#1 how is the vertex found?
#2 Use a graphing calculator to sketch the graph of the quadratic equation, and then state the domain and range.

Answer:

equation for the new circle is;

(x - 8)² + y² = 36

Step-by-step explanation:

There are two types of translations and they are translation horizontally and vertically. Combining both of them in the context of this question, to translate a circle 6 units to the right and 4 units up, we take our equation,

(x - 2)² + (y + 4)² = 36 and subtract 6 from the x - term and 4 from the y - term to get the equation of the new circle.

This gives us;

(x - 2 - 6)² + (y + 4 - 4)² = 36

This gives;

(x - 8)² + y² = 36

Step-by-step explanation:

4x - 13 = 3x + 7

4x - 3x = 7 + 13

x = 20

Therefore x = 20

Answer:

Step-by-step explanation:

(2, 3) and (5, 6) are the endpoints of a line segment that is not parallel to either axis and does not intersect either axis.

An ordered pair contains the coordinates of one point in the coordinate system. A point is named by its ordered pair of the form of (x, y). The first number corresponds to the x-coordinate and the second to the y coordinate.

A line segment is a piece or a part of line having two end points.

Since, a line segment is parallel to the either one axis if its one coordinate point is zero, whether it's y or x.

So for not parallel to either axis and does not intersect either axis  we will choose those points which are not zero.

Therefore,

The coordinates of the end points of a line segment that is not parallel to either axis and does not intersect either axis will be (2, 3) and (5, 6).

Similarly, you can use any point using this concept like (7,9) ad (2,3) and many.

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Answer:

y= x/4 - 3

Step-by-step explanation:

Answer:

A = 100π units²

Step-by-step explanation:

To answer this we first find the circumference C = 2πr, and then multiply this C by the height:

C = 2πr, or C = πd.  Here, C = π(10 units).

Then the lateral area of the cylinder is A = C*(10 units), or

A = 10π(10) units², or

A = 100π units²

The lateral surface area of the given right cylinder is 314 square units.

The lateral surface area of a right cylinder is the product of the circumference of the base and the height of the cylinder.

Given, the base diameter(d) of the cylinder is 10 units.

Therefore, the base radius(r) of the cylinder is

[tex]= \frac{10}{2} units\\= 5 units[/tex]

The height(h) of the cylinder is 10 units.

Therefore, the lateral surface area of the cylinder is

= 2πrh square units

[tex]= 2(3.14)(5)(10)[/tex] square units

[tex]= 314[/tex] square units

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Answer:

[tex]\angle ADE =[/tex] [tex]69^\circ[/tex]

Step-by-step explanation:

Given:

[tex]\angle ABD = 32^\circ[/tex]

BA = BD

CB = CD

In [tex]\triangle ABD:[/tex]

BA = BD

We know that in a triangle, angles opposite to equal sides will also be equal.

[tex]\Rightarrow \angle BAD = \angle BDA[/tex]

We know that sum of internal angles of a triangle is equal to [tex]180^\circ[/tex]

[tex]\angle BAD + \angle BDA +\angle ABD=180^\circ\\\Rightarrow \angle BAD + \angle BDA +32=180\\\Rightarrow \angle BAD + \angle BDA = 180 -32\\\Rightarrow \angle BAD + \angle BDA = 148\\\Rightarrow \angle BAD = \angle BDA = \dfrac{148}{2} = 74^\circ[/tex]

Quadrilateral ABCD is cyclic so, sum of opposite angles is equal to [tex]180^\circ[/tex].

[tex]\angle BAD + \angle BCD = 180^\circ\\\Rightarrow 74 + \angle BCD = 180\\\Rightarrow \angle BCD = 180-74 = 106^\circ[/tex]

In [tex]\triangle BCD:[/tex]

BC = CD

We know that in a triangle, angles opposite to equal sides will also be equal.

[tex]\Rightarrow \angle DBC = \angle CDB[/tex]

We know that sum of internal angles of a triangle is equal to [tex]180^\circ[/tex]

[tex]\angle DBC + \angle BCD +\angle CDB=180^\circ\\\Rightarrow \angle DBC + 106 +\angle CDB=180\\\Rightarrow \angle DBC +\angle CDB=180 - 106\\\Rightarrow \angle DBC =\angle CDB=\dfrac{74}{2} = 37^\circ[/tex]

It is given that the line CDE is a straight line, so the sum of angles on one side of point D is [tex]180^\circ[/tex].

[tex]\angle CDB + \angle BDA +\angle ADE = 180^\circ\\\text{Putting values of } \angle CDB \text{ and }\angle BDA:\\\Rightarrow 37 + 74 + \angle ADE = 180\\\Rightarrow \angle ADE = 180 -111\\\Rightarrow \angle ADE = 69^\circ[/tex]

So, the answer is [tex]\angle ADE =[/tex] [tex]69^\circ[/tex]

The size of ∠ADE of the cyclic quadrilateral is;

∠ADE = 53°

We are given;

BA = BD

CB = CD

∠ABD = 32°

Now, ΔABD is an isosceles triangle and since sum of angles in a triangle is 180°, then;

∠ABD + ∠BAD + ∠BDA = 180°

∠BAD + ∠BDA = 180 - 32

∠BAD + ∠BDA = 148°

Since isosceles, then;

∠BAD = ∠BDA = 148/2

∠BAD = ∠BDA = 74°

Now, in cyclic quadrilaterals, opposite angles are supplementary and as such add up to 180°. Quadrilateral ABCD is cyclic and Thus;

∠BAD + ∠BCD = 180°

74 + ∠BCD = 180°

∠BCD = 180 - 74

∠BCD = 106°

ΔBCD is an isosceles triangle and as such;

∠CBD = ∠CDB = 106/2

∠CBD = ∠CDB = 53°

Now, sum of angles on a straight line add up to 180°. Thus;

∠CBD + ∠BDA + ∠ADE = 180°

Plugging in the relevant values gives;

53° + 74° + ∠ADE = 180°

∠ADE = 180 - (53 + 74)

∠ADE = 53°

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[tex]7:3[/tex]

The ratio of 7 to 3.

The ratio as a fraction would be:

[tex]\frac{7}{3}[/tex]

Answer:

40.5

Step-by-step explanation:

3.75 * 2 = 7.50

48 - 7.50 = 40.5

Answer:

three hundred and one

Step-by-step explanation:

This wasn't very clear..

Answer: the number 301 can be written as three hundred one.

Step-by-step explanation: the number 301 can be written as three hundred one. To find a, take the number and move a decimal place to the right one position. Now, to find b, count how many places to the right of the decimal. There are 2 places to the right of the decimal place.

Answer:

3^2 = 9

8^2 = 64

10^2 = 100

Answer:

B

Step-by-step explanation:

its B because the input for every pair has the same output, if the input had different outputs it would be considered not a function. Imagine it like a vending machine, if you were to press 3 on the vending machine you would get whatever 3 was, but if you pressed 3 and you get something else besides whatever 3 is it would be broken. I hope this was helpful, I struggled learning this stuff but now I got it down lol.

Answer:

y = 16x +8

Step-by-step explanation:

Per means for every so and so, and a fee is one-time thing, so 16 would be with x and 8 as the y (intercept)

Answer:

2 adults and 2 senior citizens.

Step-by-step explanation:

There are 8 children, which means we need to take the number that represents the children from the graph which is 4 and multiply it by the 8 children going.

1. 4x8=32

So we have found the total for the 8 children, however there are 4 spots left

We take the total from the #1 and add 2 adults and 2 senior citizens.

32+6+6+3+3=50

We then come to the conclusion of 2 adults and 2 seniors.

Answer:

8, 18 and 36 respectively.

sum=54

1st number=x

2nd number=x+10

3rd number =2(x+10)=2x+20

x+x+10+2x+20=54

put the liketerms together

x+x+2x=54-10-20

4x=24

divide both sides by 4 to get

x=8

Input the other values

Answer:

The ball will hit the ground at 0.968 seconds.

Step-by-step explanation:

Please refer to the attached graph in the answer area.

The given equation of height according to input variable time 't' is:

[tex]h = - 16 t^{2} + 15 ...... (1)[/tex]

h is in feet

t is in seconds

Both the values 't' and 'h' will be positive. (Time and height can never be negative)

To determine the time, at which the ball hits the ground, i.e. the height becomes 0.

Putting value of h = 0 in equation (1)

[tex]0 = - 16 t^{2} + 15 \\\Rightarrow t^{2} = \dfrac{15}{16}\\\Rightarrow t = \sqrt{\dfrac{15}{16}}\\\Rightarrow t = 0.968\ sec[/tex]

Hence, the time at which the ball hits the ground is 0.968 seconds.

Hey!Here is ur answer:

Danielle is wrong cause 'she has included a decimal'.

U might doubt that zero is might not be an integer but it is a neutral integer.

            HOPE IT MAKES UR DAY BETTER!!

Danielle says that her set of numbers are integers the statement is wrong as the set contain decimal number because decimal numbers are not integers, so option C is correct.

All whole numbers and negative numbers are considered integers. This means that if we combine negative numbers with whole numbers, a collection of integers results.

Given:

Danielle says that her set of numbers are integers. Left-brace negative 253, negative 45, negative 0.9, 0, 26 Right-brace,

Write the above phrase in the mathematical form as shown below,

(-253, -45, -0.9, 0, 26)

As we know that integers are whole numbers, they can't be a decimal numbers or a fraction,

Thus, the set of numbers are integers is wrong because it contains decimal numbers.

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Answer:

EF = 34, FG = 25

Step-by-step explanation:

EG is the total of the two smaller segments, EF and FG.

Therefore:

8x-14 + 4x+1 = EG

8x-14 + 4x+1 = 59

Now we can solve this equation.

8x-14 + 4x+1 = 59

12x-13 = 59

12x = 72

x = 6

Now, we can plug in the values of x into the expressions for the lengths of EF and FG:

EF

8x-14

8(6)-14

48-14

= 34

FG

4x+1

4(6)+1

24+1

= 25

Answer:

The number of different combinations of three students that are possible is 35.

Step-by-step explanation:

Given that three out of seven students in the cafeteria line are chosen to answer a survey question.

The number of different combinations of three students that are possible is given as:

7C3 (read as 7 Combination 3)

xCy (x Combination y) is defines as

x!/(x-y)!y!

Where x! is read as x - factorial or factorial-x, and is defined as

x(x-1)(x-2)(x-3)...2×1.

Now,

7C3 = 7!/(7 - 3)!3!

= 7!/4!3!

= (7×6×5×4×3×2×1)/(4×3×2×1)(3×2×1)

= (7×6×5)/(3×2×1)

= 7×5

= 35

Therefore, the number of different combinations of three students that are possible is 35.

There are 35 different combinations to chose 3 students from the 7 students

The given parameters are:

Students, n = 7

Selected , r = 3

The number of different combinations is calculated using:

Combination = nCr

This gives

Combination = 7C3

Using the combination formula, we have:

Combination = 35

Hence, there are 35 different combinations to chose 3 students from the 7 students

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Answer:

Since, company A charge of $423.5 is less than company B charge of $450

Hence,

Company A should be hired to get the better deal.

Step-by-step explanation:

Dimension of room: 11 * 14 foot

Area of rectangle is given by length * width

Thus,

area of room using above formula = 11*14 square foot = 154 square foot

For company A

charge  for 1 square foot = $2.75

Charge for room = charge  for 1 square foot * area of room

                           = 2.75 * 154 = 423.5

Thus, Total money charged by company  A as calculated above is $423.5

Given,

company B charges $450 per room

Since, company A charge of $423.5 is less than company B charge of $450

Hence,

Company A should be hired to get the better deal.

Answer:

Company B

Step-by-step explanation:

Answer:

b 2/7

Step-by-step explanation:

Because there is a 6/21 chance and 2/7=6/21

Answer:

4n + 4

Step-by-step explanation:

Azhar - n years old now.

Last year he was  (n-1).

His mother was 4(n -1) last year.

Now his mother 4(n-1) + 1.

7 years later she will be 4(n - 1)  + 1 + 7 = 4n - 4 + 8 = 4n + 4

Answer:

I THINK its the last one (8 root 10 to the power of 3x)

Step-by-step explanation:

A square root is the same thing as raising something to the 1/2. So the expression we have is (10^1/2)^3/4x.

Due to exponent rules we can multiply to get

10^3/8x which is the same thing as 10^3x/8

The 8 goes to the root and the 3x becomes the exponent

In this exercise we have to have knowledge about the properties of powers, so we have to:

Letter D

Recalling some properties of power, we find that:

Are returning to the exercise and using the properties informed, we find that:

[tex](10^{1/2})^{3/4x}\\10^{3/8x} = 10^{3x/8}[/tex]

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Answer:

2(x+8)(x-5)

Step-by-step explanation:

2x^2 + 6x − 80

Factor out a 2

2(x^2 + 3x − 40)

What 2 numbers multiply to -40 and add to 3

8*-5 = -40

8+-5 = -3

2(x+8)(x-5)

The right answer is 2(x-5)(X+8)

please see the attached picture for full solution

Hope it helps

Good luck on your assignment...

[tex]\text{Solve:}\\\\2x+3=2(x+3)\\\\\text{Use the distributive property:}\\\\2x+3=2x+6\\\\\text{Subtract 2x from both sides}\\\\3=6\\\\\text{Since 3 doesn't equal 6, this equation is not true}\\\text{Therefore, there are no solutions}\\\\\boxed{\text{No solutions}}[/tex]

Hey!!

Solution,

3x^2+6x

take the common,

3x(X+2)

hope it helps

Good luck on your assignment

Answer:

GCF= 16

Step-by-step explanation:

factors of 32= 32, 16, 8, 4, 2, 1

factors of 16= 16, 8, 4, 2, 1

16 is the largest factor both numbers have in common

Answer: 16

Step-by-step explanation:

Answer:

Factored Form:        x = y/2 + 7

Standard Form: 2x - y = 14

Step-by-step explanation:

Answer: D is incorrect

Step-by-step explanation: