The vertical height in feet of a projectile on a planet in our solar system at a given time t in seconds is represented by the function h(t)=−6t2+24t . Re-write h(t) in the form h(t)=a(t-h)^2+k and determine the maximum height of the projectile. Show all work.
Answers
We are given the following function:
[tex]h(t)=-6t^2+24t[/tex]We will take "-6" as a common factor:
[tex]h(t)=-6(t^2-4t)[/tex]Now, we will complete the square in the expression inside the parenthesis by adding and subtracting the following term:
[tex]undefined[/tex]Related Questions
GIVEN: AD is angle bisector of
Answers
Given:
AD is angle bisector of angle BAC.
AB = AC.
The objective is to prove BD = DC.
Step 1:
Statement: AD is angle bisector of angle BAC.
Reason: Given.
Step 2:
Statement:
[tex]\angle BAD=\angle\text{DAC}[/tex]Reason: Definition of angle bisector.
Step 3:
Statement:
[tex]AB\cong AC[/tex]Reason: Given
Step 4:
Statement: AD = AD.
Reason: Reflexive.
Step 5:
Statement:
[tex]\Delta BAD\text{ }\cong\text{ }\Delta CAD[/tex]Reason: By SAS criteria.
Step 6:
Statement:
[tex]BD\cong DC[/tex]Reason: By Corresponding parts of congruent triangles (CPCT).
Hence, the required results are obtained.
The expression 81√ ⋅ 100√ represents the number of feet between home plate and first base. What is the distance, in feet, between home plate and first base?
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Using perfect squares to solve the expression √81-√100 the distance between home plate and first base is 1 feet
Which numbers are perfect square?The perfect square is the number which can be written as the square of some integer.
A number x is a perfect square if x=y² for some y. or y =√x
Given:
The number of feet between home plate and first base = |√81-√100|
|x| absolute function is put because number of feet need to be a positive number
81 is a perfect square ∵ 81 = 9×9 = 9²
As 81 = 9²
⇒ √81 = √9² = 9
100 is also a perfect square ∵ 100= 10×10 =10²
As 100=10²
⇒ √100= √10² = 10
The expression √81-√100 = 9-10 = -1
The distance between home plate and first base = Number of feet between home plate and first base = |√81-√100| = |-1| = 1 feet
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The complete question is given below:
The expression √81-√100 represents the number of feet between home plate and first base. What is the distance, in feet, between home plate and first base?
Identify the values of the variables that complete the table to show the equivalent fractions, decimals, and percents.
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1.2 as a fraction is computed as follows:
[tex]1.2=1.2\cdot\frac{10}{10}=\frac{1.2\cdot10}{10}=\frac{12}{10}=\frac{6}{5}=a[/tex]Computing 1 divided by 9, we get:
[tex]\frac{1}{9}=0.11111\ldots=b[/tex]To convert 5/3 to percent, we have to multiply it by 100, as follows:
[tex]\frac{5}{3}\cdot100=\frac{500}{3}=166\frac{2}{3}\text{ \% = c}[/tex]the position from its starting point of a small plane preparing for takeoff is given by x(t)=1.64t^2 meters…
Answers
Given:
The position of the small plane is given by,
[tex]x(t)=1.64t^2[/tex]Explanation:
The accelration of plane can be obtained by double derivative of the position function.
Determine the double derivative of the position function.
[tex]\begin{gathered} \frac{d^2}{dt^2}x(t)=\frac{d^2}{dt^2}(1.64t^2) \\ a(t)=1.64\cdot\frac{d}{dt}(2t) \\ =3.28\cdot1 \\ =3.28 \end{gathered}[/tex]So acceleration of the small plane is 3.28 m/s^2
Answer: 3.28
What’s the Missing angle
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Answer: 60
Step-by-step explanation: All angles are equal in a triangle if one angle is 60 degrees because 60x3=180
sales tax is caculated as a percantage of the sales price . if sales tax 5% what is the sales tax on clothing that cost 170
Answers
*GEOMETRY*please help me find the surface area of the solid along with the volume of it step by step!
