What is the area of the shaded region?

Answer:

Step-by-step explanation:

The inverse of the function f(x) = 2·x - 4, is the option;

g(x) = (1/2)·x + 2

The completed statement is; Because f(x) is one to one, its inverse is a function

The inverse of a function is one that takes the output of a specified function to produce the input of the function.

The inverse of the function f(x) = 2·x - 4, can be found by making x the subject of the function equation as follows;

f(x) = 2·x - 4

f(x) + 4 = 2·x

2·x = f(x) + 4

x = (f(x) + 4)/2 = f(x)/2 + 2

x = f(x)/2 + 2

Substituting f(x) = x and x = g(x) in the above equation, we get;

g(x) = x/2 + 2

The function f(x) = 2·x - 4 is a one to one function, and the condition of a one to one function guarantees that the inverse of the function is also a function

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Answer:

A

Step-by-step explanation:

is one to one

Answer:

I wish you good luck in finding your answer

The equation to determine the initial amount of money Cecilia had is x = 0.

Let's denote the initial amount of money Cecilia had as "x" dollars.

According to the given information, Cecilia spent one-fourth (1/4) of her money on a book, which is (1/4)x dollars. After buying the book, she had (x - (1/4)x) dollars left.

Next, Cecilia spent half (1/2) of the remaining money on a comic, which is ((1/2)x - 8) dollars. After buying the comic, she had ((x - (1/4)x) - ((1/2)x - 8)) dollars remaining.

Since she had $8 left, we can set up the equation:

((x - (1/4)x) - ((1/2)x - 8)) = 8

To simplify the equation, we can first combine like terms:

(x - (1/4)x - (1/2)x + 8) = 8

Now, let's solve the equation step by step:

(x - (1/4)x - (1/2)x + 8) = 8

Multiplying the fractions by their common denominator, which is 4, we get:

(4x - x - 2x + 32) = 32

Simplifying further:

(x + 32) = 32

Subtracting 32 from both sides:

x = 0

Therefore, the equation to determine the initial amount of money Cecilia had is x = 0.

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The values in the expression is as follows:

a = 2

b = 0

c = -1

The expression can be solve using the exponential law. Therefore,

g = 2³ × 3 × 7²

h = 2 × 3 × 7³

Therefore, let's solve the following:

g/h = 2ᵃ × 3ᵇ × 7ⁿ

Therefore,

g = 2³ × 3 × 7² = 2 × 2 × 2 × 3 × 7 × 7

h = 2 × 3 × 7 × 7 × 7

Hence,

g / h =  2 × 2 × 2 × 3 × 7 × 7 / 2 × 3 × 7 × 7 × 7

Hence,

g / h = 2 × 2 / 7

g . h = 2² × 3° × 7⁻¹

Hence,

a = 2

b = 0

c = -1

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The point (2, 7π / 2) does not belong to the implicit curve 8 · x · y + π · sin y = 55π and tangent and normal lines cannot be determined.

In this question we find the definition of an implicit curve, in which we must determine if point (2, 7π / 2) belongs to the curve. First, we check that point:

8 · x · y + π · sin y = 55π

8 · 2 · (7π / 2) + π · sin (7π / 2) = 55π

56π + 0.191π = 55π

56.191π = 55π

56.191 = 55 (CRASH!)

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The solution to the polynomial division in quotient and remainder form is: (x + 2) + (-5x + 4)/(x² - 2x + 1)

The polynomials we want to divide are:

x³ - 8x + 6 by x² - 2x + 1 and as such we can write it as:

                x + 2

x² - 2x + 1|x³ - 8x + 6

             -  x³ - 2x² + x

                     2x² - 9x + 6

                  -  2x² - 4x + 2

                            -5x + 4

Thus, the solution expressed in quotient and remainder form is:

(x + 2) + (-5x + 4)/(x² - 2x + 1)

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The speed of the plane is equal to 120 mph.

In Mathematics and Geometry, speed is the distance covered by a physical object per unit of time. This ultimately implies that, speed can be measured by using miles per hour (mph).

Mathematically, the speed of any a physical object can be calculated by using this formula;

Speed = distance/time

Time = distance/speed

Let the variable s represent the speed of the plane in miles per hour. Therefore, an equation that models the situation can be written as follows;

240/s = 80/s - 80

80s = 240s - 19200

19200 = 160s

s = 19200/160

s = 120 mph.

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Answer:

f(x) = 4x² - 2x + 11

f'(x) = 8x - 2

m = f'(3) = 8(3) - 2 = 24 - 2 = 22

41 = 22(3) + b

41 = 66 + b

b = -25

y = 22x - 25

Answer:

try gauth. math! Take a photo of each question and upload the photo to see if it works

Ki Tae used 54 meters of fencing to construct a 6-sided outdoor dog pen. Two of the sides are each 15 meters long, while the remaining four sides are each 6 meters long.

Let's solve the problem step by step. We know that Ki Tae used a total of 54 meters of fencing to construct a 6-sided outdoor dog pen. Two of the sides have a length of 15 meters each.

Let's denote the length of the remaining four sides as "x."

Since the dog pen has six sides, we can set up an equation based on the total length of the fencing:

15 + 15 + x + x + x + x = 54

Simplifying the equation, we have:

30 + 4x = 54

Subtracting 30 from both sides, we get:

4x = 24

Dividing both sides by 4, we find:

x = 6

Therefore, each of the remaining four sides has a length of 6 meters.

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Answer : Focus is (0,3)

To find the focus of the parabola defined by the equation (y - 3)² = -8(x - 2), we can compare it with the standard form of a parabolic equation: (y - k)² = 4a(x - h).

In the given equation, we have:

(y - 3)² = -8(x - 2)

Comparing it with the standard form, we can determine the values of h, k, and a:

h = 2

k = 3

4a = -8

Solving for a, we get:

4a = -8

a = -8/4

a = -2

Therefore, the vertex of the parabola is (h, k) = (2, 3), and the value of 'a' is -2.

The focus of the parabola can be found using the formula:

F = (h + a, k)

Substituting the values, we get:

F = (2 + (-2), 3)

F = (0, 3)

Therefore, the focus of the parabola defined by the equation (y - 3)² = -8(x - 2) is at the point (0, 3).

Answer:

Focus = (0, 3)

Step-by-step explanation:

The focus is a fixed point located inside the curve of the parabola.

To find the focus of the given parabola, we first need to find the vertex (h, k) and the focal length "p".

The standard equation for a sideways parabola is:

[tex]\boxed{(y-k)^2=4p(x-h)}[/tex]

where:

If p > 0, the parabola opens to the right, and if p < 0, the parabola opens to the left.

Given equation:

[tex](y-3)^2=-8(x-2)[/tex]

Compare the given equation to the standard equation to determine the values of h, k and p:

The formula for the focus is (h+p, k).

Substituting the values of h, p and k into the formula, we get:

[tex]\begin{aligned}\textsf{Focus}&=(h+p,k)\\&=(2-2,3)\\&=(0,3)\end{aligned}[/tex]

Therefore, the focus of the parabola is (0, 3).

Answer:

Step-by-step explanation:

By conducting a statistical test with the provided data and using a significance level of 0.05 and a critical value of 0.811, the educator can determine whether the number of absences significantly affects the final grade of the students.

To analyze the relationship between the number of absences and the final grade of students, an educator collected data from a sample. The obtained data reveals that for 10 absences, the corresponding final grade was 70. In order to determine whether the number of absences significantly impacts the final grade, a statistical test is needed.

The information provided, "Test at α = 0.05, XCV = 0.811," suggests that the educator is referring to a significance level (α) of 0.05 and the critical value (XCV) associated with this level is 0.811.

To conduct a hypothesis test, the educator needs to set up the null (H0) and alternative (Ha) hypotheses. In this case, the null hypothesis would assume that the number of absences does not have a significant effect on the final grade. The alternative hypothesis would assume that the number of absences does have a significant effect on the final grade.

Using the obtained data, the educator would perform the statistical test, such as a correlation analysis or a regression analysis, to determine the strength and significance of the relationship between absences and final grade.

If the test statistic (such as the correlation coefficient or regression coefficient) exceeds the critical value, the null hypothesis would be rejected, suggesting that the number of absences does have a significant impact on the final grade.

The educator can then interpret the results, considering factors such as the direction and strength of the relationship. Additionally, they may explore other variables or factors that could be influencing the final grade and further refine their analysis.

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The evaluation of the constraints with regards to the production of the polo and t-shirts, and to maximize the profit, using linear programming indicates that we get;

a. x = The number of polo shirts produced, y = The number of t-shirts produced

b. The inequalities representing the constraints are;

2·x + y ≤ 84

x + 2·y ≤ 106

x ≤ 36

x ≥ 0, y ≥ 0

c. P = 30·x + 22·y

d. Please find attached the graph of the feasible region

To maximize profit, the company should produce;

21 polo shirts and 43 t-shirts

Linear programming is a method used for optimizing (maximizing or minimizing a value) operations with some specified constraints.

a. The details indicates that the question is related to linear programming. Let x represent the number of polo shirt produced, and let y represent the number of t-shirts produced.

x = The number of polo shirt produced

y = The number of t-shirts produced

b) The constraints are;

Pattern and cutting section; 2·x + y ≤ 84

Sewing section; x + 2·y ≤ 106

Sales constraints; x ≤ 36

The values of x and y are non negative, numbers, therefore;

x ≥ 0, y ≥ 0

c) The objective of the company is to maximize profit, P, therefore, the objective function is; P = 30·x + 22·y

d) The graph can be plotted from the constraint inequalities, by making y the subject in the inequalities that includes both x and y as follows;

2·x + y ≤ 84, therefore; y ≤ 84 - 2·x

x + 2·y ≤ 106, therefore; y ≤ 53 - x/2

x ≤ 36

Please find attached the graph of the inequalities, showing the feasible region which is the polygon with boundaries which are the lines representing the constraints.

The objective function evaluated at the vertices of the feasible region indicates that we get;

[tex]\begin{tabular}{ | l | l | c | }\cline{1-3}(x, y)& 30\cdot x + 22\cdot y & P(\$) \\ \cline{1-3}(0, 53 & 30\times 0 + 22\times 53 & 1166 \\\cline{1-3}(21, 42.5 & 30\times 21 + 22\times 42.5 & 1565 \\\cline{1-3}(32, 12) & 30\times 36 + 22\times 12 & 1344 \\\cline{1-3}(36, 0) & 30\times 36 + 22\times 0 & 1080 \\\cline{1-3}(0, 0) & 30\times 0 + 22\times 0& 0 \\\cline{1-3}\end{tabular}[/tex]

The feasible region and the objective function indicates that the values of x and y that maximizes the profit is; (x, y)  = (21, 42.5)

Therefore, to maximize profit, the number of polo and t-shirts the company should produce are 21, and 42.5 ≈ 43 respectively.

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Answer:  the store sold 14 jugs of milk, 42 loaves of bread, and 168 pieces of cheese today.

Step-by-step explanation:

a) Let's represent the number of jugs of milk as 'm', the number of loaves of bread as 'b', and the number of pieces of cheese as 'c'. According to the given information:

The total number of items sold today is 224. Therefore, we can write the equation:

m + b + c = 224

The store sold three times as many loaves of bread as jugs of milk. We can write this as:

b = 3m

The store sold four times as many pieces of cheese as loaves of bread. We can write this as:

c = 4b

b) Now, let's solve the equation:

Substituting the value of 'b' from equation (2) into equation (3):

c = 4(3m)

c = 12m

Substituting the values of 'b' and 'c' from equations (2) and (3) into equation (1):

m + 3m + 12m = 224

16m = 224

m = 224 / 16

m = 14

Using the value of 'm' in equation (2):

b = 3m

b = 3(14)

b = 42

Using the value of 'b' in equation (3):

c = 4b

c = 4(42)

c = 168

Answer:

Step-by-step explanation:

a) Let's denote the number of jugs of milk as 'x', the number of loaves of bread as 'y', and the number of pieces of cheese as 'z'.

Based on the given information, we can form two equations:

1) The total number of items sold today is 224:

x + y + z = 224

2) The store sold three times as many loaves of bread as jugs of milk:

y = 3x

3) The store sold four times as many pieces of cheese as loaves of bread:

z = 4y

b) To solve the equations and find the number of jugs of milk, loaves of bread, and pieces of cheese the store sold today, we will substitute equation (2) and equation (3) into equation (1):

x + y + z = 224

x + 3x + 4y = 224

4x + 4y = 224

Now, substitute y = 3x into the equation:

4x + 4(3x) = 224

4x + 12x = 224

16x = 224

Divide both sides by 16:

x = 224 / 16

x = 14

Now substitute the value of x back into equation (2) to find y:

y = 3x

y = 3(14)

y = 42

Finally, substitute the value of y into equation (3) to find z:

z = 4y

z = 4(42)

z = 168

Therefore, the store sold 14 jugs of milk, 42 loaves of bread, and 168 pieces of cheese today.

The two options that would prove that ΔABC ~ ΔXYZ include the following:

A. BA/YX = BC/YZ = AC/XZ

C. AC/XZ = BA/YX, ∠A≅∠X

In Mathematics and Geometry, two triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Based on the side, side, side (SSS) similarity theorem, we can logically deduce the following congruent angles and similar triangles:

BA/YX = BC/YZ = AC/XZ (ΔABC ≅ ΔXYZ)

Based on the side, angle, side (SAS) similarity theorem, we can logically deduce the following congruent angles and similar sides:

AC/XZ = BA/YX, ∠A≅∠X

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Yuri is 2 years younger than triple Karina’s age

Answer:

yo

Step-by-step explanation:

i think its d

Brianna will owe $23,249.33 on her new vehicle after applying the down payment and taking advantage of the 33% off sale.

We need to follow these steps:

Calculate the discount on the Silverado:

Discount = 33% of $57,999

Discount = 0.33 * $57,999

Discount = $19,079.67

Subtract the discount from the original price of the Silverado:

Price after discount = $57,999 - $19,079.67

Price after discount = $38,919.33

Subtract Brianna's down payment from the price after discount:

Amount owed = Price after discount - Down payment

Amount owed = $38,919.33 - $15,670

Amount owed = $23,249.33

So, Brianna will owe $23,249.33 on her new vehicle after applying the down payment and taking advantage of the 33% off sale.

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The height of a person whose length of forearm is 24.5 cm is equal to 163.38 centimeters.

In this exercise, we would plot the length of forearm on the x-axis of a scatter plot while height would be plotted on the y-axis of the scatter plot through the use of Microsoft Excel.

On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display a linear equation for the line of best fit on the scatter plot;

y = 3.01x + 89.63

Based on the equation of the line of best fit above, the height of a person whose length of forearm is 24.5 cm can be determined as follows;

y = 3.01x + 89.63

y = 3.01(24.5) + 89.63

y = 163.375 ≈ 163.38 centimeters.

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Conditional probability, denoted as P(A|B), represents the probability of event A occurring given that event B has occurred. If events A and B are independent, P(A|B) = P(A) and P(B|A) = P(B).

The notation P(A|B) reads the probability of Event (A occurring given that Event B has occurred). If two events are independent, then the probability of one event occurring (does not affect the probability of the other event occurring). Events A and B are independent if (P(A|B) = P(A), P(B|A) = P(B), P(A|B) = P(B|A)).

To understand the relationship between conditional probability and independent events, let's consider two events A and B. The conditional probability P(A|B) represents the probability of event A occurring given that event B has already occurred. It measures the likelihood of event A happening under the condition that event B has already taken place.

On the other hand, if two events A and B are independent, it means that the occurrence or non-occurrence of one event has no effect on the probability of the other event happening. In other words, the probability of event A happening is not influenced by the occurrence or non-occurrence of event B, and vice versa.

Mathematically, if events A and B are independent, it implies that P(A|B) = P(A) and P(B|A) = P(B). This means that the probability of event A occurring is the same whether or not event B has occurred, and the probability of event B occurring is the same whether or not event A has occurred.

Therefore, the concepts of conditional probability and independent events are related in the sense that if two events are independent, the conditional probabilities P(A|B) and P(B|A) become equal to the unconditional probabilities P(A) and P(B) respectively.

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Answer:

25,

-7

Step-by-step explanation:

r ° q= r(q(x))= (-x+2) ^2

So, using perfect square trinomial,

[tex](-x+2)^{2} =x^{2} -4x+4[/tex]

Thus q(-3)=25

q(r(x))= (-x^2)+2=-7

Answer:

D The base is 7 units and the height is 3 units.

Step-by-step explanation:

The answer is d I counted the width/base then the height/length and found answer.

Answer: 18.18%

Step-by-step explanation:

First, let's calculate the surface area of the original piece of wood. The surface area (SA) of a rectangular prism is given by the formula:

[tex]$$SA = 2lw + 2lh + 2wh$$[/tex]

where [tex]\(l\)[/tex] is the length, [tex]\(l\)[/tex] is the width, and [tex]\(h\)[/tex] is the height. For the original piece of wood, [tex]\(l = 10\) inches[/tex], [tex]\(w = 4\) inches[/tex], and [tex]\(h = 5\) inches[/tex].

After the piece of wood is cut in half, the length becomes 5 inches, but the width and height remain the same. So, for each of the two new pieces of wood, [tex]\(l = 5\) inches[/tex], [tex]\(w = 4\) inches[/tex], and [tex]\(h = 5\) inches[/tex]. The total surface area of the two new pieces of wood is twice the surface area of one of the new pieces.

The percent increase in the total surface area is given by the formula:

[tex]$$\text{Percent Increase} = \frac{\text{New Total SA} - \text{Original SA}}{\text{Original SA}} \times 100\%$$[/tex]

Let's calculate these values.

The percent increase in the total surface area when the piece of wood is cut in half is approximately 18.18%.

Step-by-step explanation:

If we wanted to extend the discussion beyond what has been shared so far, an additional question we could ask is:

"What is the ratio of adult tickets to children's tickets sold in a day?"

This question would provide insight into the distribution of ticket sales between adults and children and help us understand the demand for different movie genres or screenings among the audience.

If 23 plants were planted on Monday, 28 plants on Tuesday and 29 plants on Wednesday, and 90 plants were planted on Thursday, we can determine that we started with 10 plants initially.

To determine how many plants to start with initially, we need to perform a series of calculations based on the information provided.

On Monday 23 plants were planted, on Tuesday 28 plants were planted and on Wednesday 29 plants were planted. If on Thursday there were a total of 90 plants, we can add all the plants planted until Thursday and then subtract them from the total to obtain the initial amount.

Adding the plants planted:

23 + 28 + 29 = 80

Then, we subtract this amount from Thursday's total:

90 - 80 = 10

Therefore, we started with 10 plants initially.

In summary, if 23 plants were planted on Monday, 28 plants on Tuesday and 29 plants on Wednesday, and 90 plants were planted on Thursday, we can determine that we started with 10 plants initially. This is obtained by adding the plants planted until Thursday and then subtracting that amount from the total for Thursday.

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The solution to the inequality[tex](x/4) - 3 > 2 is x > 20.[/tex]

To solve the inequality [tex](x/4) - 3 > 2,[/tex]we'll follow these steps:

Step 1: Eliminate the fraction by multiplying both sides of the inequality by the denominator, which is 4 in this case. This step allows us to get rid of the fraction and simplify the inequality.

[tex](x/4) - 3 > 2[/tex]

Multiply both sides by 4:

[tex]4 * [(x/4) - 3] > 4 * 2[/tex]

This simplifies to:

x - 12 > 8

Step 2: Isolate the variable on one side of the inequality by adding 12 to both sides:

x - 12 + 12 > 8 + 12

This simplifies to:

x > 20

So, the solution to the inequality is x > 20. This means that any value of x greater than 20 will satisfy the inequality.

To represent this solution graphically, we can plot the number line and shade the region to the right of 20, indicating that any value greater than 20 is a valid solution.

---------------------------------

   -∞     20      +∞

       --------------------------

               ●=================

---------------------------------

In the number line above, the shaded region represents the solution x > 20. Any value to the right of 20, including 20 itself, will satisfy the original inequality.

In summary, the solution to the inequality [tex](x/4) - 3 > 2 is x > 20.[/tex]

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