Find the domain and the range of the relation shown on the graph to the right. Use the vertical line test to determine whether the graph is the graph of a function.

The equations that enable us to compute x are tanx=3/4 and x=tan⁻¹(3/4)

In mathematics, trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. The six trigonometric functions are Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent.

Given here: length of the pole=3m and distance of the stake from the pole=4m and the angle that the rope makes with the pole is x

We know Arctan function is the inverse of the tangent function. It is usually denoted as arctan x or tan⁻¹x. The basic formula to determine the value of arctan is θ = tan-1(Perpendicular / Base).

Thus we have the value of x as

x=tan⁻(perpendicular/Base)

=tan⁻¹(3/4)

=36.87°

Thus the two possible ways to compute the angle x are:

tanx=3/4 and x=tan⁻¹(3/4)

Hence, The equations that enable us to compute x are tanx=3/4 and x=tan⁻¹(3/4)

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The polynomial divided by (x + 3), with quotient is x² - x + 8, and remainder of -5 is f(x) = x³ + 2x² + 5x + 19

The polynomial division algorithm states that for two polynomials, f(x) and g(x), where the degree of g(x) a divisor is less than or equal to the degree of f(x), there exist unique polynomials, q(x) the quotient and r(x) the remainder, such that f(x) = g(x)q(x) + r(x) and the degree of r(x) is less than the degree of g(x). This is also known as synthetic division.

f(x) = (x + 3)(x² - x + 8) + (-5)

but expansion;

f(x) = x³ + 3x² - x² + 8x - 3x + 24 - 5

f(x) = x³ + 2x² + 5x + 19

Therefore, the polynomial f(x) = x³ + 2x² + 5x + 19 divided by (x + 3), will give the quotient x² - x + 8, and remainder of -5.

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If row 3 were to be deleted, it would show a deletion anomaly. This is so that this entry won't be deleted along with the entire database for the Legend book.

This oddity happens when we change a few rows in the database, and if it causes the table to become inconsistent. Updation anomalies are this kind of abnormality.

Due to the duplicate data in each of these rows, this is an update anomaly. If that data is altered in one row but not the other, there will be an update anomaly. There will be two addresses if we miss even one row during the update, which will result in inconsistent and incorrect databases.

If row 3 were to be deleted, it would show a deletion anomaly. This is so that this entry won't be deleted along with the entire database for the Legend book. There is nothing about this book in any other row. Deleting one row wouldn't result in the entire disappearance of the book data because all other books are represented in at least two rows.

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The standard form equation of a circle given the center of (-7, -15) is (x+7)^2+(y+15)^2 = 9.

What is Circle?

All points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.

What is equation of circle?

(x - h)^2+ (y - k)^2 = r^2 is the formula for the equation of a circle, where (h, k) stands for the circle's center's coordinates and r for the radius. A circle touches the x-axis at (3,0) if it is tangent to the x-axis at that location.

Given;

center (-7,-15) and A = 9π

[tex]S = \pi r^2[/tex]

[tex]r = \sqrt{\frac{A}{\pi} }[/tex]

r = [tex]\pi ^{2}[/tex]

From the equation of circle, we get;

⇒(x - h)^2+ (y - k)^2 = r^2

⇒(x+7)^2+(y+15)^2 = [tex]\pi ^{2}[/tex]

So,The standard form equation of a circle given the center of (-7, -15) is (x+7)^2+(y+15)^2 = 9.

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Answer: We can start by using the following formula to find the time it takes for David to catch up with James:

time = (James' lead) / (David's rate - James' rate)

In this case, James' lead is 6 hotdogs, and we know that James eats 1 hotdog every 2 minutes, so his rate is 1/2 hotdog per minute. David's rate is 1.25 hotdogs per minute.

So, substituting these values into the formula:

time = (6) / (1.25 - (1/2))

time = 6 / (0.75)

time = 8 minutes

So it takes David 8 minutes to catch up with James.

Step-by-step explanation:

The graph of 3x-2y≤6 is the third graph, for 3x-2y<6 is the first graph, for 3x-2y>6 is the fourth graph and for 3x-2y≥6 is the second graph. The solution has been obtained using concept of linear inequality.

What is linear inequality?

A linear inequality is one that would produce a linear equation if the equals relation were used instead of the inequality. When multiplying or dividing both sides by a negative number in order to solve the inequality, the direction of the inequality is reversed. The entire set of solutions to an inequality is known as the solution set.

We are given for graphs, of which two graphs are dotted and two are simple straight line graphs.

The dotted graphs are drawn for the inequalities having < or >

Whereas the simple straight line graphs are drawn for the inequalities having ≤ or ≥.

Now, to notice the shaded pattern, we will see whether the equations are true for (0,0) or not

1. 3x-2y≤6

⇒ 0≤6

So, the equation is true for the point.

Hence, the third graph represents this equation.

2. 3x-2y<6

⇒ 0<6

So, the equation is true for the point.

Hence, the first graph represents this equation.

3. 3x-2y>6

⇒ 0>6

So, the equation is false for the point.

Hence, the fourth graph represents this equation.

4. 3x-2y≥6

⇒ 0≥6

So, the equation is false for the point.

Hence, the second graph represents this equation.

Hence, the graphs are matched with the inequalities.

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Since, there are multiple questions so, the question answered above is attached below.

Answer: 300

Step-by-step explanation:

Step 1:

Multiply:

1200*0.25=300

Answer: 300

Step-by-step explanation: Just multiply 1200 x 1/4 and that's your answer

The information in assertion 2 that says Retrievers make up 15 percent of the dogs at the event is untrue.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Given, 35% of the dogs at a dog show are German shepherds. 10% of the dogs are poodles, 45% of the dogs are spaniels, and the rest were retrievers.

Since the rest dog breed was retrievers,

Thus, retrievers = 100- 45-35-10

retrievers = 10%

Therefore, statement 2 which states Retrievers account for 15 percent of the dogs at the show is incorrect.

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The coordinates of point C are C(0,-sqrt(36 - x²))

An equilateral triangle has all sides of equal length and all angles of 60 degrees. Since the triangle is in the fourth quadrant, so we know that both the x and y coordinates of point C must be negative.

We can use the distance formula to find the length of the sides of the triangle:
AB = sqrt((0 - 0)² + (-6 - 0)²) = 6
BC = sqrt((x - 0)²+ (y - 0)²) = AC = sqrt((x - 0)² + (y - (-6))²) = sqrt(x² + (y + 6)² = 6

We may now use the notion that all angles in an equilateral triangle equal 60 degrees. We know that point A is at (0,-6) and point B is at (0,0), therefore we can use the slope of line AB and the length of the side to compute point C's coordinates.


Line AB has a slope of (0 - (-6))/(0 - 0) = 6/0 = undefined.The slope of a line perpendicular to AB is the negative reciprocal of AB's undefined slope; so, line AB is parallel to the x-axis. So C(x,y) has the same x-coordinate as B(0,0) but a different y-coordinate.

The length of the side is 6, so we can use this information to find the y-coordinate of point C:
y = sqrt(6² - x²) = sqrt(36 - x²)= -sqrt(36 - x²)

So, the coordinates of point C are C(0,-sqrt(36 - x²))

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The account balance after eleven years would be ₱14,925.08. Calculate the future value of the account: FV = PV x (1 + r)^n = 820 x (1 + 0.025)^22 = ₱14,925.08. total number of semi-annual periods: 11 years x 2 semi-annual periods per year = 22 semi-annual periods.

The account balance after eleven years would be ₱14,925.08.

1. Calculate the compounded interest rate: 5% per year compounded semi-annually = 2.5% per semi-annual period.

2. Calculate the total number of semi-annual periods: 11 years x 2 semi-annual periods per year = 22 semi-annual periods.

3. Calculate the future value of the account: FV = PV x (1 + r)^n = 820 x (1 + 0.025)^22 = ₱14,925.08.

The account balance after eleven years would be ₱14,925.08.

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Answer:

see below

Step-by-step explanation:

length = 10

circumference = 2πr = 8 π, so r=4

8π=25.12

cut half so length = 5, so lateral surface = 8π*5 = 40π =125.6

top circle area = πr² = 3.14*4² = 3.14 *16 = 50.24

top & bottom = 2*50.24 = 100.5

so total surface of EACH after cut in half = 100.5+125.6 =226.1

TWO of them = 2*226.1 =452.2

Answer: $940

Step-by-step explanation:

30% can also be represented as 0.3.

You can solve and find 100%, or the original price, by cross-multiplying.

282 x 1 = 282

282 / 0.3 = 940

The price yesterday was $940.

We have designed a situation where the probability of one event (event A) is 1/5 and the probability of another event (event B) is 1/10.

To quantify the probability of each event, we can define the following events:

Then, the probability of event A is 1/5, since 1 in every 5 units of product A is defective. Similarly, the probability of event B is 1/10, since 1 in every 10 units of product B is defective.

Now, let's consider a scenario where the company receives an order for 100 units of products, with 60 units of product A and 40 units of product B. The company wants to determine the probability of the following events:

To calculate the probability of event C, we need to consider the probability of selecting a defective unit from product A and from product B, and the proportion of each product in the order. Since the order has 60 units of product A and 40 units of product B, the probability of selecting a unit of product A is 60/100 = 3/5, and the probability of selecting a unit of product B is 40/100 = 2/5.

Using the probabilities of event A and event B, we can calculate the probability of selecting a defective unit from product A or from product B as follows:

Therefore, the probability of event C can be calculated as follows:

P(C) = P(A) * P(A in order) + P(B) * P(B in order)

= (1/5 * 3/5) + (1/10 * 2/5)

= 3/25

So the probability of selecting a defective unit from the order is 3/25.

To calculate the probability of event D, we can use the complement rule, which states that the probability of an event and its complement (i.e., the event not happening) add up to 1. Therefore, the probability of event D can be calculated as follows:

P(D) = 1 - P(C)

= 1 - 3/25

= 22/25

So the probability of selecting a unit from the order at random and finding that it is not defective is 22/25.

In summary, we have designed a situation where the probability of one event (event A) is 1/5 and the probability of another event (event B) is 1/10. We have also calculated the probability of two other events (event C and event D) in a scenario where a manufacturing company produces two types of products, with different probabilities of defects, and receives an order with a certain proportion of each product.

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The figure does not represent a dilation, as the scale factors for the two sides of the right triangle are different.

A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.

The scale factors for this problem are given as follows:

They are different, meaning that the figure in this problem is not a dilation.

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The area of the customer's yard is 580π.

The distance formula is given as -

d = √(x₂ - x₁)² + (y₂ - y₁)²

Given is that this grid represents the customer’s yard. The bottom left corner is the origin point  O(0, 0), and the x- and y- axes represent the two fences. The rose bush is at point P(16, 18).

We can write the area of the customer's yard -

A = πr²

Here -

r = d

r² = d²

We can write -

A = πd²

A = π {(x₂ - x₁)² + (y₂ - y₁)²}

A = π{16 x 16 + 18 x 18}

A = 580π

Therefore, the area of the customer's yard is 580π.

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A triangle is a shape used to represent the components of total health. True

The increase in the minimum wage from $8.10 to $15, indicates that the percentage increase in the minimum wage is 85.[tex]\overline{185}[/tex]%

A percentage represent the number, amount, proportion or ratio of an item to another (possibly larger) item per hundred (100) units of the comparison or larger item.

Percentages, quantitatively describes the idea of the amount of a substance. It is a measure of the amount or occurrence of an item.

The specified original minimum wage at Ben's Burger = $8.10

The new amount to which the minimum wage is increased = $15

The percentage increase can be obtained using the formula;

[tex]\% \ increase = \frac{New - Original}{Original} \times 100[/tex]

The percentage increase is therefore; ((15 - 8.10)/8.1) × 100 = 85.[tex]\overline{185}[/tex] %

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For the imaginary roots, the value of c must be greater than the value of d that is c > d. Then the correct option is A.

The discriminant of a quadratic is a number that depends on the components and allows some characteristics of the roots to be deduced without calculating them.

The quadratic equation is ax² + bx + c = 0. Then the discriminant is given as,

D = b² - 4ac

The equation is given as,

2(c² + d²)x² + (c - d)x + 9 = 0

Then the discriminant is given as,

D < 0

(c - d)² - 4 × 2(c² + d²) × 9 < 0

(c - d)² > 72 (c² + d²)

The expresssion (c - d)² must be positive. Then we have

(c - d)² > 0

c - d > 0

c > d

For the imaginary roots, the value of c must be greater than the value of d that is c > d. Then the correct option is A.

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The approximate distance the truck tire will travel in 1 full rotation is 62.8 inches.

The total distance travelled by truck on completing one full rotation will be equal to the circumference of the circle. The circumference of the circle is given by the formula -

Circumference = 2πr, where r refers to radius of truck tire.

Radius = diameter/2

Radius = 20/2

Radius = 10 inches

Keep the values in formula to find the distance travelled on full rotation of truck tire.

Circumference = 2×3.14×10

Performing multiplication on Right Hand Side of the equation

Circumference = 62.8 inches

Hence, the distance covered will be 62.8 inches.

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As the cable between the towers has the shape of a parabola, the height of the cable 200 feet from a tower is 40 feet.

Consider the origin of coordinate system at the bridge level midway between the towers and the cable has the shape of a parabola. It is the vertex of the parabola. The general equation of a parabola is given by y = a(x – h)^2 + k where (h, k) denotes the vertex. Hence, based on the provided information, the equation is;

y = a^x^2

The height of the tower above the road is 160 feet which is 400 feet from the vertex. Hence, x = 400 feet and y = 160 feet.

Substituting the values,

160 = a^(400)^2

a = 0.001

Hence, the equation of the given parabola is:

y = 0.001x^2

In order to calculate the height of the cable at 200 feet from the tower, the value of x = 400 – 200 = 200 feet

y = 0.001(200)^2 = 40 feet

Note: The question is incomplete. The complete question probably is: The towers of a suspension bridge are 800 feet apart and rise 160 feet above the road. The cable between the towers has the shape of a parabola and the cable just touches the sides of the road midway between the towers. What is the height of the cable 200 feet from a tower?

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The correct alternatives are -

Given is the proportional relationship.

A line begins at point (0, 0) and continues to the right.

Direct variation of {y} with {x} means that as {x} increases, {y} increases uniformly with it. Mathematically -

{K} = y/x = constant

Scale factor {K} is a dimensionless value that indicates the constant ratio value indicating direct variation.

Therefore, the correct alternatives are -

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The total cost (c) to put on the seminar is c = 6,930 + 130x + 575x, where x represents the number of students who enroll in the seminar.

The total cost (c) to put on the seminar can be modeled using the following equation -

c = 6,930 + 130x + 575x

here, x represents the number of students who enroll in the seminar.

The above equation takes into account the fixed costs of the conference room, instructor compensation, lab assistants, and promotion (6,930), as well as the variable costs of renting computers (130x) and the seminar fee charged to each student (575x).

As more students enroll in the seminar, the total cost will increase due to the additional computer rental and seminar fee costs.

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Answer: We can start by figuring out how much of the pizza was covered before Mrs. Magsanoc returned by adding the portion that she covered before the phone rang to the portion that Mr. Magsanoc covered while she was away.

Mrs. Magsanoc covered 3/8 of the pizza before the phone rang.

Mr. Magsanoc covered 1/3 of the pizza while she was away.

To add the two portions, we need to find a common denominator, which is the least common multiple of 8 and 3. That is 24.

3/8 of the pizza is (3/8) * (24/8) = 3/24

1/3 of the pizza is (1/3) * (24/3) = 8/24

So, the total portion of the pizza that was covered before Mrs. Magsanoc returned is 3/24 + 8/24

Which is 11/24 or 0.458 of the pizza.

Step-by-step explanation:

The greatest sum Greg can obtain is 975 by adding two numbers. Greg should use the digits 6,5 and 4 for the first number and 3,2 and 1 for the second number

Greatest sum :

                               654 + 321 = 975

To get the greatest sum, Greg should use the digits 6,5 and 4 for the first number and 3,2 and 1 for the second number. This is because these are the largest digits and by putting them in the leftmost side of the number, it will make the number the largest possible number.

The greatest sum is the maximum value that can be obtained from adding two or more numbers. It is the largest possible outcome from an addition operation. The answer or result obtained by adding two or more numbers or terms is known as the sum. As a result, the sum is a way to combine things. To put it another way, adding two or more numbers together to get a new total is called the sum.

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The father had read the most, having finished half the book. The mother had read a third of it, while the daughter was still in the first chapter. The son had only read a few pages.

They discussed their progress and made an agreement to read a certain number of chapters each week to ensure they finished the book at the same time.

Therefore, the father had read the majority of the book, having completed it. While the daughter was still in the first chapter, the mother had already read about a third of it. Only a few pages have been read by the son.

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Rectangle with the given ratio of length to diagonal has measure of the width equals to 27.35 feet.

Actual length of the rectangle = 6 feet

Ratio of the length to diagonal = 3 : 14

⇒Length/ diagonal = 3:14

⇒6/ diagonal = 3:14

⇒Diagonal = (14×6)/3

⇒Diagonal = 28 feet

Let 'x' be the width of the rectangle.

Length , width , and diagonal forms a right angle triangle in a rectangle.

Using Pythagoras theorem ,

Width² = Diagonal² - length²

⇒x² = 28² - 6²

⇒ x = √784 -36

⇒x = 27.35 feet ( nearest hundredth )

Therefore, the width of the given rectangle with the given ratios and dimensions is equal to 27.35 feet.

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Answer:

Step-by-step explanation:

Answer:

f(-5)=50

Brief explanation:

Well we plug -5 for x

f(x)=2x^2

f(-5)=2(-5)^2

f(-5)=2(25)

f(-5)=50

hence the answer

study hard

Answer:

The answer is B.

Step-by-step explanation:

A placebo is a fake medicine

You can learn more about a placebo by reading a book called Mesmerized. It basically talks about the origin of the placebo effect and all that.

The length of segment EF is 6 cm.

The distance between two ends determines the length of a segment.

A segment may be straight, curved, or both straight and curved.

As the distance between two points on a line, a straight segment is the most basic kind of segment. The positions at the segment's ends are known as the endpoints.

It is possible to determine the length of a straight segment by first calculating the difference between the x- and y-coordinates of the two endpoints.

To determine the overall length of the segment, this information is then combined together. It is slightly more difficult to measure a piece that is curved.

This is so because a curved segment's length is frequently different at each location.

Both trapezoids are similar,

⇒ AB / DC = FE / GH                 [Sides are in same ratio]

⇒ 24 / 30 = x / 7.5

⇒ x = 6

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