Simplify the Radical Expression
3V2 - V8 +4V12+53

Answer:

The annual depreciation rate is 72.86%.

Step-by-step explanation:

The information provided are:

From the above data we know that the band's popularity depreciated.

The initial cost of a signed Black Diamond poster was, a = $500.

After three years the cost of a signed Black Diamond poster was, y = $10.

It can be seen that the value of a signed Black Diamond poster is decreasing exponentially over the years.

The formula for exponential decay or depreciation is:

[tex]y=a(1-r)^{x}[/tex]

Here,

y = final value

a = initial value

r = rate of depreciation

x = time

Compute the annual depreciation rate as follows:

         [tex]y=a(1-r)^{x}[/tex]

        [tex]10=500\times (1 -r)^{3}[/tex]

[tex](1-r)^{3}=\frac{10}{500}[/tex]

 [tex](1-r)=\sqrt[3]{\frac{1}{50}}[/tex]

    [tex]1-r=0.2714[/tex]

          [tex]r=1-0.2714\\\\r=0.7286[/tex]

Thus, the annual depreciation rate is 72.86%.

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{x = 4.4}}}}}[/tex]

Step-by-step explanation:

Given,

Length of the rectangle ( l ) = 3x + 5

Breadth of the rectangle ( b ) = 2x - 1

Perimeter of the rectangle ( P ) = 52

Finding the value of x

[tex] \boxed{ \sf{perimeter \: of \: rectangle = 2(l + b)}}[/tex]

⇒[tex] \sf{52 = 2(3x + 5 + 2x - 1)}[/tex]

⇒[tex] \sf{52 = 2(5x + 4)}[/tex]

⇒[tex] \sf{52 = 10x + 8}[/tex]

⇒[tex] \sf{10x + 8 = 52}[/tex]

⇒[tex] \sf{10x = 52 - 8}[/tex]

⇒[tex] \sf{10x = 44}[/tex]

⇒[tex] \sf{ \frac{10x}{10} = \frac{44}{10} }[/tex]

⇒[tex] \sf{x = 4.4 \: }[/tex]

Hope I helped!

Best regards!! :D

Answer:

focus and belive on your self

Step-by-step explanation:

Answer:

Option B, 163 caps.

Step-by-step explanation:

The price of caps are = $6 per cap.

Shipping charge = $25

The total budget of the Laura = $1000

Since the $25 is shipping charge so subtract it from the budget = 1000 – 25 = $975

Here $975 will be used to buy the caps at the price of $6 per cap.

Thus, the number of caps = budget after subtracting the shipping fee / per cap price

Total caps = $975 / 6

Total caps = 162.5 or 163 caps.

Answer:

the last one

Step-by-step explanation:

i took the test

If you plug x = 3 into choice A, then you dont have any division by zero errors or square roots of negative values.

Choice B in contrast has x-9 = 3-9 = -6 under the square root, so this leads to an imaginary/complex result. Choice D is similar.

Choice C will have zero in the denominator after plugging in x = 3 since x^2-9 = 3^2-9 = 9-9 = 0.

Answer:

The answer is

Step-by-step explanation:

f(x) = 6x² + 3

To find the inverse of the function above equate it to y

That's

f(x) = y

So we have

y = 6x² + 3

Next interchange the variables that's x becomes y and y becomes x.

x = 6y² + 3

Next make y the subject

Subtract 3 from both sides

That's

6y² + 3 - 3 = x - 3

6y² = x - 3

Divide both sides by 6

That's

Next find the square root of both sides

We have the final answer as

Hope this helps you

Answer:

Step-by-step explanation:

1=

option b= 4

2.

option b=60miles per hour

Hope it helps

Answer:

x=-1

Step-by-step explanation:

2x+6=3-x

Step 1: Simplify both sides of the equation.

2x+6=3−x

2x+6=3+(−x)

2x+6=−x+3

Step 2: Add x to both sides.

