11. What is the reciprocal of 6/5?
OA. 12/20
OB.11/5
OC.1
OD.576

Answer:

[tex]g(x)=x+6[/tex]

Step-by-step explanation:

The problem gives one the following information:

[tex]h(x)=(f\ \ o\ \ g)(x)\\\\h(x)=\sqrt[4]{x+7}\\f(x)=\sqrt[4]{x+1}[/tex]

This problem now requires one to find the function ([tex]g(x)[/tex]).

The format:

[tex](f\ \ o\ \ g)(x)[/tex]

Is another way of writing a composition of a function. In essence, it indicates this operation:

[tex](f(g(x))[/tex]

This means that one has to input one function into another. In other words, substitute one function into another in place of the variable, then simplify and solve to find the new function that is derived from this operation. Since it is given that ([tex]h(x)[/tex]) is the function resulting from the composition of ([tex]f(g(x))[/tex]), an equation can be formed. Treat the evaluator ([tex]g(x)[/tex]) as another variable. Then simplify and solve the equation to find the function that represents ([tex]g(x)[/tex]).

[tex]h(x)=f(g(x))[/tex]

Substitute,

[tex]h(x)=f(g(x))[/tex]

[tex]\sqrt[4]{x+7}=\sqrt[4]{(g(x)+1}[/tex]

Since both numbers are equivalent to each other when one takes the quartic root of the numbers, the numbers underneath the radical must be equivalent to each other. Therefore, one can state the following:

[tex]\sqrt[4]{x+7}=\sqrt[4]{(g(x)+1}[/tex]

[tex]x+7=(g(x))+1[/tex]

Inverse operations:

[tex]x+7=(g(x))+1[/tex]

[tex]x+7-1=g(x)\\[/tex]

[tex]x+6=g(x)[/tex]

Answer:

B and D

Step-by-step explanation:

in B the ratio of x/y = 1 for all pairs.

in D the ratio of x/y = 4 for all pairs.

in all other sets there are different ratios inside the set.

Answer:

The pairs (2, 2), (4, 4), and (6, 6) have ratios of 1 and the pairs (4, 1), (4, 1),      (8, 2), and (12, 3) have ratios of 4. The other pairs do not have similar ratios.

Step-by-step explanation:

Step 1; In order to pair up the pairs with equivalent rations, we first need to calculate the ratios for all the pairs by dividing the first value with the second value. The same procedure must be followed throughout to be able to pair them up.

Step 2; By dividing the values, the ratios are;

For (1, 2), the ratio is  = 0.5,

For (2, 3), the ratio is  = 0.6666,

For (4, 7), the ratio is  = 0.5714,

For (2, 2), the ratio is  = 1,

For (4, 4), the ratio is  = 1,

For (6, 6), the ratio is  = 1,

For (3, 1), the ratio is  = 3,

For (4, 1), the ratio is  = 4,

For (5, 1), the ratio is  = 5,

For (4, 1), the ratio is  = 4,

For (8, 2), the ratio is  = 4,

For (12, 3), the ratio is  = 4,

For (2, 1), the ratio is  = 2,

For (4, 3), the ratio is  = 1.333,

For (5, 4), the ratio is  = 1.25.

Step 3; Now we pair up the sets with the same ratios, out of these 15 pairs. The pairs (2, 2), (4, 4), and (6, 6) have ratios of 1 and the pairs (4, 1), (4, 1),      (8, 2), and (12, 3) have ratios of 4. The other pairs do not have similar ratios.

I hope this is right and it helps you !!!!!!!!!!

Work Shown:

[tex]7x^2*\sqrt{2x^4}*6\sqrt{2x^{12}}\\\\7*6x^2*\sqrt{2x^4*2x^{12}}\\\\42x^2*\sqrt{4x^{4+12}}\\\\42x^2*\sqrt{4x^{16}}\\\\42x^2*\sqrt{(2x^8)^2}\\\\42x^2*(2x^8)\\\\42*2x^{2+8}\\\\84x^{10}\\\\[/tex]

So that's why the answer is choice C

The requirement that x is nonzero isn't technically necessary. The original expression simplifies to choice C even when x = 0 is the case. Also, we don't have issues such as division by zero errors that could arise. It's a bit curious why your teacher put in that condition.

Answer:

C.

Step-by-step explanation:

7x²×sqrt(2x⁴)×6×sqrt(2x¹²)

we see right away that as constant multiplication factor we have 7×6 = 42.

and then we get from each sqrt expression a sqrt(2), which leads to sqrt²(2) = 2 and therefore 42×2=84.

the only answer option with 84 is C.

now, to be completely sure, and to get some practice, let's look at the other parts :

sqrt(2x⁴) = sqrt(2)×sqrt(x⁴) = sqrt(2)×x²

sqrt(2x¹²) = sqrt(2)×sqrt(x¹²) = sqrt(2)×x⁶

=>

7x²×sqrt(2)×x²×6×sqrt(2)×x⁶ =7×6×2×x²×x²×x⁶ = 84x¹⁰

perfect. C is confirmed.

1 cup per 8 oz

48/6 = 8

every 1 cup of water 8 oz of tomato paste.

Answer:

Their daily consumption of milk is of 0.93 liters.

Step-by-step explanation:

Weekly consumption:

6.5 liters.

Daily consumption:

A week has 7 days.

Each day the amount consumed is the same, so the daily consumption is:

6.5/7 = 0.93

Their daily consumption of milk is of 0.93 liters.

Answer:  D. No, because the line doesn't pass through the origin, point (0,0)

Explanation:

A direct proportional graph is always a straight line through the origin.

Algebraically, the form of any direct proportion equation is y = kx, where k is some constant. It plays the role as the slope.

We can rewrite y = kx as y = kx+0 to see that the y intercept is always 0 for these types of equations.

Unfortunately, this line shown has a y intercept of 2 instead of 0. So it's not a direct proportion.

Answer:

It is decreased by 9%

Step-by-step explanation:

First, find out how much money is decreased. To do this, subtract 13,000-11,830=1170. Finally, figure out how much percent 1170 is of the original price of $13,000.

The answer is 7%.

Hope this helps :)

Answer:

3/4

Step-by-step explanation:

tan C = opposite side/ adjacent side = AB / BC = 24 /32 = 3*8/ 4*8 = 3/4

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Answer:

  see attached

Step-by-step explanation:

A rotation 270° CCW is the same as a rotation 90° CW. To see what the figure looks like in its new location, make a copy on a semi-transparent medium, then align the +x axis on the copy with the -y axis on the original graph, keeping the origin in the same place.*

Algebraically, the transformation is ...

  (x, y) ⇒ (y, -x)

For example, ...

  S(7, -6) ⇒ S'(-6, -7)

In the attachment, the rotated figure is in red.

_____

* The exercise of physically doing this on paper or with transparencies can give you the insight you need to learn to do it mentally.

⬆⬆⬆⬆⬆⬆⬆⬆⬆⬆⬆⬆⬆

THAT IS THE RIGHT ANSWER

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Answer:

  24.1

Step-by-step explanation:

The third angle is C = 180° -55° -19° = 106°. The law of sines can be used to find the other two sides:

  a/sin(A) = c/sin(C)   ⇒   a = c(sin(A)/sin(C))

  b/sin(B) = c/sin(C)   ⇒   b = c(sin(B)/sin(C))

Then the sum of the lengths of the sides is ...

  P = a + b + c = c(sin(A)/sin(C)) +c(sin(B)/sin(C)) +c

  = c(1 +(sin(A) +sin(B))/sin(C)) = 11(1 +(0.8192 +0.3256)/0.9613)

  ≈ 11(1 +1.1909) ≈ 24.0994

The perimeter of the triangle is about 24.1 units.

Answer:

The 80% confidence interval for the population mean is (2.156, 2.394).

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 8 - 1 = 7

80% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 7 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.8}{2} = 0.9[/tex]. So we have T = 1.415

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 1.415\frac{0.238}{\sqrt{8}} = 0.119[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 2.275 - 0.119 = 2.156

The upper end of the interval is the sample mean added to M. So it is 2.275 + 0.119 = 2.394

The 80% confidence interval for the population mean is (2.156, 2.394).

Answer:

x = 15

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

(4[tex]\sqrt{2}[/tex] )²

= 4[tex]\sqrt{2}[/tex] × 4[tex]\sqrt{2}[/tex]

= 4 × 4 × [tex]\sqrt{2}[/tex] × [tex]\sqrt{2}[/tex]

= 16 × 2

= 32

Answer:

no solution

Step-by-step explanation:

25y² +36 = 24

(5y + 6) (5y + 6)

roots -6/5, -6/5

solution is always a positive root

Answer:

There don't seem to be any limits/asymptotes to the function.

The graph would look something similar to this:

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Answer:

  54.8 km

Step-by-step explanation:

The sketch and the applicable trig laws cannot be completed until we understand what the question is.

Given:

  two boats travel for 3 hours at constant speeds of 22 and 29 km/h from a common point, their straight-line paths separated by an angle of 39°

Find:

  the distance between the boats after 3 hours, to the nearest 10th km

Solution:

A diagram of the scenario is attached. The number next to each line is the distance it represents in km.

