Evaluate 0.5^3 and 0.5^-3 as fraction

The equation -x² + 3x - 3 = 0 has the sum of the roots as 3. Given that a quadratic equation's roots add up to three.

A quadratic polynomial in terms of the zeroes (α,β) is given by

x2 - (sum of the zeroes) x + (product of the zeroes)

f(x) = x2 -(α +β) x +αβ

From the options,

A) 2x² - 3x + 6 = 0

Dividing by 2,

x² - 3/2x + 3 = 0 ------------------ (2)

Comparing (1) and (2),

α + β = 3/2

Therefore, the sum of the roots of the equation is 3/2.

B) -x² + 3x - 3 = 0

The equation can be written as x² - 3x + 3 = 0 ------------- (3)

By comparing (1) and (3),

α + β = 3

Therefore, the sum of the roots of the equation is 3.

C) √2x² - 3/√2x + 1 = 0

Dividing by √2,

x² - 3/2x + 1/√2 = 0 ------------ (4)

By comparing (1) and (4),

α + β = 3/2

Therefore, the sum of the roots of the equation is 3/2.

D) 3x² - 3x + 3 = 0

Dividing by 3,

x² - x + 1 = 0 -------------------------- (5)

By comparing (1) and (5),

α + β = 1

The equation's roots are added together, and the result is 1.

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The solution of the equation 8x + 3y = 5 and 3x + 2y = 5 is x = -5/7 and y = -7/24

In math the term called equation is defined as a mathematical statement that shows that two mathematical expressions are equal

Here we have given that the equation 8x + 3y = 5 and 3x + 2y = 5 and we need to solve the equation to find the values of x and y.

in order to solve the equation we have to multiply 2 with the equation (1), then we get,

=> 16x + 6y = 10

And then we have to multiply 3 with the equation (2), then we get,

=> 9x + 6y = 15

Now, we have to subtract these two equation then we get,

=> 7x = -5

=> x = -5/7

Then the value of y is calculated as,

=> 8(-5/7) + 3y = 5

=> -40/7 + 3y = 5

=> 3y = -35/40

=> 3y = -7/8

=> y = -7/24

Therefore, the solution is found.

Complete Question:

What is the solution of the equations 8x + 3y = 5 and 3x + 2y = 5?

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Expression and polynomial are both mathematical terms that are used to represent mathematical equations.

An expression is any combination of symbols, numbers, and operations that represent a value or a quantity. Expressions can be represented as algebraic equations, numerical equations, or verbal phrases.

A polynomial is a specific type of expression that is composed of one or more terms with each term containing a power of a single variable. A polynomial can be represented with a single variable or multiple variables.

A formula is an expression or equation that represents an idea or a relationship between two or more variables. A calculation is the actual process of evaluating an expression or equation to determine a numerical value or answer.

In summary, an expression is any combination of symbols, numbers, and operations that represent a value or quantity, while a polynomial is a specific type of expression composed of one or more terms with each term containing a power of a single variable.

A formula is an expression or equation that represents an idea or relationship between two or more variables, while a calculation is the actual process of evaluating an expression or equation to determine a numerical value or answer.

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The solution is, 1) f+g =3x^3+x^2+2x-9 and, 2)  f+g = x^2-6x +2√(x-2)+17

Addition is a way of combining things and counting them together as one large group. ... Addition in math is a process of combining two or more numbers.

here, we have,

given that,

            g(x) = x^2+8x-9

so, f+g

=3x^3+x^2+2x-9

and,

             g(x)=2√(x-2)+10

so, f+g

= x^2-6x +2√(x-2)+17

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A discounted surfing lesson costs $50, and a discounted parasailing trip costs $80.

Let x represent the discounted cost per person for a surfing class.

Let y represent the reduced cost per person for surfing instruction.

