-2(c+2.5)-5(1.2c+4) simplify this expression

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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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 building is 39.06 yards tall.

The area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

Given:

Hypotenuse (ramp)= 60 yards

Angle of Elevation = 41°

Using Trigonometry

sin 41= P/H

0.651 = P/60

P= 39.06 yard.

Hence, the height is 39.06 yard.

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The length of the segment after dilation with a scale factor of -4 is -12.

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor.

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is a picture with the same shape as the original. However, there is a variation in the shape's size.

Given that the segment LP is dilated with a scale factor of -4. In simple words, the length of the segment is increased to -4 times of its original length.

This is represented as follows:

L'P' = -4 (LP)

Substitute the value of LP = 3:

L'P' = -4 (3)

L'P' = -12

Hence, the length of the segment after dilation with a scale factor of -4 is -12.

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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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The average number of burgers per person is 96

Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given here; The function f(d) =200d³+542d²+179d+1605

The number of visitors is given by g(d)=100d+321

Thus in 7 days, The total number of burgers sold are given by

f(7)=200×7³+542×7²+179×7+1605

    =68600+26558+1253+1605

    =98016

And the number of visitors is given by g(7)=100×7+321

                                                                      =1021

Thus, The average number of burgers per person is given by

Avg= 98016/1021

      =96

Hence, The average number of burgers per person is 96

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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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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 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 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 monthly payment on a loan of $4,500 at 12% interest for a period of 48 months is: $128.34.

The monthly payment for a $4,500 loan at 12% interest for 48 months can be calculated using the formula:

M = P * (r(1 + r)^n) / ((1 + r)^n - 1)

Where:

M = the monthly payment

P = the principal (the amount of the loan)

r = the monthly interest rate (12% divided by 12 months)

n = the number of payments (48 months)

So the calculation is:

M = 4,500 * (0.01(1 + 0.01)^48) / ((1 + 0.01)^48 - 1)

This comes out to be $128.34.

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Answer:

C & D

Step-by-step explanation:

The key formula will be y = mx + b

y = the function

m = slope

b = y - intercept

Another term for slope is rate of change

They asked for negative rare of change, so negative slope, which takes it to

y = -mx + b

The only two that work are C & D because C shows -4x and D shows -2x, both negative.

A & B are 7x and 2/3x, both positive.

The equation of the new function is  f'(x) = -1/2x³

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

F(x) = x³

The transformations are given as

The rule of the above transformations is

f'(x) = -1/2f(x)

substitute the known values in the above equation, so, we have the following representation

f'(x) = -1/2x³

hence, the equation is f'(x) = -1/2x³

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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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The probability of getting a green wrinkled pea from a yyrr x yyrr cross is 1/4.

A cross was made between a pure round yellow seeded pea plant (RRYY) with wrinkled green seeded pea plant (rryy). The yellow colour is dominant over green and round seed shape is dominant over wrinkled seed shape.

The possibility of the result of any random event is known as probability. This phrase refers to determining the likelihood that any given occurrence will occur.

All of the children were yellow because yellow has a dominant gene over green. The green phenotype was no longer present. To see how the second generation would appear, let the yellow pea plants self-fertilize.

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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 dosage for Devon's body weight is 5.25 ounces.

Note that 50 pounds of body weight require 1.5 ounces of medication,

Here by dividing the given amount of medication by 50 find the amount of medication for 1 pound of body  

Now multiply the result by the present body weight of the Devons.  

Here we have

The dosage of the medication is 1.5 ounces for every 50 pounds

Weight of Devon = 190 pounds    

If he loses 15 pounds, present Devon's weight = 190 - 15 = 175

Dosage for Devon's body = [tex]\frac{1.5}{50} \times 175[/tex]  

= [tex]0.03 \times 175[/tex]  

= 5.25

Therefore,

The dosage for Devon's body weight is 5.25 ounces.    

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The equation shown below can be used to find, the total number of ounces of almonds in the last bag.

y = 8/2 + 1 And y = 5 ounces of almonds in the last bag.

Two algebraic expressions having same value and symbol '=' in between are called as an equation.

Given:

Isabel has 8 ounces of almonds to divide equally into 2 bags

In the last bag, she adds an ounce of almonds.

The equation shown below can be used to find, the total number of ounces of almonds in the last bag.

y = 8/2 + 1

y = 4 + 1

y = 5 ounces of almonds in the last bag

Therefore,  5 ounces of almonds in the last bag

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The complete question:

Isabel has 8 ounces of almonds to divide equally into 2 bags. In the last bag, she adds an additional ounces of almonds. The equation shown can be used to find, the total number of ounces of almonds in the last bag. How many ounces of almonds are in the last bag?

Answer: Frank owes $212 on his credit card and then charges $105 more, so the new balance on Frank's credit card is:

$212 + $105 = $317

So the new balance on Frank's credit card is $317.

Step-by-step explanation:

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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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:

If a city's population doubles every 6 years, the city's population, 12 years from now, will be 2,152,000.

Every six months, the population increases by two times the current number.

Using multiplication by 2 or 4, we can determine the population in 12 years.

The current population of the city in Year 0 = 538,000

Doubling time = every 6 years

The estimated time = 12 years

In the first six years, the population will be 1,076,000 (538,000 x 2)

In the second six years, the number of people in the city will be 2,152,000 (1,076,000 x 2) or (538,000 x 4)

Thus, in 12 years, the city's population will become 2,152,000 people.

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Answer:

2,152,000

Step-by-step explanation:

Graph the equation y = x + 1l on a separate sheet of graph paper, and then click on the graph to make the right one appear. appears to be a house's roof. From the (0,0) line, it has moved forward one space.

The graph of y equal to the value of x minus 3 is the one that needs to be chosen in this challenge. Since these 3 units will now be moved to the right, the vertex will no longer be at the origin, where it normally is. You should choose the graph that has a form similar to what I'm going to create when I move 3 to the right .

The graph cannot represent a function if a vertical line can cross it at two or more different locations. To put it another way, the graph is said to reflect a function if a vertical line drawn anywhere only intersects it once, indicating that each x value has a single corresponding y value.

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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:

All the given statements for the function g(x) is true.

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

For the function g(x) -

When the value of x = 1, then the value of y = 22.

When the value of x = 3, then the value of y = -5.

When the value of x = 5, then the value of y = 6.

When 1 is an input, 22 is an output.

The point (-5, 3) lies on the graph of the function.

The solution to g(x) = -5 is x = 3.

When 6 is an input, 5 is an output.

The point (-5, 3) lies on the graph of the function.

The point, (5, 6) lies on the graph of the function.

Therefore, all the statements are true.

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Answer: Martha earned $13,728.12 in interest over 8 years.

Step-by-step explanation:

The future value of Martha's investment can be calculated using the formula:

FV = PV (1 + r/n)^(nt)

Where:

PV = present value (initial investment) = $14,200

r = annual interest rate = 6%

n = number of times the interest is compounded per year = 12 (monthly)

t = number of years the investment is held = 8

Plugging in the values, we get:

FV = 14,200(1 + 0.06/12)^(12*8) = $27,928.12

The interest earned on her investment is the difference between the future value and the present value:

$27,928.12 - $14,200 = $13,728.12

So Martha earned $13,728.12 in interest over 8 years.

Answer:

$22,920.83

Step-by-step explanation:

assuming 6% is annual rate

so 12 months in a year = 6%/12 = 0.5% per month

so every month she gets  (1+0.5%)  growth on her previous balance

so for 8 years = 96 months,

she'll get that growth 96 times

so it'll be 14,200 *(1+0.5%) ^ 96 =22,920.83

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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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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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