Solve for x in the diagram below.

Answer:

-4.2

Step-by-step explanation:

First me put a and b in

2x12

24

(24 - 3) = 21

b: -20

-20 divided by 4 = -5

21 divided by -5

Answer= -4.2

The maximum value of f(x, y)=x2-x-y on the region where 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1 is 1.

To find the maximum value, we can set up a system of inequalities and solve it:

0 ≤ x ≤ 1
0 ≤ y ≤ 1
f(x, y)=x2-x-y

Since both x and y are greater than or equal to 0, their product will also be greater than or equal to 0. Therefore, the maximum value of the equation is when x = 1 and y = 0, since it maximizes the positive value of x2 while minimizing the negative value of -x-y. This means that the maximum value of f(x, y) is 1.

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The maximum value of f(x,y)=x^{2}-x-yf(x,y)=x 2 −x−y on the region where \{(x, y): 0 \leq x \leq 1,0 \leq y \leq 1\} is 0.

To find the maximum value, we need to find the critical points of the function and test them within the given region. The critical points are where the partial derivatives of the function are equal to 0.

The partial derivative with respect to x is:
f_x(x,y)=2x-1

The partial derivative with respect to y is:
f_y(x,y)=-1

Setting these partial derivatives equal to 0, we get:
2x-1=0 --> x=1/2
-1=0 --> no solution for y

So the only critical point within the given region is (1/2, y) for any value of y. However, since the partial derivative with respect to y is always -1, the function is decreasing with respect to y. Therefore, the maximum value will occur when y is at its smallest value, which is 0.

Plugging in x=1/2 and y=0 into the original function, we get:
f(1/2,0)=(1/2)^{2}-(1/2)-0=0

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1. The values of x, y, and z are x = 15.5, y = 9.54, and z = 0. 2. The values of x and y are x = 1.4375 and y = 8. 3. The values of x and y are x = 6 and y = 52.5. 4. X can have any value and the triangles will still be similar

1. We are given that ΔPRS is congruent to ΔCFH.

From ΔPRS, we know that:

∠P = 180 - 28 - ∠R

∠P = 152 - 13y

From ΔCFH, we know that CH is the hypotenuse and CF is one of the legs. So, using the Pythagorean Theorem, we have:

CH^2 = CF^2 + FH^2

39^2 = 24^2 + FH^2

FH^2 = 39^2 - 24^2

FH = sqrt(39^2 - 24^2) = 30

Since ΔPRS is congruent to ΔCFH, their corresponding sides are equal. Therefore:

PS = CH = 39

2x - 7 = CF = 24

Solving for x and y:

2x - 7 = 24

2x = 31

x = 15.5

39 = 2x - 7

46 = 2x

x = 23

∠P = 152 - 13y

28 = 152 - 13y

124 = 13y

y = 9.54

Solving for z:

PS = 2x - 7

39 = 2(15.5) - 7

39 = 31

z = 0

Therefore, the values of x, y, and z are x = 15.5, y = 9.54, and z = 0.

2. We are given that ΔABC is similar to ΔDEF. Therefore, the corresponding sides are proportional:

AB/DE = BC/EF = AC/DF

Substituting the given values:

8/(y-6) = 19/(4x-1) = 14/DF

We can solve for x and y using any two of the three ratios.

Let's first solve for x and y using the first two ratios:

8/(y-6) = 19/(4x-1)

Cross-multiplying, we get:

8(4x-1) = 19(y-6)

Expanding the brackets, we get:

32x - 8 = 19y - 114

32x - 19y = -106

Now let's use the third ratio:

14/DF = 8/(y-6)

Cross-multiplying, we get:

14(y-6) = 8DF

Simplifying, we get:

y = (4/7)DF + 6

Substituting this into the equation we got earlier:

32x - 19y = -106

32x - 19[(4/7)DF + 6] = -106

32x - (76/7)DF - 114 = -106

32x - (76/7)DF = 8

Multiplying both sides by 7, we get:

224x - 76DF = 56

Using the equation we got from the third ratio:

14(y-6) = 8DF

14y - 84 = 8DF

14y = 8DF + 84

y = (4/7)DF + 6

Substituting this into the equation we just got:

14[(4/7)DF + 6] = 8DF + 84

8DF + 84 = (56/7)DF + 84

8DF = (56/7)DF

DF = 7

Substituting DF = 7 into the third ratio:

14/DF = 8/(y-6)

14/7 = 8/(y-6)

2 = y-6

y = 8

Now we can substitute y = 8 into the equation we got earlier:

32x - 19y = -106

32x - 19(8) = -106

32x - 152 = -106

32x = 46

x = 1.4375

Therefore, the values of x and y are x = 1.4375 and y = 8.

