what set has a fixed number of elements

Answer:

square root of 1.9321 = 1.39

Step-by-step explanation:

Answer:

Hence, the equation of a sphere with one of its diameters with endpoints (-9, -12, -6) and (11, 8, 14) is [tex](x-1)^{2}+(y+2)^{2}+(z-4)^{2} = 30[/tex].

Step-by-step explanation:

There are two kew parameters for a sphere: Center ([tex]h[/tex], [tex]k[/tex], [tex]s[/tex]) and Radius ([tex]r[/tex]). The radius is the midpoint of the line segment between endpoints. That is:

[tex]C(x,y,z) = \left(\frac{-9+11}{2},\frac{-12+8}{2},\frac{-6+14}{2} \right)[/tex]

[tex]C(x,y,z) = (1,-2,4)[/tex]

The radius can be found by halving the length of diameter, which can be determined by knowning location of endpoints and using Pythagorean Theorem:

[tex]r = \frac{1}{2}\cdot \sqrt{(-9-11)^{2}+(-12-8)^{2}+(-6-14)^{2}}[/tex]

[tex]r = 10\sqrt{3}[/tex]

The general formula of a sphere centered at (h, k, s) and with a radius r is:

[tex](x-h)^{2}+(y-k)^{2}+(z-s)^{2} = r^{2}[/tex]

Hence, the equation of a sphere with one of its diameters with endpoints (-9, -12, -6) and (11, 8, 14) is [tex](x-1)^{2}+(y+2)^{2}+(z-4)^{2} = 30[/tex].

Step-by-step explanation:

Remember:

X = 2.5

Y = 1.5

Z = 1

The chart:

         X             Y           Z

I      10000    7000    8000

II     6000     10000   5000

X

The first column represents X. Since X's value is 2.5, we multiply both those numbers by 2.5.

[tex]10,000*2.5=25,000[/tex]

[tex]6000*2.5=15,000[/tex]

These are the values of X.

Y

The second column represents Y. Since Y's value is 1.5, we multiply both of the values by 1.5.

[tex]7,000*1.5=10,500[/tex]

[tex]10,000*1.5 = 15,000[/tex]

These are the values of Y.

Z

The last column represents Z. Since Z's value is 1, we do not need to multiply the numbers, since they are already multiplied by 1.

[tex]8,000[/tex]

[tex]5,000[/tex]

These are the values of Z.

ADDING

Now that we have are 6 numbers solved, all we have to do is add them all together.

[tex](25+15+10.5+15+8+5)\\25,000+15,000+10,500+15,000+8,000+5,000=78,500[/tex]

Our final answer: $78,500 is the total. (first option)

Answer:

[tex]4x^3-7x^2-23x-10[/tex]

Step-by-step explanation:

So we have the expression:

[tex](4x+5)(x^2-3x-2)[/tex]

Distribute. Multiply (4x+5) to each term:

[tex](x^2)(4x+5)+(-3x)(4x+5)+(-2)(4x+5)[/tex]

Distribute:

[tex]=(4x^3+5x^2)+(-12x^2-15x)+(-8x-10)[/tex]

Combine like terms:

[tex]=(4x^3)+(5x^2-12x^2)+(-15x-8x)+(-10)[/tex]

Add and simplify:

[tex]=4x^3-7x^2-23x-10[/tex]

And this is in descending order, so it's in standard form.

Answer:

138

Step-by-step explanation:

f(x)= 18x + 12

Let x = 7

f(7) = 18*7 +12

     = 126+12

     = 138

Answer:

f(7) = 138

Step-by-step explanation:

[tex]f(x)= 18x + 12\\f(7) = ?\\\\f(7) = 18(7) +12\\f(7) = 126+12\\f(7)=138[/tex]

Answer:

Two other names for WQ are QW and line g.

Step-by-step explanation:

A line can have as many points as possible. The two other names for WQ are QW and line g

From the given plane, we can observe the following:

This means that, we can rename WQ as

Hence, the two other names for WQ are QW and line g

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Answer:

B. (13-6) n - 55

Step-by-step explanation:

The number of shirts to be sold is n

The cost to purchase one shirt is $13

The cost of making each shirt is $6

Let's assume the shirt is one

Profit for a Shirt = (13-6)

But then there are no number of shirts

Profit= (13-6)n

But then also, an advert was run for the total shirts combined

Profit= (13-6)n -55

Answer:

b. (13-6)n-55

ap3x

Answer:

  z = {1 +i, 1 -i, -1 +i, -1 -i}

Step-by-step explanation:

