Answers
h(0) = -3(0 - 3)² + 108
Parenthesis first
h(0) = -3(-3)² + 108
Exponents next
h(0) = -3(9) + 108
Multiplication
h(0) = -27 + 108
Combine like terms
h(0) = 81: The height of the hovercraft at the time of takeoff is 81 meters!
Hope this helps :)
Related Questions
Find the number of ways that an organization consisting of 15 members can elect a president, a treasurer, and q secretary. (assuming no person is elected to more than one position)
Answers
Total Members = 15
For electing present number of members = 15
For electing treasurer the numbers of members =14
For electing secretary the numbers of members =13
Find the numbers of possible ways for election of members= ?
Possible ways for election =15*14*13
=2730
Given that (-3,7) is on the graph of f(x), find the corresponding point for the function f(x + 5).
Answers
(-3,7) is on the graph of f(x), find the corresponding point for the function
f(x + 5)
we know that
in the transformation f(x)-------> f(x+5)
the point (x.y) in f(x) becomes a point (x-5,y) in f(x+5)
so
(-3,7)-----------> becomes a point (-3-5,7)------> (-8,7)
the answer is
(-8,7)
Answer: (-8,7)
Step-by-step explanation: It;s right
Sam and Brett share £54 in the ratio of 5:4 how much does each person get
Answers
[tex]\bf \cfrac{Sam}{Brett}\qquad 5:4\qquad \cfrac{5}{4}\qquad \qquad \cfrac{5\cdot \frac{54}{5+4}}{4\cdot \frac{54}{5+4}}\implies \cfrac{5\cdot 6}{4\cdot 6}\implies \cfrac{30}{24}[/tex]
hey can you please help me posted picture of question
Answers
We can conclude that the correct answer is B. Quadratic parent function.
which of the following statements is false?
A. 2 is greater than or equal to 8
B. 2 is less than or equal to 8
c. 8 is less than or equal to 8
Answers
how do I do this question 4x-2=6
Answers
X=2
4 x 2 - 2 = 6
Hope this helps!
a player gets to throw 4 darts at the target shown. Assuming the player will always hit the target, the probability of hitting an odd number three times is *blank* times more than the probability of hitting an even number 3 times
Answers
Answer: The probability of hitting an odd number three times is [tex]3\dfrac{3}{8}[/tex] times more than the probability of hitting an even number 3 times.
Step-by-step explanation:
From the given picture , the total total number of sections in the spinner = 5
Sections having Odd numbers = 3
Sections having Even numbers =2
We know that , [tex]\text{Probability}=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]
So , probability of hitting an odd number = [tex]\dfrac{3}{5}[/tex]
Probability of hitting an even number = [tex]\dfrac{2}{5}[/tex]
Since all events are independent of each other ,
So , probability of hitting an odd number three times = [tex](\dfrac{3}{5})^3=\dfrac{27}{125}[/tex]
Probability of hitting an even number three times = [tex](\dfrac{2}{5})^3=\dfrac{8}{125}[/tex]
Divide [tex]\dfrac{27}{125}[/tex] by [tex]\dfrac{8}{125}[/tex] , we get
[tex]\dfrac{27}{125}\div\dfrac{8}{125}\\\\=\dfrac{27}{125}\times\dfrac{125}{8}=\dfrac{27}{8}=3\dfrac{3}{8}[/tex]
Hence, the probability of hitting an odd number three times is [tex]3\dfrac{3}{8}[/tex] times more than the probability of hitting an even number 3 times.
Answer:
3.375
Step-by-step explanation:
PLEASE PLEASE HELP ME?!?!!? PLEASSEE I ONLY HAVE 2 QUESTIONS!!!
When the function f(x) = 6(9)x is changed to f(x) = 6(9)x + 1, what is the effect?
Select one:
a. There is no change to the graph because the exponential portion of the function remains the same.
b. All input values are moved 1 space to the right.
c. The x-intercept is 1 space higher.
d. The y-intercept is 1 space higher.
Evaluate fourth root of 9 multiplied by square root of 9 over the fourth root of 9 to the power of 5 . (5 points)
Select one:
a. 9 to the power of negative 1 over 2
b. 9 to the power of negative 1 over 4
c. 9
d. 92
Answers
1. Changing f(x) to f(x) + 1 adds 1 to every output value of the function, moving that value "1 space higher". This is true for the y-intercept, too.
___
2. The rules of exponents apply:
a^b · a^c = a^(b+c)1/a^b = a^-bYou apparently want to simplify ...
... 9^(1/4) × 9^(1/2) / 9^(5/4)
... = 9^(1/4 + 1/2 - 5/4)
... = 9^((1+2-5)/4)
... = 9^(-2/4) = 9^(-1/2)
for a bake sale violet wants to use the recipe at the right. If she wants to double the recipe, how much flour will she need
Answers
If f(x)=4x-6 and g(x) =2x find f(x) •g(x)
Answers
(2x)4x - (2x)6 = 8x² - 12x
Final answer: 8x² - 12x
Hope this helps.
f(x) = 4x - 6
g(x) = 2x
Using the values, we can write:
f(x) · g(x) = (4x - 6)(2x)
= 8x² - 12x
Thus, the answer is 8x² - 12x
These tables of values represent continuous functions. In which table do the values represent an exponential function?
A.
x y
1 3
2 6
3 9
4 12
5 15
B.
x y
1 2
2 6
3 18
4 54
5 162
C.
x y
1 10
2 22
3 34
4 46
5 58
D.
x y
1 7
2 8
3 9
4 10
5 11
Answers
Answer:
The correct option is B.
Step-by-step explanation:
A function is called an exponential function if it has common ratio.
A function is called an linear function if it has common difference.
In option A.
[tex]\frac{f(2)}{f(1)}=\frac{6}{3}=2[/tex]
[tex]\frac{f(3)}{f(2)}=\frac{9}{6}=\frac{3}{2}[/tex]
[tex]2\neq \frac{3}{2}[/tex]
Since the given table has different ratio, therefore it is not an exponential function. Option A is incorrect.
In option B.
[tex]\frac{f(2)}{f(1)}=\frac{6}{2}=3[/tex]
[tex]\frac{f(3)}{f(2)}=\frac{18}{6}=3[/tex]
[tex]3=3[/tex]
Since the given table has common ratio, therefore it is an exponential function. Option B is correct.
In option C.
[tex]\frac{f(2)}{f(1)}=\frac{22}{10}=\frac{11}{5}[/tex]
[tex]\frac{f(3)}{f(2)}=\frac{34}{22}=\frac{17}{11}[/tex]
[tex]\frac{11}{5}\neq \frac{17}{11}[/tex]
Since the given table has different ratio, therefore it is not an exponential function. Option C is incorrect.
In option D.
[tex]\frac{f(2)}{f(1)}=\frac{8}{7}[/tex]
[tex]\frac{f(3)}{f(2)}=\frac{9}{8}[/tex]
[tex]\frac{8}{7}\neq \frac{9}{8}[/tex]
Since the given table has different ratio, therefore it is not an exponential function. Option D is incorrect.
Answer:
Table B represents an exponential function.
Step-by-step explanation:
An exponential function is a function which has common ratio. Using this fact we will evaluate the functions given in the form of a table.
Table A.
f(1) = 3
f(2) = 6
f(3) = 9
Now [tex]\frac{f(2)}{f(1)}=\frac{6}{3}=\frac{2}{1}[/tex]
[tex]\frac{f(3)}{f(2)}=\frac{9}{6}=\frac{3}{2}[/tex]
Ratios are not equal so it's not an exponential function.
Table B.
f(1) = 2
f(2) = 6
f(3) = 18
[tex]\frac{f(2)}{f(1)}=\frac{6}{2}=\frac{3}{1}[/tex]
[tex]\frac{f(3)}{f(2)}=\frac{18}{6}=\frac{3}{1}[/tex]
Here ratios are same therefore it's an exponential function.
Table C.
f(1) = 10
f(2) = 22
f(3) = 34
[tex]\frac{f(2)}{f(1)}=\frac{22}{10}=\frac{11}{5}[/tex]
[tex]\frac{f(3)}{f(2)}=\frac{34}{22}=\frac{17}{11}[/tex]
Ratios are not equal therefore it's not an exponential function.
Table D.
f(1) = 7
f(2) = 8
f(3) = 9
[tex]\frac{f(2)}{f(1)}=\frac{8}{7}[/tex]
[tex]\frac{f(3)}{f(2)}=\frac{9}{8}[/tex]
Ratios are not equal so it's not an exponential function.
