The function increased at the highest rate in the interval [1/8, 1/2], as can be seen from the function value and its interval values.
What is maxima and minima?A function's maxima and minima are its highest and lowest values, respectively, either on the entire domain or inside a certain range. They are referred to as the function's extrema collectively. The plural forms of maximum and minimum for a function are respectively known as maxima and minima.
Why do we use maxima and minima?The extreme values of a function—their maximum and minimum values—are referred to by the words maxima and minima. Maximum refers to the maximum value or amount that is feasible. A function's biggest value within its range is known as its absolute maximum.
According to the given information we have:f(x)=6log2x-3
For the interval x ∈[2, 6]
f(x) ∈ [-0.678, 3]
For the interval x ∈ [1/8, 1/2]
f(x) ∈ [ -9.96, -5.32]
For the interval x ∈ [1, 2]
f(x) ∈ [-3, -0.67]
For the interval x∈ [1/2, 1]
f(x) ∈ [-5.32, -3]
The function increased at the highest rate in the interval [1/8, 1/2], as can be seen from the function value and its interval values.
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How many fruits did Anna get?
Answer: Anna got 30
Step-by-step explanation: 2x+3y=25
15+10=25
A yoga studio sells monthly memberships. the function f(x) = −x2 50x − 264 models the profit in dollars, where x is the number of memberships sold. determine the zeros, and explain what these values mean in the context of the problem.
The zeros represent the number of monthly memberships where no profit is made; x = 6, x = 44.
To determine the zeroes, calculate:The function we have is: [tex]f(x) = -x^{2} +50x-264[/tex]
That models the profit in dollars, where [tex]x[/tex] is the number of memberships sold.
In order to get the zeros we'll use the quadratic formula:
[tex]x_{1,2} =\frac{-b+-(b^{2}-4ac) }{2a} \\[/tex]
For,
[tex]a=-1,b=50,c=-264: x^{1,2} =\frac{-50+-\sqrt[]{50^{2} -4(-1)(-264)} }{2(-1)} \\x_{1} =\frac{-50+\sqrt[]{50^{2} -4(-1)(-264)} }{2(-1)} =\frac{-50+\sqrt[]{50^{2} -4*1*264} }{2(-1)}=\frac{-50+\sqrt[]{1444} }{-2} =6\\x_{2} =\frac{-50+\sqrt[]{50^{2} -4(-1)(-264)} }{2(-1)} =\frac{-50-\sqrt[]{50^{2} -4*1*264} }{2(-1)}=\frac{-50-\sqrt[]{1444} }{-2} =44\\[/tex]
So, the zeroes are [tex]x=6, x=44[/tex].
Therefore, the zeros represent the number of monthly memberships where no profit is made; x = 6, x = 44.
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The complete question is given below:
A yoga studio sells monthly memberships. The function f(x) = −x2 + 50x − 264 models the profit in dollars, where x is the number of memberships sold.
Determine the zeros, and explain what these values mean in the context of the problem.
x = 6, x = 44; The zeros represent the number of monthly memberships that produce a maximum profit.
x = 6, x = 44; The zeros represent the number of monthly memberships where no profit is made.
x = 25, x = 361; The zeros represent the number of monthly memberships where no profit is made.
x = 25, x = 361; The zeros represent the number of monthly memberships that produce a maximum profit.
Answer:
The answer is: x = 6, x = 44; The zeros represent the number of monthly memberships when no profit is made.
what is the general form of the equation for the given circle?
The general equation for a circle is [tex](x-h)^2+(y-k)^2=r^2[/tex], where [tex](h,k)[/tex] is the centre of the circle and [tex]r[/tex] is the radius.
Solving the QuestionFirst, we can determine the centre of the circle.
( _ , _ )
The point directly on top is (4,7). Because it lies on the same vertical line as the centre, they have the same x-coordinate.
(4, _ )
The point directly to the right of it is (7,4). Because it lies on the same horizontal line as the centre, they have the same y-coordinate.
(4,4)
Therefore, the centre of the circle is (4,4). Plug this into the general equation:
[tex](x-h)^2+(y-k)^2=r^2\\(x-4)^2+(y-4)^2=r^2[/tex]
Now, we can determine the radius of the circle.
