can someone help me? please​

The equation of a circle with a center at (4,−9) and a radius of 5 is

(x−4)^2+(y+9)^2=25. The correct Option C.

A circle is a set of all points which are equally spaced from a fixed point in a plane. The fixed point is called the center of the circle. The distance between the center and any point on the circumference is called the radius of the circle.

The equation of a circle with center (h, k) and radius r units is

(x−h)^2+(y−k)^2=r^2 .

where h = 4

k = -9

r = 5

The equation of the circle

(x−4)^2+(y−(-9))^2 = 5^2

The equation of the circle

(x−4)^2+(y+9)^2 = 25

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The perimeter of triangle ABC could be either approximately 27.98 cm or approximately 14.66 cm, depending on the length of AB.

What is the perimeter?

The perimeter is a mathematical term that refers to the total distance around the outside of a two-dimensional shape. It is the length of the boundary or the sum of the lengths of all the sides of a closed figure.

Let's call the length of AB x and the length of BC y.

First, we can use the fact that CD is the height of the triangle to find the area of triangle ABC:

Area of triangle ABC = 1/2 * CD * AB

Substituting the given values, we have:

1/2 * 12 * x = 6x

So the area of triangle ABC is 6x square centimeters.

We can also use the fact that angle BCD is 30 degrees to set up a trigonometric equation involving x and y:

tan(30) = x/y

Simplifying, we get:

y = x/tan(30) = x/(1/√(3)) = √(3) * x

Now we can use the formula for the area of a triangle in terms of its sides:

Area of triangle ABC = 1/2 * AB * BC * sin(B)

where B is the angle between sides AB and BC. In this case, we know that angle BCD is 30 degrees, so angle BCA is 60 degrees, and angle ABC is 90 degrees. Therefore, we have:

Area of triangle ABC = 1/2 * x * √3 * x * sin(60)

Simplifying, we get:

Area of triangle ABC = 1/4 * √3 * x²

Since we already found that the area of triangle ABC is 6x square centimeters, we can set these two expressions equal to each other and solve for x:

6x = 1/4 * √(3) * x²

Multiplying both sides by 4/√3, we get:

24/√(3) * x = x²

Simplifying, we get:

x² - 24/√(3) * x = 0

Using the quadratic formula, we get:

x = (24/√(3) ± √((24/√(3))² - 410)) / 2*1

Simplifying, we get:

x = 16√(3) / 3 or x = 8 √(3) / 3

Since we are looking for the perimeter of triangle ABC, we need to find y as well. Using the equation we derived earlier, we have:

y = √(3) * x

Therefore, we have two possible triangles:

Triangle ABC1: AB = 16 √(3) / 3, BC = 16, and AC = 8 √7 / 3

Triangle ABC2: AB = 8 √3 / 3, BC = 8, and AC = 4 √7 / 3

The perimeter of each triangle is the sum of its side lengths. Therefore:

Perimeter of triangle ABC1 = 16 √3/ 3 + 16 + 8 √7 / 3 ≈ 27.98 cm

Perimeter of triangle ABC2 = 8 √3 / 3 + 8 + 4 √7 / 3 ≈ 14.66 cm

hence, the perimeter of triangle ABC could be either approximately 27.98 cm or approximately 14.66 cm, depending on the length of AB.

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The required simplified value of the function is given as 4,

Given that,
Partial functions are given, and we have to determine the value of the function at x = 2.

Limit, which can be defined as every nearby value of a variable for a function that exists, is called limits

here,
The function given is  f(x) = 3 / x - 2 but this function is not defined for x = 2 but the value of the function at x = 2 is 4,

If we put  f(2) = 3 / 2 - 2 = infinity,

Thus, the required simplified value of the function is given as 4,

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Answer:

12

Step-by-step explanation:

48 divided by 4 is 12

Answer:

200 + 10 = 2010

Step-by-step explanation:

is wen i was born.

