Complete the statement. Explain your
reasoning
7
3
26
8 4 15 C

The equation of a graph is a mathematical statement true only for points of that graph. The equation of specified circle is: x² + y² −41 = 0

If a circle O has radius of r units length and that it has got its center positioned at (h, k) point of the coordinate plane, then, its equation is given as: (x-h)²+(y-k)² = r²

For given case, we have h = 0, and k = 0,

We know that,

The shortest distance (straight line segment's length connecting both given points) between points (p, q) and (x, y) is:

D = √(x-p)² + (y-q)²  units.

Also,

Radius = distance between O and B as length of radius, which is

r = √[(4-0)² + (5-0)²] = √[16+25] = √41   units.

Thus, we have the equation as:

(x-h)² + (y-k)² = r²

x²+ y² = (√41)²

x² + y² = 41

x² + y² - 41 = 0

Hence, The equation of specified circle is: Option b) x² + y² - 41 = 0

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The domain of the function is (-∞, ∞.)

The range of the function is {3, ∞}.

We have,

From the given quadratic function,

We see that,

The x-values are -∞ to ∞

The y-values are from 3 to ∞

Now,

The x-values are called the domain.

The y-values are called the range.

Thus,

The domain of the function is (-∞, ∞.)

The range of the function is {3, ∞}.

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Answer:

159 hwqb Step-by-step explanation:2n3wq,brudj32nwqrdb3wndj32wsd

Answer:

Add all the digits of the number, then check if that sum is divisible by 9. If yes, we know the number is divisible by 9.

Answer:

$66.08

Step-by-step explanation:

Judy bought two things, a hat and sunglasses. So, the total money spent is:

$44.67 + $110.76 = $155.43

She has $89.35 in her checking account and spent $155.43 on the two items.

So that means she spent more than she has in the account. To find how much she needs to put in her checking account, we're going to subtract how much money she spent and how much she has in her account.

$89.35 - $155.43 = -$66.08

Therefore, she needs to put in $66.08 into her account to pay off her debt at the end of the month.

Answer:

Step-by-step explanation:

The vertex is at (-3, -1)  and the leading coefficient is negative ( because  the curve is inverted)

y = -a(x + 3)^2 - 1

One point on the curve is (-2, -3) so

-3 = -a(-2+3)^2 - 1

-3 = -a - 1

-a = -2

So we have

y = -2(x + 3)^2 -  1

y = -2(x^2 + 6x + 9) - 1

y = -2x^2 - 12x - 19.

Composite Functions for : f [ g (x) ] = 3 g(x) + 7 will be f [ g(x) ] = 3 ( 5x - 5) + 7 = 15x - 8

Common functions typically have a subset of the real numbers as their domain. Any integer from the domain may be used to replace a variable.

The domain of a composite function is determined by another function, not by a collection of numbers. We refer to it as "a result of another function. Example:

If: . f (x) = 3x + 7 . f [g(x)] must be found and simplified. g(x) = 5x - 5. Due to the fact that the domain of this function is a function of another function, f (x) is a simple function or just a function.

Let's make the example I gave previously simpler.

G (x) signifies in f "Replace x with g (x) in the function f (x). The Composite function f [g (x)]

we have : f [ g (x) ] = 3 g(x) + 7 . but . g( x) = 5x - 5

replace x in f[ g(x ) ] . by. 5x - 5 and simplify

f [ g(x) ] = 3 ( 5x - 5) + 7 = 15x - 8 **

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The question seems to be wrong

Evaluating Composite Functions for : f [ g (x) ] = 3 g(x) + 7

Answer:

I am assuming you are looking for the x-intercepts and y-intercepts...here they are.

x-intercepts: (-7/2,0) , (-1,0) , (4,0)

y-intercepts: (0,-5)

Hope this helps...if not, please expound your question more.

