Convert the rectangular coordinates to polar coordinates
(1, -9)

A graph that represent the system of quadratic equations is shown in the image attached below.

In Mathematics and Geometry, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped. Based on the given quadratic function, we can logically deduce that the graph would be an upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero (0).

By expanding the bracket, we have:

f(x) = (x - 4)(x + 4)

f(x) = x² - 4x + 4x - 16

f(x) = x² - 16

Since the leading coefficient (value of a) in the given quadratic function y = x² - 8x + 12 is positive 1, we can logically deduce that the parabola would open upward and the y-intercept is given by the ordered pair (0, 12).

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The perimeter of the plot land is 78.49 units and the area of the plot land without the building and parking lot is 210 square units

From the graph, the vertices of the land are

A = (0, 20), B = (25, 19), C = (20, 2) and D = (5, 0)

Calculate the distance between adjacent vertices

So, we have

AB = √[(0 - 25)² + (20 - 19)²] = 25.02

BC = √[(20 - 25)² + (2 - 19)²] = 17.72

DC = √[(20 - 5)² + (2 - 0)²] = 15.13

AD = √[(0 - 5)² + (20 - 0)²] = 20.62

The perimeter of the plot land is

P = 25.02 + 17.72 + 15.13 + 20.62

P = 78.49 units

This is calculated as

Area = Plot land - Building - Parking lot

Using the vertices, we have

Area = 1/2 * |0 * 19 + 25 * 2 + 20 * 0 + 5 * 20 - (20 * 25 + 19 * 20 + 2 * 5 + 0 * 0)| - [1/2 *(15 - 7 + 17 - 7) * (15 - 10)] - [(18 - 10) * (10 - 5)]

This gives

Area = 295 -  45 - 40

So, we have

Area = 210

Hence, the area is 210 square units

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The measure of the first Angle is 59 degrees, the second angle is x + 18 = 77 degrees, and the third angle is x - 15 = 44 degrees

In any triangle, the sum of the measures of the three angles is always 180 degrees.

Let x be the measure of the first angle.

The second angle is x + 18 because it is given that the second angle is 18 more than the first angle.

The third angle is x - 15 because it is given that the third angle is 15 less than the first angle.

So, we have:

x + x + 18 + x - 15 = 180

Simplifying and solving for x, we get:

3x + 3 = 180

3x = 177

x = 59

Therefore, the measure of the first angle is 59 degrees, the second angle is x + 18 = 77 degrees, and the third angle is x - 15 = 44 degrees.

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Answer:

6 times with a remainder of 0

how do u not know this

skipped basic math have u?

Answer:

49 [tex]ft^{2}[/tex]

Step-by-step explanation:

a = 1/2 (bh)

a = 1/2(7x14)

a = 49

Helping in the name of Jesus.

Answer:

Step-by-step explanation:

Answer:

To find the area of the shaded region, we need to first find the x-coordinates of the points where the two functions intersect. We can set f(x) = g(x) and solve for x:

x^4 - 12x^3 + 48x^2 = 44x + 105

x^4 - 12x^3 + 48x^2 - 44x - 105 = 0

We can use a numerical method, such as the Newton-Raphson method, to approximate the roots of this equation. Using a graphing calculator or computer algebra system, we can find that the roots are approximately:

x = -1.932, x = 0.695, x = 4.149

Note that the root x = -1.932 is outside the given interval [3, 4], so we can ignore it.

The shaded region is bounded by the x-axis, the line y = 340, and the graphs of f(x) and g(x) between x = 3 and x = 4. To find the area of this region, we can integrate the difference between the two functions over this interval:

A = ∫3^4 [g(x) - f(x)] dx

A = ∫3^4 [44x + 105 - (x^4 - 12x^3 + 48x^2)] dx

A = ∫3^4 [-x^4 + 12x^3 - 48x^2 + 44x + 105] dx

We can integrate term by term using the power rule:

A = [-x^5/5 + 3x^4 - 16x^3 + 22x^2 + 105x]3^4

A = [-1024/5 + 192 - 192 + 22 + 105] - [-81/5 + 108 - 192 + 66 + 105]

A = 347.2

Therefore, the area of the shaded region is approximately 347.2 square units.

The perimeter and the area of rectangle EFGH are 24 cm and 35 square cm

From the question, we have the following parameters that can be used in our computation:

Side length, AB = 5 cm

Extension AE=AH=FC=GC = 2cm

Using the above as a guide, we have the following:

Dimension of the rectangle = 5 cm By (5 + 2) cm

So, we have

Dimension of the rectangle = 5 cm By 7 cm

The perimeter is then calculated as

P = 2 * (5 + 7) = 24 cm

The area is calculated as

A = 5 * 7 = 35 square cm

Hence, the perimeter and the area of rectangle EFGH are 24 cm and 35 square cm

See attachment for figure

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Answer:

p(large or green) = 0.794

Step-by-step explanation:

If a marble is randomly selected from the box, we need to find the

probability that it is small or green

1. Find P(large) ⇒ P(l)

2.Find P(green) ⇒ P(g)

3. Find P(large and green) ⇒ P(l and g)

4. Use the rule P(large or green) = P(l) + P(g) - P(l and g)

∵ The box contains 18 large marbles and 16 small marbles

∴ The total number of marbles = 18 + 16 = 34

∴ P(l) = 18/34

∵ There are 7 large green marbles

∵ There are 18 large marbles

∴ P(l and g) = 7/34

∴ P(g) = 16/34

∵ P(large or green) = P(l) + P(g) - P(l and g)

∴ P(large or green) = 18/34 + 16/34 - 7/34

∴ P(large or green) = 27/34

= 0.7941176471

If a marble is randomly selected from the box, then the probability that it is large or green is 0.794

Average is the total sum of the given values divided by the number of values.

The average low temperature for the week is -3°F.

We have,

It is the total sum of the given values divided by the number of values.

We have,

Temperatures for one week:

Day                   Temperature

Sunday          −5 °F ​

Monday         −8 ​°F ​

Tuesday         −6​°F ​

Wednesday     −8​°F ​

Thursday         −3 ​°F

Friday                2° F

Saturday           7° F

The average of the low temperature:

= [ -5 + (-8) + (-6) + (-8) + (-3) + 2 + 7 ] / 7

= (-5 - 8 - 6 - 8 - 3 + 2 + 7) / 7

= -30 + 9 / 7

= -21 / 7

= -3

Thus,

The average low temperature for the week is -3°F.

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complete question:

Christopher recorded the low temperature each day for 1 week and recorded his results in this table.

Day Sunday Monday Tuesday Wednesday Thursday Friday Saturday

Low −5 °F ​ −8 ​°F ​ −6 ​°F ​ −8​°F ​ −3 ​°F 2° F 7° F

What is the average low temperature for the week?

The value of y is 3 when x = 25.

When two variables, x, and y, vary inversely, it means that as one variable increases, the other decreases in a proportional manner. In other words, their product is constant.

Mathematically, this relationship can be expressed as:

y = k/x

where k is the constant of proportionality.

To solve the problem, we are given that y = 5 when x = 15, which can be rewritten as:

5 = k/15

To find the value of y when x = 25, we need to first determine the value of k. We can do this by rearranging the equation above to solve for k:

k = 5 x 15 = 75

Now that we know the constant of proportionality, we can use it to find the value of y when x = 25:

y = k/x = 75/25 = 3

Therefore, when x = 25, y = 3. This means that as x increases from 15 to 25, y decreases from 5 to 3, in accordance with the inverse variation relationship between x and y.

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Answer:

250 students and 310 adults

Step-by-step explanation:

so if  students are charged 1.25 and adults are charged 2.25 and 560 people attended if you divided from it should equal

The water rises 10 inches each hour. The water is 4 inches deep is the water after four hours. It will take 8 hours for the water to reach a depth of 80 inches.

A pipe cracked overnight and started to leak into a basement.

The graph represents the depth (d) of the water over time (t).

As per the given graph, the required solution would be as:

Take two points (1, 10) and (5, 50) in the given graph

The linear function will be :

d - 10 = (50-10)/(5-1)(t - 1)

d - 10 = (40/4)(t - 1)

d = 10(t - 1) + 10

d = 10t - 10 + 10

d = 10t

Here slope of the given function is 10, which means 10 inches the water rise each hour.

The value of time (t) = 4 hr corresponds to the depth of water (d) is

d = 10(4) = 40

So, the water is 40 inches deep is the water after four hours

The value of depth of water (d) = 80 in corresponds to the time (t) is

80 = 10t

t = 80/10 = 8

So, It will take 8 hours for the water to reach a depth of 80 inches

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Option A is correct: the cross-section of a sphere must be a circle.

When a sphere is cut by a plane, the resulting cross-section will always be a circle, regardless of the orientation or angle of the cut. This is because all cross-sections of a sphere have the same shape and size as a great circle, which is a circle that passes through the center of the sphere and divides it into two equal halves.

Option B is not correct because an ellipse is not a possible cross-section of a sphere.

Option C is not correct because the cross-section of a sphere can only be a circle, not an ellipse.

Option D is not correct because a line is not a possible cross-section of a sphere. A line can only be a cross-section of a cylinder or a cone, but not a sphere.

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The total surface area of the triangular prism is is 1872 square meters

From the question, we have the following parameters that can be used in our computation:

The triangular prism

The surface area of the triangular prism from the net is calculated as

Surface area = sum of areas of individual shapes that make up the of the triangular prism

Using the above as a guide, we have the following:

Area = 1/2 * 12 * 16 * 2 + 35 * (20 + 16 + 12)

Evaluate

Area = 1872

Hence, the surface area is 1872 square meters

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Answer:

The solution is (-2, 0).

The IRA that is best is C. The Roth IRA is the best choice because the employee will pay more in taxes during employment than in retirement.

When contributing to a Roth IRA, one must use after-tax dollars, resulting in taxes being paid on the money prior to it being deposited into the account. Withdrawals made from a Roth IRA that meet the necessary qualifications are completely exempt from taxation, thus employees will not be required to pay any taxes on the amount withdrawn during their retirement period.

It is probable that an employee's retirement income tax bracket will be higher than their current bracket, given the anticipated increase in their income and tax rate.

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Answer:

Done

Step-by-step explanation:

To solve the problem, we can use a Venn diagram to visualize the information provided in the question.

Let's draw three overlapping circles to represent the three groups of people: those who eat fruits, those who eat vegetables, and those who eat cheese.

We know that:

- 37 people eat fruits, so we write "37" in the circle representing fruits.

- 33 people eat vegetables, so we write "33" in the circle representing vegetables.

- 9 people eat both cheese and fruits, so we write "9" in the overlap between the cheese and fruits circles.

- 12 people eat both cheese and vegetables, so we write "12" in the overlap between the cheese and vegetables circles.

- 10 people eat both fruits and vegetables, so we write "10" in the overlap between the fruits and vegetables circles.

- 12 people eat only cheese, so we write "12" in the part of the cheese circle that does not overlap with the other circles.

- 3 people eat all three offerings, so we write "3" in the intersection of all three circles.

Here's what the Venn diagram looks like:

```

Cheese

+----9----+----3----+----12---+

| | Cheese | | |

| Fruits +----6----+--4 | |

| | | | |

+----10---+----3----+----8---+---+

| Vegetables |

+------------+

9 24 15

```

To find out how many people eat cheese, we add up the numbers in the cheese circle: 9 + 3 + 12 = 24. So, 24 people eat cheese.

To find out how many people do not eat any of the offerings, we need to add up the numbers in the regions that are not part of any circle: the region outside of all circles, and the region in the center of the Venn diagram. These regions add up to 9 + 15 = 24. So, 100 - 24 = 76 people do eat at least one of the offerings.

These two events are independent because the outcome of both doesn't affect each other.

An independent event is the type of event that occurs when the outcome of one event does not affect the outcome of the second event it is compared with.

A dependent event is the type of event that it's outcome affects the outcome of the second event it is compared with.

That Abigail chose an entree in a town different from Zeke doesn't affect her ability to attend the wedding.

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Hello,

tan = opposite/ adjacent

[tex]tan0 = \frac{5}{\sqrt{11} } = \frac{5\sqrt{11} }{11}[/tex]

it's the first answer

Answer:

According to the empirical rule (also known as the 68-95-99.7 rule), for a bell-shaped distribution, approximately:

- 68% of the data falls within one standard deviation of the mean.

- 95% falls within two standard deviations of the mean.

- 99.7% falls within three standard deviations of the mean.

In this case, the mean number of phone calls answered by each receptionist is 36, and the standard deviation is 3.

To calculate the percentage of daily phone calls numbering between 33 and 39, we need to find the proportion of data within one standard deviation of the mean in either direction.

The range of interest (33 to 39) is within one standard deviation of the mean, so approximately 68% of the data will fall within this range.

Therefore, the approximate percentage of daily phone calls numbering between 33 and 39 is 68%.

Answer:

[tex]y = 1- |x + 1| [/tex]

Hello,

x = departure's sallary

x*1,1*0,9 = 0,99x

the net change in my salary is 1%

The minimum speed at which the car was traveling is 52.9 miles per hour.

To find the minimum speed at which the car was traveling during the skid, we can use the formula for calculating skid speed:

Skid speed = (Chord length x Chord length x Drag factor) / (2 x Middle ordinate)

Plugging in the given values:

Chord length = 70 feet

Middle ordinate = 9 feet

Drag factor = 1.13

Skid speed = (70 x 70 x 1.13) / (2 x 9)

Skid speed = 1391 / 18

Skid speed ≈ 77.3 feet per second

To convert the speed to miles per hour, we can multiply it by 3600/5280

= 77.3 x (3600/5280)

≈ 52.9 miles per hour

Therefore, the minimum speed at which the car was traveling is 52.9 miles per hour.

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Answer:

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

Find the combination of 2 out of 7:

There are 21 combinations.

Answer: A = 470 in²

Step-by-step explanation:

          If the given prism is a rectangular prism, we can use the given formula to solve for the surface area of a rectangular prism.

A = 2((8 in)(15 in) + (5 in)(15 in) + (5 in)(8 in))

A = 2(120 in² + 75 in² + 40 in²)

A = 2(235 in²)

A = 470 in²

Answer:

c

Step-by-step explanation:

The two angles on the bottom are equal.

All 3 angles equal 180 degrees.

We know one angle is 130.

The other two are 180-130= 50 combined.

Since those angles are equal, divide by two.

50/2= 25 degrees each.

2.883

I used Desmos graphing calculator to find this answer.