Evaluate 2 sin 60° + tan 45° + cos²60°​

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:

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:

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: 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:

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.

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:

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

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:134.7

Step-by-step explanation:

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:

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: When combining like terms, add or subtract the coefficients. Keep the exponents as they are.

Step-by-step explanation:

You can combine 2x^2 + 3x^2 to get 5x^2. If x =3, 3^2=9 So 2(3)^2 is 18 and 3(3)^2 is 27. 18+27=45 And 5(3)^2= 45. Same result!

You can not combine 2x^2 and 2x^3. If the value of x is 3, 2(3)^2 this term works out to =18 and 2(3)^3 =54

If you add the exponents x^5 becomes 2(3)^5 or 2×243=486. Vastly different values! Don't add exponents unless you are multiplying terms.

Yes, when combining like terms with exponents, you add the exponents only if the terms have the same base.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

When combining like terms with exponents, you add the exponents only if the terms have the same base.

For example,

3x² + 9x²

= (3 + 9)x²

= 12x²

And,

2² x 2³

= [tex]2^{2 + 3}[/tex]

= [tex]2^5[/tex]

Thus,

Yes, we add the exponents.

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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:

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:

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]

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 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:

(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.

Answer:

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

10/10= 1

20/10= 2

10/20= 1/2

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:

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:

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:

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:

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

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:

[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