(1 point) Suppose f(x,y) = xy(1 - 4x - 2y). f(x,y) has 4 critical points. List them in increasing lexographic order. By that we mean that (x,y) comes before (z, w) if x

The areas meet the  Pythagorean's theorem, with that we conclude that the area of square 3 is 13 square centimeters.

If you look at the shape between the 3 squares, you can see that we have a right triangle.

Then, by Pythagorean's theorem we can conclude that the area of square 2 plus the area of square 3 must be equal to the area of the square 1.

Then we can write:

Area 2 + Area 3 = Area 1.

We know that:

area 1 = 25 cm²

area 2 = 12 cm²

area 3 = x

then we can write:

x + 12cm² = 25cm²

x = 25cm² - 12cm² = 13cm²

So the correct option is D.

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The critical value for this two-tailed test is 2.6759.

To conduct a two-tailed test at the 0.01 level of significance with a sample of 55 observations, we use the t-distribution because the population standard deviation is unknown. The critical value is determined by dividing the significance level (0.01) by 2 to account for both tails of the distribution. This gives an alpha level of 0.005. Using the degrees of freedom for a sample of size 55 (54 degrees of freedom), we find the corresponding critical value from a t-distribution table or calculator. In this case, the critical value is approximately 2.6759 when rounded to four decimal places.Since the population standard deviation is unknown, we'll use the t-distribution instead of the standard normal distribution. The degrees of freedom for a sample of size 55 is 54. Using a t-distribution table or a statistical calculator, the critical value for an alpha level of 0.005 and 54 degrees of freedom is approximately 2.6759 (rounded to four decimal places).

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To find Mx, My, and (x, y) for the laminas of uniform density rho bounded by the graphs of the equations y = 8x, y = 0, and x = 8, we need to calculate the moments of the laminas.

Mx represents the moment about the y-axis, My represents the moment about the x-axis, and (x, y) represents the centroid of the laminas.

To calculate Mx, we integrate the product of the density rho, the y-coordinate squared, and the differential area element dA:

Mx = ∫∫ y^2 * rho * dA

Since the laminas have uniform density, rho is constant, and we can simplify the equation:

Mx = rho * ∫∫ y^2 * dA

To calculate My, we integrate the product of the density rho, the x-coordinate squared, and the differential area element dA:

My = ∫∫ x^2 * rho * dA

Again, since the laminas have uniform density, rho is constant, and we can simplify the equation:

My = rho * ∫∫ x^2 * dA

To find the centroid (x, y), we divide the moments Mx and My by the total mass (m) of the laminas:

x = Mx / m

y = My / m

To calculate these values, we need to set up the appropriate double integrals over the region bounded by the given equations.

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The graphs cross at x=-1 and x=1. Those are the solutions to to the equation

We know that, If two functions are equal then there solution is the intersection point of the curves.

When we determine the graph the intersection points are (0,2) and (1,1.25).

The values of x of the intersection points are the solutions of the system

Using a graphing tool, there are two intersection points and therefore the solutions are x = -1 and x [ 1.

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Answer:

To find out, we need to subtract the distance Carmen has already gone from the total distance to her school:

5 2/3 - 1 1/5

We need to find a common denominator of 15:

5 10/15 - 1 3/15

Now we can subtract the whole numbers and the fractions separately:

4 - 7/15

To turn the fraction into a mixed number, we need to divide the numerator (7) by the denominator (15):

7 ÷ 15 = 0 remainder 7

Then we can write the mixed number:

4 7/15

Therefore, Carmen still has to jog 4 7/15 miles to get to school.

Step-by-step explanation:

EXPLANATION

We have an equilateral triangle because the 3 angles are congruent as shown in the picture and all legs are congruent:

So, 5x-12 = 3x - 4

Adding +12 to both sides:

5x - 12 + 12 = 3x - 4 + 12

Simplifying:

5x = 3x + 8

Subtracting both sides by -3x:

5x - 3x = 3x - 3x + 8

Simplifying:

2x = 8

Dividing both sides by 2:

x = 8/2

Simplifying:

x=4

Now, replacing in any equation, as 5x - 12:

5*(4) - 12= 8

In conclusion, all the legs are congruent and equal to 8.

