Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

Answer: for d the answer is yes

Step-by-step explanation:

a line is in the form of y=mx+c or y=mx+b, as p(x)=3x+5 then the equation passes by being compatible with the general equation of a line

Step-by-step explanation:

1d.

yes.

f(x) = 2x + 3

g(x) = x + 2

p(x) = f(x) + g(x) = (2x + 3) + (x + 2) = 3x + 5

p(x) is still a linear function (highest exponent of x is 1). therefore it is a line.

Answer:

it would be at point (6,3)

Step-by-step explanation:

If you were to reflect it over the x-axis you would get (-6,3)

The focus so far has been on similar triangles, but there are also theorems that deal with similar polygon

Theorems of similar triangles are important properties that hold true for any pair of similar triangles. Some of the most commonly used theorems are:

AA Similarity Theorem: If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

SSS Similarity Theorem: If the three sides of one triangle are proportional to the three corresponding sides of another triangle, then the triangles are similar.

SAS Similarity Theorem: If two sides of one triangle are proportional to two sides of another triangle and the included angles are congruent, then the triangles are similar.

These theorems are also applicable to similar polygons

Read more about similar triangles at

https://brainly.com/question/14285697

#SPJ1

The focus so far has been on similar triangles, but there are also theorems that deal with similar polygons.

The inflation rate for Ken's gas expenses between the two years is approximately 42.26%.

To calculate the inflation rate for Ken's gas expenses, we can use the following formula: (Current Year Expense - Previous Year Expense) / Previous Year Expense × 100%.

In this case, the previous year's gas expense was $1,098 and the current year's expense is $1,562.

To find the difference in expenses, subtract the previous year's expense from the current year's expense: $1,562 - $1,098 = $464.

Now, divide this difference by the previous year's expense: $464 / $1,098 ≈ 0.4226.

Finally, multiply the result by 100% to get the inflation rate: 0.4226 × 100% ≈ 42.26%.

You can learn more about the inflation rate at: brainly.com/question/31635911

#SPJ11

Here is the probability distribution table:

|Outcome|Probability|
|-------|-----------|
|$0     |1/10       |
|S100   |4/10       |
|$200   |3/10       |
|$500   |2/10       |

To create the table, you simply list each possible outcome (in this case, the different amounts that could be won on the spinner), and then calculate the probability of each outcome occurring. In this case, there are 10 sectors in total, so the probability of landing on each sector is 1/10. There is 1 sector that says "$0," so the probability of getting that outcome is 1/10.

There are 4 sectors that say "S100," so the probability of getting that outcome is 4/10, or 2/5. Similarly, there are 3 sectors that say "$200," so the probability of getting that outcome is 3/10, or 3/10.

And finally, there are 2 sectors that say "$500," so the probability of getting that outcome is 2/10, or 1/5.

To know more about probability distribution table, refer to the link below:

https://brainly.com/question/12385304#

#SPJ11

The value of the side lengths b and h in the right-angle triangle is [tex]3\sqrt{2} , and[/tex] 8.

Trigonometric ratios are the ratios of a right triangle's sides. The sine (sin), cosine (cos), and tangent are three often used trigonometric ratios. (tan).

The given figure is a right-angle triangle.

To find the value of b and h we need to apply the trigonometric ratio.

In the first triangle,

[tex]cos45 = \frac{adjacent}{hypotenuse}[/tex]

[tex]cos45 = \frac{b}{6}[/tex]

[tex]\frac{1}{\sqrt{2} } = \frac{b}{6}[/tex]

[tex]b = \frac{1}{\sqrt{2} } * 6[/tex]

[tex]b = 3\sqrt{2}[/tex]

In the second triangle

[tex]cos60 = \frac{adjacent}{hypotenuse} \\cos60 = \frac{4}{h} \\\frac{1}{2} = \frac{4}{h} \\h= 2 *4\\h = 8[/tex]

Therefore the value of the b and h is [tex]3\sqrt{2}[/tex] , and 8 respectively.

Learn more about trigonometric ratios here:

https://brainly.com/question/25122825

#SPJ1

Answer:

d=1

Step-by-step explanation:

(i have to write this cuz i cant write less than 20 words)

Answer:

60 square inches

Step-by-step explanation:

Pt refers to Pythagoras Theorem. You know two sides of a right angled triangle, how do you find the 3rd side? Pythagoras Theorem. Then the rest is easy. Just do the area of all of the 4 triangles and the area of the square and add them up

The variance of the actuary's wait time is 36 / 121.

From the information, at the airport, there are three counters for checking the luggage. the employees at each counter work independently with the time for each customer modeled as an exponential distribution. the average time is one minute for one counter, two for the next, and three minutes for the third. an actuary, who is next in line, will take the next available counter,

From the complete question, the variance of the actuary's wait time will be:

= 1 / (11/6)²

= (6/11)²

= 36 / 121

Learn more about variance on

https://brainly.com/question/9304306

#SPJ1

Answer:

89

Step-by-step explanation:

construct the formula to obtain the total of marks in first 9 tests:

79 = x/9

79 * 9 = 711

x = 711

so to get 80% in the next test we construct this formula:

80 = 711 + y / 9 + 1

the value we get for y is 89

to confirm the answer, 711+89/10 gives us 80, which is the correct value we want

To show that Maria's claim is incorrect, we need to find a fraction that is located between 1/5 and 1/7 on a number line but does not have a denominator of 6.

One way to do this is to find the least common multiple (LCM) of 5 and 7, which is 35, and then find a fraction with a denominator of 35 that falls between 1/5 and 1/7.

To do this, we can find the equivalent fractions of 1/5 and 1/7 with a denominator of 35:

1/5 = 7/35

1/7 = 5/35

Now we need to find a fraction between 7/35 and 5/35. One such fraction is:

6/35

This fraction is located between 7/35 and 5/35 on the number line, but its denominator is 35, not 6. Therefore, Maria's claim is incorrect.

Another way to show that Maria's claim is incorrect is to find a counterexample by simply listing all the fractions between 1/5 and 1/7 and showing that not all of them have a denominator of 6. For example:

1/6, 1/7, 1/8, 1/9, 1/10, ..., 1/34, 1/35

As we can see, not all of these fractions have a denominator of 6, so Maria's claim is incorrect.

Answer:

13/70

Step-by-step explanation:

In order to  show that Maria's claim is incorrect, we need to find a fraction that is located between 1/5 and 1/7 on a number line,  but does not have a denominator of 6.

Let's  find the  common multiple (CM) of 5 and 7, which is 70, or 35. But this case try 70  and then find a fraction with a denominator of 70 that falls between 1/5 and 1/7.

equivalent fractions of 1/5 and 1/7 with a denominator of 70
1/7 < x < 1/5 , will be equivalent to 1/7 ( 10/10 ) < x < 1/5 ( (14/14)
10/70 < x < 14/70..
x is the fraction   between 10/70  and 14 /70.  Unknown  fraction is:

13/70

This fraction is located between 10/70  and 14/70  on the number line, but its denominator is 70 , not 6. Therefore, Maria's claim is incorrect.

Using substitution method, the cost of a chicken is $44.56 and the cost of a rabbit is $36.78.

Let's use the substitution method to solve the problem.

Let's assume that the cost of a chicken is "x" dollars and the cost of a rabbit is "y" dollars.

From the first statement, we know that:

5x + 8y = 517 --- equation (1)

And from the second statement, we know that:

8x + 11y = 761 --- equation (2)

Now we can solve for one of the variables in terms of the other from one of the equations, and then substitute that expression into the other equation to solve for the remaining variable.

Solving equation (1) for "y", we get:

y = (517 - 5x) / 8

Now we can substitute this expression for "y" into equation (2), and solve for "x":

8x + 11[(517 - 5x) / 8] = 761

Multiplying both sides by 8 to eliminate the fraction, we get:

64x + 11(517 - 5x) = 6088

Expanding the brackets, we get:

64x + 5687 - 55x = 6088

Combining like terms, we get:

9x = 401

Dividing both sides by 9, we get:

x = 44.56

So the cost of a chicken is $44.56.

