What are the restrictions of the domain of f(g(x))?

a) x is not equal to -5
b) x is not equal to -3
c) x is not equal to 2
d) There are no restrictions.

Problem 1.

My thinking is that the furthest you can get is have two points at each opposite corner, so the distance between them is sqrt(2). If we have two other points with this property, then all four corners are filled up. It is possible to pick two points where the distance is 1 unit.

Then a fifth point can be placed at the center such that the distance from it to any of the corners is sqrt(2)/2. We placed the fifth point at the center to try to get as far away as possible from the other four points.

Basically we're trying to find the worst case scenario (leading to the largest distance possible) and seeing how we can fill up the square. This establishes the upper bound. Any other kind of scenario will have a distance less than the upper bound.

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Problem 2.

For this one, I'm not sure what to make of it. The terminology is a bit strange so I'm not going to be fairly helpful here. Sorry about that.

If I had to guess, I'd assume it has something to do with the fact that a plane is uniquely defined by 3 points. That fourth point is not coplanar with the other three, which helps define the semi-spherical portion. The fifth point is just extra. The points can't be all collinear or else a plane won't form. Though to be honest, I'm still not sure about problem 2. I'd get a second opinion.

Answer:

(5,5) and (5,-11)

Step-by-step explanation:

You can find this out by plotting a circle with the diameter of 10 on the point "(-1,-3)". Then find all the times the circle is on the x axis of 5.

Answer:

so when the mughal emperor humayun had died akbar his son was put as kind of india he was 10 yearls old when his father died and then Bairam Khan was elected as a regent for Akbar.

Step-by-step explanation:

Answer:

A = 6.9%

B = 0.1%

AB = 1.6%

Step-by-step explanation:

A=0.41=41/100

B=0.1=1/10

AB=0.25=1/25

41/100³ = 0.41³ = 0.069 = 6.9%

1/10³ = 0.1³ = 0.001 = 0.1%

1/25³= 0.25³ =0.016 = 1.6%

I did to the power of 3 because the equation just looks like this

41/100 x 41/100 x 4/100

this is because you are multiplying each number by the amount of students selected.

Answer:

[tex]\mathbf{V = [\dfrac{ 8 \pi }{3}] }[/tex]

Step-by-step explanation:

Given that:

y = 6x - x² , y = 8  about  x = 2

To find the volume of the region bounded by the curves about x = 2; we have the radius of the cylindrical shell to be x - 1, the circumference to be 2 π (x -2 ) and the height to be 6x - x² - 8

6x - x² - 8

6x - x² - 8 = 0

-x² + 6x - 8 = 0

x² - 6x + 8 = 0

(x -4) (x - 2  ) = 0

So;

x = 2 , x = 4

Thus, the region bound of the integral  are from a = 2 and b = 4

Therefore , the volume of the solid can be computed as :

[tex]V = \int \limits ^b _a \ 2x \times f(x) \ dx[/tex]

[tex]V = \int \limits ^4_2 2 \pi (x -2) (6x -x^2 -8) \ dx[/tex]

[tex]V = 2 \pi \int \limits ^4_2 (6x^2 - x^3 -8x -12 x - 2x^2 +16) \ dx[/tex]

[tex]V = 2 \pi \int \limits ^4_2 (8x^2 -x^3-20x +16) \ dx[/tex]

[tex]V = 2 \pi \int \limits ^4_2 ( -x^3+8x^2-20x +16) \ dx[/tex]

[tex]V = 2 \pi [\dfrac{ -x^7}{4}+\dfrac{8x^3}{3} -\dfrac{20x^2}{2} +16x]^4_2[/tex]

[tex]V = 2 \pi [\dfrac{ -(4^4-2^4)}{4}+\dfrac{8(4^3-2^3)}{3} -\dfrac{20(4^2-2^2)}{2} +16(4-2) ]^4_2[/tex]

[tex]V = 2 \pi [\dfrac{ -(256-16)}{4}+\dfrac{8(64-8)}{3} -10(16-4)} +16(2) ][/tex]

[tex]V = 2 \pi [\dfrac{ 4}{3}][/tex]

[tex]\mathbf{V = [\dfrac{ 8 \pi }{3}] }[/tex]

White figure Area = 128[tex]\pi[/tex]

White surface area = appro. 301

Yellow area = 320[tex]\pi[/tex]

Yellow Surface area = approx. 653

Area found with = 2πrh+2πr2

Surface Area found with = 2πrh+2πr2

You need to memorize them for tests

Hope that helped!!! k

Answer:

  Your table is filled in below.

