Using expanded forms, explain why the following problems with unlike bases do not follow the multiplication and division rules of exponents

Pls hurry and thank you!!!!

On solving the provided question, we can say that by permutation 26 possible letters  x  10 possible digits  = 260 possible plates

The permutation of a set in mathematics is essentially the rearranging of its elements if the set is already ordered, or the arrangement of its members in a linear or sequential order. The act of altering the linear order of an ordered set is referred to as a "permutation" in this context. The mathematical calculation of the number of possible arrangements for a given set is known as permutation. Permutation, in its simplest form, refers to the variety of possible arrangements or orders. The placement of the elements matters with permutations. The placement of items in a specific order is known as a permutation. Here, the set's components are sorted in either chronological order or linear order. like in the case of

26 possible letters  x  10 possible digits  =

26 x 10   =

260 possible plates

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Answer:

-131

Step-by-step explanation:

2×2×3×4-15×2×2×3+-1

48-179

=-131

The measure of the angle ∠SUT will be 30°. Then the correct option is C.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The exterior angle of a triangle is almost always equal to the addition of the interior and opposing interior angles. The term "external angle property" refers to this feature.

The measure of the angle ∠SUT is calculated as,

∠SUT + ∠UTS = ∠JST

∠SUT + 80° = 110°

∠SUT = 110° - 80°

∠SUT = 30°

The measure of the angle ∠SUT will be 30°. Then the correct option is C.

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Answer:

[tex]80^{\circ}[/tex]

Step-by-Step Explanation:

The interior angles of the triangle are [tex]70^{\circ}, (14+6x)^{\circ}[/tex], and [tex](3x-3)^{\circ}[/tex].

Angles in a triangle add to [tex]180^{\circ}[/tex].

[tex]70+14+6x+3x-3=180 \\ \\ 81+9x=180 \\ \\ 9x=99 \\ \\ x=11[/tex]

So, [tex]m\angle A=14+6(11)=80^{\circ}[/tex].

Answer: 14 pieces.

Step-by-step explanation: 1 foot = 12 inches

12 feet of rope = 144 inches of rope

144 / 20 = 7.2 = 7 sections can be cut from each package.

The greatest number of pieces from 2 packages = 14 pieces

Answer

14 pieces

Step-by-step explanation:

First you need to convert the 24 feet into inches. Do this by multiplying 24 (feet) by 12 (inches) since 1 foot has 12 inches in it and you have 12 feet. This means he has 288 inches of rope. Then divide 288 by 20 since he wants to see how many 20 inch pieces he can cut. You should get 14.4 but since it asks for the greatest number of pieces you need to round it down to 14 since he wants full 20 inch pieces.

No, 1, 2, and 3 are not valid side lengths for a triangle. So 1, 2 and 3 cannot make a triangle.                                                                      

In order for a shape to be a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. This is known as the triangle inequality theorem.                                                              

3 + 2 = 5 > 1

3 + 1 = 4 > 2

1 + 2 = 3 not greater than 3

So as 1 + 2 not greater than 3, these set of side lengths does not follow the theorem. Thus a triangle cannot be formed with sides of length 1, 2, and 3.

--The question is incomplete, answering to the question below--

" Can 1, 2 and 3 make the sides of a triangle?"

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Each child's real height falls between 1.60 and 1.28, with the tallest child's height difference at 0.32 and the smallest child's height difference at 0.04 respectively.

a) The ranges that each child's actual height falls within is ;

Here, Daisy is 1.28 meters short while Isaac is 1.56 meters tall at his tallest.

b) The largest height difference between the tallest and shortest child is 1.60-1.28 =0.32m , while the smallest height difference is 1.60-1.56 = 0.04meters.

A number's possible range of values before being rounded or truncated is known as an error interval. Inequalities are frequently used to express error intervals as a range having a lower bound and an upper bound.

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Answer:   The mystery number is 5.5

5.5 converts to the fraction 11/2.