Now we can substitute this value for "x" into equation (1) to solve for "y":

5(44.56) + 8y = 517

Simplifying, we get:

222.80 + 8y = 517

Subtracting 222.80 from both sides, we get:

8y = 294.20

Dividing both sides by 8, we get:

y = 36.78

So the cost of a rabbit is $36.78.

Therefore, the cost of a chicken is $44.56 and the cost of a rabbit is $36.78.

To learn more about substitution method here:

https://brainly.com/question/14619835

#SPJ4

Answer:

x=6

Step-by-step explanation:

5x+150=180

-150 -150 (subtract 150 from both sides)

5x=30

x=6

Answer:

x = 6

Step-by-step explanation:

Supplementary angles add up to 180 degrees, and lines A and B are parallel, so:

180 - 150 = 30

30/5 = x

6 = x

The volume of the pyramid is approximately 41.67 cubic meters.

To find the volume of the pyramid, we can use the formula:

V = (1/3) x base area x height

Since the base of the pyramid is a square with side length 5 meters, its area is:

base area = side² = 5² = 25 square meters

The height of the pyramid is also given as 5 meters.

Now, we need to find the area of one of the square cross-sections. Since the pyramid has congruent triangular sides, we know that each of these triangles is similar to the original base square.

Therefore, the side length of each square cross-section is proportional to the height of the pyramid, and we can use the ratio of corresponding side lengths to find the area of one of the squares:

5 / 5 = x / 5

where x is the side length of the square cross-section.

Solving for x, we get:

x = 5

Therefore, each of the square cross-sections has an area of 5 x 5 = 25 square meters.

Now, we can substitute the values we have found into the formula for the volume:

V = (1/3) x base area x height

= (1/3) x 25 x 5

= 41.67 cubic meters

Therefore, the volume of the pyramid is approximately 41.67 cubic meters.

Learn more about Pyramid

brainly.com/question/17615619

#SPJ11

The statements that  gives the best reasons that ben’s rent payment is an essential (fixed) expense is he agreed to pay the same amount every month. The correct answer is D.

In personal finance, an essential expense is a regular expenditure that is necessary for maintaining a basic standard of living. These expenses are typically fixed, meaning that they do not fluctuate from month to month, and are difficult or impossible to eliminate without sacrificing basic needs like food, housing, or healthcare.

Since, this is his rent, the amount of money that he is legally bound to pay every month in order to keep on living in that location.

He has an agreement with his landlord to pay $215 each month and thus he has to do it.

Essential expenses are often considered a top priority in budgeting because they are critical to maintaining health, safety, and overall well-being. In the given scenario, Ben's rent payment is an essential expense because it is a fixed expense that is necessary for maintaining his housing, which is a basic need. The correct answer is D.

Learn more about essential expense at https://brainly.com/question/30804860

#SPJ11

To solve for the surface area of a rectangular prism, you'll need to find the area of each of its six faces and add them together.

A rectangular prism has three pairs of faces: two each for length (L), width (W), and height (H).

First, find the area of the two faces with dimensions L x W. The area is calculated by multiplying length by width: A₁ = L * W. Since there are two such faces, the total area for these is 2A₁ = 2(L * W).

Next, find the area of the two faces with dimensions L x H. The area is calculated by multiplying length by height: A₂ = L * H. The total area for these faces is 2A₂ = 2(L * H).

Finally, find the area of the two faces with dimensions W x H. The area is calculated by multiplying width by height: A₃ = W * H. The total area for these faces is 2A₃ = 2(W * H).

To find the total surface area of the rectangular prism, add the areas of all six faces together: Surface Area = 2A₁ + 2A₂ + 2A₃ = 2(L * W) + 2(L * H) + 2(W * H).

So, the formula for the surface area of a rectangular prism is Surface Area = 2(L * W + L * H + W * H).

Learn more about surface area here: https://brainly.com/question/27704128

#SPJ11

The shape of the distribution  in histogram is skewed left and mean=43.071429 and standard deviation= 15.886445 are used together to measure the center and spread of the data.

What is histogram?

A grouped frequency distribution with continuous classes is graphically represented by a histogram. It is an area diagram, and its size is proportional to the frequencies in the associated classes. Due to the base's coverage of the spaces between class boundaries, all of the rectangles in such representations are contiguous.

We can make a sideways histogram. (makes it easier if typing text, but if you are writing on paper then you don't have to make it sideways) Each row will represent a range of 10 (1st row is 10 to 19, 2nd row is 20 to 29, etc)

=> 13 23 28 33 34 38 44 45 49 50 55 59 65 67

The data looks like it is slightly skewed left (hump towards the right [down]). The mean and the standard deviation are used together to measure the center and spread of the data.

Mean = [tex]\frac{ 13+23+28+33+34+38+44+45+49+50+55+59+65+67}{14}=\frac{603}{14}[/tex] = 43.071429

Standard deviation = 15.886445

Hence the shape of the distribution  in histogram is skewed left and mean=43.071429 and standard deviation= 15.886445 are used together to measure the center and spread of the data.

To learn more about histogram refer the below link

https://brainly.com/question/2962546

#SPJ4

The component form of u + v can be found using the given lengths and angles and it  is (6, √3).

To find the component form of u + v given the lengths of u and v and the angles that u and v make with the positive x-axis we will sum the u and v.

Given Ilull = 5 and Ou = 0°, we can represent vector u as (5, 0) in component form. Given |Iv|I = 2 and Ov = 60°, we can represent vector v as (2cos60°, 2sin60°) = (1, √3) in component form.

To find u + v, we add the corresponding components of u and v. This gives us:

u + v = (5, 0) + (1, √3) = (5+1, 0+√3) = (6, √3)

Therefore, the component form of u + v is (6, √3).

For more questions like Vector click the link below:

https://brainly.com/question/29740341

#SPJ11

Measures of center are statistical tools used to determine the central tendency of a dataset, including mean, median, and mode.

The difference between these tools is how they capture the central tendency.

Variability of grades refers to how much grades fluctuate from week to week, which can be measured using statistical tools such as range, variance, and standard deviation. Without specific information about the test, it is not possible to draw conclusions.

However, analyzing the measures of center and variability can provide insights into student performance and grading consistency.

Further analysis, such as comparing grades to class averages or identifying patterns over time, may reveal additional information.

To learn more about central tendency https://brainly.com/question/30218735

#SPJ4

10mL of the baraclude oral solution to the patient.

To determine the amount of the oral solution of baraclude (entecavir) to administer, we need to use the following formula:

Amount to administer (mL) = Desired dose (mg) / Strength (mg/mL)

In this case, the desired dose is 0.5mg and the strength is 0.05mg/mL. Plugging in these values, we get:

Amount to administer (mL) = 0.5mg / 0.05mg/mL = 10mL

Therefore, you will administer 10mL of the baraclude oral solution to the patient.
Hi! To calculate the number of mL to administer, you need to consider the prescribed dose and the strength of the oral solution. The order is for Baraclude (entecavir) 0.5mg PO daily, and the solution's strength is 0.05 mg/mL.

To find the required mL, divide the prescribed dose by the solution's strength:

0.5 mg (prescribed dose) ÷ 0.05 mg/mL (solution's strength) = 10 mL

You will administer 10 mL of Baraclude (entecavir) oral solution daily.

To know more about required mL click here:

brainly.com/question/14143257

#SPJ11

The mZDPC is approximately 15 degrees.

We know that the length of an arc of a circle is given by the formula:

length of arc = (central angle / 360°) × 2πr

where r is the radius of the circle.

In this case, the length of arc DC is 9.77 inches and the radius of the circle is 8 inches. Let's use the above formula to find the central angle mZDPC:

9.77 = (mZDPC / 360°) × 2π(8)

Simplifying this equation, we get:

mZDPC = (9.77 / (2π(8) / 360°))

mZDPC = (9.77 / 0.670206) degrees

mZDPC ≈ 14.58 degrees

Rounding to the nearest degree, we get:

mZDPC ≈ 15 degrees

Learn more about Length of arc

brainly.com/question/16403495

#SPJ11

The linearization of the function f(x, y) = e-¹⁰x-⁸y - 8y at (0, 0) is L(x, y) = -10x - 8y + 1. The correct option is C.

