Answer the following questions that follow up with the picture.

The coordinates of the pint of tangency of the two circles is(_,_)

The radius of the circle with the center N has a length of ___ units.
The radius of the circle with center P has a length of ___ units.
The diameter of the circle with center N has a length of ___ units.

You define complex numbers as the reals, i, as usually defined, and their linear combinations using real coefficients, then,

The reals are complex numbers, even if you haven’t fully defined their properties.

If you define complex numbers as the form (a,b) with and a, b are real numbers, then you can say that each real number a is isomorphic with that complex number,

if b=0 once you define their properties.

A complex number can be visually represented as a pair of numbers (a, b) forming a vector on a diagram called an Argand diagram, representing the complex plane.

Of course, (0,1) will be i. You’ll have to define the multiplication rule, etc.

In actual usage, we gloss over the distinction, and real numbers are complex numbers with no imaginary part.

To learn more about the complex number visit:

https://brainly.com/question/10662770

#SPJ1

Answer:

x= 1.5, y= 3.5

or x= -5, y= 10

Step-by-step explanation:

Let's solve by substitution.

Label the two equations:

y= 2x² +6x -10 -----(1)

y= -x +5 -----(2)

Substitute (2) into (1):

2x² +6x -10= -x +5

2x² +6x +x -10 -5= 0

Simplify:

2x² +7x -15= 0

Factorise:

(2x -3)(x +5)= 0

2x -3= 0 or x +5= 0

2x= 3 or x= -5

x= 1.5

Now that we have found the value of x, we can find the value of y through substitution.

Substitute into (2):

y= -1.5 +5 or y= -(-5) +5

y= 3.5 or y= 10

Supplementary:

Do check out the following should you wish to learn more about solving quadratic equations!

Answer: 112

Step-by-step explanation:

area of the parallelogram is base times height

Answer: 5.3

Step-by-step explanation:

[tex]12.6-(5.1+2.2)\\\\=12.6-7.3\\\\=5.3[/tex]

Answer:

Step-by-step explanation:

***I hope this helps and the explanation is helpful!***

Step-by-step explanation:

5 x 0.7 = 3.5

Answer:

[tex]\displaystyle{y-1=5(x+6)}[/tex]

Step-by-step explanation:

A point-slope form is written in the equation of  [tex]\displaystyle{y-y_1=m(x-x_1)}[/tex]. Where [tex]\displaystyle{(x_1,y_1)}[/tex] is a coordinate point and [tex]\displaystyle{m}[/tex] is slope.

The definition of parallel is to both lines have same slope. The given line equation has slope of 5. Therefore, we can write the equation in point-slope form as:

[tex]\displaystyle{y-y_1=5(x-x_1)}[/tex]

Next, we are also given the point p(-6,1). Substitute [tex]\displaystyle{x_1}[/tex] = -6 and [tex]\displaystyle{y_1}[/tex] = 1 in:

[tex]\displaystyle{y-1=5[x-(-6)]}\\\\\displaystyle{y-1=5(x+6)}[/tex]

Hence, the line equation that’s parallel to y = 5x - 4 and passes through a point (-6,1) is y - 1 = 5(x + 6)

Answer:

y - 1 = 5 ( x + 6 )

Step-by-step explanation:

       Here,

          m ⇒ slope

    y = 5x - 4 ← equation of the old line

         Now it is clear to us that,

         m ⇒ slope of the line ⇒ 5

         c  ⇒ y-intercept ⇒ -4

                 That is, m = 5

                   y - y₁ = m ( x - x₁ ).

        m = slope

           ( -6 , 1 ) ⇔ ( x₁ , y₁ )

        Let us solve this now

         y - y₁ = m ( x - x₁ )

         y - 1 = 5 ( x - ( -6) )

         y - 1 = 5 ( x + 6 )

                y - 1 = 5 ( x + 6 )

The coordinate of the vertex is; (h, k) = (3, -5)

The final equation of the parabola is; y = 5(x - 3)² - 5

The vertex is the coordinate of the crest or trough of the curve. Now, in the given graph, we only have a Trough which is the lowest point of the graph.

