The maximum height that the dolphin jumps is 8 ft.
What is a parabola?A parabola is a planar curve which symmetrical across its vertex.
What is the standard equation of a parabola?The standard equation of a parabola is given by:
y = (x-h)² + k
Where (h, k) is the vertex of the parabola.
The maximum height that the dolphin reaches is the y-coordinate of the vertex of the parabola. We can change the given quadratic equation to standard form as follows:
h = -8t² + 16t
Subtract and add 8:
h = -8t² + 16t - 8 + 8
h = -8 (t² - 2t + 1) + 8
h = -8 (t - 1)² + 8
The negative coefficient outside the square term means that the parabola opens downward. From this standard form, we can see that the vertex of the parabola is (1, 8). This means that the maximum height that the dolphin can reach is 8 ft.
Therefore, we have found that the maximum height the dolphin jumps is 8 ft.
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Final answer:
The dolphin reaches its maximum height after 2 seconds and jumps 32 feet.
Explanation:
To find the maximum height the dolphin jumps, we need to determine the time it takes for the dolphin to reach its highest point. The equation given is h = -8t^2 + 16t, where h represents the dolphin's height at any given time t. Since the dolphin jumps straight up, its final velocity at the highest point is 0. Setting h = 0 and solving the resulting quadratic equation, we can find the time it takes for the dolphin to reach its maximum height.
Using the equation -8t^2 + 16t = 0, we can factor out -8t to get t(-8t + 16) = 0. This yields two solutions: t = 0 and t = 2. As time cannot be negative, we discard t = 0. Therefore, the dolphin reaches its maximum height after 2 seconds.
To find the maximum height, we substitute t = 2 in the equation h = -8t^2 + 16t. Plugging in the value, we get h = -8(2)^2 + 16(2) = -8(4) + 32 = 0 + 32 = 32 feet. Thus, the maximum height the dolphin jumps is 32 feet.
From the equation, find the axis of symmetry of the parabola.
y = 2x2 + 4x - 1
a. X=3
C. X=-3
b. x=-1
X = 1
Answer:
B. x= -1
Step-by-step explanation:
axis of symmetry is: [tex]x=\frac{-b}{2a}[/tex]
[tex]x=\frac{-4}{2(2)} \\x=\frac{-4}{4}\\x=-1[/tex]
The axis of symmetry for the given parabola equation y = 2x²+ 4x - 1 is x = -1.
The axis of symmetry of a parabola in the form y = ax² + bx + c can be found using the formula x = -b/(2a). For the given equation y = 2x² + 4x - 1, we can identify a as 2 and b as 4. Substituting these values into the formula for the axis of symmetry gives us x = -4/(2²) = -1.
The top if an end table is in the shape of a trapezoid. The area is 152 square inches. The bases are 11 inches and 27 inches. What is the height?
Answer:
The height is [tex]h=8\ in[/tex]
Step-by-step explanation:
we know that
The area of a trapezoid is equal to
[tex]A=\frac{1}{2}[b1+b2]h[/tex]
we have
[tex]b1=11\ in[/tex]
[tex]b2=27\ in[/tex]
[tex]A=152\ in^{2}[/tex]
substitute in the formula and solve for h
[tex]152=\frac{1}{2}[11+27]h[/tex]
[tex]304=[38]h[/tex]
[tex]h=304/38[/tex]
[tex]h=8\ in[/tex]
Simplify expression 8- ( 8-2) \ 3
Answer:
6
Step-by-step explanation:
In order to solve this we must use order of operations or PEMDAS.
Parentheses:
First perform operations within parentheses. In this case, do 8-2.
Now we have 8 - 6 / 3.
Exponents:
There are no exponents.
Multiplication or Division:
Divide 6 by 3.
Now we have 8 - 2.
Addition or Subtraction:
Subtract 8-2.
The answer is 6
What is the total of the Thompson’s liabilities? NEED HELP ASAP NO ROCKY
The liabilities only is 57,379
Please include work in the answer.
