6.
(06.02)
Which of these is the algebraic expression for "some number to the power of 4?" (3 points)


x4

4x

4x

x + 4

Answer:

Domain : {10, 15, 19, 32}

Range: {-1, 5, 9}

Step-by-step explanation:

As the table of the relation is given as follows:

X                Y

10               5

15               9

19               -1

32             5  

From this table, we can define the relation by combining the ordered pairs from the table. Each and every order pair consists of x-coordinate and corresponding y-coordinate of any corresponding point.

So, the relation from the table can be made as follows:

                            relation : {(10, 5), (15, 9), (19, -1), (32, 5)}

Domain of a relation consists of all the x-coordinates (first elements) of order pairs.

Range of a relation consists of all the y-coordinates (second elements) of ordered pairs.

So, domain  and range of relation will be as follows:

                                  Domain : {10, 15, 19, 32}

                                  Range: {-1, 5, 9}

Note: If there is any duplicate element in any x or y-coordinate of any ordered pair, it will be written only once when we determine domain and range. Here, in this example, 5 is duplicate, so, it will be mentioned only one time when we determine the range of this relation.

Keywords:  domain, relation, range

Learn more about domain and range of a relation from brainly.com/question/11422136

#learnwithBrainly

The domain and range of the relation given in the table are the sets of x-values and y-values respectively. In this case, the domain is {-1, 5, 9} and the range is {10, 15, 19, 32}, which corresponds to Option A.

To determine the domain and range of the relation shown in a table, we must look at the set of ordered pairs provided. The domain consists of all the first elements in these pairs, which represent the x-values, while the range consists of all the second elements, which are the y-values. Looking at the table, we can list the x and y values separately to clearly identify the domain and range.

If the table of the relation presents the ordered pairs as (X, Y), interpreting the question that the domain should be {-1, 5, 9} and the range should be {10, 15, 19, 32}, then the correct option would be:

Option A.

Domain: \{-1, 5, 9\} and Range: \{10, 15, 19, 32\}.

It is essential to note that a function is a special relation where each element of the domain maps to a unique element in the range. In this case, as each x-value maps to a distinct y-value, it suggests the relation is indeed a function.

Answer:

The answer is 3000.

Step-by-step explanation:

Start to count from ones->tens->hundreds->thousands (from right to left). When it says nearest thousands, you should look at the previous no. which is in hundreds place. As the no. at hundreds place is lesser than 5, there's nothing to add up. (If no. is greater than 5, you should add 1 to the thousands place)

Answer:

The fourth option gives the result.

Step-by-step explanation:

We have to find f(x) and g(x) from options given such that y = f[g(x)] is equivalent to [tex]y = \frac{8}{\sqrt{2x + 4}}[/tex].

Here, the fourth option gives the result.

If [tex]f(x) = \frac{8}{\sqrt{x} }[/tex] and g(x) = 2x + 4, then the composite function [tex]f[g(x)] = \frac{8}{\sqrt{2x + 4}}[/tex]

⇒ [tex] y = \frac{8}{\sqrt{2x + 4}}[/tex] ( Answer )

Answer:

Step-by-step explanation:

A.  The conversion ratio is that 16 oz = 1 lb

B.  7.75 lb × [tex]\frac{16oz}{1lb}[/tex]

From there the label of lb cancels out, leaving you with the label oz.  Multiply straight across the top to get 124 oz.

You would use long division to determine that 8/12 = 0.667 approximately. The steps would go something like this

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

Step 1) Write 8 under a long division bar and place 12 to the left and outside the bar

Step 2) Change the 8 into 8.0000 (you can have as many trailing zeros as you want)

Step 3) While 12 doesn't go into 8, 12 does go into 80. So you can think of 8.0 as 80. Ask yourself "how many times does 12 go into 80?". The answer is 6 times because 6*12 = 72 (note how 7*12 = 84 is too big). So we write a "6" above the 8.0000 such that it is above the first "0". So far we have 0.6 as the quotient.

Step 4) Multiply that 6 by 12 to get 72. We write the 72 under the 80 and then subtract to get 80 - 72 = 8. Pull down the second 0 from "8.0000" to change that 8 into 80.

Step 5) We effectively repeat steps 3 and 4 again. So thats why we get another 6 as the next part of the quotient, and why the 6's repeat forever. The only reason why there's a 7 at the end is because of rounding.

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

The long division is shown in the image attachment below. The gridlines are there to show how things line up though when you write out the long division steps (to show to your teacher) you wont use any grid lines.

side note: the fraction 8/12 reduces to 2/3. You divide both top and bottom by the GCF 4. So 8/4 = 2 and 12/4 = 3.

Answer:

40%

Step-by-step explanation:

Percentage Passed = 36 ÷ 90 × 100 = 40%

Answer:

- 59.4

Step-by-step explanation:

The given function is [tex]f(x) = 120(0.1)^{x}[/tex]

Therefore, at x = 0, [tex]f(0) = 120(0.1)^{0} = 120[/tex] and  

at x = 2, [tex]f(2) = 120(0.1)^{2} = 1.2[/tex]

Hence, the average rate of change of the given function from x = 0 to x = 2 will be  

[tex]\frac{f(2) - f(0)}{2 - 0}[/tex]

= [tex]\frac{1.2 - 120}{2 - 0}[/tex]

= - 59.4 (Answer)

Answer:

x^2-5x+4

Step-by-step explanation:

(x-3)^2+(x-3)-2

x^2-3x-3x+9+x-3-2

x^2-6x+9+x-5

x^2-5x+9-5

x^2-5x+4

Robin can clean 108 rooms in 9 days, given she cleans 72 rooms in 6 days; this is determined by calculating her daily cleaning rate and extending it over the 9-day period.

The student asks how many rooms Robin can clean in 9 days if she can clean 72 rooms in 6 days. To solve this problem, we first need to determine the rate at which Robin cleans rooms per day, which is done by dividing the total number of rooms by the total number of days. Once we have the daily rate, we can then multiply this rate by 9 to find out how many rooms can be cleaned in 9 days.

First, we calculate the daily rate:

Rate = Total Rooms / Total Days

Rate = 72 rooms / 6 days

Rate = 12 rooms/day.

Now, we multiply the daily rate by 9 days:

Rooms in 9 days = Rate times Number of Days

Rooms in 9 days = 12 rooms/day times 9 days

Rooms in 9 days = 108 rooms.

Therefore, Robin can clean 108 rooms in 9 days.

Answer:

The length of prism is  9 centimetres.

Step-by-step explanation:

Given:

The volume of a rectangular prism is 72 cubic centimeters.

The prism is 2 centimeters wide and 4 centimeters high.

Now, to find the length of prism:

Let the length be [tex]l[/tex].

Width = 2 centimeters.

Height = 4 centimeters.

Volume = 72 cubic centimeters.

So, putting the formula to get the length of prism:

[tex]Volume = length\times width\times height[/tex]

[tex]72=l\times 2\times 4[/tex]

[tex]72=l\times 8[/tex]

Dividing both sides by 8 we get:

[tex]9=l[/tex]

Length = 9 centimetres.

Therefore, the length of prism is  9 centimetres.

Answer:

sum=2a

diff.=-2b

Step-by-step explanation:

a-b+a+b=

2a

a-b-a-b=-2b

Answer:

x = -32

Step-by-step explanation:

¾ x = -24

Multiply both sides by 4.

3x = -96

Divide both sides by 3.

x = -32

Answer:

x = -2

Step-by-step explanation:

Divide -24 by 3 = -8

4x=-8

Divide -8 by 4 = -2

x = -2

Answer: y = -3x - 5

Step-by-step explanation: since the two lines are parallel, it implies that

m1 = m2. From the equation given,

m1 = -3 , m2 = -3

Substantial for m2 in y = mx + c

We now have

y = -3x - 5 since the new line is not passing through any coordinate.

Answer:

The answer is y=-3x-2

I hope it's not too late;)

Step-by-step explanation:

Answer:

0.9375

Step-by-step explanation:

Do the long division and you'll find the answer.

Answer:

x=-2

Step-by-step explanation:

-2+8=6

subtract 8 from six and you get your answer since it is a simpler linear  equation. hoped this helped a little bit

Answer:2

Step-by-step explanation:

-X+8=6

Answer:

Degree = 1

Step-by-step explanation:

Given:

The differential equation is given as:

[tex]\frac{d^2y}{dx^2}+(\frac{dy}{dx})^2+6y=0[/tex]

The given differential equation is of the order 2 as the derivative is done 2 times as evident from the first term of the differential equation.

The degree of a differential equation is the exponent of the term which is the order of the differential equation. The terms which represents the differential equation must satisfy the following points:

The above differential equation doesn't involve any of the above conditions. The exponent to which the first term is raised is 1.

Therefore, the degree of the given differential equation is 1.

Answer:

What are we finding for X?

Step-by-step explanation:

Because the polygons are similar... we can create this proportion relationship.

[tex]\frac{8}{10} = \frac{4}{x}[/tex]

Using cross multiplication...

4·10=8x

8x=40

x=5

answer: x=5

Answer:

2K + 12L ≥ 87 and 1.5K + 8L > 63

Step-by-step explanation:

It takes 2 wooden sticks and 1.5 square feet of paper to make a kite, and it takes 12 wooden sticks and 8 square  feet of paper to make a lamp.

If K denotes the number of kites that Min-Young made and L denotes the number of lamps she made then  

2K + 12L is the number of wooden sticks that she used which is greater than equal to 87

i.e. 2K + 12L ≥ 87 ........ (1)

Again, 1.5K + 8L is the number of square feet of paper that she used which is greater than 63 sq. feet

i.e. 1.5K + 8L > 63 ........... (2)

Hence, inequalities (1) and (2) are the required answer. (Answer)

Answer:

1) 2K + 12L ≥ 87

2) 1.5K + 8L > 63

Step-by-step explanation:

Answer:

none of the above

Step-by-step explanation:

Answer:

Sorry for the incorrect answer everyone!

Step-by-step explanation:

My old answer: Perpendicular bisector

Reasons:

I know I made a mistake before, but this is better late than never! I hope this helps for the future! *^-^*

- sincerelynini

Answer: 8 ft and 4 in, 8 1/3 ft

Step-by-step explanation:

100/12=50/6=25/3=8.3333333...

1/3 of a foot is 1/3x12 which is 12/3 which is 4 in.

Final answer:

100 inches is equal to 8 feet and 4 inches or 8.33 feet.

Explanation:

To solve this problem, you can convert 100 inches to feet using the unit equivalence:

1 foot = 12 inches

Multiply the number of inches by the unit equivalence:

100 inches ÷ 12 inches per foot = 8 feet and 4 inches

Answer:

The answers are given below.

Step-by-step explanation:

7. Simplified Fractions/Integers:

a. [tex]$ (25)^{\frac{-3}{2}} $[/tex]

= [tex]$ (5^2)^{\frac{-3}{2}} $[/tex]

= [tex]$ 5^{-3} $[/tex]

= [tex]$ \frac{1}{5^3} = \frac{1}{125} $[/tex] is the required answer.

b. [tex]$ \bigg ( \frac{1}{7} \bigg )^{2} $[/tex]

= [tex]$ \bigg( \frac{1}{7^2} \bigg) $[/tex]

= [tex]$ \frac{1}{49} $[/tex] is the required answer.

c. [tex]$ \bigg ( \frac{1}{7} \bigg) ^{-3} $[/tex]

= [tex]$ \bigg ( \frac{1}{7^{-3}} \bigg )$[/tex]

= [tex]$ 7^{3} $[/tex] = 343 is the required answer.

8. Simplified Fractions:

a. [tex]$ \bigg( \frac{27}{8} \bigg ) ^{\frac{2}{3}}$[/tex]

= [tex]$ \bigg ( \frac{3^3}{2^3} \bigg ) ^{\frac{2}{3}} $[/tex]

= [tex]$ \bigg ( \frac{3}{2} \bigg) ^2  $[/tex]

[tex]$ = \frac{9}{4} $[/tex] is the required answer.

b. [tex]$ \bigg ( \frac{4}{25} \bigg)^{\frac{-3}{2}} $[/tex]

= [tex]$ \bigg ( \frac{2^2}{5^2} \bigg)^{\frac{-3}{2}}[/tex]

= [tex]$ \bigg ( \frac{2^{-3}}{5^{-3}} \bigg ) $[/tex]

= [tex]$ \bigg( \frac{5^3}{2^3} \bigg ) $[/tex]

= [tex]$ \frac{125}{8} $[/tex] is the required answer.

9. Index Forms:

a. √3

= [tex]$ 3^{\frac{1}{2}} $[/tex] is the required answer.

b. ∛3

= [tex]$ 3^{\frac{1}{3}} $[/tex] is the required answer.

c. [tex]$\sqrt[6]{2} $[/tex]

= [tex]$ 2^{\frac{1}{6} $[/tex] is the required answer.

d. [tex]$ \sqrt{5^3} $[/tex]

= [tex]$ 5^{\frac{3}{2}} $[/tex] is the required answer.

e. [tex]$ \frac{1}{(\sqrt[3]{5})^2} $[/tex]

= [tex]$ \frac{1}{5^{\frac{2}{3}}} $[/tex]

= [tex]$ 5^{\frac{-2}{3}} $[/tex] is the required answer.

Answer:

company  B

Step-by-step explanation:

the company is good!

Final answer:

To find the cost to the family of each company's phone plan, we calculated the total cost for four phone lines and four unlimited texting plans, as well as the cost for two international calls. Based on the calculations, John's family should use Company A because it has the lowest total cost of $100.50.

Explanation:

To find the cost to the family of each company's phone plan, we need to calculate the total cost for four phone lines and four unlimited texting plans, as well as the cost for two international calls. Let's calculate the cost for each company:

Company A:

Cost for four phone lines = 4 * $20 = $80

Cost for four unlimited texting plans = 4 * $5 = $20

Cost for two international calls = 2 * $0.25 = $0.50

Total cost for the family with Company A = $80 + $20 + $0.50 = $100.50

Company B:

Cost for four phone lines = 4 * $15 = $60

Cost for four unlimited texting plans = 4 * $10 = $40

Cost for two international calls = 2 * $0.50 = $1

Total cost for the family with Company B = $60 + $40 + $1 = $101

Company C:

Cost for four phone lines = 4 * $25 = $100

Cost for four unlimited texting plans = 4 * $8 = $32

Cost for two international calls = 2 * $0.15 = $0.30

Total cost for the family with Company C = $100 + $32 + $0.30 = $132.30

Therefore, John's family should use Company A because it has the lowest total cost of $100.50.

Answer:

26 2/3

Step-by-step explanation:

We could turn both of these numbers into decimals, but I find fractions easier.

so 5 1/3 as an improper fraction is 16/3

0.2 as a fraction is 2/10 or 1/5

so now we have the equation 16/3 ÷ 1/5 or 16/3 x 5/1

this give me 80/3, then when simplified gives me 26 2/3.

Answer:

12.5 centimeters per minute

Step-by-step explanation:

From the graph, the rate at which the diameter increasing would be inthe units of cm/min

The rate is basically the slope of the line. The slope (m) has formula:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Where

[tex](x_1,y_1)[/tex]  is any point from the graph

and

[tex](x_2,y_2)[/tex]  is another point from the graph

Let's take the origin (0,0) as the first point and (4,50) as the second point. Now lets calculate the slope:

[tex]m=\frac{y_2-y_1}{x_2-x_1}\\m=\frac{50-0}{4-0}\\m=\frac{50}{4}\\m=12.5[/tex]

Thus, we can say:

The diameter of the hot air balloon is increasing at a rate of 12.5 centimeters per minute

Answer:

50

Step-by-step explanation:

150 divided by 3 is 50 and since you shared only one third the answer will be 50

Answer:50

Step-by-step explanation:

One third equals 1/3 of 150

1/3 ×150 =50

Answer:

$638.25

Step-by-step explanation:

The interest is 5.5% yearly and it is simple interest.

Now, if we consider a deposit of $575 into the bank account that earned 5.5% simple interest each year, then after 2 and half years James will get interest only for 2 years as the 3rd year's interest will be added after the 3rd year.

Therefore, if no money was deposited into or withdrawn from the account, then after 2.5 years the sum will be  

[tex]575(1 + \frac{5.5 \times 2}{100}) = 638.25[/tex] dollars. (Answer)

Answer:

0.714

Step-by-step explanation:

Answer:

0.714...

Step-by-step explanation:

5/7 means 5 divided by 7=

0.71428571...= 0.714(rounded)

Solve for x.

20% × x = 35

0.2x=35

x=175

answer: 175

Answer: 175

Step-by-step explanation: We can change this problem to mean the same thing but it will say 20% of what number is 35.

To answer the question 20% of what number is 35, we translate the question into an equation. First we have 20% which we need to write as a decimal and remember to write 20% as a decimal, we move the decimal point 2 places to the left and we get 0.20.

Next we have "of what number" that's times x, "is 35" = 35. Now we have the equation (.20)(x) = 35.

Not to solve for x, since x is being multiplied by .20, we need to divide by .20 on both sides of the equation. On the left side of the equation the .20's cancel and we have x. On the right side of the equation we have 35 divided by .20 which is 175.

This means that 20% of 175 is 35.

Answer:

[tex]\large\boxed{\dfrac{1}{x-4}\ \text{for}\ x\neq5\ \wedge\ x\neq4}[/tex]

Step-by-step explanation:

[tex]\dfrac{x-5}{(x-5)(x-4)}\\\\\text{Domain:}\ (x-5\neq0\ \wedge\ x-4\neq0)\Rightarrow(x\neq5\ \wedge\ x\neq4)\\\\\dfrac{x-5}{(x-5)(x-4)}\qquad\text{cancel}\ (x-5)\\\\=\dfrac{1}{x-4}[/tex]

Answer:

Domain[tex]=\{1,2,3,4,5,6,7,8,9,10,11,12,,13,14,15,16,17,18,19,20\}[/tex]

In other words Domain[tex]=\{x|x\ is\ an\ integer\ and\ 1\leq x\leq20\}[/tex]

Step-by-step explanation:

[tex]C(x)=80-4x[/tex]

Let after [tex]t[/tex] weeks she has left no money.

[tex]c(t)=0\\80-4t=0\\4t=80\\t=20[/tex]

That means she can have money for ice cream from the week 1 to week 20 and after that she will have no money.

So [tex]x[/tex] can be any number between [tex]1[/tex] and [tex]20[/tex]

Hence Domain[tex]=\{x|x\ is\ an\ integer\ and\ 1\leq x\leq20\}[/tex]