A horizontal line contains points A, C, B. 2 lines extend from point C. A line extends to point E and another line extends to point D. An arc represents angle A C D.
Ray CE is the angle bisector of AngleACD. Which statement about the figure must be true?

mAngleECD = One-halfmAngleECB
mAngleACE = one-halfmAngleACD
AngleACE Is-congruent-to AngleDCB
AngleECDIs-congruent-to AngleACD

\(x^2 -4x +1 = 0\)

According to the Zero-Product Property, if you have the Quadratic Equation, \((x +a)(x +b) =0\), it's roots will be \(x = -h\) and \(x = -k\).

If we want our roots to be \(2 -\sqrt 3\) and \(\frac{1}{2 -\sqrt 3}\\\), then \(-h = 2 -\sqrt 3\) and \(-k = \frac{1}{2 -\sqrt 3}\\\).

Solving for \(h\):

\(-h = 2 -\sqrt 3 \\ -h \cdot -1 = (2 -\sqrt 3) \cdot -1 \\ h = \sqrt 3 -2\)

Solving for \(k\):

\(-k = \frac{1}{2 -\sqrt 3} \\ -k \cdot -1 = \frac{1}{2 -\sqrt 3} \cdot -1 \\ k = \frac{1}{\sqrt 3 -2}\)

Writing the equation:

\((x +h)(x +k) = 0 \\ (x +(\sqrt 3 -2))(x +\frac{1}{\sqrt 3 -2}) = 0\)

Unsurprisingly, the answer shouldn't be that because it shouldn't be that easy. By that, we have to apply the distributive property.

\((x +(\sqrt 3 -2))(x +\frac{1}{\sqrt 3 -2}) = 0 \\ x(x +(\sqrt 3 -2)) +\frac{1}{\sqrt 3 -2}(x +(\sqrt 3 -2)) = 0 \\ x^2 +(\sqrt 3 -2)x +\frac{1}{\sqrt 3 -2}x +\frac{1}{\sqrt 3 -2}(\sqrt 3 -2) = 0 \\ x^2 +((\sqrt 3 -2) +\frac{1}{\sqrt 3 -2})x +1 = 0 \\ x^2 + (\frac{(\sqrt 3 -2)^2}{\sqrt 3 -2} +\frac{1}{\sqrt 3 -2})x +1 = 0 \\ x^2 +\frac{3 -4\sqrt 3 +4 +1}{\sqrt 3 -2}x +1 = 0 \\ x^2 +\frac{8 -4\sqrt 3}{\sqrt 3 -2}x +1 = 0 \\ x^2 +\frac{-4(\sqrt 3 -2)}{\sqrt 3 -2}x +1 = 0 \\ x^2 -4x +1 = 0\)

The quadratic equation will be y = (x - 2 - √3)[x - 1/(2-√3)].

Let b, c, d, and e be the zeroes of the polynomial. And 'a' be the leading coefficient.

Then the polynomial is given as,

⇒ a(x - b)(x - c)(x - d)(x - e)

The degree of the polynomial will be greater than or equal to the number of zeroes.

Write a quadratic equation if its roots are: 2-√3, and 1/(2-√3) assuming that the leading coefficient a = 1.

Then the equation of the quadratic equation will be

y = 1(x - 2 - √3)[x - 1/(2-√3)]

y = (x - 2 - √3)[x - 1/(2-√3)]

The quadratic equation will be y = (x - 2 - √3)[x - 1/(2-√3)].

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Answer:

I THINK Vertical ( I'm not positive) Goodluck

Answer:

B) Decreasing

It getting smaller every time

Answer:

300

Step-by-step explanation:

30+30+w+x+y+z = 360 (all angles round a point add up to 360)

Simplifying :

60 + w+x+y+z = 360

Subtracting 60 from both sides :

w+x+y+z = 300

Hope this helped and brainliest ?

Sum of entire angle=360°

so

Answer:

x= 20

Step-by-step explanation:

5.70x3x=17.1x

17.1x+4.05x=21.15x

21.15x=423

423/21.15=20

x=20

Hope this is the answer you were looking for.

Step-by-step explanation:

First make an equation.

y=0.0725(499)

This equation would solve for the sales tax.

y=36.1775 or 36.18 because you have to round it l.

To find the total cost, you would do 499+36.18= $537.18

The center of the circle is (h,k) = (-2,-3)

The radius of the circle is r = 2

The standard form of equation of the circle is

\({(x + 2)}^{2} + {(y + 3)}^{2} = 4\)

The general form of equation of the circle is

\( {(x - h)}^{2} + {(y - k)}^{2} = {r}^{2} \)

Here, (h,k) means centre of the circle.

r means radius of the circle.

given that coordinate points of centre of circle is (-2,-3).

Hence the (h,k) = (-2,-3)

Now to find the radius of the circle

The distance from a circle's centre to its circumference is its radius.

The distance from a circle's centre (-2,-3) to its circumference (0,-3) is its radius.

using the formula, distance between the two points to obtain radius.

\(d = \sqrt{(x1 - x2) {}^{2} + {(y1 - y2)}^{2} } \\ r = \sqrt{ {( - 2 - 0)}^{2} + {( - 3 - ( - 3))}^{2} } \\ r = \sqrt{ {( - 2)}^{2} + {( - 3 + 3)}^{2} } \\ r = \sqrt{ {4}^{2} + 0 } \\ r = \sqrt{4} \\ r = 2\)

(h,k) = (-2,-3)

r = 2

subtitue the (h,k) and r values to get the standard form of equation of the circle.

\((x - h) {}^{2} + {(y - k)}^{2} = {r}^{2} \)

\( {(x - ( - 2))}^{2} + {(y - ( - 3))}^{2} = {r}^{2} \)

\( {(x + 2)}^{2} + {(y + 3)}^{2} = 4\)

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The width of the basketball court is 10 meters

The area of the basketball court = \(30\sqrt{20}\) meter square

The length of the basketball court = \(6\sqrt{5}\) meter

The basketball is in rectangular shape. So we have to find the width of the rectangle

The area of the rectangle = The length of the rectangle × The width of the rectangle

The width of the rectangle = The area of the rectangle / The length of the rectangle

Substitute the values in the equation

The width of the rectangular basketball court = \(30\sqrt{20}\) ÷ \(6\sqrt{5}\)

Divide the terms

= 10 meters

Hence, the width of the basketball court is 10 meters

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The maximum amount you can finance is $896.

We are given that;

The monthly gross income = $3,200

Now,

28% of your gross monthly income on your mortgage, including taxes and insurance

The percentage = 28%

3200* 28/100

=32*28

=896

Therefore, by percentage the answer will be $896.

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Answer:

 X values make the ordered pair X comma negative to a solution of the system of inequalities represented by the graph below so let's look at this so we're constraining ourselves to all of the points of the form X comma negative 2 which is another way of saying we're going to constrain ourselves to Y equaling negative 2 if we constrain ourselves to Y equaling negative 2 what do what has to be true of X in order for this point to be a solution too.

Answer:

The answer is 0.372 because you jus dividing it by 10 jus like 0.372 x 10= 3.72 you jus putting the 0 first when dividing .

Step-by-step explanation:

\(let \: x \: be \: the \: length \\ let \: y \: be \: the \: width\)

\(perimeter = 2x + 2y \\ area = xy\)

\(2x + 2y = 80 \\ xy = 380 \\ \\ x + y = 40 \\ xy = 380 \\ \\ x = 40 - y \\ (40 - y)y = 380 \)

\(40y - y {}^{2} = 380 \\ y {}^{2} - 40y + 380 = 0 \\ y {}^{2} - 40y + 400 = 20 \\ (y - 20) {}^{2} = 20 \\ y - 20 =± \sqrt{20} \\ y_{1}=20-√20≈15.52786\\ y_{2}=20+√20≈24.4721\)

The line perpendicular to the equation and has the same y-intercept with another is y = - 4 / 3 x + 4.

