The equation of a given circle in. general form is x^2+y^2+12y+27=0. Write the equation in standard form, (x-h)^2+(y-k)^2=r^2, by completing the squares in the equation. Show your work in the table.

Answer:

Percent error for the length of the soccer field is 1.4 %

Step-by-step explanation:

The actual length of the soccer field  = 500 ft

The measured length of he field = 493 ft

ERROR in the measurement = ACTUAL LENGTH - MEASURED LENGTH

                                                =  500 ft - 493 ft = 7 ft

So, there is an error of 7 ft in measuring the length of the field.

[tex]\textrm{ERROR PERCENTAGE} = \frac{\textrm{Error}}{\textrm{Actual Measuement}} \times 100\\= \frac{7}{500} \times 100 = 1.4[/tex]

Hence, percent error for the length of the soccer field is 1.4 %

The percent error for the length of the soccer field is 1.4%.

We are asked to find the percent error for the length of a soccer field when the actual length is 500 feet, but a broken measuring instrument shows it to be 493 feet.

Calculating percent error:

Find the absolute difference: |493 - 500| = 7 feet.

Calculate percent error: (7/500) x 100%

Percent error = 1.4%.

The solution is [tex]x = 2 \text{ and } y = \frac{1}{2}[/tex]

Solution:

Let us assume,

[tex]a = \frac{1}{x}\\\\b = \frac{1}{y}[/tex]

Given system of equations are:

[tex]\frac{2}{x} - \frac{3}{y} = -5[/tex]

[tex]\frac{4}{x} + \frac{6}{y} = 14[/tex]

Rewrite the equation using "a" and "b"

2a - 3b = -5 ------------ eqn 1

4a + 6b = 14 -------------- eqn 2

Let us solve eqn 1 and eqn 2

Multiply eqn 1 by 2

2(2a - 3b = -5)

4a - 6b = -10 ------------- eqn 3

Add eqn 2 and eqn 3

4a + 6b = 14

4a - 6b = -10

( - ) --------------------

8a = 4

[tex]a = \frac{4}{8}\\\\a = \frac{1}{2}[/tex]

Substitute a = 1/2 in eqn 1

[tex]2(\frac{1}{2}) -3b = -5\\\\1 - 3b = -5\\\\3b = 6\\\\b = 2[/tex]

Now let us go back to our assumed values

Substitute a = 1/2 in assumed values

[tex]a = \frac{1}{x}\\\\\frac{1}{2} = \frac{1}{x}\\\\x = 2[/tex]

Substitute b = 2 in assumed value

[tex]b = \frac{1}{y}\\\\2 = \frac{1}{y}\\\\y = \frac{1}{2}[/tex]

Thus the solution is [tex]x = 2 \text{ and } y = \frac{1}{2}[/tex]

Answer:

No, lisa will not be able to feed both the tanks same amount of food.

Step-by-step explanation:

No, lisa will never be able to feed both tanks the same amount of food.Let tank A contains x number of fish then according to the information given Tank B contains 2/3x number of fishLisa feds 1 gm of food in tank A that means  Lisa feds 2 gm of food in tank B that means we have to tell whether lisa will ever feed both tanks the same amount it will be possible if   which is not possibleTherefore, lisa will not be able to feed both the tanks same amount of food.

Answer:

If the painter will paint for $25 per hour, then the amount of dollars for h number of hours is $25h , if the cost of paint is $15 per can, 10 cans will be $150. The cost C of painting the house is

C= 25h +150

The amount of hours the painter paints is make h the subject of the formula

h= (C - 150)/25

The equation to find the cost of painting the house in terms of the hours worked by the painter is C = 25h + 150

The equation that can be used to find the cost of painting the house in terms of the amount of hours the painter paints is C = 25h + 150. This equation represents the cost of the labor ($25 per hour) plus the cost of the paint (10 cans at $15 per can, which equals $150). The variable h represents the number of hours the painter works.

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STEPS:

1. Start my distributing the 8 through the parentheses on the left side of the equation. 8 times 2x is 16x and 8 times 9 is 72. So we have 16x + 72 = 56.

2. Next, isolate the x-term by adding 72 to both sides of the equation

and we get 16x = -16.

3. Divide both sides by 16 and x = -1.

Answer:

Step-by-step explanation:

The inequality [tex]2y \leq 6[/tex] means [tex]y \leq 3[/tex].

y = 0, satisfies the above inequality, so the arrows will be towards the x axis.

Now, we need to draw 5x < 8 + 4y.

First, lets draw the equation of 5x = 8 + 4y.

y = 1 gives x = 2.4 & y = 0 gives x = 1.6.

Hence, the above equation passes through (2.4, 1) and (1.6, 0).

The point (0, 0) satisfies the inequality 5x < 8 + 4y. Hence, the arrows will be towards the origin.

The solution will be the area of APQ except any point on PQ, as PQ is nothing but the line 5x = 8 + 4y.

Answer:

V=πr2h

Step-by-step explanation:

Answer:

V=πr2h

That's the formula for the volume of a cylinder

Step-by-step explanation:

we have given that Kayla is 4 years younger than her sister .

this the age of Kayla would be 4 less than x,

So the algebraic expressions is :

Answer:

19 meters

Step-by-step explanation:

When Arman finished, Babken is 10 meters behind. So, Babken has 10 meters left.

Ex: Babken has 10 meters left, Cecilia is 9 meters behind.

So, the answer is 10+9=19.

19 meters.

Cecilia's position is  19 m behind when Arman is at the finish line.

Arman, Babken, and Cecilia 3 decided to compete in a 100m run.

Distance is defined as the difference in position.

Here,

Cecilia covers 90% of Babken's covered distance. Babken Covered 90% of Arman distance. So distance covered by Cecilia is.
= 90/100 * 90/100 x 100
= 81m

Now, distance between Cecilia and Arman when he crossed the finish line,
= 100m-81m

=19m

Thus, Cecilia's position is  19 m behind when Arman is at the finish line.

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Answer:

[tex]x=70^o[/tex]

[tex]y=110^o[/tex]

Step-by-step explanation:

we know that

In a parallelogram, opposite angles are congruent and consecutive angles are supplementary

In this problem the quadrilateral ABCD is a parallelogram

so

[tex]x=70^o[/tex] -----> by opposite angles in a parallelogram

[tex]x+y=180^o[/tex] ---> by consecutive angles in a parallelogram

substitute the value of x

[tex]70^o+y=180^o[/tex]

[tex]y=180^o-70^o=110^o[/tex]

Answer:

d. 24/7 i belive

Step-by-step explanation:

Final answer:

To find the value of tanC in the triangle, calculate the angles A, B, and C using the cosine rule and understanding the relationship between these angles.

Explanation:

The value of tanC in the triangle can be calculated using the given information.

Answer:

(2, -1)

Step-by-step explanation:

When line 1 intercepts with line 2, they meet at (2, -1). Therefore that's the solution.

Answer:

What is the question that you are asking?

Step-by-step explanation:

Answer:

I believe the answer to this question is: 3/2 simplified to 1  1/2.

The given shapes area is found to be 132 square feet.

Step-by-step explanation:

Step 1; To determine the area of an indefinite shape we must divide it into the shapes that we know. The shape that is given can be split into a rectangle with a triangle on top of it.

Step 2; To determine the area occupied by a different shape, we must sum the areas of the triangle and the rectangle. The given rectangle measures a length of 11 feet and a width of 9 feet. The area of any given rectangle is the multiplication of its length and width. Area of Rectangle = Length * Width = 11 feet * 9 feet = 99 square feet.

Any given triangles area is half the multiplication of its base value and its height value. In the given diagram, the base of the triangle measures a length of 11 feet (same as the rectangle's length) and the length from base to top is 6 feet (Entire shape's height which is 15 feet - the calculated value of the rectangle's width which is 9).

Area of Triangle = [tex]\frac{1}{2}[/tex]* base * height = [tex]\frac{1}{2}[/tex] * 11 feet * 6 feet = 33 square feet.

Step 3; To find the total area of the shape we must add the areas of the rectangle and the triangle.

Area of given shape = Area of rectangle + Area of Triangle

Area of given shape = 99 square feet + 33 square feet = 132 square feet.

Answer:

12x^2 - 164x + 504

Step-by-step explanation:

(3x-14)(4(x-9)) equals this, as I used an algebra calculator.

Answer:

3$

Step-by-step explanation:

12÷4=3

each muffin cost 3$

Answer:

[tex]y =-\frac{1}{3}-2[/tex]

Step-by-step explanation:

We are given;

We are required to determine the equation a line passing through a point (6, -4) and perpendicular to the given line;

y = 3x -3

But; m₁ × m₂ = -1 (For perpendicular lines)

Therefore;

m₂ = -1 ÷ 3

    = -1/3

Therefore, the slope of the line in question is -1/3 and the line passes through (6, -4).

To get its equation, we get another point (x, y)

Then;

[tex]\frac{y+4}{x-6}=\frac{-1}{3}[/tex]

Thus;

[tex]3(y+4) = -1(x-6)\\3y + 12 = -x+6[/tex]

In the form of slope-intercept, the equation will be;

[tex]3y = -x - 6\\y =-\frac{1}{3}-2[/tex]

Thus, the equation of the line is;

[tex]y =-\frac{1}{3}-2[/tex]

Answer: [tex]-i\sqrt{10}[/tex]

Step-by-step explanation:

Assuming that you need to simplify the expression, below is the explanation to do it.

Given the following expression:

[tex]-\frac{1}{3}\sqrt{-90}[/tex]

You need to decompose the radicand (The number inside the square root) into its prime factors:

[tex]90=2*3*3*5=2*3^2*5[/tex]

Knowing that, you can rewrite the expression in this form:

[tex]=-\frac{(1)(\sqrt{-2*3^2*5})}{3}=-\frac{\sqrt{-2*3^2*5}}{3}[/tex]

Since [tex]\sqrt{-1}=i[/tex], you must substitute it into the expression:

[tex]=-\frac{i\sqrt{2*3^2*5}}{3}[/tex]

Now you need to remember the following property:

[tex]\sqrt[n]{a^n}=a^{\frac{n}{n}}=a[/tex]

Then, applying that property, you get:i:

[tex]=-\frac{3i\sqrt{2*5}}{3}=-\frac{3i\sqrt{10}}{3}[/tex]

Finally, you must divide the numerator and the denominator by 3. So, you get:

[tex]=-\frac{i\sqrt{10}}{1}=-i\sqrt{10}[/tex]

Answer:

.018, 1.8, 18, 18

Step-by-step explanation:

ascending means going from smallest to largest, so you order the numbers from smallest to largest

Answer:

018, 1.8, 18, 18

Step-by-step explanation:

Answer:

Step-by-step explanation:

6 in to 13 ft = 9 in to x ft

6 / 13 = 9 / x.....cross multiply because this is a proportion

(6)(x) = (13)(9)

6x = 117

x = 117/6

x = 19.5 (or 19 1/2) ft <====

Answer: 241 days a year

Step-by-step explanation: 365*0.66=240.9 and then you round up to 241

The total number of days in a year the sun shines in Tampa will be equal to 241 days.

The Latin term "per centum," which signifies "by the hundredth," was the source of the English word "percentage." Segments with a denominator of 100 are considered percentages. In other terms, it is a relationship where the worth of the entire is always considered to be 100.

As per the instructions given in the question,

The total number of days in a year is 365 days.

Then, 66% of the total number of days in a year will be,

365 × 66/100 = 240.9 or,

The number of days of sunshine will be 241 days after rounding up the value.

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Answer:

13/20

Step-by-step explanation:

65%=65/100

65/100=13/20

Answer:

-2

Step-by-step explanation:

Answer:

-2 is 100% correct !

Step-by-step explanation:

Answer:

The two numbers are 25 and 15.

Step-by-step explanation:

Let's find out the two numbers, this way:

x = first number

y = second number

This is the equations system:

x + y = 40

x - y = 10

Solving for x in the first equation:

x + y = 40

x = 40 - y

Solving for y in the second equation:

40 - y - y = 10

40 - 2y = 10

-2y = 10 - 40

-2y = - 30

y = -30/-2 = 15

Solving for x:

x + y = 40

x + 15 = 40

x = 40 - 15

x = 25

The two numbers are 25 and 15.

The rate of change is 0.5 which means that each game cost .50 cents

The initial value is 2 which means that you must initially pay $2.00

The rate of change of the function C = 0.5g + 2 is 0.5, indicating a cost increase of $0.50 per game. The initial value is 2, representing the fixed entry fee at the arcade.

The rate of change of the function C = 0.5g + 2, which represents the cost, C, in dollars, of playing g games at an arcade game center, is the coefficient of g, whic h is 0.5. Thisvalue means that for each additional game played, the cost increases by $0.50. The initial value of the function is the constant term, which is 2. This represents the starting fee or fixed cost at the arcade game center before any games are played.

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Answer:

Option C

Step-by-step explanation:

we know that

If two angles are complementary, then their sum is equal to 90 degrees

In this problem we have

Option C

One angle measure 35 degrees and the other angle measure 55 degrees (90-35=55)

so

[tex]35^o+55^o=90^o[/tex]

therefore

The pair of angles are complementary

Answer:

C.)

Step-by-step explanation:

Final answer:

The decimal 0.15151515151 can be written as the simplified fraction 5/33.

Explanation:

To express the decimal number 0.15151515151 as a fraction, we can observe the repeating pattern. The 15 sequence repeats indefinitely, so we can represent it as 15/99. Finally, we simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which in this case is 3. Therefore, the decimal 0.15151515151 can be written as the simplified fraction 5/33.

Recognizing the recurring pattern in the decimal as 0.15(15), we express it as a fraction, obtaining 15/99. Simplifying the fraction by dividing both numerator and denominator by their greatest common divisor, which is 3, yields the final result: 5/33. This process highlights the conversion of repeating decimals to fractions.

The factored form of given expression is:

[tex]40x + 24y - 56 = 8(5x + 3y-7)[/tex]

Solution:

Given that we have to factor the given expression

Given expression is:

40x + 24y - 56

We can factor the expression by taking the greatest common factor out

When we find all the factors of two or more numbers, and some factors are the same , then the largest of those common factors is the Greatest Common Factor.

Find G.C.F of 40, 24 and 56

The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24

The factors of 40 are: 1, 2, 4, 5, 8, 10, 20, 40

The factors of 56 are: 1, 2, 4, 7, 8, 14, 28, 56

Then the greatest common factor is 8

Thus factor out 8 from given expression

[tex]40x + 24y - 56 = 8(5x + 3y-7)[/tex]

Thus the given expression is factored