Find the length of side xx in simplest radical form with a rational denominator.
30°
60°
x
4

Answer:

(x-8)² + (y-5)² = 400

Step-by-step explanation:

general equation of a circle : (x-h)² + (y-k)² = r²

where (h,k) is at center and r = radius

here we are given the center as well as a point on the circle

first we will need to identify the radius by  finding the distance between the center and the point on the circle using using the distance formula ( we know this is the radius because the radius is a line that goes on the center of the circle to any point on the circle )

Identifying the radius using the distance formula

Distance formula : [tex]d=\sqrt{(x_2-x1)^2+(y_2-y_1)^2}[/tex]

where the x and y values are derived from the two given points

Given points are (8,5) and (-4,21)

Assigning variables we get (x1,y1) = (8,5) , so x1 = 8 and y1 = 5

and (x2,y2) = (-4,21) so x2 = -4 and y2 = 21

Plugging this into the formula we get

[tex]d=\sqrt{(-4-8)^2+(21-5)^2}[/tex]

==> subtract values inside of parenthesis

[tex]d=\sqrt{(-12)^2+(16)^2}[/tex]

==> evaluate exponents

[tex]d = \sqrt{144+256}[/tex]

==> add 144 and 256

[tex]d=\sqrt{400}[/tex]

==> take the square root of 400

[tex]d=20[/tex]

so the radius is 400

Finding the equation of the circle

again we have the general equation of a circle as (x-h)² + (y-k)² = r²

where (h,k) is at center and r = radius

here the center is at (8,5) and the radius is 20

so (h,k) = (8,5) so h = 8 and k = 5 and radius is 20 so r = 20

plugging these values into the general equation of a circle we get

(x-8)² + (y-5)² = 20²

==> evaluate exponent

(x-8)² + (y-5)² = 400

and we are done!

For more validation check the attached image :)

Answer:

27 5/8

Step-by-step explanation:

12 5/8 + 2(7 1/2) = 12 5/8 + 15 = 27 5/8

The amount of space needed by John will be 27⁵/₈ inches.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that John must mount a box which is 12⁵/₈ inches wide. He wants to leave 7¹/₂ inches on each side of the box.

The amount of space needed by John will be calculated as below:-

E = 12⁵/₈ + 2(7¹/₂)

E = 12⁵/₈ + 15

E = 27⁵/₈ Inches

Hence, the amount of space needed by John will be 27⁵/₈ inches.

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Answer:

a=79, b=101

Step-by-step explanation:

the consecutive angles are supplementary angles, and the opposite ones are congruent.

Answer:

Probably A?

Step-by-step explanation:

Answer:

[tex]\sf x^2 + \boxed{\sf 5} \ x - \boxed{\sf 14}[/tex]

Explanation:

Given zero's of a polynomial function:

Answer:

y = x² + 5x - 14

Step-by-step explanation:

If the zeros of a polynomial are 2 and -7, then:

⇒ x = 2  ⇒  (x - 2) = 0

⇒ x = -7  ⇒  (x + 7) = 0

Therefore, we can write the polynomial as:

y = a(x - 2)(x + 7)   where a is some constant

As the first term of the given polynomial is x², we can say that its coefficient is 1.  Therefore, a = 1

⇒ y = 1(x - 2)(x + 7)

⇒ y = (x - 2)(x + 7)

To write the polynomial in standard form  ax² + bx + c

simply expand the brackets:

⇒ y = (x - 2)(x + 7)

⇒ y = x² + 7x - 2x - 14

⇒ y = x² + 5x - 14

Answer:

ex:  25+25 (square numbers) = 50 (not a perfect square)

Step-by-step explanation:

all in the example

Answer:

x=0; x=-2

Step-by-step explanation:

so first you do (x+2)^2 which is x^2+2x+4

4x^2 +8x +16 = 16

Subtract 16 from both sides

4x^2 +8x = 0

factor out 4x:

4x(x+2) = 0

Answer:

below

Step-by-step explanation:

Mathematically there cant be 150 student though since 85 + 70 = 155  

Answer:

A. -18

Step-by-step explanation:

» Application

To find the value of f(-2), we have to plug in the value of -2 for each x in the equation.

» Solution

Thus, f(-2) = A. -18.

Answer:

56.52 cm

Step-by-step explanation:

The path to convert coal into electricity is Boiler to Turbine to Generator to Power lines, the correct option is A.

Those fuels which have originated from decayed plants and animals over a long period of time are called Fossil fuels.

The correct path energy follows when coal or oil is burnt to produce electricity is

When coal is fired the heat is used to convert water into steam in a boiler.

The steam at high pressure is sent to turbines.

The steam spins the generator to produce electricity which is then sent to the power lines.

Therefore, the correct path is mentioned in option A.

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Answer:

1/6

Step-by-step explanation:

cube = 1 in 6

coin = 1 in 2

3 or 5 = 2 in 6

1 in 3

1 in 3 x 1 in 2 = 1 in 6

1/6

The probability that the next person will purchase no costume is 7/166 if the 7 visitors purchased no costume.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words the probability is the number that shows the happening of the event.

Total number of visitors = 7+143+16 = 166

Number of visitors purchased no costume = 7

The probability that the next person will purchase no costume:

= 7/166

Thus, the probability that the next person will purchase no costume is 7/166 if the 7 visitors purchased no costume.

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Answer:

There is 166.1 grams of sugar in 5.5 yards of licoroce

Step-by-step explanation:

If 1.5 yards of licorice = 45.3 grams of sugar

5.5 yards of licorice = x

Cross multiply:

45.3grams * 5.5yards / 1.5yards

= 249.15 grams/yards / 1.5yards

= 166.1 grams of sugar

C) without an external energy source, fiction stops the car

Sure hope this helps you

Answer:

C

Step-by-step explanation:

The friction stops the car because there is no more energy pushing the car forward. Also this should be in the science section.

Answer:

y alpha 1 /x

y = k / x

( y = ? , x = 2, k = 5 )

y = 5 /2

y = 2.5

C. Two-thirds vote

To help with checks and balances, the consitution allows congress to override a presidential veto with a two-thirds vote; also known as a constitutional majority.

Intial Vote

When Congress first votes on a normal bill (not a consitutional change) all that is required is a simple majority. A simple majority means more than 50 percent.

Presidential Veto

Just because something is passed by Congress does not mean that it will be a law. The President still has to sign the bill into law. However, the President has the option to veto the bill.

Overriding a Veto

If a bill is overridden, Congress can move to override the veto. If they want to override the veto, there must be a 2/3's majority that agrees to pass the bill again.

Additionally, when overriding a veto any votes that are not affirmative, this includes abstentions and absent voters, are considered opposing votes. For example, if 2 congressmen did not show up to vote, then their votes would automatically be counted against the bill.

Answer:

<-8,-12,-9>

Step-by-step explanation:

got it right on edge

The value of a, b, c, h, k, and foci coordinates are 4, 3, 5, 2, -1, and (5, 0) and (-5, 0) respectively.

It's a two-dimensional geometry curve with two components that are both symmetric. In other words, the number of points in two-dimensional geometry that have a constant difference between them and two fixed points in the plane can be defined.

We have given a hyperbola equation:

[tex]\rm \dfrac{(x-2)^2}{16}-\dfrac{(y+1)^2}{9}=1[/tex]

We know the standard form of a hyperbola is given:

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

After comparing:

a² = 16 ⇒ a = 4

b² = 9 ⇒ b = 3

[tex]\rm c^2 = a^2+b^2\\\\\rm c^2 = 16+9 \Rightarrow 25[/tex]

c = 5

(h, k) is the center of the hyperbola:

(h, k) = (2, -1)

Vertices will be (a, 0) and (-a, 0):

(4, 0) and (-4,0)

Foci will be at (c, 0) and (-c, 0):

(5, 0) and (-5, 0)

Thus, the value of a, b, c, h, k, and foci coordinates are 4, 3, 5, 2, -1, and (5, 0) and (-5, 0) respectively.

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The value of a=4 , b=3 , k=-1 and h=2 for the hyperbola having the equation

[tex]\dfrac{(x-2)^2}{16}-\dfrac{(y+1)^2}{9}=1[/tex]

A hyperbola is the symmetrical open curve formed by the combination of a circular cone with a plane at a minimum angle with its axis than the side of the cone.

Here the general form of the equation of hyperbola will be:

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

And we have a equation given as:

[tex]\dfrac{(x-2)^2}{16}-\dfrac{(y+1)^2}{9}=1[/tex]

By comparing the equation we the solutions

[tex]a=4 , b=3 , k=-1 \ and\ h=2[/tex]

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Answer:

Sin(45) = [tex]\frac{\sqrt{2} }{2}[/tex] , therefore Letter E is the answer ..

Step-by-step explanation:

Sin(45) = [tex]\frac{\sqrt{2} }{2}[/tex] , therefore Letter E is the answer ..

Answer:

take sin 45

Step-by-step explanation:

Answer:

B. Shows relationship between events, explains how one thing happens as a result of another

Answer:

I will guess C because a matrix can only have 3 pivot positions.

Answer:

4/8

Step-by-step explanation:

Answer:

The Correct answer is D. 312 Cubic inches.

Hope this helps you!!

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Answer:

The Correct answer is D. 312 Cubic inches.

Hope this helps you!!

Please Mark me Brainleast!!

Answer:

16

Step-by-step explanation:

the answer is 16

Recall the series expansion of the exponential function,

[tex]\displaystyle e^x = \sum_{n=0}^\infty \frac{x^n}{n!}[/tex]

By comparison, the given sum is [tex]e^x[/tex] evaluated at x = ln(2), so

[tex]\displaystyle 1 + \ln(2) + \frac{\ln^2(2)}{2!} + \cdots = \sum_{n=0}^\infty \frac{\ln^n(2)}{n!} = e^{\ln(2)} = \boxed{2}[/tex]

[tex]\text{Given that,}~f(x) = 3x^2 -15~~ \text{and}~~ g(x) = 1- \dfrac 23 x\\\\(f \circ g)(-6)\\\\=f(g(-6))\\\\=f\left(1- \dfrac 23\cdot (-6)\right)\\ \\=f(1+4)\\\\=f(5)\\\\=3(5)^2 -15\\\\=75 -15\\\\=60\\\\\text{Hence the answer is B.}[/tex]

F(2) means the value of x is 2. Replace x with 2 then solve for b:

3(2) + b = 12

6 + b = 12

Subtract 6 from both sides

B = 6

answer: b = 6

Answer:

x = 18

Step-by-step explanation:

the square on the angle means the angle is 90 degrees

4x + x = 90

5x = 90

x = 18

Answer:

[tex]\boxed{\bf x = 1 {8}^{o} }[/tex]

Step-by-step explanation:

In the given figure....

[tex]\boxed{\bf m\angle BOA = 9 {0}^{o}} [/tex]

[tex]\bf m\angle BOA + m\angle COA = 9 {0}^{o} [/tex]

Combine like terms. 4x + x = 5x

Divide both sides by 5.