Step-by-step explanation:

The scale factor is the ratio of image size to original size. In part (d), the image height is "blocks" while the original height is "feet". So, the units of the scale factor are "blocks/ft".

Sometimes a scale factor has units, like this, and sometimes it is expressed as a pure number. A map scale factor might be the pure number ratio 1 : 62500, or it could also be expressed with units as 1 in : 1 mile.*

__

* actually, these are slightly different scales. 1:62500 is about 0.98643 inches per mile.

Answer: Image

Step-by-step explanation:

took the test

Answer:

20 and 1/4.

Step-by-step explanation:

9x^2 * y^(-2), for x = -3 and y = 2.

9(-3)^2 * 2^(-2)

= 9 * 9 * (1/4)

= 81 * 1/4

= 81 / 4

= 20.25

= 20 and 1/4.

Hope this helps!

Answer:

Step-by-step explanation:

Let's fill the values in.

9(-3)*2(2)*-2

Using PEMDAS, we would first multiply the two numbers where x and y used to be.

-27 * 4 * -2

Now we would finish multiplying this.

216.

Hope this helps!! <3

Answer:

26°

Step-by-step explanation:

AC=tan 64

BC=x=sec 64

Using sine rule

(Sin 64)/tan 64 = (sin BAC)/sec 64

Cos 64 = (sin BAC)(cos 64)

Sin BAC= 1

BAC=90

ACB+ 64+90=180

ACB= 26°

Answer:

[tex]\boxed{5}[/tex]

Step-by-step explanation:

[tex](p-q)(2)[/tex]

[tex]p(2)-q(2)[/tex]

[tex]\sf When \ x \ is \ 2, \ p(x) \ is \ 3 \ and \ q(x) \ is \ -2.[/tex]

[tex](3)-(-2)[/tex]

[tex]3+2=5[/tex]

Answer:

28 units²

Step-by-step explanation:

→ Work out the size of the triangle if it was a full rectangle

Height = 4 and Base = 2

→ Work out area of triangle

0.5 × Height × Base ⇒ 0.5 × 4 × 2 ⇒ 2 × 2 ⇒ 4

→ Minus the area of the triangle from the "imaginary full' rectangle

Area of rectangle = Length × Width ⇒ 8 × 4 ⇒ 32

32 - 4 = 28

Answer:

[tex]\huge\boxed{28\ units^2}[/tex]

Step-by-step explanation:

The figure consists of a triangle, a square and a rectangle.

Area of Triangle:

[tex]\sf \frac{1}{2} (Base)(Height)\\Where \ Base = 2 , Height = 4 \\=> \frac{1}{2} (2)(4)\\=> 4\ units^2[/tex]

Area of Square:

[tex]\sf (Length)(Length)\\(4)(4)\\=> 16\ units^2[/tex]

Area of rectangle:

[tex]\sf (Length)(Width)\\Where \ Length = 4 , Width = 2\\=> (4)(2)\\=> 8 \ units^2[/tex]

Area of the whole figure:

=> 4 + 16 + 8

=> 28 units²

Answer:

x = 13

Arc RQ = 180°

Step-by-step explanation:

PEQ is an inscribed angle and the measure of an inscribed angle in a circle is equal to half of the arc it sees.

The perimeter of a circle is always 360° therefore

2 × (5x + 15) + 9x + 17 + 6x - 12 = 25x + 35 = 360°

25x = 360 - 35

25x = 325

x = 13

Since arc RQ is equal to 10x + 30 we replace x with the value we just got

10×13 + 30 = 160°

Answer:

its 28 dude, because it says that adults and children are played more on saturday.(adults on Saturday=$8 and children under 12 are $4

Answer:

The answer is "[tex]\bold{\frac{x^{'}^2}{17}-\frac{y^{'}^2}{31}=1}[/tex]"

Step-by-step explanation:

In the given question there is some mistyping error if the given value is this. so, its solution can be defined as follows:

[tex]19x^2 + 24\sqrt{3} xy - 5y^2 - 527 = 0...................(1) \\\\ \theta = 30^{\circ}[/tex]

Formula:

[tex]\bold{x=x'\cos \theta -y' \sin \theta}[/tex]            [tex]_{where} \ \ \ \ \theta =30[/tex]

  [tex]=x' \cos 30- y' \sin 30\\\\ =x' \frac{\sqrt{3}}{2}- y' \frac{1}{2}\\\\ =\frac{1}{2}(x' \sqrt{3}- y')....(a)\\\\[/tex]          

[tex]\bold{y=x'\sin \theta +y' \cos \theta}[/tex]            [tex]_{where} \ \ \ \ \theta =30[/tex]

  [tex]=x' \sin 30+y' \cos 30\\\\ =x' \frac{1}{2}+y' \frac{\sqrt{3}}{2}\\\\ =\frac{1}{2}(x'+ y'\sqrt{3})....(b)\\\\[/tex]          

put the equation (a) and equation (b) value in equation 1:

equation:

[tex]\to 19x^2 + 24\sqrt{3} xy - 5y^2 - 527 = 0...................(1) \\\\[/tex]

[tex]\to 19(\frac{1}{2}(x'\sqrt{3}- y'))^2+24\sqrt{3}(\frac{1}{2}(x'\sqrt{3}- y))( \frac{1}{2}(x'+y'\sqrt{3}))- 5(\frac{1}{2}(x'+y'\sqrt{3}))^2-527= 0\\[/tex]

[tex]\to \frac{19}{4}(3x^{'}^2+ y^{'}^{2}-2\sqrt{3}x' y')+6\sqrt{3}(\sqrt{3}x^{'}^{2}+2x'y'-\sqrt{3}y^{'}^2)-\frac{5}{4}(x^{'}^2+ 3y^{'}^{2}-2\sqrt{3}x' y')-527=0[/tex]

[tex]\to \frac{57}{4}x^{'}^2+\frac{19}{4}y^{'}^2-\frac{19 \sqrt{3}}{2}x^{'}^2y^{'}^2+18x^{'}^2+12\sqrt{3}x^{'}^2y^{'}^2-18y^{'}^2-\frac{5}{4}x^{'}^2-\frac{15}{4}y^{'}^2-\frac{5\sqrt{3}}{2}x^{'}^2y^{'}^2-527=0\\\\\to 31x^{'}^2-17y^{'}^2-527=0\\\\\to 31x^{'}^2-17y^{'}^2=527\\\\\to \frac{x^{'}^2}{17}-\frac{y^{'}^2}{31}=1\\\\[/tex]

Answer:The answer is The answer is ""

Step-by-step explanation:

Answer:

x=9

Step-by-step explanation:

PQ + QR + RS = PS

2x-6 + 1 + x-4 = 18

Combine like terms

3x -9 = 18

Add 9 to each side

3x-9+9= 18-9

3x = 27

Divide by 3

3x/3 = 27/3

x = 9

Answer:

RS=5

Step-by-step explanation:

solve for x:

2x-6+1+x-4 = 18

combine like terms

3x-9=18

subtract both sides to make x isolated

3x=27

divide by 3 to get x

x=9

RS=x-4

RS=9-4

RS=5

Let's think about the square root of 33 here for a second.

What two perfect squares surround 33?

The answer is 25 and 36.

Then, let's take the square root of both 25 and 36, which are 5 and 6. Therefore, since the square root of 25 and 36 are both nearest to the square root of 33, then the square root of 3 must be between 5 and 6.

The correct answer is A (or option 1): 5 < root 33 < 6

Hope this helps! :)

Answer:

a (the first choice)

Step-by-step explanation:

To start, you should think of square root values near 33 that you know the answer to. For example, the square root of 25 is 5, and the square root of 36 is 6. Therefore, you know that the square root of 33 is 5.something because it is in between 25 and 36.

Answer:

My answer is in the attached image.

Answer:

A. 30 degrees

Step-by-step explanation:

Set the two angles equal to each other:

3x-15 = 45-x

Solve for x:

4x -15 = 45

4x = 60

x = 15

Finally, plug in the x to one of the equations (preferably 45 - x since it's easier to solve) and solve for x.

45 - 15 = 30

Answer:

A 30 degrees

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

It would take 3 faucets 6/4 = 1.5 minutes to fill a 25-gallon tub since when the number of faucets stays the same, the volume of the tub and the time needed to fill the tub are directly proportional. However, when the volume of the tub stays the same, the number of faucets used and the time needed to fill the tub are inversely proportional, therefore, if I double the number of faucets used, it will half the time needed, so the answer is 1.5 / 2 = 0.75 minutes or 45 seconds.

Answer:

[tex]\large\boxed{45 seconds}[/tex]

Step-by-step explanation:

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

Variable Key

Faucets = f

Minutes = m

Gallons = g

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

Write an equation to display how long it takes for the 3 faucets to fill up a 100 gallon tub.

100g = 6m

Divide both sides of the equation by 6

m = 16.67g

This means that approximately 16.67 gallons are filled up per minute with 3 faucets. We found the measurement (gallons), which is based on the time (minutes). This is called the unit rate.

