If f(x)=2x and g(x)= 1/x, what is the domain of (f*g) (x)

Answer:

$0.036

Step-by-step explanation:

I will be solving this questions in a rational, proportional way.

This question given is directly proportional. There are two types of proportion.

Direct - Let's say there are two values, x and y. In direct proportion, while x   increases, y increases with it.  

Inverse- Taking x and y, in inverse proportion, while x increases, y decreases or while y increases, x decreases.

In the given example, there are two values, number of plates and cost of plates. While the number of plates increases, the cost would surely increase. Therefore, giving us that it is a direct proportion.

500 plates : $18.00 :: 1 : $x

500 plates is to 18 dollars, then, 1 plate is to how many dollars?

In direct proportion, the product of extremes is equal to the product of means.

500(x) = 18(1)

500x = 18

x = 18 / 500

x = 0.036

Hence, one plate costs $0.036 or 3.6 cents

Answer:

each plate cost:  .036 each

18.00 divided by 500

Step-by-step explanation:

Answer:

AC=16.2 units

Step-by-step explanation:

we know that

The triangle ABC is an isosceles triangle

so

AX=XC

because triangles ABX and CBX are congruents

AC=2*AX

see the attached figure to better understand the problem

therefore

AC=2*8.1=16.2 units

Final answer:

To find the length of AC, we add the lengths of segments AX and BC, giving us AC = 8.1 + 18.5, which equals 26.6 units.

Explanation:

If we are given that AB = 18.5 units, AX = 8.1 units, and BC = 18.5 units, then to find the length of AC, we simply need to add the lengths of segments AX and BC together, since AX and BC are adjacent segments on line AC. The formula to calculate AC in this situation is:

AC = AX + BC

Substituting the given values into this formula gives us:

AC = 8.1 units + 18.5 units = 26.6 units

Therefore, the length of segment AC is 26.6 units.

Answer:

1/2x-5=13

Step-by-step explanation:

Let x= Frankie’s mother’s age

Half his mother’s age= 1/2x

5 less than that=1/2x-5

We know that Frankie is 13 so that equation is equal to Frankie’s age, which is 13.

Hope this helps.

To determine Franky's mother's age, we can create an equation using the given information. By solving the equation, we find that Franky's mother is 36 years old.

To determine Franky's mother's age, we can create an equation based on the given information. Let's assume Franky's mother's age is M. According to the information given, Franky's age is 5 years less than half of his mother's age. So, Franky's age can be represented as (1/2)M - 5.

We are also given that Franky is 13 years old. So we can set up the equation:

(1/2)M - 5 = 13

To solve for M, we can simplify the equation:

(1/2)M = 13 + 5

(1/2)M = 18

M = 18 * (2/1)

M = 36

Therefore, Franky's mother's age is 36 years old.

Answer: 432ft. shadow

Step-by-step explanation:

Because Nora is 5’3”, you need to convert every numerical value into inches by multiplying them by 12 (12in = 1 ft.)

5’ x 12 = 60” + 3” = 63”

9’ x 12 = 108”

252’ x 12 = 3,024”

Then create equivalent fractions.

63/108 = 3,024/x

108 x 3024 = 326,592/63 = 5,184in.

Then convert it back into feet.

5,184/12 = 432ft.

Final answer:

Using the proportion of similar triangles, we find that if Nora, who is 63 inches tall, casts a 108-inch shadow, then the 3024-inch tall monument will cast a shadow that is 5184 inches long, or 432 feet.

Explanation:

To find the length of the shadow casted by the monument, we can use the concept of similar triangles. The proportion between the heights and shadows of Nora and the monument will be the same because the angle of the sunlight is the same for both. Nora is 5'3" tall, which is 63 inches, and she casts a 9-foot shadow, which is 108 inches. The monument is 252 feet tall, which is 3024 inches. Setting up the proportion, we have:

Nora's height : Nora's shadow = Monument's height : Monument's shadow

63 inches : 108 inches = 3024 inches : x inches

To solve for x (the length of the monument's shadow in inches), we cross-multiply and divide:

63 * x = 3024 * 108

x = (3024 * 108) / 63

x = 5184 inches

To convert this back to feet, we divide by 12 inches per foot:

x = 5184 inches / 12 inches/foot

x = 432 feet

Therefore, the length of the shadow cast by the monument is 432 feet.

Answer:

Isosceles

Step-by-step explanation:

Consider triangle ABC, BD is the median and the altitude drawn to the side AC. This segment (BD) divide the triangle ABC into two triangles: ABD and CBD.

In these triangles:

Thus, by SAS postulate, triangles ABD and CBD are conruent. Congruent triangles have congruent corresponding sides. Hence, AB=CB.

If in triangle ABC, AB=BC, then this triangle is isosceles.

Answer:

Isosceles (apex)

Step-by-step explanation:

The median is 133.5, the first quartile is 128, the third quartile is 139, and the interquartile range is 11.

It is the middle value of the given set of numbers after arranging the given set of numbers in order.

We have,

To find the median, first we need to order the data set from least to greatest:

106, 127, 129, 132, 135, 138, 140, 158

There are 8 data points, so the median is the average of the 4th and 5th numbers:

Median = (132 + 135) / 2 = 133.5

To find the quartiles, we need to divide the data set into four equal parts. Since there are 8 data points, the first quartile (Q1) is the median of the first half of the data set, and the third quartile (Q3) is the median of the second half of the data set.

Q1 = median of {106, 127, 129, 132} = (127 + 129) / 2 = 128

Q3 = median of {135, 138, 140, 158} = (138 + 140) / 2 = 139

The interquartile range (IQR) is the difference between the third quartile and the first quartile:

IQR = Q3 - Q1 = 139 - 128 = 11

Therefore,

The median is 133.5, the first quartile is 128, the third quartile is 139, and the interquartile range is 11.

Learn more about median here:

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Final answer:

The median of the given data set is 133.5, with the first quartile (Q1) at 128 and the third quartile (Q3) at 139. The interquartile range (IQR) is 11, and the range is 52.

Explanation:

To find the median, first quartile (Q1), third quartile (Q3), and interquartile range (IQR) of a set of data, we first need to list the data in ascending order. The given data is: 106, 127, 129, 132, 135, 138, 140, 158.

The median is the middle number when the data set is ordered. Since there are 8 numbers, the median will be the average of the 4th and 5th numbers: (132 + 135) / 2 = 133.5. So the median is 133.5

To find the first quartile, which is the median of the lower half of the data (excluding the median if the number of data points is odd), we look at the first four numbers: 106, 127, 129, 132. The median of this subset is (127 + 129) / 2 = 128. So Q1 is 128.

Similarly, Q3 is the median of the upper half of the data. For the numbers 135, 138, 140, 158, the median is (138 + 140) / 2 = 139. So Q3 is 139.

The IQR is the difference between Q3 and Q1, so IQR = 139 - 128 = 11.

The range of the data is the difference between the max and min values, which is 158 - 106 = 52.

What your are going to want to do is look for the average of the number (hope this helps some what!) good luck

Answer:

3

Step-by-step explanation:

The given function is

[tex]f(x)=-x^2+6x+13[/tex]

The average rate of change is simply the slope of the secant line connecting any two point on the graph of the function.

The average rate of change  of this function over the interval;

[tex]-1\le x\le 5[/tex] is given by:

[tex]\frac{f(5)-f(1)}{5-1}[/tex]

[tex]f(5)=-(5)^2+6(5)+13[/tex]

[tex]f(5)=-25+30+13=18[/tex]

[tex]f(-1)=-(-1)^2+6(-1)+13[/tex]

[tex]f(-1)=-1-6+13=18[/tex]

[tex]f(-1)=6[/tex]

The average rate of change now becomes;

[tex]\frac{18-6}{4}[/tex]

[tex]\frac{12}{4}=3[/tex]

Answer:

Circumference=37.6991 or 38

Step-by-step explanation:

c=2[tex]\pi[/tex]r

c=2[tex]\pi[/tex]6

c=37.6991

Answer:

Step-by-step explanation:

c=2\pir

Answer:

A. 16

Step-by-step explanation:

We have to find rate of change of function from x=3 to x=5

The average rate of change for the interval a≤x≤b is given by:

Rate of change=  (f(b)-f(a))/(b-a)

In our question,

a=3

and

b=5

We can see from the table that at x = 3, the value of function is 18

So,

f(a)=18

and

At x=5, the value of function is 50

f(b)=50

Rate of change=(50-18)/(5-3)

=32/2

=16

So the rate of change of function between x=3 and x=5 is 16 ..  

Option A is the correct answer..

Answer:

Answer D:  7/5

Step-by-step explanation:

Combine like terms:  add 21 to both sides, obtaining:

25n = 35, or n = 35/25, or n = 7/5 (Answer D)

Answer:

D. 7/5

Step-by-step explanation:

To solve -21 + 25n = 14 for n, you must first isolate the variable.To do this add 21 on each side of the equation, 21+-21 cancels out and 21 + 14 equals 35.

You now have 25n = 35. To then further isolate the variable, divide each side by 25.25 and 25 cancels out so you get n = 1.4.

7/5 is equal to 1.4

So it is D!!!!!!!!!!!!!

ANSWER

[tex](b + 3)(1 - c)[/tex]

EXPLANATION

The given expression is:

[tex](b + 3) - c(b + 3)[/tex]

We can rewrite this to reveal the invisible 1 multiplying the first term.

[tex]1(b + 3) - c(b + 3)[/tex]

There is a common factor of (b+3).

We factor to get;

[tex](b + 3)(1 - c)[/tex]

Therefore the completely factored form of the given expression is

[tex](b + 3)(1 - c)[/tex]

Answer: About 134% of last years earnings

Step-by-step explanation:

Do 36 divided by the amount of sides the hexagon has. I think I am not sure

Answer:

see explanation

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

y + 8 = - [tex]\frac{1}{9}[/tex] (x - 7) is in this form

with slope = - [tex]\frac{1}{9}[/tex] and (a, b) = (7, - 8)

Answer: 15 feet

Step-by-step explanation: 28-13

The phrase "eight times the sum of a number and 16 is at least -28" translates into the inequality 8(w + 16) >= -28. After solving, it shows that w must be greater than or equal to -19.5.

The student's question involves creating and solving an inequality. The inequality represents the phrase 'eight times the sum of a number and 16 is at least -28' and uses the variable w for the unknown number. The inequality in mathematical terms is:

8(w + 16) = -28

To solve the inequality, we first distribute 8 across the parenthesis:

8w + 128 = -28

Subtract 128 from both sides to get:

8w =-28 - 128

8w = -156

Now divide both sides by 8:

w = -19.5

This inequality shows that the number w must be greater than or equal to -19.5 to satisfy the original statement.

The solution to the inequality is [tex]\( w \geq -19.5 \)[/tex]

[tex]\[ w \geq \frac{-28 - 8 \times 16}{8} \][/tex]

[tex]\[ w \geq \frac{-28 - 128}{8} \][/tex]

[tex]\[ w \geq \frac{-156}{8} \][/tex]

[tex]\[ w \geq -19.5 \][/tex]

To solve this inequality, we'll first rewrite the given statement in mathematical terms. The problem states that "eight times the sum of a number and 16 is at least -28." Let's represent the unknown number by [tex]\( w \)[/tex]. According to the statement, we can write the inequality as:

[tex]\[ 8(w + 16) \geq -28 \][/tex]

To solve for [tex]\( w \)[/tex], we'll isolate it by performing operations to both sides of the inequality. First, we distribute the 8:

[tex]\[ 8w + 128 \geq -28 \][/tex]

Next, we'll subtract 128 from both sides to isolate the [tex]\( 8w \)[/tex] term:

[tex]\[ 8w \geq -28 - 128 \][/tex]

[tex]\[ 8w \geq -156 \][/tex]

Now, to solve for [tex]\( w \)[/tex], we divide both sides by 8:

[tex]\[ \frac{8w}{8} \geq \frac{-156}{8} \][/tex]

[tex]\[ w \geq -19.5 \][/tex]

So, the solution to the inequality is [tex]\( w \geq -19.5 \)[/tex]. This means that any number greater than or equal to -19.5 will satisfy the given condition. Therefore, the set of solutions is all real numbers greater than or equal to -19.5.

Complete question:

Eight times the sum of a number and 16 is at least -28 Use the variable w for the unknown number

Answer:

The sales tax is equal to [tex]\$2.3[/tex]

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

Let

y-----> the cost of the purchase

x ----> the sales tax

step 1

Find the value of k

For [tex]y=76, x=3.80[/tex]

substitute

[tex]k=y/x[/tex]

[tex]k=76/3.8[/tex]

[tex]k=20[/tex]

The linear equation is equal to

[tex]y=20x[/tex]

step 2

what would be the sales tax on a purchase of $46

For [tex]y=46, x=?[/tex]

substitute in the equation

[tex]46=20x[/tex]

[tex]x=46/20[/tex]

[tex]x=\$2.3[/tex]

Answer:

$2.30

Step-by-step explanation:

We have been given that the amount of sales tax varies directly with the cost of the purchase.

We know that a direct variation in in form [tex]y=kx[/tex], where, y varies directly with x and k is constant of variation.

First of all, we will find constant of variation as:

[tex]\text{Sales tax}=k*\text{Cost of purchase}[/tex]

[tex]\$3.80=k*\$76[/tex]

[tex]\frac{\$3.80}{\$76}=\frac{k*\$76}{\$76}[/tex]

[tex]0.05=k[/tex]

To find the amount of sales tax on a purchase of $46, we will substitute [tex]k=0.05[/tex] in our equation as:

[tex]\text{Sales tax}=0.05*\$46[/tex]

[tex]\text{Sales tax}=\$2.30[/tex]

Therefore, the sales tax would be $2.30.

let's bear in mind that 1 Cup = 8 fl oz.

a) is absolutely correct, 18oz and thus they can fit fine in the 24oz container.

b) is correct, 24 - 18 = 6, we can fit in 6 more oz, which is 3/4 of a cup.

c) is correct as well

d)

we just need to convert c) units to fluid ounces

[tex]\bf 2\frac{1}{4}\implies \cfrac{9}{4}\cdot 8\implies \boxed{18}~\hfill 3\cdot 8\implies \boxed{24} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{juice}}{18}+\stackrel{\textit{water}}{12}+\stackrel{\textit{ice cream}}{24}\implies 54~\textit{fluid ounces}[/tex]

Answer:

Take x and 5x for example.

5x is a multiple of x.

If you were to add x and 5x, you'd get 6x.

So basically, when you add x and a multiple of x, just add 1 to the number in front of the multiple of x.

[Like how we did earlier, 5x + (1)x = 6x]

Answer:

add x and a multiple of x, and 1

Step-by-step explanation:

Answer:

5 years             I think....

Step-by-step explanation:

B Specie    A Specie      

5000         2000

10000       4000

                 6000

                 8000

                 10000

Answer:

30.54 yrs

Step-by-step explanation:

We have been given the following exponential growth functions;

Species A;

[tex]p=2000e^{0.05t}[/tex]

Species B;

[tex]p=5000e^{0.02t}[/tex]

where t = 0 in 2010.

We are required to determine the number of years it will take for the populations of both species to be equal.

To do this we simply equate the two exponential functions and solve for t;

[tex]2000e^{0.05t}=5000e^{0.02t}\\\\2e^{0.05t}=5e^{0.02t}\\\\\frac{5}{2}=\frac{e^{0.05t} }{e^{0.02t} }\\\\2.5=e^{0.03t}\\\\ln(2.5)=0.03t\\\\t=\frac{ln(2.5)}{0.03}=30.543[/tex]

Answer:

11: b = c - 0.5, where b is the bread and c is the cheese

12: h = b + 2, where h is the height and b is the base

13: p = 25b, where p is the plane ticket and b is the bus ticket

Answer:

The answer is 7!

Step-by-step explanation:

Step-by-step explanation:

if p = 0.5, then 8p =4

if q =7, then 3q =21

thus 8p + 3q -18 = 4 + 21 -18 = 7

Answer:

Given graph represents function.

