A water ride with heights above and below the starting point can be modeled by the function y = 3 sin ⁡ ( π 2 ( x + 3 ) − 2 ) . Within the interval 0 < x < 5 , when does the ride have a height 1 foot below the starting point?

Step-by-step explanation:

{-1,2,3,4,5,6,8} is the answer

Answer:

[tex]27[/tex]

Step-by-step explanation:

[tex]g(f(0))=g(2(0)+3)=g(3)=3^3=27[/tex]

Answer:

Step-by-step explanation:

Several trig identities are involved in the proof of this. This is the order in which they are used.

Starting with the left side, we can transform it into the right side.

  [tex]2\cos(2x)=2(\cos^2(x)-\sin^2(x)) = 2(\cos^2(x)-(1-\cos^2(x)))\\\\=2(2\cos^2(x)-1)=2\left(\dfrac{2}{\sec^2(x)}-\dfrac{\sec^2(x)}{\sec^2(x)}\right)\\\\=\boxed{\dfrac{4-2\sec^2(x)}{\sec^2(x)}}[/tex]

Answer:

Given - AC is parallel to DE

angle 3y + 28 = angle X ( Vertically opposite angles are equal).

3y + 28 = X

X + Y = 180° ( supplementary angles).

3y - X = (-28)

Solving both the equation we get

multiply eq 1 with 3

3x + 3y = 540

-X + 3y = (-28)

subtracting

4x = 568

x = 142°

3y + 28 = 142

3y = 142 - 28

3y = 114

y = 38°

Answer:

Step-by-step explanation:

The domain is the set of x-values and the range is the set of y-values.

This graph represents the equation y = -3

Part A

The notation [tex]\lim_{x \to 2^{+}}f(x)[/tex] means that we're approaching x = 2 from the right hand side (aka positive side). This is known as a right hand limit.

So we could start at say x = 2.5 and get closer to 2 by getting to x = 2.4 then to x = 2.3 then 2.2, 2.1, 2.01, 2.001, etc

We don't actually arrive at x = 2 itself. We simply move closer and closer.

Since we're on the positive or right hand side of 2, this means we go with the rule involving x > 2

Therefore f(x) = (x/2) + 1

Plug in x = 2 to find that...

f(x) = (x/2) + 1

f(2) = (2/2) + 1

f(2) = 2

This shows [tex]\lim_{x \to 2^{+}}f(x) = 2[/tex]

Then for the left hand limit [tex]\lim_{x \to 2^{-}}f(x)[/tex], we'll involve x < 2 and we go for the first piece. So,

f(x) = 3-x

f(2) = 3-2

f(2) = 1

Therefore, [tex]\lim_{x \to 2^{-}}f(x) = 1[/tex]

===============================================================

Part B

Because [tex]\lim_{x \to 2^{+}}f(x) \ne \lim_{x \to 2^{-}}f(x)[/tex] this means that the limit [tex]\lim_{x \to 2}f(x)[/tex] does not exist.

If you are a visual learner, check out the graph below of the piecewise function. Notice the gap or disconnect at x = 2. This can be thought of as two roads that are disconnected. There's no way for a car to go from one road to the other. Because of this disconnect, the limit doesn't exist at x = 2.

===============================================================

Part C

You'll follow the same type of steps shown in part A.

However, keep in mind that x = 4 is above x = 2, so we'll deal with x > 2 only.

So you'd only involve the second piece f(x) = (x/2) + 1

You should find that f(4) = 3, and that both left and right hand limits equal this value. The left and right hand limits approach the same y value. The limit does exist here. There are no gaps to worry about when x = 4.

===============================================================

Part D

As mentioned earlier, since [tex]\lim_{x \to 4^{+}}f(x) = \lim_{x \to 4^{-}}f(x) = 3[/tex], this means the limit [tex]\lim_{x \to 4}f(x)[/tex] does exist and it's equal to 3.

As x gets closer and closer to 4, the y values are approaching 3. This applies to both directions.

Answer:

5 and a 250,000

Step-by-step explanation:

A quarter million = 1,000,000 · [tex]\frac{1}{4}[/tex] = 250,000

Answer:

It is: 5,250,000

Answer:

C. 3x - 9

Step-by-step explanation:

3x – y = 9 ___(1)

8x – 4y = 0 ___(2)

From (1) eq.

3x – y = 9

– y = 9 – 3x

y = - (-3x + 9)

y = 3x – 9

Hence, 3x - 9 should be substituted in the second equation to get the required answer.

Answer:

c

Step-by-step explanation:

solve for y in the first equation

y = 3x - 9

when you substitute, you will get a value of 9 for x and 18 for y

Answer: The data cannot be modeled by an exponential function because the data is for a linear function (as there is a constant increase in f(x) each time x increases by 1)

Answer:

b. x = -4 or x = -3

Step-by-step explanation:

[tex]x^{2} +7x+12[/tex]

To factor this, come up with two numbers that can be multiplied together to get 12, but add to get 7.

We get 4 and 3.

4 + 3 = 7

4 x 3 = 12

Now we can factor with these two numbers:

[tex](x+4)(x+3) = 0[/tex]

Now, solve for x by separating the factors:

[tex]x + 4 = 0[/tex]

[tex]x = -4[/tex]

And,

[tex]x + 3 = 0[/tex]

[tex]x = -3[/tex]

So, the answers are -4 and -3.

The inequality equation will be -5x + 20 < -10.

Inequality is defined as an equation that does not contain an equal sign.

The weather report says the temperature is 20°c and will drop 5°c per hour for the next 6 hours.

Daryl plans to be gone at least 6 hours, and he has a plant outside.

If he wants the plant to remain in temperatures above -10° should Daryl move the plant to a warmer location before leaving will be

The inequality equation will be

-5x + 20 < -10

where x is the number of hours.

Then we have

-10 < -5x + 20

5x > 30

   x > 6 hours

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A, -9 ≤ -3X -6 ≤ 6

Inequality is an algebraic statement that shows that two quantities are unequal.

Analysis:

From the above, only A, is the correct inequality represented above.

solving for x in A, we have,

-9 ≤ -3x - 6 ≤ 6

splitting,

-9 ≤ -3x -6

-3 ≤ -3x

1 ≥ x

x ≤ 1

-3x-6 ≤ 6

-3x ≤ 12

x ≥ 12/-3 ≥ -4

-4 ≤x ≤1, A

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Answer: 4/30

Step-by-step explanation:

it does

Answer:

.7692307692 or 10/26

Step-by-step explanation:

You solve this problem by finding the total number of sports playing students and dividing it by the total, in this case 26. Since we know there are 5 students that play both sports, you subtract that 5 from the total number of basketball plyers and baseball players, so 16-5=11 and 9-5=4, then add those together, so 11+4=15. From there you add back in the students that play both which is 5, so 15+5=20. 20/26 is your answer.

Answer:

See Pictures

Step-by-step explanation:

Answer:

you got that

Step-by-step explanation:

wet wet wet

Answer:

{ x : x > 2 }

Step-by-step explanation:

4x - 3 + 6x > 5x + 7 , that is

10x - 3 > 5x + 7 ( subtract 5x from both sides )

5x - 3 > 7 ( add 3 to both sides )

5x > 10 ( divide both sides by 5 )

x > 2

The value of the function at t=0 is 9 , 6<x<7 is -t+5, 1<n<2 is 9, for [tex]m^{2} +1[/tex] is 9.

Given function which is 9 for 0 to 5 , -t+5 for 5 to 8 and [tex]\sqrt{t-1}[/tex] for 8<t<11.

A) We have to find the function at t=0 which is 9 because it lies between 0<=t<5.

B) In this we have to find the value of the function when x=t lies between 6 and 7. is -t+5.

C) In this we have to find the value of Q(n) when n lies between 1 and 2 and the value becomes 9 because it lies between 0 and 5.

D) In this we have to find the function at [tex]m^{2} +1[/tex] when m belongs to [tex]\sqrt{7} and \sqrt{10}[/tex] the value of m lies between 2 and 4 and the value of m square +1 lies between 3 and 5. Hence the value of function at m square plus one is 9.

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: log_{6}(5) [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: log_{6}(25) - log_{6}(5) [/tex]

[tex]\qquad \tt \rightarrow \: log_{6}(5) {}^{2} - log_{6}(5) [/tex]

[ property : x² = 2 log x ]

[tex]\qquad \tt \rightarrow \: 2 \: log_{6}(5) {}^{} - log_{6}(5) [/tex]

[tex]\qquad \tt \rightarrow \: log_{6}(5) [/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

The corresponding part of PQ is WX

The congruent statement is given as:

polygon WXYZ ≅ polygon PQRS.

This means that the corresponding points are:

W and P, X and Q, Y and R, Z and S

When two points Q and P are joined together, we have:

polygon WX ≅ polygon PQ

Hence, the corresponding part of PQ is WX

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Answer: (23, 46)

Step-by-step explanation:

The equation of the line is y = 2x, and we can thus represent point P as (x, 2x)

Substituting into the distance formula,

[tex]\sqrt{2645}=\sqrt{(x)^{2}+(2x)^{2}}\\\\2645=x^2 + (2x)^2\\\\2645=x^2 + 4x^2\\\\2645=5x^2\\\\529=x^2\\\\x=23[/tex]

Thus, the coordinates of P are (23, 46)

The inequality describes the price $375  she can afford for 25

individual box of supplies will be $375 ≥ 25x.

An inequality is comparison of  two values, showing if one is less than, greater than, or simply not equal to another value.

Let the price of each box is $x.

The inequality describes the price can she afford for each

individual box of supplies will be $375 ≥ 25x.

Therefore inequality is $375 ≥ 25x.

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Answer:

$4,000.343

Step-by-step explanation:

Divided the months of the year and caculate the intrest.

Answer:

option B or 40%

Step-by-step explanation:

Well if 14/35 of the class is male. You divide 14 by 35. And after using calculator I see the answer is 40% of the class is male.

Thank

Answer:

u = -18

Step-by-step explanation:

[tex]\frac{-5u}{6} =15[/tex]

Multiply both sides by 6.

-5u = 15 × 6

-5u = 90

Divide both sides by -5.

u = -18

No, your paycheck is incorrect. The gross salary will be 342.25.

The amount of money paid to any employee without any deductions of the taxes or anything is called as gross salary.

The gross salary will be calculated as follows:-

40x 7.25= $290.00 (base salary)

5x  7.25 = 36.25  (overtime)

.02x 800= 16.00 (commission)

Gross salary will be = 36.25 + 16  + 290 = $324.25

Therefore your paycheck is incorrect. The gross salary will be 342.25.

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Answer:

y = 1

x = -2

Step-by-step explanation:

During the substitution method, you are substituting one function into another. Because both functions are set equal to "x", you can make the functions equal each other. This allows you to 'get rid' of the "x" variable and simplify to find the value of "y".

5A) x = -2y

5B) x = 2 - 4y

-2y = 2 - 4y                     <----- Set both equations equal

2y = 2                             <----- Add 4y to both sides

y = 1                                <----- Divide both sides by 2

Now that you know what "y" equals, you can plug that value into the "y" variable into one of the equations. This will allow you to then simplify and find the answer for "x".

x = -2y                             <----- Equation 5A

x = -2(1)                           <----- Plug 1 into "y"

x = -2                              <----- Multiply -2 and 1

Answer:

shown below

Step-by-step explanation:

4 x 2 = 8

1 x 2 = 2

a⁸b²

(a⁵b²)(a²b⁶)

a⁷a⁵b⁶b²a²b⁸

a¹⁴b¹⁶

8 - 14 = -6

2 - 16 = -14

a^-6 b^-14

next one

25^3x-21

/

25^2x+14

1^x-35