Answer:

x = 0.75

Step-by-step explanation:

first make the x term the subject

-7 = 12x - 16

-7 + 16 = 12x

add the like terms

9 = 12x

solve for x

9÷ 12 = 12x ÷ 12

0.75 = x

Answer:

hello your question is incomplete  below is the complete question

A company's human resources department was interested in the average number of years that a person works before retiring. The sample of size 11 follows: 12 16 18 19,21 21, 21,22 24 24 26What is the arithmetic mean, median and mode? what is the most likely shape of the distribution

answer :

i) mean = 20.36

ii) median = 21

iii) mode = 21

iv) The most likely shape is a Bell - shaped curve

Step-by-step explanation:

sample size = 11

values ( observations ) = 12, 16, 18, 19,21,21,21,22,24,24,26

i) mean

 = ∑ values / sample size = 224 / 11 = 20.36

ii) median

median is the value of the data located at the center of the string of data

to determine the middle position = ( n+1 / 2 )

where n = sample size

hence position of median value = 11 + 1 / 2 = 12 / 2 = 6

the value at the 6th position = 21 ( median )

iii) mode

mode = most repeated value in the series of data

hence mode value = 21

Answer:

B. 136

Step-by-step explanation:

∆ABC is similar to ∆EDC, therefore the ratio of their corresponding side lengths would be the same.

Thus:

AC/EC = AB/ED

(144 - x)/x = 51/3

(144 - x)/x = 17/1

Cross multiply

(144 - x)*1 = 17*x

144 - x = 17x

144 - x + x = 17x + x

144 = 18x

Divide both sides by 18

144/18 = 18x/18

8 = x

x = 8

✔️AC = 144 - x

Plug in the value of x

AC = 144 - 8

AC = 136

Answer: 340

Step-by-step explanation:

10 x 5 = 50

10 x 5 = 50

10 x 8 = 80

10 x 8 = 80

8 x 5 = 40

8 x 5 = 40

50 + 50 + 80 + 80 + 40 + 40

100 + 160 + 80

340

Answer:

2 m

Step-by-step explanation:

10*x=50

x=5

25*y=50

y=2

Answer:

the set of all real numbers -1≤y≤1

Step-by-step explanation:

according to the definition of 'sin'-function, the max value of it is '+1' and the min is '-1'. Finally, the correct answer is B. the set of all real numbers -1≤y≤+1.

The investigators should conclude (C) There is insufficient evidence that the vitamin improves the health of adults because, at the 0.05 significance level, one could easily get statistically significant results in 2 out of 85 tests just due to chance variability.

In statistical hypothesis testing, a significance level of 0.05 indicates that there is a 5% chance of obtaining a statistically significant result due to chance variability if the null hypothesis is true.

In this study, the investigators performed 85 separate tests, increasing the chance of obtaining at least one false positive result due to chance variability.

This is known as the multiple comparisons problems, and to control for this issue, the investigators should have used a correction for multiple comparisons, such as the Bonferroni correction, which would have adjusted the significance level to 0.05/85 = 0.0006.

Therefore, finding two statistically significant results out of 85 tests does not provide sufficient evidence to conclude that vitamin improves the health of adults. Further studies with larger sample sizes, corrected for multiple comparisons, and controlling for confounders, are needed to draw a valid conclusion.

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Answer:

8

Step-by-step explanation:

65.29/8.23≈7.933

7.933 rounds to 8

The surface area of the prism for the given dimensions is equal to option B. 180 square centimeters.

