If f(x) and g(x) are polynomial functions, what is the domain of f(x) + g(x) ?

[tex]\bf{9x > -36 }[/tex]

Divide both sides by 9.

[tex]\bf{\dfrac{9x}{9} > \dfrac{-36}{9} }[/tex]

[tex]\bf{x > -4 \ \ \to \ \ \ Answer}[/tex]

Answer:

{x | x > -4}

Step-by-step explanation:

{a few basic reminders:  > means greater than; < means less than; ≥ means greater than or equal to; ≤ means less than or equal to

for example: 4 < 7

                     4 ≤ 4

                     4 ≥ 3

                     4 > 3}

When we see an inequality, such as 9x > -36, we are trying to figure out what possible numbers x can be to make this statement true.

We can either use logic / words (see below), or in a much more efficient manner, we can solve this algebraically [as though it were an equation]

So, like when working with any other variable, we want to isolate x:
9x > -36

÷9    ÷9

   x > -4  

just in case none of this makes sense (it can be quite confusing at first),

here's how we can think about it logically

we know that whatever multiplies with 9 must be more than -36, and because -4 multiples with 9 to be exactly -36, any number greater than -4 also will be greater than -36

meaning that x must be more than -4, which we express as: x > -4

So, the solution set (solution set means set of possible solutions) is

{x | x > -4}

hope this helps!! have a lovely day :)

Answer:

The linear equation for the line which passes through the points given as (1,5) and (4,11), is written in the point-slope form as y=2x+3.

Step-by-step explanation:

A condition is given that a line passes through the points whose coordinates are (1,5) and (4,11).

It is asked to find the linear equation which satisfies the given condition.

Step 1 of 2

Determine the slope of the line.

The points through which the line passes are given as (1,5) and (4,11). Next, the formula for the slope is given as,

[tex]$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$[/tex]

Substitute 11&5 for [tex]$y_{2}$[/tex] and [tex]$y_{1}$[/tex] respectively, and [tex]$4 \& 1$[/tex] for [tex]$x_{2}$[/tex] and [tex]$x_{1}$[/tex] respectively in the above formula. Then simplify to get the slope as follows,

[tex]$$\begin{aligned}m &=\frac{11-5}{4-1} \\m &=\frac{6}{3} \\m &=2\end{aligned}$$[/tex]

Step 2 of 2

Write the linear equation in point-slope form.

A linear equation in point slope form is given as,

[tex]$$y-y_{1}=m\left(x-x_{1}\right)$$[/tex]

Substitute 2 for [tex]$m, 1$[/tex] for [tex]$x_{1}$[/tex], and 5 for [tex]$y_{1}$[/tex] in the above equation and simplify using the distributive property as follows,

[tex]$$\begin{aligned}&y-5=2(x-1) \\&y-5=2 x-2 \\&y=2 x-2+5 \\&y=2 x+3\end{aligned}$$[/tex]

This is the required linear equation.

Hello,

[tex]3(3x + 5y)[/tex]

if x = 1 and y = 5 :

[tex]3(3 \times 1 + 5 \times 5) = 3(3 + 25) = 3 \times 28 = 84[/tex]

⊰__________________________________________________________⊱

Answer:

Step-by-step explanation:

[tex]\large\displaystyle\text{$\begin{gathered} \sf {Substitute \ the \ values-\!\!:} \\ \sf{3(3*1+5*5)} \\ \sf{3(3+25)=3(28)=84} \end{gathered}$}}[/tex]

[tex]\pmb{\tt{done \ !!}}[/tex]

⊱__________________________________________________________⊰

Answer:

2300

Step-by-step explanation:

53%=1219

100=X

X=[(1219)(100)]/53=2300

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Required percentage value = a

total value = b

Percentage = a/b x 100

53% = 1219

100% = 2300

The total number of seats in the theater is 2300

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Number of seats filled by all the students = 1219

1219 is 53% of the total seats in the theater.

This means,

53% = 1219

Now,

Total number of seats in the theater = 100%

53% = 1219

Multiply 100/53 on both sides.

100/53 x 53% = 100/53 x 1219

100% = 2300

Thus,

The total number of seats in the theater is 2300

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Step-by-step explanation:

3y-13>-9

3y-13<-1

3y>4

3y<12

12>3y>4

y=2,3,4

Answer:

[tex]\left[ \dfrac{4}{3},4 \right][/tex]

Step-by-step explanation:

Inequality 1

[tex]3y-13\geq -9[/tex]

Add 13 to both sides:

[tex]\implies 3y-13+13\geq -9+13[/tex]

[tex]\implies 3y\geq 4[/tex]

Divide both sides by 3:

[tex]\implies \dfrac{3y}{3}\geq \dfrac{4}{3}[/tex]

[tex]\implies y \geq \dfrac{4}{3}[/tex]

Therefore, y is equal to or bigger than 4/3.

Inequality 2

[tex]3y-13\leq -1[/tex]

Add 13 to both sides:

[tex]\implies 3y-13+13\leq -1+13[/tex]

[tex]\implies 3y\leq 12[/tex]

Divide both sides by 3:

[tex]\implies \dfrac{3y}{3}\leq \dfrac{12}{3}[/tex]

[tex]\implies y\leq 4[/tex]

Therefore, y is equal to or smaller than 4.

Therefore, the solution to the inequalities in interval notation is:

[tex]\left[ \dfrac{4}{3},4 \right][/tex]

The number is 5 if two increased by a number is a dozen. In other words, the correct answer is 5 by solving equations.

Step 1: Write the given information as an equation. "Two increased by a number" can be represented as 2 + x, where x is the unknown number.

Step 2: Translate "Two increased by a number is a dozen" into an equation. The word "a dozen" refers to the number 12.

[tex]2 + x = 12.[/tex]

Step 3: Solve the equation for x. To isolate x, subtract 2 from both sides of the equation:

[tex]2 + x - 2 = 12 - 2.[/tex]

This simplifies to x = 10.

Step 4: Verify the solution. Substitute the value of x back into the original equation:

2 + 10 = 12.

This equation is true, so x = 10 is indeed the solution.

Therefore, the number is 10.

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Answer:

Step-by-step explanation:

    Cost =  fixed rate + number of guests* cost per meal.

Let  x be the number of guests.

a)  Pin hall:

       Fixed rate = $ 500

      Cost per meal = $15

      Cost = 500 + 15*x

    [tex]\sf \boxed{\bf C = 500 + 15x}[/tex]

Bloom place:

       Fixed rate = $350

   Cost per meal = $18

         [tex]\sf \boxed{\bf C = 350 +18x}[/tex]

b) Given the charges are same at both halls.

  350 + 18x = 500 + 15x

             18x = 500 + 15x - 350

              18x = 150 + 15x

        18x -15x = 150

                3x  = 150

                  x = 150 ÷ 3

                  x = 50

When the number of guests is 50, the cost is same at both the halls

Hello!

Forming the equations :

y = mx + b

m = rate per hour

b = fixed charge

[tex]\fbox {y = 15x + 500}[/tex]

[tex]\fbox {y = 18x + 350}[/tex]

Solving for number of guests at which cost is the same :

15x + 500 = 18x + 350

3x = 150

x = 25 guests

Hello,

f(x) = 1/9x + 2 ⇔ y = 1/9x + 2 ⇔ 1/9x = y - 2 ⇔ x = 9(y - 2)

                                                                            x = 9y - 18

⇒ f⁻¹(x) = 9x - 18

[tex]\frak{Hi!}[/tex]

[tex]\orange\hspace{300pt}\above3[/tex]

                         If we have a function, we can find its inverse if we do the

                         following-:

                        [tex]\tiny\bullet[/tex] replace f(x) with y.

                        [tex]\boldsymbol{\sf{y=\displaystyle\frac{1}{9}x+2}}[/tex]

                        [tex]\tiny\bullet[/tex] switch the places of x and y

                        [tex]\boldsymbol{\sf{x=\displaystyle\frac{1}{9}y+2}}}[/tex]

                         [tex]\bullet[/tex] solve for y

                        [tex]\boldsymbol{\sf{x\times9=\frac{1}{9}y\times9+2\times9}}[/tex]

                         [tex]\boldsymbol{\sf{9x=y+18}}[/tex]

                         [tex]\boldsymbol{\sf{-y=-9x+18}}[/tex]

                          [tex]\boldsymbol{\sf{y=9x-18}}}[/tex]

                        [tex]\boldsymbol{\sf{f(x)^{-1}=9x+18}}[/tex]

[tex]\orange\hspace{300pt}\above3[/tex]

Answer:

Step-by-step explanation:

[tex] \bf \cfrac{AB}{DE} = \cfrac{BC}{EF} [/tex]

So, ∆ABC ～ ∆DEF by SAS.

The number line that represents the solution set of the inequality can be seen below.

Here we have the inequality:

15 > n ≥ 3

Then we need to have a open dot at the number 15 on the number line, and then a line that goes to the left until the value 3, where we must have a closed dot (because n = 3 is a solution of the inequality). The number line can be seen below.

