form the equation: maha's father is 46 years old. He is 6 years older than four times maha's age. (let maha's age be x)​

Answer:

equation: y=15x+95

it would cost $1250

Answer:

f(x) = 95 + 15x

Cost for 77 people = $1250

Step-by-step explanation:

15 x 77 = 1155

1155 + 95 = 1250

The fraction of KM that is required to obtain 20% Vmax is [S] = 0.2 KM.

The Michaelis-Menten equation is given by: V = Vmax[S] / (KM + [S])where, V is the velocity of the reaction, Vmax is the maximum velocity of the reaction,[S] is the substrate concentration, and KM is the Michaelis constant of the enzyme.

Substituting V = 0.2V

max and rearranging the equation,

0.2Vmax = Vmax[S] / (KM + [S])

Multiplying both sides by

(KM + [S]),0.2V

max(KM + [S]) = Vmax[S]

Expanding the equation,

0.2VmaxKM + 0.2Vmax[S]

= Vmax[S]0.2VmaxKM

= 0.8Vmax[S]

Dividing both sides by

Vmax,0.2KM = 0.8[S]

Simplifying the equation,

[S] = 0.2 KM / 0.8[S] = 0.25 KM

Therefore, the fraction of KM that is required to obtain 20% Vmax is [S] = 0.2 KM, which is option (a).

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Answer:

fourth option

Step-by-step explanation:

Given

3x³ + 3x² - 18x ← factor out 3x from each term

= 3x(x² + x - 6) ← factor the quadratic

Consider the factors of the constant term (- 6) which sum to give the coefficient of the x- term (+ 1)

The factors are + 3 and - 2, since

3 × - 2 = - 6 and 3 - 2 = + 1, thus

x² + x - 6 = (x + 3)(x - 2) and

3x³ + 3x² - 18x = 3x(x + 3)(x - 2) ← in factored form

Answer:

The focus would lie at (-8,16)

Step-by-step explanation:

a)Using the Trapezoidal Rule with n=4: T4 = 1.06450

b)Using the Midpoint Rule with n=4: M4 = 1.14750

c)M4 overestimates the area while T4 underestimates the area

d) The true value of the integral is T4<∫10cos(x2)dx and M4<∫10cos(x2)dx

What is Trapezoidal Rule?

The Trapezoidal Rule is a numerical integration method that approximates the area under a curve by approximating it with a series of trapezoids and summing their areas.

According to the given information:

(a) Using the Trapezoidal Rule with n=4:

Δx = (1-0)/4 = 0.25

f(0) = cos(0) = 1

f(0.25) = cos(0.0625) ≈ 0.998

f(0.5) = cos(0.25) ≈ 0.968

f(0.75) = cos(0.5625) ≈ 0.829

f(1) = cos(1) ≈ 0.540

T4 = Δx/2 * [f(0) + 2f(0.25) + 2f(0.5) + 2f(0.75) + f(1)]

≈ 0.25/2 * [1 + 2(0.998) + 2(0.968) + 2(0.829) + 0.540]

≈ 1.06450

(b) Using the Midpoint Rule with n=4:

Δx = (1-0)/4 = 0.25

x1 = 0 + Δx/2 = 0.125

x2 = 0.125 + Δx = 0.375

x3 = 0.375 + Δx = 0.625

x4 = 0.625 + Δx = 0.875

f(x1) = cos(0.015625) ≈ 0.999

f(x2) = cos(0.140625) ≈ 0.985

f(x3) = cos(0.390625) ≈ 0.921

f(x4) = cos(0.765625) ≈ 0.685

M4 = Δx * [f(x1) + f(x2) + f(x3) + f(x4)]

≈ 0.25 * [0.999 + 0.985 + 0.921 + 0.685]

≈ 1.14750

(c) Looking at a sketch of the graph of the integrand, it appears that the function is decreasing on the interval [0,1], so the area under the curve should be decreasing. The Midpoint Rule tends to overestimate the area under a decreasing curve, while the Trapezoidal Rule tends to underestimate it. Therefore, the answers are:

M4 overestimates the area

T4 underestimates the area

(d) We can conclude that the true value of the integral is between the estimates given by the Trapezoidal Rule and the Midpoint Rule, since the Trapezoidal Rule underestimates and the Midpoint Rule overestimates. Therefore, we can say:

E. T4<∫10cos(x2)dx and M4<∫10cos(x2)dx

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Answer:

.

Step-by-step explanation:

Answer:

(-3.2 , 12.3)

(0.7 , 3.6)

Step-by-step explanation:

The rule :

(x, y)→(x−7.5, y+6.8)

For the x - coordinate ; Subtract 7.5

For the y - coordinate `; add 6.8

First input : (4.3, 5.5)

Output :

x = 4.3 - 7.5 = - 3.2

y = 5.5 + 6.8 = 12.3

Output = (4.3, 5.5) →(-3.2 , 12.3)

Second input : (8.2, -3.2)

Output :

x = 8.2 - 7.5 = 0.7

y = - 3.2 + 6.8 = 3.6

Output = (8.2, -3.2)→(0.7 , 3.6)

The outputs obtained are :

(-3.2 , 12.3) and (0.7 , 3.6)

Answer:

 it would be 9/8 as the perimeter

Step-by-step explanation:

you would add all the sides together

1/8+3/4+1/4 = 9/8

Answer:

1 1/8 in.

Step-by-step explanation:

you have to add up all of the sides. 3/4 plus 1/4 equals 1. 1 plus 1/8 equals 1 1/8. Hope I helped you : )

Answer:

210

Step-by-step explanation:

The answer for 7p3 is : 210. This can be solved in the following way: 7p3 is an expression for permutation which means the number of ways of arranging 3 items from a total of 7 items.

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The number of different spanning trees for each graph is: a) K3: 1, b) K4: 4, c) K2,2: 2 and d) C5: 5.

a) The complete graph K3 consists of 3 vertices, and in a spanning tree, we need to have exactly 3 vertices connected without forming any cycles. Therefore, K3 has only one possible spanning tree.

b) The complete graph K4 has 4 vertices. To form a spanning tree, we need to connect all 4 vertices without creating any cycles. K4 can be thought of as a tree with 4 branches extending from a central vertex. Each branch can be connected to any of the other vertices. Hence, there are 4 possible spanning trees for K4.

c) The complete bipartite graph K2,2 consists of 4 vertices divided into two sets, each containing 2 vertices. To form a spanning tree, we need to connect all 4 vertices without creating any cycles. Since there are only two possible edges between the two sets, there are only two possible spanning trees for K2,2.

d) The cycle graph C5 consists of 5 vertices arranged in a circular shape. To form a spanning tree, we need to connect all 5 vertices without creating any cycles. Removing any one of the edges from the cycle will result in a tree. Therefore, C5 has 5 different spanning trees.

Therefore, the number of different spanning trees for each graph is:

a) K3: 1

b) K4: 4

c) K2,2: 2

d) C5: 5  

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Answer:

when x = -5 y is -48

when x is -1 y is -8

when x is 0 y is 2

when x is 1 y is 12

Step-by-step explanation:

The equation of line that passes a point (–3, 7) and has slope of 4, in the point-slope form is y - 7 = 4 (x + 3)

A linear equation can be expressed in three forms:

- slope intercept form : y = mx + c

- point-slope form: y - y₁ = m (x - x₁)

- standard form: Ax + By + C = 0

Where:

m = slope

(x₁, y₁) = point on the line

A, B, C are constant

In this problem, the point is (–3, 7) and the slope is 4. Hence,

x₁ = –3

y₁ = 7

m = 4

Plug these parameters into the equation:

y - y₁ = m (x - x₁)

y - 7 = 4 (x - (-3))

y - 7 = 4 (x + 3)

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Answer:

D

Step-by-step explanation:

when x=1, y should = 2

2(1)=2

so y=2x is correct

While guessing and checking is one way to do this problem, I will show you how to do it algebraically.

Let one side be A

Let the other side be B

2(A+B)=16

A*B=15

First equation because the perimeter is 16 and the second because the area is 15. Now solve the system of equations

A+B=8

A=8-B

Substitute into equation two

B(8-B)=15

-B^2+8b-15=0

B^2-8b+15=0

(B+3)(B+5)=0

B=3,5

A=5,3 respectively

From this we can see that one side is 5 meters long while the other side is three meters long.

Step-by-step explanation

Since we're looking at a rectangle, let's consider its perimeter and area formulas.

Perimeter: 2x + 2y (A rectangle has four sides, with two equal sides, so this is x + x + y + y simplified)

Area: (x)(y) (length x breadth so, x times y)

So we have two equations: 2x + 2y = 16 and x*y = 15. Solve simultaneously. Refer to the attached image.

When the above is simplified using Boolean Algebra, we have F = x' + y' + w'xy.

We can simplify  the Boolean function F = xy'z' + xy'z+ w'xy +   w'x'y' + w'xy using the following Boolean Algebra rules.

Absorption - x + xy = x

Commutativity -  xy = yx

Associativity - x(yz) = (xy)z

Distributivity - x(y + z) = xy + xz

Using the above , we   have

F = xy'z' + xy'z+ w'xy + w'x'y' +   w'xy

= xy'(z + z') + w'xy(x + x')

= xy' +  w'xy

= (x' + y)(x' + y')  + w'xy

= x' + y' + w'xy

This means that the simplified expression is F = x' + y' + w'xy.

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The equation that isolates one of the variables is:

B =3A-5

To isolate one of the variables, we need to rearrange the equations so that the variable appears by itself on one side of the equation.

In the given equations:

1) 3A - B = 5

2) 2A - 3B = -4

To isolate variable B, we can start with equation 1 and add B to both sides:

3A - B + B = 5 + B

Simplifying, we have:

3A = 5 + B

Similarly, to isolate variable A, we can start with equation 2 and subtract 2A from both sides:

2A - 3B - 2A = -4 - 2A

Simplifying, we have:

-3B = -4 - 2A

Thus, the equation that isolates variable B is B = 3A-5. This equation allows us to express B solely in terms of A, with the variable B appearing alone on one side.

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the complete question is:

Which of the following equations isolates one of the variables (A or B) from the given system of equations:

1) 3A - B = 5

2) 2A + 3B = -4

a) 3B = -2A - 4

b) B = 5 - 3A

c) B = 3A - 5

d) 2A = -3B - 4

Which equation, among the options a) to d), expresses one of the variables (A or B) by itself on one side of the equation, following the guideline that isolating a variable is easiest when one of the equations has a coefficient of 1 for that variable?

Answer:

Step-by-step explanation:

Sample Space

off  even numbers

= {2,4,6,8,10}.

There are 5 outcomes in the sample space,

Double-check the input and review the solution provided by the matrix calculator to ensure accuracy.

The matrix calculator is a useful tool for solving equations involving matrices. To find the values of the variables in the matrix calculator, follow these steps:

1. Enter the coefficients of the variables and the constant terms into the calculator. For example, if you have the equation 2x + 3y = 10, enter the coefficients 2 and 3, and the constant term 10.

2. Select the appropriate operations for solving the equation. The calculator will provide options such as Gaussian elimination, inverse matrix, or Cramer's rule. Choose the method that suits your equation.

3. Perform the selected operation to solve the equation. The calculator will display the values of the variables based on the solution method. For instance, Gaussian elimination will show the values of x and y.

4. Check the solution for consistency. Substitute the obtained values back into the original equation to ensure they satisfy the equation. If they do, you have found the correct values of the variables.Remember to double-check the input and review the solution provided by the matrix calculator to ensure accuracy.

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Answer:

Hope it will help you a lot.

Answer:

The solutions to the quadratic equations will be:

\(x=\sqrt{57}+6,\:x=-\sqrt{57}+6\)

Step-by-step explanation:

Given the expression

\(x^2-12x\:=\:21\)

Let us solve the equation by completing the square

\(x^2-12x\:=\:21\)

Add (-6)² to both sides

\(x^2-12x+\left(-6\right)^2=21+\left(-6\right)^2\)

simplify

\(x^2-12x+\left(-6\right)^2=57\)

Apply perfect square formula: (a-b)² = a²-2ab+b²

i.e.

\(x^2-12x+\left(-6\right)^2=\left(x-6\right)^2\)

so the expression becomes

\(\left(x-6\right)^2=57\)

\(\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=\sqrt{a},\:-\sqrt{a}\)

solve

\(x-6=\sqrt{57}\)

add 6 to both sides

\(x-6+6=\sqrt{57}+6\)

Simplify

\(x=\sqrt{57}+6\)

also solving

\(x-6=-\sqrt{57}\)

add 6 to both sides

\(x-6+6=-\sqrt{57}+6\)

Simplify

\(x=-\sqrt{57}+6\)

Therefore, the solutions to the quadratic equation will be:

\(x=\sqrt{57}+6,\:x=-\sqrt{57}+6\)

Answer:

$35

Step-by-step explanation:

Let x represent the price of Douglas fir trees and y represent the noble fir trees

11x + 9y= 1006........equation 1

14x + 9y= 1111.........equation 2

Multiply equation 1 by 14 and equation 2 by 11

154x + 126y= 14,084

-

154x + 99 y= 12,221

27y= 1863

Divide both sides by the coefficient of y which is 27

27y/27 = 1863/27

y= 69

Substitute 69 for y in equation 1

11x + 9y= 1006

11x + 9(69) = 1006

11x + 621= 1006

11x = 1006 -621

11x = 385

x = 385/11

x = 35

Hence the Douglas fir free costs $35

The parametrization  occurrence of X (studying) increases the probability of Y (performing well on the exam) happening given Z (knowledge) in the v-structure X → Z ← Y.

In a v-structure X → Z ← Y, the occurrence of X indeed increase the probability of Y happening given Z, depending on the parametrization of the variables.

To illustrate this, let's consider a different example:

Suppose the v-structure X → Z ← Y, where X represents a student studying for an exam, Z represents the student's knowledge, and Y represents the student's performance on the exam.

Assume the following parametrization:

If the student studies (X = 1), their knowledge (Z) improves, increasing the probability of performing well on the exam (Y = 1).

If the student does not study (X = 0), their knowledge (Z) does not improve, decreasing the probability of performing well on the exam (Y = 1).

In this parametrization, that the occurrence of X (studying) increases the probability of Y (performing well on the exam) happening given Z (knowledge). When the student studies (X = 1), their knowledge (Z) improves, leading to a higher chance of performing well on the exam (Y = 1). Conversely, if the student does not study (X = 0), their knowledge (Z) does not improve, reducing the probability of performing well on the exam (Y = 1).

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Answer For The Number 22: Factors of 22 are 1, 2, 11, 22. There are 4 integers that are factors of 22. The greatest factor of 22 is 22. 3.

Answer For The Problem 2x3 (Divide it by the numbers I give you meaning divide the number two by what I give yo and the other number 3 by it.

The common factors for 2,3 are −1,1 . The numbers do not contain any common variable factors. The GCF (HCF) of the numerical factors −1,1 is 1 .The number is one.

Answer For The Problem 2x5 is also 1 so decide both 2&5 by 1 then multiply. After doing that for answers 2&3 add them. last if you then subtract 22 that might be the answer so put that & also put the answer of the greatest common factor of 22 which is 3. Make sure to include that the one where you subtracted 3 was the greatest common factor for 22.

Answer:

Probably  c:  f(x) = y + 3

Step-by-step explanation:

See attached worksheet

It is true that when you design an algorithm, it should be general enough to provide a solution to many problem instances, not just one or a few of them.

In mathematics, an algorithm is a process, a description of a series of steps that may be used to solve a problem; however, they are now far more prevalent than that.

Although many areas of research (and daily life) employ algorithms, long division's step-by-step process is probably the most prevalent example.

Thus, It is true that when you design an algorithm, it should be general enough to provide a solution to many problem instances, not just one or a few of them.

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Answer:

B: 72

Step-by-step explanation:

Here, we want to find the measure of arc AC

Mathematically, we will use an angle arc relationship here

The angle arc relationship to use here is that the arc AC is twice the measure of angle ABC

Thus, we have the arc AC as 2 * 36 = 72 degrees

Answer:

BX = 7 inches

Step-by-step explanation:

Since ABCD is a rectangle, the diagonals are equal and bisect each other

⇒ AC = BD and

AX = CX = BX = DX = AC/2 = BD/2

⇒ BX = A/2

⇒ BX = 14/2

⇒ BX = 7

Answer:

You would need $18 total to buy the racks needed.

Step-by-step explanation:

First, every 20 CDs needs a new rack, so you would divide 120 by 20.

120 / 20 = 6 racks

Second, you would multiply the price ($3) of a rack by how many racks needed.

3 * 6 = $18

Answer:

25,36,49,64,81,100

................................

Answer:

Your answer is 1, 4, 9, 16, 25, 36, 49, 64, 81, 100.

Step-by-step explanation:

1 - 4  

+ 3

4 - 9

+ 5

9 - 16

+ 7

+9, +11, +13, +15, +17, +19...

Answer:

The number is 24

Step-by-step explanation:

Let x = number

Add 16 to the number

x+16

Is equal to 40

x+16 = 40

Subtract 16 from each side

x+16-16 = 40-16

x = 24