Chana and Josiah started skating at the same time in the same direction, but Josiah had a head start 10 meters past the starting line. Chana skated 3 meters per second and Josiah skated 2 meters per second.

What does point I represent in this context?

CORRECT (SELECTED)
Chana's distance from the starting line at a time when she is behind Josiah

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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The monthly interest payment is 162

Interest, in its most simple form, is calculated as a percent of the principal.

First,

monthly interest rate,

= 0.24/12

= 0.02.

Now,

Average monthly interest,

=0.02×$675

= $13.50.

Thus, the annual interest payments,

= 12×$13.50

= $162

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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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Answer:

  18x

Step-by-step explanation:

The HCF is the highest factor common to both expressions. We can find it by factoring both expressions and identifying common factors.

  36(x³+x²y-12xy²) = 18x·2·(x +4y)(x -3y)

  54(x³y+4x³y²-21xy) = 18x·3y·(x +7)(x -3)

The highest common factor is 18x.

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

Answer:

4.12310562562, 4.23, 4.5

Answer:

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

Step-by-step explanation:

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

Solution: Check the picture I uploaded.

The price of the washer and the dryer set is $720.

The commission earned by Alice is $36.

Percentage can be described as a fraction an amount expressed as a number out of hundred. Percentage is a measure of frequency.

Price after the mark up = ( + percentage mark up) x cost price

(1  + 0.20) x $600  = $720

Commission earned by Alice = 5% x 720 = $36

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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]

Answer:

p=10

Step-by-step explanation:

-7+p=3

+7-7+p=3+7

p=10

Answer:

Hello! The answer to this question is 10.

Step-by-step explanation:

You have to get p by itself so we will add 7 to both sides:

-7 + p = 3

+7        +7

-------------

p = 10

When doing so, we get p = 10.

You can check your work:

-7 + 10 ⇒ 10 - 7 = 3

Therefore, p = 10 is the correct answer.

Answer:

Step-by-step explanation:

The vertex and direction of opening can be read from the vertex-form equation of a quadratic.

Consider the "parent" quadratic function ...

  y = x²

For this function, the value of y cannot be negative. Larger positive values of x will give larger positive values of y. And, negative values of x that have greater magnitude (are farther from the y-axis) will also give larger positive values of y.

This means that the farther away from the y-axis an x-value is, the farther away from the x-axis is the corresponding y-value. The graph of this is said to "open upward." This will be the case for any positive coefficient of x². (Red graph in the first attachment.)

If the coefficient of x² is negative, then larger-magnitude x-values result in more negative y-values. This makes the graph "open downward." (Blue graph in the first attachment.)

The vertex form of a quadratic equation is ...

  y = a(x -h)² +k . . . . . . vertex (h, k); vertical scale factor 'a'

The value of 'a' is the coefficient of the x² term when this is simplified to standard form: y = ax² +bx +c. That is, the sign of 'a' tells you whether the graph opens upward (a > 0) or downward (a < 0).

The other constants in the vertex form equation tell you how the function has been translated. The value of k is a vertical translation quantity. Since it is added to each function value, it tells the number of units the function is translated upward.

The value h is a horizontal translation quantity. It seems slightly counter-intuitive that the function graph is translated to the right h units when h is subtracted from the x-value. That is the case.

As you may have noticed from the graphs in the first attachment, the vertex (turning point) of the parent function graph is at (x, y) = (0, 0). The vertex of the function ...

  y = a(x -h)² +k

is located at (x, y) = (h, k).

You want the opening direction of y = -2(x +3)² -1. You need look no further than the leading minus sign. It tells you the graph opens downward. (Red graph in the second attachment.)

Of course, the -1 at the end of the equation is the vertical translation of the vertex. That vertex is (-3, -1), as shown by the graph.

You want the vertex of y = -1/2(x +5)² +7. Writing this so the binomial term has a minus sign, we have ...

  y = -1/2(x -(-5))² +7

Comparing this to the vertex form ...

  y = a(x -h)² +k

we identify the parameters to be ...

  a = -1/2 . . . . opens downward

  h = -5

  k = 7 . . . . the vertex is (h, k) = (-5, 7)

The graph is the blue graph in the second attachment. It opens downward and has its vertex at (-5, 7).

