In the diagram, a circle centered at the origin, a right triangle, and the Pythagorean theorem are used to derive the equation of a circle, x2 + y2 = r2.

On a coordinate plane, circle Q is centered at the origin with radius r. Triangle P Q S is shown. Point Q is at (0, 0) and points P is at (x, y). The length of Q P is r, the length of P S is y, and the length of Q S is x. Angle P S Q is a right angle.

If the center of the circle were moved from the origin to the point (h, k) and point P at (x, y) remains on the edge of the circle, which could represent the equation of the new circle?

(h + x)2 + (k + y)2 = r2
(x – h)2 + (y – k)2 = r2
(k + x)2 + (h + y)2 = r2
(x – k)2 + (y – h)2 = r2 7-foot radius.

The forward differences for this data is 1, 1, 1, 1, 1, 1 (since 10 - 9 = 1, 11 - 10 = 1, etc). Since we only need one iteration of differences, a linear polynomial will fit the data exactly.

The solution for the given equation will be x=7.8873 and x=0.112699.

The polynomial having a degree of two or the maximum power of the variable in a polynomial will be 2 is defined as the quadratic equation and it will cut two intercepts on the graph at the x-axis.

Find the Solution for

9x²−72x+8=0

using the Quadratic Formula where

a = 9, b = -72, and c = 8

[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

[tex]x=\dfrac{(-72)\pm\sqrt{(-72)^2-4(9)(8)}}{2(9)}[/tex]

x=   [tex]\dfrac{72\pm4896}{\sqrt{18}}[/tex]

The discriminant b2−4ac>0

so, there are two real roots. After solving for plus and then minus we will get two values as follows.

x=7.8873

x=0.112699

Therefore the solution for the given equation will be x=7.8873 and x=0.112699.

To know more about quadratic equations follow

https://brainly.com/question/1214333

#SPJ1

The domain of the given graph is [−3, ∞) and the range is (−∞, 4].

We need to find the domain and range of the given graph.

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values that it can take.

We can observe that the graph extends horizontally from −3 to the right without a bound, so the domain is [−3, ∞). The vertical extent of the graph is all range values 4 and below, so the range is (−∞, 4].

Therefore, the domain of the given graph is [−3, ∞) and the range is (−∞, 4].

To learn more about domain and range visit:

https://brainly.com/question/1632425.

#SPJ1

The correct answer is option C which is 230p – 1010 = 650p – 400 – p this expression is same as of 2.3p – 10.1 = 6.5p – 4 – 0.01p.

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

Given expression:-

2.3p – 10.1 = 6.5p – 4 – 0.01p

The same expression will be calculated as:-

Multiply the given expression by 100 we will get our answer.

E = 100 (s 2.3p – 10.1 = 6.5p – 4 – 0.01p )

E = 230p – 1010 = 650p – 400 – p

Therefore  the correct answer is option C which is 230p – 1010 = 650p – 400 – p this expression is same as of 2.3p – 10.1 = 6.5p – 4 – 0.01p.

To know more about expression follow

https://brainly.com/question/723406

#SPJ1

Answer:

The answer is incorrect because the slope formula was used incorrectly in step 1 (parentheses weren't used during the substitution and/or the wrong values were substituted).

y=4x-6

Step-by-step explanation:

The equation we're looking for in slope intercept form looks like [tex]y=mx+b[/tex], where "m" is the slope, "b" is the y-coordinate of the y-intercept, and "x" and "y" are variables that have a certain mathematical relationship through this equation.

To find the equation itself, it usually is easier to find slope before finding the y-intercept.

There are many ways to represent slope (usually represented by the letter m), and while they all mean the same thing, they look different, some examples are shown below:

[tex]m=\frac{rise}{run} =\frac{\text{horizontal change}}{\text{vertical change}}=\frac{\Delta{y}}{\Delta{x}} =\frac{\text{change in }y}{\text{change in }x}=\frac{y_2-y_1}{x_2-x_1}[/tex]

For this problem, since we are given ordered pairs, probably the most useful version will be the last one:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Substituting the values from the ordered pairs, it's important to remember that the ordered pairs are (x,y)... that the first coordinate is an x (and will go into the denominator, or bottom, of the fraction), and the second coordinate is a y (and will go into the numerator, or top of the fraction).

It actually doesn't matter which point we choose to be point 1, and which point we choose to be point 2.  For the least amount of confusion, I choose the first point they gave to be point 1, and the second point they gave to be point 2.

So, [tex]\text{Point 1: } (1,-2)[/tex], and [tex]\text{Point 2: } (3,6)[/tex]

If I could give only one piece of advice, it would be "ANY time you substitute, use parentheses."  You can always simplify later, but for the initial substitution, keep them (this is why the "mistake" happened in this problem, and is the thing we need to fix).

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{(6)-(-2)}{(3)-(1)}[/tex]

Simplifying...

[tex]m=\frac{(6)+(2)}{(3)-(1)}[/tex]

[tex]m=\frac{8}{2}[/tex]

[tex]m=4[/tex]

Thus, the equation we want in slope intercept form, with the new information we know plugged in, looks like this:

[tex]y=(4)x+b\\y=4x+b[/tex]

"b" is still the y-coordinate of the y-intercept (which we don't know yet), and "x" and "y" are variables related through this mathematical equation.

With "m" solved for, we can solve for the "b" by using the relationship in the equation we have so far.

We know that every "x" and "y" ordered pair is an "x" related to the "y" by this specific equation.  Even though we don't know the specific value of "b", we know that the equation must be true for every ordered pair on the line.

While we don't know many associated "y" values and "x" values (for instance, we don't know what the "y" value is when the x is 10, and we don't know what the x value is the "y" is 26), we do know two associations for sure... from the two ordered pairs

[tex]\text{Point 1: } (1,-2)[/tex], and [tex]\text{Point 2: } (3,6)[/tex], so

 [tex]x=1 \text{ is related to } y=-2[/tex], and [tex]x=3 \text{ is related to } y=6[/tex]

... and they're related through this equation that we've almost found!

Now, in our equation, there is only room to associate one x and y value at a time, so we need to pick one known association, and substitute those values in.  Since this equation is supposed to relate the x to the y, it should be true for both points (so, we can try both, and it should work out the same.  If you don't want to try both, if you see one ordered pair that has numbers that look easier, use that one):

Substituting Point 1 to find b

[tex]y=4x+b[/tex]

[tex](-2)=4(1)+b[/tex]

simplifying the right side, 4*1 is 4...

[tex](-2)=4+b[/tex]

subtracting 4 from both sides of the equation, and simplifying the left hand side

[tex]-2-4=b\\-2+-4=b\\-6=b[/tex]

Substituting Point 2 to find b (not necessary, but a good double-check)

[tex]y=4x+b[/tex]

[tex](6)=4(3)+b[/tex]

simplifying the right side, 4*3 is 12...

[tex]6=12+b[/tex]

subtracting 4 from both sides of the equation, and simplifying the left hand side

[tex]6=12+b\\6-12=b\\6+-12=b\\-6=b[/tex]

So, as a verification, we get the same value of b (which we should have, because this equation is supposed to work for every pair of (x,y) that has this relationship, and those were the only two points that we knew that did).

Substituting the value we found for b:

[tex]y=4x+(-6)[/tex]

...and simplifying...

[tex]y=4x-6[/tex]

Answer:

y= x +4

Step-by-step explanation:

The slope-intercept form of an equation is given by y= mx +c, where m is the slope and c is the y-intercept.

Start by finding the slope of the line.

[tex]\boxed{\text{slope}=\frac{y_1-y_2}{x_1-x_2} }[/tex]

Slope

[tex]=\frac{5-3}{1-(-1)}[/tex]

[tex]=\frac{2}{1+1}[/tex]

[tex]=\frac{2}{2}[/tex]

= 1

Substitute m= 1:

y= x+c

Finally, find c by substituting a pair of coordinates.

When x= 1, y= 5,

5= 1 +c

c= 5 -1

c= 4

Thus, the equation of the line is y= x +4.

Additional:

For more questions on slope-intercept form, do check out

For the matrix given , the element a₂₃ is the number at 2nd row and 3 column ,which is 6 , Option B is the correct answer.

It is a table or a rectangular array of numbers or expressions arranged in rows and columns ,

For a Matrix of m x n , m is the no. of rows and n is the no. of column

For the matrix given the element a₂₃ is the number at 2nd row and 3 column ,

which is 6 ,

Therefore Option B is the correct answer.

To know more about Matrix

https://brainly.com/question/9967572

#SPJ1

Answer:

6n-5

Step-by-step explanation:

Some different types of sequences

To find sequence patterns, often the sequences are arithmetic (adding by a constant amount) or geometric (multiplying by a constant amount).  

To test if something is a geometric sequence, find the quotient of (divide) adjacent terms.

To test if something is an arithmetic sequence, find the difference of (subtract) adjacent terms.

Finding the type of our sequence

Note the following:

19-13=6

13-7=6

7-1=6

So, to get each next term, add 6.  However, what is the nth term?

Finding an expression for our sequence

You'll be adding up "n" sixes to get there (expressed with multiplication, because multiplication is shorthand for repeated addition), but we need a starting point so that when n=1, the expression equals 1, and when n=2, the expression equals 7... and so on.  This starting point shifts the "6n" piece of our expression so that it lines up on the sequence.  I'm going to call this starting point "b" for the base that is supporting this sequence.

So the expression will look something like [tex]6n+b[/tex]

Knowing that the expression needs to equal 1 when n=1, we can set up an equation and solve for "b".

[tex]6n+b=n^{\text{th}} \text{ term}\\6(1)+b=(1)\\6+b=1\\(6+b)-6=(1)-6\\b=-5[/tex]

So, the expression for the nth term of the sequence is [tex]6n-5[/tex]

Verifying

To verify that the expression we found is right, we can test our expression for each of the terms we do know:

The first term (n=1) is 1

[tex]6n+b=n^{\text{th}} \text{ term}\\[/tex]

[tex]6(1)-5 \overset{?}{=} (1)[/tex]

[tex]6-5 \overset{?}{=} 1[/tex]

[tex]1 \overset{\checkmark}{=} 1[/tex]

The second term (n=2) is 7

[tex]6n+b=n^{\text{th}} \text{ term}\\[/tex]

[tex]6(2)-5 \overset{?}{=} (7)[/tex]

[tex]12-5 \overset{?}{=} 7[/tex]

[tex]7 \overset{\checkmark}{=} 7[/tex]

The third term (n=3) is 13

[tex]6n+b=n^{\text{th}} \text{ term}\\[/tex]

[tex]6(3)-5 \overset{?}{=} (13)[/tex]

[tex]18-5 \overset{?}{=} 13[/tex]

[tex]13 \overset{\checkmark}{=} 13[/tex]

The fourth term (n=4) is 19

[tex]6n+b=n^{\text{th}} \text{ term}\\[/tex]

[tex]6(4)-5 \overset{?}{=} (19)[/tex]

[tex]24-5 \overset{?}{=} 19[/tex]

[tex]19 \overset{\checkmark}{=} 19[/tex]

When you acquire stock in a firm, you are acquiring a little portion of that company known as a share. The correct option is A.

When you acquire stock in a firm, you are acquiring a little portion of that company known as a share. Investors buy stocks in firms they believe will increase in value. If this occurs, the value of the company's shares rises as well.

For a 70-year-old investor, selling a weak stock at a loss may be a smart move to avoid potential additional future losses.

Hence, the correct option is A.

Learn more about Stocks:

https://brainly.com/question/365124

#SPJ1

Answer: 45

Step-by-step explanation: I used a graphing calculator and input all the equations and all the restraints, and I found that you can’t use the first equation since x has to be less than or equal to -3, and the question calls for x to be -2. So, in the second equation, there’s a point (-2, 16) and in the third equation there’s a point (1, -3). You know you have to use these two points since in the second equation, the restraint only lets you use numbers greater than -3 or less than 0, which cannot be one, and in the third equation, the restraint only lets you use numbers greater than 0, which can’t be -2. I hope that made some sense. So then, with substitution the equation would be 3(16)+(-3) which equals 45. 3(16)=48. 48-3+=45

Answer:

18.66

Step-by-step explanation:

Using the pythagorean theorem:

a^2 + b^2 = c^2

a^2 + 13^2 = 16^2

a^2 + 169 = 256

a^2 = 87

a = 9.33

Since we need to figure out length AC and not just AB, we can multiply our answer by 2:

9.33 x 2 = 18.66

Answer:

  71.32°

Step-by-step explanation:

The measure of angle ADB can be found using the trig relation ...

  Cos = Adjacent/Hypotenuse

__

  cos(ADB) = DB/AD = 13/16

Using the inverse function, ...

  ∠ADB = arccos(13/16) ≈ 35.659°

Arc AC has the same measure as angle ADC, which is double the measure of angle ADB.

  Arc AC = 2×35.659° = 71.318° ≈ 71.32°

The measure of arc AC is about 71.32°.

_____

Additional comment

The length of arc AC is the product of the radius and its radian measure:

  length AC = (16)(71.32π/180) ≈ 19.92 . . . units

1B + 26M - 26K

Answer That!! Hehehehe

Answer: none

Step-by-step explanation:

[tex]\boldsymbol{5x+15=30}[/tex]

Subtract 15 from both sides.

Subtract 15 from 30 to get 15.

Divide both sides by 5.

Divide 15 by 5 to get 3.

Let x=3.

Checked ✅

[tex]\huge \red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]

Answer:

45750 cm²

Step-by-step explanation:

    a = 4 and c = 5

 base length = 3ac²

                      = 3 * 4 * 5 * 5

                     = 300 cm

    height = 5 cm more than the base length

               = 300 + 5

               = 305 cm

      [tex]\sf \boxed{\bf Area \ of \ triangle = \dfrac{1}{2}*base \ length * height}[/tex]

                                    [tex]\sf =\dfrac{1}{2}*300*305\\\\= 150 * 305\\\\= 45750 \ cm^2[/tex]

Answer:

x=10, y=14

Step-by-step explanation:

added in the picture

1) Rotate triangle A 90° clockwise around O

C (5, 6) ⇒ D (1, 2)

2) Move triangle A' 6 spaces to the right

O (1, 6) ⇒ O' (7, 6)

D (1, 2) ⇒ D' (7, 2)

So Shape A ⇒ Shape B

Answer:

A) City A was 5°C and City B was 4°C

Step-by-step explanation:

let temperature of City A be x and City B be y

According to the conditions of the question

4x = 8 + 3y (first temperature)

x - 2y = -3 (second temperature)

x = -3 + 2y

4(x) = (-3 + 2y)×4

4x = -12 + 8y

But it's already given that 4x = 8 + 3y

So,

8 + 3y = -12 + 8y

8 + 12 = 8y - 3y

20 = 5y

y = 20/5

y = 4

That means City B temperature was 4°C

So Option A

If you want you can find x to find City A temperature

Can you please mark Brainliest

Answer:

1/11 = 0.090909090909090909........................

Answer:

Step-by-step explanation:

ore energy entered the Earth system than exited due to the greenhouse effect, solar energy trapping systems like solar panel, etc.

How CO₂ changed the energy in the Earth system due to many reasons:-

Carbon dioxide forces the Earth's energy budget out of balance by absorbing thermal infrared energy radiated by the surface. It absorbs thermal infrared energy with wavelengths in a part of the energy spectrum that other gases, such as water vapor, co₂, etc.

The greenhouse effect also increases energy in the earth's system.

An increase in the amount of carbon dioxide creates an overabundance of greenhouse gases that trap additional heat.

These greenhouse gas emissions have increased the greenhouse effect and caused the earth's surface temperature to rise.

Learn more about the greenhouse effect here: brainly.com/question/19521661

Answer:

4x^2+3x+1

Step-by-step explanation:

4x^2+3x+1 is the answer I hope this helps

The value of the boolean variable x is 0

The boolean equation is given as:

x . 1 = 0

The above means that:

x and 1 = 0

The law of the and operator is that;

The output is 0 if both inputs are different.

One of the inputs is 1.

So, the other input is 0

Hence, the value of x is 0

Read more about boolean variable at:

https://brainly.com/question/18089222

#SPJ11

Answer:

k=7,y=2.33 and y=k/x^2

Step-by-step explanation:

y=k/x^2

7=k/1

k=7

y=k/x^2

y=7/3

y=2.33

hope it helpful

Answer:

The coordinates of A' are (-1,-3) , B' are (-2,-2) , C' are (-4,-3).

Step-by-step explanation:

The answer choice which explains whether the function is a direct variation or not is; This function represents a direct variation because it passes through the origin and has a constant rate of change of $5 per hour.

It follows from the task content that the function passes through the origin and hence, if the function was represents as a linear function, it's y-intercept would be zero.

Furthermore, the slope, otherwise termed it's rate of chage is constant and is evaluated as; $5 per hour. Hence, the aforementioned form the basis for the classification of the function as a direct variation.

Read more on variation;

https://brainly.com/question/6499629

#SPJ1

By using trigonometric rules and expressions we find that the expression [tex]x = \sqrt{\frac{1-\cos 170^{\circ}}{2} }[/tex] is equivalent to single trigonometric expression x = sin 85°.

In this question we must apply trigonometric rules to simplify a given number, in which case we can take advantage of this expression:

[tex]\sin \frac{\theta}{2} = \sqrt{\frac{1 - \cos \theta}{2} }[/tex]

If we know that [tex]x = \sqrt{\frac{1-\cos 170^{\circ}}{2} }[/tex], then the rewritten expression is:

x = sin 85°

By using trigonometric rules and expressions we find that the expression [tex]x = \sqrt{\frac{1-\cos 170^{\circ}}{2} }[/tex] is equivalent to single trigonometric expression x = sin 85°.

To learn more on trigonometric expressions: https://brainly.com/question/10083069

#SPJ1

Answer:

253=232×k

Step-by-step explanation:

please mark me as brainlest