Therefore Table B is the correct option.
Please help me I need help
Answers
260*.25=65
260-65=195
hey can you please help me posted picture of question
Answers
f (x) = 4x ^ 2 - 16
Horizontal translations
Suppose that h> 0
To graph y = f (x-h), move the graph of h units to the right.
We have then:
f (x) = 4 (x-5) ^ 2 - 16
Then,
Vertical translations
Suppose that k> 0
To graph y = f (x) -k, move the graph of k units down.
We have then:
f (x) = 4 (x-5) ^ 2 - 16 - 2
f (x) = 4 (x-5) ^ 2 - 18
Answer:
f (x) = 4 (x-5) ^ 2 - 18
option C
5 units to right means subtracting 5 from the value of x. So the function will be:
4(x-5)² - 16
2 units down means subtracting 2 from the entire function.
So, the expression will be
4(x-5)² - 16 - 2
=4(x-5)² - 18
The above expression gives the equation after both the given translations have been applied.
So, the correct answer is option C
A pattern on a quilt is made up of pieces of fabric in the shape of parallelograms. One piece of fabric is shown. What is the area of one piece of fabric? Enter your answer in the box.
Answers
A = (1/2) * (b) * (h)
Where,
b: base of the parallelogram
h: height of the parallelogram
Substituting values we have:
A = (1/2) * (3.1 + 3.3) * (4.1)
A = 13.12 cm ^ 2
Answer:
The area of one piece of fabric is:
A = 13.12 cm ^ 2
When designing a building, you must be sure that the building can withstand hurricane-force winds, which have a velocity of 73 mi/h or more. The formula f=0.004av^2 gives the force F in pounds exerted by a wind blowing against a flat surface. A is the area of the surface in square feet, and v is the wind velocity in miles per hour. How much force is exerted by a wind blowing at 81 mi/h against the side of the building shown?
Answers
10825.65 pounds
The first step is calculate the surface area of the flat surface shown
Surface area of the rectangle = length * width = 25*12.9 = 322.5 square feet
Surface area of the triangle = 1/2 *base*height = 1/2*25*7.2 = 90 square feet
Total surface area = 322.5 +90 = 412.5 square feet
Total force = 0.004*a*v^2 = 0.004*412.5*81^2 = 10,825.65 pounds
which equation is shown in the graph?
y = [[x]]
y = [[x + 3]]
y = [[x]] - 3
y = |x - 3|
Answers
a floor() function, namely ⌊x⌋ like that, will floor the decimal values, so ⌊2.5⌋ floors to 2, because 2.5 is between 2 and 3, and the smallest is 2, the "floor", the 3 will be the "ceiling".
so for a floor function, ⌊1.5⌋ is 1, 1.5 is between 1 and 2, 1 is the smallest, ⌊-3.5⌋ is -4, recall that on the negative side, the closer to 0, the larger, so -1 is much larger than -1000.
and say ⌊-1.35⌋ is -2, -1.35 is between -2 an -1 and -2 is the smallest, the "floor".
that said
x = 2.5 ⌊ 2.5 + 3⌋ is ⌊5.5⌋ which is 5
x = 1.5 ⌊ 1.5 + 3 ⌋ is ⌊4.5⌋ which is 4
x = -2.749 ⌊ -2.749 + 3⌋ is ⌊0.251⌋ which is 0
anyway and so on, so you can pretty much see is the floor function of ⌊ x + 3⌋.
