Find an equation through a horizontal line of (5, -7)

The equation \(x^2 + y^2 + 10y + 20 = 0\) represents a circle with center (0, -5) and radius 5.

To determine if the equation represents a circle, we need to rewrite it in standard form. The standard form of a circle equation is \((x - h)^2 + (y - k)^2 = r^2\), where (h, k) represents the center of the circle and r represents the radius.

Completing the square for the y terms:

\(x^2 + y^2 + 10y + 20 = 0\\ x^2 + y^2 + 10y = -20\\ x^2 + y^2 + 10y + 25 = -20 + 25\\ x^2 + (y + 5)^2 = 5\)

Now the equation is in standard form, \((x - 0)^2 + (y + 5)^2 = 5^2\), which represents a circle.

By comparing the equation to the standard form, we can determine the center and radius of the circle. The center is given by the values (h, k), which in this case is (0, -5). Therefore, the center of the circle is (0, -5).

The radius is determined by the term \(r^2\), which in this case is \(5^2 = 25\). Therefore, the radius of the circle is 5.

In summary, the equation x^2 + y^2 + 10y + 20 = 0 represents a circle with center (0, -5) and radius 5. The completion of the square allowed us to rewrite the equation in standard form, making it evident that it represents a circle. The center of the circle is determined by the values of x and y, and the radius is determined by the value of r.

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The height of the seedling after one week is approximately 11.695 cm, given that it grew approximately 0.045 cm each day and started at a height of 11.38 cm.

To determine the approximate height of the seedling after one week, we need to calculate how much it will grow in one week and add that to its initial height.

Since the seedling grows approximately 0.045 cm each day, it will grow approximately

0.045 cm/day × 7 days/week = 0.315 cm/week

Therefore, after one week, the height of the seedling will be approximately

11.38 cm + 0.315 cm = 11.695 cm

So the approximate height of the seedling after one week is 11.695 cm.

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Answer:

1). 6 eggs = 7.5 waffles 2). 8 ounces for 24 biscuits

Step-by-step explanation:

A representative sample based on the hospital scenario is option A

A subset of a larger population that accurately reflects the traits, diversity, and distribution of the total population is referred to as a representative sample.

Due to time, financial, or logistical limitations, it is frequently not possible or practical to investigate an entire population when conducting research or gathering data. In these situations, researchers choose a representative sample from which to deduce generalizations about the total population.

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well, from 1990 to 1998 is 8 years, and we know the amount went from $4800 to $6300, let's check for the rate of growth.

\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$6300\\ P=\textit{initial amount}\dotfill &\$4800\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{years}\dotfill &8\\ \end{cases} \\\\\\ 6300=4800(1 + \frac{r}{100})^{8} \implies \cfrac{6300}{4800}=(1 + \frac{r}{100})^8\implies \cfrac{21}{16}=(1 + \frac{r}{100})^8\)

\(\sqrt[8]{\cfrac{21}{16}}=1 + \cfrac{r}{100}\implies \sqrt[8]{\cfrac{21}{16}}=\cfrac{100+r}{100} \\\\\\ 100\sqrt[8]{\cfrac{21}{16}}=100+r\implies 100\sqrt[8]{\cfrac{21}{16}}-100=r\implies \stackrel{\%}{3.46}\approx r\)

now, with an initial amount of $4800, up to 2007, namely 17 years later, how much will that be with a 3.46% rate?

\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &4800\\ r=rate\to 3.46\%\to \frac{3.46}{100}\dotfill &0.0346\\ t=years\dotfill &17\\ \end{cases} \\\\\\ A=4800(1 + 0.0346)^{17} \implies A=4800(1.0346)^{17}\implies A \approx 8558.02\)

Answer:

The answer to your problem is,

Arc de Triomphe:

Step-by-step explanation:

Depends which arc you are talking about I will do the:

Arc de Triomphe

Measurements

164 feet (50 metres)

high and 148 feet (45 metres) wide

It all depends on which arc

Thus the answer to your problem is,

Arc de Triomphe:

Uber is cheaper for the 10 mile ride and Lyft is cheaper for the 35 mile ride

Given:

Uber charges 0.90 per mile and a booking fee of $1.50

Lyft charges 0.87 per mile and a service fee of $2.45.

10m ride

For Uber:

price = 10(0.90) + 1.5 = 9 + 1.5 = $10.5

For Lyft:

price = 10(0.87) + 2.45 = 8.7 + 2.45 = $11.15

35m ride

For Uber:

price = 35(0.90) + 1.5 = 31.5 + 1.5 = $33

For Lyft:

price = 35(0.87) + 2.45 = 30.45 + 2.45 = $32.9

Therefore, for the 10 mile ride Uber is cheaper while for the 35 mile ride, Lyft is cheaper

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Step-by-step explanation:

US nickels are .077  inches thick per nickel

1250 ft = 1250  ft * 12 inches / ft = 15 000 inches

15000 inches /  ( .077 in / nickel ) =

        194 805  nickels  ( stacked on their flat sides) equals the Empire State building

Answer:

Step-by-step explanation:

The actual length of the explanation is 6 meters.

Answer:

2nd and 4th

Step-by-step explanation:

-2×2-4=0

4×2×2=16

They need to put 14.4 grams of onion powder in each bottle.

Given,

The quantity of onion powder in a seasoning blend = 4%

We have to find the quantity of pure onion powder should they include in a 72g bottle to make the final blend have 20% onion powder;

How much is a percentage?

A percentage is a certain number or part in every hundred. It is a fraction with the denominator 100, and the symbol for it is "%."

Here,

Let x be the seasoning blend.

Now, 4% of 72=20% of x

⇒ 0.04×72=0.2×x

⇒ 0.2x=2.88

⇒ x=2.88/0.2

⇒ x=14.4 g

Therefore, a container should contain 14.4 grams of onion powder.

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To calculate the earnings of a person based on sales and commission, we can multiply the sales amount by the commission rate.

Given:

Sales amount: $42,000

Commission rate: 2% (which can be written as 0.02)

Earnings = Sales amount * Commission rate

Earnings = $42,000 * 0.02

Earnings = $840

Therefore, the person would earn $840 in a week based on the given sales amount and commission rate.

The commission amount represents the additional income earned based on sales. However, to determine the total earnings for the week, we need to consider the base salary or any other fixed compensation the person receives. For the sake of this calculation, let's assume there is no base salary.

Thus, the person's total earnings for the week would be $840, which is solely from the commission on sales.

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Answer:

The answer is 8000

Step-by-step explanation:

In 8078 the place value of 8 is thousand and to round to the nearest thousand you must look for the the number with place value thousand and if the number to the right is 5 or more then you add 1 to the number with place value thousand then change the other number(s) to zero(s).

In this case the number to the right of 8 is 0 so you add nothing to 8 = 8000

I believe the balance would be $10,601.42

Hopefully that is the right answer

4.4 using the principle of substitution, we can conclude that \(\overline{A+B+C} = \bar{A}\bar{B}\bar{C}.\)

4.5 we have shown that A+\(\bar{A}\)B = A+B using the principle of duality

To prove that DeMorgan's theorem with two variables \(\overline{A+B} = \bar{A}\bar{B}\) can be applied to the three-variable case \(\overline{A+B+C} = \bar{A}\bar{B}\bar{C}\), we can use the principle of substitution.

Starting with the three-variable expression \(\overline{A+B+C}\), we can apply DeMorgan's theorem for two variables to the expression A+B+C:

\(\overline{A+B+C} = \overline{(A+B)+C}\)

Expanding the expression inside the complement:

\(\overline{(A+B)+C} = \overline{A+B} \cdot \overline{C}\)

Now, we can apply DeMorgan's theorem for two variables to \(\overline{A+B}\):

\(\overline{A+B} \cdot \overline{C} = \bar{A}\bar{B} \cdot \overline{C}\)

Finally, using the principle of substitution, we can conclude that \(\overline{A+B+C} = \bar{A}\bar{B}\bar{C}.\)

To prove the expression A+\(\bar{A}\)B = A+B using the principle of duality, we can start with the given expression and apply DeMorgan's theorem:

A+\(\bar{A}\)B

Using DeMorgan's theorem, we can write \(\bar{A}\)B as \(\overline{\bar{A} + B}\):

\(A+\bar{A}B = A + \overline{\bar{A} + B}\)

Now, we can simplify the expression using the principle of duality:

A + \(\overline{\bar{A} + B}\) = A + B

Therefore, we have shown that A+\(\bar{A}\)B = A+B using the principle of duality.

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Answer:

Step-by-step explanation:

1.5 (x+4)-3=4.5(x-2)=

1.5x+6-3=4.5x-9=

1.5x+3=4.5x-9=

1.5x-4.5x=-3-9=

-3x=-12

x=4

Answer:

x=4

Step-by-step explanation:

1.5(x+4)-3=4.5(x-2)

-Use distributiive prop. to simplify

1.5x+6-3=4.5x-9

-Simplify 6-3

1.5x+3=4.5x-9

-Subtract 1.5x from both sides

3=3x-9

-Isolate the x's by subtracting 9 from both sides

12=3x

-divide by 3

4=x

:) ur welcome

She have 1 hour 17 minutes remaining for the second section.

what is total time ?

Time can be defined as an ongoing and continuous sequence of events that occur in succession, from past through the present, and to the future. Time is used to quantify, measure, or compare the duration of events or the intervals between them, and even, sequence events.

Given:

Total time : two hours

Time taken to complete the first section =  forty-three minutes

Now , minutes she have remaining on the second section

= Total time - Time taken to complete the first section

= 2 hours - 43 minutes

= 1 hour 17 minutes

Hence , she have 1 hour 17 minutes remaining for the second section.

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Where the above is given, the required angle m∠BAC = 45°.

In triangle ABC. AC represents the foreman’s line of sight to the top of the landfill. Landfill height is BC

The triangle is geometric shape which includes 3 sides and sum of interior angle should not grater than 180°

According to conditions angle b = 90°

The sum of angles of a triangle= 180°

That is a + b + c = 180

Therefore, c = a

       a = (180 - b)/2

          = (180 - 90) / 2

          = 90 / 2

          = 45°

Hence, the required angle m∠BAC = 45°

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Full Question:

Although part of your question is missing, you might be referring to this full question:

Question 1 Create Triangle ABC by drawing AC. Segment AC represents the foreman’s line of sight to the top of the landfill. What is Angle m BAC?

Answer:

is this helpful or do i need to add more because this is all i could figure out :/

Step-by-step explanation:

one solution = -82 - 30=- 112

many solution = 6y - 12

no solution = -5n = 3 - 5n

infinite solution = -32 = 8 - 2

hope this helps

Answer:

To find the slope of the tangent line to the polar curve r = cos(θ/3) at the point specified by θ = π, we need to first find the derivative of r with respect to θ, and then evaluate it at θ = π.

We can use the chain rule to find the derivative of r with respect to θ:

dr/dθ = d/dθ(cos(θ/3)) = -(1/3)sin(θ/3)

Next, we can evaluate this expression at θ = π:

dr/dθ|θ=π = -(1/3)sin(π/3) = -(1/3)(sqrt(3)/2) = -sqrt(3)/6

This gives us the slope of the tangent line to the polar curve r = cos(θ/3) at the point where θ = π. Therefore, the slope of the tangent line is -sqrt(3)/6.

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Answer: Imma need a picture to find the volume love.

Step-by-step explanation:

Answer: Width = 4.7 meters, Length = 6.7 meters

Step-by-step explanation:

Let the width be \(w\). It follows that the length is \(w+2\).

\(w(w+2)=32\\\\w^2+ 2w-32=0\\\\w=\frac{-2 \pm \sqrt{2^2 -4(1)(-32)}}{2(1)}\\\\w \approx 4.7 \text{ } (w > 0)\\\\\implies w+2 \approx 6.7\)

Answer:

The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes. (In grammar school, you probably called the domain the replacement set and the range the solution set.

Answer:

B. -∞ \(\leq\) x \(\leq\) ∞

Step-by-step explanation:

The domain of a graph is all the x-values it covers. Since this graph does not have any arrows at its end or beginning points, we can assume it goes on forever. Lines that go on forever always have an infinite domain.

The rhetorical device that is used in the following passage from Thomas Paine's pamphlet "The Crisis, No.1"? Sec. 7 are anaphora and parallelism.

The passage from Thomas Paine's pamphlet "The Crisis, No.1"? states "The far and the near, the home counties and the back, the rich and the poor, will suffer or rejoice alike. The heart that feels not now, is dead: the blood of his children will curse his cowardice, who shrinks back at a time when a little might have saved the whole, and made them happy."

The rhetorical device used in this quote is anaphora, the repetition of the word "the." Additionally, the phrase "will suffer or rejoice alike" and the mention of "the heart that feels not now" are examples of parallelism, where the writer is emphasizing the idea of universality by presenting it in a balanced and repetitive manner.

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Answer:(3x) + 2(5x) + 4(3x) + (4)(2)area = 15x² + 10x + 12x + 8area

Step-by-step explanation:

Define the length and the width of the rectanglelength = 5x + 4width = 3x + 2

Determine the areaarea = length × widtharea = (5x + 4) (3x + 2)area = (5x)(3x) + 2(5x) + 4(3x) + (4)(2)area = 15x² + 10x + 12x + 8area = 15x² + 22x + 8

The area of the rectangle is (15x² + 22x + 8) units²

Let

x = Trey's savings

x + 27 = Tyler's savings

The sum of their savings is $85, which can be translated to

(x) + (x+27) = 85

Simplify the equation

x + x + 27 = 85

2x + 27 = 85

A man drinks 5/6 of a gallon on the second day.

Multiplication is an arithmetic operation that involves combining two or more numbers to find their product. It is the process of repeated addition or counting in equal groups.

The man starts with 2 gallons of water. On the first day, he drinks 3/4 of a gallon, leaving him with:

2 - 3/4 = 1 1/4 gallons

On the second day, he drinks 2/3 of what he had left from the first day, which is 1 1/4 gallons. To find out how much he drinks, we can multiply 1 1/4 by 2/3:

1 1/4 * 2/3 = (5/4) * (2/3) = 10/12 = 5/6

Therefore, he drinks 5/6 of a gallon on the second day.

To summarize:

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Answer:

Step-by-step explanation:

Surface area of the triangular prism = 2B + ph

B is the base area = 11 * 14

B =  154 sq. cm

p is the perimeter of the base =

According to 10th Amendment it defines the Federal Government only has those powers delegated in the Constitution .

No law establishing a particular religion, forbidding its practice, restricting press or speech freedom, or restricting the right of the people to peacefully assemble and petition the government for redress of grievances may be passed by Congress.

An amendment is a change or improvement that essentially maintains the integrity of the original document. The Bill of Rights is the collective name for the first ten Amendments of the Constitution. It describes Americans' constitutional rights in relation to their government. People are granted civil liberties and rights, such as the freedom of speech, the press, and religion.

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