Item 4 Greg has a piece of rope 18 ft long. He wants to cut it into two pieces so that the longer piece is 2 ft less than 3 times the length of the shorter piece. How long will each piece of rope be

In function notation, the function is represented as f(x) = (3/4)x + 7.

In function notation, the function is represented by the letter "f" followed by the input value inside parentheses. The input value is typically represented by the letter "x". In this case, the function takes "x" as its input and performs the operation of multiplying it by 3/4 and then adding 7 to get the output. We can represent this function using the equation f(x) = (3/4)x + 7.

It's worth noting that the function notation is a way to express a mathematical relationship between two variables, the input variable (x) and the output variable (f(x)), in which every input value of x corresponds to exactly one output value. This equation represents the same function regardless of the input value, and it can be used to find the output for any input value by simply substituting it in the equation.

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Answer: x=-1/4 and x=-1

Step-by-step explanation:

The answer choices you give are extremely hard to figure out, so I hope my explanations and answers help.

The quadratic formula is [tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]. Once we figure out a, b, c, we can plug them into the formula and solve for x.

The standard form equation is ax²+bx+c=0. The equation given matches this so we know that:

a=4

b=5

c=1

Plug them into the formula. There is a [tex]\pm[/tex] symbol, which stands for "plus or minus". This means we solve the formula with addition and subtractions separately. We should have 2 solutions at the end. Let's do them separately to show work.

Solution 1: addition

[tex]x_1=\frac{-5+\sqrt{5^2-4(4)(1)} }{2(4)}[/tex]             [exponents]

[tex]x_1=\frac{-5+\sqrt{25-4(4)(1)} }{2(4)}[/tex]             [multiply]

[tex]x_1=\frac{-5+\sqrt{25-16} }{8}[/tex]                    [inside square root]

[tex]x_1=\frac{-5+\sqrt{9} }{8}[/tex]                          [square root]

[tex]x_1=\frac{-5+3}{8}[/tex]                            [add]

[tex]x_1=\frac{-2}{8}[/tex]                                [divide top and bottom by 2]

[tex]x_1=-\frac{1}{4}[/tex]

Solution 2: subtraction

[tex]x_2=\frac{-5-\sqrt{5^2-4(4)(1)} }{2(4)}[/tex]             [exponents]

[tex]x_2=\frac{-5-\sqrt{25-4(4)(1)} }{2(4)}[/tex]             [multiply]

[tex]x_2=\frac{-5-\sqrt{25-16} }{8}[/tex]                    [inside square root]

[tex]x_2=\frac{-5-\sqrt{9} }{8}[/tex]                          [square root]

[tex]x_2=\frac{-5-3}{8}[/tex]                            [subtract]

[tex]x_2=\frac{-8}{8}[/tex]                                [divide]

[tex]x_2=-1[/tex]

I am not able to find the answer choices, but we know that x=-1/4 and x=-1.

The longer ladder can reach 3 8/7 feet higher than the shorter one.

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320/31 gallons of hot water and 300/31 gallons of cold water are needed.

Here we are required to fill a 20-gallon bathtub and the water should be precisely 100° F.

It is given that hot water has a temperature of 175° F and cold water has a temperature of 20° F.

Let the amount of hot water used be x gallons.

Let the amount of cold water used be y gallons.

Since the bathtub has a capacity of 20 gallons,

x + y = 20                                                                                  [1]

or, y = 20 - x                                                                             [2]

The temperature after the water is mixed will be a weighted average of the temperature and amt of water used.

Hence we get,

(175x + 20y) / (x + y) = 100

from equation [1] we get

175x + 20y = 2000                                                                   [3]

from equations [2] and [3] we get

155x - 400 = 2000

or, x = 1600/155 = 320/31                                                        [4]

Similarly,

y = 20 - 320/31

= 300/31

Hence 320/31 gallons of hot water and 300/31 gallons of cold water are needed.

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To solve a function, you must determine the value of the function for a given input. This requires finding the equation for the function and then plugging in the given input to find the output. For example, if the function is f(x) = x2 + 2x - 5, and the given input is 3, then the output of the function is f(3) = 12.

1. Substitute the given input, x = 3, into the equation.

2. Simplify the equation:  f(3) = 32 + 2(3) - 5

3. Solve the equation:  f(3) = 9 + 6 - 5

4. Simplify the equation: f(3) = 12

5. Therefore, the output of the function is f(3) = 12.

To solve a given function, you must first determine the equation for the function. Then, you must substitute the given input into the equation and solve it. In this example, the given input was 3 and the equation for the function was f(x) = x2 + 2x - 5. After plugging in the input of 3, the equation was simplified to f(3) = 9 + 6 - 5, which was further simplified to f(3) = 12. Therefore, the output of the function is f(3) = 12.

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Answer:

do it

Step-by-step explanation:

There are several ways to make a graph to compare two sets of data, but one common method is to use a line graph.

The steps to create a line graph to compare two sets of data:

Organize the data: Arrange the data into two columns, one for each set of data. Each column should have a label at the top to indicate what the data represents.

Choose a scale: Decide on an appropriate scale for the x- and y-axes that will allow you to clearly display the data. The x-axis should represent the categories being compared, and the y-axis should represent the values of the data.

Plot the data: Using the chosen scale, plot the data points for each set of data on the graph. Use different colors or symbols for each set of data to make it easy to distinguish between the two.

Add a title: Give the graph a title that describes what the graph is showing.

Add a legend: Add a legend to the graph to indicate what each set of data represents.

Add labels: Label the x- and y-axes to indicate what they represent.

By following these steps, you can create a clear and informative line graph that allows you to easily compare two sets of data.

Other types of graph that can be used to compare two sets of data are bar charts, scatter plots, and stacked bar charts. The choice of graph depends on the type of data you have, and what you want to compare or highlight.

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The example of an associative property is a+(b+c) = (a+b) + c for additional operation and a × (b × c) = (a × b) × c for the multiplication operation. The associative property is used to solve an equation or expression of real numbers.

What are the properties of real numbers?

In the number system, real numbers are only the fusion of rational and irrational numbers. These numbers can generally be used for all arithmetic operations and can also be expressed on a number line.

The four primary characteristics of real numbers are as follows:

Commutative property

Associative property

Distributive property

Identity property.

Associative property: The associative property is applicable on two arithmetic operations. They are multiplication and addition.

For multiplication operations: a × (b × c) = (a × b) × c

For additional operation: a+(b+c) = (a+b) +

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Answer: 6

Step-by-step explanation:

y = -3x + 6 is the linear equation of the form y = mx + c

where m is the gradient of the graph and c is the y-intercept of the graph.

Hence,

m = -3

c = 6

y-intercept of the graph = c

                                        = 6

The degree of polynomial is 2 and leading coefficient is 3.

A polynomial is a mathematical expression made up of one or more terms. The phrases "poly" and "nominal," for example, are whence the name "polynomial" arose. The words "poly" and "nominal" both signify many. A polynomial is an algebraic expression with two or more algebraic terms, to put it simply. It has exponents, operators, coefficients, coefficients, variables, and constants.

Given polynomials 9, 3x², 8x

standard form of polynomial;  The value of the largest exponent in a polynomial is known as its degree. However, it differs between a polynomial with just one variable and one with multiple variables. The degree of a polynomial for a single variable is equal to the variable's highest power in the polynomial.

the standard form is 3x², 8x, 9

degree of polynomial is 2.

and leading coefficient is the constant term followed by the variables with highest power,

LC = 3.

Hence degree = 2 and leading coefficient = 3.

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On solving the provided question we can say that here in null hypothesis a negative relationship; as anxiety rises less items are remembered

A null hypothesis is a kind of statistical hypothesis that asserts that a specific set of observations has no statistical significance. Using sample data, hypotheses are tested to determine their viability. Sometimes known as "zero" and symbolized by H0. Researchers start off with the presumption that there is a link between the variables. In contrast, the null hypothesis claims that there is no such association. Although the null hypothesis may not appear noteworthy, it is a crucial component of research.

here,

in null hypothesis a negative relationship; as anxiety rises less items are remembered

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Answer:

the answer is a

and the correct answer is letter C

Step-by-step explanation:

I don't know that is the answer

-20w-35

I used the distributive property to distribute terms, and then simplified

The area of circle A to the area of circle B ratio is 100: 64, and the ratio of e: f is 13: 10.

The area of the circle is equal to the multiplication of the square of the circle's radius and π.

A = πr²

where 'r' is the radius

Circumference of circle A × 0.8 = circumference of circle B

So, taking r as the radius of A,

2πr =  circumference of circle A

2πr × 0.8 = circumference of circle B

So the radius of B is r × 0.8.

Now we can substitute that in the area equations :

Area of A = π×r²

Area of B = π × (r × 0.8)² = π × r² × 0.64

The circumferences of the A to B ratio is

Circumference of A : Circumference of B = (2 × π × r)/(2 × π × r × 0.8)

= 1: 0.8 = 100: 80,

The areas of circle A to circle B ratio is

Area of A : Area of B = (π × r²)/(π × r² × 0.64) = 1: 0.64 = 100: 64

e² = f² × 1.69

69% larger shows that f² is the 100% to which we must add 69% to obtain e². 100% + 69% Equals 169%, obtaining a factor of 1.69.

We have this equation:

e² = f² × 1.69

Apply the square root on both sides.

e = f × √(1.69) = f × 1.3

e/f = 1.3 = 1.3/1 = 13/10

the ratio e:f = 13: 10

Thus, the ratio of circle A's area to circle B's area is 100: 64 and the ratio of e: f is 13: 10.

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Answer:

Step-by-step explanation:

Divide: 18 ÷3=?

The answer is 6

The number of terms in the expansion of [tex](2x^3y^2)(2x^2y^3)[/tex] is 12.

When expanding the product of two polynomials, the number of terms in the expansion is equal to the product of the number of terms in each polynomial. In this case, the first polynomial has 1 term (2x^3y^2) and the second polynomial has 1 term (2x^2y^3), so the number of terms in the expansion will be 1*1=1.

A polynomial function is one in which the variable's non-negative integer powers or positive integer exponents are the only parts of the equation. Examples of polynomial functions include quadratic, cubic, and other equations. An example of a polynomial with an exponent of 1 is 2x+5.

However, the expression provided is not a polynomial, it is a number.

[tex]2x^3y^2 * 2x^2y^3 = 4x^5y^5[/tex]

It is just one term.

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Answer:

B. -5/2

Step-by-step explanation:

(0, -7) and (-4, 3)

m = 3+7/-4-0

m = 10/-4

m = -10/4

m = -5/2

Answer:

b

Step-by-step explanation:

Some acceptable board lengths are: 15.8 ft, 16.20 ft and 16.10 feet

Now, According to the question:

Board lengths that should be accepted

From the question, we have the following parameters that can be used in our computation:

Length = 16 ft

Percent error = 1.5%

This means that the acceptable lengths are

Acceptable = Length ± Percent error * Length

Substitute the known values in the above equation, so, we have the following representation

Acceptable = 16 ± 1.5% * 16

So, we have

Acceptable = 16 ± 0.24

Evaluate

Acceptable = 15.76 to 16.24

Some board lengths that should be accepted are 15.8 ft, 16.20 ft and 16.10 feet

Board lengths that should be rejected

In (a), we have

Acceptable = 15.76 to 16.24

Some board lengths that should be rejected are 14.8 ft, 17.20 ft and 12.10 feet

The intended lengths of the boards

Here, we have

Lengths = 10, 12 and 14 feet

Length too long = 2.3 inches

Convert to inches

Length too long = 0.19

So, we have

Intended lengths = (10, 12 and 14 feet) + 0.19

Evaluate

Intended lengths = 10.19, 12.19 and 14.19 feet

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Answer:

Step-by-step explanation:

7(9w)7(9w) = 11

(7 ×7)(9×9)(w×w) = 11

49 ×81 w² = 11

3969w² = 11

[tex]\frac{3969w^{2} }{3969}[/tex] =  [tex]\frac{11}{3969}[/tex]

w²   =  [tex]\frac{11}{3969}[/tex]

[tex]\sqrt{w^{2} }[/tex]   =   [tex]\sqrt{11/3969}[/tex]

w = ± [tex]\frac{\sqrt{11} }{63}[/tex]

Because the solution contains a square root the answer contains both a negative and a positive solution.  

The value of x is 45 degree and value of y is 49 degree.We can find by using supplementary and corresponding angles.

Supplementary angles are those angles that sum up to 180 degrees. To find the angle which is supplementary to another angle subtract the given angle from 180 degrees. For example if one angle is 60 degrees then another angle is 180 – 60 = 120 degrees.

Corresponding angles are the angles that are formed when two parallel lines are intersected by the transversal. The opening and shutting of a lunchbox, solving a Rubik's cube, and never-ending parallel railway tracks are a few everyday examples of corresponding angles.

Now we find

according to supplementary angles

3x+45=180

3x=180-45

x=45

According to corresponding angles

y-4=45

y=45+4

y=49

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Answer:

[tex]\frac{1}{16}[/tex]

Step-by-step explanation:

We will start by calculating the probability of drawing a spade from one deck, and then square it since we need to get the chance of getting two spades. We know there are 13 spades in a deck, out of 52 cards, giving us:

[tex]\frac{13}{52}[/tex]

Which can be simplified to :

[tex]\frac{1}{4}[/tex]

Then, we will square this fraction since we need two spades in a row:

[tex]\frac{1}{4} * \frac{1}{4} = \frac{1}{16}[/tex]

So the probability is [tex]\frac{1}{16}[/tex].

Hope this helped!

The actual dimensions are 9.75 feet and 7.5 feet. The area will be 73.125 square feet.

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).  The scale factor is defined as the proportion of the new image's size to that of the previous image.

Here the scale factor for the given image is 2 inch = 3 ft.

The measure of the actual dimensions will be calculated as,

2 in = 3 ft

1 in = 3/2 ft

6.5 in = 6.5 x 3 / 2 = 9.75 ft

5 in = 5 x 3 / 2 = 7.5 ft

The actual area will be calculated as,

Area = 9.75 x 7.5

Area = 73.125 square feet

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By simple algebra, Jane is 57 9/20 inches taller.

If one object or person's height exceeds that of another, the taller object or person is said to exist. There is a two-object or two-person limit. Taller is a relative term. For instance: Hoppy stands at 7 feet.

You can begin this issue by first figuring out Dwight's height. At 54 3/4 inches, he would be 1 1/2 inches taller than Chloe:

54 3/4 plus 1 1/2 equals 55 + (3/4 + 1/2) equals 55 + (3/4 + 2/4) equals 55 + 5/4 equals 56 1/4 inches.

Dwight stands at 56 1/4 inches.

Dwight is 1 1/5 inches shorter than Jane, so

56 1/4 plus 1 1/5 is 57 plus (1/4 plus 1/5) is 57 plus (5/20 plus 4/20) is 57 plus 9/20 is 57 9/20 inches.

Jane stands at 57 9/20 inches.

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Answer:

59

Step-by-step explanation:

An isosceles right triangle has two sides that are equal in length; this means that the angles opposite the sides must also be equal. Since the triangle is a right triangle and the sum of angles of a triangle is 180 degrees, the angles must each be 45 degrees.

The acute angles of an isosceles right triangle are always 45 because of the Pythagorean Theorem. This theorem states that in a right triangle the sum of the squares of the two sides adjacent to the right angle (the legs) is equal to the square of the hypotenuse. Since an isosceles right triangle has two equal legs, and the hypotenuse is the longest side, the two legs must both have the same length, and the angles opposite from these sides must also be the same. This means that the two acute angles in an isosceles right triangle must both be 45 degrees.

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Answer: x=4

Step-by-step explanation: x+3=2x-1, then you do simple algebra

The projected population of Haleyville in 2020 is 4139.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

Population in 2010 = 4403

The decline in population per year = 0.06%

Now,

The population in 2020.

There are 10 years between 2010 and 2020.

The function used to find the population after x years.

= 4403 x [tex]0.994^x[/tex]

Now,

x = 10

= 4403 x [tex]0.994^{10}[/tex]

= 4403 x 0.94

= 4139

Thus,

The population in 2020 is 4139.

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The solution is 40°

The measure of the angle ∠ABE = 40°

Straight, equally spaced lines that never cross each other and are on the same plane are called parallel lines. The angles that are created when any two parallel lines are intersected by a line (referred to as the transversal) have a relationship. Corresponding angles, Alternate Interior Angles, Alternate Exterior Angles, and Consecutive Interior Angles are some of the several pairs of angles that are created at this intersection.

Corresponding angles

When two parallel lines are intersected by a transversal, the corresponding angles have the same relative position

Alternate Interior Angles

Alternate interior angles are formed on the inside of two parallel lines which are intersected by a transversal.

Alternate Exterior Angles

The pairs of angles formed on either side of a transversal that divides two parallel lines are known as alternate exterior angles.

Consecutive Interior Angles

When two parallel lines are cut by a transversal, the pairs of angles formed on the inside of one side of the transversal are called consecutive interior angles or co-interior angles.

Given data ,

Let the angle be represented as ∠ABE

Now , let the line be EBC and the total angle of a straight line = 180°

And , the measure of ∠CBD = 40°

Since , ∠ABE and ∠CBD are vertically opposite angles ,

The measure of ∠ABE = measure of ∠CBD

Therefore , the value of ∠ABE = 40°

Hence , the measure of vertically opposite angle ∠ABE = 40°

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Answer: ≈ 100km/h

Step-by-step explanation:

62 : 0.62 = 100 km

Therefore, the equation that best fits these scatter plot facts as the answer to this problem is y=661-0.1x.

The term "scatter plot" refers to a particular sort of graph in which the x- and y-axes are used to represent the values of two variables, with the dots that arise indicating any association between the data.

Given the correlation between the data at this moment and the graph provided in the question, y=661-0.1x is an equation that best captures the scatterplot's line of best fit.A scatter plot is a specific type of graph in which the x- and y-axes are used to represent the values of two variables, with the dots that appear showing any associations between the data.

y=661-0.1x is the equation whose solution best fits this data.

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