Suppose you Just purchased a used truck. The number of miles on the odometer can be represented by the equation y = x + 40, 000, where y is the number of miles on the odometer, and x is the number of miles you have driven it. Write this equation using function notation, f(x).

Answer:

(r+q)+s

Step-by-step explanation:

The parentheses make it clear that r and q need to be added first.

Answer:

Ratio of their surface area = 9:16

Step-by-step explanation:

Volume of cube A = a^3

Volume of cube B = b^3

Ratio of their volumes= 27:64

Volume of cube A = a^3

27 = a^3

a= 3√27

= 3

Volume of cube B = b^3

64 = b^3

b =3√64

= 4

Surface area of cube a = 6a^2

=6 × 3^2

= 6 × 9

= 54

Surface area of cube b = 6b^2

= 6 × 4^2

= 6 × 16

= 96

Surface area of cube a : surface area of cube b

= 54:96

= 9:16

Answer:

$210

Step-by-step explanation:

Answer:  4 hours

Step-by-step explanation:

distance (d) = [rate (r) - current (c)] × time (t)

Given: d = 40, r = 15, c = 5

40 = (15 - 5)t

40 = 10t

4 = t

Answer:

8 + 10

Step-by-step explanation:

Step 1: Define sum

The sum of any 2 numbers means "add" or "combine" the 2 numbers together.

Step 2: Write out expression

"Sum" = add or +

8 + 10

Answer:

(a) aₙ = 22 + 6(n - 1)

(b) The 14th row has 100 seats

Step-by-step explanation:

1. (a) Remember that an arithmetic series has the general formula a + (n - 1)d. Here a = the first term, and d = difference between first and second term, or in other words the difference between the nth and (n + 1)th terms.

aₙ = 22 + 6(n - 1)

This is our iterative rule for this arithmetic series, aₙ = 22 + 6(n - 1).

(b) Here n = the row number. We want to know the row number that has 100 seats. Let's equate the expression '22 + 6(n - 1)' to 100, and solve for n.

100 = 22 + 6(n - 1),

100 = 22 + 6n - 6,

100 = 16 + 6n,

6n = 84,

n = 84 / 6 = 14

=> the 14th row has 100 seats

Answer:

20 roses at $23 is the better buy

Step-by-step explanation:

Here, we have Alonzo who wants to purchase Roses. He has two buying options.

Either he buys 12 roses at $15 or buys 20 roses at $23. We want to know which of the two options is better for him.

what we shall do here is to get the unit price per each of the roses in each set. The set having the lower rose to dollar value is the better buy.

Firstly, 12 roses for $15.

Price per rose here is 15/12 = $1.25 per rose

For 20 roses at $23

Price per rose here is 23/20 = $1.15 per rose

Since 1.15 is less than 1.25, then the second option is the better buy.

Answer:

The experimental probability is the same as the theoretical probability.

Step-by-step explanation:

The given data is:

color            observed frequency               relative frequency

Red                            15                                          3/10

Blue                           12                                          6/25

Green                         8                                           4/25

Yellow                        10                                          1/5

Purple                         5                                           1/10

The experiment was repeated 50 numbers of times.

Solution:

Theoretical probability is basically what is expected to happen without experimenting and experimental probability is what actually happens as a   results of an experiment.

Theoretical probability =  favorable outcomes / all possible outcomes

Experimental probability = no. of times outcome occurs / no. of times

                                                                                      experiment is performed The experimental probability  and theoretical probability are same i.e. 1/5

This can be seen from the table:

Experimental probability = 1/5

As the experiment is performed 50 times and the outcome (yellow tile) occurs 10 times so using the formula of experimental probability:

10/50 = 1/5

Now as given, there are 5 number of tiles (red,blue,green,yellow,purple) so number of possible outcomes is 5. Yellow tile among these 5 tiles is 1. So the favorable outcomes is 1. So looking at the given formula of theoretical probability:

1/5

So

experimental probability = 1/5

theoretical probability = 1/5

Hence the experimental probability is the same as the theoretical probability.

Answer: A

Step-by-step explanation: it’s A for the lazy people

Answer:

A

Step-by-step explanation:

A contains √3 --> irrational number because 3 is not a square number

For other choices:

- All numbers in the form a/b (a,b are integer numbers) are rational numbers

- √36, √9, √4, √25, √49, √100 are integer numbers because (36, 9, 4,....) are square numbers

- All given decimal numbers can be written in the fraction form

0.5 = 1/2

39.77 = 39 + 77/100 = 3977/100

0.15151578 and 0.00010001 are finite decimals, 0.303030... is infinite repeating decimal, so technically they are rational numbers.

Answer:

2.33 × 10^6

Step-by-step explanation:

I just used a calculator, to be honest. It was super simple.

2.33 * 10^6

2.33 * (10*10*10*10*10*10)

which then equals 2,330,000

Answer:

Step-by-step explanation:

[tex] {7}^{2} \times {7}^{0} \div 7[/tex]

Follow PEDMAS order of operations

[tex] {7}^{2} = 49 \\ {7}^{0} = 1 \\ = 49 \times 1 \div 7 \\ = 49 \div 7 \\ = 7[/tex]

If you have any more questions, please let me know.

Answer:  B  

Step-by-step explanation:

They've given you two functions  f(x) = x^2 + 1 and g(x) = 3x +1  And they are you to find 2 * f(4) then g(x) is not needed so input in  4 for the function f(x) and multiply the output by 2.

F(4) = 4^2 + 1

F(4) = 16 +1

f(4) =  17  

   17  * 2 = 34

Answer:

Step-by-step explanation:

[tex]f( x ) = x^ 2 + 1 \\ g( x ) = 3 x + 1\\\\f(4) \times 2 = ?\\f(4) = 4^2 +1\\\\=( 16+1) \times 2\\\\= 17\times 2\\\\= 34[/tex]

Answer:

a) 86,314.

b) 9,162,500.

Step-by-step explanation:

(a) 838(100 + 3)

= 83800 + 2514

= 86314.

(b) 91625 x 179 - 91625 x 79

= 91625(179 - 79)

= 91625 x 100

= 9162500.

Answer:

a,b are the right answers

Step-by-step explanation:

Hi there! Hopefully this helps!

------------------------------------------------------------------------------------------------------

[tex]\frac{175-172}{\frac{29}{\sqrt{20} } }[/tex]

Subtract 172 from 175 to get 3.

[tex]\frac{3}{\frac{29}{\sqrt{20} } }[/tex] ≈ 0.462634754

Factor [tex]20=2^{2} \times 5[/tex]. Rewrite the square root of the product [tex]\sqrt{2^{2} \times 5 }[/tex] ≈ [tex]4.472135955[/tex] as the product of square roots [tex]\sqrt{2^{2} } \sqrt{5}[/tex] ≈ 4.472135955. Take the square root of [tex]2^{2}[/tex] ≈ [tex]4[/tex]

[tex]\frac{3}{\frac{29}{2\sqrt{5} } }[/tex]

Rationalize the denominator of [tex]\frac{29}{2\sqrt{5} }[/tex] ≈ [tex]6.484597135[/tex] by multiplying numerator and denominator by [tex]\sqrt{5}[/tex] ≈ [tex]2.236067977.[/tex]

[tex]\frac{3}{\frac{29\sqrt{5} }{2(\sqrt{5} )^{2} } }[/tex]

The square of [tex]\sqrt{5}[/tex] ≈ [tex]2.236067977[/tex] is 5.

[tex]\frac{3}{\frac{29\sqrt{5} }{2 \times 5 } }[/tex] ≈ [tex]0.462634754[/tex]

Multiply 2 and 5 to get 10.

[tex]\frac{3}{\frac{29\sqrt{5} }{10 } }[/tex] ≈ [tex]0.462634754[/tex]

Divide 3 by [tex]\frac{29\sqrt{5} }{10}[/tex] ≈ 6.484597135 by multiplying 3 by the reciprocal of [tex]\frac{29\sqrt{5} }{10}[/tex] ≈ [tex]6.484597135.[/tex]

[tex]\frac{3\times 10}{29\sqrt{5} }[/tex] ≈ [tex]0.462634754[/tex]

Rationalize the denominator of [tex]\frac{3\times 10}{29\sqrt{5} }[/tex] ≈ 0.462634754 by multiplying numerator and denominator by [tex]\sqrt{5}[/tex] ≈ [tex]2.236067977.[/tex]

[tex]\frac{3\times 10\sqrt{5} }{29(\sqrt{5})^{2} }[/tex] ≈ [tex]0.462634754[/tex]

The square of [tex]\sqrt{5}[/tex] ≈ [tex]2.236067977[/tex] is 5.

