a function is a relation in which each possible input value leads to exactly one output value. the input values make up the range and the output values make up the domain

answer

4

2

Step-by-step explanation:

4x+3y=19

4x=19-3y

4x=16

x=16/4

x=4

2x+5y=20

5y=20/2x

5y= 10

y=10/5

y=2

Answer:

w \(\leq\) 3,600

Step-by-step explanation:

\(\leq\)  means less than or equal to.

Answer:

-43

Step-by-step explanation:

a12 = a1 + (12-1)×-5 =12-55 =-43

The length of the third side of an isosceles triangle is 9 cm.

Define isosceles triangle.

A triangle with two sides that are congruent or that are the same length is known as an isosceles triangle.

Define perimeter.

The sum of the lengths of the three sides of an isosceles triangle can be used to determine its perimeter. Two of the sides of an isosceles triangle are equal in length. Therefore, if we know the base length and the other two equal side lengths, we can determine the perimeter.

Given data -

Perimeter of an isosceles triangle  = 47cm

The sum of the equal sides = 38 cm

Let a be the length of equal sides.

Therefore 2a = 38

Perimeter of an isosceles triangle = 2a + b

47 = 38 + b

b = 47 - 38

b = 9 cm

The length of the third side of an isosceles triangle is 9 cm.

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The complete question is

"If the perimeter of an isosceles triangle is 47 cm and the sum of the equal sides is 38 cm. Find the length of the third side."

1. We see 5 different terms .

2. 5m

3. 4p

4. 3

5. m , p

6. -2, 4, 5, 3

Answer:

Step-by-step explanation:

1. 5 (-2m, 4p, 5m, -1p, 3)

2. -2m and 5m are like terms.

3. -p and 4p are like terms

4. 3 is the constant

5. The variables are m and p

6. The coefficients are -2, 4, 5, -1

Hope this helps!

Answer:

9m²-n²

Step-by-step explanation:

(3m+n)(3m-n)

This is so easy algebraic expression.

Just rewrite as,

Simplifying,

[Alternate method is there]

Answer:

Area of Triangle A = 4 cm²

Area of Rectangle = 24 cm²

Area of Triangle B = 4 cm²

Area of Trapezoid = 32 cm²  

Step-by-step explanation:

The formula to find the area of a triangle is: \(\frac{h_bb}{2}\)

The base (b) is 2 and the height (h) is 4.

Now multiply,

2 times 4 = 8

Then divide,

\(\frac{8}{2}\) which equals 4.

So the area of Triangle A and B is 4 cm² because they are the same triangles.

The formula to find the area of a rectangle is: a times b.

a=6 and b=4

Multiply,

6 times 4 = 24

So the area of the rectangle is 24 cm²

The formula to find the area of a trapezoid is: \(\frac{a+b}{2}h\)

A=6

B=10

H=4

So now,

\(\frac{6+10}{2}4\)

6+10=16

16 divided by 2 is 8.

Last multiply,

8 times 4 is 32.

The area of the trapezoid is 32 cm²

Hope this helped! And have a great day!

The y-intercept of the line represented by the equation is; 60.

It follows from the task content that the y-intercept of the line represented by the equation is to be determined.

On this note, we must recall that the y-intercept of an equation is the value of y when x = 0.

Therefore, we have;

-60 (0) + 2y - 120 = 0

2y = 120

y = 60.

Hence, the y-intercept of the line represented by the equation is; 60.

Consequently, it can be inferred that the Ernesto is wrong in his evaluation of the y-intercept as 30.

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Answer:

x and y can be any two numbers greater than zero such that y is also greater than x

D.no more than 45

C.50 miles per hour

Step-by-step explanation:

Let the two numbers be such that x< y because we have been given y/x>1 and x/y< 1 .

Suppose we take y= 9 and x= 3 then

9/3 > 1

3>1

Also

3/9 < 1

1/3 < 1

x and y can be any two numbers greater than zero such that y is also greater than x

2. Total weight that can be carried is 3000 pounds.

The big machine is 300 pounds. The weight that the truck can carry beside the big machine is 3000-300= 2700 pounds.

The smaller machines weigh 60 pounds

The number of smaller machines that can be carried is 2700 ÷ 60= 45 other than the big machine.

3. Total distance = Speed * time

                           = 48 * (40/60) = 32 miles

New distance = 32+ 8= 40 miles

New time = 48 minutes

Speed = distance / time = 40/ 48/60=  50 miles per hour

The domain of the function -2g(x) + f(x) is all real numbers (-∞, +∞).