To find the linearization of the given function at the point (0, 0), we need to compute the partial derivatives with respect to x and y and then evaluate them at the given point.

The function is f(x, y) = [tex]e^{(-10x-8y)[/tex] - 8y.

First, find the partial derivative with respect to x:
∂f/∂x = [tex]-10e^{(-10x-8y).[/tex]

Now, evaluate ∂f/∂x at (0, 0):
∂f/∂x(0, 0) = [tex]-10e^{(0)[/tex] = -10.

Next, find the partial derivative with respect to y:
∂f/∂y = [tex]-8e^{(-10x-8y)[/tex] - 8.

Now, evaluate ∂f/∂y at (0, 0):
∂f/∂y(0, 0) = [tex]-8e^{(0)[/tex] - 8 = -8 - 8 = -16.

Now, we can form the linearization:
L(x, y) = f(0, 0) + ∂f/∂x(0, 0)(x - 0) + ∂f/∂y(0, 0)(y - 0).

Evaluate f(0, 0):
f(0, 0) = [tex]e^{(-10(0)-8(0))} - 8(0) = e^{(0)} - 0 = 1.[/tex]

Finally, substitute the values into the linearization formula:
L(x, y) = 1 - 10x - 16y.

Comparing to the given options, the answer is:
C) L(x, y) = -10x - 8y + 1

For more such questions on Linearization.

https://brainly.com/question/31403141#

#SPJ11

La fuerza resultante sobre q3 debe calcularse considerando la interacción de las cargas q1, q2 y q3.

Para determinar la fuerza resultante sobre q3, debemos calcular la magnitud y la dirección de las fuerzas ejercidas por q1 y q2 sobre q3.

Usando la Ley de Coulomb, podemos calcular la fuerza entre dos cargas puntuales utilizando la fórmula: F = k * (|q1| * |q2|) / r^2, donde k es la constante de Coulomb, |q1| y |q2| son los valores absolutos de las cargas, y r es la distancia entre las cargas.

Dado que las cargas q1 y q3 son iguales, y q2 tiene una carga negativa, las fuerzas ejercidas por q1 y q2 en q3 tendrán direcciones opuestas. Debido a la simetría del triángulo rectángulo, las fuerzas tendrán componentes horizontales y verticales iguales en magnitud.

La magnitud de la fuerza resultante sobre q3 se calcula sumando las magnitudes de las fuerzas ejercidas por q1 y q2. La dirección de la fuerza resultante será la misma que la de las fuerzas individuales ejercidas por q1 y q2.

Por lo tanto, para calcular la fuerza resultante sobre q3, debemos encontrar la magnitud de la fuerza ejercida por q1 y la magnitud de la fuerza ejercida por q2, y luego sumarlas. La dirección será la misma que las fuerzas individuales.

Learn more about determinar

brainly.com/question/30457159

#SPJ11

Answer:

11

Step-by-step explanation:

Because of the parallel lines 5x=6x-11, so x=11.

Step-by-step explanation:

this is the answer being alternate exterior angles

Therefore, 32 1/2 can be written as a radical form of 32 + √2.

In mathematics, a fraction is a numerical quantity that represents a part of a whole or a ratio between two numbers. Fractions are written in the form of one integer, called the numerator, written above a line, and another integer, called the denominator, written below the line. The denominator represents the total number of equal parts into which a whole is divided, while the numerator represents the number of those parts being considered.

