What are the vertex, focus, and directrix of the parabola with equation y=x² +8 x+18 ?

Answer:

38.46

Step-by-step explanation:

using the formula A=πr^2, which is the formula of the area of a circle, you get 38.46, when rounded, ehich the diameter is 2 times the radius, we divide 7 by 2z leaving us with r=3.5, so 38.46=3.14(3.5)^2.

Answer:

y = 60.5 or 11

Step-by-step explanation:

If this is intended to be 2y = 121 (2 times y), that would mean the answer would be 60.5.
This is because you’d divide both sides by 2, resulting in y = 60.5.

However, should this be intended as [tex]y^{2}[/tex]= 121, the answer would be 11.

What we do to find the pure equivalent of y is square root both sides as y is squared.

[tex]\sqrt{y^{2} } = \sqrt{121}[/tex]

We come to find that the square root of 121 is 11

[tex]y = 11[/tex]

Answer: S=6x²+25x+14

Step-by-step explanation:

[tex]\displaystyle\\S=S_1+2S_2\\S_1=(2x+7)(x+3)\\S_1=(2x)(x)+(7)(x)+(2x)(3)+(7)(3)\\S_1=2x^2+7x+6x+21\\S_1=2x^2+13x+21\\\\S_2=\frac{(\frac{2x+7)}{2})(4x-2) }{2} \\\\S_2=\frac{(2x+7)(4x-2)}{(2)(2)} \\\\S_2=\frac{(2x)(4x)+(7)(4x)+(2x)(-2)+(7)(-2)}{(2)(2)} \\\\S_2=\frac{8x^2+28x-4x-14}{(2)(2)} \\\\S_2=\frac{8x^2+24x-14}{(2)(2)} \\\\S_2=\frac{(2)(4x^2+12x-7)}{(2)(2)} \\\\S_2=\frac{4x^2+12x-7}{2} \\Hence,\\S=2x^2+13x+21+2*\frac{4x^2+12x-7}{2} \\S=2x^2+13x+21+4x^2+12x-7\\S=6x^2+25x+14[/tex]

Point B's coordinates are (7, -4).

Assume we have two line segment endpoints:

The coordinates are as follows:

So, M is AB's midpoint, and its coordinates are as follows:

Point B's x-coordinate:

Point B's y-coordinate:

Therefore, point B's coordinates are (7, -4).

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If function g(x)= [tex]3(4)^{x}[/tex], then the value of g(2) is 48

The function g(x) = [tex]3(4)^{x}[/tex]

Function is the expression the defines the relationship between between a set of inputs having one output each. The set of all possible input of the function is called domain and set of all possible output of the function is called range

Here the function is  g(x)= [tex]3(4)^{x}[/tex]

The values of x = 2

Substitute the value of x in the function

g(x)= [tex]3(4)^{2}[/tex]

First find the value of [tex]4^{2}[/tex]

g(x)= 3×16

Multiply it

g(x)= 3×16

g(x)=48

The value of g(2) is 48

Hence, If function g(x)= [tex]3(4)^{x}[/tex], then the value of g(2) is 48

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The following procedure mistakes are listed below:

In this question we find six cases of equations with fractions, whose intended procedures are shown, of which we must determine in what step a mistake is done:

Case 1

x / 2 + 3 = 9                       Given

x + 6 = 18                           Compatibility with multiplication / Distributive property / Definition of multiplication

x = 12                                 Compatability with addition / Existence of additive inverse / Modulative property

A mistake was made in the first step. (Misuse of distributive property)

Case 2

(2 · x - 1) / 3 + x = 3             Given

2 · x - 1 + 3 · x = 3               Compatibility with addition / Distributive property

5 · x - 1 = 3                          Commutative, associative and distributive properties / Definition of addition

5 · x = 2                              Compatibility with addition / Commutative, associative and modulative properties / Existence of additive inverse

x = 2 / 5                             Compatibility with multiplication / Existence of multiplicative inverse / Associative and modulative properties / Result

A mistake was made in the first step. (Misuse of distributive property).

Case 3

(5 · x + 5) / 10 + (2 · x + 6) / 10 = 6             Given

5 · x + 5 + 2 · x + 6 = 60                            Compatibility with multiplication / Existence of multiplicative inverse / Commutative, associative and distributive properties

7 · x + 13 = 60                                            Associative, commutative and distributive properties

7 · x = 47                                                    Compatibility with addition / Existence of additive inverse / Commutative, associative and distributive properties

x = 47 / 7                                                    Compatibility with multiplication / Existence of multiplicative inverse / Modulative property / Result

A mistake was made in the first step (Misuse of distributive property and compatibility with multiplication).

