To find three positive integers x, y, and z that satisfy the given conditions, we need to use the concept of maximizing a function subject to certain conditions. Solving for y and z, we have y = 15 and z = 16.
In this case, we want to maximize the function P= xy^2z, subject to the condition that the sum of x, y, and z is 32.
To maximize P, we need to find the values of x, y, and z that make P as large as possible. One way to do this is to use the method of Lagrange multipliers, which involves finding the critical points of a function subject to a constraint.
In this case, we have the function P= xy^2z and the constraint x+y+z=32. Using Lagrange multipliers, we can set up the following equations:
∂P/∂x = λ∂(x+ y+ z)/∂x
y^2z = λ
∂P/∂y = λ∂(x+ y+ z)/∂y
2xyz = λ
∂P/∂z = λ∂(x+ y+ z)/∂z
xy^2 = λ
x+y+z=32
Solving these equations simultaneously, we get:
y^2z/x = 2xyz/y = xy^2/z = λ
Simplifying, we get:
y^2z/x = 2yz = xy^2/z
Rearranging, we get:
x = 2y^3/z
y = (x/2z)^(1/3)
z = (x/4y^2)^(1/3)
Substituting these expressions for x, y, and z into the constraint x+y+z=32, we get:
2y^3/z + (x/2z)^(1/3) + (x/4y^2)^(1/3) = 32
Solving this equation for x, y, and z, we get:
x = 16
y = 4
z = 2
Therefore, the three positive integers x, y, and z that satisfy the given conditions are x=16, y=4, and z=2. These values make P= xy^2z a maximum, since any other values of x, y, and z that satisfy the constraint x+y+z=32 would yield a smaller value of P.
To find three positive integers x, y, and z that satisfy the given conditions, we need to consider the following:
1. The sum of x, y, and z is 32: x + y + z = 32
2. The product P = xy^2z is a maximum.
First, let's express z in terms of x and y using the sum condition:
z = 32 - x - y
Now, substitute this expression for z into the product P:
P = xy^2(32 - x - y)
To maximize P, we should make y as large as possible, since it has the largest exponent in the product formula. Let's allocate the majority of the remaining sum to y. For example, if x = 1, we get:
1 + y + z = 32
Solving for y and z, we have y = 15 and z = 16. Now let's check the product:
P = (1)(15^2)(16) = 3600
This is one possible solution for x, y, and z that gives a maximum product P with the given conditions. The three positive integers are x = 1, y = 15, and z = 16, and the maximum product P = 3600.
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The radius of a circle measures 7 inches. A central angle of the circle measuring 4π15 radians cuts off a sector.
What is the area of the sector?
Enter your answer, as a simplified fraction
The area of sector is 14π/3 square inches for a circle having a radius of 7 inches and measures an angle of 4π/15 radians.
Radius of circle = 7 inches
Angle of circle = 4π/15 radians
The area of a sector of a circle can be calculated by using the formula:
A = (θ/2) × [tex]r^2[/tex]
A = The area of the sector
θ = central angle in radians
r = radius of the circle.
Substituting the given values in the formula:
Area = (θ/2) × [tex]r^2[/tex]
Area = (4π/15 × 1/2) × [tex]7^2[/tex]
Area= (2π/15) × 49
Area = 14π/3
Therefore, we can conclude that the area of the sector is 14π/3 square inches.
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What’s my gpa?
For school
Answer:
2.2
Step-by-step explanation:
To find your GPA, use the attached image:
After you've written down your numerical scores, divide it by the total classes you're taking, which is 7.
So, your GPA is 2.2
Gilberto Brought $36. 50 to the state fair. He bought a burger a souvenir and a pass. The burger was 1/3 as much as the souvenir and the souvenir cost 1/2 the cost of the pass. Gilberto had $4. 00 left over after buying these items
Gilberto brought $69.00 to the state fair.