2x+6+x=−x+3+x

3x+6=3

Step 3: Subtract 6 from both sides.

3x+6−6=3−6

3x=−3

Step 4: Divide both sides by 3.

3x/3=−3/3

x=−1

Answer:

x=−1

Answer:

X=1/2. X=4/3

Step-by-step explanation:

6x2+5X-4=0

6X2+8X-3X-4=0

2x(3x+4) - 1(3x+4)=0

2x-1) (3X-4)

X=1/2. X=4/3

The Solution of Equation is x = -4/3 or x= 2.

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 the Equation:

6x² + 5x - 4 = 0

Solving the Quadratic equation

6x² + 5x - 4 = 0

6x² -3x + 8x - 4 = 0

3x( x- 2) +4 (x-2)= 0

(3x + 4) (x-2) = 0

3x +4 = 0 or x-2 = 0

x = -4/3 or x= 2

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Answer:

9 9/14

Step-by-step explanation:

[tex]4\frac{1}{2}\times\:2\frac{1}{7}\\\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\quad 4\frac{1}{2}=\frac{9}{2}\\\\\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\quad 2\frac{1}{7}=\frac{15}{7}\\\frac{9}{2}\times\frac{15}{7}\\\\\mathrm{Multiply\:fractions}:\\\quad \frac{a}{b}\times\frac{c}{d}=\frac{a\:\times\:c}{b\:\times\:d}\\\\=\frac{9\times\:15}{2\times\:7}\\\\=\frac{135}{14}\\\\[/tex]

[tex]\mathrm{Convert\:improper\:fractions\:to\:mixed\:numbers}:\quad \frac{135}{14}\\=9\frac{9}{14}[/tex]

Unfortunately, I do not go to Harvard Business School so I am unable to solve this complex equation.

Answer: -9

Step-by-step explanation: you want to take away 12 from 3, which will leave you in the negatives

Answer:

(x+5) (x=3)

(X+5) (x+1)

Step-by-step explanation:

A removeable discontinuity is always found in the denominator of a rational function and is one that can be reduced away with an identical term in the numerator. It is still, however, a problem because it causes the denominator to equal 0 if filled in with the necessary value of x. In my function above, the terms (x + 5) in the numerator and denominator can cancel each other out, leaving a hole in your graph at -5 since x doesn't exist at -5, but the x + 1 doesn't have anything to cancel out with, so this will present as a vertical asymptote in your graph at x = -1, a nonremoveable discontinuity.

Rationalizing the denominator involves exploiting the well-known difference of squares formula,

[tex]a^2-b^2=(a-b)(a+b)[/tex]

We have

[tex](\sqrt{16}-\sqrt2)(\sqrt{16}+\sqrt2)=(\sqrt{16})^2-(\sqrt2)^2=16-2=14[/tex]

so that

[tex]\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{\sqrt{32}(\sqrt{16}+\sqrt2)}{14}[/tex]

Rewrite 16 and 32 as powers of 2, then simplify:

[tex]\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{\sqrt{2^5}(\sqrt{2^4}+\sqrt2)}{14}[/tex]

[tex]\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{2^2\sqrt2(2^2+\sqrt2)}{14}[/tex]

[tex]\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{4\sqrt2(4+\sqrt2)}{14}[/tex]

[tex]\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{16\sqrt2+4(\sqrt2)^2}{14}[/tex]

[tex]\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{16\sqrt2+8}{14}[/tex]

[tex]\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{8\sqrt2+4}7[/tex]

So we have A = 8, B = 2, C = 4, and D = 7, and thus A + B + C + D = 21.

The rationalized form of the given surd is [tex]\frac{8\sqrt{2}+4}{7}[/tex], and the minimum possible value of A + B + C + D = 8 + 2 + 4 + 7 = 21

From the question, we are to rationalize the denominator of the given surd.

We are to write the answer in the form

[tex]\frac{A\sqrt{B}+C}{D}[/tex]

and find the minimum possible value of A + B + C + D

The given surd is

[tex]\frac{\sqrt{32}}{\sqrt{16}-\sqrt{2}}[/tex]

To rationalize the surd, we will multiply the numerator and denominator by the conjugate of the denominator

The conjugate of the denominator is [tex]\sqrt{16}+\sqrt{2}[/tex]

Therefore,

[tex]\frac{\sqrt{32}}{\sqrt{16}-\sqrt{2}} \times \frac{\sqrt{16}+\sqrt{2}}{\sqrt{16}+\sqrt{2}}[/tex]

[tex]= \frac{\sqrt{32}(\sqrt{16}+\sqrt{2})}{(\sqrt{16}-\sqrt{2})(\sqrt{16}+\sqrt{2})}[/tex]

[tex]= \frac{\sqrt{512}+\sqrt{64})}{(\sqrt{16})^{2} -(\sqrt{2})^{2} }[/tex]

[tex]= \frac{16\sqrt{2}+8}{16-2}[/tex]

[tex]= \frac{16\sqrt{2}+8}{14}[/tex]

[tex]= \frac{2(8\sqrt{2}+4)}{2(7)}[/tex]

By comparing with, [tex]\frac{A\sqrt{B}+C}{D}[/tex]

A = 8, B = 2, C = 4, and D = 7

Then, the minimum possible value of A + B + C + D = 8 + 2 + 4 + 7 = 21

Hence, the rationalized form of the given surd is [tex]\frac{8\sqrt{2}+4}{7}[/tex], and the minimum possible value of A + B + C + D = 8 + 2 + 4 + 7 = 21

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Answer:

1

Step-by-step explanation:

Using the sum to product formulae and the exact values

sin x + sin y = 2sin([tex]\frac{x+y}{2}[/tex] )cos([tex]\frac{x-y}{2}[/tex] )

cos x + cos y = 2cos([tex]\frac{x+y}{2}[/tex] )cos([tex]\frac{x-y}{2}[/tex] )

sin45° = cos45° = [tex]\frac{1}{\sqrt{2} }[/tex] , cos30° = [tex]\frac{\sqrt{3} }{2}[/tex]

Given

[tex]\frac{sin75+sin15}{cos75+cos15}[/tex]

= [tex]\frac{2sin(\frac{75+15}{2})cos(\frac{75-15}{2}) }{2cos(\frac{75+15}{2})cos(\frac{75-15}{2}) }[/tex]

= [tex]\frac{2si45cos30}{2cos45cos30}[/tex]

= (2 × [tex]\frac{1}{\sqrt{2} }[/tex] × [tex]\frac{\sqrt{3} }{2}[/tex] ) ÷ (2 × [tex]\frac{1}{\sqrt{2} }[/tex] × [tex]\frac{\sqrt{3} }{2}[/tex] )

= 1

Answer:  1

Step-by-step explanation:

sin 75 = sin(30 + 45) = sin30 · cos45  + cos30 · sin45

                                 [tex]=\dfrac{1}{2}\cdot \dfrac{\sqrt2}{2}+\dfrac{\sqrt3}{2}\cdot\dfrac{\sqrt2}{2}\qquad =\dfrac{\sqrt2+\sqrt6}{4}[/tex]

sin 15 = sin(45 - 30) = sin45 · cos30  - cos45 · sin30

                                  [tex]=\dfrac{\sqrt2}{2}\cdot \dfrac{\sqrt3}{2}-\dfrac{\sqrt2}{2}\cdot\dfrac{1}{2}\qquad =\dfrac{\sqrt6+\sqrt2}{4}[/tex]

cos 75 = cos(30 + 45) = cos30 · cos45  - sin30 · sin45

                                   [tex]=\dfrac{\sqrt3}{2}\cdot \dfrac{\sqrt2}{2}-\dfrac{1}{2}\cdot\dfrac{\sqrt2}{2}\qquad =\dfrac{\sqrt6-\sqrt2}{4}[/tex]

cos 15 = cos(45 - 30) = cos45 · cos30  + sin45 · sin30

                                   [tex]=\dfrac{\sqrt2}{2}\cdot \dfrac{\sqrt3}{2}+\dfrac{\sqrt2}{2}\cdot\dfrac{1}{2}\qquad =\dfrac{\sqrt6+\sqrt2}{4}[/tex]

       [tex]\dfrac{\sin 75+\sin 15}{\cos 75+\cos 15}[/tex]

   [tex]=\dfrac{\frac{\sqrt2+\sqrt6}{4}+\frac{\sqrt6-\sqrt2}{4}}{\frac{\sqrt6-\sqrt2}{4}+\frac{\sqrt6+\sqrt2}{4}}\\\\\\=\dfrac{\frac{\sqrt6}{2}}{\frac{\sqrt6}{2}}\\\\\\=1[/tex]

Answer:

4 7/24

Step-by-step explanation:

Answer:

103/24 or 4.29 or 4 7/24

Step-by-step explanation:

15 5/12 - 11 1/8

185/12 - 89/8

370/24 - 267/24 = 103/24

or

15 10/24 - 11 3/24 = 4 7/24

Answer:

Step-by-step explanation:

$2.50g + $5 = $15

$2.50g = 10

g = 4 games

The equation that is used to find the number of games that Max bowled is [tex]5+2.50x=15.[/tex]

Charge for shoe rental [tex]=[/tex] $[tex]5[/tex].

Charge per game [tex]=[/tex] $[tex]2.50[/tex].

Let [tex]g[/tex] represents the number of games.

The total charge is the sum of shoe rental charge and charge per game times the number of games.

Total money spent [tex]=[/tex] $[tex]15[/tex].

[tex]5+2.50x=15[/tex]

This is the equation that is used to find the number of games that Max bowled.

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Answer:f(x) indicates applying the function to the value x and can also represent the actual value obtained by applying the function to x

Step-by-step explanation:

Answer:

f(x) means y

Step-by-step explanation:

You use f(x) when it is representing y in a function

Answer: 40/7, if you need, the mixed fraction is 5 5/7

Step-by-step explanation:

First of all, convert all the mixed fraction into improper fraction.

2 2/3=8/3

2 1/7=15/7

Then do the multiplication.

8/3 × 15/7=120/21=40/7 (You can directly simplify it to 40/7 since you can use 15 divided by 3 to get 5 left in the numerator)

Hope this helps!! :)

Please let me know if you have any question

Answer:

5.71

Step-by-step explanation:

two two by three × two one by seven

=8/3×15/7

=8×5/7 as 15 and three will divide and 15 will change to 5

=40/7

=5.71

Answer:

Yes . Divide by 10 for 10/20 to get 1/2.

10/10= 1

20/10= 2

10/20= 1/2

Answer:

To show that a conjecture is false, you have to find only one example in which the conjecture is not true. So an example could be a drawing, a statement, or a number.

Answer:

The cost in 2007 - 2008  =  $15,795.5

The linear model for the data is y = $650.5·x + $9290.5

Step-by-step explanation:

The given data can be presented as follows;

College year,                         x,                 Estimated tuition, y

1997-1998,                             0,                 $9412

1998-1999,                             1,                  $9941

1999-2000,                            2,                 $10561

2000-2001,                            3,                 $11242

2001-2002,                            4,                  $11965

2002-2003,                            5,                  

2003-2004,                            6,                  

2004-2005,                            7,                

2005-2006,                            8,                

2006-2007,                            9,                  

2007-2008,                            10,                  

With points (1, 9941) and (3, 11242), we have the slope given by the equation;

[tex]m = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]

Which gives;

[tex]m = \dfrac{11242 - 9941}{3 - 1}= 650.5[/tex]

Therefore;

y - 11242 = 650.5 × (x - 3)

y= 650.5·x - 650.5 ×3 + 11242

y = 650.5·x + 9290.5

Therefore from the above table at 2007 - 2008, the value of x should be 10, we therefore have;

y = 650.5×10 + 9290.5 = $15,795.5

The cost (estimated tuition) in 2007 - 2008  =  $15,795.5

The linear model for the data is y = 650.5·x + 9290.5.