Answer: DE= 8

By using sum or difference formulas, cos(-a) can be written as - cos(a). Explanation: We know that cosine is an even function of x, therefore,\(cos(-x) = cos(x)\) .Then, by using the identity \(cos(a - b) = cos(a) cos(b) + sin(a) sin(b)\), we can say that:\(cos(a - a) = cos²(a) + sin²(a).\)

This simplifies to:\(cos(0) = cos²(a) + sin²(a)cos(0) = 1So, cos(a)² + sin(a)² = 1Or, cos²(a) = 1 - sin²\)(a)Similarly,\(cos(-a)² = 1 - sin²(-a)\) Since cosine is an even function, \(cos(-a) = cos(a)\) Therefore, \(cos(-a)² = cos²(a) = 1 - sin²(a)cos(-a) = ±sqrt(1 - sin²(a))'.\)

This is the general formula for cos(-a), which can be written as a combination of sine and cosine. Since cosine is an even function, the negative sign can be written inside the square root: \(cos(-a) = ±sqrt(1 - sin²(a)) = ±sqrt(sin²(a) - 1) = -cos\).

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∠1 = 26°

∠2 = 154°

∠3 = 26°

∠4 = 26°

∠5 = 154°

∠6 = 154°

∠7 = 26°

Step-by-step explanation:

So, we have two parallel lines cut by a transversal (C).

Vertical angles are always equal.

∠2 = 154° (vertical angles)

Linear pair make up 180°.

∠1 = 180° - 154° = 26° (linear pair)

∠1 = ∠3 = 26° (vertical angles)

Corresponding angles are always equal.

∠5 = 154° (corresponding angles)

∠5 = ∠6 = 154° (vertical angles)

Alternate Interior angles are always equal.

∠3 = ∠4 = 26° (alternate interior angles)

∠4 = ∠7 = 26° (vertical angles)

The system capacity is 2 units per minute, the bottleneck stage is Stage A, and the utilization of Stage 3 is 100%.

A line process has three processing stages with the characteristics given below:

Stage A B C Unit processing time(minutes) 1 2 3 Number of machines 1 1 2 Machine availability 90% 100% 100% Process yield at stage 100% 100% 100%

To determine the system capacity and the bottleneck stage and utilization of Stage 3:

The system capacity is calculated by the product of the processing capacity of each stage:

1 x 1 x 2 = 2 units per minute

The bottleneck stage is the stage with the lowest capacity and it is Stage A. Therefore, Stage A has the lowest capacity and determines the system capacity.The utilization of Stage 3 can be calculated as the processing time per unit divided by the available time per unit:

Process time per unit = 1 + 2 + 3 = 6 minutes per unit

Available time per unit = 90% x 100% x 100% = 0.9 x 1 x 1 = 0.9 minutes per unit

The utilization of Stage 3 is, therefore, (6/0.9) x 100% = 666.67%.

However, utilization cannot be greater than 100%, so the actual utilization of Stage 3 is 100%.

Hence, the system capacity is 2 units per minute, the bottleneck stage is Stage A, and the utilization of Stage 3 is 100%.

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Answer:

c (c - 8)

Step-by-step explanation:

c² - 8c

First, you have to find the GCF

The Greatest Common Factor is the factor that all have in common. Here the GCF is c

So, we factor c out and has left (c - 8)

So, our equation is

c (c - 8)

Answer:

option A , x=-2

Step-by-step explanation:

6-x =4(5+x)-4

6 - x = 4 × 5 + 4 × x - 4

6 - x = 20 + 4x - 4

6 - x = 4x + 16

-x - 4x = 16 - 6

-5x = 10

x = 10/-5

x = -2

therefore, option A is the correct option

hope it helps you

Answer:

First, finish the brackets

6-x=20+4x-4

Collect like terms

-x-4x=20-4-6

Solve

-3x=10

x=-10/3

x=-3.33333333333 Or x≅3.34

Step-by-step explanation:

Please give me brainliest

22 students study both subjects.

What is Venn diagram in math ?

N=55,n(M)=23,n(P)=24,n(C)=19,n(M∩P)=12,n(P∩C)=7,n(M∩C)=9,n(M∩P∩C)=4

Now, number of students who studying only Mathematics

n(M∩P)∩C =n(M)−n(M∩P)−n(M∩C)+n(M∩P∩C)    (by  Venn diagram) diagram=23−9−12+4=6

number of students who studying only Physics

n(P∩M )∩C  =n(P)−n(P∩M)−n(P∩C)+n(P∩M∩C)    (by Venn diagram)

                =24−12−7+4=9

Now, number of students  who studying only Chemistry

n(C∩M  )∩P =n(C)−n(C∩M)−n(C∩P)+n(M∩P∩C)    (by Venn diagram)

                    =19−9−7+4=7

So, how many students study only one of the three disciplines in detail                                                            6+9+7=22

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Answer:

infinity 2 is the slope for these point .

Step-by-step explanation:

given points are

(-2,-5) and (3,5)

comparison to

(x1,y1) and (x2,y2)

here ,

\(slope = \frac{y2 - y1}{x2 - x1} \)

slope= 5-(-5)/3-(-2)

slope =10/5

slope=2

glad to help you this may help you :)

The answer is m∠1 = 84°

Step-by-step explanation:

m∠4 = m∠2 so m∠2 = 96°

m∠1 + m∠2 = 360 - m∠4 - m∠2

m∠1 + m∠2 = 360 - 96 - 96

m∠1 + m∠2 = 168

m∠1 = 168/2

m∠1 = 84°

Answer:

90

Step-by-step explanation:

Answer:

Your answer is 90

Step-by-step explanation:

You take 150 and multiply it by .6 to get 90

Answer:

12

Step-by-step explanation:

i know that

a) the dimension of its column space is also 2. b) the rank of A is 2. c) the nullity of matrix A is 1. d) the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

(a) The dimension of the row space of a matrix is equal to the dimension of its column space. So, if the dimension of the row space of matrix A is 2, then the dimension of its column space is also 2.

(b) The rank of a matrix is defined as the maximum number of linearly independent rows or columns in the matrix. Since the dimension of the row space of matrix A is 2, the rank of A is also 2.

(c) The nullity of a matrix is defined as the dimension of the null space, which is the set of all solutions to the homogeneous equation Ax = 0. In this case, the matrix A is a 3 x 3 matrix, so the nullity can be calculated using the formula:

nullity = number of columns - rank

nullity = 3 - 2 = 1

Therefore, the nullity of matrix A is 1.

(d) The dimension of the solution space of the homogeneous system Ax = 0 is equal to the nullity of the matrix A. In this case, we have already determined that the nullity of matrix A is 1. Therefore, the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

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The sample size needed to obtain a 99% confidence interval with a margin of error of 0.05 for the true proportion of homes in the city that are heated by oil is 666.

To calculate the required sample size, we need to use the formula n = \((z^2 * p * q) / e^2\), where z is the z-score for the desired confidence level (2.58 for 99% confidence), p is the estimated proportion of homes heated by oil, q is 1-p, and e is the desired margin of error (0.05).

Using the information given in the question, we can estimate p as 0.5 (assuming equal probability of homes being heated by oil or other means) and q as 0.5. Plugging these values into the formula, we get n = \((2.58^2 * 0.5 * 0.5) / 0.05^2\), which simplifies to n = 665.64. Therefore, we would need a sample size of at least 666 homes to obtain a 99% confidence interval with a margin of error of 0.05 for the true proportion of homes in the city that are heated by oil.

Thus, the answer is 666.

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Answer:

Step-by-step explanation:

[8 * (7÷7)]² = [8 * 1]²

                 = 8²

                 = 64

The operation in the inside parenthesis should be done first.

