Suppose that the functions r and s are defined for all real numbers x as follows.
r(x)=x-2
s(x)=3x+6

Write the expressions for (r+s) (x) and (r-s)(x) and evaluate (r·s)(−1).
(r+s)(x) =
(r-s)(x) =
(r.s) (-1) =

Answer:

No, it is not true.

Perpendicular lines meet one another at 90°​.

Answer:

It is false

Step-by-step explanation:

It is false because perpendicula line meet in 90 degree

The total cost paid by the senior citizen for 3 days = $50

The function representing the total cost of the annual pass is:

f(x) = 20x + 80

A senior citizen pays $20 less than half of this price for x days

The total cost paid by the senior citizen = [tex]\frac{f(x)}{2} -20[/tex]

The total cost paid by the senior citizen =[tex]\frac{20x+80}{2} -20[/tex]

Simplify the resulting expression:

The total cost paid by the senior citizen =10x + 40 - 20

The total cost paid by the senior citizen = 10x + 20

x represents the number of days

Substitute x = 3 into the resulting equation

The total cost paid by the senior citizen for 3 days  =10(3)+20

The total cost paid by the senior citizen for 3 days = $50

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Answer:

0.14×0.25= 0.035 KM

so it can travel 0.035KM in 0.25 hr

Answer:

0.035 kilometers

Step-by-step explanation:

Proportions:

0.14 kilometers ⇒ 1 hour

A kilometers ⇒ 0.25 hour

A = 0.14 kilometers * 0.25 hour / 1 hour

A = 0.035 kilometers

It is not a function with domain as { 9 / 2 , 0} and range as {1 / 4, -4, 6}.

We are given a relation:

{(9 / 2, 1 / 4),(4 1 / 2, -4),(0, 5 / 6)}

We can also write it as:

{(9 / 2, 1 / 4),(9 / 2, -4),(0, 5 / 6)}

The domain of the relation will be:

Domain = { 9 / 2 , 0}

The range of the relation will be:

Range = {1 / 4, -4, 6}

We know that every function can be a relation but every relation cannot be a function.

A relation means the connection between the input and the output.

A function means that for every input there should only be one output.

Here, this relation is not a function because:

The input 9 / 2 has 2 outputs as 1 / 4 and -4 which is not possible in a function.

Therefore, we get that it is not a function with domain as { 9 / 2 , 0} and range as {1 / 4, -4, 6}.

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Answer:

x =(2-√52)/6=(1-√ 13 )/3= -0.869

x =(2+√52)/6=(1+√ 13 )/3= 1.535

it has either 0.868 or -1,85

The function of the number of DVDs Angel owns (a) will be a = p + 10

From the information, Angel owns 10 more DVDs than Philip.

The number of DVD that Philip owns was represented asp.

Therefore, the function of the number of DVDs Angel owns (a) will be:

a = p + 10

Therefore the function is a = p + 10

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By using a linear equation, we can see that after the 19 day the population will be less than 1000 mold spores.

We know that the population decays at a rate of 30 spores per day, and we have an initial population of 1560 mold spores.

Then, the population of spores after x days is given by the linear equation:

P(x) = 1560 - 30*x

The population will be exactly 1000 spores when:

P(x) = 1000 =  1560 - 30*x

We need to solve that for x.

30x = 1560 - 1000 = 560

x = 560/30 = 18.67

So after 18.67 days the population is 1000, this means that after the 19 day the population will be less than 1000 mold spores.

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Mary has left with a 1 kilometer  i.e. [tex]\frac{2}{7}[/tex] of the journey is incomplete

Given that Mary is going for a 3.5 km walk. So far she’s walked 1.55 km through the park, 0.6 km across the bridge, and 0.35 km up the hill and asked to find the  fraction of the walk she has left

Total journey distance = 3.5 kilometers

Distance walked by mary on the bridge=0.6 kilometers

Distance walked by mary through the park=1.55 kilometers

Distance walked by mary up the hill=0.35 kilometers

Total distance traveled by mary=(0.6+1.55+0.35)kilometers

Total distance traveled by mary=2.5 kilometers

The distance left=3.5 kilometers-2.5 kilometers

The distance left=1 kilometer

1 kilometer is  [tex]\frac{2}{7}[/tex] of the journey by assuming 3.5 kilometer will complete the jouney

Therefore, Mary has left with a 1 kilometer  i.e. [tex]\frac{2}{7}[/tex] of the journey is incomplete

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Answer:

1,700

Step-by-step explanation:

5x10^-7 is 0.0000005, while 8.5x10^-4 is 0.00085

0.00085/0.0000005=1700

Thus5 x [tex]10^{-7}[/tex] is 1700 times smaller than  8.5 x [tex]10^{-4}[/tex].

Option C is the correct answer.

Given,

5 x [tex]10^{-7}[/tex] and 8.5 x [tex]10^{-4}[/tex]

We need to find how many times smaller is 5 x [tex]10^{-7}[/tex] than 8.5 x [tex]10^{-4}[/tex].

Exponents are the power of a given number.

Example: a²

a - base

2 - exponent

Compare 5 x [tex]10^{-7}[/tex] and 8.5 x [tex]10^{-4}[/tex].

5 x [tex]10^{-7}[/tex]  can be written as 5 / 10000000

8.5 x [tex]10^{-4}[/tex] can be written as 8.5 / 10000

Now,

5 / 10000000 = 0.0000005

8.5 / 10000 = 85 / 100000 = 0.00085

We see that,

0.0000005 is less than 0.00085

Now,

0.0000005 x 1700 = 0.00085

5 x [tex]10^{-7}[/tex] is 1700 times smaller than  8.5 x [tex]10^{-4}[/tex].

We can also write as:

5 x [tex]10^{-7}[/tex] x 17 x 10 ²  

= 5 x 17 x [tex]10^{-7}[/tex] x 10²

= 85 x [tex]10^{-7 + 2}[/tex]

= 85 x [tex]10^{-5}[/tex]

= 85/10 x 10 x [tex]10^{-5}[/tex]

= 8.5 x [tex]10^{-5 + 1}[/tex]

= 8.5 x [tex]10^{-4}[/tex]

Thus 5 x [tex]10^{-7}[/tex] is 1700 times smaller than  8.5 x [tex]10^{-4}[/tex].

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Answer:

(i)

Step-by-step explanation:

express the ratio as a fraction, that is

4 : 5 = [tex]\frac{4}{5}[/tex]

to convert the fraction to a percentage multiply it by 100%

[tex]\frac{4}{5}[/tex] × 100% = 4 × 20% = 80%

Answer:

17.7 m

Step-by-step explanation:

57 m / 30 m/s = time in the air = 1.9 s

vertical drop for 1.9 s

 vertical d = 1/2 a t^2 = 17. 7 m

After solving for x in the constructed equation, 97100 bushels were harvested last year.

What is an equation?

Constructing equation to determine no. of bushels.

Bales from the previous year = x + 0.45 x

= 140795 1.45 x

= 140795 X

= 97100 bales

After solving for x in the constructed equation, 97100 bushels were harvested last year.

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Answer:97100

Step-by-step explanation:

The equivalent form of the compound inequality where the compound inequality is given as  -22 > -5x - 7 ≥ -3 is -15 > -5x  ≥ 4

The compound inequality is given as

-22 > -5x - 7 ≥ -3

Add 7 to all sides of the compound inequality

So, we have

7 -22 > -5x - 7 + 7 ≥ -3 + 7

Evaluate the sum in the above compound inequality

So, we have

-15 > -5x  ≥ 4

Hence, the equivalent form of the compound inequality where the compound inequality is given as  -22 > -5x - 7 ≥ -3 is -15 > -5x  ≥ 4

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Answer: mark as brainliest please

Step-by-step explanation:
V=4/3 x 3.14 x 3^3

V= 113.04

SA= 4 x 3.14 x 3^2

SA= 113.04

Answer:

38

Step-by-step explanation:

5 x 10 -7= 43

8.5 x 10 -4= 81

81-43= 38

Answer:

[tex] 1.7 \times 10^3 = 1700 [/tex]

Step-by-step explanation:

To find how many times x is smaller than y, divide y by x.

Here we want to find how many times 5 × 10^-7 is smaller than 8.5 × 10^-4, so we divide 8.5 × 10^-4 by 5 × 10^-7.

[tex] \dfrac{8.5 \times 10^{-4}}{5 \times 10^{-7}} = [/tex]

[tex] = \dfrac{8.5}{5} \times \dfrac{10^{-4}}{10^{-7}} [/tex]

[tex] = 1.7 \times 10^{-4 - (-7)} [/tex]

[tex] = 1.7 \times 10^{-4 + 7} [/tex]

[tex] = 1.7 \times 10^3 = 1700 [/tex]

The time it would take Shirley to mow the lawn alone is 3 hours

From the information given;

Let Shirley's working hours be x

Let Pam's working hours be y

We have  that;

Shirley and Pam work 6 hours together, this is expressed as;

x + y = 6

Given that Pam work 3 hours alone, we have;

y = 3

Substitute the value of y as 3 in the equation

x + 3 = 6

x = 6 - 3

x = 3

Thus, the time it would take Shirley to mow the lawn alone is 3 hours

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Answer:

give me those points boy=o >:)

Step-by-step explanation:

While horizontal and vertical shifts involve adding constants to the input or to the function itself, a stretch or compression occurs when we multiply the parent function

f

(

x

)

=

b

x

by a constant

|

a

|

>

0

. For example, if we begin by graphing the parent function

f

(

x

)

=

2

x

, we can then graph the stretch, using

a

=

3

, to get

g

(

x

)

=

3

(

2

)

x

and the compression, using

a

=

1

3

, to get

h

(

x

)

=

1

3

(

2

)

x

.

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

Work Shown:

Recall that the imaginary number i has the definition of [tex]i = \sqrt{-1}[/tex]

List out the first few powers of i

I'm skipping steps when I listed out those terms, so let me know if you need to see them.

The process repeats every 4 items. This means we'll divide the exponent by 4 to look at the remainder.

Let's do that for the first exponent

12/4 = 3 remainder 0

The remainder 0 tells us that i^12 = i^0 = 1

Also,

22/4 = 5 remainder 2

The remainder 2 means i^22 = i^2 = -1

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

In short:  i^12  = 1 and i^22 = -1

which means 6i^12 + 7i^22 = 6(1) + 7(-1) = -1

Answer:

#1) & #5) are the rates that have the same constant rate of change as Micheal's rate.

given points P( 13 ,14) and Q( 18,9 )

we have to calculate distance

[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}d = distance(x_1, y_1) = coordinates of the first point(x_2, y_2) = coordinates of the second point[/tex]

d= [tex]\sqrt{( 18-13)^2+(9-14)^2}[/tex]

d=5[tex]\sqrt{2}[/tex]

now calculating midpoints

s= 13+18 /2 =31/2

t= 14+9 / 2= 23/2

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Three rational numbers between

1/3 and 1/5 are 4/15, 3/10, and 7/30

Given:The two numbers are 1/3 and 1/5

To find:The rational number between two numbers

Solution:Now, to find the rational number, add the numbers and divide their sum by 2.

(i) First rational number between

1/3, 1/5 = 1/3+1/5=8/5

Divide 18/5 by 2------> 8/15 x 1/2= 8/30= 4/15

The series becomes, 1/3, 4/15, 1/5

(ii) Second rational number

= 4/15+1/5 = 7/15

Divide

7/15 by 2 ------> 7/15 x 1/2 = 7/30

Hope this helps!

The measure of each of the supplementary angles are: 88.6° and 91.4°.

Based on the definition of supplementary angles, the sum of two angles that are supplementary equals 180 degrees.

Given the following:

Let one of the angles equal x

The second angle would be expressed as: x + 2.8

Therefore, we would have the equation:

x + 2.8 + x = 180 [supplementary angles]

2x + 2.8 = 180

2x = 180 - 2.8

2x = 177.2

x = 177.2/2

x = 88.6

Thus:

One of the angles = x = 88.6°

Th second angle is: x + 2.8 = 88.6 + 2.8 = 91.4°

Therefore, the measure of each of the supplementary angles are: 88.6° and 91.4°.

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The Average return rate for the investment will be 3.2%.

The Return Rate can be defined as a profit that is made on investment .

In the Question

let the investment be "x" .

25% stocks in Company A have return rate of 6%.

Investment in Company A = (25% of x)

Return is 6% of investment = (25% of x) + 6% of (25% of x)

Return from company A= (25% of x)(1+0.06)     ...as 25%=0.25 & 6%=0.06

                                        = 0.25*x*(1.06)     ...(i)

40% stocks in Company B have return rate of 2.5%.

Investment in Company B = (40% of x)

Return is 2.5% of investment = (40% of x) + 2.5% of (40% of x)

Return from company A = (40% of x)(1+0.025)         ...

                                        = 0.40*x*(1.025)     ...(ii)

Stocks in Company C = 100 - 25 - 40 = 35%

35% stocks in Company C have return rate of 2%.

Investment in Company C = (35% of x)

Return is 2.5% of investment = (35% of x) + 2% of (35% of x)

Return from company C = (35% of x)(1+0.02)         ...

                                        = 0.35*x*(1.02)     ...(iii)

Total Return = Return from Company A + Return from Company B + Return from Company C .

From equation (i) ,(ii) and (iii) we get

Total Return = 0.25*x*(1.06) + 0.40*x*(1.025) + 0.35*x*(1.02)

= 0.265x + 0.41x + 0.357x

= 1.032x

The Average rate of return  = [tex]\frac{return- investment }{investment } \times100[/tex]

Substituting the value we get,

= (1.032x - x ) / x  *100

= 0.032x /x  * 100

= 0.032*100

= 3.2%

Therefore , the Average return rate for the investment will be 3.2%.  

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This statement in the article is wrong because $2.69 is not the mean price ($2.81)

The prices from 5 gas stations surveyed are given as:

$2.79, $2.99, $2.69, $2.89, and $2.69.

There are no outliers in the dataset

So, the dataset can be summarized by the mean

The mean is

Mean = Sum/Count

So, we have

Mean = ($2.79+ $2.99+ $2.69+ $2.89+$2.69)/5

Evaluate

Mean = 2.81

The article quoted $2.69 as the typical price

This statement in the article is wrong because $2.69 is not the mean price ($2.81)

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convert 81°into radian

81°=(81×pie/180)=9pie/20 pie=22/7

now,

radius=arc length/θ in radian

then 69/(9pie/20)

=48.79

All cookies are made with sugar Oreos are a cookie so Rosa knows Oreos are made with sugar is Inductive.

A cookie is a compact, flat, and sweet baked or cooked snack or dessert. It is often made using flour, sugar, an egg, and some kind of oil, fat, or butter. Other components such as raisins, oats, chocolate chips, almonds, and so on may be used.

Sandwich biscuits with marshmallows or jam filling and often dipped in chocolate or another sweet coating, such as custard creams, Jammie Dodgers, Bourbons, and Oreos, are examples of biscuit or cookie varieties. Cookies are frequently served with liquids such as milk, coffee, or tea, and are occasionally "dunked," a method of releasing more flavor from confections by diluting the sugars and reducing their texture.

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Answer:

will be 1

Step-by-step explanation:

..............

Answer:1

Step-by-step explanation:

The average change is 3 degrees per hour.

To calculate the average of any data we have to divide the change by the time taken for that change.

let us suppose there is a data 4,5,6,7 and 8.

Average of the data will be the sum of data divided by the number of terms.

Average=[tex]\frac{4+5+6+7+8}{5}[/tex]

            =[tex]\frac{30}{5}[/tex]

            = 6

So now we will calculate the average change in temperature per hour,

Given that there is a fall of 12 degrees in 4 hours.

Average change per hour=[tex]\frac{12}{4}[/tex]

                                        = 3 degrees per hour

So, the required change is 3 degrees per hour.

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Answer:

B and D

Step-by-step explanation:

The wording in the answer choices make a huge difference. It is possible implies that there is a possibility

A is false. The range of a function is the output value of the function for the input value in the domain of the function. So we can say with certainty that 7 is in the range since it is an output. But we cannot state that 4 is in the range because we have only one output value 7 for g(4)

A good example is a constant function such as g(x) = 7. Here, whatever the value of x, the y value is always 7. This represents a horizontal line passing through y = 7. So the range is just a single number {7}

B can be true. It is possible but not a certainty that f(a) = 4 for some value of a. For example, consider the function g(x) = x + 3.

At x = 4, g(4) = 4 .1 + 3 = 7

At x = 1, g(1) = 1 + 3 = 4 so it is possible for 4 to be an output

C is false. A well-defined function has only a unique value for a specific input of x. So we cannot get two different values for a single x value.

D is true. Since at x =4, y = g(x) = 7, this corresponds to a point on the graph. The point will be (x=4, y =7) or (4,7)

E is false. The x, y coordinates have been interchanged in this answer choice

The true statements are B and D.

The wording in the answer choices make a huge difference.

It is possible implies that there is a possibility

A. 4 is in the range of g.

A is false.

The range of a function is the output value of the function for the input value in the domain of the function. So we can say with certainty that 7 is in the range since it is an output. But we cannot state that 4 is in the range because we have only one output value 7 for g(4)

A good example is a constant function such as g(x) = 7.

Here, whatever the value of x, the y value is always 7.

This represents a horizontal line passing through y = 7.

So the range is just a single number {7}

B. For a value a, it is possible that g (a) = 4.

B can be true.

It is possible but not a certainty that f(a) = 4 for some value of a.

For example, consider the function g(x) = x + 3.

At x = 4, g(4) = 4 .1 + 3 = 7

At x = 1, g(1) = 1 + 3 = 4 so it is possible for 4 to be an output.

C. For a value y, it is possible that g (4) = y.

C is false.

A well-defined function has only a unique value for a specific input of x. So we cannot get two different values for a single x value.

D. The point (4,7) is on the graph of y = g (x).

D is true.

Since at x =4, y = g(x) = 7, this corresponds to a point on the graph.

The point will be (x=4, y =7) or (4,7)

E. The point (7, 4) is on the graph y = g(x).

False. The statement doesn't provide any information about g(7), and we cannot determine whether the point (7, 4) lies on the graph of the function y = g(x) based solely on the given information.

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