The cost of taking a surfing lesson and going parasailing is $130

x + y = 130--------------(i)

25 people take

Surfing lessons and 30 people go parasailing and a total of $3,650 is collected

25x + 30y = 3650--------------(ii)

We solve for y using equ (i):

y = 130 - x ------------(iii)

Substitute equ (iii) to equ (ii) and solve for x

25x + 30(130 - x) = 3650

25x + 390 - 30x = 3650

-5x = -250

-x = 50

We solve for y using equ (iii):

y = 130 - x

y = 130 - 50

y = 80

Thus, a discounted surfing lesson costs $50, and a discounted parasailing trip costs $80.

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Answer:

48, 60, 72

Step-by-step explanation:

4 + 5 + 6 = 15

The sum of interior triangles is 180

15/180 = 12

Multiply each part by 12

4 x 12 = 48

5 x 12 = 60

6 x 12 = 72

Answer:

17.6

Step-by-step explanation:

Tomo can make more one whole batch of brownies. Tomo can make exactly four batch(es) of brownies with the sugar he has.

Based on the information provided, we can logically deduce the following parameters:

Number of cups of sugar is equal to 4/3 cups of sugar.

Number of cups of sugar to make one whole batch of brownies is equal to 1/3 cup of sugar.

In order to determine the exact batches of brownies which Tomo can make based on the number of cups of sugar he has, we would divide the  number of cups of sugar by the number of cups of sugar that is required to make one whole batch of brownies as follows;

Batch of brownies = 4/3 ÷ 1/3

Batch of brownies = 4/3 × 3

Batch of brownies = 12/3

Batch of brownies = 4 batches of brownies.

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Complete Question:

Tomo is making brownies he has 4/3 cups of sugar. He needs 1/3 cup of sugar to make one whole batch of brownies. Tomo can make _____ one whole batch of brownies. Tomo can make exactly _____ batch(es) of brownies with the sugar he has.

Answer:

583 adults.

437.50/.50 = 583.333333333

Step-by-step explanation:

Hope it helps! =D

Answer: acute and scalene

Step-by-step explanation:

we can see from the figure that no side has an angle greater than 90°. Therefore triangle must be an acute angled triangle

Also given in the figure that no two or all sides are equal that is all sides are of different length which means it is a scalene triangle

Hence the answer is acute and

Answer: Two equivalent ratios are, 16:28 and 24:42

Step-by-step explanation:

The Real Numbers collection does not contain the square root of a negative number. truly intended. Mathematicians "created" a new number, i, to address this issue.

Since it was not part of the set of "Real Numbers," this number was referred to as an "imaginary number."

With the exception of zero, all numbers have positive and negative square roots. The positive square root, abbreviated as b, is the principal square root. Write b to denote the negative root, and b to denote both roots.

Theorem: Square Roots of a Negative Number Simplifying an expression involving the square root of a negative number by simplifying the number as if it were a positive number and putting an i in front of it as a coefficient is one method. To put it another way, x=ix x = i x for every x where x is a positive number and where x is a negative number.

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Answer:

Step-by-step explanation:

You want to know the numbers of calories in a cheeseburger and an order of fries if 4 cheeseburgers and 3 fry orders have 4100 calories, and 5 cheeseburgers and 6 fry orders have 6250 calories.

If we let c and f represent the calories in a cheeseburger and an order of fries, respectively, then we can describe the calories in the two orders by ...

Subtracting the second equation from twice the first gives ...

  2(4c +3f) -(5c +6f) = 2(4100) -(6250)

  3c = 1950 . . . . . . . simplify

  c = 650 . . . . . . . divide by 3

Then the calories in the fries can be found by substituting in the first equation:

  4(650) +3f = 4100

  3f = 1500 . . . . . . . . . subtract 2600

  f = 500 . . . . . . . . divide by 3

There are 650 calories in one cheeseburger, and 500 calories in one order of fries.

__

Additional comment

The attachment shows solution of these equations using the matrix functions of a graphing calculator. It reduces the augmented matrix of coefficients of the equations to a form that makes the variable values apparent.

The method of solution shown above uses the "elimination" technique to eliminate the 'f' variable from the equations. We noticed that the coefficient of 'f' in the second equation was double that in the first equation, so subtracting 2 times the first from the second makes the 'f' coefficient zero. We chose that subtraction so the 'c' coefficient would end up positive.

Answer: cheeseburger: 650 calories     fries: 500 calories

Step-by-step explanation:

Hope this helps!

Mark me brainliest!

Pls and ty!

You need only Two stamp. If you are tranfering from the United States of America to the United States of America, you just have to pay $0.550 for a Domestic Forever Stamp. Your letter will reach the destination within 1 to 3 working days.

How cool is that? Just 50 cents for such quick delivery should be truly cherished

Carry in mind though, that this covers the first ounce. As soon as your wrapper goes over that weight, you need to add an extra 15-20 cents per ounce onto the price.

Do not stress, we’re going to know this in more detail

There are following requirements that your envelope must fit to be eligible for posting this way. These rules are as follows:

1. The envelope needs to be at least 4-5 inches by 3.5 inches but not much bigger than 11.5 inches by 6.125 inches, and no thicker than ¼ inches.

2. It needs to have a constant thickness.

3. It must be rectangular.

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The expression for the nth term of the sequences in terms of n is 2n + 7

9 11 13 15 17

Where,

nth term = a + (n - 1)d

= 9 + (n - 1)2

= 9 + 2n - 2

nth term = 2n + 7

Therefore, 2n + 7 is the expression which represents the nth term of the given sequence.

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From the situation described in the problem: all the required values are given below.

The distribution of values in a field is described by a statistical distribution, often known as a probability distribution. In other words, the statistical distribution identifies the typical and unusual values. The bell-shaped normal distribution is one of many varieties of statistical distributions.

Given:

The dot plots show the distribution of the length, in centimeters, of 25 shark teeth for an extinct species of shark and the length, in centimeters, of 25 shark teeth for a closely related shark species that is still living.

The shape of the distribution:

For living species - Left-skewed distribution

For extinct species - The symmetric distribution.

Measures of the center:

For living species - mean = 2.32

For extinct species - mean = 3.02

The measures of variability:

For living species - 0.13

For extinct species - 0.55

Therefore, all the required values given above.

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The vertex, zeros, and y-intercept for the given quadratic equation f(x)=       -x² - 4x+5 are respectively,

Vertex- (2, 1)

Zeros-  (2 + i)

Y-intercept- 5

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

For example, 3x+2y=0.

Types of equation

1. Linear Equation

2. Quadratic Equation

3. Cubic Equation

Given that,

f(x) = y =  -x² - 4x+5

y = -x² - 4x+5

For making it perfect square, we can add and subtract square value of half of coefficient of x

So,  adding and subtracting +4 and -4 in the given equation

y = -x² - 4x+5+4-4

  = -x² - 4x+4+5-4

  = (-x +2)² +1

y-1 = (-x +2)²

So, for vertex

-x +2 = 0

x = 2

y-1 = 0

y = 1

For Zeros, y = 0

y-1 = (-x +2)²

(-x +2)² = -1

x = 2 + i,   -2-i

the zeros are imaginary

For y intercept, x = 0

y-1 = (-x +2)²

y   = 1 + (2)²

y   = 5

Hence,  vertex, zeros, and y-int. are respectively (2, 1), (2 + i), 5

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The volume of right prism is equal to 464 cubic inches.

Volume of right prisms (V), in cubic inches, is equal to the product of cross area (A), in square inches, and height (h), in inches:

V = A · h

According to figure, cross area is the result of adding the areas of three rectangles. Area formula for rectangles is:

A' = w · l

Where:

First, determine the cross area of the prism:

A = 2 · (3 in) · (7 in) + (4 in)²

A = 42 in² + 16 in²

A = 58 in²

Second, calculate the volume of the right prism:

V = (58 in²) · (8 in)

V = 464 in³

The right prism has a volume of 464 cubic inches.

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Answer:

9

Step-by-step explanation:

x/6=12/8

x=12*6/8

x=72/8

x=9

-14 is the value of the expression b - 3a at a =6 and b = 4.

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.

Given an expression b - 3a

For this expression given,

a = 6 and b = 4

Thus the value of expression at given values

=> b - 3a

=> 4 - 3 * 6

=>4 - 18

=> -14

Therefore, the value of the expression b - 3a at a =6 and b = 4 is -14.

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The value for f(1) is -2. The solution has been obtained by forming equations of graphs of functions.

What is equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

First let's find the equation f(x)

Vertex form of parabola is y = a(x-h)^2 + k

where (h,k) is the location of the vertex.

Here, h= -1 and k = -4

We get y = a(x+1)^2 -4

Now, the parabola passes through (-4,0.5)

So,

0.5 = a(-4+1)^2 -4

We get a=0.5

Thus, f(x) is 0.5(x+1)^2 - 4

So, f(1)= 0.5(1+1)^2 - 4

⇒f(1)= 0.5*4 - 4

⇒f(1)= 2 - 4

⇒f(1)= -2

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Since the question contains multiple questions, the question I answered is

Use the graphs to evaluate the following:

1. f(1) =_

Gradient of given equation x-intercept: a=−32 y-intercept: b=3

The gradient of a function is defined to be a vector field. Generally, the gradient of a function can be found by applying the vector operator to the scalar function. (∇f (x, y))

The given equation of line:

y=2x+3

Comparing above equation with the standard slope-intercept form

y=mx+ c,

we get

Slope:

m=2

Now, given equation can be re-written as

2x−y=−3

x−32+y3=1

Comparing above equation with intercept form:

x a + y b =1,

we get

x-intercept:

a=−32

y-intercept:

b=3

Now, the given straight line intersects the coordinate axes at

(−32,0) & (0,3)

Specify these points on XY-plane & join them by a straight line to get plot.

Gradient of given equation x-intercept: a=−32 y-intercept: b=3

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The total number of minutes Carter played the basketball game is 25 minutes.

The correct answer choice is option C.

Total minutes of the basketball game= 40 minutes

Minutes Carter played= 5/8 of Total minutes of the basketball game

= 5/8 × 40

= 0.625 × 40

= 25 minutes

Hence, Carter played the basketball game for 25 minutes.

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The value of x is -3 for the given equation.

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.

Given an expression 4 *3 + 4*x = 0

Simplify the equation using PEMDAS

=> 4*3 + 4*x = 0

=> 12 + 4x = 0

=> 4x = -12

=> x = -3

Therefore, the simplified value of the Given equation is x = -3.

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Jesse's train is faster than Khalid's since 150 is greater than (>) 140 and she is traveling at 150 mph as opposed to 140 mph.

In order to put the equation in y-intercept (y=mx+b) form and determine the equation of a graphed line, first determine the slope and y-intercept. The slope is the ratio of the y-to-x change. Draw a sloping triangle connecting the two spots you find on the line.

According to the graph, the climb is 140 and the run is 1.

Since 140/1 equals 140, Khalid's slope is 140.

The slope is 150 according to the equation (y = 150x; y = mx).

Jesse's train is faster than Khalid's since 150 is greater than (>) 140 and she is traveling at 150 mph as opposed to 140 mph.

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Complete Question -

The product between functions f(x) and g(x) is:

(fg)(x) = x^3 - 4x^2 - 16x + 4

Here we have two functions:

f(x) = x - 4

g(x)  = x^2 - 16

We want to find the product:

(f times g)(x)

So we just need to take the product between the two functions:

(x - 4)*(x^2 - 16)

x^3 - 4x^2 - 16x + 4

Then the product of the functions is:

(f times g)(x) = x^3 - 4x^2 - 16x + 4

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The total caps does Sid have is 55% of x = 33

x = (33 * 100)/55

x = 60

In programming, a collection is a class used to represent a set of similar data type items as a single unit. These unit classes are used for grouping and managing related objects.A collection has an underlying data structure that is used for efficient data manipulation and storage. Code readability and maintenance improves when collections are used in logical constructs.

Collections are designed to group certain objects with a logical connection. For example, a StudentCollection object may be used to maintain university student details. Details may include the total number of students or offer a student search facility based on attributes, such as name, class or grade.

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