The linear model for the data is y = 650.5x + 9290.5 and The cost of college tuition in 2007-2008 is $15795.5

A linear equation is in the form:

y = mx + b

where y, x are variables, m is the rate of change and b is the initial value of y.

Let y represent the cost of tuition of battery after x years.

From the table using the points (1, 9941) and (3, 11242):

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\ \\ y-9941=\frac{11242-9941}{3-1}(x-1)\\ \\ y=650.5x+9290.5[/tex]

The linear model for the data is y = 650.5x + 9290.5

At 2007-2008 (x = 10:

y = 650.5(10) + 9290.5 = 15795.5

The cost of college tuition in 2007-2008 is $15795.5

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Answer:

[tex]=7x^2+8x-2[/tex]

Step-by-step explanation:

So, on Monday, Tuesday, and Wednesday, he mowed:

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

yards, respectively.

To determine how many yards he mowed in the three days, simply add the three expressions. Thus:

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

Combine like terms:

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

Add or subtract:

[tex]=7x^2+8x-2[/tex]

And it cannot be simplified further :)

Answer:

No

Step-by-step explanation:

2 to the fourth power is equal to 16.

On the other hand, 2 times 4 is equal to 8.

So, they are not equivalent because 16 [tex]\neq[/tex] 8

4² is the same as the question 4 x 4 which is 16

Answer:

p

Step-by-step explanation:

Answer:

The radius, r₂, of the ball that uses one-half the amount of rubber coating used to cover the 16-inch ball is approximately 4.66 inches

Step-by-step explanation:

The dimension of the ball with known radius = 16-inch

The surface area of the ball with 16-inch radius = 4×π×r² = π·D² = π×16² = 804.24772 in.²

Given that the ball uses one-half the rubber material coating used to cover the 16-inch ball, we have the surface area of the ball = 804.24772 in.²/2 = 402.12386 in.²

The radius, r₂ of the new ball is found as follows;

402.12386 in.² = 4×π×r₂²

r₂² = 402.12386 in.² /(4×π) ≈ 32

r₂ = √32 = 4·√2 ≈ 4.66 inches

The radius, r₂, of the ball that uses one-half the amount of rubber coating used to cover the 16-inch ball ≈ 4.66 inches.

Answer:134.7

Step-by-step explanation:

Answer:

Step-by-step explanation:

The question is lacking appropriate diagram. Find the diagram to the question attached.

From the diagram, it can be seen that AD = AB+BC+CD

Given the following

AD = 23units

AB = 4units

CD = 12units

To get C=BC, we will substitute the given segments into the expression above as shown;

23 = 4+BC+12

23 = BC + 4 + 12

23 = BC+16

Subtract 16 from both sides

23-16 = BC+16-16

7 = BC

Hence the length of segment BC is 7units.

Answer:

no

Step-by-step explanation:

The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

9+10 > 21

19 >21

This is not true so it cannot make a triangle

Answer:

The square root of 85

Step-by-step explanation:

The formula to find out the distance between the points is shown below:

The Distance is

[tex]= \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

where,

x_1 = -3

y_1 = -1

x_2 = 4

And, the y_2 = 5

Now place these values to the above formula

So, the distance is

[tex]= \sqrt{(4+3)^2 + (5+1)^2} \\\\= \sqrt{49 + 36} \\\\= \sqrt{85}[/tex]

= 9.22 units

Hence, the distance between points M and N is 9.22 units or the square root of 85

Hence, the second option is correct