sketch the solution to each system of inequalities

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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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!

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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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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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Answer:

583 adults.

437.50/.50 = 583.333333333

Step-by-step explanation:

Hope it helps! =D

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 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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The circumcenter of the triangle is at the point (22, 36). This is the point where the three thin strips of wood cross and where Mike attached the kite's string.

The point of concurrency of the lines perpendicular to the sides of a triangle is known as the circumcenter of the triangle. To find the circumcenter of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), you can use the following formula:

x = (x1 + x2 + x3) / 3

y = (y1 + y2 + y3) / 3

Plugging in the coordinates of the three vertices, we get:

x = (0 + 44 + 0) / 3 = 22

y = (58 + 36 + 0) / 3 = 36

So the circumcenter of the triangle is at the point (22, 36).

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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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-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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Equivalence relations are important in maths because of the following parts,

A relation R on a set A is called an equivalence relation if and only if the relation R is recursive, symmetric, and transitive. An equivalence relation is a relation on sets, and is generally represented by the symbol “~”. For example: "Equal to (=)" is the equivalence relation on any set of numbers A for all elements a, b, c ∈ A,

Reflexive: a = a ,

Symmetric: a = b ⇒ b = a and

Transitive: a = b, b = c ⇒ a = c.

This means that (=) is recursive, symmetric, and transitive. Equivalence relations are used in several areas of mathematics.

does not satisfy || f || = 0 <=> f=0.

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Complete question:

Why is equivalence relation important in maths?.

Answer:

17.6

Step-by-step explanation:

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 -

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.

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) =_

The probability that both cards are sevens is 0.0044
What is probability?

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

There are 52 cards, 4  are sevens.  

So the probability of picking the first 7 is 4/52.  

If you don't replace the card, then there are only 51 cards left, 3 of which are sevens.

So the probability of picking a seven on the second draw is 3/51.  

The probability of picking sevens on both draws is:

P(picking two sevens) = (4/52)·(3/51) =0.076*0.058=0.0044

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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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Answer:

9

Step-by-step explanation:

x/6=12/8

x=12*6/8

x=72/8

x=9

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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According to the information, the correct option is C. . 4x^2 − 13x + 9, since the expression is a polynomial.

To add the expressions we must add each of its components (those that are similar) to form a single expression. Below is the procedure:

Now we must reassemble the expression that would look like this.

4x^2 - 13 + 9. Additionally, we know that it is a polynomial because none of the terms related to x are affected by a square or fractional root.

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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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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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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 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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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:

the answer is A because you can know