4. Write an equation of the circle that has a diameter with endpoints (12, 3) and

(-18, 3). (Lesson 6-4)

The linear equation f(x) is  4x - 10 and the quadratic equation f(k) is -5/2k^2 + 4k - 1 for the two given points.

The linear equation can be found using the slope-intercept form (y = mx + b), where m is the slope of the line and b is the y-intercept. To find the slope (m) we can use the two points given:

m = (y2 - y1) / (x2 - x1) = (18 - 2) / (7 - 3) = 16/4 = 4

The y-intercept (b) can be found using one of the points and the slope:

b = y - mx = 2 - 4(3) = -10

So the linear equation in standard form is:

f(x) = 4x - 10

For the quadratic equation, we know that it's in the form of y = ax^2 + bx + c. We have 2 points, so we have 2 equations with 2 unknowns. We can use this information to solve for a, b and c.

Let's (3,2) point 1 and (7,18) point 2.

f(k) = ak^2 + bk + c....(1)

point 1: f(3) = 2 = 9a + 3b + c...(2)

point 2: f(7) = 18 = 49a + 7b + c...(3)

Now we have 2 equations and 3 unknowns.

using theirs first equation and substitute it in the second and third equation

18 = 49a + 7b + c

2 = 9a + 3b + c

c = 2 - 9a - 3b

18 = 49a + 7b + (2 - 9a - 3b)

18 = 49a + 7b + 2 - 9a - 3b

18 = 40a + 4b + 2

16 = 40a + 4b

now this equation is used to solve for a and b

b = (16 - 40a) / 4

so a,b and c are

a = -5/2

b = 4

c = -1

so the quadratic equation in standard form is:

f(k) = -5/2k^2 + 4k - 1

4x - 10 is the linear equation f(x)  and -5/2k^2 + 4k - 1 is the quadratic equation f(k) for the two given points.

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9514 1404 393

Answer:

  $125

Step-by-step explanation:

For x = 140, the function definition for x ≥ 100 is used.

p(140) = 95 +0.75(140 -100) = 95 +30 = 125

The customer will owe $125 for items with a value of $140.

Answer:

A)  The function has a maximum value of 1

Step-by-step explanation:

Since the parabola opens downward, then its maximum would be 1 and its minimum would be -∞

In "Gilgamesh: A New English Version," several pieces of evidence support the conclusion that Gilgamesh is an epic hero.

Gilgamesh is the king of Uruk: He is the main character of the story, and his actions and deeds are the focus of the epic. As a king, he holds a position of power and authority and is responsible for the well-being of his people.

Gilgamesh undertakes a quest: He embarks on a journey to find immortality after the death of his dear friend Enkidu. His quest takes him to the ends of the earth and shows his determination and courage.

Gilgamesh faces challenges and monsters: During his journey, Gilgamesh faces several challenges and monsters, such as the giant Humbaba and the Bull of Heaven. His bravery in overcoming these obstacles demonstrates his heroic qualities.

Gilgamesh has supernatural strength and abilities: He is two-thirds god and one-third man, which means he is gifted with supernatural strength, speed and endurance. He is able to perform deeds that would be impossible for a mortal.

Gilgamesh demonstrates wisdom and self-awareness: Throughout his journey, Gilgamesh comes to understand the limitations of human life and the importance of living a meaningful existence. He demonstrates wisdom and self-awareness which are the hallmark of a true epic hero.

These examples of Gilgamesh's character and actions support the conclusion that he is an epic hero and his story is an epic.

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Answer:

0.44

Step-by-step explanation:

Sin∠ D= EC/DC

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

hope it helps...

have a great day!!

Answer:

sin D = 0.44

Step-by-step explanation:

sin D = opp/hyp

The side opp D must be CE  since the side opp D cannot contain D

opp = CE = 39

The hypotenuse must be DC since it's the longest

hyp = DC = 89

sin D = 39/89

sin D = 0.4382022472

To the nearest hundredth

sin D = 0.44

Geoff is therefore 15 years old.Rearranging terms in an equation to get the solution is known as "solving by rearranging.

Age of Myrka = 3x + Age of Geoff

3x + 3 = 48

3x = 48 - 3

3x = 45 x = 15

Geoff is therefore 15 years old.

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Step-by-step explanation:

(-2,5), refer to the step-by-step. Feel free to comment any questions you may have!

Step-by-step explanation:

Given the system of equation, \left \{ {{x+6y=28} \atop {2x-3y=-19}} \right.{

2x−3y=−19

x+6y=28

, solve by elimination.

\left \{ {{-2(x+6y=28)} \atop {2x-3y=-19}} \right.{

2x−3y=−19

−2(x+6y=28)

, multiply the top equation by -2.