The answer is 3. You would just match up the sides and combine the common things. 3z times z is 3z^2 because it would be the same number twice, not times two. Then 9 times 8 is 72. Z times 8 is 8z because it would be 8 times whatever number the variable was. Then lastly it’s 9 times 3 z. You’ll multiply the 9 times 3 to get 27. Then it would be 27z. 27z and 3z^2 cannot be added together because they are preforming different things. One is multiplying by the variable another is multiplying by 3 and the the variable to the 2nd power.
if f(x)=2(x)^2+5sqrt(x+2), complete the follwoing statement ( round your answer to the nearest hundreth) : f(0)=_____
Answer:
[tex]f(0)=7.07[/tex]
Step-by-step explanation:
We have the function [tex]f(x)=2(x)^2+5\sqrt{(x+2)}[/tex]
In this case we want to find the value of f0)
To find f(0) you must replace the x in the function with the number 0 and solve as shown below
[tex]f(0)=2(0)^2+5\sqrt{(0+2)}[/tex]
[tex]f(0)=0+5\sqrt{(0+2)}[/tex]
[tex]f(0)=5\sqrt{(2)}[/tex]
Therefore
[tex]f(0)=7.07[/tex]
What is the approximate area of the triangle below?
a)72.8 sq. cm.
b)111.9 sq. cm.
c)142.0 sq. cm.
d)164.7 sq. cm.
Answer:
Option a)72.8 sq. cm.
Step-by-step explanation:
step 1
Find the measure of the third internal angle of the triangle
Remember that
the sum of the internal angles of a triangle must be equal to 180 degrees
so
95°+35°+A=180°
A=180°-95°-35°
A=50°
step 2
Applying the law of sines
Find the length side opposite to the angle of 35 degrees
14/sin(50°)=b/sin(35°)
b=[14/sin(50)]*sin(35)
b=10.48 cm
step 3
Applying the law of sines find the area of the triangle
A=(1/2)(14)(10.48)sin(95°)=73.10 cm²
therefore
The approximate area of the triangle below is 72.8 sq. cm
Answer:
72.8 sq. cm
Step-by-step explanation:
Given:
two angles and a side of a triangle that are 95°, 35° and 14 cm receptively
Area of triangle=?
Finding 3rd angle
=180-(95+35)
= 180-130
=50
Area of triangle can be calculated by using ASA i.e.
Area= a^2sinBsinC/2sinA
Putting values of a=14, B=95, C=35 and A=50, we get
Area= 14^2(sin95)(sin35)/2(sin50)
=98(0.74591)
=73.099
Closest option is a)72.8 sq. cm!
Which expression represents the distance between point (0,a) and point (a,0) on a coordinate grid?
You can always compute the distance between two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] using the pythagorean theorem:
[tex]d = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]
In your case, we have
[tex]d = \sqrt{(0-a)^2+(a-0)^2} = \sqrt{2a^2}=a\sqrt{2}[/tex]
Answer:
[tex]\sqrt{2}a[/tex]
Step-by-step explanation:
We are asked to find the distance between point (0,a) and point (a,0) on a coordinate grid.
We will use distance formula to solve our given problem.
The distance between two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by formula:
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex], where D represents distance between two points.
Let point [tex](0,a)=(x_1,y_1)[/tex] and point [tex](a,0)=(x_2,y_2)[/tex].
Substitute the values in distance formula:
[tex]D=\sqrt{(0-a)^2+(a-0)^2}[/tex]
[tex]D=\sqrt{(-a)^2+(a)^2}[/tex]
[tex]D=\sqrt{a^2+a^2}[/tex]
[tex]D=\sqrt{2a^2}[/tex]
Factor out perfect square:
[tex]D=\sqrt{2}a[/tex]
Therefore, the distance between two points would be [tex]\sqrt{2}a[/tex].
two circles have the same center one circle has the radius of 3 centimeters and the orner has a radius of 1 centimeter what is the locus of the points equidistant from the two circles?
Answer:
Step-by-step explanation:
It has to be another circle with its center as the same center as the other two.
It must be equadistant from both.
The circle must have a radius of 2 which makes it one away from the 3 cm circle and 1 away from the 1 cm circle.
Help please I can’t solve please
Answer:
d = 52 inC = 6π mm²Step-by-step explanation:
The formula of a circumference:
[tex]C=2\pi r=d\pi[/tex]
r - radius
d - diameter
We have [tex]C=52\pi\ in[/tex].