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Surface area of the solid = 7.1781 in²
Volume of the solid = 0.804 in³
Explanation:
Surface area of the solid = surface area of the square prism - 2(base of the cylinder) + lateral surface of cylinder
surface area of a square prism = 2(lw + lh + wh)
l = length = 1 in
w = length = 1 in
h = height = 1 in
[tex]\begin{gathered} \text{Surface area = 2(1}\times1\text{ + 1}\times1\text{ + 1}\times1) \\ \text{Surface area = 2(1 + 1 + 1) = 2(3)} \\ \text{Surface area = 6 in }^2 \end{gathered}[/tex]using the value π as it is on the calculator
Base area of a cylinder = πr²
2(Base area of cylinder) = 2πr² = 2π(0.25)² = 0.3927
Lateral surface area = 2πrh = 2π(0.25)(1) = 1.5708
Surface area of the solid = 6 - 0.3927 + 1.5708
Surface area of the solid = 7.178 in²
Volume of the solid = Volume of the square prism - volume of the cylinder
Volume of square prism = length × width × height
length = 1 in, width = 1 in, height = 1 in
Volume of the solid = 1 in × 1 in × 1 in = 1 in³
Volume of a cylinder = πr²h
Volume of the cylinder = π × 0.25 × 0.25 × 1 = 0.196
Volume of the solid = 1 - 0.196
Volume of the solid = 0.804 in³
hat is the value of ?The solution is
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l5l - l-5l - (-5)
the absolute value of l5l and l-5l is 5
5 - 5 - (-5)
Subtracting a negative number is the same as adding that number
5 - 5 + 5
5
Answer = 5
Michael has 2 1/2 cups of orange juice in a jar he pours the juice into glasses that each hold 3/4 cups how many glasses can he fill?
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Number of glasses Michael can fill is [tex]3\frac{1}{3}[/tex] or 3.33 cups
How to find amount of 1 when amount of many are given ?A number is divided in division, which is a straightforward procedure. The simplest way to conceptualize it is as a set of objects being distributed among a set of individuals, as in the example given above. Of course, in order to be fair, you should always pay each person the same amount.
In mathematics, division is the process of dividing a number into equal parts and calculating the maximum number of equal parts that may be formed. For instance, dividing 15 by 3 results in the division of 15 into 3 groups of 5 each.
Given: Number of cups Michael have = 2 1/2 cups = 2 + 0.5 = 2.5 cups
To find : How many glasses he can fill .
So since each glass holds 3/4 cups = 0.75
Thus number of glasses which can be filled = 2.5 / 0.75
= 3.33 or [tex]3\frac{1}{3}[/tex]
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1. Andre is building a tower out of different foam blocks. These blocks come in three different thicknesses: -foot, -foot, and foot. Andre stacks two-foot blocks, two-foot blocks, and two-foot blocks to create a tower. What will the height of the tower be in foot? Explain or show how you know.
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Height of the tower = 1.75 ft
Explanations:The thickness of the blocks are 1/2 ft, 1/4 ft, and 1/8 ft
Two 1/2 ft blocks will have a thickness of:
2 x 1/2 = 1 ft
Two 1/4 ft blocks will have a thickness of:
2 x 1/4 = 1/2 ft
Two 1/8 ft blocks will have a thickness of:
2 x 1/8 = 1/4 ft
The height of the tower = 1 + 1/2 + 1/4
The height of the tower = (4 + 2 + 1) / 4
The height of the tower = 7/4 = 1.75 ft
Multiply. State any excluded values. Simplify your answer. Type your answer in factored form.
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Multiplication:
[tex]\frac{f(x)}{g(x)}\cdot\frac{h(x)}{j(x)}=\frac{f(x)h(x)}{g(x)j(x)}[/tex]For the given functions:
[tex]\begin{gathered} \frac{x}{x-7}\cdot\frac{x-2}{x-3}=\frac{x(x-2)}{(x-7)(x-3)} \\ \end{gathered}[/tex]The expression cannot be simplified and is already written in factored form.
The exclude values are those that make the denominator be equal to zero: 7,3
[tex]\begin{gathered} (x-7)(x-3)=0 \\ \\ x-7=0 \\ z=7 \\ \\ x-3=0 \\ x=3 \end{gathered}[/tex]In which quadrant does -336 lie?A. IVOB.IOC. IID. IIIReset Selection
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Recall that an angle Θ:
1) Lies in quadrant 1 if Θ is coterminal to an angle between 0 and 90 degrees.
2) Lies in quadrant 2 if Θ is coterminal to an angle between 90 and 180 degrees.
