A large pizza pie with 15 slices is shared among x students such that each student's share is 3 slices. Write it as a mathematical statement.

Whereas working with laws of exponents, when splitting the exponential equations with the same base, the exponents ought to be subtracted.

Basically, the Quotient of Powers rules is used to decrease the number of terms when parts like terms with exponents. In order to get the solution, just remove the exponents while dividing the terms with the same base, it is applicable to exponents with the same bases. when powers are multiplied,  for two whole numbers of the same bases the exponents are added, whereas when powers are divided for two whole numbers of the same bases,  exponents are subtracted. The zero exponent rule basically states that when any number is raised to the power of zero it results in 1.

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The solution of the given equation w.r.t m is m = 3 ,i.e., option A

With one exception, algebraic equations are essentially algebraic expressions.

An = sign is required in all algebraic equations.

No matter what kind of equation it is, all equations use the = sign.

The next topic is algebraic expression, which lacks the operators =,,, >, and.

To put it simply, there is no comparison between two terms in an algebraic statement.

Algebraic expressions frequently use terms like polynomial and square root.

So you now recognize the distinction between the two?

1) An algebraic equation has the symbol =, and 2) an algebraic expression lacks any comparison symbols (such as > and =).

As per the question:

[tex]6\frac{1}{9} + 3\frac{1}{3} =28\frac{1}{3}[/tex]

55/9 + 10/3 = 85/3

(55m+30m)/9 = 85/3

85m/9 = 85/3

85m = (85*9)/3

85m = 85*3

m = (85*3)/85

∴ m = 3

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We will determine the final price as follows:

So, the final price is approximately $12.74.

1) Since the equation of the circle is given by:

And we've been told the Center (1,-5) and one point located at the circumference, (2,1). So let's find the radius, i.e. the distance from the center to any point to the circumference.

2) Let's use the Formula for the distance between (1,-5) and (2,1), derived from the Pythagorean Theorem:

3) So d = radius, and now we can plug those pieces of information into the formula of the circle:

So we now have the formula for that circle.

Answer:

Radius (R) is equal to the distance between the points (-2,1) and (3,1)

R² = (1 - 5)² + (1 - 1)² = (-24)² + 0 = 579

R =  23.16

Answer:

80,200

Step-by-step explanation:

There is a formula for the sum of a series of numbers from a_1 to a_n.

S = (a_n * a_n+1)/2

This formula means: multiply the last number of the series by what would be the next number, and divide by 2.

The last number you have is 400. The next number would be 401.

Multiply 400 by 401 and divide by 2. That is the sum of the 400 numbers.

S = (401 * 402)/2

S = 160400/2

S = 80200

Answer: The sum is 80,200

Here's a way to understand the formula.

You are adding 400 numbers, from 1 to 400.

Write the first 200 numbers on a line:

1   2   3   4   5   6   7   8   9   10   11   12   13   14   15   ...   198   199   200

Now write the next 200 numbers, from 201 to 400 under these numbers, but start from 400 and go down 1 each number to the right.

You end up with these two lines:

1        2       3        4       5       6        7        8      9        ...     198   199   200

400  399   398   397   396   395   394   393  392    ...    203  202   201

Now add every two numbers in the same column.

1        2       3        4       5       6        7        8      9        ...     198   199   200

400  399   398   397   396   395   394   393  392    ...    203  202   201

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

401   401   401    401    401    401    401    401   401     ...    401   401   401

Now you have 200 times the number 401.

200 * 401 = 80,200

Answer:

The total surface area is;

Explanation:

Given the square pyramid as show in the attached image.

The total surface area is the sum of the area of the base square and the area of the four triangles.

Given;

substituting the given values;

Therefore, the total surface area is;

We get that the distance is

so the answer is 5

The most appropriate choice for the similarity of figures will be given by:

So,

(A) HIJK∼WXYZ [Given].

(B) The two triangles are similar [Given].

(C) 5cm on the drawing represented 2 miles on the ground.

Let 22.5 cm on the drawing represent x miles on the ground.

The problem:

x = 9 miles22.5 cm on the drawing represented 9 miles on the ground.