Using Euler's formula, you can write this as ...

  z^4 = 4e^(i(π+2kπ))

Then the 4th root is ...

  z = 4^(1/4)e^(i(π/4 +kπ/2)) = √2(cos(π/4+kπ/2) +i·sin(π/4+kπ/2))

for integers k in the range 0 to 3.

  z = √2(±1/√2 ±i·1/√2) . . . signs are independent

  z = ±1 ±i . . . . . . signs are independent; hence 4 solutions

  z = {1 +i, 1 -i, -1 +i, -1 -i}

_____

Comment on roots of complex numbers

In the complex domain, each number has a number of roots equal to the index of the root. That is, there are four 4th roots. They all have the same magnitude, but their angles are separated by 360°/(root index) = 90°. Here, the principal fourth root of 4∠180° is 4^(1/4)∠(180°/4) = √2∠45° = 1+i.

Adding 90° is equivalent to multiplying by i, so the other 3 roots are √2∠135° = -1+i, √2∠225° = -1 -i, and √2∠315° = 1 -i.

 z = {1 +i, 1 -i, -1 +i, -1 -i}

Answer:

749.95+ 44.997 *or 45.00 giving 794.95

Answer: 49

Step-by-step explanation:

We know, x = -2

Substituting value of x in [tex]8x^{2} -7x+3[/tex],

[tex]8(-2)^{2} - 7(-2) + 3\\=8(4) -7(-2) + 3\\=32+14+3\\=49[/tex]

Answer:

f(-2)=8*(-2)^2-7*(-2)+3=8*4+14+3=32+17=49

Step-by-step explanation:

Answer: Jenna did not multiply how much 4 goes into 14 which is 3.5 she should have multiplied 4*3.5=14 and 6*3.5=21

Step-by-step explanation:

so the answer should have been 4/6 is equivalent to 14/21

Multiplication

2, 56, 0, 56, 18, 0, 3, 0, 20, 12

12, 54, 7, 64, 18, 25, 24, 0, 0, 28

14, 8, 6, 24, 35, 9, 27, 48, 40, 1

0, 3, 18, 16, 8, 7, 0, 0, 36, 48

49, 28, 40, 42, 15, 6, 27, 16, 36, 8

0, 32, 81, 4, 30, 0, 0, 9, 32, 10

30, 2, 45, 16, 5, 0, 0, 14, 35, 18

0, 54, 0, 12, 36, 24, 4, 8, 10, 18

72, 6, 63, 12, 0, 21, 0, 24, 63, 0

21, 20, 9, 15, 45, 0, 6, 72, 5, 4

Answer:

θ = 5π/6 rad and 11π/6 rad

Step-by-step explanation:

Given the expression cotθ+√3=0

Subtract √3 from both sides

cotθ+√3-√3=0-√3

cotθ = -√3

Since cotθ = 1/tanθ

1/tanθ = -√3

Reciprocate both sides:

tanθ = -1/√3

θ = tan^-1(-1/√3)

θ = -30°

Since the angle is negative, and tanθ is negative in the second and fourth quadrant.

In the second quadrant;

θ = 180-30

θ = 150°

Since 180° = πrad

150° = 150π/180

150° = 5π/6 rad

In the fourth quadrant;

θ = 360-30

θ = 330°

Since 180° = πrad

330° = 330π/180

330° = 11π/6 rad

Hence the solutions are 5π/6 rad and 11π/6 rad.

Answer:

x² + xy - 6y²

Step-by-step explanation:

FOIL

(x+3y)(x-2y)

F= x²

O= -2xy

I= 3xy

L= -6y²

Add these together = x² + xy - 6y²

Step-by-step explanation:

Hey, there!

Let me simply clear you.

While multiplying algebraic expression, you must be very careful about sign and brackets.

Here,

[tex](x + 3y)(x - 2y)[/tex]

Let's multiply (x-2y) by (x+3y)

[tex] = x(x - 2y) + 3y(x - 2y)[/tex]

[tex] = ({x}^{2} - 2xy) + (3xy - 6 {y}^{2}) [/tex]

Open brackets.

[tex] = {x}^{2} - 2xy + 3xy - 6 {y}^{2} [/tex]

Simplify the like terms.

[tex] = {x}^{2} + xy - 6 {y}^{2} [/tex]

Therefore, the answer is x^2 + xy- 6y^2.

Hope it helps.....

Answer:

16 degrees

Step-by-step explanation:

Add 20 to -4

-4 + 20

= 16

So, the temperature at noon was 16 degrees

Answer:

16 degrees

Step-by-step explanation:

The question states that it increased +20 degrees by noon from 6:00 am. So,

-4 + 20 = 16

The temp would be 16 degrees at noon.

Step-by-step explanation:

[tex]\huge{\purple{\underline{\underline{\bf{\pink{Answer}}}}}}[/tex]

[tex]\huge{\purple{\underline{\underline{\bf{\pink{Given}}}}}}[/tex]

It is a parrelogram

[tex]\huge\star{\underline{\mathtt{\red{To}\pink{f}\green{i}\blue{n}\purple{d}\orange{-:}}}}⋆[/tex]

X and Y

Solution

angle a = c. (opposite angles of 11gm is equal)

put the values of and c

x+45 = 3x-13

now take the variables to the l.H.S and number to R.H.S

x-3x = -13-45

-2x. = 58

x. = 58÷2

x. = 29

angle d + c = 180° (cointerior angle)

y + 3(29) + 13 =180°

y + 100 = 180°

y. = 80

Hope it helps

Answer:

a. is false

Step-by-step explanation:

4 liters= 1.057 gal

1.057 is greater than 1

Hope this helps :)

Answer:

(0,3)

Step-by-step explanation:

You need to pick a point, P, that will give you a distance from A to P that is twice as long as from P to B, or ration 2:1

Point A is (-2,-7), point B is (1,8), and I picked (0.3) because it looked like it could be, but now we need to test it.

Distance formula is:

[tex]d=\sqrt{(x_{2}-x_{1})^{2} + {(y_{2}-y_{1})^{2} } \\[/tex]

So AP would be

[tex]AP=\sqrt{(0--2)^{2} + {(3--7)^{2} } \\[/tex]

[tex]AP=\sqrt{(2)^{2} + {(10)^{2} } \\[/tex]

Do the same with PB, and you will find it's 5.1, giving an approximate ratio of 2:1.

Answer:

The answer is A) the speed at which the car has traveled

Step-by-step explanation:

Answer:

Interest for the month = $12.25

Step-by-step explanation:

Given:

Amount in bank = $700

Rate of interest per month = 21% / 12 = 0.0175

Find:

Interest for the month

Computation:

Interest for the month = Amount in bank × Rate of interest per month

Interest for the month = $700 × 0.0175

Interest for the month = $12.25

Answer:

Square Root 34

Step-by-step explanation:

Answer:

[tex]\sqrt{34}[/tex]

Explanation:

sub in the values for x1, x2, y1 and y2

[tex]\sqrt{(-2-3)^2+(2-(-1))^2}[/tex]

subtract and evaluate

= [tex]\sqrt{(-5)^2+3^2}[/tex]

= [tex]\sqrt{25+9}[/tex]

= [tex]\sqrt{34}[/tex]

Answer:

1) 1

2) (2,3)

3) x⁴

Step-by-step explanation:

1)

We have the expression:

[tex]7x+1[/tex]

The degree of an equation is the largest exponent of the equation.

We can rewrite our expression as:

[tex]=7x^1+1x^0[/tex]

1 is the largest exponent.

Thus, our degree is 1.

2)

We have the system of equations:

[tex]x+y=5\\3x-y=3[/tex]

To solve, we can use substitution.

From the first equation, subtract x from both sides:

[tex]y=5-x[/tex]

Substitute this into the second equation:

[tex]3x-(5-x)=3[/tex]

Simplify:

[tex]3x-5+x=3[/tex]

Add 5 to both sides:

[tex]3x+x=8[/tex]

Combine like terms:

[tex]4x=8[/tex]

Divide both sides by 4:

[tex]x=2[/tex]

So, x is 2.

Substitute this back into the first equation:

[tex]x+y=5[/tex]

Substitute x for 2:

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

Subtract 2 from both sides:

[tex]y=3[/tex]

Our solution is (2,3)

3)

We have the expression:

[tex]\frac{x^4}{x^0}[/tex]

Anything to the zeroth power (except for 0) is 1. Assuming x is not 0:

[tex]=x^4/1\\=x^4[/tex]

And that's the simplest it can get.

Answer:

[tex]\Huge \boxed{\mathrm{1. \ 1}} \\ \\ \\ \Huge \boxed{\mathrm{2. \ (2,3)}} \\\\\\ \Huge \boxed{{3. \ x^4 }}[/tex]

Step-by-step explanation:

The degree is the largest exponent on the variable.

[tex]7x^1 + 1x^0[/tex]

The largest exponent on the variable is 1.

The degree is 1.

System of equations:

[tex]x+y=5 \\ \\ 3x-y=3[/tex]

Solving y for the first equation.

Subtracting x from both sides.

[tex]y=5-x[/tex]

Substitution method.

[tex]3x-(5-x)=3[/tex]

Distribute negative sign.

[tex]3x-5+x=3[/tex]

Combining like terms.

[tex]4x-5=3[/tex]

Adding 5 to both sides.

[tex]4x=8[/tex]

Dividing both sides by 4.

[tex]x=2[/tex]

Substitution method.

[tex]y=5-2 \\ \\ \\ y=3[/tex]

[tex]\displaystyle \frac{x^4 }{x^0 }[/tex]

Subtract exponents with same bases when dividing.

[tex]x^{4-0}[/tex]

[tex]x^4[/tex]

Answer:

B C D

Step-by-step explanation:

i did the assignment

Answer:

rectangle, triangle,trapezoid

Step-by-step explanation:

Answer:

Find a number that can be divided by both 6 and 9, which is 18. That means they will do laundry on the same day every 18 days.

Answer: 18 Days

Step-by-step explanation:

Let's look at their indivigual schedules for hte nex little While

<-0------6------12---->

t=Tim does laundry every 9 days

<-0---------9---------->

They haven't done laundry on the same day again yet, so let's keep going!

When we keep goin, we see thar the multiple first meet at 18

Ronal

<-0----6----18----27---->

Tim

<-0----9----18----27--->

Mathematically, we say that 18 is the least common multiple of 6 and 9. in math notation this looks like:

lcm (6, 9) = 18

Answer:

in picture

Step-by-step explanation:

Answer:

The absolute maximum and minimum of [tex]f(x) = 5 + 54\cdot x -2\cdot x^{3}[/tex] on [tex][0,4][/tex] are 113 and 5.

Step-by-step explanation:

Let be [tex]f(x) = 5 + 54\cdot x -2\cdot x^{3}[/tex], the first and second derivatives of the function are, respectively:

[tex]f'=54-6\cdot x^{2}[/tex]

[tex]f''=-12\cdot x[/tex]

Now, let equalize the first derivative to zero and solve the resulting expression:

[tex]54-6\cdot x^{2} = 0[/tex]

[tex]x^{2} = 9[/tex]

[tex]x =\pm 3[/tex]

According to the given interval, only [tex]x=3[/tex] is a valid outcome. Lastly, this is evaluated in the second derivative expression:

[tex]f''=-12\cdot(3)[/tex]

[tex]f'' = -36[/tex]

[tex]x = 3[/tex] leads to an absolute maximum.

[tex]f(3) = 5 + 54\cdot (3) -2\cdot (3)^{3}[/tex]

[tex]f(3) = 113[/tex]

The absolute minimum is determined by evaluating at each extreme of the interval:

[tex]x = 0[/tex]

[tex]f(0) = 5 + 54\cdot (0) -2\cdot (0)^{3}[/tex]

[tex]f(0) = 5[/tex]

[tex]x = 4[/tex]

[tex]f(4) = 5 + 54\cdot (4) -2\cdot (4)^{3}[/tex]

[tex]f(4) = 93[/tex]

The absolute maximum and minimum of [tex]f(x) = 5 + 54\cdot x -2\cdot x^{3}[/tex] on [tex][0,4][/tex] are 113 and 5.

Answer:

Step-by-step explanation:

If A ⊂ B, that is, A is a subset of B

Also, B ⊂ A, that is, B is a subset A

Therefore, A = B in all respect.

A set is a mathematical model for a collection of items. If two sets are subsets of each other, the other relationship they must have is that they both are equal.

A set is a mathematical model for a collection of items; it comprises elements or members, which may be any mathematical object: numbers, symbols, points in space, lines, other geometrical structures, variables, or even other sets.

If there exist two subsets such that A is a subset of B, also, B is the subset of A. Then the two sets are equal or the same.

Hence, If two sets are subsets of each other, the other relationship they must have is that they both are equal.

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Answer:

x=0

Step-by-step explanation:

4(x-5) = 4(4+x)

4x-20 = 16+4x

4x-4x = 16+20

0x=36

x = 36/0

x = 0

hope it might help

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Answer:

Because the base of this expression is not same.