Now that we found the unit rate for 3 faucets, let's find the unit rate for 6 faucets by multiplying our unit rate by 2.

3f = 16.67g per minute

6f = (16.67g per minute)(2)

6f = 33.34 g per minute

We now know the unit rate for 6 faucets, so now all we have to do is divide that by 25 gallons, the second tub.

25g / 33.34 g = 0.75 minutes

Convert to seconds

0.75 minutes = 3/4 of a minute

1 minute = 60 seconds

Substitute

3/4(60)

[tex]\large\boxed{45 seconds}[/tex]

Hope this helps :)

Answer:

A function normally tells you what y is if you know what x is.

Answer: please find the answer in the explanation.

Step-by-step explanation:

1.) The distance is not proportional to time. Because the distance was constant from time = 3 seconds to 10 seconds.

2.) A person running down a field to score a touchdown. Not enough information.

3. A dog jogging at a constant speed for 20 minute. The distance is proportional to time because of the constant speed.

4.) The distance is proportional to time because their is increase in distance covered and increase in time taken.

5.) A truck passing through the 4 cities at a constant speed. The distance is proportional to time because the speed is constant.

6.) A horse running around a race track. Distance is not proportional to time because this is not a linear motion.

Answer:

1  :2

Step-by-step explanation:

12 are yellow, 4 are pink

To find the number of red

24 -12 -4 = 8

There are 8 red balls

We want the ratio of

red: yellow or pink

8 : 12+4

8 :16

Divide each side by 8

8/8 : 16/8

1  :2

Answer:1:2

Step-by-step explanation: 12 yellow + 4 pink= 16

24 balls total minus 16 =8 red balls so 8:16=1:2

Answer:

6cot 50

Step-by-step explanation:

Tan 50=6/x

x= 6/(tan 50)

x= 6cot 50°

Answer:

? = 6 cot 50

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp /adj

tan 50 = 6 /?

? tan 50 = 6

? = 6 / tan 50

We know that 1 / tan 50 = cot 50

? = 6 cot 50

Answer:

Slope: [tex]\frac{5}{3}[/tex]

Y-intercept: -2

Step-by-step explanation:

Conveniently, this equation is already in slope-intercept form.

The slope is always the constant of proportionality, which we multiply x by.

Therefore the slope is  [tex]\frac{5}{3}[/tex].

The y-intercept is always the constant that comes after the x term, which is -2.

So the y-intercept is -2.

Hope this helped!

Answer:

Slope: 5/3

Y-intercept: -2

Step-by-step explanation:

Since your equation is already in slope intercept form, it makes it easier for you to identify the slope and y-intercept.

In your equation ([tex]y = \frac{5}{3} x -2[/tex]) the coefficient of 5/3 is your slope and your constant of -2 is your y-intercept.

Hope that helps and maybe earns a brainliest!

Have a great day! :)

Answer:

5/6, 0.23, -5 3/8

Step-by-step explanation:

Any rectangle is also a parallelogram (but not the other way around). So AB is parallel to CD. The angles BAC and ACD are alternate interior angles that are congruent due to the parallel sides mentioned.

(angle BAC) = (angle ACD)

3x+4 = x+28

3x-x = 28-4

2x = 24

x = 24/2

x = 12

So,

angle BAC = 3x+4 = 3*12+4 = 40 degrees

and

angle CAD = 90 - (angle BAC) = 90 - 40 = 50 degrees

With any rectangle, the four interior angles are always 90 degrees. So that's why angles BAC and CAD add to 90.

Answer:

x = 16

Step-by-step explanation:

3x - 10 = 2(x+3)

First step is solve this:

2(x+3) = 2*x + 2*3 = 2x + 6

then:

3x - 10 = 2x + 6

3x - 2x = 6 + 10

x = 16

Check:

3*16 - 10 = 2(16+3)

48 - 10 = 2*19 = 38

Answer:

x = 16

Step-by-step explanation:

you start off by isolating the variable

Answer: interval from -8 to 5

In interval notation, we would write [-8, 5]

The domain is the set of allowed x inputs to a function. The left-most point is (-8,0) so x = -8 is the smallest x value allowed. The largest x value allowed is x = 5 due to the point (5,0) being the right-most point.

The use of square brackets in interval notation says "include this endpoint as part of the interval".

The building would be 100ft tall. You have to take 20/6 = ?/30 The difference between 6 and 30 is x5. Then all you have to do is 20x5 and you get 100ft.

Answer :

The building would be 100ft tall. You have to take 20/6 = ?/30 The difference between 6 and 30 is x5. Then all you have to do is 20x5 and you get 100ft.