Solve cos x +sqrt2 = -cos x for x over the interval (0,2pi) .

Answer: [tex]\text{Area}=9.8\ \text{square centimeter}[/tex]

Step-by-step explanation:

Given: The height of the triangle h= 3.0 cm

The base corresponding to the given height b= 6.5 cm

We know that the area of a triangle is given by :-

[tex]\text{Area}=\frac{1}{2}bh\\\\\Rightarrow\text{Area}=\frac{1}{2}(3)(6.5)\\\\\Rightarrow\text{Area}=\frac{19.5}{2}\\\\\Rightarrow\text{Area}=9.75\approx9.8\ \text{square centimeter}[/tex]

Prius can travel up to 4.23 × x kilometers on 16 liters of gasoline.

It is given that Prius runs on gasoline.

We have to find out that how many kilometers it can run if amount of gasoline is 16 liters.

What will be the value of 16 times of a number x ?

The value will be ; 16 × x .

No. of kilometers Prius travels depends on what is the model of Prius . Also quality of roads makes a difference.

∵ 1 liter = 0.264172 gallons

⇒ 16 liters = 16 × 0.264172 = 4.23 gallons

Let's say a Prius travels x kilometers per gallon.

So ; on 16 liters of gasoline , Prius will travel ;

x × 4.23 = 4.23 × x kilometers

Thus , Prius can travel up to 4.23 × x kilometers on 16 liters of gasoline.

To learn more about algebraic expressions click here ;

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Final answer:

The height difference between Amersham station (147 meters above sea level) and Waterloo station (21 meters below sea level) is 168 meters.

Explanation:

To find the height difference between Amersham station, which is the highest station in the London Tube at 147 meters above sea level, and Waterloo station, the lowest at 21 meters below sea level, we simply add the two values together, treating the below sea level as a negative altitude.

147 meters (Amersham altitude above sea level) + (-21 meters) (Waterloo altitude below sea level) = 168 meters.

Therefore, the height difference between Amersham and Waterloo stations is 168 meters.

Answer:

c) -16 ≤ x < 5

Step-by-step explanation:

The given function is f(x) = -3x + 2 and domain is  -1 < x ≤ 6

The maximum value of the domain is 6 and the minimum value of the domain is -1.

To find the range, plugin the maximum and minimum value of the domain.

Plug in x = 6 in the given function, we get

f(6) = -3(6) + 2 = -18 +2 = -16

f(-1) = -3(-1) + 2 = 3 + 2 = 5

So the range is -16 ≤ x < 5

Answer:

Correct option is A.          

Step-by-step explanation:

Given the following functions we have to choose the option which illustrates a change in amplitude.

Multiplying a sine or cosine function by a constant changes the graph of the parent function i.e results in change in the amplitude of function. Amplitude is the measure of distance from the sinusoidal axis to the maximum or the minimum.

Option A:  y = 3cos4x

The parent function is f(x) = cos x.

The amplitude of function changes from 1 to 3.

Option B:  y = 1+sinx

The parent function is f(x) = sin x

The amplitude remains same i.e 1

Option C: y = -2-cos(x - pi)

Here also remains same.

Option D: y = tan 2x

The tangent function does not have an amplitude because it has no maximum or minimum value.

Hence, correct option is A.

Answer:

y= 3cos4x

Step-by-step explanation:

The total distance between the two women would simply be the sum of the hypotenuse formed by the triangular path they created.

For each women:

c^2  = a^2 + b^2

c^2 = 3^2 + 4^2

c^2 = 9 + 16

c^2 = 25

c = 5 m

Therefore the distance between the two is:

distance between the two women = 2 * c

distance between the two women = 10 m

Answer:

34 inches.

Step-by-step explanation:

90-7 =83 degrees

height = 3 miles

divide 3 by the cos of 83 degrees

3/cos(83) = 24.6165

rounded to nearest mile = 25 miles

Answer with explanation:

⇒Consider a Non Zero Rational Number = 2, 3, [tex]\frac{2}{3}[/tex], 53,....

The decimal Expansion of Rational number is Either terminating or  Non Teminating repeating.

⇒ Irrational Number = π, √2,√7,...

The decimal Expansion of Irrational number is Non terminating Non repeating.

⇒Product of a non-zero rational number and an irrational number

  =2 ×√2 or 3 × √2 or 3 π

are all Irrational number.

In terms of decimals:

                     (c)⇒a non-repeating, non-terminating decimal=(Irrational Number)

Option C

3x +4y =12

2x = y-6 Rewrite this as y = 2x+6

 now replace that for y in the first equation

3x + 4(2x+6) = 12

now do all the calculations:

3x + 8x +24 =12

11x + 24 = 12

11x = -12

x = -12/11 = -1 1/11

 now substitute -12/11 for x in the 2nd equation and solve

y = 2x+6

y = 2(-1 1/11) +6

y = 42/11 = 3 9/11

Answer:

 32,760 is the correct answer, the first person is wrong! Took the test and this is it!

Step-by-step explanation:

Answer:

Option (B) is correct.

To prove

As given the epression in the question is given by

[tex]= 5\sqrt{8} - \sqrt{18} - 2 \sqrt{2}[/tex]

Now simplify the above

Terms are written as

[tex]\sqrt{8} = \sqrt{2\times 2\times 2} = 2 \sqrt{2}[/tex]

[tex]\sqrt{18} = \sqrt{3\times 3\times 2} = 3 \sqrt{2}[/tex]

Put in the above expression.

[tex]= 5\times 2 \sqrt{2} -3 \sqrt{2} - 2 \sqrt{2}[/tex]

[tex]= 10 \sqrt{2} -5 \sqrt{2}[/tex]

[tex]=5 \sqrt{2}[/tex]

[tex]Therefore\ the\ expression\ 5\sqrt{8} - \sqrt{18} - 2 \sqrt{2}\ is\ equivalent\ to\ 5 \sqrt{2} .[/tex]

Answer:

We are given,

The transformed function is [tex]f(x)=\sqrt{x+1}-5[/tex].

So, we can see that,

The parent function is [tex]f(x)=\sqrt{x}[/tex].

Then, we have,

The parent function is translated 1 units to the left to give [tex]\sqrt{x+1}[/tex].

Then, it is translated 5 units downwards to give the function  [tex]\sqrt{x+1}-5[/tex].

Hence, we have,

The parent function f(x) = √x has been shifted 1 unit left and 5 units down

The parent function of a square root function is represented as:

[tex]f(x) = \sqrt x[/tex]

When the function is shifted 1 unit left, we have the following equation

[tex]f(x) = \sqrt {x + 1}[/tex]

When the function is shifted 5 units down, we have the following equation

[tex]f(x) = \sqrt {x + 1} - 5[/tex]

Hence, the parent function f(x) = √x has been shifted 1 unit left and 5 units down

Read more about function transformation at:

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Answer:

The value of 25th percentile equals:

 lower quartile

Step-by-step explanation:

We have to find the value of the 25th percentile

25th percentile is equal to the lower quartile.

50th percentile is equal to the median.

and 75th percentile is equal to the upper quartile.

Hence, the value of 25th percentile equals:

 lower quartile

Answer:

Option B.[tex]\sqrt[6]{200}[/tex]

Step-by-step explanation:

The given expression is ∛5.√2 and we have to find the product.

In this question ∛5 can be written as [tex]5^{\frac{1}{3} }[/tex] and [tex]\sqrt{2}=2^{\frac{1}{2}}[/tex]

We know to multiply these terms we should have the same powers of both the terms.

Now we will convert these terms to the terms having same powers.

first term [tex]5^{\frac{1}{3}}=5^{(\frac{1}{3}).(\frac{2}{2})}[/tex]

=[tex]5^{\frac{2}{6}}[/tex]

=[tex]25^{\frac{1}{6}}[/tex]

Second term √2 = [tex]2^{\frac{1}{2}}[/tex]

= [tex]2^{(\frac{1}{2}).(\frac{3}{3})}[/tex]

= [tex]2^{\frac{3}{6}}[/tex]

= [tex]8^{\frac{1}{6}}[/tex]

Now we multiply these terms

[tex]25^{\frac{1}{6}}.8^{\frac{1}{6}}[/tex]

= [tex]200^{\frac{1}{6} }[/tex]

Therefore option B is the answer.