√12 + √10 − √2) is

(a) A positive rational number

(b) Equal to zero

(c) An irrational number

(d) A negative integer

Answers

Answer 1

Hello!

[tex] \bf \sqrt{12} + \sqrt{10} - \sqrt{2} = [/tex]

[tex] \bf \sqrt{ {2}^{2} \times 3} + \sqrt{10} - \sqrt{2} = [/tex]

[tex] \bf \sqrt{ {2}^{2} } \sqrt{ 3} + \sqrt{10} - \sqrt{2} = [/tex]

[tex] \bf \boxed{ 2 \sqrt{3} + \sqrt{10} - \sqrt{2}} [/tex]

Answer: (c) An irrational number

Good luck! :)


Related Questions

The time it takes me to wash the dishes is uniformly distributed between 8 minutes and 17 minutes.

What is the probability that washing dishes tonight will take me between 14 and 16 minutes?

Give your answer accurate to two decimal places.

Answers

The time it takes to wash has the probability density function,

[tex]P(X=x) = \begin{cases}\frac1{17-8}=\frac19&\text{for }8\le x\le 17\\0&\text{otherewise}\end{cases}[/tex]

The probability that it takes between 14 and 16 minutes to wash the dishes is given by the integral,

[tex]\displaystyle\int_{14}^{16}P(X=x)\,\mathrm dx = \frac19\int_{14}^{16}\mathrm dx = \frac{16-14}9 = \frac29 \approx \boxed{0.22}[/tex]

If you're not familiar with calculus, the probability is equal to the area under the graph of P(X = x), which is a rectangle with height 1/9 and length 16 - 14 = 2, so the area and hence probability is 2/9 ≈ 0.22.

Write the equation of the line that passes through the points (- 5, 1) and (2, 0) . Put your answer in fully reduced slope intercept form, unless it is a vertical or horizontal line

Pls help me with this one:(

Answers

Answer:

y=-1/7x + 12/7

Step-by-step explanation:

Start by finding the slope

m=(1-0)/(-5-2)

m=-1/7

next plug the slope and the point (-5,1) into point slope formula

y-y1=m(x-x1)

y1=1

x1= -5

m=-1/7

y- 1 = -1/7(x - -5)

y-1=-1/7(x+5)

Distribute -1/7 first

y- 1=-1/7x + 5/7

Add 1 on both sides, but since its a fraction add 7/7

y=-1/7x + (5/7+7/7)

y=-1/7x+12/7

Answer:

Step-by-step explanation:

(-5,1) (2,0)

m=(y-y)/(x-x)

m = (0-1)/2- -5)

m = -1/7

(2,0)

y-0= -1/7 (x-2)

y = -1/7x + 2/7

HURRY plSSSSSSSSSSSSSSSSSSSSSS
What is the measure of the unknown angle?

Image of a straight angle divided into two angles. One angle is eighty degrees and the other is unknown.

Answers

Answer:

The unknown is 100

Step-by-step explanation:

A straight line is 180 degrees

We have two angles x, and 80

x+80 = 180

x = 180-80

x= 100

Part b c and d please help

Answers

Answer:

b) Y =5.73X +4.36

C)  =5.73225*(21)X +4.359

    124.73625

D) 163.728 = 5.73X +4.36  

     X = (163.728 - 4.36)/5.73

     X = 27.81291449

  Year would be 2027

Step-by-step explanation:

x1 y1  x2 y2

4 27.288  16 96.075

   

(Y2-Y1) (96.075)-(27.288)=   68.787  ΔY 68.787

(X2-X1) (16)-(4)=    12  ΔX 12

   

slope= 5 41/56    

B= 4 14/39    

   

Y =5.73X +4.36      

use induction method to prove that 1.2^2+2.3^2+3.4^2+...+r(r+1)^2= n(n+1)(3n^2+11n+10)/12

Answers

Base case (n = 1):

• left side = 1×2² = 4

• right side = 1×(1 + 1)×(3×1² + 11×1 + 10)/12 = 4

Induction hypothesis: Assume equality holds for n = k, so that

1×2² + 2×3² + 3×4² + … + k × (k + 1)² = k × (k + 1) × (3k ² + 11k + 10)/12

Induction step (n = k + 1):

