Simplify 12.856677878

Answer:

1. f⁻¹(x) = ±²√(-⅓(x + 6)) + 4

2. y = ²√(x–3) + 4

3. y = (x/4)³

9514 1404 393

Answer:

Step-by-step explanation:

To find the inverse function, solve for y the equation ...

  x = f(y)

__

1.

  [tex]x=f(y)\\\\x=-3(y-4)^2-6\\\\x+6=-3(y-4)^2\qquad\text{add 6}\\\\\pm\sqrt{\dfrac{x+6}{-3}}=y-4\qquad\text{divide by -3, square root}\\\\4\pm\dfrac{1}{3}\sqrt{-3(x+6)}=y\qquad\text{add 4, rationalize the denominator}\\\\\boxed{f^{-1}(x)=4\pm\dfrac{1}{3}\sqrt{-3x-18}}\qquad\text{simplify the radical}[/tex]

__

2.

  [tex]x=\sqrt{y-4}+3\\\\x-3=\sqrt{y-4}\qquad\text{subtract 3}\\\\(x-3)^2=y-4\qquad\text{square both sides}\\\\\boxed{y=(x-3)^2+4}\qquad\text{add 4}[/tex]

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3.

  [tex]\displaystyle x=4\sqrt[3]{y}\\\\\frac{x}{4}=\sqrt[3]{y}\\\\\left(\dfrac{x}{4}\right)^3=y\qquad\text{cube both sides}\\\\\boxed{y=\dfrac{x^3}{64}}[/tex]

Answer:

Step-by-step explanation:

The route makes a right triangle with legs 3 mi and 4 mi, and the hypotenuse of x mi.

Use Pythagorean to find the distance:

Vector Review Practice Answers:

1. B - initial (14,-5); terminal (0,0)

2. A - sqrt(22^2 + 4^2)

3. B - <4,12>

4. D - Yes, the two vectors have the same magnitude and direction.

5. D - Vectors u and v are neither because the angle between the two vectors is not equal to 0 degrees, 90 degrees, or 180 degrees

6. C - approximately 4 mi. at a direction angle of 56 degrees northeast

7. A - approximately 174 mph at a direction angle of 58 degrees northeast

8. A - -200

9. D - W = 59 ft*lbs

10. C - u = 4/5i - 3/5j

Answer: $46.08

Step-by-step explanation:

Find the surface Area of the box

the bases are 12*12= 144 times 2 bases 144*2= 288

The area of each side is 12*18=216 times 4 sides 216*4=864

add the totals together to find the total surface area 288+864=1152

total surface area is 1152 inches. Multiply by the cost per square inch

1152*.04= 46.08

Answer:

A, Yes, he has 1 cup left

Step-by-step explanation:

5.25 at the start

5.25 - 3.5 = 1.75

1.75 + 2 = 3.75

3.75 - 2.75 = 1

Answer:

1

Step-by-step explantion:

bam theres the answer, its 1.

yes he has 1 cup left

Answer:

2 * 7 * 7 = 98

hope this answer helps you!

Answer:

45/4     7/2     9/2

Step-by-step explanation:

I'm not sure if this is what you wanted so if its not sorry.

Answer: 15 Yards 2 feet

Step-by-step explanation:

3 feet in a yard

45/3 = 15

2 remaining = 2 feet

Answer:

15.667 in yards

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

the answer is 32 ounces

Answer:

In 2 pounds, there are 32 ounces.

Explanation:

1 pound = 16 ounces

Answer:

-45x-90

Step-by-step explanation:

-9*5x=-45

-9*10=-90

Answer:

The second one, -11/12

Step-by-step explanation:

I used a website so sorry I don't have an explanation

Answer:

the length will be 9cm because a square has equal sides it not the same as the rectangle

Answer:

40

Step-by-step explanation:

It tells you what Q, R is for the opening. That means that it is 40

The measure of angle PQR is 70 degrees

We have a right triangle - r is 90 degrees

based on geometric rules: angle RPQ = 20    

 40 : 2

90 + 20 = 110

110 + x = 180

What is the perimeter of the triangle?

The perimeter of the triangle is 180 degrees

The triangle has 180 degrees.

This means that 180 - 110 =70 degrees.

The measure of angle PQR is 70 degrees.

Answer:

what view?

and whats the question?

Step-by-step explanation:

Answer:

5/13

Step-by-step explanation:

1. We are given tan(x)=5/12 .....(2)

2. On comparing the quantities we get that p=5 and b=12

3. We require the value of hypotenuse(h),

for this we apply the Pythagoreum theorum: p^2+b^2=h^2

⇒h^2=5^2+12^2

⇒h^2=25+144

⇒h^2=169

⇒ h=√169

⇒ h=13

Sin=p/h

p=5

h=13

Sin=5/13

Answer:

0.121 = 12.1% probability of observing a sample mean of 30.5 grams of fat per pound or less in a random sample of 34 farm-raised trout.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Farm-raised trout contain an average of 32 grams of fat per pound, with a standard deviation of 7.5 grams of fat per pound.

This means that [tex]\mu = 32, \sigma = 7.5[/tex]

Sample of 34:

This means that [tex]n = 34, s = \frac{7.5}{\sqrt{34}} = 1.2862[/tex]

Find the probability of observing a sample mean of 30.5 grams of fat per pound or less in a random sample of 34 farm-raised trout.

This is the pvalue of Z when X = 30.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{30.5 - 32}{1.2862}[/tex]

[tex]Z = -1.17[/tex]

[tex]Z = -1.17[/tex] has a pvalue of 0.121

0.121 = 12.1% probability of observing a sample mean of 30.5 grams of fat per pound or less in a random sample of 34 farm-raised trout.

Answer:

around 36 is the diameter

Step-by-step explanation:

C=2Pir or pi*d

113.04=pi*d

113.04/pi=d

d≈36

give me brainliest[tex]≈[/tex]

36 units is the diameter of the circle.

The perimeter of a two-dimensional form is the space surrounding it. It represents the total length of the shape's sides. The units used to measure the sides of the form, such as meters, centimeters, inches, or feet, determine the units used to measure the perimeter.

We can use the formula for the circumference of a circle, C = πd,

where C is the circumference and d is the diameter.

Substituting the given value, we have:

113.04 = πd

To solve for d, we can divide both sides by π:

d = 113.04/π

Using a calculator to evaluate this expression, we get:

d ≈ 36

Therefore, the diameter of the circle is approximately 36 units.

Learn more about perimeter here:

https://brainly.com/question/6465134

#SPJ3

que mats soya de mućha la pañe trasdeće

Answer:

See below

Step-by-step explanation:

[tex]1) \: \frac{1}{2} \times 5 \times 6 = 15 \: {cm}^{2} \\ \\ 2) \: \frac{1}{2} \times 10 \times 6 = 30 \: {cm}^{2} \\ \\ 3) \: 5 \times 3 = 15 \: {cm}^{2} \\ \\ 4) \: 10 \times 6= 60\: {cm}^{2} [/tex]

Answer:

She can only spend 300 of her monthly salary on rent.

Step-by-step explanation:

Answer:

376.99in³

Step-by-step explanation:

no proof but a g00gle calculator, you're just gonna have to trust me on this one

Answer:

SA = 376.8 in²

Step-by-step explanation:

area of top:

π4² = 50.24 in²

50.24 x 2 = 100.48 in²   (for both ends)

area of side:

circumference = 2 x 4 x π = 25.12 in

area = 25.12 x 11 = 276.32 in²

276.32 + 100.48 = 376.8 in²

Answer:

A =  225 π  c m [tex]x^{2}[/tex]

Step-by-step explanation:

the area of a circle formula with radius  

A  =  π r[tex]x^{2}[/tex]  

in this case

A = π ×  15[tex]x^{2}[/tex]  

A  =  225 π  c m[tex]x^{2}[/tex]

Answer:

Step-by-step explanation:

Area of a circle = π r²        you are given the r  radius =  15cm

   area = π 15² cm

Equation:  (1 2/3)(2 1/3) = x

Answer:  3 8/9 cups

Step-by-step explanation:

x represents the amount of flour she will need in cups.

To solve, convert the mixed numbers to improper fractions and multiply...

1 2/3 becomes 5/3

2 1/3 becomes 7/3

Now we have

(5/3)(7/3) = x

  35/9 = x

35/9 is 3 8/9 as a mixed number

Answer:

1. Surface Area = 122                Volume = 84

2. Surface Area = 1632             Volume = 2880

3. Surface area = 168                Volume = 144

4. Volume = 1350[tex]\pi[/tex]

Step-by-step explanation:

1. This is a rectangular prism. To find the surface area it is the same thing. Find the area of all sides and add them together.  Because this is a rectangular prism most of the sides are equal so we will only need to find the area of three sides. To find the area of the right side, just do 4*3=12. That would be the same for the opposite side. Then to find the front side, do 7*4= 28. That would also be the same for the opposite side. Then to find the top side, do 7*3= 21. That is the same for the bottom side. Add them all together and you will get your answer. 28+28+21+21+12+12 = 122.

To find the volume of a rectangular prism the formula is V = l*w*h.

Plug in: V = 7*3*4 and then you will get 84.

2. This is a triangular prism. First find the area of the the triangular surface by multiplying the base x height and dividing by 2. (16*12)/2 = 96.  That is the same for the opposite side. Then find the area of the bottom rectangular surface. 12*30 = 360. Then find the area of the back rectangular surface. 16*30 = 480. Then find the area of the final base rectangle. 30*20 = 600. Add them together and you will get 1632. Basically, find the area of all sides and then add them together.

To find volume the formula is, V = (1/2)a*c*h

Fill that in: V = (1/2)16*12*30 and then you will get 2880.

3. This is a trapezoidal prism. To find the surface area you would find the area of all sides then add them together. To find the are of a trapezoid, the formula is: A = [tex]\frac{a+b}{2}[/tex]h

Fill that in: A = [tex]\frac{4+12}{2}[/tex](6) and then you will get 48.

That is the same for the opposite side. Then you need to find the area of the rectangular side of the trapezoidal prism. 3*4= 12. This is also the same as the opposite side. The bottom side is 12*3= 36. The top side is 3*4= 12.

Add all of them together and you get 168.

1/2(4+12)*6

To find volume, V =  [tex]\frac{1}{2}[/tex]h(b₁+b₂)h.

Fill in: V =  [tex]\frac{1}{2}[/tex]6(12+4)3 and then you will get 144.

4. This is a cylinder. The formula to find the volume is A=[tex]\pi[/tex]r²h. Because you are leaving the answer in terms of pi, do not multiply pi into the equation.

So you would do r²h. 15² = 225. 225*6= 1350. So your answer would be 1350[tex]\pi[/tex].

Answer:

The right answer to the question is A

Answer:

36

Step-by-step explanation:

The axis of symmetry goes through the x-value. 4. So your equation for your axis of symmetry is going to be x equals. 0 (undetermined)

- branliest will be appreciated

Thanks

Answer:

Step-by-step explanation:

Given

x^2 + y^2 - 16y - 36 = 0

x^2 + y^2 - 16y = 36

x^2 + y^2 - 16y + (16/2)^2 = 36 + 8^2

x^2 + (y - 8)^2 = 64 + 36

x^2 + (y - 8)^2 = 100

The center is at (0,8) and the radius is 10

Try and follow it from the graph below.