__

Additional comment

A lot of math is about matching patterns. Here, you're asked to match the given equations to the "vertex form" pattern, and identify corresponding parts of the pattern: the leading coefficient (a), the horizontal translation (h), and the vertical translation (k). Once you know what the parts of the pattern mean, you can answer the questions easily.

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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[tex]y = 2x {}^{2} + e {}^{ - x {}^{4} } [/tex]

[tex] \frac{dy}{dx} = 4x +( e {}^{ - x {}^{4} } )( - 4x {}^{3} )[/tex]

[tex] \frac{dy}{dx} = 4x - 4x {}^{3} e { }^{ - x {}^{4} } [/tex]

[tex] \frac{dy}{dx} = 4x(1 - x {}^{2} e {}^{ - x {}^{4} } )[/tex]

[tex] \frac{dy}{dx} = 0 \\ 4x = 0 \: \: \: \: \: 1 - x {}^{2} e {}^{ - x {}^{4} } = 0[/tex]

[tex]4x = 0 \\ x = 0 \: \: \: \: \: \: y(0) = 0 + e {}^{0} = 1[/tex]

Answer:

step-by-step explanation:

A 7/1 ARM is a mortgage that has a fixed interest rate in the beginning, then switches to an adjustable or variable one. The 7 in 7/1 indicates the initial fixed period of seven years. After that, the interest rate adjusts once yearly based on the index stated in the loan agreement, plus a margin set by the lender.

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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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:

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:

60 ways

Step-by-step explanation:

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

Answer:

Anne has n

Fiona has 3n

3n=6

so n=2

so Anne have 2

Answer:

False

Step-by-step explanation:

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

Answer:

its D

Step-by-step explanation:

Answer:

(x+10,y-3)

Step-by-step explanation:

Answer:

The perimeter of the garden is [tex]12a[/tex].

Step-by-step explanation:

[tex]3a+14+4(a-6)+10+5a=12a[/tex]

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 function for the given situation is f(x)=35.0-0.7x.

Given that, Mark bought 10 pound of two types of candies, caramel candies for $2.80 per pound and chocolate candies for $3.50 a pound.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Now, the function for the given situation is as follows:

If x is the weight of the less expensive candy, the 10-x is the weight of the high expensive candy.

So, f(x)=2.80x+3.50(10-x)

⇒ f(x)=2.80x+35.0-3.50x

⇒ f(x)=35.0-0.7x

Therefore, the function for the given situation is f(x)=35.0-0.7x.

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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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Answer:

16.95

Step-by-step explanation:

use a calculator

The area of the square of the leg 6 is 36 square units.

The area of the square of the leg 8 is 64 square units.

The area of the square of the hypotenuse square is 100 square units.

The length of the hypotenuse is 10 units.

Formula Used

Area of square, A = [tex](a)^{2}[/tex]

Here, [tex]a[/tex] is the length of the side of the square.

Pythagoras Theorem is given as,

[tex]h^{2} =p^{2} +b^{2}[/tex]

Here, [tex]h, p, b[/tex] are the hypotenuse, perpendicular, and the base of a right angle triangle respectively.

Area of the Square of the Leg 6

Length of the edge of the square = 6 units

Area of square = 6*6

= 36 square units

Area of the Square of the Leg 8

Length of the edge of the square = 8 units

Area of square = 8*8

= 64 square units

Area of the Hypotenuse Square and the Length of the Hypotenuse

Applying Pythagoras theorem,

[tex]h^{2} = (8)^{2} +(6)^{2}[/tex]

[tex]h^{2} = 64+36[/tex]

[tex]h = \sqrt{100}[/tex]

[tex]h = 10 units[/tex]

Therefore, the area of the hypotenuse square is 100 square units and the length of the hypotenuse comes out to be10 units.

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Answer: in the picture

Step-by-step explanation: