What is the equation of a circle with a radius of 4 and a center located at (2,3)

The solution to the given system of equation is (3, 3, 3)

Given the following system of equation expressed as:

2x-y+5z=16

X-6у +2z=-9

3x+4y- z=32

Multiply equation 2 by 2 to have:

2x-y+5z=16

2X-12у +4z=-18

Subtract

10y+z = 34 .........4

Similarly

3X-18у +6z=-27

3x+4y- z=32

Subtract

-22y+7z = -59 ........... 5

Equate 4 and 5

10y+z = 34 .........4 * 7

-22y+7z = -59 ........... 5 * 1

_______________________

70y+7z = 238

-22y+7z = -59

Subtract

92y = 297

y = 3

Recall that

10y+z = 34

10(3) + z = 34

z = 3

Since x - 6y +2z = -9

x-6(3)+2(3) = -9
x - 18 + 6 = -9
x = 3

Hence the solution to the given system of equation is (3, 3, 3)

Learn more on system of equation here: https://brainly.com/question/25976025

#SPJ1

The boat in discuss is 9.03 miles from lighthouse B.

The distance of the boat from lighthouse B as required can be determined by means of the cosine law in which case we have;

c² = 10² + 6² - (2×6×10Cos 63)

c = 81.52

c = 9.03miles.

Read more on cosine rule;

https://brainly.com/question/2491835

#SPJ1

Answer: D. slides the graph 1 unit right

Step-by-step explanation:

See attached image.

Answer:

The answer is choice C from the given alternatives.

it would take Janis 14 minutes to complete a package alone

From the information given,

Let's say that

Carol working time = x = 30 minutes

Janis working time = y

x + y = 16 minutes

Let's make 'y' the subject

30 - 16 = y

y= 14 minutes

Thus, it would take Janis 14 minutes to complete a package alone

Learn more about word problems here:

https://brainly.com/question/13818690

#SPJ1

Answer: 23 inches by 7 inches

Step-by-step explanation:

161 = 7 x 23 (or 1 x 161 but that doesn't help...)

And to check:

7 x 3 + 2 = 23

Answer:

23inches by 7inches

Step-by-step explanation:

7 ×3+2=23

Answer:

what is the monthly payment or ask for the mileage use for the car

[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Information : The given ellipse is a horizontal ellipse, and it's centre lies on origin, as the foci are given on x - axis.

The foci of the ellipse can be written in form :

[tex]\qquad \sf  \dashrightarrow \: ( \pm ae , 0)[/tex]

So,

[tex]\qquad \sf  \dashrightarrow \: ae = 5[/tex]

and Vertex of the ellipse can be written as

[tex]\qquad \sf  \dashrightarrow \: (\pm a,0)[/tex]

Now, plug the value in first equation ~

[tex]\qquad \sf  \dashrightarrow \: ae = 5[/tex]

[tex]\qquad \sf  \dashrightarrow \: 11e = 5[/tex]

[tex]\qquad \sf  \dashrightarrow \: e = \cfrac{5}{11} [/tex]

Now, we have to find b (length of semi minor axis)

we can use the formula ~

[tex]\qquad \sf  \dashrightarrow \: b {}^{2} = {a}^{2} (1 - {e}^{2} )[/tex]

[tex]\qquad \sf  \dashrightarrow \: b {}^{2} = 121(1 - \frac{25}{121} )[/tex]

[tex]\qquad \sf  \dashrightarrow \: b {}^{2} = 121( \frac{121 - 25}{121} )[/tex]

[tex]\qquad \sf  \dashrightarrow \: b {}^{2} = 96[/tex]

Now, we can write the equation of ellipse as :

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ {x}^{2} }{ {a}^{2} } + \cfrac{ {y}^{2} }{ {b}^{2} } = 1[/tex]

[ plug the values ]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ {x}^{2} }{ {121}^{} } + \cfrac{ {y}^{2} }{ {96}^{} } = 1[/tex]

Answer:

[tex]\dfrac{x^2}{121}+\dfrac{y^2}{96}=1[/tex]

Step-by-step explanation:

General equation of an ellipse:

[tex]\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1[/tex]

where:

If a > b the ellipse is horizontal, a is the major radius, and b is the minor radius.

If b > a the ellipse is vertical, b is the major radius, and a is the minor radius.

Given:

Therefore, the ellipse is horizontal with its center at (0, 0):

⇒ h = 0 and k = 0

⇒ a = 11

⇒ c = 5

To find b², use  c² = a² − b²:

⇒ 5² = 11² − b²

⇒ b² = 11² − 5²

⇒ b² = 96

Therefore, the standard form of the equation of the ellipse is:

[tex]\implies \dfrac{(x-0)^2}{11^2}+\dfrac{(y-0)^2}{96}=1[/tex]

[tex]\implies \dfrac{x^2}{121}+\dfrac{y^2}{96}=1[/tex]

a)

b) Conditions:[tex]\sigma[/tex] is understood to have a regular distribution of weights

c) Interpretation: 80 percent of the time, this range will include the actual average weight of Allen's hummingbirds, hence its reliability may be counted on

d) sample size [tex]n \approx 27[/tex].

Generally,
Here n = 17

T= 3.15

[tex]\sigma=0.40[/tex]

confidence level =c = 0.80

Here we will usethe  z critical value.

z critical value for (1+c) /2 = (1+0.80)/2

z critical value for (1+c) /2= 0.9

Zc = 1.28

Critical value = 1.28

a) Margin of error (E) :

[tex]E = Zc*\frac{\sigma}{\sqrt{n}}\\\\\E = 1.28*\frac{0.40}{\sqrt{17}}[/tex]

E =0.124

Margin of error = E =0.124

Lower limit = x-E

L= 3.15 - 0.124

L= 3.026

Lower limit =3.026

Upper limit = x + E

U= 3.15 + 0.124

U= 3.274

Upper limit =  3.274

The following is a confidence interval with a value of 80 percent for the mean weights of Allen's hummingbirds in the area under study: (3.02,3.28)

b) Conditions:[tex]\sigma[/tex] is understood to have a regular distribution of weights

c) Interpretation: 80 percent of the time, this range will include the actual average weight of Allen's hummingbirds, hence its reliability may be counted on.

d) When is already known, the following equation may be used to determine the appropriate number of samples, n:

[tex]n=(\frac{z_c*\sigma }{E})^2[/tex]

Margin of error = 0.13

Sample size (n):

[tex]n= (\frac{z_c*\sigma }{E})^2[/tex]

[tex]n=(\frac{ 1.28*0.36}{0.09})^2[/tex]

n = 26.21

[tex]n \approx 27[/tex]

Read more about probability

https://brainly.com/question/795909

#SPJ1

Answer:

1±2i.

Step-by-step explanation:

1. if to evaluate the expression given, it can be written

(x-5)(x²-2x+5)=0;

2. where the nonreal roots are 1±2i.

Answer:

C) The volume of the prism is equal to the volume of the cylinder.

Step-by-step explanation:

volume of triangular prism = area of base × height

volume of cylinder = area of base × height

The cross sectional area are equal, so the bases have the same area.

The heights are also equal.

The volumes must be equal.

Answer: C) The volume of the prism is equal to the volume of the cylinder.

Answer:

C) The volume of the prism is equal to the volume of the cylinder.

Step-by-step explanation:

If the cross-sectional areas of the triangular prism and the right cylinder are congruent, it means that when you look at their shapes from the top or bottom, they have the same size and shape.

Since both the triangular prism and the right cylinder have a height of 5 units, and their cross-sectional areas are the same, it implies that they have the same volume as well. So, the volume of the triangular prism is equal to the volume of the cylinder.

Please mark me as Brainliest if you're satisfied with this answer

Answer:

about 19.31 years

Step-by-step explanation:

[tex]10000( {1.11}^{x} ) = 75000[/tex]

[tex] {1.11}^{x} = 7.5[/tex]

[tex]x ln(1.11) = ln(7.5) [/tex]

[tex]x = \frac{ ln(7.5) }{ ln(1.11) } = 19.31[/tex]

The number of square feet of carpet needed for the rooms is 889 ft².

The total square footage of your house is 1200 square feet.

He wants to put new carpet in all rooms except for  the kitchen, dining room and bathroom.

Therefore,

total area = 1200 ft²

Area of the other rooms with no carpet  = (10 × 12) + (11 × 13) + (6 × 8)

Area of the other rooms with no carpet  = 120 + 143 + 48

Area of the other rooms with no carpet  = 311 ft²

Hence, the number of square feet for the house = 1200 - 311 = 889 ft²

learn more on area here: https://brainly.com/question/15280811

#SPJ1

The area of the shaded part is 52 sq. inches. The correct option is b. 52 sq. inches

From the question, we are to determine the area of the shaded part

In the given diagram, the shaded part is a rectangle

Area of a rectangle = Length × Width

Length of the shaded part = 18 inches - 4 inches - 1 inch = 13 inches

Width of the shaded part = 6 inches - 2inches = 4 inches

Then,

Area of the shaded part = 13 inches × 4 inches

Area of the shaded part = 52 sq. inches

Hence, the area of the shaded part is 52 sq. inches. The correct option is b. 52 sq. inches

Learn more on Calculating area here: https://brainly.com/question/12529348

#SPJ1

A logarithmic function is the inverse of an exponential function.

A logarithmic function is the inverse of an exponential function.

Now we have the function;

f(x) = log(x) and the translated function f(x) = log (x-h) + k.

Similarly;

Learn more about logarithmic function:https://brainly.com/question/3181916

#SPJ1

Missing parts;

Use the graphing calculator to graph the parent function.

f(x) = log(x)

Add the translated function.

f(x) = log (x-h) + k

Plug in different values of h and k to answer the following questions.

What happens when h is positive?

What happens when h is negative?

What happens when k is positive?

What happens when k is negative?

Answer:

When h is positive: horizontal shift to the right

When h is negative: horizontal shift to the left

When k is positive: vertical shift up

When k is negative: vertical shift down

Step-by-step explanation:

got it right on Edge

Answer: [tex]m\angle BAM=30^{\circ}[/tex]

Step-by-step explanation:

[tex]AD=x\sqrt{3}[/tex] (Pythagorean theorem)

[tex]m\angle ACD=60^{\circ}[/tex] (30-60-90 triangle)

[tex]m\angle MCA=30^{\circ}[/tex] (angle subtraction)

[tex]m\angle MAC=30^{\circ}[/tex] (base angles theorem)

[tex]m\angle CAD=30^{\circ}[/tex] (30-60-90 triangle)

[tex]m\angle BAM=30^{\circ}[/tex] (angle subtraction)

Distance formula ds = v(dx² + dy²) s = ? v(1 + (dy/dx)²) dx ......... s = the arc length y = 171 - x²/45

chegg

someone solved it on this

https://youtu.be/UGjXlMVdZvc

It is possible to arrange the total of mangoes by using 20 piles of 9 mangoes, 18 piles of 10 mangoes, or 15 piles of 12 mangoes.

The conditions for mangoes to be arranged are that the piles should have either 9, 10 or 12 mangoes and reminders are not allowed. This means you need to fit all the mangoes and no mangoes can be left.

Based on the conditions and the total number of mangoes (180 mangoes), here are the possibilities that you can determine using division:

Learn more about division in https://brainly.com/question/369266

#SPJ1

The ways to illustrate the shapes are given.

11.  In each new figure, one vertex is introduced, and each vertex is joined to each other vertex.

12.  In each new figure, 2 rows and 1 column are introduced, and the shading at the corner moves 90 degrees clockwise.

13.  In each new figure, one row and one column are introduced, and exactly half of the rectangles are shaded.

14.  In each new figure, except at the bottom vertex, two perpendicular lines are introduced at the remaining vertices.

15.  In each new figure, one inverted white triangle is inscribed in the orange triangle.

16.  The number of squares increases in the pattern. There are blue circles inscribed in one diagonal square and there are yellow circles inscribed in the remaining squares. Also, the blue circles in the diagonal alternate.

Learn more about shapes on:

https://brainly.com/question/25965491

#SPJ1

Answer:

there shouldnt be an answer, they are not like terms, for a proper answer it would have to be like terms, for example:

x^2+x^2=2x^2

or

w^12+w^12=2w^12

they need to have the same exponent for addition to happen

The quantity of product that would result in the same profit is 1 thousand. Option A

Given the polynomial function as;

P(t) = –2t³ + 8t² + 2t

Where;

Let's equate the values

–2t³ + 8t² + 2t = 8

–2t³ + 8t² + 2t - 8 = 0

Factorize the expression

(-2t³ + 8t²) + ( 2t -8) = 0

- t² ( 2t - 8) + (2t -8) = 0

We take the similar factor

2t - 8 = 0

2t = 8

t = 8/2

t = 4

But we have that the company produced 4 thousand products for $8 million profit, so we have

= 4/ 4

= 1 thousand

Thus, the quantity of product that would result in the same profit is 1 thousand. Option A

Learn more about polynomial function here:

https://brainly.com/question/7693326

#SPJ1

Answer:

70

Step-by-step explanation:

45+90=135

180-45=45

q=45

45+65=110

180-110=70

70-45=25

p=25

45+25=70

Answer: 70°

Step-by-step explanation:

We know that the sum of all 3 angles in a triangle is 180°. Hence, we can just set all measures to be equal to 180° and solve for the variables.

[tex]p+65+90=180\\p+155=180\\p=25[/tex]

[tex]45+90+q=180\\135+q=180\\q=45[/tex]

[tex]p+q=25+45=70[/tex]

The sum of p and q is 70°.

based on the given results, the coefficient of variation can be found to be 45.54.

first, find the mean:
= (30 + 60 + 90 + 45) / 4

= 56.25

find the standard deviation using a spreadsheet:

= 25.61737691

the coefficient of variation is therefore:

= standard deviation / mean x 100

= 25.61737691 / 56.25 x 100

= 45.54

find out more on the coefficient of variation at https://brainly.com/question/13293164.

#SPJ1

30 Jagged rocks are the same 3 shiny rocks using the exchange rates provided(i.e. option D)

What is an exchange rate?

Exchange rate means the rate at which one item exchanges hands with another, for instance, in this case, 6 jagged rocks are equivalent to 2 smooth pebbles.

6 jagged rocks=2 smooth pebbles

divide both sides by 2

6/2 jagged rocks=2/2 smooth pebbles

3 jagged rocks=1 smooth pebble

We can rewrite as below:

1 jagged rock=1/3 smooth pebble

30jagged rocks=1/3*30 smooth pebbles

30 jagged rocks=10 smooth pebbles

Now we need to convert 10 smooth pebbles to shiny rock equivalence

3 smooth pebbles=1 shiny rock

1 smooth pebble=1/3 shiny rock

10 smooth pebbles=1/3*10 shiny rocks

10 smooth pebbles=3 shiny rocks( even though it is 3.33, but the final answer should be rounded to a whole number)

Read more about exchange rate in the link below:

https://brainly.com/question/2202418

#SPJ1

Answer:

18.75 percent

Step-by-step explanation:

150 / 800 x 100 = 18.75

Answer: The graph of f(x) is horizontally stretched