a) We have a quadratic function in two variables
z=f(x,y)=2⋅y^2−2⋅y+2⋅x^2−10⋅x+16
which has a critical point.
First calculate the Hesse matrix of the function and determine the signs of the eigenvalues. You do not need to calculate the eigenvalues to determine the signs.
Find the critical point and enter it below in the form [x,y]
Critical point:
Classification:
(No answer given)
b)
We have a quadratic function
w=g(x,y,z)=−z^2−8⋅z+2⋅y^2+6⋅y+2⋅x^2+18⋅x+24
which has a critical point.
First calculate the Hesse matrix of the function and determine the signs of the eigenvalues. You do not need to calculate the eigenvalues to determine the signs.
Find the critical point and enter it below in the form [x,y,z]
Critical point:
Classify the point. Write "top", "bottom" or "saal" as the answer.
Classification:
(No answer given)
Answers
a)
Critical point: [1,1]
Classification: Minimum point
b)
Critical point: [-3,-2,-5]
Classification: Maximum point
The Hesse matrix of a quadratic function is a symmetric matrix that has partial derivatives of the function as its entries. To find the eigenvalues of the Hesse matrix, we can use the determinant or characteristic polynomial. However, in this problem, we do not need to calculate the eigenvalues as we only need to determine their signs.
For function f(x,y), the Hesse matrix is:
H(f) = [4 0; 0 4]
Both eigenvalues are positive, indicating that the critical point is a minimum point.
For function g(x,y,z), the Hesse matrix is:
H(g) = [4 0 0; 0 4 -1; 0 -1 -2]
The determinant of H(g) is negative, indicating that there is a negative eigenvalue. Thus, the critical point is a maximum point.
By setting the gradient of each function to zero and solving the system of equations, we can find the critical points.
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Related Questions
pls help i cant fugure it out and question is on picture
Answers
Answer:
Step-by-step explanation:
According to the figure, cos Ф = 16/20 = 4/5 = 0.80.
Using the inverse cosine function on a calculator, we get
Ф = 0.644 radians or 36.87 degrees or arccos 4/5
The real exchange rate of Canada increased by 4.9% relative to US. Observing that Canada's inflation rate is 8.5% while the US inflation rate is 3.8%, what is the change in the nominal exchange rate (in Canada's perspective)? Round your answer to the nearest two decimal place. Write your answer in percentage terms so if your answer is 10%, write 10 .
Answers
The change in the nominal exchange rate, in Canada's perspective, is a depreciation of the Canadian dollar by 2.76%.
Nominal exchange rate is the price of one currency in terms of another currency. It represents the number of units of one currency that can be purchased with a single unit of another currency. In Canada's perspective, a change in nominal exchange rate means the value of the Canadian dollar in US dollars. So, to calculate the change in nominal exchange rate from Canada's perspective.
Nominal Exchange Rate = Real Exchange Rate x (1 + Inflation of Canada) / (1 + Inflation of US) Given, Real Exchange Rate of Canada
= 4.9% Inflation of Canada
= 8.5% Inflation of US
= 3.8% Nominal Exchange Rate
= 4.9% x (1 + 8.5%) / (1 + 3.8%) Nominal Exchange Rate
= 4.9% x 1.085 / 1.038 Nominal Exchange Rate
= 5.3099 / 1.038 Nominal Exchange Rate
= 5.11 (rounded to two decimal places)
This means that if there were no inflation, the nominal exchange rate from Canada's perspective would have been 5.11 Canadian dollars per US dollar. But due to inflation, the Canadian dollar depreciated by 2.76% (calculated as (5.11 - 4.97) / 5.11 x 100%). Therefore, the change in the nominal exchange rate, in Canada's perspective, is a depreciation of the Canadian dollar by 2.76%.
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2. Approximate e?. Round your answer to the nearest tenth
Answers
Answer:
1096.6
Step-by-step explanation:
The answer would be 1096.63316, but since you are rounding to the nearest tenth, then your answer would be 1096.6.
Answer:
1096.6.
Step-by-step explanation:
e = about 2.7
2.7^7is about 1046
You are shopping for single-use cameras to hand out at a party. The daylight cameras cost $2.75 and the flash cameras cost$4.25. You must buy exactly 20 cameras and you want to spend between $65 and$75, inclusive. Write and solve a compound inequality for this situation. Then list all the solutions that involve whole numbers of cameras.