Surface area of the prism

= Area of two right triangles + Area of rectangle 1 + Area of rectangle 2 + Area of the rectangle3

In a Triangle ,

Base = 12cm

height = 5cm

Area of the triangle = ( 1/2 ) × base × height

                                 = (1/2)× 12 × 5

                                 = 30 cm²

Length of rectangle 1 = 12cm

Width of rectangle 1 = 4cm

Area of rectangle 1 = 12 × 4

                                = 48 cm²

Length of rectangle2= 13cm

Width of rectangle 2 = 4cm

Area of rectangle 2= 13 × 4

                                = 52 cm²

Length of rectangle 3 = 5cm

Width of rectangle 3 = 4cm

Area of rectangle 3 = 5 × 4

                                = 20 cm²

Surface area of the prism

= Area of two right triangles + Area of rectangle 1 + Area of rectangle 2 + Area of the rectangle3

Substitute the values of the area we have,

⇒ Surface area of the prism  = 2(30 ) + 48 + 52 + 20

⇒ Surface area of the prism  =  180 square centimeters

Therefore, the surface area of the prism is equal to option B. 180 square centimeters.

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Answer:

The answer is C.

Step-by-step explanation:

Given, two points are (-8, 4) and (8, -4).

We have to find the change in the value of y.

We know that

Change in the value of y = 4 - (-4) = 8 units

Therefore, the change in the value of y is 8 units.

I didn't feel like writing an explanation myself so I found this one on Cuemath

a) The total cost of buying the car with HST is given as follows: $36,160.

b) The amount of money saved by the customer leasing the car instead of buying is given as follows: $14,760.

c) The customer should lease a new car, as according to the two options in this problem, leasing is more economic than purchasing a new car.

The costs are obtained applying the proportions in the context of this problem.

The HST tax is the Ontario Sales Tax, which means that an additional 13% of taxes has to be paid when purchasing the car.

Hence the total cost of buying the car, considering the HST tax, is given as follows:

1.13 x 32000 = $36,160.

The costs for leasing the car are given as follows:

Hence the total cost for leasing the car is given as follows:

1000 + 48 x 425 = $21,400.

Then the amount saved by the customers when he/she decides to lease the car instead of purchase is given as follows:

36160 - 21400 = $14,760.

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a) The only outcome that satisfies both events X and Y is the letter C.

b) The outcomes that satisfy either event X or event Y are {A, B, C, E, G}.

c) The complement of event X is {D, E, F, G}.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

The outcomes for each of the following events are:

(a) Event "X and Y": {C}

To satisfy both events X and Y, the letter selected must come before "D" (which includes the letters A, B, and C) and must be one of the letters in the word "CAGE" (which includes only the letter C). Therefore, the only outcome that satisfies both events X and Y is the letter C.

(b) Event "X or Y": {A, B, C, E, G}

The outcomes that satisfy event X are A, B, and C (since they come before "D"), and the outcomes that satisfy event Y are C, A, G, and E (since they are letters found in the word "CAGE"). Therefore, the outcomes that satisfy either event X or event Y are {A, B, C, E, G}.

(c) The complement of event X: {D, E, F, G}

The complement of event X is the set of outcomes that do not satisfy event X. The outcomes that do not satisfy event X are D, E, F, and G (since they come after or are equal to "D"). Therefore, the complement of event X is {D, E, F, G}.

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When a test is two-sided and one-sided: We will reject the null hypothesis at the = X 0.01 0.050. 10 significance level if the value of interest falls outside a 95% confidence interval. If the value of interest falls outside a 99% confidence interval, the null hypothesis will be rejected at the = 0.010.

A confidence interval is a range of estimates for an unknown parameter in frequentist statistics. A confidence interval is calculated at a specified confidence level; the 95% confidence level is most commonly used, but other levels, such as 90% or 99%, are occasionally used. The confidence interval is the range of values within which you expect your estimate to fall a certain percentage of the time if you repeat your experiment or re-sample the population in the same manner.

Here,

When a test is two-sided and one-sided: If the value of interest falls outside a 95% confidence interval, we will reject the null hypothesis at the = X 0.01 0.050. 10 significance level. The null hypothesis will be rejected at = 0.010 if the value of interest falls outside a 99% confidence interval.

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Answer:

two sided.