Here,

We can write 32 1/2 as a mixed number, which is equivalent to the fraction 65/2. To express 65/2 as a radical form, we can simplify the fraction by finding a perfect square that divides evenly into both the numerator and the denominator. In this case, 4 is a perfect square that divides into 64 (the nearest perfect square to 65) and 2, so we can write:

65/2 = (64 + 1)/2

= 64/2 + 1/2

= 32 + 1/2

Now, we can express the fraction 1/2 as a radical by taking the square root of the denominator, which gives:

32 1/2 = 32 + √2

To know more about fraction,

https://brainly.com/question/24638688

#SPJ1

The missing lengths of BE and IJ using the concept of similar quadrilaterals are:

BE = 32

IJ = 18

Similar quadrilaterals are defined as quadrilaterals that have the same shape, but their sizes may vary. Thus, if two quadrilaterals are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

From the image, we are told that Quadrilateral GHIJ is similar to Quadrilateral BCDE.

Thus:

GJ/BE = IJ/DE = HI/CD

Thus:

12/BE = 6/16

BE = (16 * 12)/6

BE = 32

Similarly:

IJ/48 = 6/16

IJ = (48 * 6)/16

IJ = 18

Read more about Similar Quadrilaterals at: https://brainly.com/question/16261621

#SPJ1

The resultant component of the vector addition is (-9, 0).

The resultant component of the vector is calculated as follows;

a = (-9, 6)

b = (3, 1)

The result of 1/3a = ¹/₃ (-9), ¹/₃(6) = (-3, 2)

The result of 2b = 2(3, 1) = (6, 2)

The result of the vector addition is calculated as follows;

1/3a - 2b

= (-3, 2) - (6, 2)

= (-3 -6, 2 -2)

= (-9, 0)

Learn more about vector addition here: https://brainly.com/question/30426215

#SPJ1

Using the Adjusted Balance Method:

Interest: $4.15

New Balance: $569.15

To calculate the interest and new balance using the Adjusted Balance Method, we need to first find the adjusted balance.

This method takes the previous balance, adds the purchases made before the payment, and then subtracts the payment.

Here's the calculation:

Calculate the adjusted balance:

Previous balance: $500

Purchases before May 20: $25 (May 12)

Subtotal: $525

Payment: $110

Adjusted balance: $525 - $110 = $415

Calculate the interest:

Interest rate: 1% per month

Interest: $415 * 1% = $4.15

Calculate the new balance:

Adjusted balance: $415

Purchases after May 20: $100 (May 22) + $50 (May 30) = $150

Interest: $4.15

New balance: $415 + $150 + $4.15 = $569.15

So, using the Adjusted Balance Method:

Interest: $4.15

New Balance: $569.15

Read more about adjusted balance here:

https://brainly.com/question/1808408

#SPJ1

Let's call the initial number of bacteria in the petri dish as $N_0 = 100$. After 12 hours, the number of bacteria triples, which means there are now $3N_0$ bacteria. After another 12 hours, the number of bacteria triples again, which means there are now $3(3N_0) = 9N_0$ bacteria.

We can see a pattern here that after every 12 hours, the number of bacteria is multiplied by 3. Let's calculate the number of bacteria after 1 hour:

$\sf\implies\:N_1 = N_0 \times 3^{1/12}$

After simplifying:

$\sf\implies\:N_1 = 100 \times 3^{1/12}$

Using a calculator, we can find that $\sf\:3^{1/12} \approx 1.1548$. Therefore:

$\sf\implies\:N_1 \approx{\boxed{115.48}}$

So the equivalent hourly rate at which the number of bacteria is increasing is approximately 15.48% per hour.

In general, if the number of bacteria triples every $t$ hours, the equivalent hourly rate can be calculated as:

$\sf\implies\:r = 3^{1/t} - 1$

where $r$ is the hourly rate expressed as a decimal.

[tex]\begin{align}\huge\colorbox{black}{\textcolor{yellow}{\boxed{\sf{I\: hope\: this\: helps !}}}}\end{align}[/tex]

[tex]\begin{align}\colorbox{black}{\textcolor{white}{\underline{\underline{\sf{Please\: mark\: as\: brillinest !}}}}}\end{align}[/tex]

[tex]\textcolor{lime}{\small\textit{If you have any further questions, feel free to ask!}}[/tex]

[tex]\huge{\bigstar{\underline{\boxed{\sf{\color{red}{Sumit\:Roy}}}}}}\\[/tex]