Answer:

A: (x-4) squared

B: x+2

C: 9

D: 14

E: 7

F: 2

Step-by-step explanation:

A: This is because x^2 - 8x + 16 factored is (x-4) squared

B: Square root of something squared will remove the square root

C: Minus the variable x and 2 from the right side

D: Factor

E/F: These numbers make the right side become zero

1. K(x) = (3x)2 -x + 2 -x + 1

k(x) = g(x) ∘ h(x)

2. K(x) = 2 ^3x + 2

k(x) = g(x) × h(x)

3. K(x) = 2^x - 3x - 2

k(x) = h(x) ÷ g(x))

4. K(x) = 3(2 x) + 2

k(x) = h(x) ∘ g(x)

5. K(x) = 2^x + 3x + 2

k(x) = g(x) - h(x)

6. K(x) = 2^x(3x + 2)

k(x) = g(x) + h(x)

Answer:

$150

Step-by-step explanation:

we can make a ratio

20/100=30/x

cross multiple

20x=30(100)

20x=3,000

/20     /20

x=150 hopes this helps

Its going to be on quadrants 1 and 4.

Answer:its b i think

Step-by-step explanation:

Answer: D, polygenis because a trait is controlled by three different genes.

Step-by-step explanation: I got 100 of the test ^^

m∠MAR is 68°. Answer: 38°.

What is the angle bisectors?

In geometry, an angle bisector is a line or ray that divides an angle into two equal parts. More formally, given an angle ABC, an angle bisector is a line or ray AD such that it divides the angle ABC into two equal angles: ∠ABD ≅ ∠CBD.

Since ray AT bisects ∠MAR, we know that m∠MAT + m∠RAT = m∠MAR.

Substituting the given values, we get:

(4x - 5)° + (2x + 7)° = m∠MAR

Simplifying and solving for x, we get:

6x + 2° = m∠MAR

Now, we know that the sum of the angles in a triangle is 180°. So:

m∠MAT + m∠RAT + m∠MAR = 180°

Substituting the given values and the expression we found for m∠MAR, we get:

(4x - 5)° + (2x + 7)° + (6x + 2°) = 180°

Simplifying and solving for x, we get:

x = 11°

Finally, we can substitute x = 11° into the expression we found for m∠MAR:

6x + 2° = 6(11°) + 2° = 68°

Hence, m∠MAR is 68°. Answer: 38°.

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For the two parallelogram to be congruent, their corresponding sides must be equal

Two figures are said to be congruent if they are of the same shape and their corresponding sides and angles are congruent to each other. The SSS congruency theorem states that two figures are congruent of all their sides are congruent.

For the two parallelogram to be congruent, their corresponding sides must be equal

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Answer: CPCTC

Step-by-step explanation:

edge 23

The value of the variable x can be determined using the circle theorem to

determine the angle formed by x.

The correct responses are;

Reasons:

(1) From circle theorem, we have;

Therefore;

Angle subtended by \(\displaystyle \widehat {AB}\) at center = Angle subtended by \(\widehat {BC}\) at the center;

Therefore;

Angle subtended by \(\displaystyle \widehat {AB}\) at the circumference = Angle subtended by \(\mathbf{\widehat {BC}}\) at the circumference

Which gives;

(2) \(\displaystyle \widehat {AB} = \mathbf{\widehat {CD}}\) given

Angle subtended by arc \(\widehat {CD}\) at the center = x

Equal arcs subtend equal angles at the center of a circle.

Therefore;

Angle subtended by arc \(\mathbf{\widehat {AB}}\) at the center = x

Angle at center = 2 × angle at circumference

Therefore;

x = 2 × 50° = 100°

x = 100°

(3) \(\displaystyle \widehat {AC} = \mathbf{ 3 \times \widehat {AB}}\) given

By definition, we have;

Angle subtended by \(\widehat {AC}\) at the center = 3 × Angle subtended by \(\widehat {AB}\) at the center

According to circle theorem, we have;

Angle at the center = 2 × Angle at the circumference

Let y represent the angle subtended at the circumference by \(\widehat {AB}\), we have;

y = 20°

\(\widehat {AB}\) = 2·y

\(\widehat {AC}\) = 3 × \(\widehat {AB}\) = 3 × 2·y = 6·y

Therefore;

\(\widehat {AC}\) = 6 × 20° = 120°

\(\widehat {AC}\) = 120°

\(\widehat {AC}\) = 2·x

Therefore;

2·x = 120°

\(\displaystyle x = \frac{120^{\circ}}{2} = \mathbf{ 60^{\circ}}\)

x = 60°

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