The height of the ball according to the function h(t) is 16 feet after 1.92 seconds and after 0.46 seconds.
A function is defined as a expression containing one or more variables.
Technically speaking, a function is a means of linking a set of inputs to a set of outputs.
The height of the ball at any time t is given by the function:
[tex]h(t)=-16t^2+38t+2[/tex]
Now the required height of the ball(in feet) is 16 feet. We have to find the value of t for which h(t)=16.
Let us substitute the values:
[tex]\implies h(t)=-16t^2+38t+2\\\implies 16=-16t^2+38t+2\\\implies 16t^2-38t+14=0\\\implies 8t^2-19t+7=0[/tex]
This is in the form of a quadratic equation in t.
Solving by using the quadratic formula:
We know that for a quadratic equation [tex]ax^2+bx+c=0[/tex]
[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Therefore for the above quadratic equation:
[tex]t=\frac{-(-19)\pm \sqrt{(-19)^2-4(8)(7)}}{2(8)}\\t=\frac{19+\sqrt{137}}{8},t=\frac{19-\sqrt{137}}{8}\\t=1.919...,t=0.455...[/tex]
Therefore the ball reaches the height of 16 feet at times 1.92 seconds and at 0.46 seconds.
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In a study conducted by a human resource management organization, human resource professionals were surveyed. Of those surveyed, % said that their companies conduct criminal background checks on all job applicants. Complete parts (a) through (d).
What is the exact value that is 41% of 379 survey subjects?
(Type an integer or a decimal. Do not round.)
The exact value is ____
Using proportions, it is found that the exact value of 41% of 379 is of 155.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
The proportion of 41% of 379 is given as follows:
0.41 x 379 = 155.39.
Since 0.39 < 0.5, the exact value is rounded to 155.
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What numbers are a distance of 34 unit from 18 on a number line?
Select the locations on the number line to plot the points.
Answer:
[tex]\dfrac{7}{8} \textsf{ and } -\dfrac{5}{8}[/tex]
Step-by-step explanation:
To find numbers that are [tex]\dfrac{3}{4}[/tex] units distance from [tex]\displaystyle \dfrac{1}{8}[/tex] , add and subtract [tex]\dfrac{3}{4}[/tex] to and from [tex]\displaystyle \dfrac{1}{8}[/tex]
One of the points is at [tex]\displaystyle \dfrac{1}{8} + \dfrac{3}{4}[/tex] units away and the other at [tex]\displaystyle \dfrac{1}{8} - \dfrac{3}{4}[/tex] units away
Compute [tex]\displaystyle \dfrac{1}{8} + \dfrac{3}{4} :[/tex]What is the solution to this inequality?
X-8>-3
OA. x < -11
OB. x>-11
OC. x<5
OD. x>5
Answer:
OD
Step-by-step explanation:
move the -8 to the right, and change its sign
x > 5
If anyone can help me to solve this!!
Answer:
[tex]\textsf{1.} \quad x=-6, \quad x=6[/tex]
[tex]\textsf{2.} \quad x=-5, \quad x=2[/tex]
[tex]\textsf{3.} \quad x=-3, \quad x=7[/tex]
[tex]\textsf{4.} \quad x=\dfrac{-5 +\sqrt{57} }{4}, \quad x=\dfrac{-5 -\sqrt{57} }{4}[/tex]
[tex]\textsf{5.} \quad x=\dfrac{7+ \sqrt{309} }{10}, \quad x=\dfrac{7-\sqrt{309} }{10}[/tex]
Step-by-step explanation:
Question 1Method: Extracting the Square Root
[tex]\begin{aligned}& \textsf{Given}: & x^2 & = 36\\& \textsf{Square root both sides}: & \sqrt{x^2} & = \sqrt{36}\\& \textsf{Simplify}: & x & = \pm 6\\&\textsf{Solution}:&x& = -6, 6\end{aligned}[/tex]
Question 2Method: Factoring
[tex]\begin{aligned}& \textsf{Given}: & x^2+3x-10 & = 0\\& \textsf{Split the middle term}: & x^2+5x-2x-10 & = 0\\& \textsf{Factor the first two and the last two terms}: & x(x+5)-2(x+5)&=0\\& \textsf{Factor out the common term $(x+5)$}: & (x-2)(x+5)&=0\\& \textsf{Apply the zero-product property}: & (x-2)=0 \implies x&=2\\ &&(x+5)=0 \implies x&=-5\\ & \textsf{Solution}: & x&=-5,2\end{aligned}[/tex]
Question 3Method: Factoring
[tex]\begin{aligned}& \textsf{Given}: & x^2-4x-21 & = 0\\& \textsf{Split the middle term}: & x^2-7x+3x-21 & = 0\\& \textsf{Factor the first two and the last two terms}: & x(x-7)+3(x-7)&=0\\& \textsf{Factor out the common term $(x-7)$}: & (x+3)(x-7)&=0\\& \textsf{Apply the zero-product property}: & (x+3)=0 \implies x&=-3\\&&(x-7)=0 \implies x&=7\\& \textsf{Solution}: & x & = -3, 7\end{aligned}[/tex]
Question 4Method: Quadratic Formula
[tex]\boxed{\begin{minipage}{4 cm}\begin{center}\underline{Quadratic Formula}\end{center}\\\\\begin{center}$x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$\end{center}\\\\\\\begin{center}when $ax^2+bx+c=0$\end{center}\end{minipage}}[/tex]
Given:
[tex]5x-4=-2x^2[/tex]
Rearrange into standard form by adding 2x² to both sides:
[tex]\implies 2x^2+5x-4=0[/tex]
Therefore:
[tex]a=2, \quad b=5, \quad c=-4[/tex]
Substitute the values into the quadratic formula and solve for x:
[tex]\implies x=\dfrac{-5 \pm \sqrt{5^2-4(2)(-4)} }{2(2)}[/tex]
[tex]\implies x=\dfrac{-5 \pm \sqrt{25+32} }{4}[/tex]
[tex]\implies x=\dfrac{-5 \pm \sqrt{57} }{4}[/tex]
Therefore, the solutions are:
[tex]x=\dfrac{-5 +\sqrt{57} }{4}, \quad x=\dfrac{-5 -\sqrt{57} }{4}[/tex]
Question 5Method: Quadratic Formula
[tex]\boxed{\begin{minipage}{4 cm}\begin{center}\underline{Quadratic Formula}\end{center}\\\\\begin{center}$x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$\end{center}\\\\\\\begin{center}when $ax^2+bx+c=0$\end{center}\end{minipage}}[/tex]
Given:
[tex]5x^2-7x-13=0[/tex]
Therefore:
[tex]a=5, \quad b=-7, \quad c=-13[/tex]
Substitute the values into the quadratic formula and solve for x:
[tex]\implies x=\dfrac{-(-7) \pm \sqrt{(-7)^2-4(5)(-13)} }{2(5)}[/tex]
[tex]\implies x=\dfrac{7 \pm \sqrt{49+260} }{10}[/tex]
[tex]\implies x=\dfrac{7 \pm \sqrt{309} }{10}[/tex]
Therefore, the solutions are:
[tex]x=\dfrac{7+ \sqrt{309} }{10}, \quad x=\dfrac{7-\sqrt{309} }{10}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: [/tex]
Find the critical points of [tex]f_1[/tex] and [tex]f_2[/tex].
By the fundamental theorem of calculus,
[tex]{f_1}'(x) = \displaystyle \prod_{j=1}^{21} (x-j)^j = (x-1) (x-2)^2 (x-3)^3 \cdots (x-21)^{21}[/tex]
and [tex]{f_1}'=0[/tex] for [tex]x\in\{1,2,3,\ldots,21\}[/tex]. The stationary points at odd values have odd multiplicity, while the even ones have even multiplicity. At the points of odd multiplicity, [tex]{f_1}'[/tex] passes through the [tex]x[/tex]-axis and the sign of [tex]{f_1}'[/tex] changes, while at the points of even multiplicity, [tex]{f_1}'[/tex] is tangent the to [tex]x[/tex]-axis. We also have
[tex]\displaystyle \lim_{x\to-\infty} {f_1}'(x) = (-1)^{1+3+5+\cdots+21} \infty = (-1)^{11^2} \infty = -\infty[/tex]
[tex]\displaystyle \lim_{x\to\infty} {f_1}'(x) = \infty[/tex]
so the plot of [tex]{f_1}'[/tex] looks more or less like the attached curve. (Not drawn to scale)
Wherever the sign of [tex]{f_1}'[/tex] changes from negative to positive, as it does in the case of [tex]x\in\{1,5,9,13,17,21\}[/tex], there is a local minimum, so [tex]m_1 = 6[/tex]. Similarly, wherever the sign changes from negative to positive, as it does when [tex]x\in\{3,7,11,15,19\}[/tex], there is a local maximum, so [tex]n_1 = 5[/tex].
Repeat for [tex]f_2[/tex].
[tex]{f_2}'(x) = 4900 (x-1)^{49} - 29400 (x-1)^{48} = 4900 (x-1)^{48} (x-7)[/tex]
has roots at [tex]x=1[/tex] and [tex]x=7[/tex], but only the latter is a critical point due to odd multiplicity. A rough sketch of the plot of [tex]{f_2}'[/tex] is also attached. The sign of [tex]{f_2}'[/tex] changes from negative to positive at [tex]x=7[/tex], so [tex]m_2 = 1[/tex] and [tex]n_2=0[/tex].
We conclude that
Q.9) [tex]2m_1+3n_1+m_1n_1 = \boxed{57}[/tex]
Q.10) [tex]6m_2+4n_2+8m_2n_2 = \boxed{6}[/tex]
The U.S. Census Bureau defines a household as all of the people who occupy a housing unit as their usual
place of residence. The number of households is not equal to the population because multiple people may
live in the same housing unit.
82.1% of Cincinnati households have a computer. If 111.804 households in Cincinnati have a computer, how
many households are there altogether in Cincinnati? Show your work. Round to the nearest whole number.
Answer: total household present are 136
Step-by-step explanation:
Given:
82.1% of Cincinnati households have a computer.
111.804 households in Cincinnati have a computer.
According to ratio and proportions we have:
let total number of houses be x;
then
(111.804/x)*100=percentage of Cincinnati households having a computer. [[tex]gain/total*100 =gain %[/tex]]
then
(111.804/x)*100=82.1
cross multiplying we have
x=(111.804*100)/82.1
x=136 households (Round to the nearest whole number.)
so total household present are 136
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group of 280 elementary school students and 40 adults are going on a field trip. They are planning to use two different types of buses to get to the destination. The first type of bus holds 50 people and the second type of bus holds 56 people.
Andre says that 3 of the first type of bus and 3 of the second type of bus will hold all of the students and adults going on the field trip.
Is Andre correct?
Answer:
yes!!! because the first 3 types of bus can hold 50 people and the other 3 types of bus can hold 56 people so the total will be 320 people
What is the greatest common factor of 18 12 16
The greatest common factor of 18 12 16 is the number 2.
Linear Equations: Mastery Test
Select the correct answer.
Which property of equality was used to solve this equation?
X-5=-14
X-5+5=14+5
X=-9b
A addition property of equality
B. subtraction property of equality
C. multiplication property of equality
D. division property of equality
The property of equality was used to solve this equation is addition property of equality
Addition property of equalityThe property states that the additive property of equality states that if we add or subtract the same number to both sides of an equation, the sides remain equal.
Given the expression
X-5=-14
Add 5 to both sides to have;
x-5 + 5 = -14 + 5
x = -14 + 4
x = -9
Hence the property of equality was used to solve this equation is addition property of equality
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A certain hybrid car can travel 1 9/11 times as far as a similar no hybrid car will on one gallon of gasoline . If the non hybrid car can travel 33 miles per gallon of gasoline, how far can the hybrid travel on 4/5 gallon of gasoline ?
On 4/5 gallon of gasoline, hybrid car will travel a distance of 48 miles.
How to solve Algebra Word Problems?Suppose, non hybrid car travel "x" distance in 1 gallon of gasoline
Then, hybrid will travel " 1 ⁹/₁₁ * x" distance in 1 gallon of gasoline
Given that, non hybrid car travel distance per gallon is; x = 33 miles per gallon
Then, hybrid car travel, 1 ⁹/₁₁ * x = 1 ⁹/₁₁ * x * 33 = 60 miles per gallon
On 1 gallon of gasoline hybrid car travel 60 miles
On 4/5 gallon of gasoline hybrid car will travel = 4/5 * 60 = 48 miles
On 4/5 gallon of gasoline, hybrid car will travel 48 miles of distance.
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Use the factor theorem to write a polynomial equation that has solutions of 2, -2, and 4. (Hint: Suppose the solutions of a quadratic equation are 3 and 5. This means that x = 3 or x = 5 which gives us x - 3 = 0 or x - 5 = 0. The expressions are the factors of the polynomial which means that the equation is (x - 3)(x - 5) = 0.)
The equation of the polynomial with the given roots of 2, -2, and 4 is x³ - 4x² - 4x + 16 = 0.
What is the polynomial equation that has solutions of 2, -2, and 4?Roots are the points where the graph intercepts with the x-axis ( y = 0 ).
Given the roots in the question;
x = 2, -2, 3
Now, the root of x = 2 was found solving for x when x - (2) = y but y = 0.
Hence, (x - 2) is a factor.
Next, the root of x = -2 was found solving for x when x - (-2) = y but y = 0.
Hence, (x + 2) is a factor
And the root of x = 4 was found solving for x when x - (4) = y but y = 0.
Hence, (x + 2) is a factor
Now, combine all the factors into a single equation and simplify.
( x-2 )( x + 2 )( x - 4 ) = y
( x² + 2x - 2x - 4 )( x - 4) = 0
( x² - 4 )( x - 4) = 0
x( x² - 4 ) -4( x² - 4 ) = 0
x³ - 4x - 4x² + 16 = 0
x³ - 4x² - 4x + 16 = 0
x³ - 4x² - 4x + 16 = 0
Therefore, the equation of the polynomial with the given roots of 2, -2, and 4 is x³ - 4x² - 4x + 16 = 0.
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What do I write for 23???
when a pipe constricts as shown in the figure below, the velocity v of fluid flowing through the pipe is inversely proportional to the pipes cross sectional area a. suppose water flows through a section of pipe of area 10 cm^2 at a velocity of 4 m/s. if the pipe constricts to an area of 2.5 cm^2, what will its velocity be in this section of pipe
Answer:
A because of the way the pipe is designed
the points on the table are in a line what is the slope
Answer:
the slope of the table is -0.857
pls help asap I’ll give brainliest immediately.. plsss..
Answer:
You have the right form (vertex form). All that you have left to do is learn what parts of the equation signify what.
Step-by-step explanation:
Explanation:
In a quadratic function of form y = a
(
x
−
p
)
2
+ q, the axis of symmetry is found at x = p. As a result, in y = -4
(
x
−
8
)
2
+ 3, the axis of symmetry is at x = 8, since the formula is x - p = x - (+8).
The vertex of a parabola is at (p, q). As for the axis of symmetry, the p value is 8, and in this function the q value is 3. So the vertex is at (8,3).
With this information, the x and y intercepts, and a few other points found by plugging in x values and solving for y, you will be able to graph this parabola. Your graph, if done properly, will look like the following:
graph{y = -4(x - 8)^2 + 3 [-20, 20, -10, 10]}
How do I factor 7.2x2y - 0.9xy2
Answer:
[tex]xy\left(7.2x-0.9y\right)[/tex]
Step-by-step explanation:
[tex]Rule: a^{b+c}=a^ba^c\\(x^2y=xxy,\:xy^2=xyy)\\=7.2x(xy)-0.9xyy\\=xy\left(7.2x-0.9y\right)[/tex]
Order the numbers from least to greatest -3 , -8, |-6|, 2
Answer: -8, -3, 2, |-6|
Step-by-step explanation:
-3 , -8, |-6|, 2
|-6|=6
6>2
-3>-8 since a negative number closer to 0 is the greater number.
Order: -8, -3, 2, 6 ==> -8, -3, 2, |-6|
The value of the 7 in 57,264 is ten times greater than the value of the 7 in which of these numbers?
A. 17,810
C. 78,893
B. 61,715
D. 95,371
C.78893
Step-by-step explanation:
-_-_+_(*;#-✓✓
i need help with 23-26 help please
2.5, 0.92, 0.75, 0.925
maths geometry question
Step-by-step explanation:
with ABCD and ABDE being parallelograms, this means a indicated by the marks
AB = ED = CD
and with BD = DF that means that the line segments BF and CE are intersecting each other at their midpoint.
so they represent a pair of diagonals of a parallelogram, which makes BCFE a parallelogram.
What kind of passenger be considered a true negative ?
Answer: A someone with dangerous material passed by security
Step-by-step explanation:
i need help asap. plsss give me the right answer
Answer:
x < 3
Step-by-step explain: I used quizlet
Apply it
What is the value of the expression 4(x - y)
when x = 7 and y = 1?
A 26
7
B 29
C 32
D 48
Apply your thinking
Students, write your response!
Pear Deck Interactive Slide
Curriculum Associal Do not remove this bar
Answer:
USE AIR MATH!!
Step-by-step explanation:
Find X if
• B is between A and C;
• AB = x+5;
BC= 2 (x-3); and
AB ~ BC
a parte inferior de una escalera debe colocarse a 3 pies de una pared. La escalera mide 10 pies de largo. ¿Qué tan por encima del suelo toca la escalera la pared?
[tex]\sqrt{10^2 - 3^2}=\boxed{\sqrt{91} \text{ ft}}[/tex]
to construct a rectangle you must have one side and :
(1) it’s opposite sides
(2) it’s adjacent sides
(3) two angles
(4) four angles
If u answer this question i will give brainlyest and 40 marks
Answer:
Adjacent sides.
Step-by-step explanation:
Answer:
To construct a rectangle, you must have the measurement of one side and it's adjacent side.
Step-by-step explanation:
to construct a rectangle you must have one side and :
(1) it’s opposite sides
(2) it’s adjacent sides
(3) two angles
(4) four angles
what is the angle of depression zipline
Answer and Explanation:
The problem provides the following information:
Hypotenuse
=
h
y
p
=
5129
ft
Vertical drop
=
o
p
p
=
1275
ft
To find the angle of depression, the best trigonometric ratio to use is the sine ratio. After equating it with the ratio of the opposite side over the hypotenuse, get the inverse of the sine ratio as shown:
sin
θ
=
o
p
p
h
y
p
θ
=
sin
−
1
(
o
p
p
h
y
p
)
θ
=
sin
−
1
(
1275
ft
5129
ft
)
θ
=
sin
−
1
(
0.2485864691
)
θ
=
14.3938824691
≈
14.4
∘
The angle of depression is
14.4
order of operations MC
Joshua purchased a game card for the arcade for a total of $15. He played two basketball hoop games for $2.75 each and three rounds of air hockey for $1.25 each. How much did he have left on the game card?
Answer: $5.75
Step-by-step explanation: 2.75 x 2 = 5.5 1.25 x 3 = 2.75 2.75 + 5.5 = 9.25 $15 - $9.25 = $5.75
Find the area of a rectangle that has a length of 4.5 units and a width of 7.2 units. Write the numerical answer only.
An octopus dives 10 meters per second for 12 seconds then rises 15 meters which expression represents this situation
Answer: -10s +15
-10 = 10 meters down
s = seconds
+ 15 = 15 meters risen