To perform the function operation -2g(x) + f(x), we first need to substitute the given functions into the expression:

-2g(x) + f(x) = -2(x² - 3x + 2) + (2x + 5)

Next, we simplify the expression:

-2(x² - 3x + 2) + (2x + 5) = -2x² + 6x - 4 + 2x + 5

Combining like terms:

-2x² + 8x + 1

The resulting function is -2x² + 8x + 1.

To determine the domain of the function, we need to consider any restrictions on the values of x that make the function undefined. Since the given functions f(x) = 2x + 5 and g(x) = x² - 3x + 2 are both polynomial functions, their domain is all real numbers.

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The number of brownies and large cookies will be same that is 20 each.

What are inequalities ?

When two values are compared , an inequality represents whether one is greater than, less than, or not equal to the other.

It is given that the brownies cost $4 each and large cookies cost $6 each.

Let's assume the number of brownies be x and large cookies be y.

And as per the question , She is trying to make at least $200 but wants to make no more than 75 items.

So , to represent this we need an inequality which will be as follows:

Cost of x brownies = 4x

Cost of y cookies = 6y

So , inequality will be :

4x + 6y ≤ $200 --- --- --- --- --- --- --- -- - Equation 1

and

Number of brownies and cookies should not be more than 75 items. i.e.,

x + y < 75 --- --- --- --- --- --- --- -- -- -- -- -- -- Equation 2

Let's check for which value of x and y this is suitable. So , simplify equation 1 : (dividing by 2 )

2x + 3y ≤ $100

If we put x = 20 and y = 20 , then

2 × 20 + 3 × 20 = $100

$100 = $100

So , the equation is satisfied which meant the number of brownies and cookies will be equal which is 20.

Let's check it with equation 2 also :

So ,

20 + 20 < 75

40 < 75

This is also satisfied.

Therefore ,  the number of brownies and large cookies will be same that is 20 each.

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The cartesian equation of the curve \(r=2 \hspace{0.1cm} csc \hspace{0.1cm} \theta\) is \(y=2\).

A Cartesian equation is essential in mathematics. It corresponds to a mathematical formula that expresses the connection between elements as a function of their positions on a plane known as Cartesian.

A two-dimensional coordinate scheme called the Cartesian plane employs a horizontal x-axis and an upward y-axis to identify locations in space.

Given that, \(r=2 \hspace{0.1cm} csc \hspace{0.1cm} \theta\).

So, \(csc\hspace{0.1cm}\theta=cosec \hspace{0.1cm}\theta\).

The equation becomes as follows:

\(r=2cosec\hspace{0.1cm} \theta\)

By using the trigonometric equation \(cosec\hspace{0.1cm} \theta=\frac{1}{sin\hspace{0.1cm}\theta}\), we get

\(r= \frac{2}{sin \hspace{0.1cm} \theta}\)

Multiplying both sides by \(sin\hspace{0.1cm}\theta\), we get

\(r \hspace{0.1cm}sin\hspace{0.1cm}\theta =2\hspace{0.1cm}\frac{sin\hspace{0.1cm}\theta}{sin\hspace{0.1cm}\theta}\)

\(rsin\hspace{0.1cm}\theta=2\)

By the parametric equations \(x=rcos\hspace{0.1cm}\theta\) and \(y=rsin\hspace{0.1cm}\theta\), we get

\(y=2\)

It is a horizantal line.

Hence, the cartesian equation of the curve \(r=2 \hspace{0.1cm} csc \hspace{0.1cm} \theta\) is \(y=2\).

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The cartesian equation for the curve is: y = 2 This is a horizontal line passing through the point (0,2).

To find a Cartesian equation for the curve given by the polar equation r = 2 csc(θ), we will convert the polar coordinates (r, θ) into Cartesian coordinates (x, y) using the following relationships:

x = r * cos(θ)
y = r * sin(θ)

Step 1: Express r in terms of θ
r = 2 csc(θ)

Step 2: Since csc(θ) = 1 / sin(θ), rewrite the equation as
r = 2 / sin(θ)

Step 3: Express x and y in terms of r and θ
x = r * cos(θ)
y = r * sin(θ)

Step 4: Substitute r from Step 2 into the y equation
y = (2 / sin(θ)) * sin(θ)

Step 5: Simplify the equation
y = 2

The Cartesian equation for the given polar equation is y = 2, which represents a horizontal line passing through the point (0, 2).

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Answer:

a = 1/2

Step-by-step explanation:

1) Subtract 3/2 from both sides.

2) Simplify the expression

3) Solution = 1/2

TO CHECK: 1/2 + 3/2 = 2

Answer:

do u have a picture of theroblem?

Answer:

The answer is D) $13.50

Step-by-step explanation:

So first what you're gonna do it subtract $9.50 from $36.50 which will get you to $27.00.

Then you'll have to figure out what half of $27.00 is.

That will get you to the answer of D) $13.50

Answer:

x² - 16

Step-by-step explanation:

Use the FOIL method here where

F = first

O = outer

I = inner

L = last

F = x * x = x²

O = -4 * x = -4x

I = 4 * x = 4x

L = -4 * 4 = -16

Combine the terms to get x² - 16.

Answer: 5.099

Step-by-step explanation:

(x1 , y1) = (-4, -2)

(x2 , y2) = (5 , -2)

A translation is a transformation that occurs when a figure is moved from one location to another location without changing its size, shape or orientation.

How to Translate a Triangle

Step 1: Identify the coordinates of each of the vertices of the triangle.

Step 2: Translate each point by adding the horizontal translation value to the x-coordinate of each vertex and the vertical translation value to the y-coordinate of each point. For these translations, add a negative number if the horizontal translation is to the left or if the vertical translation is downward.

Step 3: Plot the three translated points and draw the triangle by connecting each pair of points with a straight line.

Coordinates are written as (x, y) meaning the point on the x axis is written first, followed by the point on the y axis.

Given data

(x1 , y1) = (-4, -2)

(x2 , y2) = (5 , -2)

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Answer:

The product of a number and its reciprocal is 1.

For i.e : 4/3 and its reciprocal 3/4, 4/3 x 3/4 = 1

Hope this helps!

:)

The supremum of the set A does not exist (it is negative infinity), and the infimum of the set A is 1.

To define the supremum and infimum of the set A, we first need to determine the properties of the set.

The set A is defined as A = {(x-3)/(x-2) ∈ R : x < 0}.

To find the supremum (also known as the least upper bound) of A, we need to find the smallest value that is greater than or equal to all the elements of A. In other words, we are looking for the least upper bound of the set A.

Let's analyze the elements of A:

For x < 0, the expression (x-3)/(x-2) can take on different values depending on the value of x. We need to find the maximum value that this expression can reach for all x < 0.

As x approaches 0 from the left side, (x-3)/(x-2) approaches negative infinity. Therefore, there is no finite supremum for the set A.

Next, let's find the infimum (also known as the greatest lower bound) of A. We need to find the largest value that is less than or equal to all the elements of A. In other words, we are looking for the greatest lower bound of the set A.

Again, analyzing the elements of A:

As x approaches negative infinity, (x-3)/(x-2) approaches 1. Therefore, the infimum of the set A is 1.

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Answer:

he led the constitutional convention because he was respected throughout the nation

Step-by-step explanation:

The best states George Washington’s connection to the 1787 Constitutional Convention is: He led the Constitutional Convention because he was respected throughout the nation.

The Philadelphia Convention is also known as the Constitutional Convention took place between May 14 and September 17, 1787, to resolve the problems of the United States government.  

The delegate elected to George Washington to led the convention, the presence of Washington a national hero respected by all helped to legitimize the convention. This result of the Convention was the Constitution of the United States of America.

The best states George Washington’s connection to the 1787 Constitutional Convention is: He led the Constitutional Convention because he was respected throughout the nation.

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Answer:

448$

Step-by-step explanation:

100-24/100×589$

76/100×$589

divide 76 by 100 and multiple with the price which is 589$

when 76 is divided=0.76

now we multiple 0.76times 589$

Answer:

65%

Step-by-step explanation:

To find percentage, we take the fraction of the total and multiply it by 100.

\(\frac{325}{500} \times=\frac{325}{5}=65\)

Answer:

\(153.84\%\)

Step-by-step explanation:

\( 1. \: \frac{500}{3.25} \\ 2. \: 153.84\%\)

By the principle of mathematical induction, we can conclude that for any natural number n, the number n(n + 1) is even.

To prove that for any natural number n, the number n(n + 1) is even, we can use mathematical induction.

Step 1: Base Case

Let's start by verifying the statement for the base case, which is n = 1.

When n = 1, we have 1(1 + 1) = 2, which is indeed an even number. Therefore, the statement holds true for the base case.

Step 2: Inductive Hypothesis

Assume that the statement holds true for some arbitrary natural number k, i.e., k(k + 1) is even. This is our inductive hypothesis.