3) Lies in quadrant 3 if Θ is coterminal to an angle between 180 and 270 degrees.
4) Lies in quadrant 4 if Θ is coterminal to an angle between 270 degrees and 360 degrees.
Now, recall that Θ and Θ+360 degrees are coterminal angles.
Notice that:
[tex]-336^{\circ}+360^{\circ}=24^{\circ}.[/tex]Since:
[tex]0^{\circ}<24^{\circ}<90^{\circ},[/tex]and -336 degrees is coterminal to 24 degrees, then -336 degrees lies on quadrant I.
Answer: Option B.
Suppose contact lenses cost $300 for a year’s supply or $30 for a month’s supply. Which is less expensive to order per year, paying for 12 months at one time or paying for 1 month at a time?
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The cost that is less expensive is paying for 12 months at one time for $300.
How to calculate the value?From the information, contact lenses cost $300 for a year’s supply or $30 for a month’s supply.
In this case, for the $30 for a month’s supply, the amount that will be paid yearly will be:
= $30 × 12
= $360
In this case, the one time payment for $300 is cheaper.
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Given the graph of f (x), determine the domain of f –1(x).
Radical function f of x that increases from the point negative 3 comma negative 2 and passes through the points 1 comma 0 and 6 comma 1
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The domain of the inverse function f-1(x) is [-2, oo)
How to determine the representation of the domain of the inverse function ?The graph represents the given parameter
On the graph, we can see that:
The y values starts from y = -2 and it extends upwards to the positive axis
This means that the range of the function is
Range = [-2, oo)
When the function is inverted, the range becomes the domain
This implies that
Domain of the inverse function = Range of the function = [-2, oo)
Hence, the inverse function has a domain of [-2, oo)
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which system of linear equations has the ordered pair (-4,-12)as it's solution?
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In order to find which system has the ordered pair (-4, -12) as a solution, let's check this pair in each system.
We can see that the first two options have the function x = (1/3)y and the last two have the function y = (1/3)x.
Looking at the ordered pair, we have that x is 3 times smaller than y, therefore the correct equation is x = (1/3)y.
Then, the second equation has a constant value for the sum "x + y".
Calculating x + y using the coordinates of the ordered pair, we have a value of -16.
Therefore the correct equation is x + y = -16.
So the option that has the correct system is the second one.
Using a trigonometric ratio to find an angle measure in a right
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ANSWER :
x = 33.6 degrees
EXPLANATION :
Recall that the cosine function is :
[tex]\cos\theta=\frac{\text{ adjacent}}{\text{ hypotenuse}}[/tex]From the problem, the adjacent to the angle x is 15 and the hypotenuse is 18.
Using the formula above :
[tex]\begin{gathered} \cos x=\frac{15}{18} \\ \\ \text{ take the arccos :} \\ x=\arccos(\frac{15}{18}) \\ \\ x=33.56\sim33.6 \end{gathered}[/tex]Aidan buys a bag of cookies that contains 5 chocolate chip cookies, 8 peanut butter cookies, 5 sugar cookies and 8 oatmeal cookies.
What is the probability that Aidan reaches in the bag and randomly selects a peanut butter cookie from the bag, eats it, then reaches back in the bag and randomly selects an oatmeal cookie? Write your answer as a percent. Round to the nearest tenth of a percent.
Answers
Answer- 62%
Step-by-step explanation
5+5+8+8= 26 There are 8 peanut butter cookies,so 8/26 is the chance we will get a peanut butter cookie. In percentage form that is 0.307692308 or 30% chance that a peanut butter cookie will be selected. This also means that since there are 8 oatmeal there is a 30% percent chance for those as well.5/26 is 0.192307692, which is almost 20 percent. 30 +30 +20+20 is 100 percent. Now that we know there is a 30 percent for both peanut butter and oatmeal, we would have to have the percent of 8+8/26. 16/26 is 0.615384615. This means that the chance of picking a peanut butter then oatmeal cookie, back-to-back would be around 62%
Hope this helps good luck.
is [tex]1.2345 \: repeating \: \times \sqrt{4} [/tex]irrational or rational?
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If we can write this expression as a fraction, then this will be rational. Otherwise, irrational.
First, let's write the repeating decimal as fraction. Excluding the 1 point to the left of the decimal.
We have:
0.234523452345...