[tex]\frac{3\times 10\sqrt{5} }{29 \times {5} }[/tex] ≈ [tex]0.462634754[/tex]

Multiply 3 and 10 to get 30.

[tex]\frac{30\sqrt{5} }{29 \times {5} }[/tex] ≈ [tex]0.462634754[/tex]

Multiply 29 and 5 to get 145.

[tex]\frac{30\sqrt{5} }{145 }[/tex] ≈ [tex]0.462634754[/tex]

[tex]\frac{175-172}{\frac{29 }{\sqrt{20} } } = \frac{3}{\frac{29}{\sqrt{20} } } =\frac{3\sqrt{20} }{29}=\boxed{\frac{6\sqrt{5} }{29} } = \boxed{0.463}[/tex]

Refer to the attached image for further explanation:

Answer:

x = 10

PQ = 27

QR = 20

Step-by-step explanation:

You can add up PQ and QR and set it equal to PR.  Solve for x.

(2x + 7) + (2x) = 47

2x + 7 + 2x = 47

4x + 7 = 47

(4x + 7) - 7 = 47 - 7

4x = 40

4x/4 = 40/4

x = 10

Now, use the solved x-value to find PQ and QR.

PQ = 2x + 7

PQ = 2(10) + 7

PQ = 20 + 7

PQ = 27

QR = 2x

QR = 2(10)

QR = 20

Answer:

15.41

Step-by-step explanation:

Answer:

[tex]y=2x-2[/tex]

Step-by-step explanation:

Because the coordinates for x = 0 is (0,-2) so that's your y- intercept.

Then if you all you have to do is make sure that you have the correct slope.

So i just made a table on paper and started going up and seeing what slope i'd need to match the table on the screen.

[tex]2(0)-2=-2\\2(1)-2=0\\2(2)-2=2\\2(3)-2=4[/tex]

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{112 \: {inches} \: ^{2} }}}}}[/tex]

Step-by-step explanation:

Given,

Height of a parallelogram ( h ) = 8 inches

Base of a parallelogram ( b ) = 14 inches

Area of a parallelogram ( A ) = ?

Finding the area of a parallelogram

[tex] \boxed{ \sf{area \: of \: parallelogram \: = \: base \: \times \: height}}[/tex]

⇒[tex] \sf{area \: of \: parallelogram \: = \: 14 \: \times 8}[/tex]

⇒[tex] \sf{area \: of \: parallelogram = 112 \: {inches}^{2} }[/tex]

Hope I helped!

Best regards! :D

Answer:

8

Step-by-step explanation:

x=3

y=6

to find x+y-1, sub in x and y

3+6-1 = 8

Answer: 8

Step-by-step explanation:

x+y+(-1), given x=3, y=6, and z=-4

---------

 x+y+(-1)

=(3)+(6)+(-1) ⇔ substitute x and y

=9+(-1) ⇔ add 3 and 6

=8

Hope this helps!! :)

Please let me know if you have any questions

Answer:

Step-by-step explanation:

Hello,

[tex]\dfrac{x^2-100}{x+10}=\dfrac{x^2-10^2}{x+10}=\dfrac{(x-10)(x+10)}{x+10}=x-10\\\\\text{so, we can conclude.}\\\\\displaystyle \lim_{x\rightarrow-10} \ \dfrac{x^2-100}{x+10}=-10-10=-20[/tex]

Thanks

Answer:

[tex]\frac{17}{2}[/tex]

Step-by-step explanation:

To convert a mixed fraction to a improper fraction, you have to multiply the denominator (2) by the whole number (8). 8 multiplied by 2 is 16. Then add the numerator (1). 16+1=17. That becomes your numerator, the denominator (2) stays the same.

I hope this helps!

Answer:

23

Step-by-step explanation:

8+c

Let c = 15

8+15

23

Answer: 23

Step-by-step explanation:

If c is 15 then plot 15 into the expression and add them

8 + 15 = 23

Answer:

$1.49

Just divide 7.45 by 5 and you'll get your answer

Answer:

1. x = 10  2. x = 7  3. x = 1  4. x = 6

Explanation:

1. -2x + 81 = 61 (Subtract 81 from 61)

  -2x = -20 (Divide)

   x = 10

2. 9x - 58 = 5 (Add 58 to 5)

   9x  = 63 (Divide)

   x = 7

3. 21 +10x = 3x + 28 (Rearrange expression)

   21 - 28 = 3x - 10x (Combine like terms)

   -7 = -7x (Divide)

    x = 1

4. 9x - 42 = 2x (Rearrange)

   9x - 2x = 42 (Combine like terms)

   7x = 42 (Divide)

   x = 6

Hope you find this Helpful

Answer:

Step-by-step explanation: let me drive the bus

Answer:

[tex]Rate = 0.125[/tex]

Step-by-step explanation:

Given

[tex]Daily\ Cups = 500[/tex]

[tex]Weekly\ Cups =4000[/tex]

Required

Determine the day to week rate

This can be calculated by dividing the daily medicine cups by the weekly cups;

[tex]Rate = \frac{Daily}{Weekly}[/tex]

Substitute 500 for Daily and 4000 for Weekly

[tex]Rate = \frac{500}{4000}[/tex]

[tex]Rate = 0.125[/tex]

Hence, the rate of the daily to weekly medicine cup is 0.125

Answer: x=5 and x=-1

Step-by-step explanation:

X^2-4x-5=0

(X-5) (x+1)=0

X-5=0. And. X+1=0

Answer:

30 ft

Step-by-step explanation:

6 x 5 = 30

you multiply 6 times 5 and you get 30

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

f(x)=(x-3)(x²+2x+2)

when solve for x using quadratic formula fo x in (x²+2x+2):

x=(-b±√b²-4ac)/2a  a=1,b=2,c=2

x=-1±i

f(x)=(x-3)(x+1-i)(x+1+i)

The complete factored form of the polynomial is F(x) = (x - 3)(x + 1 + i)(x + 1 - i).

To find the complete factored form of the polynomial F(x) = x³ - x² - 4x - 6, we can factor it using various methods such as synthetic division or factoring by grouping.

Factoring the polynomial, we get:

F(x) = (x + 3)(x - 1)(x + 2)

Comparing the factored form with the options provided:

A. F(x) = (x + 3)(x + 1)(x - 1)

This option does not match the factored form of the polynomial.

B. F(x) = (x - 3)(x + 1 + i)(x + 1 - i)

f(x)=(x-3)(x²+2x+2)

When solve for x using quadratic formula fo x in (x²+2x+2):

x=(-b±√b²-4ac)/2a  

x=-1±i

f(x)=(x-3)(x+1-i)(x+1+i)

So, the is the required factored form.

C. F(x) = (x - 3)(x + 1 + i)(x - 1 - i)

This option does not match the factored form of the polynomial.

D. F(x) = (x + 3)(x + 1 + i)(x + 1 - i)

This option does not match the factored form of the polynomial.

Learn more about Factor here:

https://brainly.com/question/15872577

#SPJ6

Answer:

When an equation that has no solution, it means that the equation does not have an answer and that there is no way that the equation will be true regardless of the values given to variables or where the variables are on one side or both sides of the equation because of the way the equation was set up or constructed.

Step-by-step explanation:

For example, the following equation with variables on both sides of the equal sign that has no solution, we have;

21 + 9·x = 15+ 5·x + 4·x

21 + 9·x = 15+ 9·x

Subtracting 9·x from both sides gives;

21 + 9·x - 9·x  = 15+ 9·x - 9·x

21 + 0 = 1 5 + 0

21 = 15 (Which not true and cannot be true because 21 ≠ 15)

For example of equation with variables on one side of the equal sign has no solution, we have;

21 + 9·x - 5·x - 4·x = 15

21 + 9·x - 9·x  = 15

21 + 0  = 15

21 = 15 (Which not true and cannot be true because 21 ≠ 15).

Answer:

they don't always have solutions