Please help!!!!!
The equation of a circle is x² + y² – 8x + 10y + 37 = 0. What is the center and the radius of the circle? Show all your work.

Answer:

The answer options seem to be missing their exponents for the 10 unit.

Answer is:  5.435778 x [tex]10^{6}[/tex]

Step-by-step explanation:

5,435,778

Move the decimal point to the left until it is between the 5 and 4.  Scientific notation means rewriting the number with only one digit to the left of the decimal point and adding the "x [tex]10^{x}[/tex] after to account for the number of positions the decimal point was moved.  

Count the number of places required for the move.

5,435,778     0

543577.8      1

54357.78      2

5435.778      3

543.5778      4

54.35778      5

5.435778      6

Each move reduces the number by a factor of 10.  This means that the final move to make the number 5.435778 required dividing the original number by 10 a total of 6 times.  By multiplying this last number by 10 a total of 6 times, we obtain the original number.  

We could write this as:    (5.435778)*(10)*(10)*(10)*(10)*(10)*(10)

but that defeats the purpose of scientific notation, which is to simplify the number so that it is 1) easier to read, 2) saves printers paper and ink, and 3) reduces transcription errors.

So scientific notation is the process of writing this as:

5.435778 x [tex]10^{6}[/tex]

Answer:

16

Step-by-step explanation:

x^2+16x+16

(x+4)(x+4)

x^2+ 4x+4x+16

Answer:

The answer is C.) 64 on edge.

Answer:

y = -0.5x - 3.5

Explanation:

Take two points: (1, -4), (3, -5)

Find slope:

[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]

[tex]\rightarrow \sf slope \ (m) : \dfrac{-5-(-4)}{3-1} = -\dfrac{1}{2}[/tex]

Equation:

[tex]\sf y- y_1 = m (x - x_1)[/tex]

[tex]\rightarrow \sf y- (-4) = -\dfrac{1}{2} (x -1)[/tex]

[tex]\rightarrow \sf y+ 4 = -\dfrac{1}{2} x + \dfrac{1}{2}[/tex]

[tex]\rightarrow \sf y = -\dfrac{1}{2} x + \dfrac{1}{2} - 4[/tex]

[tex]\rightarrow \sf y = -0.5 x -3.5[/tex]

The formula of a line is:

[tex]f(x) = kx + b[/tex]

k — stands for tg of line angle
b — stands for the y value of a point where the line crosses y axis.

We can see 2 points:
A (1, -4)
B (3, -5)

We can make a system of equations:

[tex]k*1+b=-4\\k*3+b=-5\\[/tex]

From second equation:

[tex]b = -5 - 3k[/tex]

Let's put b in first equation:

[tex]k-5-3k=-4\\-2k=1\\k=- \frac{1}{2}[/tex]

Now we can find b:

[tex]b = -5 -3*- \frac{1}{2}\\b = -5 + 1.5\\b = -3.5[/tex]

The answer is:
-0.5x -3.5

The first and foremost rule for determining if 2 triangles are similar is checking if their angles are the same. Obviously, in this example, the angles are completely different, so the triangles are not similar.

Have a nice day!

And good luck on the assignment!

The missing statements with regard to the mathematical proof are:

It is to be noted that an intercepted arc is the arc that sits inside the inscribed angle. See the attached image.

Thus, it is correct to state that

The missing statements with regard to the mathematical proof are:

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Answer:     [tex]\boldsymbol{2(x-2)(5x+7)}[/tex]

========================================================

Work Shown:

[tex](4x^2-16)+3(2x-4)(x+1)\\\\4(x^2-4)+3*2(x-2)(x+1)\\\\4(x-2)(x+2)+3*2(x-2)(x+1) \ \text{ ... difference of squares rule}\\\\2*2(x-2)(x+2)+3*2(x-2)(x+1)\\\\2(x-2)(2(x+2)+3(x+1))\\\\2(x-2)(2x+4+3x+3)\\\\\boldsymbol{2(x-2)(5x+7)}\\\\[/tex]

The answer has been confirmed with WolframAlpha which is basically a calculator app, but does a ton more than any average calculator.

The CAS (computer algebra system) in the app GeoGebra is another tool I use all the time.

Yet another way to confirm the answer is to graph the original expression and the answer as separate functions. You should find they produce the exact same curve. One curve perfectly overlaps the other. This visually verifies the two expressions are the same thing, just written a different way of course.

Let me know if you have any questions about any step. The basic idea I did was to pull out the GCF and then combine like terms.

Answer:

14

Step-by-step explanation:

you can write an equation to represent the situation:

let x represent the number of lawns he has to mow

then, the monthly profit would be 25x - 100.

in order to make $250, this equation has to be equal to 250:

[tex]25x-100=250[/tex]

now, solve this:

add 100 to both sides

[tex]25x = 350[/tex]

divide both sides by 25

[tex]x = 14[/tex]

he must mow 14 lawns

Answer:

See Below

Step-by-step explanation:

The equation for this scenario would be  ( compounded annually)

6600 ( 1 + .006)^6         = £ 6841.19

Answer:

Brian will have £6841.19 after 6 years.

Step-by-step explanation:

The compound interest formula is:

[tex]A = P( 1 +\frac{r}{100} )^{n}[/tex] ,

where A is the final amount, P is the initial (principal) amount invested (£6600), r is the interest rate (0.6%) and n is the number of years the money is kept for (6 years).

Using the formula:

[tex]A = 6600(1 + \frac{0.6}{100} )^{6}\\\\A = 6841.19[/tex]

The value of CD is 10.7 cm , Option C is the right answer.

A line segment is a line of fixed measure.

From the figure , as Triangle ABC is a right angled triangle

sin 30 degree = (Perpendicular / Hypotenuse)

∠ B = 30° , AB= 10 cm

sin 30 = AC/10

AC = 5 cm.

To determine CD ,

In Triangle ADC ,

tan 25 = Perpendicular / Base

tan 25 = AC / CD

tan 25 = 5 / CD

CD = 5 / 0.4663

CD = 10.7 cm

Therefore the value of CD is 10.7 cm , Option C is the right answer.

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Answer: C

Step-by-step explanation: 10.7 cm

Answer:

y=2x-8

or

f(x)=2x-8

Step-by-step explanation:

To write in slope-intercept form using this information, first use the point slope formula.

y-y1=m(x-x1)

m is slope.

y+4=2(x-2)

Use distributive property on the right side.

y+4=2x-4

Now, subtract 4 from both sides.

y+4-4=2x-4-4

y=2x-8

Written using function notation:

f(x)=2x-8

Hope this helps!

If not, I am sorry.

Answer: $329.8

[tex]3298-(\frac{90}{100} *3298)\\= 3298 - 2968.2\\= 329.8[/tex]

The amount Keiko pays annually is $329.8

To answer the question, we need to know the amount Keiko pays annually

Since Keiko health insurance premium annually is $3298 and if his employer pays 90% of the premium, we want to know how much Keiko pays.

Since the employer pays 90% of the premium, the employer pays x = 90% of $3298

= 0.9 × 3298

= $2968.2

So, the amount Keiko pays annually is y = premium - amount employer pays, x

= $3298 - $2968.2

= $329.8

So, the amount Keiko pays annually is $329.8

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Answer:

Vertex

Vertex are the end points of parabola where it opens up

locus are the group of points

latus rectum is the line parallel to it .

Answer:

a

Step-by-step explanation:

.....................

Answer:

-4

+3

12

-0.5, 12.25

x = -0.5

Step-by-step explanation:

The x intercepts are the values of x when y = 0 ie the roots of the equation
[tex]-x^2 -x +12 = 0[/tex]

or

[tex]x^2 + x - 12 = 0[/tex]

We can re-write the above as:
(x+4) (x-3) = 0
This gives the two roots as x = -4 and x = +3. Leftmost (smallest) root is -4 and rightmost(largest) root is +3

y intercept is when x = 0. Plugging into the original equation, y value at x = 0 is 12

Vertex x value is given by the formula -b/2a where a is the coefficient of x^2 and b the coefficient of x

Here a = -1, b= -1 so vertex x value = - (-1)/(-1).2 = - 1/2 = -0.5

Plugging this value of x into the original function gives the vertex y value
[tex]y = - (0.5^{2}) - (-0.5) + 12\\= -0.25 + 0.5 + 12 = 12.25[/tex]

The line of symmetry is the vertical line corresponding to the vertex x value so line of symmetry is at x = -0.5

The graph of the quadratic function shows these values

An expression is defined as a set of numbers, variables, and mathematical operations. A simplified expression for the length of the garage in terms of x is 2x-19.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

Given the width is x + 15, and the length is 49 less than 2 times the width. Therefore,  a simplified expression for the length of the garage in terms of x is,

Length = 2(x+15) - 49 = 2x + 30 - 49 = 2x-19

Hence,  a simplified expression for the length of the garage in terms of x is 2x-19.

