How many numbers greater than 4000 can be formed with the digits 2 3 4 5 and 6 when no digit is repeated?

Answer:

f(x) and g(x) have the same y-intercept.

The area of the parallelogram is 12 square units.

A parallelogram is a quadrilateral having opposing sides that are parallel, as its name indicates. As a result of this definition, the following properties of parallelograms are true: opposing sides and opposite angles are congruent, and two consecutive angles are supplementary.

A parallelogram's area is the area that it occupies in a two-dimensional plane.

A parallelogram is a special form of quadrilateral with two opposing sides that are parallel to one another. A parallelogram's opposing sides and angles are the same size and length.

Area = b × h Square units (Where “b” is the base and “h” is the height of the parallelogram)

Given that,

b = 4

h = 3

So. area = 3*4= 12 square units.

Thus, the area of the parallelogram is 12 square units.

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The Quadratic equation that relates the area of both Rectangular components is 2w^2-4w=0, value of w=2, area of combined figures=20 unit^2.

What are quadratic equations ?

A quadratic equation is a second-degree algebraic equation in x. In its usual form, the quadratic equation is ax^2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term. The first requirement for an equation to be a quadratic equation is that the coefficient of x^2 is not zero (a ≠ 0). When expressing a quadratic equation in standard form, the x^2 term comes first, then the x term, and lastly the constant term. The numeric values a, b, and c are commonly expressed as integral values rather than fractions or decimals.

Now,

As Two components have same area

w*(7-w)=w*(3+w)    (Area of rectangle = length*breadth)

2w^2-4w=0     -----  1

From 1

w(2w-4)=0

w=0/2 as w can not be zero.

So, w=2

Now area of combined figure = w*(7-w)+w*(3+w)

                                                 =2*5+2*5

        area of combined figure =20 unit^2

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Answer:

D

Step-by-step explanation:

[tex]\frac{15}{x-6}[/tex] + [tex]\frac{7}{x+6}[/tex]

before we can add the fractions we require them to have a common denominator.

the common denominator is (x - 6)(x + 6)

= [tex]\frac{15(x+6)}{(x-6)(x+6)}[/tex]  + [tex]\frac{7(x-6)}{(x-6)(x+6)}[/tex]

= [tex]\frac{15x+90+7x-42}{(x-6)(x+6)}[/tex] ← expand denominator using FOIL

= [tex]\frac{22x+48}{x^2-36}[/tex]

Answer:

3.75

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Jefferson plus 3 of his friends = 4 people

Each person needs 1.25 containers, so the total clay needed:

4 x 1.25 = 5 containers

The determinant of the matrix 3PQ is given as follows:

9630.

The matrix P for this problem is defined as follows:

P = [9 -3]

     [2 4]

The matrix Q for this problem is defined as follows:

Q = [3  -2]

      [4  6]

To multiply matrices, the rows of the first are multiplied by the columns of the second, hence:

Hence the matrix PQ is given as follows:

PQ = [15 -35]

        [22 20].

Multiplying by the constant, the matrix 3PQ is given as follows:

3PQ = [45  -105]

          [66     60]

Hence the determinant is given as follows:

45 x 60 - (-105) x 66 = 9630.

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Answer:

ratio of y/x=7/5

when value of x =15

then value of y=15*7/5=21

so value of y=21

i am from india btw

Step-by-step explanation:

Using the zero product, the solutions to the equation x² + x - 30 = 12 are  A. x=-7 or x=6

From the question, we have the following parameters that can be used in our computation:

x^2 + x - 30 = 12

Express the exponent as a proper superscript

So, we have the following representation

x² + x - 30 = 12

Subtract 12 from both sides

This gives

x² + x - 42 = 0

Expand

x² + 7x -6x - 42 = 0

When the equation is factored, we have

(x +_7)(x - 6) = 0

Solve for x

x = -7 and x = 6

Hence, the solutions are x = -7 and x = 6

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Answer:

Step-by-step explanation:

Answer:

The Number of cupcakes Team A receives is 30

Step-by-step explanation:

Given,

Number of Cup Cakes = 75

Team A = 2x

Team B = 3x

To Find : Number of Cakes Team A receives

In order to find x we Put the values in a equation

2x+3x=75

5x = 75

x = [tex]\frac{75}{5}[/tex]

x = 15

Team A = 2x = 2x15 = 30Cupcakes

Team B = 3x = 3x15 = 45Cupcakes

Hence , the number of cupcakes Team A receives is 30

Examining the graph the quadratic function is increasing at

A quadratic graph is a traces the part of a parabola, while quadratic equation is a polynomial equation with 2 degrees.

The behavior of the quadratic function is lowest at the symmetry or point of vertex. other sides by the left or right the function is increasing

The vertex is at point (3, 0) this is same as say x = 3. points above this point shows increasing values of function y and points below the value shows increasing values for function y too

this is represented as x > 3 for x above 3 and x ,< 3 for x below the value of 3

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The required equation that has no solution is given as,
(A) 2(x + 2) + 2 = 2(x + 3)+1
(B) 2x + 3(x + 5) = 5(x- 3)
(E) 5(x + 4) - x = 4(x + 5) - 1

What is simplification?

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Among the equation which have no solutions, when simplifying the variable in the equation get canceled.

(A)
2(x + 2) + 2 = 2(x + 3)+1

Simplifying,
2x + 4 + 2 = 2x + 6 + 1

Isolating the variable terms,

2x -2x = 6 + 1 - 2 -4
0 = 7 - 6

That shows the equation  2(x + 2) + 2 = 2(x + 3)+1 has no solution.

Similarly, when all the equation simplifies. It is found that,

The equation that has no solution is given as,
(A) 2(x + 2) + 2 = 2(x + 3)+1
(B) 2x + 3(x + 5) = 5(x- 3)
(E) 5(x + 4) - x = 4(x + 5) - 1

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If the hexagon has the side length as 10 units , then the area of hexagon is square units is 259.8 .

What is a Hexagon ?

A Hexagon is defined as a closed two dimensional figure that has 6 sides . and a regular hexagon has all 6 sides equal and all 6 angles equal .

the formula to calculate the area of hexagon can be written as :

Area = [tex]\frac{3\sqrt{3}\; s^{2} }{2}[/tex] ;

the side length of hexagon (s) is = 10 units ;

substituting the side length ,

we get ;

Area = [tex]\frac{3\sqrt{3}\; (10)^{2} }{2}[/tex] ;

On simplifying ,

we get ;

Area of hexagon is = 259.8 square units .

The given question is incomplete , the complete question is

How many square units is the area of the hexagon that has a side length of 10 units ?

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Club A starts off with a higher value and changes at a faster rate by 3 movies.

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to express the connection between two phrases on either side of a letter. Frequently, for example, 2x - 4 = 2.

given

Club A:

y = 0·5

y=0.75+2.25

y = 3

Club A starts off with a higher value and changes at a faster rate by 3 movies.

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The slope intercept form for the given situation is y = 2.5x+22, where x is number of weeks and y is total cost she saves.

The slope intercept of an equation refers to the equation in the form y = mx + c, where m is the slope that gives the rate of change and c is the y intercept, which is constant.

Given that, Emma started with some money from her birthday and then saved the same amount from her allowance each week. After 4 weeks of saving, Emma had $32. After 8 weeks of saving she has $42.

We are asked to find the slope intercept form for the given situation,

Let she have $c with her and a be the amount she saves every week.

We have,

4a+c = 32

8a+c = 42

Subtracting the equations,

4a = 10

a = 2.5

That means, she saves $2.5 every week.

Now finding the value of c,

4(2.5)+c = 32

c = 32-10

c = 22

Therefore, she already has $22 with her.

Now, establishing the slope intercept form,

y = 2.5x+22

Where, y is the total cost she saves, x is the number of weeks

Hence,  the slope intercept form is  y = 2.5x+22, Where, y is the total cost she saves, x is the number of weeks.

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Answer:

Below

Step-by-step explanation:

I previously answered this Q here:

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Answer:

So basically you will switch the predicate and proposition (p implies q) and we will negate it so not q implies not p. So we will say that both x and y should be 25 or greater and that the sum will be 50 or greater. Below you will find the steps. I just took this course and got a 96% so i think u should get near to full points on something along the lines of this answer. The only thing u may have to change is that we should probably use k and j for x and y but off the top of my head i cannot recall exactly how to word that. Then prove using k and j but the logic is exactly the same. Its just how proofs work. Substitute in a variables for variables ..

Step-by-step explanation:

Proof by contraposition : Let x and y be real numbers. Assume x is a real number greater than or equal to 25 and y is greater than or equal to 25 and the sum of x and y is greater than or equal to 50. We can then take the minimum 25 and 25 and the sum of this gives 50. This satisfies our minimum requirement of 50 since any other number combination will be above 50 we have proven by contraposition that for the sum of two real numbers x and y one number must be less than 25 to be create a sum less than 50

Total it can make 04 mid array comparisons it will take to find number 101.

Binary Search :

Binary search is an advanced search algorithm that searches and retrieves data from a sorted list of items. Its core working principle is to halve the data in the list until the desired value is displayed to the user in the search results. Binary search is commonly known as half-interval search or logarithmic search.

According to the question:

Given:

Array: 1 5 10 13 48 68 100 101

Required:

Determine the number of comparisons to get to 101

The length of the list is 8. So, the first index is 0 and the last is 7.

List(0) = 1 , List (1) = 5 , List (2) = 10 , List(3) = 13, List(4) = 48 , List(5) = 68 , List (6) = 100 and List (7) = 101.

The element is 101 is on the far right of the array. This means that the execution time of the algorithm will be worst. The worst-case execution time for the binary search algorithm is given by

              Tₙ = [ log₂ (n +1)]

where, [x]  is the floor function that gives the greatest integer less than or equal to x, and log₂ (n) is the logarithm of n  to base 2.

In this case, the number of elements in the array, n = 8. So,

     Tₙ = [ log₂ (n +1)]

⇒  T₈ = [log₂ (8) + 1] =4

So, the algorithm will need to make 4 mid-array comparisons to get to 101.

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No, (−5, −4) is not a solution of the system. The ordered pair (−5, −4) is a point in the Cartesian plane, but it is not necessarily a solution of any system of equations.

To determine whether an ordered pair is a solution of a system of equations, we must substitute the values of the ordered pair into the equations in the system and determine whether the equations are true.

For example, consider the following system of equations:

3x − 5y = 20

2x + 4y = 10

To determine whether (−5, −4) is a solution of this system, we must substitute the values of x and y into the equations and determine whether the equations are true.

For the first equation:

3x − 5y = 20

3(-5) − 5(-4) = 20

15 + 20 = 20

35 ≠ 20

For the second equation:

2x + 4y = 10

2(-5) + 4(-4) = 10

-10 - 16 = 10

-26 ≠ 10

Since neither equation is true when the values of (−5, −4) are substituted into the equations, we can conclude that (−5, −4) is not a solution of the system.

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Answer:

[tex]s=\sqrt[3]{V}[/tex]

Step-by-step explanation:

This is a problem in which we can utilize equation rules to solve for s. In order to isolate s, we need to remove that power of 3. To do that, we can take the cubed root of V. Thus, the answer is

[tex]s=\sqrt[3]{V}[/tex]

Answer: A

Step-by-step explanation: I took the test

A circle is considered a two-dimensional (2D) shape because it has length and width, but no thickness or depth. In other words, a circle exists in a plane and can be defined mathematically as the set of all points that are a fixed distance (the radius) away from a central point (the center).

Another way to think about it is that a circle can be drawn on a flat surface such as a piece of paper, and it can be measured in terms of its diameter and circumference, but it has no thickness or height. It's just a line that goes around and around that creates a loop. While it's a "round" shape, but it has no depth.

In contrast, a three-dimensional (3D) shape has length, width, and height or depth. Examples of 3D shapes include spheres, cubes, and cylinders, which can be thought of as "extruded" versions of 2D shapes such as circles, squares, and rectangles.

It's also important to note that, while a circle is a two-dimensional shape, it is also an important building block for many three-dimensional shapes like a sphere, cylinders, and many more solid shapes.

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Answer:

Starting with the left side of the equation:

cos² a + cos² a cot² a

We can simplify the left side by using the identity cot² a = 1/tan² a

cos² a + cos² a * (1/tan² a)

We can simplify further by using the identity tan² a = (1/cos² a) - 1

cos² a + (1 - cos² a)

Now we have the left side of the equation equals to 1 which is the right side of the equation.

Step-by-step explanation:

see above

Step-by-step explanation:

[tex]\displaystyle\\cos^2\alpha +cos^2\alpha cot^2\alpha =\\\\cos^2\alpha (1+cot^2\alpha )=\\\\cos^2\alpha (1+\frac{cos^2\alpha }{sin^2\alpha } )=\\\\cos^2\alpha (\frac{sin^2\alpha +cos^2\alpha }{sin^2\alpha } )=\\\\cos^2\alpha (\frac{1}{sin^2\alpha } )=\\\\\frac{cos^2\alpha }{sin^2\alpha }=\\\\cot^2\alpha[/tex]

The number of pieces and total cost of each shape is as follows;

1) Number of pieces = 6

Total Cost = 6 * 0.12 = $0.72

2) Number of pieces = 4

Total Cost = 4 * 0.66 = $2.64

3) Number of pieces = 3

Total Cost = 4 * 0.02 = $0.08

4) Number of pieces = 4

Total Cost = 4 * 0.04 = $0.16

5) Number of pieces = 4

Total Cost = 4 * 0.04 = $0.16

6) Number of pieces = 4

Total Cost = 4 * 0.02 = $0.08

1) This piece is a hexagon which has 6 sides and as such;

Number of pieces = 6

Cost of each piece = $0.12

Total Cost = 6 * 0.12 = $0.72

2) This piece is a trapezium which has 4 sides and as such;

Number of pieces = 4

Cost of each piece = $0.66

Total Cost = 4 * 0.66 = $2.64

3) This piece is a Triangle which has 3 sides and as such;

Number of pieces = 3

Cost of each piece = $0.02

Total Cost = 4 * 0.02 = $0.08

4) This piece is a square which has 4 sides and as such;

Number of pieces = 4

Cost of each piece = $0.04

Total Cost = 4 * 0.04 = $0.16

5) This piece is a rhombus which has 4 sides and as such;

Number of pieces = 4

Cost of each piece = $0.04

Total Cost = 4 * 0.04 = $0.16

6) This piece is a rhombus which has 4 sides and as such;

Number of pieces = 4

Cost of each piece = $0.02

Total Cost = 4 * 0.02 = $0.08

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Answer:

26 spoons

Step-by-step explanation:

[tex]\frac{2}{3}[/tex] = [tex]\frac{x}{39}[/tex]

3 x 13 = 39

2 x 13 = 26

The difference between 1.6 * 10⁸ and 8.2 * 10⁷ is 7.8 * 10⁷. This is written in scientific notation.

Using scientific notation, one can express extremely big or extremely small values. When a number between 1 and 10 is multiplied by a power of 10, the result is represented in scientific notation. For instance, 650,000,000 can be represented as 6.5* 10⁸  in scientific notation.

Given two numbers 1.6 * 10⁸ and 8.2 * 10⁷

or we can write them as 16 * 10⁷ and 8.2 * 10⁷

Difference between these two numbers=  16 * 10⁷ - 8.2 * 10⁷

Difference between these two numbers=7.8 *10⁷

Therefore, 7.8 * 10⁷ is the difference between 1.6 * 10⁸ and 8.2 * 10⁷. This is presented in notation used in science.

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|x - 30| = 10 is the correct equation for calculating Jack's maximum and minimum time to fold his laundry. he correct option is D.

The problem statement says that Jack's time can vary from the average of 30 minutes by 10 minutes. This means that the maximum and minimum time will be 30 minutes plus or minus 10 minutes, or 40 minutes and 20 minutes, respectively. We can represent these values using the variable x.

The maximum time will be represented by x + 10 and the minimum time will be represented by x - 10. We can use the absolute value function to represent the difference between these two values and the average time of 30 minutes.

The absolute value function is represented as |x|. The absolute value of x is the distance between x and 0 on a number line. For example, the absolute value of -5 is 5, because the distance between -5 and 0 on a number line is 5 units.

Using the absolute value function, we can represent the difference between the maximum and minimum times and the average time of 30 minutes as follows:

|x + 10 - 30| = |x - 30| = 10

|x - 20| = 10

|x - 30| = 10

Therefore, the correct equation is |x - 30| = 10.

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It is true that the pond will be filled up after 13 hours of pumping at the same rate of sump pump.

A rate is a special ratio in which the two terms are in different units. For example, if a 12-ounce can of corn costs 69¢, the rate is 69¢ for 12 ounces. This is not a ratio of two like units, such as shirts. This is a ratio of two unlike units: cents and ounces.

Let the volume of the pond be x cubic unit

The rate of the pumping pipe is x/5 cubic unit/hour

The rate of the draining pipe = x/8cubic unit / hour.

after 13hours

The volume pumped into the pond =

x/5 × 8 = 13x/5 cubic unit

The volume of water drained =

x/8 × 13 = 13x/8 cubic unit.

Therefore the volume of water left =

13x /5 - 13x/8 = (104x - 65x)/40

= 39/40 of x

= 0.975 of x.

approximately to the nearest cubic units = 1 of x

Therefore it is true that the pond will be filled up after 13 minutes.

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The length of the third side of the triangle given is 10 units.

Right angled triangle are those triangle for which one of the angle is 90 degrees.

For a right angled triangle, Pythagoras Theorem states that,

Hypotenuse² = Base² + Height²

Here, Base = 7 and Height = √51

Substituting these values,

Hypotenuse² = (7)² + (√51)²

                      = 49 + 51

                      = 100

Hypotenuse = √100 = 10

Hence the length of the missing side is 10.

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The entry to replenish the petty cash fund will include:.

Receipts = $383

Cash short of = $5

To replenish the petty cash fund , we need $387.

A fund is a pool of money that is allocated for a specific purpose. A fund can be established for many different purposes: a city government setting aside money to build a new civic center, a college setting aside money to award a scholarship or an insurance company that sets aside money to pay its customers’ claims. Individuals, businesses, and governments all use funds to set aside money. Individuals might establish an emergency fund—also called a rainy-day fund—to pay for unforeseen expenses or a trust fund to set aside money for a specific person.

Total Receipts and Coin = Coins in Cash Fund + Currency Plus in Receipts  = $62 + $383

= $445

Shortage of Petty Cash Account

= $445 - $450

= - $5

For recording this we debited the petty cash receipts as it increased the assets and credited the cash as it decreased the assets and the balancing is transferred to cash short and over

Thus, The entry to replenish the petty cash fund will include:.

Receipts = $383

Cash short of = $5

To replenish the petty cash fund, we need $387.

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