To do this, we can calculate the distance between the centre of the circle and one of the given points that lie on the circumference.
The centre is (4,4), and one of the points is (4,7). Because they only have a difference of 3 units in the y-direction (and none in the x-direction), this means that the radius is 3 units. Plug this into the general equation:
[tex](x-4)^2+(y-4)^2=r^2\\(x-4)^2+(y-4)^2=3^2\\(x-4)^2+(y-4)^2=9[/tex]
Answer[tex](x-4)^2+(y-4)^2=9[/tex]
If the maximum payment of $5,000 is made into a individual retirement account (ira) for 25 years at an annual interest rate of 3.2%, determine the amount in the account.round to the nearest cent. a. $187,159.62 b. $193,148.73 c. $129,082.99 d. $129,427.21
The amount in the ira's account s = $187,159.62.
How do you interest rate?
The interest rate is the amount a lender charges a borrower and is a percentage of the principal—the amount loaned. The interest rate on a loan is typically noted on an annual basis known as the annual percentage rate (APR).Future Value of an Ordinary Annuity
[tex]s = R(( 1 + i)^{n} - 1 ) / i[/tex]
where
S = the future value;
R = the periodic payment;
i = the interest rate per period;
n = the number of periods.
[tex]s = 5000 ( 1 + 0.032)^{25} - 1)/ 0.032[/tex]
[tex]s = 5000((1.032)^{25} - 1 )/0.032[/tex]
[tex]s = 5000( 2.19782157471 - 1)/0.032[/tex]
[tex]s = 5000(1.19782157471)/0.032[/tex]
[tex]s = 5000 * 37.4319242096[/tex]
s = $187,159.62
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amplificar la siguientes fracciones con tal que de un numero igual al final las fracciones son:
a. 1/2, 3/4, 5/10, 9/20
b. 3/8, 1/15, 3/20, 9/10
c. 7/9, 1/3, 5/6, 3/4
d.3/12, 1/5 7/15 1/20
The arrangement of the fractions given from the lowest to the highest is illustrated
How to illustrate the information?a. 1/2, 3/4, 5/10, 9/20.
We can change this to percentages.
1/2 = 1/2 × 100 = 50%
3/4 = 3/4 × 100 = 75%
5/10 = 5/10 × 100 = 50%
9/20 = 9/20 × 100 = 45%
Therefore, the arrangement will be 9/20, 5/10, 1/2, and 3/4.
b. 3/8, 1/15, 3/20, 9/10
3/8 = 37.5%
1/15 = 6.67%
3/20 = 15%
9/10 = 90%
The arrangement will be 1/15, 3/20, 3/8, and 9/10.
c. 7/9, 1/3, 5/6, 3/4
7/9 = 77.7%
1/3 = 33.3%
5/6 = 82%
3/4 = 75%
The arrangement will be 1/3, 3/4, 7/9, and 5/6.
d.3/12, 1/5 7/15 1/20
3/12 = 25%
1/5 = 20%
7/15 = 48%
1/20 = 5%
The arrangement will be 1/20, 1/5, 3/12, and 7/15.
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Let f(x) = xe−x if x ≥ 0 and f(x) = 0 if x < 0
Is f a probability density function?
Yes. [tex]f(x)[/tex] is a PDF if
• [tex]f(x) \ge 0[/tex] for all [tex]x[/tex] in the support; this is true, since [tex]e^{-x}>0[/tex] for all [tex]x[/tex], and multiplying a positive number [tex]x[/tex] doesn't change this fact;
• the integral of [tex]f(x)[/tex] over its support is 1; this is also true, since
[tex]\displaystyle \int_{-\infty}^\infty f(x) \, dx = \int_0^\infty xe^{-x} \, dx = 1[/tex]
which can be computed by parts.
Solve the given differential equation by separation of variables. dy dx = e4x 5y
The solution to the given differential equation [tex]\frac{dy}{dx} = e^{4x+5y}[/tex] is , [tex]\frac{e^{-5y}}{-5}=\frac{e^{4x}}{4} +c[/tex], where c is constant of integration.
For given question,
We have been given a differential equation [tex]\frac{dy}{dx} = e^{4x+5y}[/tex]
We know that for any real number a, m, n,
[tex]a^{m + n} = a^m \times a^n[/tex]
⇒ dy/dx = [tex]e^{4x}[/tex] × [tex]e^{5y}[/tex]
Separating the variables (x and its differential in one side and y and its differential in another side )
⇒ [tex]\frac{1}{e^{5y}}[/tex] dy = [tex]e^{4x}[/tex] dx
⇒ [tex]e^{-5y}[/tex] dy = [tex]e^{4x}[/tex] dx
Integrating on both the sides,
⇒ [tex]\int e^{-5y}[/tex] dy = [tex]\int e^{4x}[/tex] dx
We know that, [tex]\int e^{ax}\, dx=\frac{e^{ax}}{a} +C[/tex]
⇒ [tex]\int e^{4x}\, dx=\frac{e^{4x}}{4} +C[/tex]
and [tex]\int e^{-5y}\, dy=\frac{e^{-5y}}{-5} +C[/tex]
So the solution is, [tex]\frac{e^{-5y}}{-5}=\frac{e^{4x}}{4} +c[/tex], where c is constant of integration.
Therefore, the solution to the given differential equation [tex]\frac{dy}{dx} = e^{4x+5y}[/tex] is , [tex]\frac{e^{-5y}}{-5}=\frac{e^{4x}}{4} +c[/tex], where c is constant of integration.
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Home Run Derby
Data are shown below for three baseball players at a recent minor league home run hitting contest.
Juan:
The ball followed a path modelled by the equation h = −0.001! + 0.5 + 2.5 where h is the height of the ball in feet and is the horizontal distance in feet.
1) Represent the distance-height relationship for each player’s ball as an equation, in a table and on a graph. Record each representation and clearly label which player the information belongs to.
2) Supposed there were no obstacles.
a. Whose ball would travel the greatest distance before hitting the ground?
b. Whose ball would travel the shortest distance before hitting the ground?
3) Suppose the fence was 350 ft from home plate. At what height was each ball when it passed over the fence?
Juan's ball would travel the greatest distance while Barry's ball would travel the shortest.
Represent the distance-height relationship for each player’s ball as an equation, in a table and on a graph.Juan
Juan's equation is given as:
h = -0.001d^2 + 0.5d + 2.5
h =
Set d to multiples of 50 from 0 to 400.
So, the table of values of Juan's function is:
d (ft) h(ft)
0 2.5
50 25
100 42.5
150 55
200 62.5
250 65
300 62.5
350 65
400 42.5
See attachment for the graph of Juan's function
Mark
A quadratic function is represented as:
h = ad^2 + bd + c
Using the values on the table of values, we have:
c = 3 -- the constant value
So, the equation becomes
h = ad^2 + bd + 3
Using the two other values on the table of values, we have:
23 = a(50)^2 + b(50) + 3
38 = a(100)^2 + b(100) + 3
Using a graphing tool, we have:
a = -0.001
b = 0.45
So, Mark's equation is h(d) = -0.001d^2 + 0.45d + 3
See attachment for Mark's graph.
Barry
From the graph, we have the table of values of Barry's function to be:
d (ft) h(ft)
0 2.5
50 21
100 35
150 44
200 48
250 46
300 41
350 30
400 14
450 0
Using a graphing tool, we have the quadratic function to be:
y = -0.001x^2 +0.4x +2.5
The shortest and the greatest distance before hitting the groundFrom the graphs, equations and tables, the distance travelled by the balls are:
Juan = 505 feet
Mark = 457 feet
Barry = 450 feet
This means that Juan's ball would travel the greatest distance while Barry's ball would travel the shortest.
The height the balls hit a fence at 350 ft distanceTo do this, we set d = 350
From the graphs, equations and tables, the height at 350 ft by the balls are:
Juan = 65 feet
Mark = 38 feet
Barry = 30 feet
The above represents the height the balls hit the fence
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A variable that takes on the values of 0 or 1 and is used to incorporate the effect of categorical variables in a regression model is called?
A variable that takes on the values of 0 or 1 and is used to incorporate the effect of categorical variables in a regression model is called the dummy variable.
We know that,
A dummy variable is a binary variable that takes a value of 0 or 1.
