If your piece of graph paper goes only 20 blocks above the x-axis, then where will the
function below first go off the page?
y = 2²

Step-by-step explanation:

The equation of a trigonometric function is

[tex]y = a \sin(bx + c) + d[/tex]

or

[tex]y = a \: cos(bx + c) + d[/tex]

Let define some variables,

D is the midline, this refers to the midpoint of the highest y value and lowest y value. Some textbooks call it the vertical translations but it is the same thing.

A is the amplitude. The amplitude is the distance from the midline to the highest y value. Some distance is non negative, the formula for the amplitude is

[tex] |a| [/tex]

The period is how often the wave repeats itself on a interval.

Period can't be negative so the formula for period is

[tex] \frac{2 \pi}{ |b| } [/tex]

To find the period, look at the extreme points.

The phase shift tells us if the sinusoid have been shifted to the right or left. The formula for the phase shift

[tex]bx + c = 0[/tex]

Solving for x gives us

[tex]x = \frac{ - c}{b} [/tex]

If our x is negative, we have a phase shift to the right

If our x is Positve, we have a phase shift to the left.

Let solve this equation, Let use Sine since sin(0)=0,

The smallest y value here is 0, and the highest is 2, so the amplitude is 1.

[tex]d = 1[/tex]

Next, the distance from the max to the midline is 1, as well the min to the midline is also 1.

So

[tex]a = 1[/tex]

We have minimum at 0, and 8, so our period is 8.

[tex] \frac{2\pi}{b} = 8[/tex]

Solve for b,

[tex] \frac{\pi}{4} = b[/tex]

Plug this in the equation.

[tex]1 \sin( \frac{\pi}{4} x) + [/tex]

[tex]y = \sin( \frac{\pi}{4} x) + 1[/tex]

The graph passes through (4,2) so let see if that holds true for our equation

[tex]2 = \sin( \frac{\pi}{4} (4)) + 1[/tex]

[tex]2 = \sin(\pi) + 1[/tex]

[tex]2 = 0 + 1[/tex]

[tex]2 = 1[/tex]

This doesn't hold true, so we must have a phase shift

Notice that

[tex] \sin( \frac{\pi}{2} ) = 1[/tex]

So if we shift this pi/2 to the right, we can get our equation to be true.

[tex]y = \sin( \frac{\pi}{4} x - \frac{\pi}{2} ) + 1[/tex]

This equation works so our equation is

[tex]y = \sin( \frac{\pi}{4} x - \frac{\pi}{2} ) + 1[/tex]

The transformation is R₁R_Q ₁₈₀° option second is correct if the quadrilateral PQRS transformed into P"Q'R"S"

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have a quadrilateral PQRS shown in the picture.

From the transformation:

The image of Q(x, y) = Q'(-x, -y) will be the highest and leftmost point following the rotation since Point S is the lowest and farthest point to the right of Point Q.

The same applies to points P P' and R R'.

Thus, the transformation is R₁R_Q ₁₈₀° option second is correct.

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Answer:

Option B is the correct answer

According to the given conditions, state:

If the fraction is defined, then the denominator cannot equal 0:

Attach the inequality as the domain: x≠0

Reduce the fraction to the smallest term, canceling the greatest common factor: 1/10 = 25/x.

Multiply both sides of the equation by the common denominator:

Simplify the fractions: x = 250

Find the intersection: x = 250

get the result: x = 250

Answer: x = 250

the actual distance would be 250 feet.

Answer:

6.25

Step-by-step explanation:

BE/BC = BD/AB

5/12 = BD/15

BD = 15(5/12) = 6.25

The required points of x where the slope of tangent and secant is equal at boundary points 4 and 9.

Slope is defined as the rate of change or angle at which curve is having inclination or declination.

Since, the curve of 1/2√x defined for interval [4,9]
The curve is of increasing order so the tangent and secant having equal slope only possible at the boundaries of the curve.

Boundary conditions = (4,1) and (9, 1.5)

Equation can be given as,
y = 0.1x + 0.5

Thus, the  required points of x where the slope of tangent and secant is equal at boundary points 4 and 9.

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Answer: y = -4x/3 + 4

Step-by-step explanation:

Assuming you want to solve for y:

4x = -3y + 12

-4x/3 = y - 4

y = -4x/3 + 4

The value is 1/2

A fraction represents a part of a whole or, more generally, any number of equal parts.

Given:

(5 +(2-1.5)/1*(2))/12

=(5+ 0.5*2)/12

=(5+1)/12

=6/12

=1/2

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The height of the tower based on the angle of elevation given is

From the information given, the tower is 45m, the clinometer is set at 1.3m above the ground, and the angle of elevation is 32°.

This can be illustrated as:

tan 32° = (45 - 1.3)/x

tan 32° = 43.7/x

x = 43.7/tan 32°

x = 69.93m.

Also, for triangle ACD,

tan 47° = (43.7 + y)/x

x × tan 47° = 43.7 + y

74.49 = 43.7 + y

y = 31.29

The height of the tower will be:

= 43.7 + 31.29

= 74.99m

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Answer:

(x+10,y-3)

Step-by-step explanation:

For the given quadratic equation we only have a maximum at y = 18.

Here we have:

[tex]f(x) = -2x^2 - 4x + 16[/tex]

Notice that this is a quadratic equation of negative leading coefficient.

Then we have a maximum at the vertex, and both arms tend to negative infinity as x tends to infinity or negative infinity.

The vertex is at:

x = -(-4)/(2*(-2)) = -1

The maximum is:

[tex]f(-1) = -2*(-1)^2 - 4*(-1) + 16 = -2 + 4 + 16 = 18[/tex]

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Answer:

6

Step-by-step explanation:

The mode of a data set, is the value that occurs the most often. There can be multiple modes, if two values have the same amount of frequency in a data set as well as having the highest frequency. So in this case case it appears there is only 1 mode with that being 6, since it appears 3 times.  with no other value appearing this much in the data set.

Answer:

The answer is 29/42

Step-by-step explanation:

First, let's calculate how many people predicted they would fail. The question states that 65 people took the exam and 23 predicted they would pass, so we can find the number of people that predicted they would fail by the following calculation:

Let FP be the people who predicted they'd fail

65 = 23 + FP

65 - 23 = FP

42 = FP

Now, let's move on to the next part. The question states that a total of 31 people passed the test, from those 18 being the people who predicted they would pass and the rest are people who had predicted they would fail but ended up passing.

Let's set x as the number of people who predicted they would fail but have passed.

31 = 18 + x

31 - 18 = x

13 = x

Since 13 of the 42 FP have passed, we can calculate how many of them failed. Let y be the number of people that predicted to fail and ended up failing:

13 + y = 42

y = 42 - 13

y = 29

Finally, now we have the fraction of those who predicted that they would fail actually did fail and that's 29/42

Answer:

4.12310562562, 4.23, 4.5

The statement of stockholders’ equity for Longhorn Corporation is: $62,800

                        Common stock   Retained earning Total stakeholder equity

Beginning balance           $36,000    $17,400        $53,400              

Issuance of common stock  $4,000        -                $4,000

Add net income                          -        $5,400            $5,400

[65,700-(53,000+2,200+5,100)]

Ending balance                      $40,000    $22,800      $62,800

Therefore the statement of stockholders’ equity for Longhorn Corporation is: $62,800.

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In the case above,  the truth value for the following conditional statement is  Option B: F F → T.

The truth value that was given in the statements are:

So one can write that the truth values of :

p : false

q : false

Then, one need to find the truth value of (p → q)

Note that when as it is written, it means or implies that the truth value of any two statements is false.

If P is true and Q is false then one can say that in every condition, the truth value holds true. So we can then say that p → q: True

In the case above,  the truth value for the following conditional statement is  Option B: F F → T

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Answer:

its D

Step-by-step explanation:

Answer:

16.95

Step-by-step explanation:

use a calculator

Answer:

D

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - 2 , then

y = - 2x + c ← is the partial equation

to find c substitute (3, - 2 ) into the partial equation

- 2 = - 6 + c ⇒ c = - 2 + 6 = 4

y = - 2x + 4 ← equation of line in slope- intercept form

The correct response that would be expected based on the probability information is 164

From the information, there were 352 trials that were made and we're correct 164 times.

Therefore, the correct response that would be expected is 164.

The success rate will be:

= 164/352

= 0.466

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Answer:

60 ways

Step-by-step explanation:

 combination C 4 and 6= (6*5*4*3)/1*2*3=360/6=60 ways

Answer:

1) y = 2(x+3)^2 -4

2) x+6/x-4

3) 2x^2 + 6x +20 = 0

Step-by-step explanation:

Answer:

[tex]-6+5i[/tex]

Step-by-step explanation:

[tex]-6+\sqrt{-25}\\\\=-6+5i[/tex]

See below for the domain and the range of the functions.

As a general rule, all linear functions have a domain and a range of all set of real numbers i.e.  (−∞, ∞)

The functions (2), (3), (4), (5) and (6) are linear functions.

So, their domain and range are  (−∞,∞)

For function (1), we have:

f(x) = 3(3)^x - 1

The above is an exponential function.

The domain of an exponential function is all set of real numbers i.e.  (−∞, ∞)

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Answer:

Step-by-step explanation:

(2x-1)²+8√2xy=4

4y-√8xy-1=1

4y-2√2 x=2

multiply by 4

16y-8√2xy=8

add to first eq.

(2x-1)²+16y=12

or

16y=-(2x+1)²+12

which gives us a downward parabola.

A: Three collinear points are A, T, and B

B: Line BA is another name for line AB

C: Line L is in plane Z

D: line AB is the intersection of planes Z and W

Answer:

False

Step-by-step explanation:

A rectangle does not have 4 equal sides, it has 2 sets of equal sides.

The mistakes that were made regarding the transformation are:

It should be noted that a transformation simply means the changing of the position of an object

In this case, the transformation is incorrect as he applied the reflection to the pre-image first and used an incorrect angle of rotation around point P.

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The interest that Brain would receive is $12.03.

The interest received is a function of the amount saved, interest time and the length of time the money was saved.

Interest = amount saved x number of months x (annual interest rate / 12)

$875 x 3 x (0.055 / 12) = $12.03

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Answer: y = 3x - 2

Step-by-step explanation:

gradient = (4 - 1)/(2 - 1) = 3/1 = 3

y = 3x + c needs to work for both points

Substitute (1,1) into equation

1 = 3 x 1 + c

c = 1 - 3 = -2

y = 3x - 2