Which of these is the quadratic parent function?
A. f(x) = (1/4 x)²
B. f(x)=x²-3
C. f(x) = x² +5
D. f(x) = x²

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:

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:

2.7 is the answer!!

Step-by-step explanation:

hope this helps :)

Answer:

c

Step-by-step explanation:

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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Here, we have to perform a sum of vectors and draw the resultant vector and the resultant vector will be <4, 0>.

If we see the image, we can write the vectors as:

w = <3, 3>

u = <-3, -4>

v = <-4, -1>

Now we want to sum:

u - v + w

u - v + w

= <-3, -4> - <-4, -1> + <3, 3>

= <-3 + 4 + 3, -4 + 1 + 3>

= <4, 0>

The graph of the resultant vector can be seen below.

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The smallest angle would be 19 degrees. So option D is correct.

The sum of exterior angles of the regular octagon is 360 degrees.

Given;

The angles

x + 13 + 2x - 1 + 2x + 6 + 2x + 12 + 2x - 17 + 3x - 4 + 3x - 10 + 4x = 360

19x - 1 = 360

19x = 359

x = 18.89

The smallest angle would be

2x - 17 = 2(18.89) - 17 = 19

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Answer:

See below

Step-by-step explanation:

=  (-7)(11)(√(3*10) ) =  - 77 √(30)  

The mean is $5.769 million and the standard deviation is $3.905 million.

The mean is the average of a data set.

The standard deviation shows the measure of the dispersion from the mean.

Urban Area         Total Cost       Squared Difference

                        (millions of dollars)    (x - u)²

New York                  16                     104.65  

Los Angeles              13                      52.27

Chicago                      7                          1.51

Washington, D.C.       5                        0.59

Houston                      5                        0.59

Dallas, Fort Worth      4                         3.13

Detroit                        4                          3.13

Miami                         4                          3.13

Phoenix                     4                          3.13

Philadelphia              4                          3.13

San Francisco           3                          7.67

Boston                       3                          7.67

Atlanta                       3                          7.67

13    Total                 75                       198.27

Mean = 5.769 (75/13)                         15.251 (198.27/13)

Standard Deviation = 3.905 (square root of 15.251)

Urban Area         Total Cost

                        (millions of dollars)

New York                  16

Los Angeles              13

Chicago                      7

Washington, D.C.      5

Houston                     5

Dallas, Fort Worth     4

Detroit                       4

Miami                        4

Phoenix                    4

Philadelphia             4

San Francisco          3

Boston                     3

Atlanta                     3

Calculate the mean and standard deviation for this data set (in millions of dollars). (Round your answers to three decimal places.) mean $ million standard deviation $ million

Thus, the mean is $5.769 million and the standard deviation is $3.905 million.

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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: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.

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: 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

The answers are as follows:

Data is information that has been translated into a form that is efficient for movement or processing.

1. By substituting the values x= 1, 2, 3..

We get the point where f(x)= g(x)

So, f(5)= g(5) =2

Hence, the value of x is 5.

2. As per the given data, during year 14,

revenue from online ads is approximately $4.2 million, whereas revenue from online ads is double than revenue from printed ads.

Also, both line intersect inbetween 7 and 8th year and both online ads and printed ads generated an approximate revenue of $2.2 million.

3. Western Beach erodes from 100 ft to 70 ft.

So, rate of erosion = 30 ft/15 yr = 2 ft/yr.

and,  Dunes Beach builds up from 20 ft to 95 ft.

So,  rate of buildup = 75 ft/15 yr = 5 ft/yr.

Hence,  Dunes beach gets 5 feet every year, and every 5 years the beach loses 25 feet.

b) From the table, beaches will have the same width sometime in year 11 (2006).

c) If the rate remains constant then there is no same width cause of decrease in western beach and increase dunes beach.

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[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]

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:

ok so here we know that Baily kicked the target 6 times out of 20 that  is 6/20 and then you just reduce the fraction dividing it by 2 so it will be  3/10

Step-by-step explanation:

hope it helps :)

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.

Based on the price that Augusta Enterprises issued the bonds, the journal entries would be:

Date                  Account title                              Debit                Credit

July 1, 20x5       Cash                                      $97,000

                         Discount on Bonds payable $3,000

                         Bonds payable                                               $1,000,000

Date                  Account title                              Debit                Credit

July 1, 20x5       Cash                                     $1,020,000

                         Premium on Bonds payable                           $20,000

                         Bonds payable                                              $1,000,000

The cash received from the discounted bond is:

= 1,000,000 x 97%

= $970,000

The cash received from the premium bond is:

= 1,000,000 x 102/100

= $1,020,000

The premium is:

= 1,020,000 - 1,000,000

= $20,000

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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

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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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: C and B

Step-by-step explanation:

[tex]9x^2 - 6x+1=7\\\\9x^2 - 6x-6=0\\\\x=\frac{-(-6) \pm \sqrt{(-6)^2 - 4(9)(-6)}}{2(9)}\\\\x=\frac{6 \pm \sqrt{252}}{18}\\\\x=\frac{1 \pm \sqrt{7}}{3}[/tex]

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: 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.