The equation of a circle is given below.
(x - 5)² + (y + 2)² =81/4
What is its center?
What is its radius?
If necessary, round your answer to two decimal places.
units

Answer :

five x plus ten

The set of side measurements that could be used to form a right triangle is 3, 4 and 5 option (D) is correct.

What is a right-angle triangle?

It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.

It is given that:

The side length of the triangle is shown in the option:

As we know,

Pythagoras' theorem is the square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.

Using Pythagoras' theorem:

From option(D):

3, 4 and 5

(3)² + (4)² = 5²

9 + 16 = 25 (True)

Thus, the set of side measurements that could be used to form a right triangle is 3, 4 and 5 option (D) is correct.

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Answer:

Step-by-step explanation:

4x-15=x-3 subtract x from both sides

3x-15=-3 add 15 to both sides

3x=12 divide both sides by 3

x=4

Answer:

look it up

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hello!

The objective is to test ESP, for this, a psychic was presented with cards face down and asked to determine if each of the cards was one of four symbols: a star, cross, circle, square.

Be X: number of times the psychic identifies the symbols on the cards correctly is a size n sample.

p the probability that the psychic identified the symbol on the cards correctly

You have to calculate the sample size n to estimate the proportion with a confidence level of 95% and a margin of error of d=0.01

The CI for the population proportion is constructed "sample proportion" ± "margin of error" Symbolically:

p' ± \(Z_{1-\alpha /2} * (\sqrt{\frac{p'(1-p')}{n} } )\)

Where  \(d= Z_{1-\alpha /2} * (\sqrt{\frac{p'(1-p')}{n} } )\) is the margin of error. As you can see, the formula contains the sample proportion (it is normally symbolized p-hat, in this explanation I'll continue to symbolize it p'), you have to do the following consideration:

Every time the psychic has to identify a card he can make two choices:

"Success" he identifies the card correctly

"Failure" he does not identify the card correctly

If we assume that each symbol has the same probability of being chosen at random P(star)=P(cross)=P(circle)=P(square)= 1/4= 0.25

Let's say, for example, that the card has the star symbol.

The probability of identifying it correctly will be P(success)= P(star)= 1/4= 0.25

And the probability of not identifying it correctly will be P(failure)= P(cross) + P(circle) + P(square)= 1/4 + 1/4 + 1/4= 3/4= 0.75

So for this experiment, we'll assume the "worst case scenario" and use p'= 1/4 as the estimated probability of the psychic identifying the symbol on the card correctly.

The value of Z will be \(Z_{1-\alpha /2}= Z_{0.975}= 1.96\)

Now using the formula you have to clear the sample size:

\(d= Z_{1-\alpha /2} * (\sqrt{\frac{p'(1-p')}{n} } )\)

\(\frac{d}{Z_{1-\alpha /2}} = \sqrt{\frac{p'(1-p')}{n} }\)

\((\frac{d}{Z_{1-\alpha /2}})^2 =\frac{p'(1-p')}{n}\)

\(n*(\frac{d}{Z_{1-\alpha /2}})^2 = p'(1-p')\)

\(n = p'(1-p')*(\frac{Z_{1-\alpha /2}}{d})^2\)

\(n = (0.25*0.75)*(\frac{1.96}{0.01})^2= 7203\)

To estimate p with a margin of error of 0.01 and a 95% confidence level you have to take a sample of 7203 cards.

I hope this helps!

Answer:

The sample size should be 6157

Step-by-step explanation:

Given that the margin of error (e) = ± 0.01 and the confidence (C) = 95% = 0.95.

Let us assume that the guess p = 0.25 as the value of p.

α = 1 - C = 1 - 0.95 = 0.05

\(\frac{\alpha }{2} =\frac{0.05}{2}=0.025\)

The Z score of α/2 is the same as the z score of 0.475 (0.5 - 0.025) which is 1.96. Therefore \(Z_\frac{\alpha }{2}=Z_{0.025}=1.96\)

To determine the sample size n, we use the formula:

\(Z_{0.025}*\sqrt{\frac{p(1-p)}{n} }\leq e\\Substituting:\\1.96*\sqrt{\frac{0.2(1-0.2)}{n} } \leq 0.01\\\sqrt{\frac{0.2(0.8)}{n} }\leq \frac{1}{196}\\\sqrt{0.16} *196 \leq \sqrt{n}\\78.4\leq \sqrt{n}\\ 6146.56\leq n\\n=6157\)

So the value of b is 11

Answer:

Kayla

Step-by-step explanation:

Vertical lines are always undefined because if your answer has to be divided by zero, the answer is an undefined operation.

Horizontal lines always have the slope of zero!

The slope of a vertical line is undefined.

Kayal is correct.

The rate of change in the table is -6.

The slope of the graph is 3/2.

The slope of a is the change in the y coordinate with respect to the change in the x coordinate.

We have,

A vertical line means there is no change in the x-coordinate.

i.e slope = change in y-coordinates / change in x-coordinate

slope = change in y-coordinate / 0
slope = undefined

The slope of a vertical line is undefined.

Now,

From the given table we see that there is a change of 1 for the x-values and a change of -6 in the y-values so,

Rate of change in the table:

= change in y values/change in the x values

= -6 / 1

= -6

Now,

Take any two points on the graph such as:

(a, b) = (4, 6) and (c, d) = (-4, -6)

The slope of the graph:

= (d - b) / (c - a)

= -6 - 6 / -4 - 4

= -12 / -8
= 3 / 2

Thus,

The slope of a vertical line is undefined.

Kayal is correct.

The rate of change in the table is -6.

The slope of the graph is 3/2.

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______________________________

______________________________

This triangle is not possible.

A triangular field has sides of lengths 29, 35, and 51 miles. The largest angle of the triangle can be calculated using the Law of Cosines, which is a generalization of the Pythagorean Theorem.

Law of Cosines:The Law of Cosines is a mathematical tool used to calculate the length of a side or the size of an angle of a non-right triangle. It states that the square of any side of a triangle is equal to the sum of the squares of the other two sides,

minus twice the product of these two sides and the cosine of the angle between them.Mathematically, the law of cosines is expressed as: `a^2 = b^2 + c^2 - 2bc cos A`,

where `a` is the unknown side, and `b` and `c` are the known sides of the triangle, and `A` is the angle between sides `b` and `c`.We can use the Law of Cosines to find the largest angle in the triangle as follows:Let `A` be the largest angle,

which is opposite the longest side `51 mi`.Using the Law of Cosines, we have:`

a^2 = b^2 + c^2 - 2bc cos A``51^2 = 29^2 + 35^2 - 2(29)(35) cos A``2601 = 1681 + 1225 - 2030 cos A``2030 cos A = 1225 + 920``cos A = (1225 + 920)/2030``cos A = 2145/2030``cos A ≈ 1.057139``A = cos^-1 (1.057139)`

Since the cosine function is only defined for values between -1 and 1, `1.057139` is not a valid value for `cos A`.

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Answer:

y=7

Step-by-step explanation:

The average rate of change over is 1.

Given that;

the function is,

⇒ g (t) = - (t - 1)² + 5

Hence, We need to determine the average rate of change over the interval - 4 ≤ t ≤ 5.

The value of G(-4):

The value of G(-4) can be determined by substituting t = -4 in the function

⇒ g (t) = - (t - 1)² + 5

Thus, we have,

⇒ g (t) = - (-4 - 1)² + 5

⇒ g (t) = - 20

Thus, the value of G(-4) = -20

The value of G(5):

The value of G(5) can be determined by substituting t = 5 in the function , we get,

⇒ g (t) = - (t - 1)² + 5

⇒ g (t) = - (5 - 1)² + 5

⇒ g (t) = - 11

Thus, the value of G(5) is, -11

Now, Average rate of change:

The average rate of change can be determined using the formula,

⇒ G(b) - G (a) / (b - a)

where, a = - 4 and b = 5

Substituting the values, we get,

⇒ G(5) - G (-4) / (5 - (-4))

⇒ ( - 11 - (- 20)) / 9

⇒ 9/9

⇒ 1

Thus, the average rate of change over the interval is. 1.

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The two equations which can be used to represent the situation are;

r + s = 1787

4r + 3s = 5,792

The correct answer choice is option B and E

Reserved seat for basketball game = r

Students seat for basketball game = s

Cost of reserved seat tickets = $4

Cost of students tickets = $3

Total number of people who attended the basketball game= 1,787 people

Total amount earned for tickets sales= $5,792

r + s = 1787

4r + 3s = 5,792

Therefore, the basketball game situation can be represented by the equation r + s = 1787; 4r + 3s = 5,792

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The quadratic regressiοn equatiοn fοr the given data pοints is y = 5x² - 20x + 7

A secοnd-degree equatiοn οf the fοrm ax² + bx + c = 0 is knοwn as a quadratic equatiοn in mathematics. Here, x is the variable, c is the cοnstant term, and a and b are the cοefficients.

Tο find the quadratic regressiοn equatiοn fοr the given data pοints, we need tο fit a quadratic equatiοn οf the fοrm y = ax² + bx + c tο the data.

We can start by using the three given pοints tο set up a system οf three equatiοns:

\((1,-8): a(1)^2 + b(1) + c = -8\\\\(2,-4): a(2)^2 + b(2) + c = -4\\\\(3,6): a(3)^2 + b(3) + c = 6\)

SimpIifying each equatiοn, we get:

a + b + c = -8 (equatiοn 1)

4a + 2b + c = -4 (equatiοn 2)

9a + 3b + c = 6 (equatiοn 3)

AIternativeIy, we can use technοIοgy such as a caIcuIatοr οr spreadsheet tο sοIve the system.

SοIving the system using technοIοgy, we get:

a = 5

b = -20

c = 7

Therefοre, the quadratic regressiοn equatiοn fοr the given data pοints is:

y = 5x² - 20x + 7

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Given the division:

Let's find the next step and complete the given statements.

The firtst two steps have been completed already.

Multiply (2x - 7) by 4x, place the result under the polynomail and subtract.

(2x - 7) * 4x = 8x² - 28x

Thuu, we are to subtract 8x² - 28x from (8x² + 6x) which obtains 34x. Then bring down -5 and form the new dividend 34x - 5

We have:

ANSWER:

The next step is to subtract 8x² - 28x from (8x² + 6x) which obtains 34x. Then bring down -5 and form the new dividend 34x - 5

Answer:

  12x³y²

Step-by-step explanation:

You want the product -2x (-3x²y)(2y).

An exponent is a means of telling the number of times the base is a factor in a product. For example, the exponent 2 means the base is a factor twice in the product:

  x² = x·x

When the same factor appears a number of times in a product, an exponent can be used to represent that number.

  (-2x)(-3x²y)(2y) = (-2)(-3)(2)(x·x²)(y·y)

The factor x appears 3 times in the product, and the factor y appears twice. The numerical product can be simplified, so the result is ...

  12x³y²

Answer:

7: 63

8: 73

arithmetic sequence

y = 10x - 7

or f(n) = 10x -7

or

\(a_{n}\) = 3 + (n-1)10

Step-by-step explanation:

the output increases by 10 every time that the input increases by 1.  That gives us our common difference or slope.  The y intercept is -7. That is the value is you worked backwards until you get to n = 0.  The initial value  is 3.  That is when n is 1.

When n is 3, f(n) is 23

When n is 2, f(n) is 13

When n is 1, f(n) is 3

When n is 0, f(n) is -7

I am not sure if this is clear.  I am assuming that you have a lot of knowledge of linear equations and how to write arithmetic sequence.  If my explanation is confusing it is me and not you.

Answer:

a. 63,73

b. Arithmetic sequence

c.t(n)=10n-7

Explanation:

a. Here is the completed table:

n | t(n)

4 | 33

5 | 43

6 | 53

7 | 63

8 | 73

b.

The type of sequence is arithmetic.

An arithmetic sequence is a sequence of numbers where the difference between any two consecutive terms is constant.

In this case, the difference between any two consecutive terms is 10.

c.

The equation for the arithmetic sequence is:

t(n)=a+(n-1)d

where:

For Question:

Now

equation becomes:

t(4) = a+(4-1)10

33=a+30

a=33-30

a=3

Now, the Equation becomes

t(n) = 3+(n-1)10

t(n) = 3+10n-10

t(n)=10n-7

The area of a shape is the amount of space on the shape.

The best approximation for the area of the figure is \(14 + 16.25\pi\)

Start by calculating the diameter of the semicircle using the following distance formula:

\(d = \sqrt{(x_2 -x_1)^2 +(y_2 -y_1)^2}\)

So, we have:

\(d = \sqrt{(-4 -3)^2 +(-2 -2)^2}\)

\(d = \sqrt{65}\)

Divide by 2, to calculate the radius

\(r = \frac{\sqrt{65}}{2}\)

So, the area of the semicircle is:

\(A = \frac{\pi r^2}{2}\)

This gives

\(A = \pi (\frac{\sqrt{65}}{2})^2\)

\(A = \frac{65}{4}\pi\)

\(A = 16.25\pi\)

Next, we calculate the area of the triangle using:

\(A = 0.5 * B * H\)

Where:

\(B = 3 -(-4)\)

\(B = 7\)

\(H= 2 - (-2)\)

\(H = 4\)

So, we have:

\(A = 0.5 * 7 * 4\)

\(A = 14\)

The area of the figure is then calculated as:

\(A = 14 + 16.25\pi\)

Hence, the best approximation for the area of the figure is \(14 + 16.25\pi\)

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Answer:

a. 4.35 x 10-⁴

= 0.000435

b. 4.16 x 10¹

= 41.6

c. 9.2 x 10-³

= 0.0092

d. 1.1 x 10-⁵

= 0.000011

e. 6.5 x 10⁵

= 650000

Step-by-step explanation:

Very simple and quick

Answer:

See below

Step-by-step explanation:

Part A

\(f(g(x))=f(\frac{x}{3})=3(\frac{x}{3})=x\\g(f(x))=g(3x)=\frac{3x}{3}=x\)

Since BOTH \(f(g(x))=x\) and \(g(f(x))=x\), then \(f\) and \(g\) are inverses of each other

Part B

\(f(g(x))=f(\frac{x+1}{2})=2(\frac{x+1}{2})+1=x+1+1=x+2\\g(f(x))=g(2x+1)=\frac{(2x+1)+1}{2}=\frac{2x+2}{2}=x+1\)

Since BOTH \(f(g(x))\neq x\) and \(g(f(x))\neq x\), then \(f\) and \(g\) are NOT inverses of each other

Answer:

147.6℅

=

\( \frac{147.6}{100} \)

\(1.476\)

hope it helps you

make me brainliest if u r satisfied

Answer:  6a3b3

Step-by-step explanation:

Reformatting the input:

Changes made to your input should not affect the solution:

(1): "0.6" was replaced by "(6/10)".

STEP 1:

Equation at the end of step 1

       6

 0-(((——•(a2))•b)•(0-(2•5ab2)))

      10

STEP 2:

           3

Simplify   —

           5

Equation at the end of step 2:

         3

 0 -  (((— • a2) • b) • ( -2•5ab2))

         5

STEP 3:

Equation at the end of step 3

        3a2

 0 -  ((——— • b) • ( -2•5ab2))

         5

STEP 4:

Multiplying exponential expressions :

4.1    a2 multiplied by a1 = a(2 + 1) = a3

Multiplying exponential expressions :

4.2    b1 multiplied by b2 = b(1 + 2) = b3

Canceling Out:

4.3      Canceling out  5  as it appears on both sides of the fraction line

Equation at the end of step 4:

 0 -  -6a3b3

STEP 5:

Final result :

 6a3b3

Answer:

\(18 {x}^{3} + 80\)

Step-by-step explanation:

\( {x}^{2} \times 18 {x}^{1} + 80 \\ {x}^{2 + 1} x18 + 80 \\ {x}^{3} x18 + 80 \\ 18 {x}^{3} + 80\)

Answer:

Please check the explanation.