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The Standard form of the equation of circle is (x+21)² + (y+19)² = 849

To transform general form to a standard form, you can use completing the square method or you can convert this equation

x² + y² + Dx + Ey + F = 0 to x² + y² + (-2h)x + (-2k)y + (h²+k²-r²) = 0

Here, Given: x² + y² + 42x + 38y − 47 = 0

Required: Find the values of h, k, and r using this formula

x² + y² + (-2h)x + (-2k)y + (h²+k²-r²) = 0

On comparing we get,

-2h = 42

  h = 21

-2k = 38

 k = 19

-47 = h² + k² - r²

-47 = 21² + 19² - r²

   r² = 849

  r = √849

Thus, the Standard form of the equation of circle is (x+21)² + (y+19)² = 849

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The value of a₄₁ mean the expression in 4th row and 1st column will be 2. Then the correct option is B.

The complete question is attached below.

A matrix is a specific arrangement of items, particularly numbers. A matrix is a row-and-column mathematical structure. The [tex]\rm a_{ij}[/tex] element in a matrix, such as M, refers to the i-th row and j-th column element.

The matrix is given below.

[tex]\begin{bmatrix} 1&3&8&5&\\ 5&4&6&2\\6&7&1&8\\2&9&3&7&\\\end{bmatrix}[/tex]

Then the value of a₄₁ mean the expression in 4th row and 1st column will be 2.

Then the correct option is B.

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Answer:

-12x²-25x+13

Step-by-step explanation:

First open parenthesis.

(3 − 13x − 7x²) − (5x² + 12x − 10)

3 − 13x − 7x² − 5x² - 12x + 10

Now combine like terms.

3 − 13x − 7x² − 5x² - 12x + 10=13-25x-12x²

Now put into standard form, exponents greatest to least.

-12x²-25x+13

Hope this helps!

If not, I am sorry.

Answer:-12x²-25x+13

Step-by-step explanation:

Answer:

 17.14

Step-by-step explanation:

You have the data values {3, 4, 5, 7, 10, 12, 15}

To find the mean, [tex]\frac{3+4+5+7+10+12+15}{7} =8[/tex], yay a whole number, my favorite.

Then, [tex](3-8)^2+(4-8)^2+(5-8)^2+(7-8)^2+(10-8)^2+(12-8)^2+(15-8)^2=120[/tex].

Since n=7, σ^2≈[tex]17.14[/tex]

Answer:

a^12+8

Step-by-step explanation:

let's check all the expressions

1. a^3+18

here 18 is not a perfect cube.

2. a^6+9

here 9 is not a perfect cube.

3. a^9+16

here 16 is not a perfect cube.

4. a^16+8

here 8 is a perfect cube, thus we can write above expression by using laws of exponents as

(a^4)^3+2^3

Thus,  is a sum of cubes.

a^12+8

The reasoning that may be used for finding the measure of m∠12, is the

same side interior angles theorem.

The correct options using the drop-down menu are;

The sum of ∠1, ∠7, and ∠8 is 180°

∠8 and ∠12 are the same side interior angles

The measure of ∠12 must be = 120°

Stuart is not correct

The complete question is given below:-

In the diagram, line x is parallel to line y,m21= 65°, and m27 = 55°. Stuart says that m212 = 60°. His reasoning is shown. Step 1: mZ8 = 60°, because m21+ m27 +m28 = 180º. Step 2:28 212, because 28 and 212 are corresponding angles. Step 3: So, mZ12 = 60° Use the drop-down menus to explain whether or not Stuart is correct.​

The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet.