Case 4

3 - 5 / (x + 1) = 1                                           Given

3 · (x + 1) - 5 = x + 1                                     Compatibility with multiplication / Distributive, associative and commutative properties

3 · x - 2 = x + 1                                            Distributive property / Definition of subtraction

2 · x = 3                                                      Compatibility with addition / Existence of additive inverse / Commutative, associative and distributive properties

x = 3 / 2                                                      Compatibility with multiplication / Existence of multiplicative inverse / Modulative property / Result

A mistake was made in the first step (Misuse of distributive property and compatibility with multiplication).

Case 5

x / 3 + x = 2                                                  Given

5 · x / 3 = 2                                                   Modulative property / Existence of multiplicative inverse / Definition of division

5 · x = 6                                                        Compatibility with multiplication / Existence of multiplicative inverse / Modulative property / Definition of division

x = 6 / 5                                                        Compatibility with multiplication / Existence of multiplicative inverse / Modulative property / Definition of division / Result

A mistake was made in the first step (Misuse of existence of multiplicative inverse and distributive property).

Case 6

(2 · x + 5) / 5 + 2 = 7                                     Given

2 · x + 7 = 7                                                   Compatibility with multiplication / Distributive, associative and commutative properties

2 · x = 0                                                          Compatibility with addition / Existence of additive inverse / Commutative and associative properties

x = 0                                                               Compatibility with multiplication / Existence of multiplicative inverse / Commutative and associative properties / Cancelative property / Result

A mistake was made in the first step (Misuse of compatibility with addition).

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Answer:

50

Step-by-step explanation:

All my work shown in the screenshot provided. If you have any questions please let me know! Have a wonderful day!

Answer:

b + 12a; use a = 4, and b = 2

=2+12*4

=2+48

=50

The milliliters of blood the volunteers donate is 470 * (32 - n)

The given parameters are

Total = 32

Unqualified = n

The number of qualified volunteers would be

Qualified = 32 - n

A volunteer donates 470 ml

So, we have

Total = 470 * (32 - n)

Hence, the milliliters of blood the volunteers donate is 470 * (32 - n)

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Answer:

g(x + 2) = 10x + 24

g(x) + g(2) = 10x + 28

Step-by-step explanation:

1) If g(x) = 10x + 4, then g(x+2) = 10(x+2) + 4

g(x) = 10x + 20 + 4

g(x + 2) = 10x + 24

2) If g(x) = 10x + 4, then g(x) + g(2) = 10x + 4 + 10(2) + 4

g(x) + g(2) = 10x + 4 + 20 + 4

g(x) + g(2) = 10x + 28

If two coplanar lines are cut by a transversal so that a pair of alternate interior angles are equal then the two lines are parallel.

The four sets of opposing angles that each have their own vertex point, are on different sides of the transversal and are both either internal or exterior are called alternate angles.

In geometry, a transversal line is one that cuts across the plane in two places. It does so at two spots where two lines meet. Many right angles are produced when two transverse lines meet. There are four types of similar angles: matching, alternative interior, alternate exterior, and co-interior.

In geometry, two lines are considered parallel if and only if all pairs of alternative interior angles in any transversal are equal.

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Answer: Substitute the value of the variable into the equation and simplify.

−

408

v

a

2

l

u

t

e

2

−

14

Step-by-step explanation:

Answer: What are two beliefs about the nature of God?

The Psalms say, God is fair and just (Psalm 25:8). Omniscience - God knows everything. Christians believe that God knows every person's inner thoughts as well as knowing all that has happened and all that will happen in the future. Transcendence - God exists outside of our worldly constraints and physical laws.

Step-by-step explanation: hope this helps!!!

Answer:

He is good.

He is forgiving.

He is love.

He is our Shepperd.

He is our judge.

He is our Father.

He Is King.

Answer:

Side, Side, Side. The short cut is SSS

Answer:week 4

Step-by-step explanation:

Answer:

that would be 4/3 or 1 1/3

Step-by-step explanation:

Hey there!

6 ÷ 3 * 2/3

= 6/3 * 2/3

= 2 * 2/3

= 2/1 * 2/3

= 2 * 2 / 1 * 3

= 4/3

= 1 1/3

Therefore, your answer should be:

4/3 or 1 1/3 (they are both equivalent to each other so any should work)

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

For this case, your interest rate will be (. 11 x 100 = 11) 11%. Step 3: Apart from this, you can also calculate your time period involved, principal amount and interest amount paid in a specific time period if you have other inputs available with you. Calculate interest amount paid in a specific time period, I = Prt

Answer:

918.50 in interest over 11 years.

Step-by-step explanation:

Comment

You have to make an assumption here. The assumption is that this is simple interest.

So if the brother pays 10% each year, he is paying

10/100 * 835 each year in interest

10/100 * 835 = 83.50 every year.

There are 11 years, so the total interest paid is 11 * 83.50 = 918.50 dollars in total.. That's more than what he borrowed!

Compare and contrast the process of graphing a radical function using transformations with graphing a quadratic function using transformations.

What distinguishes glide reflection from reflection?

What do the three reflections that make up the glide reflection look like?

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The orientation of the vertices stay same after a reflection.

The orientation of the vertices is nothing but The relative arrangements of points following a transformation or after surrounding a geometric shape are known as orientation. In terms of how the points align, orientation is divided into clockwise and counterclockwise. The points are opposite the original shape when the orientation is reflected. Same orientation denotes that the points are simply a reflection of the original figure and are arranged in exactly the same manner.

The orientation of the vertices stay same after a reflection.

When you translate a figure, you slide it left, right, up, or down. This implies that the coordinates for the vertices of the figure will alter on the coordinate plane.

Apply the same change to each point to graph a.

The variations in a reflection's coordinates can be used to identify it. The figure makes a mirror image of itself when it flips across a line in a reflection. Consider the reflection in the image.

Therefore, The orientation of the vertices stay same after a reflection.

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The lines are not perpendicular because: B. the slopes of the lines are not opposite reciprocals

If two line are perpendicular to each other, they will have slope values that are the opposite reciprocals of each other.

Slope of the red line = change in y / change in x = (-9 - 11)/(0 -(-8))

Slope of the red line = -20/8 = -5/2

Slope of the blue line = (8 - 2)/(8 -(-8))

Slope of the blue line = 6/16 = 3/8

3/8 is not the opposite reciprocal of -5/2. Therefore, the lines are not perpendicular because: B. the slopes of the lines are not opposite reciprocals

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Square root is a factor that, when multiplied by itself, equals the original value.

The values of √5 = 2.236 and √7 = 2.645 then √5  < √7.

Let the values of √5 = 2.236 and √7 = 2.645

then √5  < √7.

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Step-by-step explanation:

calculate the interior angle of the pentagon then do the rest

Two rational expressions that simplify to (x+1) / (x-5) are equals to

(x+1)²/ (x+1) (x-5) and (x+1)(x-5) / (x-5)².

As given in the question,

Simply rational expression is given by (x+1) /(x-5)

Two rational expressions that simplify to given expression are as follow:

        (x+1)²/ (x+1) (x-5).

   2.  Multiply (x-5) to the numerator and denominator of the given rational                      

        expression

        (x+1)(x-5)/ (x-5)².

Therefore, two rational expressions that simplify to (x+1) / (x-5) are equals to  (x+1)²/ (x+1) (x-5) and (x+1)(x-5) / (x-5)².

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Answer:

b) 2(3x+4)

Step-by-step explanation:

Distributive formula: a(b + c)  = ab + ac

Solving steps:

a) 2(3x-4) = 2(3x) + 2(-4) = 6x - 8

b) 2(3x+4) = 2(3x) + 2(4) = 6x + 8

c) 2(4x+6) = 2(4x) + 2(6) = 8x + 12

d) 2(3x+8) = 2(3x) + 2(8) = 6x + 16

Among from all the options, option B is equivalent to 6x + 8.

Answer:

secret hukgjkkkkouugvgv uukkoygjo

Answer:

The opposite of -3/5 is 3/5 because the opposite of negative is a positive. The absolute value of -3/5 is 3/5 because the absolute value of any number is always positive.

a.) 3/5

b.) 3/5

Hope that Helps! :D

The function y=3√-x-3 is graphed only over the domain of {x 1-8 ≤x≤ 8).  is the range of the graph is b) {y  : -5 < x < - 1 }

Range is set of Y values for which the function is define.

So, in order to find the range , we need to find the corresponding y values for given domain.

Put x = -8 in  y = ∛-x -3 then we get,

                y = ∛-x -3

                y = ∛-(-8) -3

                y = ∛8 -3

                y = 2 -3

                 y = - 1

Put x = 8 in  y = ∛-x -3 then we get,

                y = ∛-(8) -3

                y = ∛-8 -3

                y = -2 -3

                 y = - 5

Hence the range of function y = ∛-x -3 over the domain of {x : -8 < x < 8 } is

{y  : -5 < x < - 1 }

correct option is b) {y  : -5 < x < - 1 }

In arithmetic, the range of a function may seek advice from either of  intently associated concepts: The codomain of the feature The image of the function Given two units X and Y, a binary relation f between X and Y is a function if for each x in X there is exactly one y in Y such that f relates x to y.

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Answer: 166 Soft Drinks

Step-by-step explanation:

250 ÷ 1.50 = 166

The distance between A(4,6) and B (9,7) is√26 or 5.1.

Let's consider we have two points (x₁, y₁) and (x₂, y₂) the distance between these two points is given by the formula;

[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]

Given the points A(4,6) and B (9,7)

Now,

x₁ = 4 ,x₂ = 9

y₁ = 6 , y₂ = 7

So,

Distance between them,

[tex]d = \sqrt {\left( {4 - 9 } \right)^2 + \left( {6 - 7 } \right)^2 }[/tex]

d = √26

d = 5.099 and by rounding to the nearest tenth.

5.099 → 5.1

Hence "The distance between A(4,6) and B (9,7) is√26 or 5.1".

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