Answer:

S₇ = 514.75

Step-by-step explanation:

the nth term of a geometric sequence is

\(t_{n}\) = a\(r^{n-1}\)

where a is the first term and r the common ratio

given t₂ = 24 and t₅ = 81 , then

ar = 24 → (1)

a\(r^{4}\) = 81 → (2)

divide (2) by (1) to eliminate a

\(\frac{ar^{4} }{ar}\) = \(\frac{81}{24}\)

r³ = \(\frac{81}{24}\) ( take cube root of both sides )

\(\sqrt[3]{r^{3} }\) = \(\sqrt[3]{\frac{81}{24} }\)

r = 1.5

substitute r = 1.5 into (1) and solve for a

a × 1.5 = 24 ( divide both sides by 1.5 )

a = 16

the sum to n terms of a geometric sequence is

\(S_{n}\) = \(\frac{a(r^{n}-1) }{r-1}\) , then

S₇    = \(\frac{16((1.5)^{7}-1)) }{1.5-1}\)

      = \(\frac{16(17.0859375-1)}{1.5-1}\)

     = \(\frac{16(16.0859375)}{0.5}\) ( divide 16 by 0.5 )

     = 32 × 16.0859375

     = 514.75

Using the Factor Theorem, the polynomial that meets these four criteria is given as follows:

\(f(x) = -x^4 + \frac{7}{3}x^3 + \frac{58}{3}x^2 + \frac{52}{3}x - 8\)

The Factor Theorem states that a polynomial function with roots(also called zeros) \(x_1, x_2, \codts, x_n\) is given by the following rule.

\(f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)\)

In which a is the leading coefficient of the polynomial, determining if it is positive(a positive) or negative(a negative).

For this problem, from criteria 2, the roots are given as follows:

\(x_1 = 6, x_2 = \frac{1}{3}, x_3 = x_4 = -2\)

Due to the four roots, the first criteria is met, while with a = -1 the third criteria is met.

Then the polynomial is given by the following rule:

\(f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)\)

\(f(x) = -(x - 6)(x + 2)(x + 2) \left(x - \frac{1}{3}\right)\)

\(f(x) = -(x - 6)(x^2 + 4x + 4)\left(x - \frac{1}{3}\right)\)

\(f(x) = -(x^3 - 2x^2 - 20x - 24)\left(x - \frac{1}{3}\right)\)

\(f(x) = -\left(x^4 - \frac{7}{3}x^3 - \frac{58}{3}x^2 - \frac{52}{3}x + 8\right)\)

\(f(x) = -x^4 + \frac{7}{3}x^3 + \frac{58}{3}x^2 + \frac{52}{3}x - 8\)

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The surface area of the sphere, to the nearest whole number, is 1318 cm².

A sphere is simply a three-dimensional geometric object that is perfectly symmetrical in all directions.

The volume of a sphere is expressed as:

Volume =  (4/3)πr³

The surface area of a sphere is expressed as:

SA = 4πr²

Where r is the radius of the sphere and π is the mathematical constant pi.

Given that the volume V is 4500 cm³.

First, we solve for the radius:

Volume =  (4/3)πr³

4500 = (4/3)πr³

4500 × 3 = 4πr³

13500 = 4πr³

r³ = 13500/4π

r = ∛( 13500/4π )

Now that we have the radius, we can calculate the surface area of the sphere using the formula:

SA = 4πr²

Substituting the radius we found:

SA = 4 × π × ∛( 13500/4π )²

SA = 1318 cm²

Therefore, the surface area is approximately 1318 cm².

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Answer:

A’ = (-2, 1.5)

B’ - (2, 1.5)

C’ - (-2, -2)

D- (2, -2)

Step-by-step explanation:

A - (-4, 3)

B- (4, 3)

C - (-4, -4)

D- (4, -4)

A’ = (-2, 1.5)

B’ - (2, 1.5)

C’ - (-2, -2)

D- (2, -2)

Answer:

have a look at the attachment image......

if dilatation center is A, connect all of the the alphabet (B, C, D)to A and the scale factor is 1 by 2. so make a dot in the middle of line that is connected to dilatation center....

if the line is D to A then the dot on the line D will be D prime.... same like that find C and B prime

if you don't understand let me know in the comments

Answer: To find out how much medication the patient receives each day, you need to determine the patient's weight in kilograms and then calculate the total dosage per day.

You can convert the patient's weight from pounds (lb) to kilograms (kg) by dividing the weight by 2.2.

So,

315/2.2 = 142.72 kg

Next, we can use this weight to determine the dosage per day:

3 mg/kg * 142.72 kg = 428.16 mg

Now, since the physician ordered twice a day, we will multiply the dosage per day with 2:

428.16 mg * 2 = 856.32 mg

So the patient receives 856.32 mg of medication each day.

Step-by-step explanation:

The inverse of the function f(x) = k/x is the expressed derived as; f⁻¹(x) = k/x

A function is said to have an inverse if it is both one-to-one and onto

we replace the function f(x) with y and make x the subject to arrive at the inverse f⁻¹(x) as follows;

Given f(x)= k/x

y = k/x

y × x = k/x × x {multiply both sides by x}

xy = k

xy/y = k/y {divide through by y}

x = k/y

f⁻¹(x) = k/y.

Therefore, the inverse of the function f(x) = k/x is the expressed derived as; f⁻¹(x) = k/x.

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Answer:the last one

Step-by-step explanation:

Answer:

b = 126.33 inches

Step-by-step explanation:

We need to find the measure of side b.

Here, c = 170 inches

\(\theta=42^{\circ}\)

It can be calcuated using trigonometry as follows :

\(\cos\theta=\dfrac{B}{H}\ ({\text{B is base and H is hypotenuse)}\\\cos(42)=\dfrac{b}{170}\\\\b=\cos(42)\times 170\\\\b=126.33\ in\)'

Hence, the length of b is 126.33 inches.

Answer:

50.24 inches^2

Step-by-step explanation:

D=8 inches, r=D/2, r=8/2=4 inches

Area of circle= πr^2

=3.14×4×4

=3.14×16

=50.24

Answer:

Step-by-step explanation:

S.I =720×6×5/100×365

=21600/36500

=0.59178

So balance will be 720+0.59178

=720.59178

Answer:

A is the direct variation equation

Answer:

perimwter = 2(4x-6 + 2x+4) = 2 (6x-2) = 12x-4

Answer:

f(x) = log x - 1 --> (10, 0)

f(x) = -(log x - 2) --> (100, 0)

f(x) = log(- x - 2) --> (-3, 0)

f(x) = -log-(x-1) --> (0, 0)

Step-by-step explanation:

An x-intercept is the position where the value of y(in this case f(x)) is 0.

Let's start with the first equation:

f(x) = log x - 1

If f(x) is 0, we would get this equation:

0 = log x - 1

Now, we solve for x:

1 = log x

x = 10

This means the x-intercept is (10, 0).

f(x) = -(log x - 2)

Again, we can set f(x) to 0, and solve for x:

0 = -(log x - 2)

0 = log x - 2

2 = log x

x = 100

This means the x-intercept is (100, 0)

Same process applies for the third:

f(x) = log(- x - 2)

0 = log(- x - 2)

1 = -x - 2

3 = -x

x = -3

(-3, 0)

f(x) = -log-(x-1)

0 = -log-(x-1)

0 = log-(x-1)

1 = -(x-1)

1 = -x + 1

0 = -x

x = 0

(0, 0)

Answer:

60 is the answer you're welcome

the new ratiο after decreasing 72 in the ratiο οf 7:18 is apprοximately 7:16.56.

Tο decrease 72 in the ratiο οf 7:18, we need tο determine hοw much οf the 7:18 ratiο 72 represents.

First, we need tο find the tοtal number οf parts in the ratiο 7:18. This can be fοund by adding the twο numbers in the ratiο:

7 + 18 = 25

Sο the ratiο 7:18 represents a tοtal οf 25 parts.

Next, we need tο determine hοw much οf the 25 parts 72 represents. Tο dο this, we set up a prοpοrtiοn:

x/25 = 72/1

where x is the number οf parts that 72 represents.

We can sοlve fοr x by crοss-multiplying:

x = 25 * 72 / 1

x = 1800

Sο 72 represents 1800/25 = 72 parts in the ratiο 7:18.

Tο decrease 72 in the ratiο 7:18, we need tο subtract 72 parts frοm the 18 parts in the ratiο:

18 - 72/25 = 16.56 (rοunded tο twο decimal places)

Therefοre, the new ratiο after decreasing 72 in the ratiο οf 7:18 is apprοximately 7:16.56.

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Answer:

So the number of ways of choosing two distinct letters at a time is (42)=6. We can then add the duplicate pairs which are O,O and N,N to give a total of 8 possible pairs.

Answer:

15

Step-by-step explanation:

There are 6 letters in the word number

This is 6 choose 2

This is a combination

The formula is 6! / ( 2! * (6-2)! )

                           6! / 2! 4!

                           (6*5*4*3*2*1) / ( 2*1 *  4*3*2*1)

Canceling like factors

                             (6*5) / ( 2*1)

                              30/2

                                 15

There are 15 possible ways to have 6 choose 2