For the given functions f and g find f•g and state it’s domain

f(x) = 3x - 6; g(x) = 8x +4

Answer:

The bench costs $325

Step-by-step explanation:

let garden table = x

let bench = y

x = y+64

x+y = 714

y+y+64 = 714 (we know, x = y+64)

2y + 64 = 714

2y = 650

y = 325

Answer:

Bench: $325

Garden Table: $389

Step-by-step explanation:

g + b = 714      Eq. 1

g = b + 64        Eq. 2

g = cost of the garden table

b = cost of the bench

Replacing Eq.2 in Eq.1

(b+64) + b = 714

2b + 64 = 714

2b = 714 - 64

2b = 650

b = 650/2

b = 325

from the Eq. 2

g = b + 64

g = 325 + 64

g = 389

Check:

from the Eq. 1

g + b = 714

389 + 325 = 714

Answer:

48 servings

Step-by-step explanation:

3tsp=tbsp

32*3=96

96/2=48

Answer:

  about 8.66 years

Step-by-step explanation:

The multiplier of account value when interest is compounded continuously is ...

  k = e^(rt)

where r is the annual interest rate, and t is the number of years.

We want to find t when k=2 and r=0.08. Putting these values in the formula gives ...

  2 = e^(0.08t)

Taking logs of both sides, we have ...

  ln(2) = 0.08t

  t = ln(2)/0.08 = 0.693147/0.08 ≈ 8.66

It takes about 8.66 years to double the amount.

__

Additional comment

If the interest rate is expressed in integer numbers of percentage points (R%), then the doubling time is ...

  t = 100·ln(2)/R ≈ 69.3147/R

Here, that is 69.3147/8 ≈ 8.66.

The "rule of 72" is used to estimate the doubling time for periodically compounded interest at rate R%. That rule tells you the time is t ≈ 72/R. For most interest rates and compounding frequencies in a reasonable range, this gives a time within a reasonable amount of error.

For continuously compounded interest, we have shown the doubling time in years is 69.3147/R. (The exact value of the constant is 100·ln(2).) For the purpose here, a constant of 69.3 gives an estimate accurate to 3 sf.

Answer:

2.7 is the answer!!

Step-by-step explanation:

hope this helps :)

The $1.25 one for 9 Oz box of rice would be the best buy.

To get the best buy among the given items and prices, we need to find the unit price. Thus, the formula is;

Unit price = Price/Quantity

A) Unit Price = 0.90/6 = 0.15

B) Unit Price = 1.93/12 = 0.15083

C) Unit price = 2.42/16

Unit Price = 0.15125

D) Unit Price = 1.25/9 = 0.138

The $1.25 one for 9 Oz box of rice would be the best buy.

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Answer: 3(4-x) + 6x = 4x + 12 - x

Step-by-step explanation:

For the solution to be all real numbers, the left hand has to be identical to the right hand side.

1) [tex]4(3-x)+7x=12-4x+7x=12+3x[/tex], so wrong.

2) [tex]4(4-x)+6x=16-4x+6x=16+2x[/tex], so wrong.

3) [tex]3(4-x)+6x=12-3x+6x=12+3x=4x+12-x[/tex], so correct.

4) Wrong variable, so eliminate immediately.

Answer:c

options A  and B

Step-by-step explanation:

the ratio between the lengths of the two legs of a 30-60-90 triangle

General ration of 30-6- 90 degrees triangle is

x : xsqrt(3) : 2x

When x=1 the ratio becomes 1 : 1 sqrt(3)

when x= 2sqrt(3) the ratio becomes

It becomes

Two sides of 30-60-90 triangle cannot be equal

so option c  and option D are not possible

sqrt(2) is also not possible  because we have sqrt(3) in general ratio

PLS MARK ME AS BRAINLIEST.

[tex]\large\displaystyle\text{$\begin{gathered}\sf \frac{2x-20}{3}=2x \end{gathered}$}[/tex]

Multiply both sides of the equation by 3.

[tex]\large\displaystyle\text{$\begin{gathered}\sf 2x-20=6x \end{gathered}$}[/tex]

Subtract 6x on both sides.

[tex]\large\displaystyle\text{$\begin{gathered}\sf 2x-20-6x=0 \end{gathered}$}[/tex]

Combine 2x and −6x to get −4x.

[tex]\large\displaystyle\text{$\begin{gathered}\sf -4x-20=0 \end{gathered}$}[/tex]

Add 20 to both sides. Any value plus zero results in its same value.

[tex]\large\displaystyle\text{$\begin{gathered}\sf -4x=20 \end{gathered}$}[/tex]

Divide both sides by −4.

[tex]\large\displaystyle\text{$\begin{gathered}\sf x=\frac{20}{-4} \end{gathered}$}[/tex]

Divide 20 by −4 to get −5.