1×2² + 2×3² + 3×4² + … + k × (k + 1)² + (k + 1) × (k + 2)²

= k × (k + 1) × (3k ² + 11k + 10)/12 + (k + 1) × (k + 2)²

= (k + 1)/12 × (k × (3k ² + 11k + 10) + 12 × (k + 2)²)

= (k + 1)/12 × ((3k ³ + 11k ² + 10k) + 12 × (k ² + 4k + 4))

= (k + 1)/12 × (3k ³ + 23k ² + 58k + 48)

= (k + 1)/12 × (3k ³ + 23k ² + 58k + 48)

On the right side, we want to end up with

(k + 1) × (k + 2) × (3 (k + 1) ² + 11 (k + 1) + 10)/12

which suggests that k + 2 should be factor of the cubic. Indeed, we have

3k ³ + 23k ² + 58k + 48 = (k + 2) (3k ² + 17k + 24)

and we can rewrite the remaining quadratic as

3k ² + 17k + 24 = 3 (k + 1)² + 11 (k + 1) + 10

so we would arrive at the desired conclusion.

To see how the above rewriting is possible, we want to find coefficients a, b, and c such that

3k ² + 17k + 24 = a (k + 1)² + b (k + 1) + c

Expand the right side and collect like powers of k :

3k ² + 17k + 24 = ak ² + (2a + b) k + a + b + c

==>   a = 3   and   2a + b = 17   and   a + b + c = 24

==>   a = 3, b = 11, c = 10

The length of a rectangle is 10 yd less than three times the width, and the area of the rectangle is 77 yd^2. Find the dimensions of the rectangle.

Answers

Answer:

W=7 and L=11

Step-by-step explanation:

We have two unknowns so we must create two equations.

First the problem states that  length of a rectangle is 10 yd less than three times the width so: L= 3w-10

Next we are given the area so: L X W = 77

Then solve for the variable algebraically. It is just a system of equations.

3W^2 - 10W - 77 = 0

(3W + 11)(W - 7) = 0

W = -11/3 and/or W=7

Discard the negative solution as the width of the rectangle cannot be less then 0.

So W=7

Plug that into the first equation.

3(7)-10= 11 so L=11

An electrician charges a fee of $40 plus $25 per hour. Let y be the cost in dollars of using the electrician for x hours. Choose the correct equation.

y = 40x - 25


y = 25x + 40


y = 25x - 40


y = 40x + 25

Answers

Answer:

y = 25x + 40

Step-by-step explanation:

The electrician charges $25 per hour.

The number of hours is x.

Therefore after x hours the electrician will charge $25x. (multiply the charge by the number of hours $25 * x)

Therefore fee(y) charged by the electrician = $40 + $25x

Hence y = 25x + 40

Solve the system of equations.

6x−y=−14
2x−3y=6

whats the answer please C:

Answers

Answer:

Step-by-step explanation:

Help me with this question please...


Each of the following statements is true or false. Which statements are true?

A. A triangle where at least two angles are acute is called an acute triangle.
B. Some polygons are neither convex nor concave.
C. The sum of the interior angles of a concave pentagon is $540^{\circ}.$
D. The interior angles of a regular $1000$-gon are greater than the interior angles of a regular $100$-gon.
E. The exterior angles of a regular $1000$-gon are greater than the exterior angles of a regular $100$-gon.

Answers

9514 1404 393

Answer:

  A. False

  B. False

  C. True

  D. True

  E. False

Step-by-step explanation:

A. False -- any triangle has at least two acute angles, whether it is acute, right, or obtuse.

B. False -- by definition, any polygon that is not convex is concave.

C. True -- the angle sum is the same regardless of whether the pentagon is convex or concave. (Provided it is a "simple" polygon, with no crossing sides.)

D. True -- the measure of the interior angle of a regular polygon increases as the number of sides increases. (see E)

E. False -- the exterior angles of a regular polygon are 360° divided by the number of sides. As the number of sides increases, the measure of each exterior angle decreases. (Interior angles are the supplement of exterior angles, so they increase as the number of sides increases.)

A box contains two blue cards numbered 1 and 2, and three green numbered 1 through 3. A blue card ins picked, followed by a green card. Select sample space for such experiment
a) {1, 1), (1, 2, (1, 3)(2, 1), (2, 2), (2, 3)}
b) {(1, 1)(1, 2), (2, 1), (2, 2), (3, 1), (3, 2)}
c) {5}
d) {6}

Answers

Answer:

The answer is a.

On Halloween, a man presents a child with a bowl containing eight different pieces of candy. He tells her that she may have three pieces. How many choices does she have

Answers

Answer:

[tex]56[/tex] choices

Step-by-step explanation:

We know that we'll have to solve this problem with a permutation or a combination, but which one do we use? The answer is a combination because the order in which the child picks the candy does not matter.

To further demonstrate this, imagine I have 4 pieces of candy labeled A, B, C, and D. I could choose A, then C, then B or I could choose C, then B, then A, but in the end, I still have the same pieces, regardless of what order I pick them in. I hope that helps to understand why this problem will be solved with a combination.

Anyways, back to the solving! Remember that the combination formula is

[tex]_nC_r=\frac{n!}{r!(n-r)!}[/tex], where n is the number of objects in the sample (the number of objects you choose from) and r is the number of objects that are to be chosen.

In this case, [tex]n=8[/tex] and [tex]r=3[/tex]. Substituting these values into the formula gives us:

[tex]_8C_3=\frac{8!}{3!5!}[/tex]

[tex]= \frac{8*7*6*5*4*3*2*1}{3*2*1*5*4*3*2*1}[/tex] (Expand the factorials)

[tex]=\frac{8*7*6}{3*2*1}[/tex] (Cancel out [tex]5*4*3*2*1[/tex])

[tex]=\frac{8*7*6}{6}[/tex] (Evaluate denominator)

[tex]=8*7[/tex] (Cancel out [tex]6[/tex])

[tex]=56[/tex]

Therefore, the child has [tex]\bf56[/tex] different ways to pick the candies. Hope this helps!

Please help on my hw

Answers

Answer:

b. The solution is a non empty set.

Step-by-step explanation:

There are no common elements.

If 5000 is divided by 10 and 10 again what answer will be reached

Answers

Hey there!

First,  divide 5,000 by 10. You will get 500.

Now, 500 ÷ 10, and you will get your answer, 50.

Hope this helps! Have a great day!

Question 19 of 28
Which of the following equations can be used to find the length of BC in the
triangle below?
B
10
А
30
с
A. BC = 30 + 10
B. (BC)2 = 102 + 302
C. BC = 30 - 10
D. (BC)2 = 302 - 102

Answers

Answer:

BC^2=10^2+30^2

Step-by-step explanation:

P=10B=30

Using pythagorean theorem

[tex]\\ \sf\longmapsto BC^2=10^2+30^2[/tex]

[tex]\\ \sf\longmapsto BC^2=100+300[/tex]

[tex]\\ \sf\longmapsto BC^2=400[/tex]

[tex]\\ \sf\longmapsto BC=\sqrt{400}[/tex]

[tex]\\ \sf\longmapsto BC=20[/tex]

Air-USA has a policy of booking as many as 22 people on an airplane that can only seat 20 people. (Past studies have revealed that only 82% of the booked passengers actually show up for the flight.) a) Find the probability that if Air-USA books 22 people, not enough seats will be available. Round your answer to 4 decimal places. P ( X > 20 )

Answers

Answer:

The answer is "0.07404893".

Step-by-step explanation:

Applying the binomial distribution:

[tex]n = 22\\\\p= 82\%=0.82\\\\q = 1-0.82 = 0.18\\\\[/tex]

Calculating the probability for not enough seats:

[tex]=P(X>20)\\\\= P(21) + P(22)\\\\[/tex]

[tex]= \binom{22}{21} (0.82)^{21}(0.18)^1+ \binom{22}{22} (0.82)^{22}(0.18)[/tex]

[tex]=0 .06134598+ 0.01270295\\\\=0.07404893[/tex]

Determine whether each relation is a function. Give the domain and range for each relation.
{(3, 4), (3, 5), (4, 4), (4, 5)}

Answers

Answer:

Not a function

Domain: {3,4}

Range: {4,5}

Step-by-step explanation:

A function is a relation where each input has its own output. In other words if the x value has multiple corresponding y values then the relation is not a function

For the relation given {(3, 4), (3, 5), (4, 4), (4, 5)} the x value 3 and 4 have more than one corresponding y value therefore the relation shown is not a function

Now let's find the domain and range.

Domain is the set of x values in a relation.

The x values of the given relation are 3 and 4 so the domain is {3,4}

The range is the set of y values in a relation

The y value of the given relation include 4 and 5

So the range would be {4,5}

Notes:

The values of x and y should be written from least to greatest when writing them out as domain and range.

They should be written inside of brackets

Do not repeat numbers when writing the domain and range

Find the area of a triangle with the given description. (Round your answer to one decimal place.)
a triangle with sides of length 14 and 28 and included angle 20°

Answers

9514 1404 393

Answer:

  67.0 square units

Step-by-step explanation:

The formula for the area is ...

  Area = 1/2ab·sin(C)

  Area = (1/2)(14)(28)sin(20°) ≈ 67.036 . . . . square units

The area of the triangle is about 67.0 square units.

14. A quadratic equation is graphed above.
Which of the following equations could be
paired with the graphed equation to create
a system of equations whose solution set is
comprised of the points (2,-2) and (-3, 3)?
A. y = x + 6
B. y = x - 6
C. y = X
D. y = -x

Answers

Answer:

D.

Step-by-step explanation:

2=-2,3=-3

2²=-2²,3²=3²

a) Everyone on the team talks until the entire team agrees on one decision. O b) Everyone on the team discusses options and then votes. O c) The team passes the decision-making responsibility to an outside person. O di The team leader makes a decision without input from the other members.

Answers

Answer:

a) Everyone on the team talks until the entire team agrees on one decision.

Step-by-step explanation:

Option B consists of voting and not everyone would like the outcome. Option C is making an outsider the decision maker, which can't be helpful since he / she won't have as strong opinions as the team itself. Option D is just plain wrong as it defeats the purpose of team work and deciding as one team. So, I believe option A makes the most sense

4) The measure of the linear density at a point of a rod varies directly as the third power of the measure of the distance of the point from one end. The length of the rod is 4 ft and the linear density is 2 slugs/ft at the center, find the total mass of the given rod and the center of the mass​

Answers

Answer:

a. 16 slug b. 3.2 ft

Step-by-step explanation:

a. Total mass of the rod

Since the linear density at a point of the rod,λ varies directly as the third power of the measure of the distance of the point form the end, x

So, λ ∝ x³

λ = kx³

Since the linear density λ = 2 slug/ft at then center when x = L/2 where L is the length of the rod,

k = λ/x³ = λ/(L/2)³ = 8λ/L³

substituting the values of the variables into the equation, we have

k = 8λ/L³

k = 8 × 2/4³

k = 16/64

k = 1/4

So, λ = kx³ = x³/4

The mass of a small length element of the rod dx is dm = λdx

So, to find the total mass of the rod M = ∫dm = ∫λdx we integrate from x = 0 to x = L = 4 ft

M = ∫₀⁴dm

= ∫₀⁴λdx

= ∫₀⁴(x³/4)dx

= (1/4)∫₀⁴x³dx

= (1/4)[x⁴/4]₀⁴

= (1/16)[4⁴ - 0⁴]

= (256 - 0)/16

= 256/16

= 16 slug

b. The center of mass of the rod

Let x be the distance of the small mass element dm = λdx from the end of the rod. The moment of this mass element about the end of the rod is xdm =  λxdx = (x³/4)xdx = (x⁴/4)dx.

We integrate this through the length of the rod. That is from x = 0 to x = L = 4 ft

The center of mass of the rod x' = ∫₀⁴(x⁴/4)dx/M where M = mass of rod

= (1/4)∫₀⁴x⁴dx/M

= (1/4)[x⁵/5]₀⁴/M

= (1/20)[x⁵]₀⁴/M

= (1/20)[4⁵ - 0⁵]/M

= (1/20)[1024 - 0]/M

= (1/20)[1024]/M

Since M = 16, we have

x' =  (1/20)[1024]/16

x' = 64/20

x' = 3.2 ft

PLEASE HELPPPPPPPPPP

Answers

Answer: SORRY NEED AN ACCOUNT ON - 10

Step-by-step explanation:

To resolve the proposed issue, an explanation is needed in which the subject is addressed

Identify the slope and y intercept of the line with equation 2y = 5x + 4

Answers

Answer:

Slope is 5/2

y-intercept is 2

Step-by-step explanation:

Turn the equation into slope intercept form [ y = mx +  b ].

2y = 5x + 4

~Divide everything by 2

y = 5/2x + 2

Remember that in slope intercept form, m = slope and b = y-intercept.

Best of Luck!

Answer:

slope: 2.5

y-intercept: 2

Step-by-step explanation:

First isolate the y variable which changes the equation to y=2.5x+2

The equation of a line is mx + b where m is the slope and b and the

y-intercept. Leading us to conclude that 2.5 is the slope and 2 is the y-intercept.

If (4x-5) :(9x-5) = 3:8 find the value of x.​

Answers

Answer:

x is 5

Step-by-step explanation:

[tex] \frac{4x - 5}{9x - 5} = \frac{3}{8} \\ \\ 8(4x - 5) = 3(9x - 5) \\ 32x - 40 = 27x - 15 \\ 5x = 25 \\ x = \frac{25}{5} \\ \\ x = 5[/tex]

Step-by-step explanation:

as you can see as i solved above. all you need to do was to rationalize the both equations

11
Select the correct answer.
Which expression is equivalent to the given expression?
In(2e/x)
O A. In 2 – In x
OB. 1 + In 2 - In x
Oc. In 2 + In x
OD. In 1 + In 2 - In
Reset
Next

Answers

Answer:

B. 1 + ln 2 - ln x

General Formulas and Concepts:

Algebra II

Natural logarithms ln and Euler's number eLogarithmic Property [Multiplying]:                                                                     [tex]\displaystyle log(ab) = log(a) + log(b)[/tex] Logarithmic Property [Dividing]:                                                                         [tex]\displaystyle log(\frac{a}{b}) = log(a) - log(b)[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle ln(\frac{2e}{x})[/tex]

Step 2: Simplify

Expand [Logarithmic Property - Dividing]:                                                      [tex]\displaystyle ln(\frac{2e}{x}) = ln(2e) - ln(x)[/tex]Expand [Logarithmic Property - Multiplying]:                                                  [tex]\displaystyle ln(\frac{2e}{x}) = ln(2) + ln(e) - ln(x)[/tex]Simplify:                                                                                                             [tex]\displaystyle ln(\frac{2e}{x}) = ln(2) + 1 - ln(x)[/tex]Rewrite:                                                                                                             [tex]\displaystyle ln(\frac{2e}{x}) = 1 + ln(2) - ln(x)[/tex]

What is the answer for 75% of test takers whovscored below average withou an unknown mean and standard deviation

Answers

Answer:

sir she hey Jen Jen Jenn receive surge

Answer:

Hello,

Step-by-step explanation:

z=0.7734

p(z<?)=0.75 ==> ?=0.7734

A flower bed is in the shape of a triangle with one side twice the length of the shortest side and a third side is 22 more than the length of the shortest side. Find the dimensions if the perimeter is 182 feet.

Answers

Answer:40, 80 and 62

Step-by-step explanation:

182-22= 160

160/4 = 40 so,

Shortest side is 40

Longest is 80

Third side is 62

can anybody help with this ?

Answers

Answer:(

fx).(gx)=D. -40x^3+25x^2+45

Step-by-step explanation:

The second term in a geometric sequence is 50. The forth term in the same sequence is 112.5. what is the common ratio in this sequence?

Answers

Answer:

1.5

Step-by-step explanation:

Let the first term be a and the common ratio be r

ATQ, ar=50 and ar^3=112.5, divide these two. r^2=2.25, r=1.5

find the value of the trigonometric ratio​

Answers

Answer:

15/17

Step-by-step explanation:

sinA = CB/CA =15/17

Answer:

15/17

Step-by-step explanation:

sine = opposite / hypotenusesin A = BC/ACsin A = 15/17

Inverse Function Question

Determine the expression of f^-1(x) for f(x)=e^x

Answers

First, find the inverse of f,

[tex]y=e^x[/tex]

[tex]x=e^y[/tex]

Now take the natural logarithm on both sides,

[tex]\ln x=\ln e^y\implies f^{-1}(x)=\boxed{\ln(x)}[/tex]

Second, find the inverse of g,

[tex]y=5x\implies g^{-1}(x)=\boxed{\frac{x}{5}}[/tex]

Now take their composition,

[tex](g\circ f)(x)=g(f(x))=\frac{\ln(x)}{5}[/tex]

Let [tex]y=\frac{\ln(x)}{5}[/tex], now again find the inverse,

[tex]x=\frac{\ln(y)}{5}[/tex]

[tex]5x=\ln y[/tex]

exponentiate both sides to base e,

[tex]e^{5x}=e^{\ln y}\implies (g\circ f)^{-1}(x)=\boxed{e^{5x}}[/tex]

Hope this helps :)

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