In regression analysis, a dummy variable is one that takes only the value 0 or 1 to indicate the absence or presence of some categorical effect that may be expected to shift the outcome.
The number of dummy variables we must create is equal to k - 1, where k is the number of different values that the categorical variable can take on.
It is an artificial variable created to represent an attribute with two or more distinct categories/levels.
These are being used in order to sort out data into mutually exclusive groups.
It is used typically in time series analysis, response modelling, bio-medical studies, economic forecasting and credit scoring.
Therefore, a variable that takes on the values of 0 or 1 and is used to incorporate the effect of categorical variables in a regression model is called the dummy variable.
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A satellite orbits the earth at a height of 343 kilometers. if the satellite makes 8 revolutions around the earth, how many kilometers does it travel? (earth's diameter is 6371 kilometers.) use 3.14 as the approximate value of pi.
The satellite makes 8 revolutions around the earth, it passes 177272 kilometers.
How many kilometers does the satellite make 8 revolutions around the earth?
The orbital velocity of the satellite exists independent of its mass. The radius of the orbit exists as the only variable. If the satellite orbits near the planet at such a low height, its orbital speed must be extremely fast. If the orbital speed exists less than the required value, the satellite will be drawn to the earth's surface by gravity.
The satellite rotates around the earth to form a circle,
diameter of circle = Diameter of earth + 2(Height)
d = 6714 + 2(343)
d = 6714+ 686
d = 7057
Perimeter = πd
Perimeter = 3.14 (7057)
Perimeter = 22158.98
Total Revolution exists 8
Therefore, 8πd = 8(22158.98)
= 177272 kilometers.
Therefore, the satellite makes 8 revolutions around the earth, it passes 177272 kilometers.
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There are 8 players on a tennis team. The team is planning to play in a doubles tournament. How many different groups of players of 2 players can the coach make, if the position does not matter?
28
64
20,160
40,320
Using the arrangements formula, it is found that there are 20,160 different groups of players of 2 players that the coach can make.
What is the arrangements formula?The number of possible arrangements of n elements is given by the factorial of n, that is:
[tex]A_n = n![/tex]
In this problem, all 8 players will play, hence considering the order, the number of ways is:
[tex]A_8 = 8! = 40320[/tex]
However, the position does not matter, as for example, João and Elisa would form the same pair as Elisa and João, hence the removing the order, the number of groups is:
40,320/2 = 20,160.
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Answer:
The answer is 28!!!
Step-by-step explanation:
Use the combinations formula:
[tex]C = \frac{n!}{r!(n-r)!}[/tex]
n = 8
r = 2
[tex]C = \frac{8!}{2!~*~6! } = 28\\[/tex]
I got it right! Look at the pic for proof.
Hope this helps!! :)
Evaluate the expression under the given conditions. tan(2); cos() = 5 13 , in quadrant i
The solution to given expression tan(2θ) is 22.615°
For given question,
We have been given an expression tan(2θ)
Given that cos(θ) = 5/13, and θ is in quadrant 1.
We know that the trigonometric identity
sin²θ + cos²θ = 1
⇒ cos²θ = (5/13)²
⇒ sin²θ = 1 - 25/169
⇒ sin²θ = 169 - (25/169)
⇒ sin²θ = 144/169
⇒ sin(θ) = 12/13
We know that the identity cos(2x) = cos²x - sin²x
⇒ cos(2θ) = cos²θ - sin²θ
⇒ cos(2θ) = 25/169 - 144/169
⇒ cos(2θ) = -119/169
And sin(2x) = 2sin(x)cos(x)
⇒ sin(2θ) = 2sin(θ)cos(θ)
⇒ sin(2θ) = 2 × 12/13 × 5/13
⇒ sin(2θ) = 120/169
We know that, tan(x) = sin(x)/cos(x)
⇒ tan(2θ) = sin(2θ)/cos(2θ)
⇒ tan(2θ) = (120/169) / (-119/169)
⇒ tan(2θ) = 120 / (-119)
⇒ tan(2θ) = -1.008
Since θ is in quadrant 1, tan(2θ) = 1.008
⇒ 2θ = arctan(1.008)
⇒ 2θ = 45.23
⇒ θ = 22.615°
Therefore, the solution to given expression tan(2θ) is 22.615°
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Phil and ava both worked 14 hours this week. phil earned $112.70, and ava earned $113.82. ava wants to know how much more per hour she earns than phil. which strategy is appropriate for ava to use?
Answer:
Find out how much each makes per hour and then compare.
Step-by-step explanation:
Phil: 112.70/14 = 8.05 Phil makes $8.05 per hour
Eva: 113.82/1 =8.13 Eva makes $8.13 per hour
Eva makes $0.08 more an hour.
Sloane kicked a soccer ball off the ground at a speed of 48 feet per second. The height of the ball can be represented by the function H(t) = −16t2 + 48t, where t is the time in seconds. How many seconds did the ball travel before returning the ground?
If the speed of the ball after kicking is 48 feet per second then the ball will return on the ground after 3 seconds.
Given that the speed of the ball after kicking is 48 feet per second and the function that represents the height of the ball is [tex]-16t^{2} +48t[/tex].
We are required to find the time that the ball took to travel before returning the ground.
We know that speed is the distance a thing covers in a particular time period.
The height of the ball after t seconds is as follows:
h(t)=[tex]-16t^{2} +48t[/tex]
It is at ground at the instants of t.
Hence,
[tex]-16t^{2} +48t[/tex]=0
-16t(t-3)=0
We want value of t different of 0, hence :
t-3=0
t=3.
Hence if the speed of the ball after kicking is 48 feet per second then the ball will return on the ground after 3 seconds.
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Answer:
B. t=3
Step-by-step explanation:
i took the test and got it right
Write two different integers x, y, and z, and meet the following conditions. they do not all have the same sign and x-y-z=0
Two different integers are the same numbers, which have different signs.
What is integers?An integer is a number that includes negative and positive numbers, including zero. It does not include any decimal or fractional part. A few examples of integers are: -5, 0, 1, 5, 8, 97.
Given that,
x, y, and z are three integers. They follow the one condition: x-y-z = 0.
Any number in the number system that has only two signs, either + or -, So we consider that the third integer is 0 because 0 is a whole number that has neither a positive nor a negative sign.
The remaining two integers are the same numbers, but they have different signs to follow the given condition.
x-y-z = 0
x = y+z
Let y,z are the same numbers, They have different signs and x = 0.
Note: The value of x is always negative and y's value is always positive.
Example:
x = 0, y = +6, z = -6
x-y-z = 0
x = y+z
0 = +6-6
0 = 0
Hence, two different integers are the same numbers, which have different signs.
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Rhett is solving the quadratic equation 0= x2 – 2x – 3 using the quadratic formula. which shows the correct substitution of the values a, b, and c into the quadratic formula? quadratic formula: x = startfraction negative b plus or minus startroot b squared minus 4 a c endroot over 2 a endfraction
Answer:
Step-by-step explanation:
0= x2 – 2x – 3
a = 1, b = -2 and c = -3.
Answer:
A on edge
Step-by-step explanation:
Give me the brainiest please
In circle D, which is a secant?
EF
DC
Line segment A B
Line G H
The secant of circle D is the 'line GH'. Where the line segment EF is the diameter of the circle, line segment DC is the radius, and the ray AB is the tangent of the given circle.
What is the secant of the circle?The line that passes through the circle and touches the circle at two points is said to be a secant line of the circle.
Which is the secant line in the given circle D?The given circle D has a center at D.
The radius of the circle is given by the line segment CD
The diameter (or) the longest chord of the circle is given by the line segment EF
The ray AB passes touches the circle at point B, which is called the tangent of the circle.
Where the line GH passes through the circle and touches at two points. So, this line GH is said to be the secant of the circle.
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Disclaimer: The given question is incomplete(needs a diagram). Here is the required diagram attached.
Question: In circle D, which is a secant?
a) EF
b) DC
c) Line segment AB
d) Line GH
Answer:
ray ab
Step-by-step explanation:
A 6-sided die is rolled. what is the probability of rolling a number less than 4?
1/2
Step-by-step explanation:
All outcomes of a single die= 6
Events less than 4 =3
probability=3/6
=1/2
Select the correct answer. which expression shows the factors of 5x2 17x 6? a. (5x 1)(x 6) b. (5x 2)(x 3) c. (5x 3)(x 2) d. (5x 6)(x 1)
Answer:
B. (5x + 2)(x + 3)
Step-by-step explanation:
5x times x = 5x^2
5x times 3 = 15x
2 times x = 2x
2 times 3 = 6
15x + 2x = 17x
5x^2 + 17x + 6
P.S. next time please word your question better. Took me a while you meant "5x^2 plus 17x plus 6", since your equation reads "5 times 2 BLANK 17 times 6".
Consider the complex number z = 27i. what are the characteristics of the cube roots of z? use the drop-down menus to complete each sentence. the cube roots are located on a circle with center at the pole and radius of . the cube roots have arguments which differ by π over 3.
The drop-down menu will be 3 and 2.
What is the complex number?Real and imaginary numbers combine to form complex numbers with two components. Complex numbers serve as the foundation for more complex math, including algebra. They have various practical applications, particularly in electronics and electromagnetism.The complex number z = 27i.
The radius of the cube root is: [tex]r\sqrt[3]{x}[/tex]
[tex]r\sqrt[3]{27}[/tex]
[tex]r=3[/tex]
Cube roots are located in a circle with a center at the origin and a radius of 3 units.
The complex number,z=a+ib is; Θ = tan⁻¹(b/a)
The complex number z=0+27i is:
Θ = tan⁻¹(27/0)
Θ = π/2
Cube roots have more than 3 arguments that differ by 2 π.
Therefore, The drop-down menu will be 3 and 2.
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The cube roots exist found on a circle with a center at the origin and a radius of 3. The cube roots contain arguments that vary by 2π over 3.
What is the complex number?A complex number is one that has both a real and an imaginary component, both of which are preceded by the letter I which stands for the square root of -1.
The given complex number as;
z = 27i
The radius of the cube root is found as;
r = ∛x
substituting the values in the above equation, we get
r = ∛27
r = 3
The cube roots are located on a circle with a center at the origin and a radius of 3 units.
The argument of a complex number, z = a+ib will be
[tex]\theta[/tex] = tan⁻¹(b/a)
The argument of a complex number z = 0+27i
[tex]\theta[/tex] = tan⁻¹(27/0)
[tex]\theta[/tex] = π/2
The cube roots have arguments that differ by 2π over 3.
Therefore, the correct answer for the drop-down menu exists in 3 and 2.
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Andre says that [tex]log_10(55)=1.5[/tex] because 55 is halfway between 10 and 100. Do you agree with Andre? Explain your reasoning.
I know that answer is false, but I don't know how to explain!!
[tex]\textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{lllllllll} \log_{\underline{10}}(10)=1&\implies &\underline{10}^1=10 ~~ \checkmark\\\\ \log_{10}(100)=2&\implies &10^2=100~~ \checkmark\\\\ \log_{10}(55)=1.5&\implies &10^{1.5}=55\implies 10^{\frac{3}{2}}=55\implies \sqrt[2]{10^3}=55\\\\ &&\sqrt{1000}\ne 55 ~~ \bigotimes \end{array}[/tex]
increments over the exponent, are not directly proportional to increments on the resulting values, namely the half-way from 10² and 10⁴ is not 10³, because 10⁴ is 100 times 10², and 10³ is simply 10 times 10².
The roots of the quadratic equation x 2 − 51x + k = 0 differ by 75, where k is a real number. Determine the sum of the squares of the roots
The sum of the squares of the root is 4113
In a quadratic equation ax² + bx + c , the sum of the roots is -b/a and the product of the roots is c/a
Let m, n be roots of the given equation.
So,
m - n = 75 -1)
m + n = 51 (as sum of roots of a quadratic equation is -b/a) -2)
adding both equations 1) and 2)
2m = 75 + 51
2m = 126
m = 63
substituting value of m in equation 1 we get
63 - n = 75
n = -12
So the sum of squares of the roots of the equation is = 63² + -12²
= 3969 + 144
= 4113
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need help!! (check picture)
Answer:
N = 2.1
M = 4.5
Step-by-step explanation:
<p is 25 degrees. I know this because the exterior angle of p corresponds with 155. Since this is a straight angle, angle p must be 25 (180-155). Now I can use the cos and the sin of 25 to find M and N
sin 25 = N/5 multiply both sides by 5 to get
5 sin 25 = N Use your calculator put in 5 sin 25
2.1 rounded to the nearest tenth.
cos 25 = M/5 Multiply both sides by
5 cos 25 = M Use your calculator
4.5
I need help, pls and thx
The solutions for the quadratic equation are given as follows:
x = -1, x = 7/5
What is a quadratic function?A quadratic function is given according to the following rule:
y = ax^2 + bx + c
The solutions are:
[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex][tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]In which:
[tex]\Delta = b^2 - 4ac[/tex]
For this problem, the equation is:
5x² - 2x - 7 = 0.
Hence the coefficients are a = 5, b = -2 and c = -7, and then the solutions are found as follows:
[tex]\Delta = (-2)^2 - 4(5)(7) = 144[/tex][tex]x_1 = \frac{2 + \sqrt{144}}{10} = \frac{7}{5}[/tex][tex]x_2 = \frac{2 - \sqrt{144}}{10} = -1[/tex]The solutions are:
x = -1, x = 7/5
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The height of water shooting from a fountain is modeled by the function f(x)= -4x^2 +24x -29 where access to distance from the spot in feet. complete the square to determine the maximum height of the path of the water.
By the use of the completing the square method, the maximum height of the path of the water 3 ±√29/4 + 9 m.
What is called distance?
Distance is a numerical measurement of how far apart objects or points are. The distance between two points is the length of the path connecting them.In everyday usage, distance may refer to a physical length or an estimation based on other criteria (e.g. "two counties over"). The distance from a point A to a point B is sometimes denoted as. .h = -4x² +24x -29
Now we have;
0 = -4x² +24x -29
-4x² +24x -29= 0
x² - 6x = -29/4
(x - 3)² = -29/4 + 3²
(x - 3)² = -29/4 + 9
x = 3 ±√29/4 + 9 m
Therefore, the maximum height of the path of the water x = 3 ±√29/4 + 9 m
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In a mathematics class, half of the students scored 79 on an achievement test. With the exception of a few students who scored 49, the remaining students scored 78. Which of the following statements is true about the distribution of scores?
Option C. The mean is less than the median in the distribution of the scores.
How to solve for the medianThe median is given as 79 + 78 / 2
= 78.5
The mode is 79 this is the number that has the highest frequency in the data.
The median is 78.5 this is the middle number in the set of scores of these students.
Hence the mean is less than the mode and the median given that it was it was brought down by the few scores of 49.
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For each of the number lines, write an absolute value equation that has the following solution set. 26 and m
On a number line, an absolute value equation that has the given solution set is |m - 4| = 2.
How to write the absolute value equation?By critically observing the given question, we can infer and logically deduce that the solution sets for this absolute value equation is given by:
m = {2, 6}
Next, we would calculate the mean of the solution sets as follows:
m₁ = (2 + 6)/2
m₁ = 8/2
m₁ = 4.
Also, we would calculate the difference in the solution sets as follows:
m₂ = (6 - 2)/2
m₂ = 4/2
m₂ = 2.
Mathematically, the absolute value equation is given by:
|m - m₁| - m₂ = 0
|m - 4| - 2 = 0
|m - 4| = 2.
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anyone think they can help me??
The kind of transformation that is illustrated based on the information given is reflection.
What is transformation?It should be noted that transformation simply means the change in the position of an object while maintaining the length and other properties.
In this case, the kind of transformation that is illustrated based on the information given is reflection.
This is the flipping of the pre image and then producing the mirror image.
Here, there'll be no change in the shape of the size. This depicts congruency.
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How old is David
please help me
Answer: 25 ?
Step-by-step explanation:
Consider the steps to solve the equation. 2 5 ( 1 2 y + 20 ) − 4 5 = 9 20 (2y − 1)
Distribute: 1 5 y + 8 − 4 5 = 9 10 y − 9 20
What is the next step after using the distributive property?
*Use the multiplication property of equality to isolate the variable term on one side of the equation.
*Use the multiplication property of equality to isolate the constant on one side of the equation.
*Combine the like terms on the right side of the equation.
*Combine the like terms on the left side of the equation.
Answer:
D
Step-by-step explanation:
I did the assignment
hope this helps :)
