An item is regularly priced at $83. It is on sale for 35% off the regular price.

The expression 4x^10 y^-3 over 12x-2y is x^8 y^-2 / 3

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression.

1. Eliminate terms from the denominator and numerator.

2. Combine terms that have been multiplied into a single fraction.

3. Add exponents together.

Here, (Given)

4x^10 y^-3 /12x-2y

solving the expression we get

4x^10 / 12x = x^8 / 3

y^-3 / 2y = y^-2

=> x^8 y^-2 / 3

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator).

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The probability of grabbing one blue pen from the given box of 12 pens.

As given in the question,

Total number of given red pens in a box = 4

Total number of given blue pens in a box = 3

Total number of given black pens in a box = 5

Total number of pens in a given box = 4+ 3+ 5

                                                            = 12

Total number of grabbing one pen from the box = ¹²C₁

Total number of grabbing one blue pen out all the pens in the box

= ⁴C₀ × ³C₁ × ⁵C₀

Probability of selecting one blue pen from the box

= (Total number of favourable outcomes )/ ( total number of outcomes)

= (  ⁴C₀ × ³C₁ × ⁵C₀ ) / ( ¹²C₁ )

= ( 1 × 3 × 1 ) / 12

= 3/12

= 1 / 4

Therefore, the probability of grabbing one blue pen from the box of 4 red, 3blue and 5 black pens is equal to ( 1/4 ).

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We can not solve the system of equation because the equations represent two parallel lines (they have no points in common).

Given that,

The system of equations are -3x+y=6 and 6x-2y=25

We must resolve the equation system.

We know that,

Take the system of equation

-3x+y=6 ------->equation(1)

6x-2y=25 ------>equation(2)

We multiply equation(1) by -2 and subtracting them

-2(-3x+y=6)

6x-2y=-12

6x-2y=25

---------------           (subtract)

-12=-25

So, we can not solve the system of equation.

Therefore, We can not solve the system of equation because the equations represent two parallel lines (they have no points in common).

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There are 135 complete revolutions each wheel of his bike will make.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The track has two straight sides each of length 40m. Each end of the track is a semicircle of radius 27m. The diameter of each wheel of Ian’s bike is 590mm.

Now,

The circumference of the wheel of Lan's bike = π × 590 mm

                                                                       = 0.59 π m

And, The perimeter of the cycle track is;

⇒ 40 × 2 + 2π × 27 = 80 + 54π

So, The number of complete revolutions each wheel of his bike will make is ;

⇒ (80 + 54π) ÷ 0.59π

⇒ 135

Thus, There are 135 complete revolutions each wheel of his bike will make.

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Answer: 134

I got this question wrong in some work, the answer is 134.

Answer: d < −7 or d > 35/3

Step-by-step explanation:

Method used to calculate the measure of diversity of species of a particular community is Simpson diversity index which is given by

d = ∑nₐ(nₐ - 1)/N(N - 1).

As given in the question,

Let us consider 'd' represents the diversity of the species in a particular community.

nₐ represents the number of organism  belongs to a particular given species .

N represents the total number of organism present.

Then calculation of Simpson diversity index is given by :

d =∑nₐ(nₐ - 1)/N(N - 1)

The range of the diversity of Simpson diversity index is in between 0 to 1.

Therefore, the calculation Simpson diversity index is given by

d = ∑nₐ(nₐ - 1)/N(N - 1).

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Answer:

$39-($12x2)=$15

$15 ÷$5=3scarves

Step-by-step explanation:

Answer: 4t+109.99=347.95

Step-by-step explanation:

The no: of packages Chelea wrapped is 24

The unitary approach involves calculating the value of a single unit, from which we may calculate the values of the necessary number of units.

a single state. This has an identity element in math, in an algebra. Whose inverse is equivalent to its adjoint (in mathematics, linear algebra, the mathematical study of a matrix or operator).

According to the given question

For every 8 packages the no: of roll used is 1/2

If the person used three 1/2 rolls

the no of packages he wrapped are 3*8

=24

The total no: of packages are are 24

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The statements are -

B(0) = 0 depth in inches 0 minutes after filling began is 0 ; that is at time = 0 ; depth = 0

B(1) represents the function one minutes after filling began. The function gives depth of water in inches 7 minutes after filling began.

B(9) = 11 depicts that the depth in inches if water 9 minutes after filling began is 11.

Solved using the concept of function.

A statement, rule, or law in mathematics specifies the connection between an independent variable and a dependent variable (the dependent variable).

A graph is considered to be a function if any vertical line formed may cross it at most one point. The graph is not a function if it has any locations where a vertical line can pass through it twice or more.

The statement B(0) = 0 means the depth in inches 0 minutes after filling began is 0 ; that is at time = 0 ; depth = 0

B(1) represents the function one minutes after filling began. The function gives depth of water in inches 7 minutes after filling began

B(9) = 11 depicts that the depth in inches if water 9 minutes after filling began is 11.

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The remaining zero of the polynomial 4x³ + 10x² - 6x - 20 is the quotient 4x² + 2x - 10 derived using synthetic division.

The polynomial p(x) = 4x³ + 10x² - 6x - 20 having a zero x = -2 implies that x + 2 is a factor and has another factor derived by dividing p(x) = 4x³ + 10x² - 6x - 20 by x + 2.

we shall derive the other factor using the synthetic division as follows;

divide the first term 4x³ of the polynomial by x (of x + 2) to give 4x²,

multiply x + 2 by 4x² to give 4x³ + 8x²

then subtract 4x³ + 8x² from 4x³ + 10x² - 6x - 20 to give 2x² - 6x - 20

divide 2x² (of 2x² - 6x - 20) by x (of x + 2) to give 2x

multiply x + 2 by 2x to give 2x² + 4x

then subtract 2x² + 4x from 2x² - 6x - 20 to give -10x - 20

divide 10x (of -10x - 20) by x (of x + 2) to give -10

multiply x + 2 by -10 to give -10x - 20

then subtract -10x - 20 from -10x - 20 to give a remainder of zero.

Hence, the results 4x², 2x, and -10 are the terms of the quotient 4x² + 2x - 10 and forms the remaining zeros of the polynomial p(x) = 4x³ + 10x² - 6x - 20.

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Answer:

The answer to this equation is x=-1

Answer:

x = -1

Step-by-step explanation:

[tex]2^{3x + 1}=\frac{1}{4}[/tex]

[tex]2^{3x+1} = \frac{1}{2^{2} }[/tex]

[tex]2^{3x+1} =2^{-2}[/tex]

[tex]3x+1 = -2\\3x = -2 -1\\3x = -3\\x =\frac{-3}{3} \\x = -1[/tex]

Answer: No

Step-by-step explanation:

Linear expression is y=mx + b

14 is just a number, it doesn't have a slope or y-intercept!

The third-degree polynomial function for the given circumstances will be 5y=2(x-1)(x+3)(x+2) with zeros of 3, 2, and 1 and passes through the point (2,8).

Sums of terms of the form k-x^n, where k is any number and n is a positive integer, make up polynomials. For instance, the polynomial 3x+2x-5. a description of polynomials. The concepts degree, standard form, monomial, binomial, and trinomial are all covered in this video. An expression that consists of variables, constants, and exponents and is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

Here,

y=a(x+3)(x+2)(x-1)

x=2 and y=8

8=a(2+3)(2+2)(2-1)

8=a*5*4

a=8/20

a=2/5

y=2/5(x+3)(x+2)(x-1)

5y=2(x+3)(x+2)(x-1)

The polynomial function for given conditions that is third-degree, with zeros of −3, −2, and 1, and passes through the point (2,8) will be 5y=2(x+3)(x+2)(x-1).

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Answer: 7/6

Step-by-step explanation:

1 3/4 can be written as 7/4

1 1/2 can be written as 3/2

7/4 divided by 3/2 equal 7/4 times 2/3 = 14/12 = 7/6

The required answer choice for the linear equation is option 2 (the line would shift up three units).

What is a linear equation?

An equation is said to be linear if the maximum power of the variable is 1. Another name for it is a one-degree equation.

Given, y = 2x

For y-intercept, x = 0

And when the y-intercept is changed to 3. then, y = 3 at x=0

Based on this condition, the equation will be y = 2x + 3

So, the line would shift up three units.

Hence, the required answer choice for the linear equation is option 2.

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Answer:

The line would shift up three units.

An apple would cost $0.6 while a plum would cost $0.25.

The total cost of buying 2 plums and 2 apples will be $1.7

Cost is the value of money that has been used or exchanged up to produce something or deliver a service. Money is an input that is gone in order to acquire something.

If 6 plums sell for $1.50, then;

1 plum will be (1.50/6) = $0.25

Also, if 5 apples cost $3.00, then;

1 apple will be (3/5) = $0.6

Therefore 2 apples will cost: 2 x $0.6 = $1.2

and 2 plums will cost: 2 x $0.25 = $0.5

Total cost for 2 apples and 2 plums will be = $1.2 + $0.5

The total cost = $1.7

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Answer:

[tex]c=5b[/tex]

Step-by-step explanation:

Since we're solving for c, it should be by itself (normally on the left). If you look at the table, c is just 5 times what it's corresponding b value is, so that's what you write as the equation.

The equation of the red graph is x² + 2

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. Mathematical algebraic equations typically have one or more variables.

Since the function in the graph is headed upward , we know the portion of  x²  is positive . And since the highest point of the red line on the y-axis is 2, we can conclude the function represented by the red line is

x² + 2

Therefore the equation of red graph is  x² + 2

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The line shows the solution of 3x−2<2x+1 by solving the inequality.

An inequality in mathematics is a comparison between two numbers or other mathematical expressions that is done in an unfair manner. On the number line, it is most typically used to compare the sizes of two numbers. With one significant exception, inequalities can be resolved in the same manner as equations by applying the same steps to both sides until the variable has been identified. If you multiply or divide by a negative number, you must flip the inequality sign.

A and b are not equal in either situation. These interactions are recognized as robust inequalities.

Given, 3x−2<2x+1

⇒3x−2x<1+2

⇒x<3 or x∈(−∞,3)

The lines y=3x−2 and y=2x+1 both will intersect at x=3

Clearly, the line shows the solution of 3x−2<2x+1.

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The fourth degree polynomial in factor form is p(x) = (x - 8) · (x + 8) · (x - i 8) · (x + i 8), whose standard form is p(x) = x⁴ - 4096.

In this problem we must determine the equation of a polynomial such that it contains the roots 8, - 8, i 8 and - i 8. This can be done by using the definition of a polynomial in factor form:

p(x) = a · Π (x - rₙ), for n = {1, 2, 3, ..., m - 1, m}

Where:

And modify the expression by algebra properties until standard form is found. First, substitute the roots:

p(x) = (x - 8) · (x + 8) · (x - i 8) · (x + i 8)

Second, expand the expression by algebra properties:

p(x) = (x² - 64) · (x² - i² 64)

p(x) = (x² - 64) · (x² + 64)

p(x) = (x² - 64) · x² + (x² - 64) · 64

p(x) = x⁴ - 64 · x² + 64 · x² - 4096

p(x) = x⁴ - 4096

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Answer:

Wdym

Step-by-step explanation:

Answer:

80 megabytes

Step-by-step explanation:

768/384= 2 megabytes per photo

40 x 2 = 80 megabytes

Since the angles are formed by cutting the parallel line, the value of x will be 8.Option A is correct.

It is defined as the angles when two lines intersect each other and at the intersecting point, some pair of angles are formed which we call vertically opposite angles, as the name describes that they have vertically opposite angles.

Since the angles are formed by cutting the parallel line the angle formed as,

15x-6 = 114

15x=114+6

15x=120

x=120/15

x=8

Thus. if the angles are formed by cutting the parallel line, the value of x will be 8.Option A is correct.

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Answer:

y=-1

x=-5

Step-by-step explanation:

Subtract the two equations together to eliminate the 8x

1) -8x+6y=34

-8x-4y=44

2) -8x+6y=34

+8x+4y=-44

3) 10y = -10

4) y=-1

Substitute: -8x+6(-1)=34

-8x=40

x=-5

Answer: False

Step-by-step explanation:

The first term equal to the function x=1

Answer: The cheetah travels 7499.25 further then the snail in 5 seconds

Step-by-step explanation:give brainliest