The equation of a line can be describe as follows:

y = mx + b

where

Therefore, lines that a perpendicular follows the rule below:

m₁m₂ = -1

Hence,

y + 6 = 3 / 4 (x - 2)

y + 6 = 3 / 4 x - 6 / 4

y =  3 / 4 x - 6 / 4 - 6

y = 3 / 4 x - 30 / 4

y = 3 / 4 x - 15 / 2

Hence,

3 / 4 m₂ = -1

m₂ = - 4 / 3

Therefore,

slope of the line is - 4 / 3

Let's find the y-intercept of the second line

4x + 5y -20 = 0

5y = -4x + 20

y = -4 / 5 x + 4

y-intercept  = 4

Therefore, the line perpendicular to the equation and has the same y-intercept with another is y = - 4 / 3 x + 4.

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Step-by-step explanation:

Given: To make smallest 3-digit number of 825.

To find: The smallest 3-digit number of 825.

Solution: We can make the smallest 3-digit number of 825 by separating the numbers and arranging it to ascending order. The given number is 825. ...

Final answer: The smallest 3-digit number of 825 is 258.

hope it helps

Answer:

258

Step-by-step explanation:

We are given 3 numbers:

8 2 5

And we are asked to find the smallest 3 digit number using those 3 digits above.

To make the smallest number, place the numbers in value from least to greatest:

2 5 8

This is your 3 digit number: 258.

Hope this helps! :)

4×11+1=45

A+B+C=180 60+75+C=180 180_130=c c=45

Answer:

The height of the telephone pole is of 408 inches = 34 ft.

Step-by-step explanation:

Each foot has 12 inches.

A 36 inch post cast a shadow of 24 inches.

This means that the shadow is \(\frac{24}{36} = \frac{2}{3}\) of the real height.

At the same time a telephone pole cast a shadow of 22 ft 8 in.

Each feet has 12 inches, so it has:

22*12 + 8 = 272 in.

2/3 of the real height is 272 in. So

\(\frac{2h}{3} = 272\)

\(h = \frac{272*3}{2}\)

\(h = 408\)

The height of the telephone pole is of 408 inches = 34 ft.

Answer:

40.39

Step-by-step explanation:

The graph of the function \(f(x) = (9/4)x^2\) is a symmetric upward-opening parabola.

Overall, the graph represents a quadratic function with a positive leading coefficient, resulting in an upward-opening parabolic curve. The graph has been attached.

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Answer:

x=3, = -2

Step-by-step explanation:

An isosceles triangle have two congruent sides and two congruent base angles.

If the vertex angle is 44 degrees and the total measure of triangle's interior angles, then the sum of the two base angles is 180 - 44 = 136 degrees.

Therefore, each base angle measures 136/2 = 68 degrees.

The coordinates of point P are (5, -3.5). The equation of the circle is \((x - 5)^2 + (y + 3.5)^2 = 1.5^2\). The equation of KL is y = (-4/3)x + 22/3.

To find the coordinates of point P, we can first find the midpoint of MN, which is the center of the circle. The midpoint formula is given by:

Midpoint = ( (x1 + x2) / 2 , (y1 + y2) / 2 )

Using the coordinates of M(3,-5) and N(7,-2), we can calculate the midpoint:

Midpoint = ( (3 + 7) / 2 , (-5 + -2) / 2 ) = (5, -3.5)

Since the midpoint of MN is the center of the circle, the coordinates of P will be the same as the coordinates of the center, which are (5, -3.5).

i. To determine the equation of the circle in the form of \((x-a)^2\) + \((y-b)^2\) = \(r^2\), we can use the center and any point on the circle. We can use point N(7,-2), which lies on the circle.

The radius of the circle is half the length of PN. Therefore, the radius is given by:

Radius =\(1/2 * \sqrt((7 - 5)^2 + (-2 - (-3.5))^2) = 1.5\)

Substituting the values into the equation, we get:

\((x - 5)^2 + (y + 3.5)^2 = 1.5^2\)

ii. To determine the equation of KL in the form of y = mx + c, we can use the slope of the tangent line.

The slope of KL can be calculated as the negative reciprocal of the slope of the radius line MN. The slope of MN is given by:

m = (y2 - y1) / (x2 - x1) = (-2 - (-3.5)) / (7 - 5) = 1.5 / 2 = 0.75

The negative reciprocal of 0.75 is -4/3, which represents the slope of KL.

Using the point N(7,-2) and the slope -4/3, we can use the point-slope form of a line to find the equation of KL:

y - (-2) = (-4/3)(x - 7)

y + 2 = (-4/3)x + 28/3

y = (-4/3)x + 22/3

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Answer: m=0.6

Step-by-step explanation:

Use the m= y2-y1/x2-x1 formula to calculate slope.

7-4=3

Divided by

3-(-2)=5

3/5= 3/5 or 0.6

Answer:

slope = 3/5

Step-by-step explanation:

slope  = rise/run

---------------------------

y rises from 4 to 7 = 3

x runs from -2 to 3 = 5

slope = 3/5

Answer:

slope intercept: y=3x-2

Step-by-step explanation:

for slope intercept you will put y because that is the intercept we are looking for

from looking at the graph you see the y intercept is -2

next, we will go ahead and found out how many blocks we go up in comparison to how many we go over. We can start at the -2,0 and see that the next time we actually touch a corner (are at a full block) is at the 1,1. We can see that we went up 3 blocks just to go over 1 block. This gives us our slope

Slope intercept form is Y=mX+b

Y is what we are looking for so we will leave it as y

m is the slope: 3/1

x is the x coordinate (we will leave it at x)

b is the y coordinate we found (-2)

fill in the blanks and you get y=3x-2

Answer:

The issue needs you to calculate Claire's airplane's speed in miles per hour.

Claire's airplane travels at a speed of 552 miles per hour.

Given:

414 miles total distance traveled

Time allotted = 3/4 hour

Total distance traveled / Total time = Speed

= 414 miles per hour

414 4/3 = 414

= (414 4 / 3)

1656 / 3 =

equals 552 miles per hour

As a result, Claire's airplane's speed in miles per hour is 552 miles per hour.

Please give brainliest

Have a nice day :D

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Answer:6.25%

Step-by-step explanation:

3.25 / 52 = 0.0625

Aircraft A has 312 seats.

Let's assume that Aircraft B has x seats.

According to the given information, Aircraft A has 105 more seats than Aircraft B. So, the number of seats in Aircraft A can be expressed as x + 105.

The total number of seats in both aircraft is 519, which can be represented by the equation:

x + (x + 105) = 519

Simplifying this equation, we have:

2x + 105 = 519

Subtracting 105 from both sides, we get:

2x = 414

Dividing both sides by 2, we find:

x = 207

Therefore, Aircraft B has 207 seats.

To find the number of seats in Aircraft A, we substitute the value of x back into the expression x + 105:

Aircraft A = 207 + 105 = 312

Hence, Aircraft A has 312 seats.

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Answer:

40 miles per hour

Step-by-step explanation:

After 1 hour the car traveled 40 miles, after 4 hours the car traveled 160 miles. 4 x 40 = 160. Therefore 40mph.

There was 4 dollar of discount on the total amount.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

We are given that Adrian bought a jacket that costs 11 dollars and a scarf that costs 15 dollars.

At the counter, he received a discount. If he only paid 22 dollars total, then

Total cost 11 + 15 = 26

But 26 - 22 = 4

Therefore, the discount was 4 dollar.

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Answer:

84

Step-by-step explanation:

7×[17-5]

7×12

84

hope it will help