to each other. Therefore,
volume of cube = L³
where
L = lengthTherefore,
L = >
volume = 216 cubic inches
volume of cube = L³
216 = L³
cube root both sides
∛216 = ∛L³
L = ∛216
L = 6 inches
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A $70,000 mortgage is $629.81 per month. What was the percent and for how many years?
9%, 20 years
9%, 30 years
7%, 20 years
9%, 25 years
Answers
The interest percent and the maturity period of the $70,000 mortgage with a monthly payment of $629.81 are A. 9%, 20 years.
How can the monthly payments be calculated?The monthly payments can be computed using the present value annuity table or formula.
However, to compute the percent interest and the maturity period, we can use an online finance calculator as below by inputting the calculated monthly payments.
Thus, at an interest rate of 9% for 20 years and a monthly payment of $629.81, the present value of $70,000 will be equal.
Data and Calculations;N (# of periods) = 240 (20 years x 12)
I/Y (Interest per year) = 9%
PMT (Periodic Payment) = $629.81
FV (Future Value) = $0
Results:
PV = $70,000.20
Sum of all periodic payments = $151,154.40 ($629.81 x 240)
Total Interest $81,154.20
The interest percent and the maturity period of the $70,000 mortgage with a monthly payment of $629.81 are A. 9%, 20 years.
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