What is the value of the function when x = 1 in the
piecewise function
g(x) =
{
3x
-2x
when x>1
when x≤1

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: 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 preparation of the income statement for Longhorn Corporation for the year ended December 31, 2021, is as follows:

Longhorn Corporation

For the year ended December 31, 2021

Service revenue                             $ 65,700

Cost of goods sold (food expense) 53,000

Gross profit                                      $12,700

Delivery expense     $2,200

Salaries expense        5,100            $7,300

Net Income                                     $5,400

The income statement also called income summary is a financial statement that shows the financial performance of a business for a defined financial period.

Thus, from the income statement, the net income and the gross profit, which represent the gains achieved by the entity, are derived.

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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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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:

6.25

Step-by-step explanation:

BE/BC = BD/AB

5/12 = BD/15

BD = 15(5/12) = 6.25

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.

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 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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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:

16.95

Step-by-step explanation:

use a calculator

Answer:

its D

Step-by-step explanation:

Answer:

I would say b since this defintally usally you aren't expeced to use math ouside of math class at school

Hope This Helps!!!

Answer:

The correct answer is C.

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

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

The reduced form of the trig expression is 7/2sin²2a

Trigonometry identities are written in terms of sine, cosine and tangent. Given the trigonometry identity

14sin² acos² a

Since sin(a)cos(a) = sin2a/2, hence

14sin²acos²a = 14[sin(a)cos(a)]²

14sin²acos²a = 14(sin2a/2)²

14sin²acos²a = 14/4(sin²2a)

14sin²acos²a = 7/2sin²2a

Hence the reduced form of the trig expression is 7/2sin²2a

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The number of hours that Jasmine can work so she can afford the new headphones x = 6 weeks.

let x represent the number of weeks it will take to save enough money.

If she saves $11 each week, then in x weeks she will save  11x dollars.

Add this to the 107 she has already saved, and at the end of 11 weeks she will have

  11x + 107 dollars.

We want the amount saved to be equal to the price of the bike, so our equation is

11x + 107 = 173

In a word problem, writing the equation is usually the hardest part. Now we solve the equation.

Subtract 107 from both sides to get

11x = 66

Divide both sides by 11 to get

x = 6 weeks.

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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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The ways that zero growth stock valuation can affect business operations is that:

The Constant  stock valuation  is known to be a kind of share evaluation as it states that the dividends paid by a firm will consistently increase at a constant growth rate.

This will help one to know especially investors on how to set or know the fair price that one needs to pay for a stock on daily basis today by due to future dividend payments.

The overall statement is that  stock value affect one's business operations as  the company's stock price is one that shows an investor perception of their capability to get profit and also if they can grow their profits in terms of future times.

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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

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:

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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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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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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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 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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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.

The graph of the parabola can be seen in the image below.

Here we have the function:

g(x) = (15x)^2

Notice that this is a contraction of scale factor 15 of the function f(x) = x^2

To graph this, we can just evaluate the function in 3 points, the vertex and two other ones.

for x = 0.

g(0) = (15*0)^2 = 0

So we have the point (0, 0).

Evaluating in x = 1 and x = -1 (give the same value) we get:

g(±1) = (±15)^2 = 225

So we have the points (1, 225) and (-1, 225).

Now we can just connect these 3 points with a parabola. The graph can be seen below.

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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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