7) Write an expression for the following situation: Francine saves money in two separate bank accounts. She deposited $200 in one account and then adds $50 monthly. In her second account she deposited $100 and puts in $75 monthly. Write an expression to show her balance after m months.​

The present value of the painting is 1287 pounds.

The English term "percentage" originates from the Latin phrase "per centum," which means "by the hundred." Percentages are fractions with a denominator of 100. In other words, it is a connection where it is always assumed that the value of the entire is 100. You may determine a percentage in one of two ways:

1. Adopt a unified perspective.

2. by setting the denominator of the fraction to 100.

According to the question,

1300 × (1 - 1%)

Rewrite the expression as

1300 × ((100 - 1)/100)

= 1300 × (99/100)

= 13 × 99

= 1287

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Answer:

Since the arithmetic mean (average) is 5, (a + b)/2 =5 so a +b = 10 The geometric mean of two numbers is the square root of their product, so square root of ab = 3. So we have a system of equations where a +b = 10 and ab = 9. if we solve the first equation for b, we get b = 10 – a. Substituting this last expression for b into ab = 9, we arrive at a(10 – a) = 9. Distributing this last equation, we see that 10a – a squared = 9. Subtracting 9 from both sides and rearranging terms from highest power to lowest power, – a squared + 10a – 9 = 0. Next, multiplying this last equation by – 1, it becomes a squared – 10a + 9 = 0. Factoring, we see that (a – 1)(a – 9) = 0. Setting each factor equal to 0, either a – 1 =0, or a – 9 = 0. Thus, a = 1 or a = 9. When a = 1, b = 9 (from the equation b = 10 – a); when a = 9, b = 1 (also from the equation b = 10 – a). So the two numbers are 9 and 1.

x² is a polynomial function of degree 2.

A polynomial function is a function that can be written in the form f(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_2x^2 + a_1x + a_0 where n is a non-negative integer and a_n, a_{n-1},...,a_2,a_1,a_0 are real numbers. The term x^n is called the leading term, and the degree of a polynomial function is defined as the degree of its leading term, in this case x² is the leading term and the degree of the function is 2.

A polynomial function of degree 2 is also called a quadratic function. It can be represented in the standard form as f(x) = ax² + bx + c, where a, b, and c are real numbers and a is not equal to 0.

Quadratic functions have a specific shape of parabola, with the vertex being the point that is the lowest or highest point of the parabola depending on the sign of the leading term.

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Based on the information provided in the chart, the scale factor of the model to the real sculpture is 1/6 (one-sixth).

This is a ratio or proportion used to create a model from an original figure. This can be used to make a smaller or bigger model.

While the sculpture measures 42x35x49, the model measures 6x5x7. This means the model is seven times smaller than the original sculpture. For example length - 42/7 = 6. Based on this the scale factor is 1/6.

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The area of the shaded region is the difference between the total area of the polygon and the area of its unobscured interior.

The shaded area in the right triangle below should have an area, therefore calculate it.

Solution

Area of shaded region equals area of the outer form minus the area of the inner shape that isn't shaded

Triangles have a base of 1/2 bh.

Size of outside shape: (12 x 15 x 10) cm2.

= 75 cm2.

Area of the inner, unshaded shape is (12 x 12 x 5) cm2.

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Now, the value of the terms in number line is

15) A = -3 + (-0.2) = -3.2

16) B = -4 + (-0.2*2) = -4.4

17) C =  1 + 0.2 = 1.2

18) D = -5 + (-0.2*4) = -5.8

19) E = 0 + 0.2*2 = 0.4

20) F = -2 + (-0.2*2) = -2.4

A number line is a depiction of a graded straight line that is used to represent real numbers visually. It is assumed that every point on a number line corresponds to a real number, and that every real number corresponds to a point.

A horizontal line with evenly spaced numerical increments is referred to as a number line. How the number on the line can be answered depends on the numbers present. The usage of the number is determined by the question that it corresponds to, such as when graphing a point.

In order to represent the numbers, a number line is a long, straight line with markers spaced equally apart. Create a number line with the numbers 0 through 10, and as they gain more knowledge, progressively raise the numbers.

In the number line there are 4 small vertical line between 2 consicutive numberts that defines they are divided in 5 parts

The value of each part is 1/5 = 0.2

Now, the value of

15) A = -3 + (-0.2) = -3.2

16) B = -4 + (-0.2*2) = -4.4

17) C =  1 + 0.2 = 1.2

18) D = -5 + (-0.2*4) = -5.8

19) E = 0 + 0.2*2 = 0.4

20) F = -2 + (-0.2*2) = -2.4

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The total cost to download 30 songs is $40.7.

An expression is combination of variables, numbers and operators.

Given that a music app charges $2 to download the app plus $1.29 per song download

This data can be written in the form of expression

2+1.29x

Here x is the number of songs.

We have to find the total cost to download 30 songs

2+1.29(30)

2+38.7

40.7

Hence, the total cost to download 30 songs is $40.7.

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In order to answer research questions and evaluate theories of change, measuring aims to obtain accurate data.

Utilizing the various advantages that working with numbers and applying mathematical principles offer is what is meant by measurement, which is the process of describing facts in terms of numbers. Analysis of the aforementioned definitions reveals that measuring is the process of quantifying a phenomenon.

Data where the values are the results of measurement, hence they could be any value within a range of integers. In order to answer research questions and evaluate theories of change, measuring aims to obtain accurate data.

It's simple to remember the distinction between the two kinds of quantitative data: information is categorized as discrete if it can be counted and as continuous if it can be measured.

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Answer:

x = 12.5

Step-by-step explanation:

Because it is a straight line, the total angle is 180

you already know that one angle is 130 so take 180 - 130 and you get 50

now you know 4x = 50

divide by 4 from both sides

x = 12.5

The slope of the horizontal line y = -2 is 0.

This is because the line is always at a constant y-value of -2 and does not have any change in x-value.

The slope of a line is the ratio of the change in the y-value to the change in the x-value.

For a horizontal line, the y-value remains constant and there is no change in the x-value, so the slope of the line is 0. This means that the line is always at the same y-value and does not move when the x-value changes.

Therefore, we can conclude that the slope of the horizontal line y = -2 is 0 since the line is always at a constant y-value of -2 and does not have any change in the x-value.

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The assertions that giant squid can reach lengths of 100 feet (30 meters) were made by Paxton.

The record for a squid's overall length (including tentacles) is 43 feet; the largest mantle length is 7.4 feet (2.25 meters); while the average distance between the tip of the top fin and the end of the arms is only around 16 feet (5 meters) (13 meters).

The assertions that giant squid can reach lengths of 100 feet (30 meters) were made by Paxton. Although the measurement of a giant squid's overall length of 19 meters (62 feet) can be contested, Paxton asserted that it isn't inconceivable. "I don't think gigantic squid can become that huge," he added.        

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The slope and y-intercept of 3x - 2y = 5 is 3/2 and -5/2 respectively.

In the given question, we have to find the slope and y-intercept of 3x-2y=5.

The general equation of line is y = mx + c, where m is the slope of line and c is the y-intercept of line.

The given equation of line is 3x - 2y = 5.

To find the slope and y-intercept we first isolate the y.

Subtract 5 on both side, we get

3x - 2y - 5 = 0

Add 2y on both side, we get

2y = 3x - 5

Divide by 2 on both side, we get

y = [tex]\frac{3}{2}x-\frac{5}{2}[/tex]

On comparing the equation by y = mx + c, we get

m = 3/2 and c = -5/2

Hence, the slope and y-intercept of 3x - 2y = 5 is 3/2 and -5/2 respectively.

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The complete question is:

What is the slope and y-intercept of 3x - 2y = 5?

A negative trend in a graph represents the trend line that has a negative slope.

We know that a negative trend in a graph is nothing but the trend line that has a negative slope.

As we know in a scatter plot, a line that closely fits the data points is nothing but a trend line

A negative trend in a graph indicates a negative relationship between the variables.

In this kind of trend, when the values of one set of data increases, the values of other set decreases, and vice versa.

When a line has negative slope, it goes down and right OR up and left. This means, as x value increases, y value decreases.

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Check the picture below.

Answer:

19

Step-by-step explanation:

If Trevon sold  8 apple pies and 6 blackberry pies for a total of $150 and  Jack sold 6 apple pies and 12 blackberry pies for a total of $210 , then the cost each of one apple pie is $9  and one blackberry pie is $13   .

For Trevon :

he sold 8 Apple Pies and 6 Black Berry Pies ,

the amount Trevon gets is = $150  ;

For Jack :

he sold 6 Apple Pies and 12 Black Berry Pies ,

the amount Trevon gets is = $210  ;

let the cost for 1 Apple Pies is = $x  ;  and

let the cost for 1 Blackberry Pies is = $y  .

the given situation can be represented in equation as :

[tex]8x + 6y = 150[/tex]  and [tex]6x+12y = 210[/tex] ;

On solving the two equations ,

we get , the values as x = 9 and y = 13   .

Therefore , the cost of apple pies is $9 and cost of blackberry pie is $13  .

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F(3) : -8

To determine x when F(x) = -9 is x = 4

What is the Function?

A function is a relationship or expression involving one or more variables.  It has a set of inputs and outputs.  Each input has only one output.  The function is the description of how the inputs relate to the output.

        So, -x = -4

        x = 4

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Answer: The two middle ones I think. This is hard to read sorry.

The discontinuity of the function is when x = -7 and the zero of the function is when x = 3.

f(x) = (x^2 + 4x - 21)/(x + 7)

Discontinuity:

When the denominator = 0, x = -7.

Zero:

When the entire equation = 0,

x^2 + 4x - 21 = 0

x = (-4 ± √(16 + 84))/2

x = (-4 ± 10)/2

x = -7 or x = 3

The function f(x) = (x^2 + 4x - 21)/(x + 7) has a discontinuity when x = -7 and a zero when x = 3. To find the discontinuity, we set the denominator equal to zero, which gives us x = -7. To find the zero, we set the entire equation equal to zero and solve for x. This gives us the quadratic equation x^2 + 4x - 21 = 0. Then, using the quadratic formula, we find that the solutions for x are x = -7 and x = 3.

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The range of the given function is expressed as;

{4, 7, 10, 13}

In mathematics, the range of a function is defined as the set of all possible output values for every possible input value.

Now, in this question, we given;

Function; f(x) = 3x + 7

Domain = {-1, 0, 1, 2}

To find the range. we will plug in each of the domain values for x in the given function to get;

when x = 1;

f(1) = 3(1) + 7

f(1) = 10

When x = 2;

f(2) = 3(2) + 7

f(2) = 13

When x = 0;

f(0) = 3(0) + 7

f(0) = 7

When x = -1;

f(1) = 3(-1) + 7

f(1) = 4

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On solving the provided question, we can say that by expression he amount of water in the solution is 80 millimeters

In mathematics, it is possible to multiply, divide, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted

The amount of water in millimeters present in the solution is 80 millimeters

Let's assume that, amount of alcohol in solution = a :

Amount of water in solution = 4a

The expression for the amount of water and alcohol and the total volume of the solution can be expressed thus :

[tex]a + 4a = 100\\5a = 100\\5a/5 = 100/5\\a = 20[/tex]

The amount of water in the solution = 4a

Amount of water = 4(20) = 80

Therefore, the amount of water in the solution is 80 millimeters

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(1,6), (1, 3), (5, 3) is  the transformation for the coordinates of the vertices of the given pairs of triangles.

The triangle's vertices' coordinates are (x1,y1), (x2,y2), and (x3,y3). The line that connects the first two is split in the ratio l:k, and the line that runs from the division point to the opposing angular point is divided in the ratio m:k+l.

Determine the coordinates of each of the triangle's vertices in step one. Step 2: Add the horizontal translation value to each vertex's x-coordinate and the vertical translation value to each point's y-coordinate to translate each.

We are aware that the distance between the two points (x 1, y 1) and (x 2, y 2) is given by the formula

d = [tex]\sqrt{}[/tex](x 2 x 1 ) 2 +(y 2 y).

(1,6), (1, 3), (5, 3) is  the transformation for the coordinates of the vertices of the given pairs of triangles.

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In three-dimensional space, coordinates are often written in the format (x, y, z), where x, y, and z represent the positions along the x-axis, y-axis, and z-axis, respectively.

These coordinates can also be written as XYZ, where X, Y, and Z represent the position along the x-axis, y-axis, and z-axis, respectively.

For example, the point (3, 4, 5) in three-dimensional space can also be written as the point XYZ = 3,4,5

It is important to note that the order of the coordinates, XYZ, is crucial when working with three-dimensional space. It is a common notation used in geometry, engineering, physics, and computer graphics.

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An expression which can be used to determine the total cost of the project if the project is not completed by the due date is: D) x - 0.15x.

In Mathematics, a mathematical expression is sometimes referred to as an equation and it can be defined as a mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables and numerical quantities (number).

Since the cost of the streetcar project is x dollars and the cost of the project is reduced by 15% if the project is not completed by the due date, a mathematical expression which can be used to determine the total cost of the project;

Total cost = x - 15% of x

Total cost = x - (15/100 × x)

Total cost = x - (0.15 × x)

Total cost = x - 0.15x

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Answer: 5

Step-by-step explanation:

-3=2-y

add y to both sides

-3+y=2

add 3 to both sides

y=5

Linear and exponential relationships differ in the way the y-values change when the x-values increase by a constant amount

Linear growth occurs when the same quantity is added in each unit of time. When an initial population grows by the same proportion or factor across equal time increments or generations, this is referred to as exponential growth.

The formula f(x) = ax defines an exponential function, where x represents the input variable as an exponent. The exponential curve is determined by the exponential function and the value of x. The exponential function is a significant mathematical function of the type. F(x) = ax. When a line has a positive slope (m > 0), y always grows when x increases and always lowers when x decreases.

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There are 1066085334130 ways.

Since we have given that

Total number of selected countries = 11

Number of selected countries from a block of 50 = 1

Number of selected countries from a block of 70 = 2

So, the remaining number of selected countries is from a block of 69.

= 11 - (1+2)

=11-3 =8

Now, we need to find the number of ways, so we will use "Combination" to select that number of countries.

[tex]50C_{1} * 70C_{2} * 69C_{8}[/tex]

= 50 * 2415 * 8361453672

= 120750 * 8361453672

=1066085334130

Hence, there are 1066085334130 ways.

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The number of values below the median is 12, the number of values below the 3rd quartile is 18, number of values between the 1st and 3rd quartiles is 12 and the interquartile range is 3.

Median is the middle element when the data set is arranged in an increasing or decreasing order.

There are 24 values in the set.

The values are,

0, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 8.

Median is the average of middle two elements, that is 12th and 13th elements.

Median = (3 + 4) / 2 = 3.5

Number of values below 3.5 = 12

Third quartile, Q₃, is found by finding the median of the second half elements.

4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 8.

Q₃ = (5 + 6) / 2 = 5.5

Number of values below 5.5 = 18

First quartile, Q₁, is found by finding the median of the first half elements.

0, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3

Q₁ = (2 + 3) / 2 = 2.5

Number of values between Q₁ and Q₃ = 12

Interquartile range = Q₃ - Q₁ = 5.5 - 2.5 = 3

Hence the first quartile, median, third quartile and the interquartile range of the given data set are 2.5, 3.5, 5.5 and 3 respectively.

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Answer:

4 units (if my logic is correct)

Step-by-step explanation:

1/2(5x-7)=x+1

5x-7=2x+2

3x=9, x=3

2x-2 --> 2(3)-2 = 6-2=4

The acres each section is 4/3 acres per section

An equation shows the relationship between numbers and variables in an expression.

Unit rate is the ratio of two quantities. The denominator of a unit rate is always equal to one.

A farmer owns a total of 9 1/3 acres of land. The land is separated into 7 equally sized sections

9 1/3 acres = 28/3 acres

To find the amount of land per section, divide the total land area by the total number of sections

Amount of land per section = (28/3)acres / 7 sections = 4/3 acres per section

There is 4/3 acres per section

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