[tex]\large\displaystyle\text{$\begin{gathered}\sf x=-5 \ \ \to \ \ \ Answer \end{gathered}$}[/tex]

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation: }[/tex]

[tex]\mathbf{\dfrac{2x - 20}{3} = 2x}[/tex]

[tex]\huge\textbf{SIMPLIFY IT or DISTRIBUTE:}[/tex]

[tex]\mathbf{\dfrac{2}{3}x - \dfrac{20}{3} = 2x}[/tex]

[tex]\huge\textbf{SUBTRACT 2x to BOTH SIDES:}[/tex]

[tex]\mathbf{\dfrac{2}{3}x - \dfrac{20}{3} - 2x = 2x - 2x}[/tex]

[tex]\huge\textbf{SIMPLIFY IT!}[/tex]

[tex]\mathbf{- \dfrac{4}{3}x - \dfrac{20}{3} = 0}[/tex]

[tex]\huge\textbf{ADD }\boxed{\rm{\bf \dfrac{20}{3}}}\huge\textbf{ to BOTH SIDES:}[/tex]

[tex]\mathbf{-\dfrac{4}{3}x - \dfrac{20}{3} + \dfrac{20}{3} = 0 + \dfrac{20}{3}}[/tex]

[tex]\huge\textbf{SIMPLIFY IT!}[/tex]

[tex]\mathbf{-\dfrac{4}{3}x = \dfrac{20}{3}}[/tex]

[tex]\huge\textbf{MULTIPLY }\boxed{\rm \bf {\dfrac{3}{-4}}}\huge\textbf{ to BOTH SIDES:}[/tex]

[tex]\mathbf{\dfrac{3}{-4}\times\dfrac{-4}{3}x = \dfrac{3}{-4}\times\dfrac{20}{3}}[/tex]

[tex]\huge\textbf{SIMPLIFY IT!}[/tex]

[tex]\mathbf{x = -5}[/tex]

[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{x = -5}}}\huge\chekmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer: it should be this M=kb^3/B^2

Step-by-step explanation:

a) The point (2, -7/5) is not a point on the graph?

b)  The value of f(x) when x is 1 is -1/3 and the point on the graph is (1, -1/3)

c) The value of x for f(x) = 2 is 22 and the point on the graph is (22, 2)

d) The domain of x is all real values of x ≠ 10

e) The x intercept is -2

f) The y intercept is -1/5

Function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output and not one input for two outputs.

Analysis:

a) To test if the point (2, -7/5) is a point on the graph, we put in x = 2 into the function,

f(2) = 2+2/2-10 = 4/-8  = -1/2 ≠ -7/5. Therefore (2, -7/5) is not a point on the graph.

b) if x = 1, f(1) = 1 +2 / 1-10 =  3/-9 = - 1/3

   The point on the graph is (1, -1/3)

c) if f(x) = 2, then 2 = x+2/x-10

     2(x-10) = x+2

     2x -20 = x+2

      2x-x = 2+20

      x = 22, the point on the graph is (22, 2)

d) The domain of the function is such that the denominator would not be zero.

so if x - 10 ≠ 0

Then the values of x ≠ 10 are the domain of the function.

e) The x intercept of the graph is the point at which f(x) = 0

  0 = x+2/x-10

   x+2 = 0

   x = -2. The x-intercept is -2.

f) the y-intercept is such that x = 0

   0+2/0-10 = 2/-10 = -1/5

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Answer:

D.  domain

Step-by-step explanation:

domain is set of x-values

range is set of y-values

Input is the set of x-values, so it is the domain.

Answer:

See below

Step-by-step explanation:

=  (-7)(11)(√(3*10) ) =  - 77 √(30)  

Answer: y = -1

Step-by-step explanation:

When x = 0, y = -1

Also, you can think about it as when the graph of the line passes the y axis

Answer:

c

Step-by-step explanation:

A ratio shows us the number of times a number contains another number. The elephant's weight on Planet B is 96 pounds.

A ratio shows us the number of times a number contains another number.

The ratio of the weight of an object on Planet A to the weight of the same object on Planet B is 100 to 3.

Weight on Planet A/ Weight on planet B = 100 / 3

Now, the weight of the elephant on planet A to Planet B will be,

elephant's weight on Planet A/elephant's weight on Planet B = 100 / 3

elephant's weight on Planet B = (3 ×3200)/100

elephant's weight on Planet B = 96 pounds

Hence, the elephant's weight on Planet B is 96 pounds.

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Answer:

13.25km

Step-by-step explanation:

25 Litres = 331.25km

1 Litre =

[tex] \frac{331.25}{25} \\ = 13.25km[/tex]

Answer:

13.25 km

Step-by-step explanation:

25 litres = 331.25 km

1 litre =

331.25

25

=13.25 km

Answer:

a

Step-by-step explanation:

The vertex is at (4,1).

Also, the graph opens down, so this eliminates e.

So, the answer is a.

Answer:

4

Step-by-step explanation:

To find f(-1)g(-1) which is f(-1)*g(-1), first, we must find what are values of f(-1) and g(-1) first which can be found by substituting x = -1 in both functions.

[tex]\displaystyle{f(-1)=(-1)^2+1}\\\\\displaystyle{f(-1)=1+1 = 2}[/tex]

Now we know that f(-1) is 2, next, we find g(-1).