We can write it as:
[tex]\frac{2345}{9999}[/tex]Tagging along the "1", we have:
[tex]1\frac{2345}{9999}[/tex]Then, we have square root of 4, which is "2".
If we multiply the fraction shown above by 2, we will definitely have a fraction.
That will be a rational number.
In a newspaper, it was reported that yearly robberies in Springfield were down 40% to 126 in 2013 from 2012. How many robberies were there in Springfield in 2012?
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Answer:
210
Step-by-step explanation:
210-40% is 126
If f(x)=x²+5 and g(x)=3x, find
a. (f+ g)(x)
b. (f -g)(x)
c. (f . g)(x)
d. (f/g)(x)
a. (f + g)(x)= _____
(Simplify your answer.)
Answers
The value of the functions are:
a. (f + g)(x) = x² + 3x + 5
b. (f - g)(x) = x² - 3x + 5
c. (f * g)(x) = 3x³ + 15x
d. (f/g)(x) = (x² + 5)/(3x)
How to Solve Functions?If we are given an expression of functions, we need to plug in each of the given functions into the equation and solve as you would simplify an algebraic expression.
We have the functions:
f(x) = x² + 5
g(x) = 3x
a. (f + g)(x) means we are going to add the functions f(x) and g(x):
(f + g)(x) = x² + 5 + 3x = x² + 3x + 5
b. (f - g)(x) means we are going to find the difference of the functions f(x) and g(x):
(f - g)(x) = x² + 5 - 3x = x² - 3x + 5
c. (f * g)(x) means we are to find the product of the two functions f(x) and g(x):
(f * g)(x) = (x² + 5)(3x) = 3x³ + 15x
d. (f/g)(x) means we are to find the quotient of the two functions f(x) and g(x):
(f/g)(x) = (x² + 5)/(3x)
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I tried to do this on my own and I got nine and they said it was incorrect so please help
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Answer:
9u
Explanation:
Given the expression:
[tex]3u(3)[/tex]First, replace the parenthesis with a multiplication sign.
[tex]\begin{gathered} =3u\times3 \\ =3\times u\times3 \end{gathered}[/tex]Next, reorder to bring the numbers together.
[tex]\begin{gathered} =3\times3\times u \\ =9u \end{gathered}[/tex]The simplified form of the expression is 9u.
Determine the x-intercepts of the graph represented by the following quadratic function. Recall that y = f(x).f(x) = x2 − 4x − 21(x, y) = (smaller x-value)(x,y)= (larger x-value)
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For this problem, we are given the expression for a quadratic equation and we need to determine the x-intercepts of its graph.
The x-intercepts coincide with the zeros of the equation, which are obtained when f(x) = 0. So we have:
[tex]x^2-4x-21=0[/tex]We need to determine the roots of the equation above.
[tex]\begin{gathered} x_{1,2}=\frac{-(-4)\pm\sqrt{(-4)^2-4\cdot1\cdot(-21)}}{2\cdot1}\\ \\ x_{1,2}=\frac{4\pm\sqrt{16+84}}{2}=\frac{4\pm\sqrt{100}}{2}=\frac{4\pm10}{2}\\ \\ x_1=\frac{4+10}{2}=\frac{14}{2}=7\\ \\ x_2=\frac{4-10}{2}=\frac{-6}{2}=-3 \end{gathered}[/tex]The intercepts are: (-3,0) and (7,0).
Ten members of the Science Club went to a history muesum. It cost $7.25 for each member of the club. If 90 members went to the muesum, how much would the total cost?
Answers
Answer: $652.5
Step-by-step explanation:
If it costs $7.25 for each member of the club, we can multiply this unit value ($7.25) by 90 to find the total cost.
$7.25 * 90 = $652.5
If 12 + _ = 0 + 12, then _ must equal:A: 120B: 12C: 1D: 10E: 0
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1) Examining this equality 12 + _ = 0 + 12 we can see that this the 0 is the neutral element then applying the Commutative Property we can state that:
12 +0 = 0+12
2) Because the order of the addends does not alter the sum.
E
What is the equation of the following line written in slope-intercept form.
y = 2 /3 x + 9 /2
y = 3 /2 x - 9 / 2
y = - 3 /2 x - 3 / 2
Answers
Answer:
y = -3/2x - 9/2
Step-by-step explanation:
The general form of a line in slope-intecept form is given by:
y = mx + c
where: m = slope, c = intercept.
from the graph, slope is calculated as:
m = (-3 - 0)/(-1 -(-3))
m = -3/2
To obtain c, choose any value of x, and corresponding y value.
we choose: (-3, 0)
using y = mx + c
0 = -3/2(-3) + c
simplify
c = -9/2
Therefore, y = -3/2x - 9/2
The school is having a bake sale and the pep squad is selling cookies. On one ticket they sold two chocolate chip cookies and five oatmeal cookies for $23. On another ticket they sold three chocolate chip cookies and three oatmeal cookies for $21.
Which system of equations below can be used to determine the price of a chocolate chip cookie and the price of an oatmeal cookie?
Let x represent the cost of a chocolate chip cookie, and let y represent the cost of an oatmeal cookie.
A.
2x + 3y = 23
5x + 3y = 21
B.
2x + 3x = 20
5y + 3y = 24
C.
5x + 8y = 44
5x - 8y = 44
D.
2x + 5y = 23
3x + 3y = 21
Answers
Answer:
[tex]\begin{aligned}\textsf{D.}\quad 2x + 5y &= 23\\3x + 3y &= 21\end{aligned}[/tex]
Step-by-step explanation:
Definition of variables:
Let x represent the cost of a chocolate chip cookieLet y represent the cost of an oatmeal cookie.Given information:
2 chocolate chip cookies and 5 oatmeal cookies = $23. 3 chocolate chip cookies and 3 oatmeal cookies = $21.Therefore, the system of equations that can be used to determine the price of a chocolate chip cookie and the price of an oatmeal cookie is:
[tex]\large\boxed{\begin{aligned}2x + 5y &= 23\\3x + 3y&= 21\end{aligned}}[/tex]
A model of a dinosaur was created using a scale factor of 1:20. The model is 3.75 feet long. How long is the actual dinosaur in feet?
Answers
ANSWER
75 feet
EXPLANATION
The scale factor means that the ratio of the model to the actual size of the dinosaur is 1 : 20.
The model is 3.75 feet long.
Let the actual length of the dinosaur be x.
So, it means that:
[tex]\begin{gathered} \frac{1}{20}\text{ = }\frac{3.75}{x} \\ \text{Cross}-\text{ multiply:} \\ 1\cdot\text{ x = 20 }\cdot\text{ 3.75} \\ x\text{ = 75 feet} \end{gathered}[/tex]The actual length of the dinosaur is 75 feet.
Need help with #9 please it’s due today
Answers
9. The equation of the line parallel to y = 2x+4 and passing through the point (-4, -1) is y = 2 x +7
Given:
line = y = 2x+4
point = (x, y)= (-4,-1)
The given equation is of the form,
y = mx+ c ---- (1)
slope= m = 2
The line parallel to this line will have the same slope,
m = 2
The new line is of the form,
y = 2 x+ c ----(2)
Substituting the given point (-4, -1) in (2)
- 1= 2(-4) + c
c = 7
Substituting c in (2)
y = 2 x +7 is the parallel line equation.
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Which is not an example of U.S. foreign policy?
President Taft turning away from military intimidation and toward monetary incentives with other nations
President Franklin Roosevelt establishing the Lend-Lease program to aid Britain during World War II
President Lyndon Johnson asking Congress to pass the Civil Rights Act of 1964
President Theodore Roosevelt sending U.S. warships to Asia to display their power
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Answer:
The correct answer is D. President Lyndon Johnson asking Congress to pass the Civil Rights Act of 1964
Step-by-step explanation:
Find the exact value of cos 4pi/3 in simplest form with a rational denominator?
Answers
The given expression is
[tex]cos\frac{4\pi}{3}[/tex]Since the angle is greater than pi, then it lies in the 3rd quadrant
Since in the 3rd quadrant the value of cosine is negative, then we will use the expression
[tex]cos\frac{4\pi}{3}=cos(\pi+\frac{\pi}{3})=-cos\frac{\pi}{3}[/tex]Since the value of cos(pi/3) = 1/2, then
[tex]\begin{gathered} cos\frac{\pi}{3}=\frac{1}{2} \\ \\ cos\frac{4\pi}{3}=-cos\frac{\pi}{3}=-\frac{1}{2} \end{gathered}[/tex]The answer is -1/2