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The recursive function of a ball with a 67% rebound is a(n) = 0.67a(n-1)

The rebound is given as:

r = 67%

Express as decimal

r = 0.67

So, the recursive function is:

a(n) = Previous height * r

This gives

a(n) = a(n-1) * 0.67

Evaluate

a(n) = 0.67a(n-1)

Hence, the recursive function is a(n) = 0.67a(n-1)

Basketball

The initial height is given as:

a(1) = 54

So, we have:

a(2) = 0.67 * 54 = 36.18

a(3) = 0.67 * 36.18 = 24.24

Tennis ball

The initial height is given as:

a(1) = 58

So, we have:

a(2) = 0.67 * 58 = 38.86

a(3) = 0.67 * 38.86 = 26.04

Table-tennis ball

The initial height is given as:

a(1) = 26

So, we have:

a(2) = 0.67 * 26 = 17.42

a(3) = 0.67 * 17.42 = 11.67

Hence, the complete table is:

Bounce               n             Height

First bounce       1               Basketball: 54 inches

                                           Tennis ball: 58 inches

                                           Table tennis ball: 26 inches

Second bounce   2            Basketball: 36.18 inches

                                           Tennis ball: 38.86 inches

                                           Table tennis ball: 17.42 inches

Third bounce       3            Basketball: 24.24 inches

                                           Tennis ball: 26.04 inches

                                           Table tennis ball: 11.67 inches

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Missing part of the question

A ball is dropped such that each successive bounce is 67% of the previous bounce's height.

Applying the midsegment theorem, the perimeter of triangle JKL is: D. 19.

The perimeter of triangle JKL = JK + JL + KL

Find the lengths of JK, JL, and KL using the triangle midsegment theorem.

JK = 2(3.5) = 7 units

JL = 2(4) = 8 units

KL = 2(2) = 4 units.

Perimeter of triangle JKL = 7 + 8 + 4

Perimeter of triangle JKL = 19 units.

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Answer:  D. 19

Step-by-step explanation:  Answer is correct on Edge. Trust Me! :)

MO, MN, and ON are the midsegments of △JKL.

Triangle M N O is inside triangle J K L. Points M, N, and O are the midpoints of sides J K, J L, and K L.

Q: What is the perimeter of △JKL?  

A:  D. 19

Answer:

Mercury - 0.39 and 0.242

Venus - 0.72 and 0.616

Earth - 1 and 1

Mars - 1.52 and 1.88

Uranus - 19.18 and 84.00

Neptune - 30.06 and 165.00

The distance between Mercury, Venus, Earth, Mars, Uranus, and Neptune from the sun is 0.39, 0.72, 1, 1.52, 19.18, and 30.06 respectively.

The length along a line or line segment between two points on the line or line segment.

Distance=√(x₂-x₁)²+(y₂-y₁)²

The distance between each planet from the sun will be given as

Mercury - 0.39 and 0.242

Venus - 0.72 and 0.616

Earth - 1 and 1

Mars - 1.52 and 1.88

Uranus - 19.18 and 84.00

Neptune - 30.06 and 165.00

Hence, the distance between Mercury, Venus, Earth, Mars, Uranus, and Neptune from the sun is 0.39, 0.72, 1, 1.52, 19.18, and 30.06 respectively.

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The value of the given expression is 1/16

Given the exponential function below as shown;

(1/2)^4

This means the product of 1/2 in 4 places. This can be expressed as;

(1/2)^4 = 1/2 * 1/2 * 1/2 *1/2

(1/2)^4 = 1/4 * 1/4

(1/2)^4 =1/16

Hence the value of the given expression is 1/16

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Answer:

K-A would make a circle because it goes across

Answer:

729

Step-by-step explanation:

I have not done this in some time so the terms may be a bit unconventional, but they work. The key to this is multiplying by -3.

1*(-3) = -3

-3*(-3) = 9

And so on.

1, -3, 9, -27, 81, -243, 729

By critically observing the two triangles, we can deduce that they: B. might not be congruent.

In Geometry, two triangles are said to be similar when the ratio of their corresponding sides are equal in magnitude and their corresponding angles are congruent.

By critically observing the two triangles, we can logically deduce that the three angles of both triangles are congruent in accordance with AAA similarity postulate:

However, AAA isn't a congruence postulate and as such all similar triangles might not be congruent.

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Answer:

w = 12

l = 18

Step-by-step explanation:

Hello!

Recall the perimeter of a rectangle is twice the sum of the length and the width of the rectangle.

Let w be the width. The length is 6 less than twice the width. That means, l is 2w - 6.

Plug it into the formula and solve, given that P is 60.

The width is 12 inches. We can plug in 12 for 2w - 6 to find the length.

The length is 18 inches.

The width is 12 inches, and the length is 18 inches.

Answer:

I didnt know but i worked it out and searched it up and i got this

Step-by-step explanation:

(2a+4c-5b+2a+5b-4c)

The probability that more than 210 people will pass in front of his store is 0.2272.

In the question, we are given that a coffee shop owner wants to examine the number of customers who pass in front of his store in the morning from 7:00 A.M to 7:30 A.M.

We are asked to find the probability that more than 210 people will pass in front of his store if the mean number of customers during this time is 210.