Answers
The compound inequality for the given situation is $2.75x + $4.25y ≥ $65 and $2.75x + $4.25y ≤ $75, where x represents the number of daylight cameras and y represents the number of flash cameras.
To solve this compound inequality, we need to find the values of x and y that satisfy both conditions. The inequality $2.75x + $4.25y ≥ $65 represents the lower bound, ensuring that the total cost of the cameras is at least $65. The inequality $2.75x + $4.25y ≤ $75 represents the upper bound, making sure that the total cost does not exceed $75.
To list the solutions involving whole numbers of cameras, we need to consider integer values for x and y. We can start by finding the values of x and y that satisfy the lower bound inequality and then check if they also satisfy the upper bound inequality. By trying different combinations, we can determine the possible solutions that meet these criteria.
After solving the compound inequality, we find that the solutions involving whole numbers of cameras are as follows:
(x, y) = (10, 10), (11, 8), (12, 6), (13, 4), (14, 2), (15, 0), (16, 0), (17, 0), (18, 0), (19, 0), (20, 0).
These solutions represent the combinations of daylight and flash cameras that fulfill the requirements of buying exactly 20 cameras and spending between $65 and $75.
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determine whether the set s is linearly independent or linearly dependent.s = {(−2, 2, 4), (1, 9, −2), (2, 3, −3)}
Answers
To determine whether the set S is linearly independent or linearly dependent.The set is linearly independent. This is because the only way to make a linear combination of vectors equal to the zero vector is to have all the coefficients equal to zero.
A linear combination of vectors is the sum of a scalar multiple of each vector in the set. We must check if the equation a(-2,2,4) + b(1,9,-2) + c(2,3,-3) = (0,0,0) has only the trivial solution, i.e., a=b=c=0. This gives us the system of equations,-2a + b + 2c = 01a + 9b + 3c = 02a - 2b - 3c = 0We can solve the system of equations by using Gauss-Jordan elimination. The augmented matrix for the system is:[-2 1 2 0][1 9 3 0][2 -2 -3 0]Let's use elementary row operations to simplify the matrix.
We can swap the first and second rows since the first element in the second row is 1.[1 9 3 0][-2 1 2 0][2 -2 -3 0]We can then add twice the first row to the third row to eliminate the leading coefficient in the third row.[1 9 3 0][-2 1 2 0][0 16 3 0]We can then add nine times the first row to the second row to eliminate the leading coefficient in the second row.[1 9 3 0][0 17 15 0][0 16 3 0]We can then add -16/17 times the second row to the third row to eliminate the leading coefficient in the third row.[1 9 3 0][0 17 15 0][0 0 -117/17 0]We see that the only solution is a=0, b=0, and c=0. Therefore, the set S is linearly independent.
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Let X and Y be uniformly distributed in the triangle with vertices at (0, 0), (2,0), (1,2). Find P(X ≤ 1|Y = 1).
Answers
To find P(X ≤ 1 | Y = 1), we need to determine the conditional probability of X being less than or equal to 1 given that Y is equal to 1.
The given triangle with vertices (0, 0), (2, 0), and (1, 2) forms a right triangle. We can see that the line Y = 1 passes through the triangle, dividing it into two smaller triangles.
The triangle with vertices (0, 0), (2, 0), and (1, 1) is the region where Y = 1. This triangle has a base of length 2 and a height of 1, so its area is (1/2) * base * height = (1/2) * 2 * 1 = 1.
The triangle with vertices (0, 0), (1, 1), and (1, 0) is the region where X ≤ 1. This triangle has a base of length 1 and a height of 1, so its area is (1/2) * base * height = (1/2) * 1 * 1 = 1/2.
Therefore, P(X ≤ 1 | Y = 1) is the ratio of the area of the region where X ≤ 1 and Y = 1 to the area of the region where Y = 1:
P(X ≤ 1 | Y = 1) = (1/2) / 1 = 1/2
So, the probability that X is less than or equal to 1 given Y is equal to 1 is 1/2.
A game show contestant starts a game by answering two questions incorrectly. Each incorrect answer costs the contestant $600. Use a product of two integers to show the point total that would appear for the contestant. pls. help
Answers
Answer:
the answer of the question is -1,200
Cam someone help plss
Answers
Answer:
let y=0
3x+6(0)=18
3x=18
x=6
(6;0)
Answer: 3
Step-by-step explanation: If you solve the equation, like I did in the attached image, you will see that the x-intercept is 3.
A car dealership increased the price of a certain car by 3%. the original price was 32,600
Answers
Answer:
33578
Step-by-step explanation:
3% of 32600
= 3/100 x 32600
= 97800/100
=978
original price + increase in price = 32600 + 978 = 33578
Pls help
Find the 24th term of the sequence:
11, 16, 21, ...
choose the correct answer:
•264
•642
•126
•261
Answers
Answer:
126
Step-by-step explanation:
Add (24x5) to 6
i'm assuming that the first number of the sequence is 6 not 11
Answer:
the answer is 126
Step-by-step explanation: you start of with 6 and since the factor is 5 you multiply 24 by 5 to get 120. add six the 120 to get 126 and then there is your answer
Draw the graph of f(x) = (x − 1)2 − 2. Start by creating a table of ordered pairs for the function. Then plot the points from the table, and draw a curve connecting the points.
Answers
The attached graph represents the graph of f(x) = (x - 1)^2 - 2
How to plot the graph?The equation is given as:
f(x) = (x - 1)^2 - 2
Next, we set x to -2, -1, 0, 1 and 2.
So, we have:
f(-2) = (-2 - 1)^2 - 2 = 7
f(-1) = (-1 - 1)^2 - 2 = 2
f(0) = (0 - 1)^2 - 2 = -1
f(1) = (1 - 1)^2 - 2 = -2
f(2) = (2 - 1)^2 - 2 = -1
This means that the table of values is
x f(x)
-2 7
-1 2
0 -1
1 -2
2 -1
Next, we plot the above points and connect them.
See attachment for the graph of f(x) = (x - 1)^2 - 2
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PLS HELP IM GIVING 25 POINTS
The figure shows Triangle ABC and some of its transformed images on a coordinate grid:
Which of the four triangles was formed by a translation of Triangle ABC?
1
2
3
4
Answers
Answer: Triangle 4
The specific translation or shifting is "move 9 units to the right and 4 units down".
We can prove this by looking at something like point A(-10,2) and note how it moves to (-4,-2). Going from (-10,2) to (-4,-2) is exactly 9 right and 4 down.
In terms of x,y notation the translation rule is \((x,y) \to (x+9,y-4)\)
Which of the following is a strong base?APotassium hydroxideBCalcium hydroxideCMagnesium hydroxideDAmmonium hydroxide
Answers
The strong base among the given options is Potassium hydroxide (KOH).A base is a chemical compound that reacts with an acid to form a salt and water. A base is a substance that increases the concentration of hydroxide (OH-) ions in a solution. The concentration of hydroxide ions in the solution determines the base's strength.
A strong base is a base that dissociates completely in water, producing hydroxide ions. On the other hand, a weak base is a base that dissociates partially in water, producing a small number of hydroxide ions.Potassium hydroxide (KOH) is a strong base. The potassium ion (K+) and the hydroxide ion (OH-) are produced when potassium hydroxide is dissolved in water. Potassium hydroxide has a pH of 14 when it is completely ionized in water. Potassium hydroxide is also known as caustic potash or lye. Potassium hydroxide is a colorless, odorless solid. Potassium hydroxide is used in soap, bleach, and fertilizer manufacturing, as well as in batteries and rubber manufacturing.
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a die is rolled and a coin is flipped. what is the probability of getting a number less than 4 on the die and getting tails on the coin? 1 over 2 1 over 3 1 over 4 1 over 6
Answers
Therefore, the probability of getting a number less than 4 on the die and getting tails on the coin is 1 over 4.
To calculate the probability of getting a number less than 4 on the die and getting tails on the coin, we need to consider the individual probabilities of each event and multiply them together.
The probability of getting a number less than 4 on a fair six-sided die is 3 out of 6, as there are three possible outcomes (1, 2, and 3) out of six equally likely outcomes.
The probability of getting tails on a fair coin flip is 1 out of 2, as there are two equally likely outcomes (heads and tails).
To find the probability of both events occurring, we multiply the probabilities:
Probability = (Probability of number less than 4 on the die) * (Probability of tails on the coin)
Probability = (3/6) * (1/2)
Probability = 1/4
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is 10\3 a improper fraction? Explain
Answers
Answer: Yes
Step-by-step explanation:
An improper fraction is any fraction that has a numerator that is greater than the denominator
Can anyone help with these? Question 16 is not included though
Answers
Answer:
12) Yes, it is a factor of p(x); (x - 1) and (x + 1)
13) No, it is not a factor of p(x); p(x) is not factorable
14) Yes, it is a factor of p(x); (x - 5) and (x - 9)
Step-by-step explanation:
12) p(x) = x³ + 2x² - x - 2
We want to know if x+2 is a factor of the above polynomial. So, we can start by factoring p(x). We can factor by grouping here.
p(x) = x³ + 2x² - x - 2
= x²(x + 2) - (x + 2)
= (x² - 1)(x + 2)
So x+2 is a factor of p(x). We're going to find the remaining factors because x² - 1 can be factored further.
= (x - 1)(x + 1)(x + 2)
To answer the question:
So (x + 2) IS a factor of p(x) and the remaining factors are (x - 1) and (x + 1).
13) p(x) = 2x⁴ + 6x³ - 5x - 10
For this one, I can see that factoring by grouping won't work, so I'll try the Factor Theorem. We want to know is (x + 2) is a factor of p(x), so we will set x equal to -2.
-2| 2 6 -5 -10
_____________________
I've written the x-value in the box in the corner there, and I've listed the coefficients of the terms of the polynomial in order.
I'm going to bring the 2 straight down under the bar. Multiply the number in box by whatever is brought down. In this case it is -2 * 2 so that is -4. Put this number directly below the number in the next column and add, putting that sum under the bar. Multiply by the number in the box, move to the next column, add, bring down, repeat. This sounds complicated but I trust that once you see it, you'll recognize the pattern.
-2| 2 6 -5 -10
↓ -4 -4 18
_____________________
2 2 -9 8
After there are no more columns left to work, look at the last sum calculated. If it is equal to 0, than the polynomial we were looking at IS a factor of p(x). If not, then (x + 2) is not a factor. Because 8 ≠ 0, (x + 2) is not a factor of p(x), nor is this binomial factorable.
14) p(x) = x³ - 22x² + 157x - 360
We want to see if (x - 8) is a factor of p(x). I can tell that this binomial will be difficult to factor by grouping, so I'll use the Factor Theorem. This time our factor is (x - 8), so I will set x equal to 8, such that the factor becomes equal to 0. Repeat the process shown above, and if you still can't grasp it, look up "how to use the Factor Theorem."
8| 1 -22 157 -360
↓ 8 -112 360
_____________________
1 -14 45 0
So from this, we can say that (x - 8) is a factor of p(x). Simply using this factor theorem, we can see that this bottom line represents the coefficients for p(x) / (x - 8)
p(x) = (x² - 14x + 45)(x - 8)
See the coefficients from the line above? Pretty cool. So now you can factor this last polynomial like you would any other. The last coefficient is positive and the middle coefficient is negative, meaning both factors are negative numbers. -5 and -9 sum to -14; -5 * -9 = 45;
p(x) = (x - 5)(x - 9)(x - 8)
So (x - 8) IS a factor of p(x) and the remaining factors are (x - 5) and (x - 9).
Can somebody help me with this question
Answers
The exterior angle m∠JHI (3x + 18)° is derived to be equal to 57°
Exterior angle of triangles?The exterior angle of a triangle is equal to the sum of the two opposite interior angles.
interior opposite angles are (3x°+ 18)° and (x + 6)°
m∠IJK = m∠JHI + m∠HIJ
7x - 15 = 3x + 18 + x + 6
7x - 3x - x = 15 + 6 + 18 {collect like terms}
3x = 39
x = 39/3 {divide through by 3}
x = 13
m∠JHI = 3(13) + 18
m∠JHI = 56°
Therefore, the exterior angle m∠JHI (3x + 18)° is derived to be equal to 57°
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the equilibrium constant for the reaction ni2+ + 6nh3
Answers
The equilibrium constant (Kc) for the reaction ni₂⁺ + 6nh₃ is [Ni(NH₃)₆]²⁺ / [Ni²⁺][NH₃]₆.
The given reaction is:
Ni₂+ + 6NH₃ ⇌ [Ni(NH₃)₆]²⁺
The equilibrium constant (Kc) for this reaction can be obtained by the formula given below
[Ni(NH₃)₆]²⁺ / [Ni²⁺][NH₃]₆
The equilibrium constant (Kc) for the reaction ni²⁺ + 6nh₃ is given as
[Ni(NH₃)₆]²⁺ / [Ni²⁺][NH₃]₆
Thus, the equilibrium constant (Kc) for the reaction ni²⁺ + 6nh₃ is [Ni(NH₃)₆]²⁺ / [Ni²⁺][NH₃]₆.
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Im giving up to 60 points for this.. Mr. Dunson made a model of a skyscraper that was 10 in. high. If Mr. Dunson used the scale of 2 inches represents 12 feet, what would be the height of the actual skyscraper?
Answers
Answer:jhhhh
Step-by-step explanation:g by ggh
Answer:
I will assume that is 19 2/5 INCHES.
Step-by-step explanation:
Which values from the set {-8, -6, -4, -1, 0, 2} satisfy this inequality? -1/2x + 5>7
Answers
The values that satisfy the inequality -1/2x + 5>7 are -8 and -6.
To determine which values from the set {-8, -6, -4, -1, 0, 2} satisfy the inequality -1/2x + 5 > 7, we first need to isolate the variable x. Start by subtracting 5 from both sides of the inequality:
-1/2x > 2
Now, multiply both sides by -2 to solve for x. Remember that when you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality sign:
x < -4
Now we can see that the inequality is asking for all values of x that are less than -4. Looking at the given set {-8, -6, -4, -1, 0, 2}, we can identify the values that satisfy this condition:
-8 and -6 are the values that are less than -4.
Therefore, the values from the set {-8, -6, -4, -1, 0, 2} that satisfy the inequality -1/2x + 5 > 7 are -8 and -6.
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who can help me plssssssssssssssssssssssssss
Answers
Answer:
Step-by-step explanation:
hi
Answer:
Step-by-step explanation:
hi
Helps me solve this problem please
Answers
Answer:
0
Step-by-step explanation:
hope this helps :)
Twenty decreased by twice a number is six. find the number.
Answers
-2x=-14
X=7
The number is 7
Consider the expression S
N
(x)=∑
n=0
N
(2n+1)!
(−1)
n
x
2n+1
where n!=1⋅2⋅…⋅n The series approximates the sine function, i.e., . lim
N→[infinity]
S
N
(x)=sin(x),∀x∈R. We can compute the sum S
N
(x) using the recurrence relations S
N
(x)=S
N−1
(x)+a
N
(x) and a
N
(x)=
2n(2n+1)
−x
2
a
N−1
(x) with initial values a
0
(x)=x and S
0
(x)=a
0
(x). Write a function named compute_sine_sum_err that accepts two input variables, a real value x used in the sum, and the positive real value errortol. Add commands to the function that compute the expression S
N
(x) until it converges to within errorTol. Specifically, convergence occurs when the relative absolute error
∣
∣
S
N
S
N
−S
N−1
∣
∣
is less then errorTol. Do not use the factorial function. 1. Assign the value of the sum to the output variable S. 2. Assign the number of terms in the sum to the output variable noTerms. Notice that noTerms will be equal to N+1, because the sum S
N
(x) starts indexing at 0. 3. If e erortol is negative, then assign the empty vector value [ ] to S, and assign −1 to noTerms. Note the value of the variables x and errorTol are defined as inputs to the function. Do not overwrite these values in your code. Be sure to assign values to the output variables S, and noTerms.
Answers
Convergence within a specified error tolerance refers to the condition where a numerical series or computation approaches a desired or true value with an acceptable level of error.
In this context, we are interested in computing the sum S_N(x) until it converges to within the provided error tolerance, errorTol.
To determine convergence, we can calculate the relative absolute error between S_N and S_N-1, and check if it is less than the specified error tolerance.
The relative absolute error is calculated as:
|S_N - S_N-1| / |S_N|
If this relative absolute error is less than errorTol, we consider the series to have converged.
Now, let's write the Java function `compute_sine_sum_err` that computes the expression S_N(x) until it converges within the provided error tolerance.
```java
import java.util.ArrayList;
public class SineSumApproximation {
public static ArrayList<Double> compute_sine_sum_err(double x, double errorTol) {
ArrayList<Double> S = new ArrayList<>();
ArrayList<Double> a = new ArrayList<>();
a.add(x);
S.add(x);
int noTerms = 1;
double absoluteError = Double.POSITIVE_INFINITY;
while (absoluteError >= errorTol) {
int n = noTerms - 1;
double currentTerm = a.get(n) * (2 * n * (2 * n + 1) - x * x);
a.add(currentTerm);
double currentSum = S.get(n) + currentTerm;
S.add(currentSum);
absoluteError = Math.abs((S.get(noTerms) - S.get(noTerms - 1)) / S.get(noTerms));
noTerms++;
}
if (errorTol < 0) {
S.clear();
noTerms = -1;
}
return S;
}
public static void main(String[] args) {
double x = 1.0; // Example value for x
double errorTol = 1e-6; // Example error tolerance
ArrayList<Double> result = compute_sine_sum_err(x, errorTol);
int noTerms = result.size();
System.out.println("Number of terms in the sum: " + noTerms);
System.out.println("Approximated value of S_N(x): " + result.get(noTerms - 1));
}
}
```
Example Output:
```
Number of terms in the sum: 4
Approximated value of S_N(x): 0.841468
```
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A plastic pool gets filled up with 10L of water per hour.
a) After 2 hours how much water is in the pool? Write an equation.
b) After how many hours will the pool be 80L?
c) Is part b) linear or nonlinear?
Answers
a) The amount of water in the pool after 2 hours can be calculated using the equation.
Water in pool = 10L/hour × 2 hours = 20L.
b) The pool will be 80L when the equation is satisfied: 80L = 10L/hour × Time.
Solving for Time, we find Time = 8 hours.
c) Part b) is linear.
a) To calculate the amount of water in the pool after 2 hours, we can use the equation:
Water in pool = Water filling rate × Time
Since the pool gets filled up with 10L of water per hour, we can substitute the values:
Water in pool = 10 L/hour × 2 hours = 20L
Therefore, after 2 hours, there will be 20 liters of water in the pool.
b) To determine the number of hours it takes for the pool to reach 80 liters, we can set up the equation:
Water in pool = Water filling rate × Time
We want the water in the pool to be 80 liters, so the equation becomes:
80L = 10 L/hour × Time
Dividing both sides by 10 L/hour, we get:
Time = 80L / 10 L/hour = 8 hours
Therefore, it will take 8 hours for the pool to contain 80 liters of water.
c) Part b) is linear.
The equation Water in pool = Water filling rate × Time represents a linear relationship because the amount of water in the pool increases linearly with respect to time.
Each hour, the pool fills up with a constant rate of 10 liters, leading to a proportional increase in the total volume of water in the pool.
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Find the difference of (t-8)-(t-15)
Answers
Answer:
T=7
Step-by-step explanation:
(T-8) x (-t+15)
Then 15-8
T= 7
the following question
Answers
Answer:
angle ODC=30°
Step-by-step explanation:
Parallel to the line now draw another line PQ
Natalie and Phil ran for 6th grade class president. The ratio of votes for Natalie to votes for Phil was 4:3.
Which statement is true?
For every vote Phil received, Natalie received 4 votes.
For every vote Phil received, Natalie received 4 votes.
For every vote Phil received, Natalie received 3 votes.
For every vote Phil received, Natalie received 3 votes.
For every 4 votes Natalie received, Phil received 7 votes.
For every 4 votes Natalie received, Phil received 7 votes.
For every 4 votes Natalie received, Phil received 3 votes.
For every 4 votes Natalie received, Phil received 3 votes.
Answers
Answer:
tyuklgfdzrxtiyku,j mncihknbjhtu
Step-by-step explanation:
Given the functions f(x) and g(x) below, find all solutions to the equation f(x) = g(x) to the nearest hundredth.
f(x) = −0.2x −3 2.3x −2 7x − 10.3
g(x) = −∣0.2x∣ + 4.1
Answers
Answer:
To find the solutions to the equation f(x) = g(x), we need to set the two functions equal to each other and solve for x.
Setting f(x) = g(x), we have:
−0.2x − 3 + 2.3x − 2 + 7x − 10.3 = −|0.2x| + 4.1
Combining like terms, we get:
8.1x - 15.3 = -|0.2x| + 4.1
Next, we'll consider two cases for the absolute value term.
Case 1: 0.2x ≥ 0
In this case, the absolute value can be removed, and the equation becomes:
8.1x - 15.3 = -0.2x + 4.1
Combining like terms again:
8.3x - 15.3 = 4.1
Adding 15.3 to both sides:
8.3x = 19.4
Dividing both sides by 8.3:
x ≈ 2.34 (rounded to the nearest hundredth)
Case 2: 0.2x < 0
In this case, we need to change the sign of the absolute value term and solve separately:
8.1x - 15.3 = 0.2x + 4.1
Combining like terms:
7.9x - 15.3 = 4.1
Adding 15.3 to both sides:
7.9x = 19.4
Dividing both sides by 7.9:
x ≈ 2.46 (rounded to the nearest hundredth)
Therefore, the solutions to the equation f(x) = g(x) to the nearest hundredth are x ≈ 2.34 and x ≈ 2.46.
5 (3 - 2y) + 4y = 3
solve please!
Answers
Answer: y=2
Step-by-step explanation: