For any two integers a and b, (a - b) squared = a squared - b squared.
^^^^
Determine if the conjecture is true or false.
If False give a counterexample.

Answer:

31.42m

Step-by-step explanation:

         [tex]C = (22/7) \times d\\C = 3.14 \times 10\\C = \mathrm{31.42m}[/tex]

So, we are to solve: [tex] {8}^{15} \div {8}^{7} \times 8[/tex]

Using the exponential rule of multiplication and division with the same bases, which are:

[tex] {a}^{m} \times {a}^{n} = {a}^{m + n} [/tex]

and:

[tex] {a}^{m} \div {a}^{n} = {a}^{m - n} [/tex]

Therefore:

[tex] {8}^{15} \div {8}^{7} \times {8}^{1} = {8}^{15 - 7 + 1} [/tex]

→[tex] {8}^{9} = 134217728[/tex]

Therefore: 134217728 is the final answer

Answer:

53.5

Step-by-step explanation:

7% of 50 is 3.5 and you add it

Answer:

See the factor tree in the attached image

Step-by-step explanation:

1575 ÷ 5 = 315
315 ÷  5 = 63

63  ÷ 7 = 9

Factors of 9 are 3 and 3

Answer: 54%

15.25500 is 54% of 28.25

Step-by-step explanation: i might be wrong but let me know if i am right (:

(6x+7) and (8x-17)° are both vertical angles; so, the value of x is 12.

When two straight lines cross, the angles that are opposite one another are called vertical angles. (These two lines should technically be on the same plane.)

Angles vertically are congruent.

According to the given value;

Let the angles be A and B; such that:

A = 6x+7

B=8x-17

By theorem of vertical angles

A = B

So, we have:

6x+7=8x-17

Collect like terms

8x-6x=7+17

2x=24

x=12

Hence the value of x is 12.

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From the given table, we have that:

1. The relation of the situation is: (20,2), (22.5, 5), (25,4), (27.5, 4), (29,4), (29,5), (30,1), (30,2), (30,3), (30,4), (30,5), (32.5, 1), (32.5, 3), (35,4), (40,2), (42.5, 3).

2. The domain is {20, 22.5, 25, 27.5, 29, 30, 32.5, 35, 40, 42.5} and the range is {1, 2, 3, 4, 5}.

3. There are inputs such as 25, 29, 30 and 32.5 that are mapped to multiple outputs, hence the relation does not represent a function.

To build the relation, we look at the graph, and write all pairs of (Age, Finishing Place), as follows:

(20,2), (22.5, 5), (25,4), (27.5, 4), (29,4), (29,5), (30,1), (30,2), (30,3), (30,4), (30,5), (32.5, 1), (32.5, 3), (35,4), (40,2), (42.5, 3).

Hence, for the given relation:

The domain is {20, 22.5, 25, 27.5, 29, 30, 32.5, 35, 40, 42.5} and the range is {1, 2, 3, 4, 5}.

A relation represents a function if each value of the input is mapped to only one value of the output.

For this problem, we have that:

There are inputs such as 25, 29, 30 and 32.5 that are mapped to multiple outputs, hence the relation does not represent a function.

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Answer:

1.6

Step-by-step explanation:

first we want to figure out the square roots. the square root of 12 would be 3.5. while the square root of 3 is 1.7

after figuring out the square roots, our equation is -3.5 + 3(1.7)

first we want to multiply 3 by 1.7

this would give us 5.1

leaving our equation as -3.5 + 5.1

our final step is to add 5.1 to -3.5

although i find it easier to just subtract 3.5 from 5.1 since 3.5 is a negative.

this would give us 1.6

The value of integer a is (-a).

To solve this problem first of all we have to understand the concept of opposite integers.

The opposite integers are nothing but an integer with two different sign but has same numerical value.

Suppose there is an integer y then the opposite of integer is -y. And the opposite of an integer -h is +h.

Here it is asked to find the opposite integer of a.

The opposite of integer a is given to be b but the value of integer is -a.

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Answer:

They are not equal.

Step-by-step explanation:

Because the equation is {3x-4}={3x-5} the equation is saying that the two equations are equal, but it is false. {3x-4} is less than {3x-5}, and {3x-5} is greater.

Answer:

This Equation has no soulution

Step-by-step explanation:

3x-4=3x-5

3x - 4 - 3x = 3x -5- 3x Simplify___-4 = -5

The total area of the new tile floor in the restaurant = 240 ft².

A geometric figure is any arrangement of points, lines, or other planes. Depending on the proportions of the figure, geometric figures are frequently categorized as space figures, plane figures, lines, line segments, rays, as well as points.

Geometric forms are any open or closed structures with specific shapes and attribute dreamed up of lines, curves, and points. Geometric shapes include square, rectangles, circles, cones, cylinders, sphere, and so on. All of these forms have characteristics that distinguish them from others.

Length of rectangle  = 15ft

width of rectangle = 12ft

hypotonus = 17ft

First finding the area of the rectangular part:

area = L x B

       = 15 x 12

       = 180 ft²

First finding the area of the triangular part:

Area = 1/2 *(B *h)

        = 1/2 * (8 * 15)

        = 1/2 * 120

        = 60 ft²

The total area of the new tile floor in the restaurant = 180 + 60

                                                                                     = 240 ft²

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The area of the actual base of the castle in square yards is 43200 yards².

From the information, Rena is building a model of a castle using a scale of 1inch = 60 yards. Her model has a rectangular base that is 3 inches wide and 4 inches long.

The normal width will be:

= 60 × 3 = 180

The length will be:

= 4 × 60 = 240

Therefore, the area will be:

= Length × Width

= 240 × 180

= 43200 yards²

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The first diagram shows the parallel lines cut by a transversal.

According to the statement

We have to explain all about the parallel lines cut by a transversal.

So, For this purpose, we know that the

A transversal line is a line that passes through two lines in the same plane at two distinct points.

And

Parallel lines are lines in a plane that are always the same distance apart.

From the given information:

In the given pictures we see that there are the presence of the two parallel lines and a one line is passes through these lines and cut the two parallel lines and there is a formation of the some angles in it.

And by property and the behavior of the transversal line to the parallel lines.

The diagram in first option shows a perfect lines that must be parallel lines cut by a transversal.

So, The first diagram shows the parallel lines cut by a transversal.

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Answer:

45

Step-by-step explanation:

=4+10×2÷4+36

=4+5+36

=45

Answer:

49x=70

Step-by-step explanation:

Answer:

x = -17

Step-by-step explanation:

You can plug in answer choices, or you can get x by itself.

I got x by itself because it is faster. Simply subtract 15 from both sides.

So, you would get x = -2 - 15. Keep change change to subtract negative numbers => -2 + -15 which equals to -17.

So x = -17.

You can also plug it in: 15 + -17 does equal -2.

A 3-by-3 magic square :

5 24 16

26 15 4

14 6 25

A square array of numbers, often positive integers, is referred to as a magic square in recreational mathematics if the sums of the numbers in each row, each column, and both main diagonals are the same.

The following values are listed in the question:

The numbers are 4​, 5​, 6​, 14​, 15​, 16​, 24​, 25​, and 26.

A 3-by-3 magic square is required.

Since the numbers are 4​, 5​, 6​, 14​, 15​, 16​, 24​, 25​, and 26.

Now the sum of all numbers is :

4​ + 5​ + 6​ + 14 + 15​ + 16​ + 24​ + 25​ + 26 = 135

There are now 3 rows and 3 columns, thus the total number is divided by 3.

5 24 16

26 15 4

14 6 25

5 + 24 + 16 = 45

5 + 26 + 14 = 45

26 + 15 + 4 = 45

24 + 15 + 16 = 45

14 + 6 + 25 = 45

5 + 15 + 25 = 45

So, the total of each row and each column is therefore 45.

Therefore, this is a​ 3-by-3 magic square that satisfies the conditions :

5 24 16

26 15 4

14 6 25

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Answer:

B

Step-by-step explanation:

Since the quadilateral rotated 90° from the third quadrant it then lands back on the second quadrant.

Answer: The number of calories burned is dependent on the number of hours working out. For a one-hour workout, there are 240 calories burned, and for a two-hour workout, there are 480 calories burned.

Step-by-step explanation:

By observing the nature of the question, we can decide that the amount of time spent working out dictates the number of calories we burn, making the workout (hours) the independent variable and the calories burned the dependent. This automatically cancels out the answers C and D.

We then just use our knowledge of the table. The hours were assigned 1, 2, and 3, and the calories were 240, 480, and 720. Just make sure the answer reflects that! That gives us answer choice B, The number of calories burned is dependent on the number of hours working out. For a one-hour workout, there are 240 calories burned, and for a two-hour workout, there are 480 calories burned.

The error occurred from line (2) to line (3) i.e., option(b) is correct.

Given that, Line (1): 8x-4 = 2(4x+1)-6, so we will procced to solve line (1) accordingly and then with the steps we will find where the error exactly occur. Let's proceed to solve this question.

8x-4 = 2(4x+1)-6

Now, open or simplify the bracket in RHS, we get

8x-4 = 8x+2-6

Now, simplify RHS accordingly, we get

8x-4 = 8x-4

Now add 4 both sides, we get

8x-4+4 = 8x-4+4

8x = 8x

Now, divide both sides by 8, we get

x = x

Now, subtract x from both sides, we get

0 = 0

Both sides are equal.

⇒ True for all x.

So, from the above calculation steps we can easily concluded that the error occurred from line (2) to line (3).

Hence, option(b) is correct.

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Answer:

What do you mean by choose inverse?

Step-by-step explanation:

We get the distance between the coordinates of the point S and T as 5 √2 units.

We are given the coordinates of two points as:

S = ( - 2, 4 )

T = ( 3, 9 )

We have to find the distance between the points S and T.

We will use the distance formula for this.

Distance = √(x₂ - x₁)² + ( y₂ - y₁)²

Here, we have:

x₁ = -2

x₂ = 3

y₁ = 4

y₂ = 9

Substituting the values in the formula, we get that:

Distance = √(3 + 2)² + ( 9 - 4)² units

Distance = √(5)² + ( 5)² units

Distance = √25 + 25 units

Distance = √50 units

Distance = 5 √2 units

Therefore, we get the distance between the coordinates of the point S and T as 5 √2 units.

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Answer:

Tabla de contenido

Cuando separamos el número 1668 en un coeficiente y una potencia de 10, se obtiene el número 1668 en forma exponencial, pero hay un número indefinido de posibilidades.

Como probablemente desees expresar el número 1668 en notación científica normalizada, el coeficiente o significando de 1668 debe estar en el intervalo de 1 a 10.

En otras palabras, el coeficiente debe ser mayor o igual a 1 y menor a 10, es decir, 1 ≤ |m| < 10.

En esta publicación nos referimos al número 1668 en la versión normalizada, a menos que se indique lo contrario.

No es una convención, pero esto refleja el uso del término en la vida diaria.

Por lo tanto: 1668 = 1.668 × 10^3.

También puedes encontrar el resultado de la conversión numérica en los campos de salida de nuestro convertidor en la parte superior del artículo.

Step-by-step explanation:

Answer:57368

Step-by-step explanation:

put all them on top like this 573                                                                                                                                                                       you can do this                     68

The coordinate of C that is 1/5 the distance from A(4, 2) to B(8, 7) is C(x,y) = {(44/6, (37/6)}

The formula for calculating the point on a line divided into ratio a:b is expressed as;

C(x,y) = {(ax₁+bx₂)/2, (ay₁+by₂)/2}

Given the following coordinate points A(4, 2) to B(8, 7) divided in the ratio 1:5 is expressed as:

C(x,y) = {(1(4)+5(8))/1+5, (1(2)+5(7))/1+5}

C(x,y) = {(44/6, (37/6)}

Hence the coordinate of C that is 1/5 the distance from A(4, 2) to B(8, 7) is C(x,y) = {(44/6, (37/6)}

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Answer:

x^2

Step-by-step explanation:

A number is automatically X. X is any number that is unknown, and the number is unknown in this problem

Answer:

x^2

Step-by-step explanation

x is the number, and since its raised to the second power its x^2

Answer: 3

Step-by-step explanation:

To find the slope you have to divide y over x: y/x or most commonly known as rise/run.

We start at the point where the line is touching a point, in this case it's -8 in the y axis.

Then we count up until we find another point that the blue line is touching. In this case at the coordinates (2, -2). So there's 6 values up from -8 and we have to move to the right 2 values to reach the point the blue line is touching.

So we use the formula rise/run or y/x:

6/2 = 3

This is very hard to explain in just text! I hope you understand

Answer:

sample mean = 12

Step-by-step explanation:

To find the mean of a sample of items, we can use the following formula:

[tex]\boxed{\mathrm{mean = \frac{sum \ of \ items}{number \ of \ items}}}[/tex].

In this question, we are given the following items: 16, 17, 5, 6, and 16.

• sum of items = 16 + 17 + 5 + 6 + 16

                        = 60

• number of items = 5

∴ mean = [tex]\frac{60}{5}[/tex]

             = 12

Therefore, the sample mean is 12.