Step 3: Inductive Step

We need to prove that the statement holds true for the successor of k, which is k + 1.

Using the inductive hypothesis, we have:

k(k + 1) is even.

Now, let's consider the expression for (k + 1)(k + 2):

(k + 1)(k + 2) = k² + 3k + 2.

We can rewrite this expression as:

k² + k + 2k + 2.

Factoring out k, we get:

k(k + 1) + 2(k + 1).

Using the inductive hypothesis, we know that k(k + 1) is even. Additionally, 2(k + 1) is even since any multiple of 2 is even.

Therefore, the sum of an even number (k(k + 1)) and an even number (2(k + 1)) is even.

Hence, we have proved that if k(k + 1) is even, then (k + 1)(k + 2) is also even.

Step 4: Conclusion

By mathematical induction, we have shown that the statement holds true for the base case (n = 1) and that if the statement holds true for an arbitrary natural number k, it also holds true for the successor of k (k + 1).

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Answer:

$40. If she bought 3 for $30, then each shirt must be equal to $10 each.

4 times 10 = 40

Step-by-step explanation:

Hope it helps you! =D

The intervals over which the function is decreasing include the following:

A. 6 ≤ x ≤ ∞

B. -∞ ≤ x ≤ -5

C. 1 ≤ x ≤ 5

In Mathematics and Geometry, a piecewise-defined function simply refers to a type of function that is defined by two (2) or more mathematical expressions over a specific domain.

Generally speaking, the domain of any piecewise-defined function simply refers to the union of all of its sub-domains.

By critically observing the graph which represent this piecewise-defined function, we can reasonably infer and logically deduce that it is decreasing over the given intervals:

6 ≤ x ≤ ∞

-∞ ≤ x ≤ -5

1 ≤ x ≤ 5

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Complete Question:

Use the graph of the piecewise function to answer the question.

(Look at the graph presented in the picture)

Over which intervals is the function decreasing?

Select all that apply (More than one)

A. 6 ≤ x ≤ ∞

B. -∞ ≤ x ≤ -5

C. 1 ≤ x ≤ 5

D. ∞ ≤ x ≤ -5

Answer:

c

Step-by-step explanation:

Temperament is to do with the personality of someone.

Thus the dog's temperament would relate to its physical and mental character.

c

Temperament is to do with the personality of someone.

Thus the dog's temperament would relate to its physical and mental character.

The probability that a child is not allergic to nuts is 0.986, or 98.6%.

The probability that a child is not allergic to nuts can be calculated by subtracting the probability of being allergic to nuts from 1.

Given the probabilities of a child being allergic to nuts, dairy, and gluten, we are interested in finding the probability that a child is not allergic to nuts.

The probability of being allergic to nuts is given as 0.014.

To find the probability that a child is not allergic to nuts, we subtract this value from 1.

P(Not allergic to nuts) = 1 - P(Allergic to nuts) = 1 - 0.014 = 0.986

Therefore, the probability that a child is not allergic to nuts is 0.986, or 98.6%.

This calculation is based on the assumption that being allergic to nuts and being allergic to other foods are independent events.

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The solution of the equation 3(2x - 7) = 3 is x = 4. The equation has only one solution.

An equation is a mathematical expression that shows that two mathematical expressions are equal. Equation shows the relationships between variables, numbers and constant.

Therefore, let's solve the equation 3(2x - 7) = 3 as follows

3(2x - 7) = 3

Open the parenthesis

3(2x - 7) = 3

6x - 21 = 3

add  21 to both sides of the equation

6x - 21 = 3

6x - 21 + 21 = 3 + 21

6x = 24

divide both sides of the equation by 6

6x / 6 = 24 / 6

x = 4

Therefore, the equation has one solution which is x = 4.

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Left-tailed test for population mean with H0: μ = 45 and Ha: μ < 45.

What is null hypothesis ?

The null hypothesis is a characteristic arithmetic theory suggesting that no statistical relationship and significance exists in a set of given, single, observed variables between two sets of observed data and measured phenomena.

This is a left-tailed test as the alternative hypothesis is less than 45 years. The test is evaluating if the population mean is significantly less than 45 years, as represented by the hypothesis being less than (not equal to) 45 years. This is a one-tailed test in the negative direction, which is a left-tailed test. Mathematically, this can be represented as:

H0: μ = 45

Ha: μ < 45

where H0 represents the null hypothesis and Ha represents the alternative hypothesis, and μ is the population mean.

Left-tailed test for population mean with H0: μ = 45 and Ha: μ < 45.

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