Calculate the area of a rectangular room that is 72 feet wide and 39 feet long.

The piecewise function will be f(x) = - 0.5x - 1.5 if -6 ≤ x ≤ - 1, f(x) = -2 if - 1 < x ≤ 3, and f(x) = (5/3)x + 7 if 3 < x ≤ 6.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The equation of the line in the interval [-6, -1] whose points are (-3, 0) and (-1, -1) is given as,

(y - 0) = [(0 + 1) / (- 3 + 1)](x + 3)

y = - 0.5x - 1.5

The equation of the line in the interval (1, 3] whose points are (0, -2) and (3, -2) is given as,

(y + 2) = [(-2 + 2) / (3 - 0)](x + 0)

y = - 2

The equation of the line in the interval (3, 6] whose points are (3, -2) and (6, 3) is given as,

(y + 2) = [(3 + 2) / (6 - 3)](x + 3)

y + 2 = (5/3)(x + 3)

y = (5/3)x + 7

The function is given as,

f(x) = - 0.5x - 1.5 if -6 ≤ x ≤ - 1

f(x) = -2 if - 1 < x ≤ 3

f(x) = (5/3)x + 7 if 3 < x ≤ 6

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We are given the following inequality.

[tex]5x+38 \leq 4(2-5x)[/tex]

Apply the distributive property on the right side:

[tex]5x+38\leq 8-20x[/tex]

Add both sides by 20x:

[tex]5x+38+20x\leq 8-20x+20x[/tex]

[tex]25x+38\leq 8[/tex]

Subtract both sides by 38:

[tex]25x+38-38\leq 8-38[/tex]

[tex]25x\leq -30[/tex]

Divide both sides by 25:

[tex]25x/25\leq -30/25[/tex]

[tex]x\leq -6/5[/tex]

Out of all the options, only option A accurately depicts this inequality. Thus, the answer is option A.

Let me know if you have any questions, thanks!

A graph which shows a solution to the given system of linear equations is: a coordinate grid with one line that passes through the points 0 comma 0 and 1 comma 4 and another line that passes through the points 0 comma negative 1 and 2 comma 1.

A graph can be defined as a type of chart that's commonly used for the graphical representation of data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate and y-coordinate.

here, we have,

In Mathematics, the graph of any proportional relationship such as a linear equation is represented by a straight line with the data points passing through the origin (0, 0) because as the values on the x-coordinate decreases or increases, the values on the y-coordinate decreases or increases simultaneously.

In conclusion, we can logically deduce that the graph (see attachment) representing the given system of linear equations shows a proportional relationship in one of the lines.

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Can't really solve it without a graph but I can show you how to get the graph

so if you have a graphing calculator you can hit the y= button and type in your problem and just switch the inequality for a =

The equation of a line perpendicular to the line y = 1/4x + 2 and passing through a point (x1, y1) is given by:

y - y1 = -4(x - x1)

This is because the slope of the original line is 1/4, so the slope of the perpendicular line must be -4 (the negative reciprocal).

A perpendicular line is a line that forms a 90-degree angle with another line. In other words, it is a line that is perpendicular to another line at their point of intersection. The slope of two perpendicular lines are negative reciprocals of each other, meaning that if one line has a slope of m, the slope of the perpendicular line is -1/m.

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The solution is,

a) Melissa's monthly payment on the promissory note is $133.10.

b) The total of Melissa's monthly payments is $6,388.80.

c) The total finance charge is $388.80.

Using an online finance calculator, we can compute the promissory note's monthly payments and finance charges (cost of credit).

The sum of the monthly payments is the total payments made by Melissa, consisting of the amount of the promissory note and the finance charges.

here, we have,

N (# of periods) = 48 months (4 years x 12)

I/Y (Interest per year) = 3.11%

PV (Present Value) = $6,000

FV (Future Value) = $0

Results:

PMT = $133.10

Sum of all periodic payments = $6,388.80

Total Interest = $388.80

Thus, Melissa's finance charge on the promissory note is $388.80, with a monthly payment of $133.10 for 4 years.

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Answer: the mean will increase but the median will be unchanged

Step-by-step explanation: (I used desmos. Plugging all values in and using functions --> statistics ----> mean/median)

before values:

median- 82

mean- 80.81

After values:

median- 82

mean- 81.76

The expressions that are completely factored are:

The expressions are considered correct because they have been completely factored, meaning they have been written in the form of "a common factor times another expression". This means that the expression on the right side of the equal sign can be simplified into its simplest form.

For example, in the expression 16a5−20a3=4a3(4a2−5), the 4a3 factor is common to both 16a5 and 20a3, so it can be factored out. The expression then becomes 4a3 times (4a2−5), which is the completely factored form.

Similarly, in the expression 12a3+8a=4(3a3+2a), the factor of 4 is common to both the expressions on the right side, so it can be factored out. This results in the completely factored form of 4 times (3a3+2a).

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Answer:

16a^5−20a^3=4a^3(4a^2−5)

and

24a^4+18=6(4a^4+3)

Step-by-step explanation:

Answer

c

explanation

A. y < -2x + 4

B. y < -4x -2

D. y < 2x + 4

C. y. < -2x - 4 This would be the correct answer

5-3y=6 so (5-3y)squared is 36

The square number or perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with itself. For example, 9 is a square number, since it equals 3² and can be written as 3 × 3.

From the question;

The equation 5 - 3y = 6. Next we are to find (5 - 3y)².

If we know 5 - 3y = 6, we can turn this equation, (5 - 3y)²

into this: 6² (because we can substitute the expression with 6)

6² is 36.

Hence,  [tex](5-3y)^{2}[/tex] is 36

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Answer:

For the muffins, she will use 3/4 cup of flour and for the topping, she will use 1/8 cup of flour.

On solving the provided question, we cans ay that ratio is 2:3=> 2x + 4x = 4 => x = total fat is 6.6666666667

Ratios show how often one number is contained in another in mathematics. For instance, the ratio of oranges to lemons in a fruit dish is 8 to 6 if there are 8 oranges and 6 lemons present. In a similar vein, the proportion of oranges to whole fruit is 8, while that of lemons to oranges is 6:8. A ratio is an ordered pair of numbers a and b that is expressed as a / b, with b not equal to zero. An equation equating two ratios is known as a ratio. The ratio can be expressed as 1:3, for instance, if there is 1 boy and 3 girls (for every boy she has 3 girls) 3/4 are girls, while 1/4 are boys.

The ratio of saturated fat to total fat in a caramel frappucino is 2 to 3

There are 4 more grams of total fat than saturated fat

ratio is 2:3

2x + 4x = 4

x = 4/6*10

x = 6.6666666667

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Answer:1.28

Step-by-step explanation:

Answer:

Step-by-step explanation:

Yes, the two lines are parallel.

Lines are parallel if they have the same slope. The slope of a line can be found by rearranging the equation into the slope-intercept form: y = mx + b, where m is the slope.

For line L: y = 5x + 1, so the slope is 5.

For line L^2: 2y - 10x + 3 = 0, rearrange to get y = -5x + (3/2). The slope of the line is -5.

Since the two lines have the same slope (both 5), they are parallel.

The equation that can be used to represent the cost of 4 markers is y = k × 4

5 markers = $6.5

Unit cost of each marker = $6.5 / 5

= $1.3 per marker.

If

y = kx

Where,

y = total cost of markers

k = unit cost of marker

x = number of markers

The equation for the cost of 4 markers:

y = kx

y = 1.3 × 4

y = $5.2

Ultimately, y = k × 4 represents the equation for total cost of 4 markers.

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The equation of the function shown in the graph is f(x) = x² + 6x + 7.

A parabola is a two dimensional figure on a plane which is U shaped and any point on the parabola is at an equal distance from a fixed point called focus and a fixed line called directrix.

We know that, equation of a parabola in vertex form is,

f(x) = a (x - h)² + k, where (h, k) represents the vertex of the parabola.

Here, it is already given that, vertex form of a quadratic function is

f(x) = (x − h)² + k

That is, a = 1

Vertex = (-3, -2)

Equation of the function is,

f(x) = (x - -3)² + (-2)

f(x) = (x + 3)² - 2

f(x) = x² + 6x + 9 - 2

f(x) = x² + 6x + 7

Hence the equation of the function is f(x) = x² + 6x + 7.

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Answer:

 f(x) = x² + 6x + 7.

Step-by-step explanation:

The solution to the inequality in this problem is given as follows:

b. x < -17 or x > 15.

The inequality for this problem is defined as follows:

0.25|x + 1| > 4.

Isolating the absolute value, we have that:

|x + 1| > 4/0.25

|x + 1| > 16.

The absolute value of a number represents it's distance from the origin, meaning that the inequality can be written as follows:

x + 1 < -16 or x + 1 > 16.

Then the first interval in the solution of the inequality is given as follows:

x + 1 < -16

x < -17.

The second interval in the solution of the inequality is given as follows:

x + 1 > 16

x > 15.

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The amount of money he will need to purchase the paper and ink is $299.04.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Cost of 1 ream = $5.89

Cost of 1 ink cartridge = $29.30

Now,

Number of reams to buy = 6

Number of ink cartridges to buy = 9

The amount needed to buy.

= 6 x 5.89 + 9 x 29.30

= 35.34 + 263.7

= $299.04

Thus,

The amount of money needed is $299.04.

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25/6=71/5-k

k=71/5-25/6

k=301/30

Answer:

Step-by-step explanation:

I think its the last one

Step-by-step explanation:

the new cocrfinations are

K' (-1, 7)

H' (-1, 5)

J' (5, 7

I' (2, 2)

The value of the 'm' and 'b' will be negative 1.44 and 3.61, respectively.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + b

Where m is the slope of the line and b is the y-intercept of the line.

The linear equation is given below.

r(t)= √3 - 0.4t√13

r(t)= √3 - (0.4√13) t

Compare the equation with the standard equation. Then we have

m = - (0.4√13)

m = - 1.44

b = √13

b = 3.61

The value of the 'm' and 'b' will be negative 1.44 and 3.61, respectively.

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Answer:

26 quarters were from Florida

Step-by-step explanation:

The total number of quarters from California and Texas is 5 + 8 = 13.

Twice the number of quarters from California and Texas is 2 * 13 = 26.

The number of quarters from Florida is 39 - 13 = 26.

So, Carol had 26 quarters from Florida.

The instantaneous rate of change of the daily receipts on day 42 is approximately -0.542 million dollars day-1.

Rate of change is a major of house quickly one quantity change in relation to another.it is parisu of the changing the changing another quantity over specified time period.

The instantaneous rate of change of the daily receipts on day 42 can be estimated by taking the difference in receipts between day 28 and day 42 and dividing it by the difference in time between them. Since day 28 and day 42 are 14 days apart, the instantaneous rate of change of the daily receipts on day 42 can be calculated as:

Rate of change = (5.587 - 14.666) / 14 = -0.542 million dollars day-1.

Therefore, the instantaneous rate of change of the daily receipts on day 42 is approximately -0.542 million dollars day-1.

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The additional charge per minute is given as follows:

$1.1.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

From the table, when the time in minutes increases by 3, from 3 to 6, the cost increases by $3.3, from $10.30 to $13.60, hence the slope m is obtained as follows:

m = 3.3/3

m = $1.1.

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

The surface area of the triangular pyramid can be found by adding the area of the base to the area of the lateral faces. The lateral faces are congruent isosceles triangles.

The area of the base can be found using the formula for the area of an equilateral triangle:

A = (s^2 * √3) / 4, where s is the length of one side of the equilateral triangle base.

Since the area of the base is given as 15.6 in², the length of one side of the base can be found:

15.6 = (s^2 * √3) / 4

s^2 = (4 * 15.6) / √3

s^2 = 64 / √3

s = 4 * √(64 / 3)

s = 4 * 4

s = 6

So, each side of the base measures 6 in.

Next, find the surface area of the lateral faces. The lateral faces are congruent isosceles triangles with a slant height of 8 in and base length of 6 in.

The area of each lateral face can be found using the formula for the area of an isosceles triangle:

A = (b * h) / 2, where b is the base length and h is the height.

For this pyramid:

b = 6 in

h = 8 in

A = (6 * 8) / 2 = 24 in²

Since there are three lateral faces, the total area of the lateral faces is 3 * 24 in² = 72 in².

Finally, the surface area of the pyramid is the sum of the area of the base and the area of the lateral faces:

A = base area + lateral face area

A = 15.6 in² + 72 in² = 87.6 in²

The place value of 5 in 2.35 x 10⁴ is 500.

In scientific notations numbers are written in the form of a base that is

0  ≤ b < 10 and multiplied by 10ⁿ where n represents integers.

We write large standard numbers in scientific form in a compact manner.

Given, A number  2.35 x 10⁴ in scientific form.

Now, The decimal form of the number is   2.35 x 10000.

= 23500.

Now, In 23500 5 is in the hundredths place,

Therefore, The place value of 5 is 500.

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Profit equals total revenue minus total costs, which is the relationship between a company's total revenue, profit, and total costs. Give an illustration of a cost that an accountant wouldn't consider a cost, such as an opportunity cost.

Profit is the result of revenues minus costs. Some expenses are subtracted from the gross profit. To calculate net profit, you subtract all expenses.

The whole cost a business incurs to produce a specific level of production is known as the overall cost in economics.

Total revenue is the total amount of money a seller can earn from selling goods or services to clients. PxQ, or the purchase price multiplied by the quantity of the goods sold, is the formula for calculating this. The term "total cost" in economics refers to the complete amount of expenses a manufacturer incurred while producing a good.

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The complete question is: What Is the Relationship Between Total Revenue Profit & Total Costs?

The difference between the median is 0.5. option D

Getting the sets of values that we have in order, we can see that we have;

12, 15, 33, 45, 46, 51, 52, 93

We can find the median between  4th and 5th numbers this is now going to give us that;  (45+46)/2 =  45.5

Median value  = 45.5

We can see that 93 is the outlier in the data set so if we remove it we would have;

12, 15, 33, 45, 46, 51, 52

The median of the data set in this case is 45.

The difference is;

45.5 - 45 = 0.5

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Missing parts;

The number of lattes sold daily for two coffee shops is shown in the table:

Lattes

12

52

93

33

51

15

46

45

Based on the data, what is the difference between the median of the data, including the outlier and excluding the outlier?

A.46

B.45.5

C.45

D.0.5