Step-by-step explanation:

We know that the slope or rate of change of the function can be:

Function 1

From the function 1 graph, it is clear that the graph is a horizontal line. We must note that the horizontal line has a slope or rate of change zero. The reason is that the horizontal line can not rise vertically. i.e. y₂-y₁=0

so using the slope formula

Rate of change = m = y₂-y₁ / x₂-x₁

Taking two points (x₁, y₁) = (0, 4), (x₂, x₁) = (1, 4)

Rate of change = m = 4-4 / 1-0

Rate of change = m = 0/1

Rate of change = m = 0

Thus, the rate of change of function 1 is zero.

Function 2

We know the slope-intercept form of linear equation is

\(y = mx+b\)

where m is the rate of change or slope of the function and b is the y-intercept

Given the function

\(y = 8x+12\)

comparing with the slope-intercept form i.e. y = mx+b

Therefore, the rate of change of function 2 = m = 8

Conclusion

The rate of change of function 1  = 0

The rate of change of function 2  = 8

as

Therefore, function 2 has 8 more rate of change of function than the rate of change of function 1.

After 36 minutes of calls, when the function returns a line with a slope of -0.13, there will be $27.56 credit.

Mathematics deals with numbers and their variants, equations and related structures, shapes and their locations, and locations where they might be found. A function is an association between inputs and outputs where each input results in a single, unique output. A domain and a codomain, or scope, are assigned to each function. Functions are typically denoted by the letter f. (x). The input is an x. On functions, one-to-one functions, many-to-one functions, within functions, and on functions are the four main categories of functions that are available.

given

Assume that the total calling time is a linear function of the credit left on a phone card (measured in dollars) (in minutes).

m(call time) + b = credit

The function produces a line with a slope of -0.14 when graphed.

After 43 minutes of calls, the card's balance is $26.02 left.

After 32 minutes of calls, there was 26.02 = -0.14(43) + b b = 26.02+6.02 b = 32.04 C(x) = -0.14x+32.04

credit?

C(32) = -0.14(32) + 32.04\sC(32) = $27.56

After 36 minutes of calls, when the function returns a line with a slope of -0.13, there will be $27.56 credit.

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Answer:

61k

Step-by-step explanation:

63+59=122

122/2=61

Answer:

61000

Step-by-step explanation:

First add 63K + 59K. You'll get 122K. Then divide that number by two. You'll get 61 K, which is 61000.

Step-by-step explanation:

√110 = 10.488

You can round that to 10.49

Hope this helps!

The number line that shows the solution to the inequality is given as follows:

First number line.

The inequality in the context of this problem is defined as follows:

-6x + 5 >= 17

-6x >= 12.

Due to the negative sign of the leading coefficient, we should change the sign of all terms, including the sign, as follows:

6x <= -12.

Then the solution is given as follows:

x <= -2.

Which is composed by the numbers to the left of the closed interval at x = -2, hence the first number line gives the solution to the inequality.

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The number line that shows the solution to the inequality is: C. graph C.

In Mathematics and Geometry, an inequality refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the inequality symbols;

Based on the information provided above, we have the following equation (inequality);

-6x + 5 ≥ 17

By subtracting 5 from both sides of the equation (inequality), we have;

-6x + 5 - 5 ≥ 17 - 5

-6x ≥ 12

x ≤ 12/6

x ≤ 2 (it would be shaded to the left with a closed circle at 2).

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