Step-by-step explanation:

We have been given a graph. Now we need to find if the given graph represents function or not.

To check if any graph represents function or not, we apply vertical line test. That means if there exists any vertical line that crosses the given graph more than once then the given graph is not a function.

Now if you draw vertical lines then you won't find any such vertical line which crosses graph more than once.

Hence given graph represents function.

Answer:

[tex]f(x=\sqrt{x}-2[/tex].

Step-by-step explanation:

We have been given graph of a function. We are supposed to find the function formula.

Upon looking at our given function, we can see that it is transformed form of a square root function.

We know that square root parent function is in form [tex]f(x)=\sqrt{x}[/tex].

We can see that our given graph is shifted down along y-axis. The rule for shifting a graph down along y-axis is: [tex]f(x)\rightarrow f(x)-a[/tex], where graph of [tex]f(x)[/tex] is shifted down by a units.

So our function will be in form [tex]f(x=\sqrt{x}-a[/tex].

From our attached file, we can see that value of 'a' is 2.

Therefore, our required function would be [tex]f(x=\sqrt{x}-2[/tex].

Answer:

[tex]y(t) = 750 -50t[/tex]

Step-by-step explanation:

We want to model the position of the submarine as a function of time.

Notice that we have a constant amount. The initial depth: 750 meters

 Then we have a factor that varies over time. Every hour the submarine ascends 50 meters. therefore as t increases the depth y(t) of the submarine decreases. Then the factor is:

-50t.

Where t represents the time in hours.

Then the equation that represents the new position of the submarine in relation to the level of the sea:

[tex]y(t) = 750 -50t[/tex]

Answer:

im pretty sure it's -750 + 4 x 50

Step-by-step explanation:

This is the only answer that really makes sense to me

Solving both equations individually, we derive n = -5 from the first and n < 2 from the second. No common solution exists due to the nature of these equations.

This problem involves two separate equations where you’re asked to find the value of n that satisfies both. We solve this by treating each equation individually.

First equation: -1 + 5n = -26

 To resolve for n we can simply add '1' to both sides, which result in: 5n = -25. Then divide both sides by '5' to isolate n, implying n = -5.

Second equation: 7n - 2 < 12

We will apply the same logic and add '2' to both sides, which gives 7n < 14. Afterwards, dividing through by '7', which gives us n < 2.

From these two solutions, there is no value of n that validates both equations simultaneously.

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Answer:

[tex]EH=12\ units[/tex]

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional

In this problem

ABCD and EFGH are similar

so

CD is proportional to GH

AD is proportional to EH

[tex]\frac{CD}{GH}=\frac{AD}{EH}[/tex]

substitute the given values and solve for EH

[tex]\frac{2}{3}=\frac{8}{EH}[/tex]

[tex]EH=3*8/2=12\ units[/tex]

ANSWER

B. Domain is (-∞,∞) and Range is (-∞,∞).

The given function is

[tex]f(x) = \sqrt[3]{x - 6} + 5[/tex]

This is function is obtained by shifting the base cubic root function 6 units to the right and 5 units up.

This function is defined for all real values of x.

Therefore the domain is all real numbers.

The range is all real numbers.

The domain for this function becomes the range for the inverse function and the range becomes the domain.

Hence the domain is (-∞,∞) and the range is (-∞,∞).

Answer:

pk=22

Step-by-step explanation:

3x+23=9x-19

x=7

3x7+23=44

44/2

22

To find PK when PQ = QR, JK = 3x + 23, and LM = 9x - 19, you can add JK and LM together to get PK = 12x + 4.

Given that PQ = QR, JK = 3x + 23, and LM = 9x - 19, we can find PK by adding JK and LM together since they are all part of the same line. So, PK = JK + LM = (3x + 23) + (9x - 19). Now simplify the expression by combining like terms: PK = 3x + 9x + 23 - 19 = 12x + 4.

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Answer:

12.56

Step-by-step explanation:

using the formula 2piR

Answer:

12.56 feet

Step-by-step explanation:

C= pie times diameter

Or

C= 2 times pie times radius

C= 3.14 times 4

Therefore, the circumference equals 12.56 feet