How much money did Gilberto bring to the state fair originally?Let's start by assigning variables to represent the unknown values in the problem:
Let x be the cost of the pass.The cost of the souvenir is half the cost of the pass, so the souvenir costs (1/2)x.The cost of the burger is 1/3 the cost of the souvenir, so the burger costs (1/3)(1/2)x = (1/6)x.According to the problem, the total amount spent by Gilberto is equal to $36.50, so we can set up an equation:
x + (1/2)x + (1/6)x = 36.5
Simplifying the equation, we can combine the like terms:
(5/6)x = 36.5
To solve for x, we can multiply both sides by the reciprocal of 5/6:
x = 36.5 / (5/6) = $43.80
So the cost of the pass is $43.80. Using the values we assigned earlier, we can find the cost of the souvenir and the burger:
The souvenir costs half the cost of the pass, which is (1/2)($43.80) = $21.90.The burger costs 1/3 the cost of the souvenir, which is (1/3)($21.90) = $7.30.Therefore, Gilberto spent $43.80 on the pass, $21.90 on the souvenir, and $7.30 on the burger, for a total of $43.80 + $21.90 + $7.30 = $73.00.
However, we are also told that Gilberto had $4.00 left over after buying these items.
So we can subtract that from the total amount spent to get the initial amount of money that Gilberto brought to the fair:
$73.00 - $4.00 = $69.00
Therefore, Gilberto brought $69.00 to the state fair.
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Center: (2, 8) radius: 3
What is the equation of a circle with the center and radius given?
Olivia and her friends went to a movie at 1:50 P.M. The movie ended at 4:10 P.M. How long was the movie?
Answer: The movie was 2 hours and 20 minutes long.
Step-by-step explanation:
basic adding + subtracting
The aquarium has a fish tank in the shape of a prism. if the tank is 3/4 full of water, how much water is in the tank?
The amount of water in the tank can be calculated by multiplying 3/4 to the volume of the tank: 3/4 x V = (3/4)L x W x H.
To calculate the amount of water in the aquarium's fish tank in the shape of a prism,
you would need to know the dimensions of the tank and then multiply the volume of the tank by 3/4.
Let's assume that the aquarium has a rectangular prism shape,
the amount of water in the tank would depend on the dimensions of the tank.
Let's assume the tank has a length of L, a width of W, and a height of H.
The volume of the tank can be calculated by multiplying the length, width, and height together: V = L x W x H.
If the tank is 3/4 full of water, the volume of water in the tank would be 3/4 of the total volume of the tank.
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Proctor & Gamble claims that at least half the bars of Ivory soap they produce are 99. 44% pure (or more pure) as advertised. Unilever, one of Proctor & Gamble's competitors, wishes to put this claim to the test. They sample the purity of 146 bars of Ivory soap. They find that 70 of them meet the 99. 44% purity advertised.
What type of test should be run?
t-test of a mean
z-test of a proportion
The alternative hypothesis indicates a
right-tailed test
two-tailed test
left-tailed test
Calculate the p-value.
Does Unilever have sufficient evidence to reject Proctor & Gamble's claim?
No
Yes
The test that should be run on the claim by Proctor & Gamble should be B. z-test of a proportion.
The alternative hypothesis indicates a c. left-tailed test.
The p - value is 0.2665. Unilever does not have sufficient evidence to reject Proctor & Gamble's claim, so A. no.
How to test the claim ?Conducting a z-test of a proportion is necessary in light of the proportion-based nature (at least half of the bars being 99.44% pure) of the inquiry, instead of means. Proctor & Gamble had asserted that over fifty percent of their bars exhibit 99.44% purity or better; Unilever wishes to investigate this assertion's accuracy.
Consequently, we run our test under null-hypothesis framework that considers fifty percent of bars possessing sufficient purity level and alternative hypothesis positing <50% do. The resultant course of action entails carrying out a left-tailed test.
The p - value. Find the test statistic:
z = ( 0. 4795 - 0.5) / √ ( ( 0.5 x (1 - 0.5) ) / 146)
z = - 0. 6236
z- table shows the p - value is 0. 2665 as a result.
With the p - value being higher than the normal significant level of 0. 05, Unilever should not reject Proctor & Gamble's claim.
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3. Let ya if (x,y) + (0,0) f(x,y) = x2 + y 0 if x=y=0. lim f(x,y) exist? Verify your claim. (x,y)+(0,0) (a) Does
Since the function approaches the same value (0) along both paths, we can claim that the limit lim(x,y)→(0,0) f(x,y) exists and is equal to 0.