Therefore, the most appropriate choice for the similarity of figures will be given by:

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The greatest common factors of 2^5 · 5· 11 and 2^3· 5^2 · 7 is equivalent to 2^3 * 5

The largest positive integer that divides each of two or more non-zero integers is known as the greatest common divisor.

This factor must be able to divide all the terms of the expression withour remainder.

Given the numbers 2^5 · 5· 11 and 2^3· 5^2 · 7. Find the factors;

2^5 · 5· 11 = 2^3 * 2^2 * 5 * 11

2^3· 5^2 · 7= 2^3 * 5 * 5 * 7

Since the number 2^3 * 5 is common to both factors, hence the GCF of these numbers 2^5 · 5· 11 and 2^3· 5^2 · 7 is 2^3 * 5

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Since the scaling factor of the dilation (0.5) is fewer than 1, it shrinks (make smaller) the triangle around the origin (zero). Intuitively, the dilation is getting the points of the triangle closer to zero (in a way that preserves the shape of the triangle).

Formally, to know the coordinates of a point of the triangle after the dilation, we just need to multiply the original coordinates of the point by the scaling factor (this works for the dilation is around zero).

The original coordinates of D are

Multiplying them by the scale factor, we get

The coordinates of D after the given dilation is

Answer:

There are 35 episodes in the show

Answer:

I think it is y

Step-by-step explanation:

The expression we have is:

We need to compare this equation of our parabola, with the general equation of a parabola in vertex form:

Where (h,k) is the vertex of the parabola, and a indicates if the parabola opens up or opens down (if a is positive the parabola opens up, and if a is negative the parabola opens down).

We take our equation:

And we arrange the terms so that it looks like the vertex form:

And we can find the values of a, h, and k:

We only need h and k for the vertex:

Answer: the vertex is at (0,-7)

The expected number of the real number in any sample size is 150.

What is sample size?

In statistics, the sample size refers to the group of people whose data is analyzed during calculation. Depending upon the constraints, the data is analyzed for the measurement. The analysis of samples is perform with the help of Binomial distribution.

According to the question, the given random sample can be solved with the help of Binomial distribution:

The sample size of teachers: n = 50

Percentage of ghost workers: 30%

Percentage of real workers: 70%

For ghost workers: n = 50 and p = 0.31 and q = 1 - p = 1 - 0.31 = 0.69

Now, to calculate the expected number of the real workers as per given samples:

For real workers: n = 50 and p = 0.70 and q = 1 - p = 1 - 0.70 = 0.30

Expected number is: (n)(q) = (50)(0.30) = 150

Hence, the expected number of the real number in any sample size is 150.

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Writing the given trigonometry expression: cos(2 tan inverse (x)) as algebraic expression gives

Data given in the question are as follows:

cos(2 tan inverse (x))

Using trigonometry (double angle formula)

cos 2x = 1 - 2sin² x

when x = tan inverse (x)

cos(2 tan inverse (x))  = 1 - 2sin² tan inverse (x)        (1)

cos² x + sin² x = 1

cos² x = 1 - sin² x

cos x = √(1 - sin x)

tan x = sin x / cos x

[tex]tan x = \frac{sinx }{\sqrt{1-sin^{2}x } }[/tex]

squaring all parts of the trigonometry expression and clearing the fraction

[tex]tan^{2}x = \frac{sin^{2} x }{1-sin^{2}x }[/tex]

[tex](tan^{2}x) (1-sin^2x) = sin^2x[/tex]

[tex]tan^{2}x-tan^{2}xsin^2x = sin^2x[/tex]

[tex]tan^{2}x = sin^2x+tan^{2}xsin^2x[/tex]

[tex]tan^{2}x = sin^2x(1+tan^{2}x)[/tex]

[tex]sin^2x = \frac{tan^{2}x}{(1+tan^{2}x)}[/tex]

since tan (tan inverse) (x) = x

[tex]1 - 2sin^2 tan^{-1} (x) = 1 - 2x^2 / (1 + x^2)[/tex]

[tex]=\frac{ 1 + x^2 -2x^2}{1+x^2}[/tex]

[tex]=\frac{ 1 -x^2}{1+x^2}[/tex]

Therefore trigonometry expression cos(2 tan inverse (x)) gives an algebraic expression in the form (1-x²) / (1+x²)

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What is the product of



In the multiplication of fractions, you multiply the numerators with each other and the denominators with each other

( - 3/5) *(-7/8)

= -3*-7 / (5*8) = (positive)

= 21/40

_____________________

Answer

= 21/40

_____________________

Do you have any questions regarding the solution?

​

solve each of the expressions

the correct operator is =.

The probability that the sales will will remain steady is; 7/30 or 0.233

We are given the numbers generated by the simulator for the sales as;

0, 1, 0, 2, 0, 0, 0, 1, 0, 3, 2, 0, 0, 0, 0, 2, 1, 2, 3, 1, 2, 0, 2, 0, 3, 0, 0, 2, 1, 0, 1

Now, we are given the following implications of the simulator as;

Now, we want to find the probability that the sales will will remain steady which is the point at which it assigns 1 from the 30 numbers generated. Thus;

P(sales will remain steady) = 7/30 = 0.233

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Answer: 695.30

Step-by-step explanation: We know that 634.8 is what the monthly mortgage is, then we use the value of $726 and divide it by 12 which represents the 12 months in a year. So 726 ÷ 12 = 60.5 therefore monthly he will additionally need to pay that amount. I don't think the annual real estate taxes are going to be used for this problem. So after this, we do the following equation. 634.8 + 60.5 = 695.3. We round this value to the nearest cent and we get 695.30. When the digit to the right is less than 5 we round toward 0... 695.3 was rounded down toward zero to 695.30

Answer:

33by 11

Step-by-step explanation:

in 41 3 games firstly we find 1 point it is 3by41

Step 1:

The ratio for 5ml to 120ml

Step 2:

The symbol of ratio is :

Therefore,

Step 3

Final answer

1 : 24

The Standard form of the equation will be;

⇒ x - 5y = -21

What is Standard form of equation?

The standard form of the equation is defined as;

Ax + By = C

Where, A, B and C are integers.

Given that;

The equation in slope - intercept form as;

⇒ y - 3 = 1/5 (x + 6)

Now,

We convert the equation in standard form as;

Since, The equation in slope - intercept form as;

⇒ y - 3 = 1/5 (x + 6)

Change into standard form as;

⇒ y - 3 = 1/5 (x + 6)

Multiply by 5 both side, we get;

⇒ 5( y - 3) = (x + 6)

⇒ 5y - 15 = x + 6

Add 15 both side, we get;

⇒ 5y - 15 + 15 = x + 6 + 15

⇒ 5y = x + 21

Subtract 21 both side, we get;

⇒ 5y - 21 = x + 21 - 21

⇒ 5y - 21 = x

Subtract 5y both side, we get;

⇒ 5y - 21 - 5y = x - 5y

⇒ - 21 = x - 5y

⇒ x - 5y = -21

Therefore,

The Standard form of the equation will be;

⇒ x - 5y = -21

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Answer:

294 grams

Explanation:

The amount of radioactive material left after t hours given that the half-life is to hours is

Now, in our case t0 = 3, t = 9 and P = 2352 g; therefore, the above equation gives

which is our answer!

Hence, the amount of radioactive copper left after 9 hours is 294 grams.

Answer

The equation in point-slope form is

y - 1 = (-10/3) (x + 2)

We can then simplify this by multiplying through by 3 to obtain

3y - 3 = (-10) (x + 2)

3y - 3 = 10x - 20

3y = 10x - 20 + 3

3y = 10x - 17

Explanation

The general form of the equation in point-slope form is

y - y₁ = m (x - x₁)

where

y = y-coordinate of a point on the line.

y₁ = This refers to the y-coordinate of a given point on the line

m = slope of the line.

x = x-coordinate of the point on the line whose y-coordinate is y.

x₁ = x-coordinate of the given point on the line

We can calculate the slope of the line and then use any of the two points given to serve as the point (x₁, y₁) in the equation

For a straight line, the slope of the line can be obtained when the coordinates of two points on the line are known. If the coordinates are (x₁, y₁) and (x₂, y₂), the slope is given as

For this question,

(x₁, y₁) and (x₂, y₂) are (-5, 11) and (-2, 1)

x₁ = -5

y₁ = 11

x₂ = -2

y₂ = 1

Slope = m = (-10/3)

Using the point (-2, 1) as (x₁, y₁), we can write the equation of the line

y - y₁ = m (x - x₁)

y - 1 = (-10/3) (x - (-2))

y - 1 = (-10/3) (x + 2)

We can then simplify this by multiplying through by 3 to obtain

3y - 3 = (-10) (x + 2)

3y - 3 = 10x - 20

3y = 10x - 20 + 3

3y = 10x - 17

Hope this Helps!!!

A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation.

The expression [tex]$&\left(\frac{\left(\frac{1}{2}\right)^{-1}}{\left(\frac{1}{2}\right)^2}\right)^3\left(\frac{1}{2^{-1}}\right)^2 \\[/tex], we get 2048.

Exponent rules include: Rule of the product of powers: When multiplying like bases, add the powers together. Rule of the quotient of powers: When splitting like bases, take the powers out. Power of powers rule: When increasing a power by another exponent, multiply all the powers together.

A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation.

Let the value be 2048

[tex]$&\left(\frac{\left(\frac{1}{2}\right)^{-1}}{\left(\frac{1}{2}\right)^2}\right)^3\left(\frac{1}{2^{-1}}\right)^2 \\[/tex]

simplifying the above expression we get

[tex]$&\left(\frac{\left(\frac{1}{2}\right)^{-1}}{\left(\frac{1}{2}\right)^2}\right)^3=512 \\[/tex]

[tex]$&=512\left(\frac{1}{2^{-1}}\right)^2[/tex]

By using exponent rule, we get

[tex]$&\left(\frac{1}{2^{-1}}\right)^2=\frac{1^2}{\left(2^{-1}\right)^2} \\[/tex]

[tex]$&=512 \cdot \frac{1^2}{\left(2^{-1}\right)^2}[/tex]

1² = 1

[tex]$&=512 \cdot \frac{1}{\left(2^{-1}\right)^2}[/tex]

[tex]$\left(2^{-1}\right)^2=\frac{1}{4}$$[/tex]

[tex]$=512 \cdot \frac{1}{\frac{1}{4}}$$[/tex]

[tex]$\left(2^{-1}\right)^2=\frac{1}{4}$$[/tex]

[tex]$=512 \cdot \frac{1}{\frac{1}{4}}[/tex]

[tex]$&\frac{1}{\frac{1}{4}}=4 \\\pi[/tex]

= 512 × 4

= 2048

By simplifying the expression [tex]$&\left(\frac{\left(\frac{1}{2}\right)^{-1}}{\left(\frac{1}{2}\right)^2}\right)^3\left(\frac{1}{2^{-1}}\right)^2 \\[/tex], we get 2048.

Therefore, the correct answer is option (b).

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Answer: 22.8 miles or 22 4/5

Step-by-step explanation:

To find the unit rate you do

28.5 ÷ 1.25 = 22.8

Answer:

C

Step-by-step explanation:

the function calculates the number of pages left to print. that means for every minute it subtracts a number of pages from the total of pages (that total being 152 pages).

the colored print only manages 30 pages per minute, while the pure black ink printing manages 33 pages per minute.

Answer:

For A and B, we have (10, 6)

For C and D, we have (12, 8)

For E and F, we have (12, 8)

Explanation:

To determine the missing numbers along each side of the triangle, we have to

*Add the two numbers at the vertex

*Subtract it from 32

*Divide it by 2

*Add 2 to it to have the 1st number

*Subtract 2 from it to have the 2nd number

So to find the pair of numbers that can be used for A and B, we'll have;

Therefore the missing numbers for A and B are 10 and 6.

So to find the pair of numbers that can be used for C and D, we'll have;

Therefore the missing numbers for C and D are 12 and 8.

So to find the pair of numbers that can be used for E and F, we'll have;

So to avoid repetition of any of the numbers between 4 and 12, we have to add and subtract 1 instead of 2.