witch of the following expression is equivalent to the logarithmic expression below. log(3)5/x^2
A)log(3) 5+2 log(3)x
B)log(3) 5-2 log(3)x
C)2 log(3) 5-log(3)x
D)log(3) 5+log(3)x
Answers
[tex]log_{3}(\frac{5}{x^2})[/tex]
remember that [tex]log(\frac{a}{b})=log(a)-log(b)[/tex]
also, [tex]log(x^m)=(m)log(x)[/tex]
so
[tex]log_{3}(\frac{5}{x^2})=[/tex]
[tex]log_{3}(5)-log_{3}(x^2)=[/tex]
[tex]log_{3}(5)-2log{3}(x)[/tex]
the answer is B
Answer: The correct option is
(B) [tex]\log_35-2\log_3x.[/tex]
Step-by-step explanation: We are given to select the expression that is equivalent to the following logarithmic expression :
[tex]E=\log_3\dfrac{5}{x^2}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We will be using the following properties of logarithms :
[tex](i)~\log_a\dfrac{b}{c}=\log_ab-\log_ac,\\\\(ii)~\log_ab^c=c\log_ab.[/tex]
From (i), we get
[tex]E\\\\=\log_3\dfrac{5}{x^2}\\\\\\=\log_35-\log_3x^2~~~~~~~~~~~~~~~~~~~~[\textup{Using property (i)}]\\\\\\=\log_35-2\log_3x.~~~~~~~~~~~~~~~~~~~~[\textup{Using property (ii)}][/tex]
Thus, the required equivalent expression is [tex]\log_35-2\log_3x.[/tex]
Option (B) is CORRECT.
*. suppose that there are 5 dollar bills in a box: three 1 dollar bills, one 5 dollar bill and one 10 dollar bill. you are allowed to pick up two bills at the same time from the box randomly. let x denote the money you get from this game. (a) what's the p.m.f. of x?
Answers
The pmf of x is 4
To determine the probability mass function (PMF) for the game, one must calculate the probability of each possible sum of money resulting from drawing two bills, with the outcomes being 2, 6, 11, and 15 dollars.
To find the probability mass function (PMF) of the variable X, which represents the money you get from the game, we first identify all possible pairs of dollar bills you could draw from the box and then calculate the probability of drawing each pair. As there are three 1 dollar bills, one 5 dollar bill, and one 10 dollar bill, the possible sums of money (X) we can get by drawing two bills are 2 dollars, 6 dollars, 11 dollars, and 15 dollars.
To calculate the PMF of X, consider:
Picking two 1 dollar bills: The probability is C(3,2)/C(5,2) = 3/10.
Picking one 1 dollar bill and the 5 dollar bill: The probability is (C(3,1) imes C(1,1))/C(5,2) = 3/10.
Picking one 1 dollar bill and the 10 dollar bill: The probability is (C(3,1) imes C(1,1))/C(5,2) = 3/10.
Picking the 5 dollar bill and the 10 dollar bill: The probability is (C(1,1) imes C(1,1))/C(5,2) = 1/10
Therefore, the PMF of X is:
P(X = 2) = 3/10
P(X = 6) = 3/10
P(X = 11) = 3/10
P(X = 15) = 1/10
The equation of a circle is (x−2)^2+(y−16)^2=169 . What is the circle's radius?
Answers
The equation for a circle is
[tex] (x-h)^{2} +(y-k)^{2} = r^{2} [/tex]
r is the radius
To find the radius we take the square root of the number in the radius spot
sqrt169 = 13
The answer is 13
Hope this helps!
Suppose the number of calls per hour to an answering service follows a poisson process with rate 4.
a.what is the probability that fewer than 2 calls came in the first hour?
Answers
[tex]P(k,\lambda)=\lambda^k*e^(-\lambda)/k![/tex]
for λ = 4, and k<2 (i.e. k=0 or 1)
P(k<2, λ )=P(k=1, λ ) + P(k=1, λ )
[tex]=4^0*e^(-4)/4!+4^1*e^(-4)/1![/tex]
[tex]=4^0*e^(-4)/4!+4^1*e^(-4)/1![/tex]
=0.01832+0.07326
=0.09158 (to the fifth place of decimal)
Note: Poisson processes have no memory, so 2 calls in first hour has the same probability as 2 calls in any other hour.
hello can you please help me posted picture of question
Answers
[tex]( \frac{-b}{2a},y( \frac{-b}{2a})) [/tex]
b = coefficient of x term = -4
a = coefficient of squared term = 1
So,
[tex] \frac{-b}{2a}= \frac{4}{2}=2 [/tex]
and
[tex]y(2)=(2)^{2}-4(2)+1=-3 [/tex]
Therefore, the vertex occurs at (2, -3)
Thus the correct answer is option D
Hey can you please help me posted picture of question
Answers
6 x 6 x 6 x 6 x 6 = 7776 different outcomes
Number of outcomes when n dice are rolled = 6^n which is 6 raised to the power n.