[tex]\displaystyle{g(-1) = 3(-1)+5}\\\\\displaystyle{g(-1)=-3+5 = 2}[/tex]

Now we know that g(-1) is 2 too. Since the question wants to find f(-1)g(-1), therefore 2*2 = 4.

Hence, the answer is 4.

Answer:

D) 4

Step-by-step explanation:

Given functions:

f(x) = x² + 1

g(x) = 3x + 5

Here, we're asked to find the value of both functions when the value of x is -1. Then, we multiply the functions in order to find the value of f(-1)•g(-1).

Note: f(-1) • g(-1) is equivalent to (f • g)(-1).

Method 1: f(-1) • g(-1)

Find the value of each function when x = -1.

f(-1) = (-1)² + 1 ⇒ f(-1) = 1 + 1 ⇒ f(-1) = 2

g(-1) = 3(-1) + 5 ⇒ g(-1) = -3 + 5 ⇒ g(-1) = 2

Multiply the functions together.

f(-1) • g(-1) ⇒ 2 • 2 ⇒ 4

Method 2: (f • g)(-1)

First, multiply the functions.

⇒ (x² + 1) • (3x + 5) [ Simplify using the Distributive Property: (a + b) • (c + d) = ac + ad + bc + bd. ]

⇒ x²(3x) + x²(5) + 1(3x) + 1(5)

⇒ 3x³ + 5x² + 3x + 5

Now, substitute -1 as the value of x.

⇒ 3(-1)³ + 5(-1)² + 3(-1) + 5 [ Exponents first. }

⇒ 3(-1) + 5(1) -3 + 5 [ Multiply the numbers. ]

⇒ -3 + 5 - 3 + 5 [ Simplify. ]

⇒ 4

Therefore, the product of both functions when x = -1 is 4.

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The students in the school would be expected to do household chores for at least two hours every week with 1020 students.

We have given

Time (in hours)                  0–  1    2–3     4–5    6–7

Number of Students         32   64          3        1

A simple random sample is a subset of a statistical population in which each member of the subset has an equal probability of being chosen.

The keyword is at least, this means anything under that number will not qualify.

So that leaves 68 out of the 100 sample students.

So if you want to have the same thing but with 1,500 students.

Take off the 2 zeros at the end of 1500 and multiply by 68 to get your answer.

This is because there are 2 zeros in 100, so to cancel out the 2 zeros in 100, take out the 2 zeros in 1500 making it a lot easier.

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The y-intercept on the x-y plane is (0, -9).

To get the y-intercept we just need to evaluate in x = 0.

Here we have:

y = 6*(x - 1/2)*(x + 3)

Evaluating the given equation in x = 0 we get:

y = 6*(0 - 1/2)*(0 + 3) = -9

Then the y-intercept on the x-y plane is (0, -9).

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Answer:

-9

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Subtracting 2 from both sides and then dividing both sides by 3 gives that x² = -2/3, which indicates the roots are complex.

Answer: 841

Step-by-step explanation:

29×29=841

The dimensions of the box of the largest volume that can be constructed are

D=18,9,3

Generally, the equation for the lenght is  mathematically given as

Lenght=(24-2x)

Widht= (15-2x)

Therefore

Volume =L*B*H

V=(24-2x)(15-2x)x

V=(360-48x-30x+4x)x

V=4x^3-78x^2+360x

Differnciating we have

dv/dx=12x^2-156x+360

put dv/dx=0

12(x^2-13x+30)=0

x^2-10x-3x+30=0

(x-10)(x-3)=0

root=10,3

Second diiferciation

d^v/dx^2=24x-156

[tex]lim _{x=3} =-84 < 0[/tex]

In conclusion,

L=24-2x

L=24-2x3

L=18in

w= 15-2x

w=15-2*3

w=9in

h=x

h=2in

Dimension=18,9,3

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The answer is 90% of the crime is between 48.63 and 51.37

The sd = 5 months

n = 36

Mean length = 50

1- 0.90

= 0.1

Critical value = alpha/2 = 1.645

Margin of error

E = 1.645 x 5/√36

= 1.37

50 -  1.37 + 50 + 1.37

= (48.63, 51.37)

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The new graphs would make it more difficult to estimate the price of a book.

To do this, we simply combine the frequencies on Felix and Tyler's table.

When this is done, we have the following dataset

3,3,3,3,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7, 8,8,8,8,9,9,9,9,9,9,9,9,9,11,11,13,13,13,13,15,15,15,16,16,18,18,18,18,18,19,19,19,19,19,19,29,32,32,36,36,36,38,38,64,64,66,66,66,68,68,69,75,75,76,76,76,76,76,78,78,79,82,82,86,86,86,89,96,96,97,97,99

Next, we create the box & whisker plot and the histogram using the new dataset

(see attachment for the graphs)

The new graphs would make it more difficult to estimate the price of a book.

This is so because the dataset used to create the graphs do not come from the same source

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Answer:

90 grams

Step-by-step explanation

Full = 120

half filled + empty = 150

half of 120 = 60

Therefore, a jar weighs 150 - 60

= 90 grams