We get, \left \{ {{-2x-12y=-56} \atop {2x-3y=-19}} \right.{

2x−3y=−19

−2x−12y=−56

+ {{-2x-12y=-56} \atop {2x-3y=-19}} \right. , add the equations together.

We get, -15y=75−15y=75 , we just eliminated the variable, x, we can now solve this equation for y.

-15y=-75 = > y=\frac{-75}{-15}−15y=−75=>y=

−15

−75

, y=\frac{75}{15} = > y=5y=

15

75

=>y=5

We just found the value y, which is y=5. Now we can take this value and plug it into y for either of the two original equations and solve for x. I will take the top equation...

x+6y=28 = > x+6(5)=28 = > x+30=28x+6y=28=>x+6(5)=28=>x+30=28 , subtract the value, 30, from both sides. We get, x=-2x=−2 .

We found the value x, x=-2.

Thus the solution to the given system of equations is (-2,5).

Answer:

Comparing given eqn of line i.e.y=4x + 1 with

y=mx+c,we get,

m=4

We know that parallel lines have same value for m and the line parallel to y=4x+1 passes through the point (-2,-5) i.e (x1,y1)

Now,using point slope formula,we get

y-(-5)=4{x-(-2)}

or,y+5=4(X+2)

or,y+5=4x+8

or,y=4x+8-5

:.y=4x+3 is the req eqn for line parallel to y=4x+1

*mark me brainliest!!!!!!!

Answer:3/4 is the answer

Step-by-step explanation:

Answer:(s)

1/4  -  7/1  =  - 27/4  

Decimal:   - 6.75

Mixed number:  - 6 3/4

Step-by-step explanation:

1/4  -  7/1  =  - 27/4  or - 6.75 or  - 6 3/4

LCM:   4, 1  = 4

Adjust Fraction Based On LCM:

1/4 - 28/4

Apply The Fraction Rule:

a/c - b/c  =  a - b/c

1 - 28/4

Subtract the numbers:

1  -  28   =  - 27

             =  -27/4

Apply Fraction Rule:

- a/b  =  - a/b

Thus:

1/4 - 7/1  =  - 27/4  

Decimal:   - 6.75

Mixed Number Form  - 6 3/4

I hope that helps you!!!

The product of (2x-3y)(2x+3y) is 4x^2-9y^2

Product= (2x-3y)(2x+3y)

Let the product of (2x-3y)(2x+3y) be P

P=2x(2x+3y)-3y(2x+3y)

P= 2x(2x)+2x(3y)-3y(2x)-3y(3y) {using distributive property of multiplication}

This property states that  multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together. The multiplication of (a-b)(a+b) is equal to a^2 - b^2. This result is used as an identity.

P= 4x^2 +6xy - 6xy -9y^2

solving 6xy-6xy=0

P= 4x^2 - 9y^2

4x^2-9y^2 is the product of (2x-3y)(2x+3y).

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Answer:

6 seconds left, 10 seconds total.

Step-by-step explanation:

40 / 4 = 10

Increases by 10% each second

60% left, so 60 / 10 = 6

Answer:

6 seconds left, 10 seconds total.

Step-by-step explanation:

40 / 4 = 10

Increases by 10% each second

60% left, so 60 / 10 = 6

Step-by-step explanation:

The measure of the angle ∠SUT will be 30°. Then the correct option is C.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The exterior angle of a triangle is almost always equal to the addition of the interior and opposing interior angles. The term "external angle property" refers to this feature.

The measure of the angle ∠SUT is calculated as,

∠SUT + ∠UTS = ∠JST

∠SUT + 80° = 110°

∠SUT = 110° - 80°

∠SUT = 30°

The measure of the angle ∠SUT will be 30°. Then the correct option is C.

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Answer:

1. Y=-2x+3

2. Y=3x+2/3

I'm sorry I can't get them all but I know these are right

Answer:

x = 72

Step-by-step explanation:

36 - x = -36

*subtract 36 from both sides*

-x = -72

*divide by -1*

x = 72

Answer:

0 is the answer of the equation

Q 1 ans supplementary

Q2 ans congurent

Q3 ans neithee

Answer:

can you tell me a little bit more?

Answer:

[tex](2,-6)[/tex]

Step-by-step explanation:

[tex]x^2-4x+y+10=0[/tex]

[tex]y=x^2+4x-10[/tex]

[tex]y=-(x^2-4x)-10[/tex]

[tex]=-(x^2-4x+4)-10+4[/tex]

[tex]=-(x-2)^2-6[/tex]

[tex]y=-(x-2)^2+(-6)[/tex]

[tex]h=2 ~and~ k=-6[/tex]

So, vertex → (2,-6)

[tex]------------[/tex]

hope it helps..

have a great day!!

Answer:

1a) 77 + 84v

1b) 70d + 10m

2a) 96 + 40r

2b) 6p + 8

3a) 27a + 24

3b) 11a + 90

Hope that helps! :)

_Aphrodite

Step-by-step explanation:

Answer:

Mathaway/algerba is a good way to figure out these problems

Step-by-step explanation:

i use it all the time haha

No, the sides of a right triangle do not include 8, 15, and 17. The sides of a right triangle must follow the Pythagorean theorem, so the sum of the squares of the two shorter sides must equal the square of the longest side. 8² + 15² does not equal 1

8² + 15² = 64 + 225 = 289

17² = 289

Therefore, 8, 15, and 17 are not the sides of a right triangle.

The Pythagorean theorem is an important mathematical concept used to determine if three numbers form the sides of a right triangle. This theorem states that the sum of the squares of the two shorter sides must equal the square of the longest side. In the case of 8, 15, and 17, 8² + 15² does not equal 17², so it is not a right triangle. To test this, we can calculate 8² + 15² = 289, and then 17² = 289. Since the two values are not equal, we can conclude that 8, 15, and 17 are not the sides of a right triangle.

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Answer:

Step-by-step explanation:

Answer:

Don't have enough infromation to answer that.

Step-by-step explanation:

Answer:

-1

Step-by-step explanation:

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

Given few inequalities and some operations are performed on them

For first inequality:

=> 4 < 7

Multiply both sides by 3, then by 2, then by 4, then by 9

=> 4 *3 * 2 * 4 * 9 < 7  *3 * 2 * 4 * 9

=> 864 < 1512

there is no change in the inequality sign and it is still true.

For the second inequality:

=>11 > -2

Add 3 to both sides, then add 3, then add (-4)

=> 11 +3 + 3 + (-4) > -2 + 3+3 + (-4)

=> 13 > 0

there is no change in the inequality sign and it is still true.

For the third inequality:

=> -2 ≤ -2

Subtract 6 from both sides, then 8, and then 2

=> -2 -6 -8 -2 ≤  -2 -6 -8 -2

=>  -18 ≤ -18

there is no change in the inequality sign and it is still true.

For the fourth inequality:

=> -4 < 8

Divide both sides by -4

=> -4 / -4 < 8 / -4

Since, after dividing or multiplying on both sides by a negative sign, inequality changes its sign

=> 1 > -2

Divide both sides by -2

=> -1/2 < 1

there are two times a change in the inequality sign and it is still true.

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Answer:

No, the point isn't in the shaded area

Step-by-step explanation:

On solving the provided question, we can say that coordinates of the point in the unit circle  S = ( cos [tex]3\pi /2[/tex] , sin [tex]3\pi /2[/tex] ) => S= ( 0 , -1 )

Every point in the plane that is a certain distance away from a certain point forms a circle (center). It is, thus, a curve formed by points moving in the plane at a fixed distance from a point. At every angle, it is also rotationally symmetric about the center. A circle is a closed two-dimensional object where every pair of points in the plane are equally spaced out from the "center." A line that goes through the circle creates a specular symmetry line. At every angle, it is also rotationally symmetric about the center.

S = (0, -1 )

coordinates of the point in the unit circle

S = ( cos [tex]3\pi /2[/tex] , sin [tex]3\pi /2[/tex] )

S= ( 0 , -1 )

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Answer: The relationship between the x-coordinates of the first and second bus stop is that the x-coordinate of the second bus stop is 4 units greater than the x-coordinate of the first bus stop.

The relationship between the y-coordinates of the first and second bus stop is that the y-coordinate of the second bus stop is 2 units greater than the y-coordinate of the first bus stop.

Step-by-step explanation:

The result of (x-3)(4x+2) using FOIL method is 4x^2 -6x +2x -6.

The FOIL method is a technique used to multiply two binomials. It stands for "First, Outer, Inner, Last" and follows these steps:

First: Multiply the first term of the first binomial by the first term of the second binomial

Outer: Multiply the first term of the first binomial by the second term of the second binomial

Inner: Multiply the second term of the first binomial by the first term of the second binomial

Last: Multiply the second term of the first binomial by the second term of the second binomial

Applying FOIL method to (x-3)(4x+2) we get:

First: 4x * x = 4x^2

Outer: 4x * -3 = -12x

Inner: -3 * 4x = -12x

Last: -3 * 2 = -6

So the result of (x-3)(4x+2) is 4x^2 -12x -12x -6 = 4x^2 -24x -6.

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