So, the number of outcomes when 5 dice are rolled = 6⁵ = 7776
Thus, when 5 dice are rolled there will be 7776 possible outcomes.
So, option A is the correct answer
Is writing an equation this way ( 4 x 5 )-9-6 correct? If not why?
Answers
Circle 1 is centered at (5,8) and has a radius of 8 cm. Circle 2 is centered at (1,-2) and has a radius of 4cm. The circles are similar because you can translate circle 1using the transformation rule (___,___) and then dialate it using a scale factor of (___).
Answers
Circle 1:
Center (5,8)
radius= 8 cm
Circle 2:
Center (1,-2)
radius= 4 cm
The above circle are similar because you can translate Circle 1 using the transformation rule (-4,-10) translation and dilate it using a scale factor of 4/8=1/2
Find the length and width of a rectangle that has the given area and a minimum perimeter. area: a square centimeters
Answers
if the surface area of two smilar spheres is 256 feet and 576 feet, what is the ratio of the volume of the smaller sphere to the volume of the largee sphere
Answers
[tex]\bf \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\\\\ -------------------------------\\\\ \cfrac{smaller}{larger}\qquad \cfrac{s}{s}=\cfrac{\sqrt{256}}{\sqrt{576}}\implies \cfrac{s}{s}=\cfrac{16}{24}\implies \cfrac{s}{s}=\stackrel{simplified}{\cfrac{2}{3}}[/tex]
The ratio of the volume of the smaller sphere to the volume of the larger sphere, given their surface areas are 256 ft² and 576 ft², is 8:27.
The student has asked about finding the ratio of the volumes of two similar spheres given their surface areas. The surface areas are 256 ft² and 576 ft². To find the volume ratio, we need to use the fact that the ratio of the surface areas of similar spheres is the square of the ratio of their radii, and thus the ratio of the volumes will be the cube of the ratio of their radii.
Let's denote the surface areas as S₁ and S₂, and the volumes as V₁ and V₂. Then, S₁:S₂ = (radius of smaller sphere)² : (radius of larger sphere)² and V₁:V₂ = (radius of smaller sphere)³ : (radius of larger sphere)³.
First, we find the square root of the surface area ratios: [tex]\sqrt{\frac{256}{576} }[/tex] = [tex]\frac{16}{24}[/tex] = [tex]\frac{2}{3}[/tex]. Then, taking the cube of [tex]\frac{2}{3}[/tex] gives us the volume ratio V₁:V₂ = [tex](\frac{2}{3} )^3[/tex] = [tex]\frac{8}{27}[/tex].
Therefore, the ratio of the volume of the smaller sphere to the volume of the larger sphere is 8:27.
Find m/AEB
A.
10
B.
70
C.
110
D.
170
Answers
Hope this Helped!
;D
∠AEB = 70°
Explanation:
1- solving for x:
When two lines intersect, the vertically opposite angles formed would be equal.
In the given, we have two intersecting lines, therefore:
∠AEB = ∠CED (vertically opposite angles)
2x + 50 = 7x
7x - 2x = 50
5x = 50
x = 50/5
x = 10
2- getting the measure of the angle:
We know that:
∠AEB = 2x + 50
x = 10
Therefore:
∠ AEB = 2(10) + 50
∠AEB = 20 + 50 = 70°
Hope this helps :)
find the measure of the requested angle. find the complement of 41*
Answers
Find the measure of the requested angle. find the complement of 41°.
Solution:
The Sum of Complementary Angles is 90°.
So, Sum of Requested Angle and Given Angle =90°
So,Requested Angle+Given angle=90°
So,Requested Angle+41°=90°
To find, Requested Angle we subtract 41° from both sides,
Requested Angle+41°-41°=90°-41°
Requested Angle+0°=49°
So, Requested Angle=49°
Answer:49°
shorty's gross pay last week was $251.20.if her hourly rate was $7.85,how many hours did she works?
Answers
A triangle has interior angles measuring 40 and 52. Which triangle are similar to this triangle? select true or false for each triangle.
Answers
If you have a triangle with 40 and 52, then the third angle is 180 - 40 - 52 = 88 degrees.
Any triangle that has at least two of the three angles ( 40 , 52 and 88) will be similar
1. FALSE
2. FALSE
3. TRUE
4. TRUE