3. Since ΔZMK ≈ ΔAPY, we know that the corresponding angles are congruent:

m∠M = m∠A

m∠K = m∠Y

Therefore, we can write two equations:

m∠M = 2y + 7

m∠K = 41°

Also, we know that:

m∠M + m∠K + (13x - 37)° = 180°

Substituting the values we have:

112° + 41° + (13x - 37)° = 180°

13x + 116 = 180

13x = 64

x = 4.9231

Substituting x into the third equation:

112° + 41° + (13x - 37)° = 180°

13x + 116 = 180

13(4.9231) + 116 + m∠K = 180

m∠K = 41°

Substituting m∠K = 41° into the second equation:

m∠K = m∠Y

13x - 37 = 41

13x = 78

x = 6

Substituting x into the first equation:

m∠M = 2y + 7

112 = 2y + 7

105 = 2y

y = 52.5

Therefore, the values of x and y are x = 6 and y = 52.5.

4. Since ΔBTS ≈ ΔGHD, we know that the corresponding angles are congruent:

m∠S = m∠H

m∠B = m∠G

Therefore, we can write two equations:

m∠S = 7y + 5

m∠B = m∠G = 21°

Also, we know that:

m∠B + m∠T + m∠S = 180°

Substituting the values we have:

21° + m∠T + 56° = 180°

m∠T = 103°

Now we can use the fact that the sum of the angles in a triangle is 180° to find m∠G:

m∠B + m∠T + m∠G = 180°

21° + 103° + m∠G = 180°

m∠G = 56°

Since we have a pair of similar triangles, we can use their side lengths to set up a proportion:

BS/BT = GD/GH

Substituting the given values:

25/31 = (4x-11)/GH

Solving for GH:

GH = (31/25)(4x-11)

Now we can use the fact that the sum of the angles in a triangle is 180° to find m∠H:

m∠G + m∠H + m∠D = 180°

56° + m∠H + 90° = 180°

m∠H = 34°

Substituting the values we have:

m∠S = 7y + 5

56 = 7y + 5

51 = 7y

y = 7.2857

Substituting y into the first equation:

m∠S = 7y + 5

m∠S = 7(7.2857) + 5

m∠S = 59

Now we can use the fact that the sum of the angles in a triangle is 180° to find m∠T:

m∠B + m∠T + m∠S = 180°

21° + m∠T + 59° = 180°

m∠T = 100°

Now we can use the fact that we have a pair of similar triangles to find x:

BS/BT = GD/GH

25/31 = (4x-11)/GH

25/31 = (4x-11)/((31/25)(4x-11))

Simplifying:

25/31 = 25/31

Therefore, x can have any value and the triangles will still be similar.

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For a rectangular granite slab purchased by Bob with area 18 sq. feet who replacing the laminate countertop, the width of slab is three feet.

We have a homeowner is replacing the laminate countertop with granite. For this he purchased a slab of granite that is 18 square feet. That is area of slab = 18 sq. feet

Length of slab, l = 6 feet

We have to determine the wide of slab. The shape of slab is rectangular. So, we have calculate the width of rectangular slab. Let the width be equal to ' x feet' . As we know, area of rectangle is written as product of length and width of rectangle. Thus, Area = l × x

=> 18 feet² = 6 feet × x

dividing both sides by 6

=> x = 3 feet

Hence, required width is 3 feet.

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Answer:

12/18

Hope this helps!

Answer:

Step-by-step explanation:

2 1/3 because I learned this exact question at school

Answer:

-22 because -22is the opposite of 22

Answer:

x=8

Step-by-step explanation:

-10+4x=22

4x=22+10

4x=32

4x/4=32/4

x=8

To find the surface area of the sphere with a unit cube inscribed, we first need to determine the radius of the sphere. A unit cube has side length 1, and its vertices are at a distance of 1 unit from each other. Since all eight vertices of the cube are on the sphere, we can consider the longest diagonal of the cube to calculate the diameter of the sphere.

The longest diagonal of the cube can be calculated using the Pythagorean theorem in three dimensions: the square of the diagonal (d²) is equal to the sum of the squares of the side lengths (a² + b² + c²), where a, b, and c are the side lengths of the unit cube. In this case, a = b = c = 1. So, d² = 1² + 1² + 1² = 3. Thus, d = √3.

The diameter (d) of the sphere is equal to the longest diagonal of the cube. Therefore, the radius (r) of the sphere is half of the diameter: r = d/2 = √3/2.

Now that we have the radius, we can calculate the surface area (A) of the sphere using the formula: A = 4πr². Plugging in the radius, we get:

A = 4π(√3/2)² = 4π(3/4) = 3π.

So, the surface area of the sphere is 3π square units.

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The answer is option d. -1.865, as it is the value that satisfies P(Z ≤ b) = 0.0311. The other options (-1.87, -1.86, -1.8) do not correspond to the given cumulative probability.

In this scenario, P(Z ≤ b) represents the cumulative probability of a standard normal distribution up to the value of b. To find the corresponding value of b, we need to find the z-score that corresponds to a cumulative probability of 0.0311.

By looking up the z-table or using a statistical calculator, we can find that the z-score corresponding to a cumulative probability of 0.0311 is approximately -1.865.

Therefore, the answer is option d. -1.865, as it is the value that satisfies P(Z ≤ b) = 0.0311. The other options (-1.87, -1.86, -1.8) do not correspond to the given cumulative probability.

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Answer:

Length is 6 feet

Step-by-step explanation:

l=A

w=12

2=6

hope you get it right

The probabilities:

a. P(Z > 1.06) = 0.1446

b. P(Z < -0.29) = 0.3859

c. P(-1.96 < Z < +1.96) = 0.95

d. Z = 1.05

a. Using a standard normal distribution table, we find that the probability of Z being greater than 1.06 is 0.1446.

b. Using the same table, we find that the probability of Z being less than -0.29 is 0.3859.

c. The probability of Z being between -1.96 and +1.96 is 0.95, which can also be found in the standard normal distribution table.

d. To find the value of Z for which only 30.85% of all possible Z-values are larger, we subtract 0.30 (1-0.3085) from 0.5 (since the normal distribution is symmetrical). This gives us 0.20. Using the standard normal distribution table, we find the corresponding Z-value to be approximately 1.05.

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Answer:  

B = 17

C = 28

D = 16

E = 15

F = 18

Hope this Helps! If not I'm sorry :/

Answer:

294cm

Step-by-step explanation:

6 × a² (length of side)

6 × 0.7²

6 × 0.7 × 0.7 = 2.94m

Final answer = 294cm.

Answer:

t = D/r

Step-by-step explanation:

D = rt

Divide each side by r to isolate t

D/ r = rt/r

D /r = t

The time required is D/r

Answer:

You would have 3 1/3 cups of milk left over.

Step-by-step explanation:

1 2/3 * 4 = 6 2/3

10 - 6 2/3 = 3 1/3

To solve the initial-value problem y'' - y' = te^(-1), we can use the method of undetermined coefficients.

Step 1: Find the homogeneous solution

First, we find the solution to the homogeneous equation y'' - y' = 0. This is a linear homogeneous differential equation, and its characteristic equation is r^2 - r = 0. Factoring out an r, we get r(r - 1) = 0. So the roots are r = 0 and r = 1.

The homogeneous solution is then given by y_h = c1e^(0x) + c2e^(1x) = c1 + c2e^x, where c1 and c2 are arbitrary constants.

Step 2: Find a particular solution

Next, we need to find a particular solution to the non homogeneous equation y'' - y' = te^(-1). Since the right-hand side contains te^(-1), we assume a particular solution of the form y_p = (Ax + B)e^(-1), where A and B are constants to be determined.

Differentiating y_p, we have y_p' = Ae^(-1) + Ae^(-1)(-1)x + Be^(-1) = (A - Ax + B)e^(-1).

Differentiating y_p' again, we have y_p'' = (A - Ax + B)e^(-1)(-1) + (A - Ax + B)e^(-1)(-1)x = (2Ax - A - B)e^(-1).

Substituting these into the original equation, we get (2Ax - A - B)e^(-1) - (A - Ax + B)e^(-1) = te^(-1).
Simplifying, we have 2Ax - A - B - A + Ax - B = t.

Matching the coefficients of x and the constant terms on both sides, we have:
2Ax + Ax = t  

--> 3Ax = t  

--> A = t/3.
-A - B - B = 0  

--> -2B = A  

--> -2B = t/3  

--> B = -t/6.

Therefore, a particular solution is y_p = (t/3)x - (t/6)e^(-1).

Step 3: Find the general solution

The general solution to the nonhomogeneous equation is the sum of the homogeneous solution and the particular solution:
y = y_h + y_p = c1 + c2e^x + (t/3)x - (t/6)e^(-1).

Step 4: Apply initial conditions

To apply the initial conditions, we substitute the values of y(0) and y'(0) into the general solution.

Given that y(0) = 1, we have:
1 = c1 + c2 + 0 - (t/6)e^(-1).

Given that y'(0) = 2, we have:
0 = c2 + 1 - (t/6)e^(-1).

Solving these equations simultaneously, we can find the values of c1 and c2.

Finally, substituting the values of c1 and c2 back into the general solution, we obtain the particular solution to the initial-value problem y'' - y' = te^(-1).

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The required graph has been attached below which represents the inequality x ≥ 11 on a number line.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

The inequality is given in the question, as follows:

x ≥ 11

In math, a number line can be defined as a straight line with numbers arranged at equal segments or intervals throughout.

A number line is typically shown horizontally and can be extended indefinitely in any direction.

Thus, the graph has been attached below which represents the inequality on a number line.

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If an nxn matrix A are linearly independent when A is invertible, because option (C) If A is invertible, then the equation Ax = 0 has the unique solution x=0. Since Ax = 0 has only the trivial solution, the columns of A must be linearly independent.

When a matrix A is invertible, it means that there exists a matrix A^-1 such that AA^-1 = A^-1A = I, where I is the identity matrix.

Now suppose that the columns of A are linearly dependent. This means that there exist scalars c1, c2, ..., cn, not all zero, such that

c1A[:,1] + c2A[:,2] + ... + cn×A[:,n] = 0

where A[:,i] represents the i-th column of the matrix A.

In other words, there exists a non-zero vector x = [c1; c2; ...; cn] such that Ax = 0.

Multiplying both sides by A^-1, we get:

A^-1(Ax) = A^-1(0)

x = 0

But this contradicts our assumption that x is non-zero. Therefore, the columns of A must be linearly independent

Therefore, the correct option is (C) If A is invertible, then the equation Ax = 0 has the unique solution x=0. Since Ax = 0 has only the trivial solution, the columns of A must be linearly independent.

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The given question is incomplete, the complete question is:

Explain why the columns of an nxn matrix A are linearly independent when A is invertible. Choose the correct answer below.

A) -1 If A is invertible, then A has an inverse matrix A Since AA = I, A must have linearly independent columns.

B) If A is invertible, then for all x there is a b such that Ax = b. Since x = 0 is a solution of Ax = 0, the columns of A must be linearly independent.

C) If A is invertible, then the equation Ax = 0 has the unique solution x=0. Since Ax = 0 has only the trivial solution, the columns of A must be linearly independent.

D) If A is invertible, then A has an inverse matrix A-1. Since AA-1 =A-1A, A must have linearly independent columns.

Answer:

\(x_1=-2,\: x_2=7\)

Step-by-step explanation:

\(x(x-5)=14\\\\x^2-5x=14\\\\x^2-5x+(\frac{-5}{2})^2 =14+(\frac{-5}{2})^2\\\\x^2-5x+\frac{25}{4}=14+\frac{25}{4}\\\\x^2-5x+\frac{25}{4}=\frac{81}{4}\\ \\(x-\frac{5}{2})^2=\frac{81}{4}\\ \\x-\frac{5}{2}=\pm\frac{9}{2}\\ \\x=\frac{5}{2}\pm\frac{9}{2}\\ \\x_1=-2,\: x_2=7\)

Answer:

g(x) = |4x+3|

Step-by-step explanation:

g(x) = f(x) - 2

=|4x+3|

Answer:

B.

Step-by-step explanation:

The set of all real numbers where  1≤x<18.

Answer:2 hours and 45 minutes

Step-by-step explanation:

11:30+30 mins =12+15 mins = 12:15 + 2 hours = 2:15

The  common ratio is 4.

The next 3 terms are 192,768, 3072

What is common ratio?

In a geometric sequence, ratio of each term to its immediately preceding term is always constant and is known as common ratio.

Here, 48/12 = 12/3 = 4  ( it is a constant ratio )

Hence it is a geometric sequence and common ratio is 4.

Next 3 terms can be found by multiplying the common ratio with the previous term.

48*4=192

192*4=768

768*4=3072

So, the next 3 terms are 192,768, 3072

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x = -1 and y = 3 in equations (i) and (ii):x + y = 2-1 + 3 = 2 (satisfied)3x + y = 0-3 + 3 = 0 (satisfied)

a) Solving the system using substitution:

We know that: x+y=2 (i)3x+y=0 (ii)We will solve equation (i) for y:y=2-x

Now, substitute this value of y in equation (ii):3x + (2-x) = 03x+2-x=0 2x = -2 x = -1

Substitute the value of x in equation (i):x + y = 2-1 + y = 2y = 3b)

Solving the system using elimination (linear combination) :

We know that: x+y=2 (i)3x+y=0 (ii)

We will subtract equation (i) from equation (ii):3x + y - (x + y) = 0 2x = 0 x = 0

Substitute the value of x in equation (i):0 + y = 2y = 2c)

Solving the system by graphing:We know that: x+y=2 (i)3x+y=0 (ii)

Let us plot the graph for both the equations on the same plane:

                                graph{x+2=-y [-10, 10, -5, 5]}

                                 graph{y=-3x [-10, 10, -5, 5]}

From the graph, we can see that the intersection point is (-1, 3)d)

We calculated the value of x and y in parts a, b, and c and the solutions are as follows:

Substitution: x = -1, y = 3

Elimination: x = 0, y = 2

Graphing: x = -1, y = 3

We can see that the value of x is different in parts a and b but the value of y is the same.

The value of x is the same in parts a and c but the value of y is different.

However, the value of x and y in part c is the same as in part a.

Therefore, we can say that the solutions of parts a, b, and c are not the same.

However, we can check if these solutions satisfy the original equations or not. We will substitute these values in the original equations and check:

Substituting x = -1 and y = 3 in equations (i) and (ii):x + y = 2-1 + 3 = 2 (satisfied)3x + y = 0-3 + 3 = 0 (satisfied)

Therefore, the values we obtained for x and y are the correct solutions.

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Answer:

Steps in attached photo.

Step-by-step explanation:

Solution is in attached photo, to find f(x), we have to make y as the subject in terms of x, which means putting y on the left hand side of the equation.

The area bounded between the curve and x-axis between x = 0 to x = 5 is -110/3 square units.

Given equation of the curve is,

y = -x² + 1.

We have to find out the x-intercepts and sketch y with the x-intercepts and also find out the area bounded between the curve and x-axis between x = 0 to x = 5.

a) To find the x-intercepts of y:For the x-intercepts, y = 0.

We can write the above equation as below:

x² = 1x = ±√1 = ±1

Thus, the x-intercepts of y are (1,0) and (-1,0)To sketch the curve, we can use these x-intercepts.

The graph will look like below:

b) To find the area bounded between the curve and x-axis between x = 0 to x = 5:

We can use the definite integral to find out the area bounded between the curve and x-axis.

Definite integral

= ∫(0 to 5) y dx

= ∫(0 to 5) (-x² + 1) dx

= [-x³/3 + x] (0 to 5)

= [-(5³/3) + 5] - [-(0³/3) + 0]

= [-125/3 + 5]

= -110/3

So, the area bounded between the curve and x-axis between x = 0 to x = 5 is -110/3 square units.

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