Given parameters;

Line x ║ line y

m∠1 = 65°, m∠7 = 55°

m∠12 = 60°

Stuart states ∠12 = 60°

The reasoning is presented as follows;

Step 1: m∠8 = 60°, because m∠1 + m∠7 + m∠8 = 180°

Step 2: ∠8 ≅ ∠12, because ∠8 and ∠12 are corresponding angles

Step 3: So, m∠12 = 60°

Using the drop-down menu, we have;

The sum of ∠1, ∠7, and ∠8 is 180° (Sum of angles in the triangle)

∠8 and ∠12 are same side interior angles (by definition)

Same side interior angles are supplementary, therefore;

∠8 +∠12 = 180°

∠12 = 180°  - ∠8

Which gives;

The measure of ∠12 must be 180° - ∠8 = 180° - 60° = 120°

The measure of ∠12 must be = 120°

Stuart is not correct

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The given expression can be simplified as [tex]96x^{9}+3x^{36} +3[/tex].

The given expression is [tex]6x^{9} (7-3).4+3x^{36} +3[/tex].

We need to simplify the given expression.

In mathematics, an algebraic expression is an expression built up from integer constants, variables, and algebraic operations.

First, multiply the numbers 6×4=24.

That is, [tex]24x^{9} (7-3)+3x^{36} +3[/tex].

Next, subtract the numbers 7-3=4.

[tex]24x^{9}.4+3x^{36} +3[/tex]

Finally, multiply the numbers 24×4=96.

[tex]96x^{9}+3x^{36} +3[/tex].

Hence, the given expression can be simplified as [tex]96x^{9}+3x^{36} +3[/tex].

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Therefore the number of two point baskets = 29 and three point baskets = 13.

A set of equation that have a common factor that satisfies them

It is given in the question that

x = the two point baskets

y = the three point baskets

A basketball team scored a total of 97 points in a basketball game

2x +3 y = 97  

They made a total of 42 two-point and three-point baskets.

x +y = 42

y = 42- x

2x + 3(42-x) = 97

On solving we get x = 29

Two point baskets = 29

and y = 13

Three point baskets = 13

Therefore the solution of the given system of equations are two point baskets = 29 and three point baskets = 13.

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Answer:

$.46 or 46 cents per foot

Step-by-step explanation:

3 yards = 4.14

1 yard is 3 feet

3 yards is 9 feet

4.14 ÷ 9 = .46

The number of postage stamps in John’s collection is 27.

We have given that,

John, Johan, and Jonathan collect postage stamps. Johan and Jonathan have the same number of stamps.

The elimination method is the process of eliminating one of the variables in the system of linear equations using the addition or subtraction methods in conjunction with the multiplication or division of coefficients of the variables.

Johan and Jonathan have the same number of stamps.

Let x be the Johan and Jonathan postal stamps.

Let y be the John postal stamps.

Two times Johan’s collection is eleven less than five times John’s collection.

2x = 5y - 11............(1)

Three times Jonathan’s collection is three less than seven times John’s collection.

3x = 7y - 3............(2)

Multiply equation 1 with 3

3(2x = 5y - 11)

⇒ 6x = 15y - 33.........(3)

Multiply equation 2 with 2

2(3x = 7y - 3)

⇒ 6x = 14y - 6.............(4)

Subtract equation 4 from equation 3

⇒ 6x - 6x = 15y - 33 - (14y - 6)

⇒ 0 = y - 27

⇒ y = 27

Hence, the number of postage stamps in John’s collection is 27.

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Answer:

x² + 4x - 21 = 0

x² + 7x - 3x - 21 = 0

x ( x + 7 ) -3 ( x + 7 ) = 0

( x - 3 ) ( x + 7 ) = 0

∴ x - 3 = 0              or              x + 7 = 0

  x = 0 + 3                               x = 0 - 7

  x = 3                                      x = -7

Answer:

1.A - B

1.B - D

1.C - [unsure]

Step-by-step explanation:

Answer:

nr.3 300x0.12=36rolls
nr.4 300x0.21=63 rolls

total number on rolls on nr.3 and nr.4= 99

Step-by-step explanation:

Calculate the probability for nr.3

Always try to get 100%

1=13%

2=5%

3=?

4=21%

5=19%

6=30%

Add all the percentage

1+2+4+5+6= 88%

now calculate the percentage for nr.3

100%-88%=12%

give a estimated total number of times the dice will land on nr.3 or nr.4 after 300 rolls

nr.3 300x0.12=36rolls
nr.4 300x0.21=63 rolls

total number on rolls on nr.3 and nr.4= 99