The distance (c) from B1 to B2 can be found using the law of cosines. We can use the formula ...

  c² = a² +b² -2ab·cos(C)

where 'a' and 'b' are the distances from the dock to boat 1 and boat 2, respectively, and C is the angle between their paths as measured at the dock.

The distance of each boat from the dock is its speed in km/h multiplied by the travel time, 3 h.

  c² = 66² +87² -2·66·87·cos(39°) ≈ 3000.2558

  c ≈ √3000.2558 ≈ 54.77

The boats are about 54.8 km apart after 3 hours.

Step-by-step explanation:

|a+b|=✓(a²+b²)

|a|+|b|=a+b

||a+b|| ≤ ||a||+|b||

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Explanation:

a) see the attachment for a graph (red curve)

__

b) The piecewise defined function can be ...

  [tex]\displaystyle C(x)=\begin{cases}0&0\le x\le 1\\5&1<x\le 3\\2x-1&3<x\le12\end{cases}[/tex]

__

c) The new cost function is ...

  [tex]\displaystyle C(x)=\begin{cases}10&0\le x\le5\\x+5&5<x\end{cases}[/tex]

The charge is a flat $10 for any period up to 5 hours, then $1 per additional hour after that, prorated for partial hours. There is apparently no upper limit on parking time as there was with the original function. (The graph shown goes beyond 15 hours; the domain of the original C(x) is 0 to 12 hours.) For reference, the new cost structure is shown in blue in the attachment.

_____

Additional comment

Under the new structure, costs are significantly higher for short-term parking, and lower once the term exceeds 6 hours.

Answer: the difference between the max is 3,200.

Step-by-step explanation:

20,000-16,800= 3,200

Answer:

the difference between the max is 3,200.

Step-by-step explanation:

20,000-16,800= 3,200

Answer:

a line passing through (negative 4, 2), (0, 0) and (4, negative 2).

Step-by-step explanation:

A function exhibiting direct variation MUST pass through the origin, (0, 0), and the graph must be a straight line.  The answer that satisfies these requirements is

a line passing through (negative 4, 2), (0, 0) and (4, negative 2).

Hello!

-41 - 2x + 6 = -24 <=>

<=> -35 - 2x = -24 <=>

<=> -2x = -24 + 35 <=>

<=> -2x = 11 <=>

<=> x = -11/2 or -5.5

Good luck! :)

The solution of the equation is only one solution.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

We have,

-41 - 2x + 6 = -24

Now, solving for x we get

-41 + 6 -2x = -24

-35 - 2x = -24

-2x = -24 + 35

-2x = 11

x = -11/2

x= -5.5

As, the equation of linear and have x= -5.5.

Thus, the equation have only one solution.

Learn more about Equation here:

https://brainly.com/question/29538993

#SPJ7

Part A

The vertex of a parabola is the lowest or highest point. The vertex in this graph is (2,-1).

Part B

You need to find the rate of change between the points when x=2 and x=3. When x=2, y=-1, and when x=3, y=0.5. You can find the average rate of change between these points by putting the difference of y over the difference of x. 0.5--1=1.5 and 3-2=1. The average rate of change is 1.5/1, or just 1.5.

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Answer:

  8x +4h

Step-by-step explanation:

  [tex]\dfrac{f(x+h)-f(x)}{h}=\dfrac{(4(x+h)^2-8)-(4x^2-8)}{h}\\\\=\dfrac{(4x^2 +8xh+4h^2)-(4x^2-8)}{h}=\dfrac{8xh+4h^2}{h}\\\\=\boxed{8x+4h}[/tex]

Answer:

$85.40

Step-by-step explanation:

All the US coin types, excluding pennies, are:

- nickels

- dimes

- quarters

Nickels are equal to 5 cents, or $0.05

Dimes are equal to 10 cents, or $0.10

Quarters are equal to 25 cents, or $0.25

Because there are only one of each coin (excluding pennies), we can just add the values written above:

$0.05 + $0.10 + $0.25 = $0.40

Next, let's add one of each bill listed in the question:

$5 + $10 + $20 + $50 = $85

Finally, let's add the value of the coins and the value of the bills to find the sum:

$85 + $0.40 = $85.40

The answer is $85.40

Hope it helps (●'◡'●)

Answer:

125.66 inches

Step-by-step explanation:

Step 1:  Calculate the circumference

The circumference formula is:  C = πd

Another way of saying that is:  C = 2πr

C = 2π(20)

C = 40π

C ≈ 125.66 inches

Answer:  125.66 inches