=================================================

Explanation:

The phrasing "subtract 10 from the number, then square the result" leads to the expression [tex](\text{x}-10)^2[/tex]

The phrasing "Square the number, then subtract 10 from the result" means we have [tex]\text{x}^2-10[/tex]

Set those expressions equal to one another so we can solve for x like shown in the steps below.

[tex](\text{x}-10)^2 = \text{x}^2-10\\\\\text{x}^2-20\text{x}+100 = \text{x}^2-10\\\\-20\text{x}+100 = -10\\\\-20\text{x} = -10-100\\\\\text{x} = -110/(-20)\\\\\text{x}=11/2\\\\\text{x} = 5.5[/tex]

The x^2 terms cancel out in the third step (since we subtract x^2 from both sides).

--------------

Check:

[tex](\text{x}-10)^2 = \text{x}^2-10\\\\(5.5-10)^2 = (5.5)^2-10\\\\(-4.5)^2 = (5.5)^2-10\\\\20.25 = 30.25-10\\\\20.25 = 20.25[/tex]

The answer is confirmed.

Answer: Maisie walked 6.4 miles.

Step-by-step explanation:

Since Maisie is walking at a constant pace of 1.6 miles per hour we can set up the following equation:

y = 1.6(x)

In this equation, Y is the number of miles Maisie walked in total and X is the number of hours she walked. All we have to do is plug in 4 hours as x and solve.

y = 1.6(4)

y = 6.4 miles.

Natha can chew between 9 to 10 chewing gum each day so that it could last for 6 days.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, Nathan had 58 pieces of gum that he wants to make last six days.

Therefore, The number of chewing gums he can chew is the total number of chewing gums he has divided by the total number of days which is,

= (58/6).

= 9.66 chewing gums but it should be a whole number.

So, Nathan can chew between 9 to 10 chewing gums each day.

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The value of  expression - a² - 2bc - |c| if a = -2, b = 3, and c = -3, is 11.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.

Given:

- a² - 2bc - |c|, a = -2, b = 3, and c = -3,

Plug the values of a, b, and c as shown below,

- a² - 2bc - |c|  = -(-2)² - 2 × (3) × (-3) - |-3|

- a² - 2bc - |c|  = - 4 - 6 × (-3) - 3

- a² - 2bc - |c|  = -4 + 18 - 3

- a² - 2bc - |c|  = 18 - 7

- a² - 2bc - |c|  = 11

Thus, the value of the expression is 11.

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[tex]\displaystyle\\Answer:\ none \ of\ these\ (m=-\frac{5}{3} );\ isosceles,\ right[/tex]

Step-by-step explanation:

1.

a) find the midpoint G of the side DE:

[tex]x_D=-2\ \ \ \ x_E=3\ \ \ \ y_D=-2\ \ \ \ y_E=1[/tex]

[tex]\displaystyle\\x_G=\frac{x_D+x_E}{2} \\\\x_G=\frac{-2+3}{2}\\\\x_G=\frac{1}{2}\\\\x_G=0.5[/tex]

[tex]\displaystyle\\y_G=\frac{y_D+y_E}{2}\\\\y_G=\frac{-2+1}{2} \\\\y_G=\frac{-1}{2} \\\\y_G=-0.5\\\\Thus,\ G(0.5,-0.5)[/tex]

b) find the midpoint I of the side DF:

[tex]x_D=-2\ \ \ \ x_F=6\ \ \ \ y_D=-2\ \ \ \ y_F=-4[/tex]

[tex]\displaystyle\\x_I=\frac{x_D+x_F}{2} \\\\x_I=\frac{-2+6}{2} \\\\x_I=\frac{4}{2} \\\\x_I=2[/tex]

[tex]\displaystyle\\y_I=\frac{y_D+y_F}{2}\\\\y_I=\frac{-2+(-4)}{2}\\\\y_I=\frac{-6}{2} \\\\y_I=-3\\\\Thus,\ I(2,-3)[/tex]

c) the slope of GI:

[tex]x_G=0.5\ \ \ \ x_I=2\ \ \ \ y_G=-0.5\ \ \ \ y_I=-3[/tex]

[tex]\displaystyle\\m_{GI}=\frac{y_I-y_G}{x_I-x_G} \\\\m_{GI}=\frac{-3-(-0.5)}{2-0.5} \\\\m_{GI}=\frac{-3+0.5}{1.5} \\\\m_{GI}=\frac{-2.5}{1.5} \\\\m_{GI}=\frac{-2.5(2)}{1.5(2)} \\\\m_{GI}=-\frac{5}{3}[/tex]

2.

Type of Δ DEF:

a) find the length of the side DE:

[tex]|DE|=\sqrt{(3-(-2)^2+(1-(-2)^2}\\\\|DE|=\sqrt{(3+2)^2+(1+2)^2} \\\\|DE|=\sqrt{5^2+3^2}\\\\|DE|=\sqrt{25+9} \\\\|DE|=\sqrt{34} \ units[/tex]

b) find the length of the side EF:

[tex]|EF|=\sqrt{(6-3)^2+(-4-1)^2}\\\\|EF|=\sqrt{3^2+(-5)^2}\\\\ |EF|=\sqrt{9+25} \\\\|EF|=\sqrt{34}\ units[/tex]

Hence, DE=EF

c)  find the m∠DEF:

[tex]\displaystyle\\cos \angle E=\frac{\overrightarrow {DE}+\overrightarrow {EF}}{|DE|*|EF|} \\\\[/tex]

Find the coordinates of the vector by the coordinates of its beginning and end points:

[tex]\displaystyle\\\overrightarrow {DE}=(x_E-x_D,y_E-y_D)\\\\\overrightarrow {DE}=(3-(-2),1-(-2))\\\\\overrightarrow {DE}=(5,3)\\\\\overrightarrow {EF}=(x_F-x_E,y_F-y_E)\\\\\overrightarrow {EF}=(6-3),-5-1)\\\\\overrightarrow {EF}=(3,-5)\\Hence,\\\\cos\angle E=\frac{5*3+3*(-5)}{\sqrt{34}*\sqrt{34} } \\\\cos\angle E=\frac{15-15}{34 }\\\\cos\angle E=\frac{0}{34 }\\\\cos\angle E=0\\\\m\angle E=90^0[/tex]

[tex]\huge\text{Hey there!}}[/tex]

[tex]\mathsf{x^2 - 4x = 0}[/tex]

[tex]\text{Factor the LEFT side of your given equation to make it easier to solve}[/tex]

[tex]\mathsf{x(x - 4) = 0}[/tex]

[tex]\text{Set the factors to equal to the number 0}[/tex]

[tex]\mathsf{x - 4 = 0\ \& \ x = 0}[/tex]

[tex]\text{Simplify find and you should be able to have your answer to the given equation}[/tex]

[tex]\mathsf{x = 4 \ \& \ x = 0}[/tex]

[tex]\huge\text{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{x = 4\ or \ x = 0}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

[tex]\{x|x\in \mathbb{Z}, 7 < x < 50\}[/tex]

Step-by-step explanation:

Basically, the above answer tells us that the set of all x such that x belongs to Z, the set of integers, and x is between 7 and 50.

Solutions refers to the answer to the problem, Real Solutions are realistic and practical whereas ideal solutions are the best cases for the solutions.

In mathematics, a solution refers to a value or set of values that satisfies a given equation, system of equations, or problem. For example, if the equation is x + 2 = 4, then the solution is x = 2, because substituting 2 for x in the equation makes it true. In the case of systems of equations or more complex problems, a solution may be a set of values that satisfies all the equations or conditions of the problem. In such case, the solution may be represented graphically or as coordinates of a point.

In mathematics, an ideal solution refers to a solution that meets all the desired criteria or requirements without any constraints. It is the "best case" scenario. A real solution, on the other hand, refers to a solution that takes into account all the limitations and constraints of a problem. It is a more practical and realistic solution.

Ideal Solutions - Best cases, Usually not possible.

Real Solutions - Practical and possible to attain.

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f(n) = 56 + 3(n − 1) is the correct option represents the formula for the sequence.

In arithmetic sequences, each term is made larger by the addition or removal of a constant called k. Unlike a geometric sequence, where each term increases by being multiplied by or divided by a fixed constant k,

If there is a consistent difference between the words in a sequence of numbers, the sequence is referred to as an arithmetic progression. Think about the mathematical progression where the numbers 5, 7, 9, 11, 13, and so on all have a common difference of 2.

An is defined as a1 + d(n - 1), where d is the average difference between terms in the series, and a1 is the first term.

Given data :

This is the formula of an arithmetic sequence.

f(n) =   a1 + d(n - 1)

An arithmetic sequence begins with 56, 59, 62, 65, 68,

=   = 56.

d = 59 - 56 = 3

so the formula is f(n) = 56 + 3(n − 1)

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The expression that best represents the value of π is 37.68 / 12.

The circumference of a circle is the distance round the circle. The radius of a circle is the distance from the center of the circle to any point on the circumference.

The formula for circumference of a circle = 2πr

Where:

π = pi

r = radius

π = circumference / 2r

π = 37.68 / (2 x 6)

π = 37.68 / 12

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Answer:

3

Step-by-step explanation:

[tex]\displaystyle \frac{4}{7}*5\frac{1}{4}=\frac{4}{7}*\frac{21}{4}=\frac{21}{7}=3[/tex]

If his plants are indoors, he must water them at least once a week or they will die.

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The solution of the equation 2x+y=4 and 3x-2y=-1 is the value of x = 1, while the value of y = 2

We have, the sets of equations as:

2x+y=4 and 3x-2y=-1?

As here, let 2x+y = 4 ----(i) and 3x-2y = -1 ----(ii)

As here to solve the value of x and y we will first equalise the co-efficient of x.

Here, the co-efficient of x in the first equation is 2, while in the second equation it is 3

So, for equalising, we will first multiply the first equation by 3 and the second by 2,

Thus, we will get it as:

6x+3y=12 ----(iii)

6x-4y=-2----(iv)

Now subtracting (iv) from (iii)

We will get,

7y = 14

=>y=2

Putting the value of y in (i),

2x=4-y = 4-2 =2

=>x = (2/2)=1

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The complete question may be like:

What is the solution of the equations 2x+y=4 and 3x-2y=-1?​

All points in Quadrant IV have a positive x-coordinate and a negative y-coordinate.

The fourth quadrant, indicated as Quadrant IV, is in the bottom right quadrant. The x-axis in this quadrant has positive values, whereas the y-axis has negative numbers.

A two-dimensional Cartesian system's axes split the plane into four infinite areas called quadrants, each of which is limited by two half-axes. These are frequently numbered from first to fourth.

A quarter of a circle; a 90° arc. the region enclosed by an arc and two radii are drawn one to each extreme. As a mechanical component, anything is shaped like a quarter of a circle.

All Quadrant I points have two positive coordinates.

Quadrant II points all have a negative x-coordinate and a positive y-coordinate.

All Quadrant III locations have two negative coordinates.

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The correct answer is option A. For P= -1/2 0 1/2 1/2 0 -1/2 0 0 1 D= 0 4 0 0 0 4 -1 0 0. The matrix can be diagonalized using the eigenvectors.

To diagonalize the matrix, the eigenvectors must be found first. The eigenvectors can be found by solving the characteristic equation and finding the eigenvalues. The eigenvalues of the matrix are 2 and -1. The eigenvectors associated with each eigenvalue are determined by solving the eigenvalue equation.

The eigenvectors for the matrix are [1, -2], [1, 2], [1, 0], and [0, 1]. After the eigenvectors are found, the matrix can be diagonalized by constructing the transformation matrix P. The transformation matrix P is composed of the normalized eigenvectors. The transformation matrix P is: P=[-1/2, 0, 1/2, 1/2, 0, -1/2, 0, 0, 1], and the diagonal matrix D is composed of the eigenvalues.

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Answer:

The union of the intervals is (0,8]

The intersection of the intervals is [1,5]

Hope this helped!

Answer: 110% of 120 minutes is equal to 132 minutes.

Step-by-step explanation:

To calculate percentiles:

A semi-circular protractor with a diameter of 15 cm has the perimeter of 38.5 cm.

What is the perimeter?

The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges. Its dimensions are expressed in linear units like centimetres, metres, inches, and feet.

The formula for perimeter of a semi-circle is -

πr+2r

Where r is the radius of the semi-circle.

The diameter d of semi-circle is 15 cm.

The radius of the semi-circle is -

r=d/2

r=15/2

r=7.5 cm

Plugging the values in the equation -

=πr+2r

=(3.14)(7.5)+2(7.5)

=23.5+15

=38.5 cm

Therefore, the value for perimeter is obtained as 38.5 cm.

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Use synthetic division to divide (3x2 + 7x - 18) by (x - 3).The result of the division is (3x + 5)/(x - 3).

The first step is to write out the dividend and the divisor, and put a 0 in the box below the dividend.

3x2  +7x  -18

x - 3   0

The next step is to divide the divisor into the first term of the dividend.

3x2  +7x  -18

x - 3   0

3  -9

Next, we multiply the divisor by the result from the previous step and subtract it from the second term of the dividend.

3x2  +7x  -18

x - 3   0

3  -9  5

Next, we multiply the divisor by the result from the previous step and subtract it from the third term of the dividend.

3x2  +7x  -18

x - 3   0

3  -9  5  -15

Finally, we divide the last result by the divisor.

3x2  +7x  -18

x - 3   0

3  -9  5  -15  3

The result of the division by synthetic division is (3x + 5)/(x - 3).

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The cuboidal tank has a volume of [tex]6m^3[/tex] with dimensions of 4 m in length, 2 m in width, and 0.75 m in height.

The total amount of room or volume that a cuboidal tank can hold is known as its capacity. By multiplying the tank's length, width, and height collectively, it is determined.

The tank in this instance measures 4 metres long, 2 metres wide, and 0.75 metres high. We must multiply these three parameters collectively to determine the tank's capacity:

[tex]4m * 2m * 0.75m = 6m^3[/tex]

The tank can therefore hold [tex]6m^3[/tex] of liquid.

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Yes, 5x - 3y = 7 is a linear equation in two variables (x and y)

A linear equation in two variables is an equation in the form ax + by = c, where a, b, and c are real numbers and a and b are not both 0. In this equation, 5x 3y, the coefficients of the variables are 5 and 3, respectively, so a = 5 and b = 3. Therefore, 5x 3y is a linear equation in two variables.

A linear equation in two variables (x and y) is an equation that can be written in the form ax + by = c, where a and b are real numbers and a and b are not both 0. This means that any equation that has two variables with real coefficients will be a linear equation. For example, 5x 3y is a linear equation in two variables because the coefficients of the variables x and y are 5 and 3, respectively. Therefore, 5x 3y is a linear equation in two variables.

the complete question is : Is 5x-3y=7 a linear equation in one variable?

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Answer:

[tex]y=0[/tex]

Step-by-step explanation:

[tex]y+25=25 \\ \\ y=25-25 \\ \\ y=0[/tex]

Answer:

[tex] \sf \: y = 0[/tex]

Step-by-step explanation:

Given equation,

→ y + 25 = 625 ÷ 25

Now the value of y will be,

→ y + 25 = 625 ÷ 25

→ y + 25 = 25

→ y = 25 - 25

→ [ y = 0 ]

Hence, the value of y is 0.