The coordinate of the vertex is; (h, k) = (3, -5)

2) Since the general equation is;

y = a(x - h)² + k

We will have;

y = a(x - 3)² - 5

At x = 2, y = 0. Thus;

0 = a(2 - 3)² - 5

a - 5 = 0

a = 5

3) The final equation of the parabola is;

y = 5(x - 3)² - 5

Read more about Parabola Vertex at; https://brainly.com/question/17987697

#SPJ1

The verbal description matches option D; Gene earns 2% interest after depositing $150 into his account.

The function is a type of relation, or rule, that maps one input to specific single output.

The function given;

f(x) = 0.02 x +150

Gene earns 2% interest after depositing $150 into his account.

Thus, this verbal description matches the function given as it represents, the total account balance Gene.

Hence, Option D is the correct answer.

To know more about Function;

brainly.com/question/12431044

#SPJ1

Answer: Give me the full answer and i will be able to answer it

Step-by-step explanation:

BC = EF

the side has to lie between the two angles

Answer:

k

Step-by-step explanation:

Answer:

The answer is option c

Answer:

The answer is B.

The statement that apply is that the volume of the cone is One-third the volume of the cylinder

volume of a cone = 1 / 3 πr²h

where

Volume of a cylinder = πr²h

where

The cone and the cylinder has the same base and height. Therefore, the radius and height are the same .

volume of the cylinder = 84π

Therefore, the volume of the cone is One-third the volume of the cylinder.

learn more on volume here: https://brainly.com/question/16031618

#SPJ1

Answer:

x=1

Step-by-step explanation:

Original Equation:

[tex]-5(5x+3)-5x+1= -44[/tex]

Distribute the -5

[tex]-25x-15-5x+1= -44[/tex]

Add like terms

[tex]-30x-14=-44[/tex]

Add 14 to both sides

[tex]-30x=-30[/tex]

Divide both sides by -30

[tex]x=1[/tex]

Answer:

x = 1

Step-by-step explanation:

-5(5x+3) - 5x + 1 = -44

(-5*5x -5*3) - 5x + 1 = -44

(-25x - 15) - 5x + 1 = -44

-25x - 5x - 15 + 1 = -44

-30x - 14 = -44

-30x = -44 + 14

-30x = -30

x = -30/-30

x = 1

Check:

-5(/5*1) + 3) - 5*1 + 1 = -44

-5(5+3) - 5 + 1 = -44

-5*8 - 5 + 1 = -44

-40 - 5 + 1 = -44

-45 + 1 = -44

Answer: [tex]\frac{\sqrt{65}}{4}[/tex]

Step-by-step explanation:

By the Pythagorean theorem, the unknown side has length

[tex]\sqrt{9^{2}-4^{2}}=\sqrt{65}[/tex]

Therefore,

[tex]\tan \theta=\boxed{\frac{\sqrt{65}}{4}}[/tex]

The measure of [tex]\theta[/tex] is 68 degrees

The complete question is in the attached image

The value of [tex]\theta[/tex] is calculate using the following cosine function

[tex]\cos(\theta) = \frac 38[/tex]

Evaluate the quotient'

[tex]\cos(\theta) = 0.375[/tex]

Take the arc cos of both sides

[tex]\theta = \cos^{-1}(0.375)[/tex]

Evaluate the arc cos

[tex]\theta = 67.97[/tex]

Approximate to the nearest degree

[tex]\theta = 68[/tex]

Hence, the measure of [tex]\theta[/tex] is 68 degrees

Read more about right triangles at:

https://brainly.com/question/2437195

#SPJ1

Answer:

5. 68 degrees :)

6. 55 degrees :)

Step-by-step explanation:

5.

A flat line is 180 degrees so we subtract to find x :)

Lets do that now :)

180 - 112 = 68

x = 68 degrees

6.

X will be the same as 55 degrees.

All lines are tipped the same what so that is why it is 55 degrees :)

Have an amazing day!!

Please rate and mark brainliest!!

The function that is graphed is f(x) = |x - 3| + 1

The parent absolute function is:

f(x) = |x|

From the graph, we have the following transformations:

This is represented as:

(x, y) = (x - 3, y + 1)

So, we have:

f(x) = |x - 3| + 1

Hence, the function that is graphed is f(x) = |x - 3| + 1

Read more about function transformation at:

https://brainly.com/question/13810353

#SPJ1

By critically observing the basketball hoop (see attachment), we can logically deduce that the basket's height from Lisa's horizontal sight is the same as the length of the shortest leg of the right-angle triangle:

Shortest leg = 8.5 - 5

Shortest leg = 3.5 feet.

In Geometry, the sum of all the angles in a triangle is equal to 180°:

x + y + z = 180

x + y + 90 = 180

x + y = 180 - 90

x + y = 90° (complementary angle).

Therefore, the angle of depression is complementary to the angle of elevation.

Also, you should use the inverse tangent function because the lengths of the opposite and adjacent sides of the right-angle triangle are known.

Angle of depression = tan⁻¹(Opposite/Adjacent)

Angle of depression = tan⁻¹(3.5/10)

Angle of depression = 19.29° ≈ 19°.

Learn more about right-angle triangle here: https://brainly.com/question/9449953

#SPJ1

Answer:

3.5

congruent

inverse tangent

19

Step-by-step explanation:

Answer:

$2

Step-by-step explanation:

If the total is $12, and he spent $6 on a notebook, he has $6 left for his 3 pencils. If each pencil costs the same, he paid $2 for each pencil.

Answer:

5 (rounded)

Step-by-step explanation:

by using the Pythagorean theorem you can calculate b

[tex]a^{2} + b^{2} = c^{2}[/tex]

here we have a and c

first lets times it by themselves

16 + b^2 = 36

now lets isolate b^2

b^2 = 36-16

= 20

now we have to get rid of the exponent ^2

b = 4.47....

rounding it would be 5!

Hope that helps :>

The weight of 45 bushels of soya beans is 1.2247 Tons

An equation is an expression that shows the relationship between two or more numbers and variables.

The conversion factor of soyabeans is 36.744 (bu/t). Hence:

45 bushels = 45 bushels / 36.744 (bu/t) = 1.2247 Tons

The weight of 45 bushels of soya beans is 1.2247 Tons

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Answer: y=[tex]\sqrt[3]{x}[/tex]-4

Step-by-step explanation:

The length of GH is 15.

GH = IG

GH = 5x - 10

IG = 3x

5x - 10 = 3x

5x - 3x = 10

2x = 10

x = 10/2 = 5

GH = 5x - 10

= 5 * 5 - 10 = 25 - 10

GH = 15

<ABD = < DBC

<ABD = 10y°

<DBC = (8y + 4)°

10y° = (8y + 4)°

10y = 8y + 4

10y - 8y = 4

2y = 4

y = 4/2 = 2

The value of y is 2

<DBE = <DBC + <CBE

<DBC = 10y°

<CBE = <DBC = 10y°

y = 2

<DBC = <CBE = 10y° = 10*2° = 20°

<DBE = 20° + 20° = 40°

Learn more about angles on:

https://brainly.com/question/25716982

#SPJ1

The unit rate for every 1 student out of school, there are 10 students going to school is 10 students going to school per 1 student out of school

An equation is an expression that shows the relationship between two or more numbers and variables.

A unit rate is a ratio between two different units with a denominator of one.

If For every 1 student out of school, there are 10 students going to school, hence:

Unit rate = 10/1 = 10 students going to school per 1 student out of school

The unit rate for every 1 student out of school, there are 10 students going to school is 10 students going to school per 1 student out of school

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Answer:

-x^3-5x^2+10x-4

Step-by-step explanation:

(−x + 1) (x ^ 2 + 6x − 4) = (-x)(x ^ 2 + 6x − 4) + 1(x ^ 2 + 6x − 4)

= -x^3-6x^2+4x+x^2+6x-4 = -x^3-5x^2+10x-4