.05

.01

Step-by-step explanation:

9514 1404 393

Answer:

  the denominator of each fraction is 2

Step-by-step explanation:

The numerator of a fraction is the number above the fraction bar; the denominator is the number below the fraction bar. In the fraction ...

  \(\dfrac{7}{2}\)

the numerator is 7, and the denominator is 2.

__

Similarly, the number 2 is below the fraction bar and is the denominator in the fraction ...

  \(\dfrac{1}{2}\)

The numerator is 1, and the denominator is 2.

_____

The denominators of both of these fractions are 2. Since they are both the same, that value (2) can be used as the common denominator of the sum or difference of these fractions:

  \(\dfrac{7}{2}+\dfrac{1}{2}=\dfrac{7+1}{2}\qquad\text{or}\qquad\dfrac{7}{2}-\dfrac{1}{2}=\dfrac{7-1}{2}\)

Answer:

{7, 9}

(Numbers from 1 to 10 equal to or greater than 7 are 7 and 9)

Step-by-step explanation:

We have to find the set of whole number greater than and equal to 7 from 1 to 10,

Now, From 1 to 10, the odd numbers are, 1,3,5,7,9,

And of these, 7 and 9 are equal to or greater than 7

So, we get the set,

{7, 9}

Answer:

5

Step-by-step explanation:

(X1,Y1) = (-1,4)

(X2,Y2) = (2,8)

Answer:

10 of CD and 10 of DVD

Step-by-step explanation:

We have to think about the fact that 200 ends in two zeros in order to get it as the sum of the CD's and DVD's. In order to get 200, we most likely have to have numbers that also end in zero.  So if easily we can try 12*10 + 8*10, becasue they will end is zeros that way... AND WHAT DO WE KNOW, WE HAVE GOT OUR ANSWER, thi is because 12*10 + 8*10 really does equal 200.

The rational function shown in the graph is:

\(y = \frac{x - 6}{x - 5}\)

First, we can see that we have an asymptote at x = 5, so the denominator becomes equal to zero when x = 5.

Then the rational function is something like:

\(y = \frac{g(x)}{x - 5}\)

We also can see that when x = 6, the function intercepts the x-axis, then we must have that:

g(6) = 0

So we can define:

g(x) = x - 6

So the rational function is:

\(y = \frac{x - 6}{x - 5}\)

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Answer:

  (x, y) = (17, 10)

Step-by-step explanation:

You want the values of x and y given three angles written in terms of x and y at a transversal crossing parallel lines.

Angles at lower right of the points of intersection are corresponding angles, and are congruent:

  (9x -16)° = (8x +1)°

  x = 17 . . . . . . . . . . . . . divide by °, add 16-8x

The marked angles at the bottom form a linear pair, so are supplementary.

  (4y +3)° = 180° -(9x -16)°

  4y +3 = 180 -9(17) +16 = 43 . . . . . . use 17 for x and simplify

  4y = 40 . . . . . . subtract 3

  y = 10 . . . . . . divide by 4

-15x and 15x is the answer

Answer:

-12y and 12y

Step-by-step explanation:

lets do the multiplication to each equation

\(\left \{ {{(6x+3y)(-4)=9(-4)} \atop {(5x+4y)3=10(3)}} \right.\)
this is
\(\left \{ {{-24x-12y=-36} \atop {15x+12y=30}} \right.\)
if we add the systems notice the values that do cancel are -12y and 12y
and the results of the adition is
\(-9x=-6\)
from this
\(x=\frac{-6}{-9} =\frac{2}{3}\)
and you can find y from any of the first equation.

\(y=3-2x=3-\frac{4}{3} =\frac{5}3}\)

\( \huge {\star }\: Answer\)

The above equation is applicable for each and every value of a,

So, Correct option is A. True

_____________________________

\(\mathrm{ \#TeeNForeveR}\)

Answer:

x^2 + 7x + 12

Step-by-step explanation:

distributive property

Answer:

\(0.04 = 4 \div 100 \)