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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.

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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If Ken's pay remains constant, he should expect to earn $69,600 in two years.

In Mathematics, a proportional relationship is a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

Next, we would determine the constant of proportionality (k) for the data points as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 14,500/5

Constant of proportionality, k = 2,900

In two (2) years, Ken's wages is given by:

y = kx

y = 2,900(24)

y = $69,600.

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Serenity is going to invest in an account paying an interest rate of 4.4% compounded continuously therefore Serenity would need to invest $400 to the nearest hundred dollars, for the value of the account to reach $670 in 11 years.

This is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.

We can solve the problem by :

1+(0.044÷365)= 1.0001205479

Yearly impounding factor, 1.0001205479^365=1.0449795838

For a period of 11 years, maturity factor,1.0449795838^11 = 1.6225043167.

$1 becomes $1.6225043167.

If Maturity value is to be,$670 which is amount to be invested,

670÷ 1.6225043167 = 412.942

To the nearest 100 dollars is $400.

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You will pay back $100.00

We know that the formula for the compound ineterst:

[tex]A = P(1 +\frac{r}{n})^{nt}[/tex]

where, A = Accrued amount

P = Principal amount

r = interest rate as a decimal

R = interest rate as a percent

r = R/100

n = number of compounding periods

t = time in years

First, convert R as a percent to r as a decimal

r = 5.2/100

r = 0.052 rate per year,

Now we solve the equation for A

[tex]A = P(1 +\frac{r}{n})^{nt}[/tex]

[tex]A = 95\times (1 +\frac{0.052}{2})^{2\times 1}[/tex]

A = 95.00 × (1 + 0.026)²

A = 100.004

A ≈ 100

Therefore, the total amount accrued with compound interest on a principal of $95.00 at a rate of 5.2% per year compounded semi annually is $100.00.

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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:

c

Step-by-step explanation:

it wouldnt just be 9, thats marias books, to get what jim ahs and hers its 9+b

b representing the amount jim read

Answer: 15.4

Step-by-step explanation: d= [tex]\sqrt{(-18)^{2} - 18^{2}) +((-19)^{2} - 11^{2})\\[/tex]

[tex]\sqrt{361 - 121}[/tex]

[tex]\sqrt{240}[/tex]

15.4

Answer:

$4

Step-by-step explanation:

Given;

Dozen long stemmed roses cost $48

Question:

What is the cost per rose?

Solve:

Based on the given, we can see that it states that a dozen long stemmed roses cost $48.

Knowing that - Dozen = 12

Since, we know that dozen equal 12. Hence, 12 long stemmed roses cost $48.

Now, divide the cost by the amount to find the cost per rose.

Thus,

48 ÷ 12 = 4.

Therefore, the cost per rose is $4.

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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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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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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 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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Answer:

A

Step-by-step explanation:

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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The average speed is S=2.033 m/s

The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance traveled by a body in a given period of time.

The unit of speed is a meter/second.

Speed formula can be used to find the speed of objects, given the distance and time taken to cover that distance.

To calculate the average speed we have a general formula:

speed = distance ÷ time.

Given distance=100m

time=49.17 s

Plugging the values in the above formula:

speed=100/49.17

speed=2.033

Therefore, the average speed is 2.033 m/s.

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1. The value of n in 3n + 19 = 28 will be 3.

2. The value of b in 34 - 4b = 18 will be 4.

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

The value of n in 3n + 19 = 28 will be:

3n + 19 = 28

Collect the like terms

3n = 28 - 19

3n = 9

Divide

n = 9 / 3

n = 3.

The value of b in 34 - 4b = 18 will be:

34 - 4b = 18

4b = 34 - 18

4b = 16

Divide.

b = 16 / 4

b = 4

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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 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: $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 fraction of the bag of sugar that Rick's dad pour into the water is 2/3

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

Fractions is a part of a whole number. It is the ratio of two numbers. The top number is the numerator while the bottom number is the denominator. Hence:

Fraction = numerator / denominator

Rick opens a 3-cup bag of sugar. Rick's dad pours 2 cups into the water. Hence:

Fraction of sugar poured into water = amount of sugar poured in water / total amount of sugar

Substituting:

Fraction of sugar poured into water = 2 cups / 3 cups = 2/3

Ricks dad pour 2/3 of the sugar into the water

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

The required inequality is d + b ≥ 11 representing the possible values for the number of donuts and brownies purchased.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

We can represent the number of donuts purchased as d, and the number of brownies purchased as b. The inequality that represents the minimum number of donuts and brownies that must be purchased altogether is:

d + b ≥ 11

This inequality states that the total number of donuts (d) and brownies (b) purchased must be greater than or equal to 11.

This inequality can be represented graphically on a number line, with point 11 being the boundary between the solutions that satisfy the inequality and those that do not.

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Answer:

To solve the equation:

39 - 3x12²÷24

Step-by-step explanation:

First, we need to simplify the expression inside the parentheses:

12² = 12*12 = 144

Then we can substitute that value into the equation:

39 - 3x144÷24

Next, we can simplify the expression inside the parentheses:

144÷24 = 6

Then we can substitute that value into the equation:

39 - 3x6

Now we can solve the equation by performing the multiplication and subtraction:

39 - 18 = 21

So the solution is 21.

Steps:

1. 12² = 144

2. 144÷24 = 6

3. 39 - 3x6 = 39 - 18 = 21

So, 39-3*12²÷24 = 21

Answer:

36

Step-by-step explanation:

39 - 3 x [tex]12^{2}[/tex] ÷ 24  First simplify the exponent

39 - 3 (12 x12) ÷ 24

39 - 3 x 24 ÷ 24  Next do multiplication and division going from left to right

39 - 72 ÷ 24

39 - 3  Subtract 3

36

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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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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