This experiment follows a Poisson Distribution with a mean (λ) = 200, and the random variable X = 210.

To find the probability that more than 210 people will pass in front of his store, we will find P(X > 200).

P(X > 200) = 1 - P(X ≤ 210).

Now, P(X ≤ 210) can be calculated using the function poissoncdf(200,210) on the calculator.

As to find the probability of a Poisson Distribution P(X ≤ x), for a mean = λ, we use the calculator function poissoncdf(λ,x).

The value of poissoncdf(200,210) = 0.77271.

Thus, the value of P(X > 210) = 1 - 0.77271 = 0.22729.

Thus, the probability that more than 210 people will pass in front of his store is 0.2272.

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Answer:

6.2 oz is lower

Step-by-step explanation:

An equation is formed of two equal expressions. The value of the constant of proportionality is 0.41.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given there exists a proportional relationship between the number of juice bottles bought, j, and the total cost in dollars and cents. Therefore,

c ∝ j

c = kj

As the relation is represented by the equation c=0.41j. Therefore, the value of the constant of proportionality is 0.41.

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Answer:

18

Step-by-step explanation:

Entire length =105 + 82 =187

subtract 22

subtract 96

subtract 51              result =18

The transformed function is:

[tex]g(x) = ( (x + 1)/3 - 2)^2 + 2*( (x + 1)/3 - 2)[/tex]

The parent function is:

[tex]f(x) = x^2 + 2x[/tex]

Here the axis of symmetry is at:

[tex]x = -2/2*1 = -1[/tex]

So first we need to apply a horizontal compression by a factor of 3 with respect to the line x = -1.

Here we can, for the moment, define a new variable that is zero when x = -1, let's define:

z = x + 1.

x = z - 1

Writing our function in terms of z, we get:

[tex]f(z) = (z - 1)^2 + 2*(z - 1)[/tex]

Now we can apply a compression by a factor of 3 around the origin. Then we have:

[tex]f(z/3) = (z/3 - 1)^2 + 2*(z/3 - 1)[/tex]

Returning to the original variable, we have:

[tex]f((x+1)/3) = ( (x + 1)/3 - 1)^2 + 2*( (x + 1)/3 - 1)[/tex]

Now we want to shift it one unit to the right, then we have:

g(x) = f( (x + 1)/3 - 1)

Replacing the actual function we get:

[tex]g(x) = f((x+1)/3 - 1) = ( (x + 1)/3 - 1 - 1)^2 + 2*( (x + 1)/3 - 1 - 1)\\\\g(x) = ( (x + 1)/3 - 2)^2 + 2*( (x + 1)/3 - 2)[/tex]

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Answer:

40

Step-by-step explanation:

The Linear inequality that is graphed with y > –x – 2 to create the given solution set is; y < x + 1

From the attached graph of inequalities, we see that one of the lines has its' y - intercept as -2 with a slope of -1. Thus, the equation in slope intercept form is; y = -x - 2.

The shaded region will have the inequality; y > -x - 2.

The other line has its' y - intercept as 1 and a slope of 1.

Thus, the equation of line is; y = x + 1.

The shaded part is above the line and as such the inequality region is represented by the inequality y < x + 1.

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Answer:

D

Step-by-step explanation:

Answer:

i 4 boys

ii 3 boys

III 5 boys

Answer:

Simplifying

x2 + 6x + 13 = 20

Reorder the terms:

13 + 6x + x2 = 20

Solving

13 + 6x + x2 = 20

Solving for variable 'x'.

Reorder the terms:

13 + -20 + 6x + x2 = 20 + -20

Combine like terms: 13 + -20 = -7

-7 + 6x + x2 = 20 + -20

Combine like terms: 20 + -20 = 0

-7 + 6x + x2 = 0

Factor a trinomial.

(-7 + -1x)(1 + -1x) = 0

Subproblem 1

Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying

-7 + -1x = 0

Solving

-7 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '7' to each side of the equation.

-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0

0 + -1x = 0 + 7

-1x = 0 + 7

Combine like terms: 0 + 7 = 7

-1x = 7

Divide each side by '-1'.

x = -7

Simplifying

x = -7

Subproblem 2

Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying

1 + -1x = 0

Solving

1 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.

1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0

0 + -1x = 0 + -1

-1x = 0 + -1

Combine like terms: 0 + -1 = -1

-1x = -1

Divide each side by '-1'.

x = 1

Simplifying

x = 1

Solution

x = {-7, 1}

Step-by-step explanation:

hope this helps if not let me know have a blessed day

The original price of each tickets is; $60 per ticket

We are told that $215 is what it costs after the discount. Thus, we add the amount taken off, back on to get;

$215 + $25 = $240

Now, since he wants to buy 4 tickets, then we divide the amount above by 4 to get the cost of each individual ticket.

Original Cost of each individual ticket = 240/4 = $60

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