Your question is asking whether the limit of the function f(x,y) exists at the point (0,0). The function f(x,y) is defined as:
f(x,y) = x^2 + y if (x,y) ≠ (0,0)
f(x,y) = 0 if x = y = 0
To verify whether the limit exists, we need to check if the function approaches a unique value as (x,y) approaches (0,0). In other words, we need to determine if lim(x,y)→(0,0) f(x,y) exists.
To verify this claim, consider the function along different paths towards (0,0). Let's examine two paths:
1) x = 0: As x approaches 0, f(0,y) = y, and the limit becomes lim(y→0) y = 0.
2) y = x: As y approaches 0 along this path, f(x,x) = x^2 + x, and the limit becomes lim(x→0) (x^2 + x) = 0.
Since the function approaches the same value (0) along both paths, we can claim that the limit lim(x,y)→(0,0) f(x,y) exists and is equal to 0.
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Which statement about the function is true? the function is increasing for all real values of x where x < –4. the function is increasing for all real values of x where –6 < x < –2. the function is decreasing for all real values of x where x < –6 and where x > –2. the function is decreasing for all real values of x where x < –4.
The function is increasing for all real values of x where x < –4.
How does the function behave for different values of x?The statement that is true about the function is: "The function is decreasing for all real values of x where x < -4."
In order to determine the behavior of the function, we look at the given options. Among the options, the only statement that aligns with the function being decreasing is the one that states the function is decreasing for all real values of x where x < -4.
If a function is decreasing, it means that as the value of x decreases, the value of the function also decreases. In this case, it indicates that as x becomes more negative, the function's values decrease.
Therefore, the statement that correctly describes the behavior of the function is that it is decreasing for all real values of x where x < -4.
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Fernando fue a comprar entradas para que él y
sus 7 amigos asistan a la Expo-Loncoche que
se realiza en La ciudad del mismo nombre.
Entre todos lograron reunir $14. 000, pero cada
entrada cuesta $ 3. 600 ¿Cuánto dinero le falta
a cada uno para comprar las entradas?
After evaluation each person is missing $1400 to purchase the tickets to enter the Expo-Loncoche that takes place in the city.
Then, the count of individuals multiplied by the price per ticket yields the total cost of the tickets. So we have to apply principles of algebraic expression.
Now, in order to solve the problem, we can first find the total cost of tickets, which is $25,200
(7 friends + Fernando = 8 people × $3,600 = $28,800).
The whole cost can then be deducted from the total amount raised,
$14,000 - $25,200 = -$11,200.
Therefore, they are short $11,200 in total.
Finally, we have to divide that sum by the required number of tickets, which is 8,
-$11,200 8 = -$1,400.
Hence, each person needs an additional $1,400 to buy tickets.
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The Complete question - Fernando went to buy tickets so that he and his 7 friends attend the Expo-Loncoche that takes place in the city of the same name. Together they managed to raise $14,000, but each the entrance costs $3,600. How much money is missing each to buy tickets?
help me please i legit need help with pythagorean theorm
Answer:
1. [tex]9^{2} + 12^2 = 15^2\\81+144=225[/tex]
Heights for 16-year-old boys are normally distributed with a mean of 68. 3 in. And a
standard deviation of 2. 9 in.
Find the z-score associated with the 96th percentile.
Find the height of a 16-year-old boy in the 96th percentile.
The height of a 16-year-old boy in the 96th percentile is approximately 73.375 inches. The z-score associated with the 96th percentile is 1.75.
To find the z-score associated with the 96th percentile, we can use the following steps:
1. Locate the percentile in a standard normal distribution table or use a calculator that can compute percentiles (e.g., a graphing calculator or an online calculator).
2. For the 96th percentile, we find the corresponding z-score. Using a standard normal distribution table or an online calculator, the z-score is approximately 1.75.
So, the z-score associated with the 96th percentile is 1.75.
To find the height of a 16-year-old boy in the 96th percentile, we can use the following formula:
Height = mean + (z-score × standard deviation)
Here, the mean height is 68.3 inches, the z-score is 1.75, and the standard deviation is 2.9 inches. Plugging these values into the formula:
Height = 68.3 + (1.75 × 2.9) ≈ 68.3 + 5.075 ≈ 73.375 inches
So, the height of a 16-year-old boy in the 96th percentile is approximately 73.375 inches.
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helpppp me please hurehshsh
Answer:
m∠W = 45°
Step-by-step explanation:
When both legs of a right triangle are congruent, we know that it is an isosceles right triangle because of the isosceles triangle theorem.
Therefore, we can identify W as:
m∠W = (180 - 90)° / 2
m∠W = 45°
Note: We get the / 2 from the fact that both non-right angles are congruent; therefore, they are half of the remaining angle measures after subtracting the right angle (90°) from the total of a triangle (180°).
D(x) is the price, in dollar per unit, that the consumers are willing to pay for x units of an item, and S(x) is the price, in dollars per unit, that producers are willing to accept for x units. Find (a) the equilibrium point, (b) the consumer surplus at the equilibrium point, and (c) the producer surplus at the equilibrium point.
D(x)=(x-7)^2, S(x)=x^2+2x+33
Find:
A) The equilibrium point
B) The consumer surplus at the equilibrium point
C) The producer surplus at the equilibrium point
32/9
So the producer surplus at the equilibrium point is 32/9 dollars.
To find the equilibrium point, we need to set D(x) equal to S(x) and solve for x:
(x-7)^2 = x^2 + 2x + 33
Expanding and simplifying:
x^2 - 14x + 49 = x^2 + 2x + 33
12x = 16
x = 4/3
So the equilibrium point is x = 4/3.
To find the consumer surplus at the equilibrium point, we need to find the difference between the maximum price consumers are willing to pay (D(4/3)) and the equilibrium price (S(4/3)) and multiply by the quantity sold (4/3):
Consumer surplus = (D(4/3) - S(4/3)) * (4/3)
= [(4/3 - 7)^2 - (4/3)^2 - 2(4/3) - 33] * (4/3)
= [49/9 - 16/9 - 8/3 - 33] * (4/3)
= -224/27
So the consumer surplus at the equilibrium point is -224/27 dollars.
To find the producer surplus at the equilibrium point, we need to find the difference between the equilibrium price (S(4/3)) and the minimum price producers are willing to accept (S(0)) and multiply by the quantity sold (4/3):
Producer surplus = (S(4/3) - S(0)) * (4/3)
= [(4/3)^2 + 2(4/3) + 33 - 33] * (4/3)
= 32/9
So the producer surplus at the equilibrium point is 32/9 dollars.
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The total weight of a shipping crate is modeled by the function c = 24b + 30, * where c is the total weight of the crate with b boxes packed inside the crate. If each crate holds a maximum of 6 boxes, then what are the domain and range of the function for this situation?
The domain of the function is 0 ≤ b ≤ 6, and the range of the function is 30 ≤ c ≤ 174.
Understanding Domain of a FunctionThe function that models the total weight of a crate with b boxes inside is given as:
c = 24b + 30
We know that each crate can hold a maximum of 6 boxes. Therefore, the number of boxes inside the crate can only take values from 0 to 6.
Domain:
The number of boxes b can take values from 0 to 6. Therefore, the domain of the function is:
0 ≤ b ≤ 6
Range:
To find the range of the function, we need to consider the maximum and minimum values that c can take when
0 ≤ b ≤ 6.
When b = 0, the crate is empty, and the total weight of the crate is:
c = 24(0) + 30 = 30.
When b = 6, the crate is full with 6 boxes, and the total weight of the crate is:
c = 24(6) + 30 = 174.
Therefore, the range of the function is:
30 ≤ c ≤ 174
We can then say the domain of the function is 0 ≤ b ≤ 6, and the range of the function is 30 ≤ c ≤ 174.
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Ethan goes to the park. The park is 85km away from his house towards south. After 2. 00 minutes,Wthan is 195km away from his house towards west. Find Ethans velocity
If after 2.00 minutes, Ethan is 195km away from his house towards west, Ethan's velocity is approximately 6393 km/h.
To find Ethan's velocity, we need to first determine the distance he traveled and the time he spent traveling.
Given:
1. Initial position: Ethan's house
2. Distance to park: 85 km south
3. Final position: 195 km west from house after 2 minutes
To find the total distance, we can use the Pythagorean theorem, as the path forms a right triangle:
Distance = √(85² + 195²) = √(7225 + 38025) = √(45250) ≈ 212.72 km
Now, let's convert the time from minutes to hours:
2 minutes = 2/60 hours ≈ 0.0333 hours
Finally, we can calculate Ethan's velocity:
Velocity = Distance / Time = 212.72 km / 0.0333 hours ≈ 6393 km/h
Ethan's velocity is approximately 6393 km/h.
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Aiden gave each member of his family a playlist of random songs to listen to and asked them to rate each song between 0 and 10. He compared his family’s ratings with the release year of each song and created the following scatterplot:
What would the linear equation be?
The linear equation in slope intercept form is:
y = -0.1x + 9
What is the Linear Equation from the Scatter Plot?The formula for finding the Linear Equation in slope intercept form is expressed in the form:
y = mx + c
where:
m refers to the slope
c refers to the y-intercept
Looking at the given graph, we can see that:
The y-intercept = 9
The y-intercept is the point where the line crosses the y-axis while x-intercept is the point where the line crosses the x-axis.
Taking the two coordinates:
(1970, 7) and (1990, 5)
Slope:
m = (5 - 7)/(1990 - 1970)
m = -2/20
m = -0.1
Thus, the Equation in slope intercept form is expressed in the form of:
y = -0.1x + 9
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White shapes are black shapes are used in a game.
Some of the shapes are circles.
All the other shapes are squares.
The ratio of the number of white shapes to the number of black shapes is 7:3
The ratio of the number of white circles to the number of white squares is 2:7
The ratio of the number of black circles to the number of black squares is 1:2
Work out what fraction of all the shapes are circles.
Give your answer as a fraction in its simplest form.
The population of a town after t years is represented by the function (t)=7248(0.983)^t. What does the value 0.983 represent in this situation
Answer:
Constant
Step-by-step explanation:
What is an exponential function?
An exponential function is a function with the general form y = abx, a ≠ 0, b is a positive real number and b ≠ 1. In an exponential function, the base b is a constant. The exponent x is the independent variable where the domain is the set of real numbers.
In this case, y=ab^x
where 0.983 is in our b term, which gives the meaning that number is our constant in this exponential function.
Deriving the Law of Cosines
Try it
Follow these steps to derive the law of cosines.
✓ 1. The relationship between the side lengths in AABD is
C2 = x2 +hby the Pythagorean theorem M
✓ 2. The relationship between the side lengths in ACBD is
Q2 = (b - x)2 +hby the Pythagorean theorem
V 3. The equation e? = (6 – x)2 + h? is expanded y to become
22 = 62 - 2x + x2 +h?
a
h
✓ 4. Using the equation from step 1, the equation
22 = 62 - 2bx +32+ hbecomes a = 62 - 2bx + 2
by substitution
A
х
D
b-x
С
Correct! You have completed this exercise.
b
1) The relationship between the side lengths in ΔABD is c² = x² + h² by the Pythagorean Theorem.
2) . The relationship between the side lengths in Δ CBD is a² = (b-x)² + h² by the Pythagorean Theorem.
3) The expanded equation is e² = x² -12x + 36 + h²
4) the expanded equation is a² = b²-x²+32
According to the Pythagorean theorem, the square of the hypotenuse (c) of a right triangle equals the sum of the squares of the other two sides (a² + b²).
So
1) The relationship between the side lengths in ΔABD is c² = x² + h² by the Pythagorean Theorem.
2) The relationship between the side lengths in Δ CBD is a² = (b-x)² + h² by the Pythagorean Theorem.
3) The equation is e² = (6 - x)² + h² when expanded
e² = 36 - 12x + x² + h²
or
e² = x² -12x + 36 + h²
4) Using this equation, we can solve for h² by subtracting (b-x)² from both sides:
a² - (b-x)² = h²
Now we can substitute this expression for h² into the equation given in step 3
2² = 6² - 2bx + (a² - (b-x)²)
Simplifying this equation, we get:
4 = 36 - 2bx + a² - (b-x)²
Expanding the square term, we get:
4 = 36 - 2bx + a² - (b² - 2bx + x²)
Simplifying further, we get:
4 = 36 - b² + x² + a²
Rearranging, we get:
a² = b² - x² + 32
So the equation expanded is a² = b² - x² + 32.
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Full Question:
For 1 and 2, see attached image.
3) The equation e²= (6 – x)² + h² is expanded y to become ?
4) Using the equation from step 1, the equation
2² = 6² - 2bx +32+ h becomes a = 62 - 2bx + 2
by substitution
22 = 62 - 2x + x2 +h?
Determine whether y=3x^2 - 12x + 1 has a minimum or a maximum value. Then find the value
Minimum
-11
Step-by-step explanation:Main concepts:
Concept 1: Identify the type of equation
Concept 2: Identify the concavity (opens up/down)
Concept 3: Finding a vertex of a parabola
Concept 1: Identify the type of equation
First, observe that the equation is a polynomial. This is a type of equation where there may be multiple terms containing an x, where each term with an x is raised to a whole number power, and may be multiplied by a real number. Additionally, there may be a constant term added (or subtracted).
For our equation, [tex]y=3x^2-12x+1[/tex], the first two terms contain an x, each raised to a whole number power, and are multiplied by a number. Additionally, there is a constant added to the end of the equation. Therefore, this is a polynomial.
The largest power of x in a polynomial is called the "degree" of the polynomial. Since the largest power of x is 2, this is called a second degree polynomial. Another common name for a second degree polynomial is a quadratic equation.
This quadratic equation is already in what is known as "Standard form" [tex]y=ax^2+bx+c[/tex]
Concept 2: Identify the concavity (opens up/down)
For quadratic equations, the graph of the equation will be a sort of "U" shape" called a parabola. The parabola either opens up or down depending on the "leading coefficient" in the quadratic equation.
The "leading coefficient" of any polynomial is the constant number that is multiplied to x in the term with the highest power. In this case, the leading coefficient is 3.
A parabola opens up or down in correspondence with the sign of the leading coefficient. If the leading coefficient is positive, the parabola opens upward. If the leading coefficient is negative, the parabola opens downward.
Since the leading coefficient is 3, the parabola for our example opens upward. The branches of the "U" will go upward forever, without a maximum. However, the bottom of the "U" will have a minimum value. We are assigned to find this minimum value (how low it goes).
Concept 3: Finding a vertex of a parabola
To find the vertex of a parabola, with an equation in standard form, there are a few methods, but the most straightforward is to use the vertex formula:
[tex]h=\dfrac{-b}{2a}[/tex]
Where "h" is the x-coordinate of the vertex, and "a" and "b" are the coefficients from the quadratic equation: [tex]y=ax^2+bx+c[/tex]
[tex]h=\dfrac{-(-12)}{2(3)}[/tex]
[tex]h=\dfrac{12}{6}[/tex]
[tex]h=2[/tex]
So, the parabola will have a vertex with an x-coordinate of "2", meaning that the lowest point will be at a position that is 2 units to the right of the origin... however, we still don't know how high that minimum is. Fortunately, the equation [tex]y=3x^2-12x+1[/tex] itself gives the relationship between any x-value and the y-value that is associated with it.
[tex]y=3x^2-12x+1[/tex]
[tex]y=3(2)^2-12(2)+1[/tex]
[tex]y=3*4+(-12)*2+1[/tex]
[tex]y=12+-24+1[/tex]
[tex]y=-11[/tex]
So, the vertex of the parabola is (2,-11).
The height of the vertex is -11, so the value of the minimum is -11.
Side note: "What is the value of the minimum" is a different question that "where is the minimum at". The minimum is at 2. The actual value of the minimum is -11.
Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, select the statement that could be true for g.
A.
g(7) = -1
B.
g(0) = 2
C.
g(-13) = 20
D.
g(-4) = -11
The option that can be true for the function g(x) is C; g(-13) = 20
Which statement could be true?Here we know that the function g(x) has:
The domain ---> -20 ≤ x ≤ 5
The range ---> -5 ≤ g(x) ≤ 45
And g(0) = -2
g(-9) = 6
There are two statements that could be true:
g(-13) = 20, because -13 belongs to the domain and 20 belongs to the range.
g(0) = 2 could also be true.
Now, we can see that g(-9) > g(0), then as x becomes smaller, g increases, then the option that seems to be correct is g(-13) = 20
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Sorry if the photo is sideways, can someone please help me
The length of AB is approximately 12.704 units.
How to find the length?To solve this problem, we can use trigonometry and the fact that the easel forms a 30° angle to find the length of AB.
According to given information:We know that RC is 22, and that angle R is 30°. Let's use the trigonometric function tangent to find AB:
tan(30°) = AB / RC
We can rearrange this equation to solve for AB:
AB = tan(30°) * RC
Using a calculator or trigonometric table, we find that tan(30°) = 0.5774 (rounded to four decimal places). Therefore:
AB = 0.5774 * 22
AB ≈ 12.704
So the length of AB is approximately 12.704 units.
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Which function is a parabola?
F(x)=5-x^2
X - 2 -1 -0 0 3
G(x) 3 0 -1 0 3
1. F(x) only
2. G(x) only
3. Both f(x) and g(x)
4.neither
Answer:
1. F(x) only-----------------------
F(x) is in the format of a quadratic function:
y = ax² + bx + c, with a = - 1, b = 0, c = 5Hence it is a parabola.
The table represents a relation with two x-intercepts and two y-intercepts (points with the coordinate of 0).
We know that parabola can have maximum of one y-intercept, hence G(x) is not a parabola.
The matching answer choice is the first one.
Let f(x)= -2x+4 and g(x)= 3x^2. Find (f+g)(x) and (f-g)(x)
State the domain of each.
Evaluate the following: (f+g)(-3) and (f-g)(-3)
The scope of both functions is all real numbers.
How to solveTo compute the values of (f+g)(x) and (f-g)(x), we apply the addition and subtraction of two distinct functions, respectively:
(f+g)(x) = f(x) + g(x) = [tex](-2x + 4) + (3x^2) = 3x^2 - 2x + 4[/tex]
(f-g)(x) = f(x) - g(x) = [tex](-2x + 4) - (3x^2) = -3x^2 - 2x + 4[/tex]
The scope of both functions is all real numbers.
Subsequently, we evaluate the expressions for x = -3:
(f+g)(-3) = [tex]3(-3)^2 - 2(-3) + 4[/tex] = 3(9) + 6 + 4 = 27 +6 +4 = 37
(f-g)(-3) = [tex]-3(-3)^2 - 2(-3) + 4[/tex]= -3(9) + 6 + 4 = -27 + 6 + 4 = -17
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La o florarie s-au adus ghivece de flori.in prima zi s-a vandut 1 supra 2 din numarul ghivecelor,a doua zi 1 supra 4 din numarul ramas si inca 7 ghivece iar a treia zi restul de 20 de ghivece.cate ghivece s-au vandut in fiecare zi si cate sau adus initial la florarie
S-au adus initial 68 de ghivece de flori, iar în fiecare zi s-au vândut, respectiv, 34, 17 și 17 ghivece.
Initial, la florărie s-au adus x ghivece de flori. În prima zi s-au vândut 1/2 * x ghivece. A doua zi, din numărul rămas s-au vândut 1/4 * (x - 1/2 * x) ghivece, adică 1/4 * 1/2 * x.
În plus față de acestea, s-au vândut încă 7 ghivece, deci în total în a doua zi s-au vândut 1/4 * 1/2 * x + 7 ghivece. În a treia zi s-au vândut restul de 20 de ghivece, deci numărul rămas la finalul celei de-a doua zile este x - 1/2 * x - 1/4 * 1/2 * x - 7. Trebuie să fie egal cu 20, deci avem ecuația x - 1/2 * x - 1/4 * 1/2 * x - 7 = 20.
Rezolvând această ecuație, obținem x = 128. Prin urmare, în prima zi s-au vândut 1/2 * 128 = 64 ghivece, în a doua zi s-au vândut 1/4 * 1/2 * 128 + 7 = 15 ghivece, iar în a treia zi s-au vândut restul, adică 20 ghivece.
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Give your answer accurate to 3 decimal places.
Claire starts at point A and runs east at a rate of 12 ft/sec. One minute later, Anna starts at A and runs north at a rate of 7 ft/sec. At what rate (in feet per second) is the distance between them changing after another minute?
______ft/sec
Solving for dz/dt, we get:
dz/dt ≈ 11.650 ft/sec.
So, after another minute, the distance between Claire and Anna is changing at a rate of approximately 11.650 ft/sec.
Hi there! To answer this question, we can use the Pythagorean theorem and implicit differentiation. Let x be the distance Claire runs east and y be the distance Anna runs north. After 1 minute, Claire has already run 12 * 60 = 720 ft. After another minute, x = 720 + 12t, and y = 7t.
Now, we can set up the Pythagorean theorem: x^2 + y^2 = z^2, where z is the distance between them. Substituting the expressions for x and y, we get (720 + 12t)^2 + (7t)^2 = z^2.
To find the rate at which the distance between them is changing (dz/dt), we need to differentiate both sides of the equation with respect to time, t:
2(720 + 12t)(12) + 2(7t)(7) = 2z(dz/dt).
Now, we can plug in the values for t = 2 minutes:
2(720 + 24)(12) + 2(14)(7) = 2z(dz/dt).
Simplifying, we get:
34560 + 392 = 2z(dz/dt).
After 2 minutes, Claire has run 12(120) = 1440 ft, and Anna has run 7(60) = 420 ft. Using the Pythagorean theorem, we can find z:
z = √(1440^2 + 420^2) ≈ 1500 ft.
Now we can find dz/dt:
34952 = 2(1500)(dz/dt).
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The measures of the interior angles of a hexagon are represented by
, and. The measure of the largest interior angle is
The measure of the largest interior angle is 105°.
What is the measure of angle?
When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.
Here, we have
Given: The measures of 5 of the interior angles of a hexagon are: 130, 120°, 80, 160, and 155. we have to find the measure of the largest interior angle.
The sum of all the six interior angles of a hexagon is 720°.
As sum of five angles is 130° + 120° + 80° + 160° +155° = 165°
The sixth angle is 720° - 165° = 75°
So the smallest interior angle of the hexagon is 75°.
and the largest exterior angle is 180° - 75° = 105°.
Hence, the measure of the largest interior angle is 105°.
Question: The measures of 5 of the interior angles of a hexagon are: 130, 120°, 80, 160, and 155 What is the measure of the largest exterior angle?
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What is the radius of a hemisphere with a volume of 324 ft³, to the nearest tenth of a
foot?
SOND
Answer:the radius of the hemisphere with a volume of 324 ft³ is approximately 6.3 feet (to the nearest tenth).
Step-by-step explanation:
The formula for the volume of a hemisphere is:
V = (2/3) × π × r³, where V is the volume and r is the radius of the hemisphere.
We have been given the volume of the hemisphere as 324 ft³, so we can substitute this into the formula:324 = (2/3) × π × r³
To find the radius r, we need to solve for it. Dividing both sides by (2/3) × π gives:r³ = (324 / ((2/3) × π))r³ = (324 × 3) / (2 × π)r³ = 486 / π
Taking the cube root of both sides gives:r = (486 / π)^(1/3)
Using a calculator to evaluate this expression, we get:r ≈ 6.3
In a laboratory experiment, the population of bacteria in a petri dish started off at 380 and is growing exponentially at 3% per day. Write a function to represent the population of bacteria after tt days, where the hourly rate of change can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage rate of change per hour, to the nearest hundredth of a percent
The function is P(t) = 380 x [tex]1.0300^{t}[/tex], which is an exponential function, and the rate of change is 1.24% each hour.
The equation P(t) = 380 x [tex](1 + 0.03)^{t}[/tex] represents the population of bacteria after t days.
Rounding to four decimal digits and simplifying:
P(t) = 380 x [tex]0.0300^t[/tex]
We can use the following formula to determine the percentage rate of change each hour:
r = [tex]100 \times e^{(ln(1 + 0.03)/24) - 1)}[/tex]
where e is the Euler's number, ln is the natural logarithm, and r is the percentage rate of change per hour.
Rounding to the nearest tenth of a percent and simplifying:
r = 1.24%
This exponential function simulates the population of bacteria multiplying exponentially at a rate of 3% each day in a petri dish.
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