Calculate the diameter using [tex]C=d\pi[/tex]:
[tex]d\pi=52\pi[/tex] divide both sides by π
[tex]d=52\ in[/tex]
-------------------------------------------------------------------------
If a circle inscribed in a square, then the diameter of a circle and a side of a square are congruent (have the same length).
We have the area of the square:
[tex]A=36\ mm^2[/tex]
The formula of an area of a square:
[tex]A=s^2[/tex]
s - side
Substitute:
[tex]s^2=36\to s=\sqrt{36}\\\\s=6\ mm[/tex]
The formula of a circumference [tex]C=d\pi[/tex]
d - diameter
d = s → d = 6 mm
Substitute:
[tex]C=6\pi\ mm[/tex]
QUESTION 6
The growth of a population each year is given by the function f(x)=250,000(1.17)* At what percent is the population growing each year?
A. 250,000%
B. 1.17%
C. 292,500%
D. 17%
Answer:
Option D. 17%
Step-by-step explanation:
we have
[tex]f(x)=250,000(1.17)^{x}[/tex]
This is a exponential function of the form
[tex]f(x)=a(b)^{x}[/tex]
where
a is the initial value
b is the base
In this problem
a=250,000 people
b=1.17
Remember that
b=1+r
so
1+r=1.17
r=1.17-1=0.17
Convert to percentage
0.17*100=17%
volume of cylinder with radius of base 7cm is 102cm³.what will be the volume of cone having same radius of base and same height
3 I believe the answer
simply (6^5/7^3) ^2
[tex]\bf \left( \cfrac{6^5}{7^3} \right)^2\implies \left( \cfrac{6^{5\cdot 2}}{7^{3\cdot 2}} \right)\implies \cfrac{6^{10}}{7^6}\implies \cfrac{60466176}{117649}\implies 513\frac{112239}{117649}[/tex]
Solve: a^2+4(3+a)
a=5
Answer:
57
Step-by-step explanation:
[tex] {a}^{2} + 4(3 + a)[/tex]
[tex] {5}^{2} + 4(3 + 5)[/tex]
[tex]25 + 12 + 20[/tex]
[tex]57[/tex]
find the equation!!! asap. 10 points
Answer:
[tex]y=\frac{1}{60}x^2[/tex]
Step-by-step explanation:
The focus of the parabola is (0,15)
and the directrix is y=-15.
The equation of this parabola is given by:
[tex]x^2=4py[/tex]
The vertex of this parabola is at the origin (0,0)
The value of p is the distance from the vertex to the focus.
p=15-0=15
The equation of the parabola is
[tex]x^2=4(15)y[/tex]
[tex]x^2=60y[/tex]
Or
[tex]y=\frac{1}{60}x^2[/tex]
sandra brings cheese and crakers for lunch every 6 days, and lily brings cheese and crakers every 8 days. if they both brought cheese and crakers today, how many days will it be before both girls bring cheese and crakers again
Answer:
24 Days
Step-by-step explanation:
The smallest common multiple of 6 and 8 is 24. Therefore, both girls will bring cheese and crackers for lunch on the same day 24 days from today.
Explanation:This question is about finding the least common multiple (LCM) of the two numbers. Sandra brings cheese and crackers for lunch every 6 days and Lily every 8 days. The first step in solving this problem is to list the first few multiples of each number to find the smallest number that both numbers have in common.
So, for Sandra, the multiples of 6 are 6, 12, 18, 24, 30, 36, etc. And for Lily, the multiples of 8 are 8, 16, 24, 32, 40, etc. The least common multiple of 6 and 8 is 24.
Therefore, it will be 24 days before both Sandra and Lily bring cheese and crackers for lunch on the same day again.
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There are 75 houses in the troll's street. If in every 4th house there is a pink troll, a blue troll in every 6th house and a yellow troll in every 8th house, then in how many houses are there all of pink, blue and yellow trolls?
Answer:
3 houses have all pink, blue, and yellow.
Answer:
The answer is 3 houses.
Step-by-step explanation:
This question is based on the Least Common Multiple (LCM) method. We will find the LCM of the numbers 4, 6 and 8.
4 = 2 x 2 = [tex]2^{2}[/tex]
6 = 2 x 3 = 2 x 3
8 = 2 x 2 x 2 = [tex]2^{3}[/tex]
So, LCM is = [tex]2^{3}\times3=24[/tex]
Therefore, at every 24th houses, we will find all three trolls colors.
And 24 is the number of houses we will find all color trolls. Then in a group of 75 houses, it will occur thrice and at every 24th place. Means. 3 houses will have all color trolls.
45% as fraction in the simplest form
Answer:9/20
Step-by-step explanation: 45/100=9/20, 45÷5=9, 100÷5=20 both the denominater and the numerator are divisible by 5.
To write a percent as a fraction in lowest terms, first remember that a percent is a ratio that compares a number to 100. 45% can be written as the ratio 45 to 100 or 45/100. Notice however that 45/100 is not in lowest terms so we need to dive both the numerator and denominator by the greatest common factor of 45 and 100 which is 5.
45 ÷ 5 = 9
100 ÷ 5 = 20
Therefore, 45% can be written as the fraction 9/20.
x/8 = 13. what does X equal?
Answer:
x equal 104
Step-by-step explanation:
since 8 needs to go into something 13 times we can multiply
8 x 13 to get
104
104 divided by 8
equals 13
Answer:
x=104
Step-by-step explanation:
x/8 = 13
Multiply each side by 8
x/8 *8 = 13*8
x = 104
Need to find the value of y
Answer:
√55
Step-by-step explanation:
Notice that the small triangle in the bottom corner shares an angle with the overall triangle. Also, they are both right triangles. Therefore, they are similar triangles.
Notice that the large triangle at the top shares an angle with the overall triangle and is also a right triangle. Therefore it is also similar to the overall triangle and the smaller triangle.
Writing a proportion between the small and large triangles:
y / 11 = 5 / y
y² = 55
y = √55
negative two and one thirds minus negative five
If your "and" means multiplication than:
[tex]-2\times\frac{1}{3}-(-5) \\
\frac{-2}{3}+5 \\
\frac{-2+15}{3} \\
\boxed{\frac{13}{3}\approx4.33\dots}
[/tex]
If it is a logical and than we are unable to solve the problem since you didn't provide any variables that would have a meaningful values.
Hope this helps.
1) Name a pair of complementary angles. 2)Name a pair of vertical angles. 3)Name a pair of supplementary angles.
Answer:
1)m<AOB,m<BOC
2)m<EOD,m<AOB
3)m<AOE,m<EOD
Step-by-step explanation:
Complementary Angles-either of two angles whose sum is 90°.
Vertical Angles-each of the pairs of opposite angles made by two intersecting lines.
Supplementary Angles-either of two angles whose sum is 180°.
Answer:2 and 5
Step-by-step explanation:
What is 1/8 of 480? Make sure it is fully reduced as well
1/8 of 480 is 480 ÷ 8
480/80 is 60
Answer ^^^^
The Answer Would Be 60
Fishing rods are discounted at 50% off the regular price of $25. How much money will be saved?
Answer:
$12.50
Step-by-step explanation:
Books at a library sale are sold for $3.50 each. A function, y = 3.50x can be used to generate an input/output table for this scenario. Which statement is true about an accurate graph of this data?
The data is discrete, so the points are connected with a line.
The data is discrete, so the graph is a series of unconnected points.
The data is continuous, so the graph is a series of unconnected points.
The data is continuous, so it does not matter whether or not the points are in a line.
Using the concept of discrete and continuous variables, the correct option is given by:
The data is discrete, so the graph is a series of unconnected points.
What are continuous and discrete variables?Continuous variables: Can assume decimal values.Discrete variables: Assume only countable values, such as 0, 1, 2, 3, …In this problem, the input is the number of books, which is a countable amount, that is, discrete, hence the graph is a series of unconnected points.
The graph is given at the end of the answer.
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Someone help me with this pls
Solve the equation of exponential decay.
A website had 342,000 hits in 2011. This is a decline of 2.3% from the previous year. Assuming this continued how many hits would the website get in 2019? Round to the nearest thousand.
Answer:
There will be approx 283908 hits.
Step-by-step explanation:
A website had 342,000 hits in 2011.
This is a decline of 2.3% from the previous year.
Decline rate = 2.3% or 0.023
So, increase rate will be [tex]1-.023=0.977[/tex]
Time = [tex]2019-2011=8[/tex]
We can calculate the answer as:
[tex]342000\times(0.977)^{8}[/tex]
= [tex]342000\times0.83014[/tex]
= 283907.88 rounding to 283908.
Therefore, there will be approx 283908 hits.
How many solutions does the equation -2y+2y+3=3have?
Cancel 3 on both sides
-2y + 2y = 0
Simplify -2y + 2y to 0
0 = 0
Since both sides are equal, there are infinitely many solutions;
= Infinitely Many Solutions
| What is the factored form of 2x2 – 200 ?
Answer:
2(x - 10)(x + 10)
Step-by-step explanation:
Given
2x² - 200 ← factor out 2 from each term
= 2(x² - 100) ← x² - 100 is a difference of squares and factors as
x² - 100 = x² - 10² = (x - 10)(x + 10), hence
2x² - 200 = 2(x - 10)(x + 10)
Answer:
Step-by-step explanation:
If your equation is [tex]2x^2-200[/tex] and you're to factor it, the first thing you do is set the expression equal to 0 so you can solve for x.
[tex]2x^2-200=0[/tex]
There's a couple of different ways in which to approach this. You can factor out a 2:
[tex]2(x^2-100)=0[/tex]
and solve it from there. The Zero Product Property says that if the equation is equal to 0, then either 2 has to equal 0 or [tex]x^2-100[/tex] has to equal 0. We know that 2 does not equal 0, so [tex]x^2-100=0[/tex]
Add 100 to both sides in the equation:
[tex]x^2=100[/tex]
and then take the square root of both sides. Because this is a second degree polynomial, we expect to have 2 solutions, and we do. Don't forget that when you take the square root of a number you have to alow for both the positive and the negative of the result. Our factored form of the given equation then is that x = 10 and x = -10.
Question 18.
A population of students in a summer program for students in
grades kindergarten to grade 8 is surveyed. Which statement
demonstrates sampling variability?
A.
In one random sample chosen from the population, the
mean age was 9.4 years. In another random sample, the
mean age was 9.8 years.
B. In one random sample chosen from the population, the
mean age was identical to that from another random sample.
C. The mean age of the population is 8.8 years, and the mean
age from a random sample was 9.2 years.
D.In one random sample chosen from the population, the
mean age was 9.4 years.
Answer: c
Step-by-step explanation:
sampling variability is the difference between the measured value of the random sample and the mean age of the population
Option A demonstrates sampling variability because the mean age changes between two random samples chosen from the same population, illustrating the concept of sampling variability in statistics.
Explanation:The subject of this question is a concept in statistics known as sampling variability. Sampling variability refers to the idea that the statistics of a random sample of a population (like mean, median, etc.) will vary from one sample to another. In essence, if we were to keep pulling samples from the same population, it's expected that our sample statistics will not always be the same.
In this context, the statement that demonstrates sampling variability is Option A: 'In one random sample chosen from the population, the mean age was 9.4 years. In another random sample, the mean age was 9.8 years.'. This demonstrates sampling variability because the mean age changes (varies) depending on the sample chosen from the population.
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What is the solution to the system of equations below?
y= 4x+6 and Y= 2x-4
0 (-8, 2)
(-8,-1)
(8, 10)
(8, -10
The solution to the system of equations y=4x+6 and y=2x-4 is (-5, -14) by solving the equations simultaneously.
Explanation:The solution to the system of equations y = 4x + 6 and y = 2x - 4 is found by setting the two equations equal to each other since they both equal y. This gives us 4x + 6 = 2x - 4. By subtracting 2x from both sides, we get 2x + 6 = -4. Subtracting 6 from both sides gives us 2x = -10. Dividing both sides by 2 gives us x = -5. Substitute x = -5 into either original equation to find y. Let's use the first equation: y = 4(-5) + 6, which simplifies to y = -20 + 6, and finally y = -14. Hence, the solution to the system of equations is (-5, -14).