Suppose that the functions r and s are defined for all real numbers x as follows.
r(x)=3x+5
s(x)=4x
Write the expressions for (r-s)(x) and (r*s)(x) and evaluate (r+s)(-2).

The value of   [tex]\dfrac{ 2}{3} log(6400) - \dfrac{1}{3} log(1600)[/tex]  in terms of s will be

[tex]\dfrac{2}{3}(400s)-\dfrac{1}{3}(1000s)[/tex]

A quantity representing the power to which a fixed number (the base) must be raised to produce a given number.

Here we have the expression:-

[tex]\dfrac{ 2}{3} log(6400) - \dfrac{1}{3} log(1600)[/tex]

So in terms of s the expression will become:-

[tex]\dfrac{2}{3}(400s)-\dfrac{1}{3}(1000s)[/tex]

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We are given that, a computer can sort x objects in t seconds, and the below relations is satisfied for each x and t

For 12 objects, we can substitute x = 12

⇒ t = (3/1000) (12)² + (1/1000) 12

⇒ t = (12/1000) (3 × 12 + 1)

⇒ t = (12×37/1000)

⇒ t = 444/1000

⇒ t = 0.444

⇒ t ≈ 0.40 seconds (2 dp)

Answer:

  g(x) = -x +1

Step-by-step explanation:

The transformation that reflects f(x) across the y-axis is replacement of x with -x.

__

For f(x) = x +1, replacement of x with -x will perform the desired transformation:

  g(x) = f(-x) = (-x) +1

  g(x) = -x +1

Reflection across y axis rule

so x turns negative

new one is

g(x)=f(-x)

Answer:

The scale factor is 5 because the increase in each side of the shape is *5

Answer:

the no. are -10 and -24

when we add -10 with -24 we get -34

Answer:

27 degress; complementary

Step-by-step explanation:

complementary is when is adds up to 90 and you need 27 more degrees to make it 90

Answer:27 degrees

Step-by-step explanation:

just need points

Answer:

The first answer is 2x + 5

The second answer is 19

Answer:

24 ways

Step-by-step explanation:

By the Fundamental Counting Principle,

Number of permutations = 4 ⋅ 3 ⋅ 2 ⋅ 1

= 4!

= 24

There are 24 different ways the teacher can order the student presentations.

Answer:

let the first number and second number be x+1 and x+3 respectively

The square pyramid with a base with edges of 6 inches and slant height of 4 inches have a surface area of 84 in².

The net of the square pyramid have a base of 6 inches and the height of each triangle is 4 inches.

An equation is an expression that shows the relationship between two or more numbers and variables.

The square pyramid with a base with edges of 6 inches and slant height of 4 inches. Hence:

Surface area = (6 * 6) + 2(6 * 4) = 84 in²

The net of the square pyramid have a base of 6 inches and the height of each triangle is 4 inches.

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Answer:

First we need to determine what cos is asking for.  Using Soh Cah Toa we can tell that we are using adjacent (a) and hypotenuse (h).  The leg that is adjacent to Q is equal to 10 while the hypotenuse is equal to 21.

[tex]cos(Q)=\frac{adjacent}{hypotenuse}[/tex]

[tex]cos(Q) = \frac{10}{21}[/tex]

After getting to this part, we have to take the inverse of cos in order to cancel the cos on the left and leave Q by itself.

[tex]cos^{-1}(cos(Q))=cos^{-1}(\frac{10}{21})[/tex]

[tex]Q = 61.56\ degrees[/tex]

In the end we are left with that our angle Q is equal to 61.56 degrees.

Hope this helps!  Let me know if you have any questions

Answer:

Step-by-step explanation:

a = 180 - 112

= 68 degrees (adjacent angles)

Answer:

The two integers should be 3 and 1

Answer:

x = -2

Step-by-step explanation:

Given

Solving

Add 3 to each side.

Subtract 5x from each side.

Answer:

Step-by-step explanation:

Answers:

===========================================================

Explanations:

When x = 1:

1³ + 1 - 3 = -1

When x = 2:

2³ + 2 - 3 = 7

Since f(x) = x³ + x - 3 is continuous, it follows from the intermediate value theorem that for some c in the interval (1, 2), we have f(c) = 0, since f(1) < 0 < f(2).

Answer:

17/18pi or 2.97

Step-by-step explanation:

170 degrees to radian

170 * pi / 180 degrees

so, 170pi/180

17/18pi or 2.97

It diverges

Step-by-step explanation:

it is an alternating sequence hence it will diverge

Answer:

36

Step-by-step explanation:

Area of a triangle = A = hb x b

A = 12 x 7 = 84                    2

84/2 = 42

rectangle area = l x w

2 x 3 = 6

42 - 6

36

Answer:

≈2825

Step-by-step explanation:

28250*10%≈2825

Pay attention to the ≈ sign

To determine the lower price, the formula should use a z-value that is less than -1.

We are given;

Mean; x' = $6.32

Standard deviation; s = $0.47

A positive z-score indicates the raw score is higher than the mean average while a negative z-score indicates the raw score is below the mean average.

Now, we want to find out the lower price from the definition above, we have to use a negative z-score which in this case will be -1.

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Answer:

7/75

Explantion:

To get the answer as a fraction you must first have a common denominator

so . .

105 is a common denominator

So . .

Multiply 5/7 by 15

Multiply 1/15 7

This comes out as

Divide = 7/75

Answer:

c/6 or c divided by 6

Step-by-step explanation:

Ok then im doing the 3rd one:

Area of a parallelogram =b.h

[tex]11 \frac{3}{4} \times 8 \frac{1}{3} \\ = 11.75 \times 8.33 \\ = 97.8775 \\ = \boxed {97.9}[/tex]

The  ability to be able to decide which prints she could order is to look at the environment especially the empty space and then visualize what is missing and what best to fit in.

Similar figures are known to be figures that are said to be of the same shape.  They are known to have the same exact size, or one may be bigger than the other.

Note that when two shapes are similar, it is said that their corresponding angles are often same.  The angles are also known to be the same because the shape is still of the same shape and as such one can be able to tell from the way or order of the similarity based on the way that the angles match up and also in the scenario above.

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Using a system of equations, it is found that each Celine episode is 65 minutes long and each Paul episode is 127 minutes long.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are given by:

Last year, Celine released 39 episodes and Paul released 42 episodes, for a total of 7,869 minutes of content, hence:

39x + 42y = 7869

Then:

[tex]y = \frac{7869 - 39x}{42}[/tex]

This year, Celine released 14 episodes and Paul released 41 episodes, which lasted a total of 6,117 minutes, hence:

14x + 41y = 6117.

Since [tex]y = \frac{7869 - 39x}{42}[/tex]:

[tex]14x + 41\frac{7869 - 39x}{42} = 6117[/tex]

14x - 38.07x = -1564.64.

x = 1564.64/24.07

x = 65.

[tex]y = \frac{7869 - 39 \times 65}{42} = 127[/tex]

Hence, each Celine episode is 65 minutes long and each Paul episode is 127 minutes long.

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Step-by-step explanation:

x + 5 = 3x -12 + 5

x + 5 = 3x - 7

Subtract 5 from both sides....

x + 5-5 = 3x -7 - 5

x = 3x - 12

Change the sign ...

12 = 3x - x

12 = 2x

12/2 = x

x = 6

hence 6 is the answer.......

[tex]\large\textsf{\textbf{Answer\::}}[/tex]

x=6

[tex]\large\textsf{\textbf{Calculations\::}}[/tex]

First , use the Distributive Property :

x+5=3(x-4)+5

x+5=3x-12+5

x+5=3x-7

subtract 3x on both sides :

x-3x+5=-7

-2x+5=-7

Subtract 5 on both sides :

-2x=-7-5

-2x=-12

divide by -2 on both sides :

x=6

We've found the value of x : x = 6 .

[tex]\footnotesize\text{hope\:helpful~}[/tex]