The number of gifts received each day of "the 12 days of christmas" is a function of the day ("on the fourth day of christmas, my true love gave to me: 4 calling birds, 3 french hetis, 2 turtle doves, and a partridge in a pear tree")

The equations are e = 18+12t and a = 45+9t

Adrian will be father along in the book after 4 days. She will be 15 pages ahead of Ethan

Ethan's page number at the beginning of the month = 18

Adrian's page number at the beginning of the month = 45

Pages read by Ethan each day = 12 pages

Pages read by Adrian each day = 9 pages

Let e represent the page of the book that Ethan is on at the end of t days into the month. Let a represent the page of the book that Adrian is on at the end of t days into the month.

Formulating the equation we get the following:

e = 18 + 12t

a = 45 + 9t

Finding the page number of both Ethan and Adrian after 4 days by substituting the values in the equations we get:

e = 18+12(4)

e = 66

a = 45 + 9(4)

a = 81

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Looking at the diagram, PQ = 18 and PR = 31

We can see that

PQ + QR = PR

Therefore,

18 + QR = 31

QR = 31 - 18

QR = 13

Move the y = x2 graph 10 units to the right, then 8 units up.

There are y= x²——————> y = (x-10)²+8

The fact that

A point (x,y) in f(x) shifts up by d as a result of f(x)+d, a

and

f(x-e) ----> a point (x, y) in f(x) becomes a——————-> (x+e, y)——> shift right by  in this issue

d=8

e=10

Therefore,

Shift the y = x2 graph.

8 up, 10 to the right

The law is

(x,y)———-> (x+10,y+8)

The vertex in the equation y=x2--------- (0,0)

The vertex in the equation y = (x-10)2+8 (10,8)

so

(10,8)------> (0,0)----------> (x+10,y+8)———> (10,8)------> (0+10,0+8)

As a result, shift the y = x2 graph 8 units up and then 10 units to the right.

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Answer:

1.65

Step-by-step explanation:

Divide 6.6 by 4

The perimeter of rectangle with the given dimensions is 6x+6.

Given that the dimensions of rectangle are 2x and x+3.

We need to find the perimeter of the given rectangle.

The overall length of the outline determines a shape's perimeter in two dimensions. We add the lengths of all four corners of a rectangle to find its perimeter. Rectangle perimeter is calculated using the formula perimeter of a rectangle = 2(l + w), where l is the rectangle's length and w is its width.

We know that, the perimeter of rectangle = 2(Length + Width)

Now, perimeter

=2(2x+x+3)

=2(3x+3) (Add like terms)

Using distributive property multiply 2 to 3x and 2 to 3

We get 6x+6

Therefore, the perimeter of rectangle with the given dimensions is 6x+6.

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just find the roots and substitute

a(x - "first root") (x - "second root")

The expression is a perfect square trinomial if and only if c = 121.

A perfect square trinomial is written as:

(a + b)^2 = a^2 + b^2 + 2ab

In this case, we have:

t^2 - 22t + c

We can rewrite this as:

t^2 - 2*11*t + c

Then we have:

a = t

b = -11

And we will have that:

c = b^2 = (-11)^2 = 121

Then we have:

t^2 - 2*11*t + 121

Which is a perfect square trinomial:

(t - 11)^2 = t^2 - 22t + 121

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Answer:

I answered one of them so yeah

ANSWER:

STEP-BY-STEP EXPLANATION:

We have that the equation of a line in its slope and y-intercept form is the following:

Now, when two equations are perpendicular, the slope of both are opposite, that is, the product between them is equal to -1, like this:

We replace the values of the point (-9, 6) and the slope to calculate the value of the y -intercept:

Therefore, the perpendicular equation that also passes through the point (-9,6) is:

Now, when two lines are parallel, the slope is the same, therefore we calculate directly that it passes through the point (-9, 6)

therefore, the equation of the line that is parallel to this line and passes through the point (-9, 6) is:

Answer: - 37

Step-by-step explanation:

so (2-5)(3+7) - (4+3) start off by the right side really doesn't matter what side you start on, but I added 4+3=7

x= (2-5)(10) - (7) Then add 3+7=10

x= (-3)(10) - (7) 3rd subtract 2-5=-3

x= -30 - 7 Next multiply -3*10=-30 because two numbers together with parenthesis means multiplication.

x= -37  Lastly subtract -30 - 7 and I got -37

Answer: (-30, 10)

Step-by-step explanation:

A proportional relationship is of the form y=kx for some constant k.

From the point (60, -20), we know that k = -1/3.

So, we are looking for a point where the y coordinate is -1/3 of the x coordinate. This is satisfied by option 3.

Answer:

Step-by-step explanation:

The domain of a function is the set of all possible inputs for the function - so all possible x values in some f(x) functions.

From the graph, you can see that the values on the x-axis below the graph are in the range -4 (exclusive) and 2 (inclusive) that's why the range is
-4 < x <=2, or simply (-4,2>

60 ml of the 55% solution is required to get the desired solution.

A unique kind of homogenous mixture made up of two or more substances is called a solution.

Let  x ml of 55% solution is taken.

therefore alcohol = 0.55x ml

water = 0.45x ml

Now it is added to 10% 75 ml solution.

Alcohol = 10% of 75 = 7.5ml

Water = 67.5 ml

New mixture = 75 + x

Alcohol = 30% of (75+x) = 22.5 + 0.3x

Therefore 22.5 + 0.3x = 7.5 + 0.55x

or, x = 60 ml

Therefore 60 ml of the 55% solution is required.

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Answer:

Step-by-step explanation:

STEP

1

:

           9

Simplify   —

           4

Equation at the end of step

1

:

                       9

 ((x2) -  5x) -  (0 -  —)  = 0

                       4

STEP

2

:

Rewriting the whole as an Equivalent Fraction

2.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  4  as the denominator :

               x2 - 5x     (x2 - 5x) • 4

    x2 - 5x =  ———————  =  —————————————

                  1              4      

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

STEP

3

:

Pulling out like terms

3.1     Pull out like factors :

  x2 - 5x  =   x • (x - 5)

Adding fractions that have a common denominator :

3.2       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

x • (x-5) • 4 - (-9)     4x2 - 20x + 9

————————————————————  =  —————————————

         4                     4      

Trying to factor by splitting the middle term

3.3     Factoring  4x2 - 20x + 9

The first term is,  4x2  its coefficient is  4 .

The middle term is,  -20x  its coefficient is  -20 .

The last term, "the constant", is  +9

Step-1 : Multiply the coefficient of the first term by the constant   4 • 9 = 36

Step-2 : Find two factors of  36  whose sum equals the coefficient of the middle term, which is   -20 .

     -36    +    -1    =    -37

     -18    +    -2    =    -20    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -18  and  -2

                    4x2 - 18x - 2x - 9

Step-4 : Add up the first 2 terms, pulling out like factors :

                   2x • (2x-9)

             Add up the last 2 terms, pulling out common factors :

                    1 • (2x-9)

Step-5 : Add up the four terms of step 4 :

                   (2x-1)  •  (2x-9)

            Which is the desired factorization

Equation at the end of step

3

:

 (2x - 9) • (2x - 1)

 ———————————————————  = 0

          4        

STEP

4

:

When a fraction equals zero :

4.1    When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

 (2x-9)•(2x-1)

 ————————————— • 4 = 0 • 4

       4      

Now, on the left hand side, the  4  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

  (2x-9)  •  (2x-1)  = 0

Theory - Roots of a product :

4.2    A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation:

4.3      Solve  :    2x-9 = 0

Add  9  to both sides of the equation :

                     2x = 9

Divide both sides of the equation by 2:

                    x = 9/2 = 4.500

Solving a Single Variable Equation:

4.4      Solve  :    2x-1 = 0

Add  1  to both sides of the equation :

                     2x = 1

Divide both sides of the equation by 2:

                    x = 1/2 = 0.500

Supplement : Solving Quadratic Equation Directly

Solving    4x2-20x+9  = 0   directly

Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula

Parabola, Finding the Vertex:

5.1      Find the Vertex of   y = 4x2-20x+9

Parabolas have a highest or a lowest point called the Vertex .   Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) .   We know this even before plotting  "y"  because the coefficient of the first term, 4 , is positive (greater than zero).

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two  x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.

Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.

For any parabola,Ax2+Bx+C,the  x -coordinate of the vertex is given by  -B/(2A) . In our case the  x  coordinate is   2.5000  

Plugging into the parabola formula   2.5000  for  x  we can calculate the  y -coordinate :

 y = 4.0 * 2.50 * 2.50 - 20.0 * 2.50 + 9.0

or   y = -16.000

Parabola, Graphing Vertex and X-Intercepts :

Root plot for :  y = 4x2-20x+9

Axis of Symmetry (dashed)  {x}={ 2.50}

Vertex at  {x,y} = { 2.50,-16.00}

x -Intercepts (Roots) :

Root 1 at  {x,y} = { 0.50, 0.00}

Root 2 at  {x,y} = { 4.50, 0.00}

Answer:

18$ with a 1/3 discount applied

Step-by-step explanation:

27 divided by 3=9

27-9=18

Answer:

$18

Step-by-step explanation:

1/3 = ~33.33% off

33.33% of 27 = 9

27-9 = 18

Hope that helps

Answer:

...

...

...

...

...

...

...

...

128 = 2^7 is a power of 2

27 = 3^3 is a perfect cube

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

Explanation:

This is something you'd find through trial and error.

The powers of 2 are

2, 4, 8, 16, 32, 64, 128, 256, ...

We double each value to get the next one.

The largest power of 2 that is smaller than 155 is 128

155-128 = 27 which is a cube number since x^3 = 3^3 = 27 as you've shown in the screenshot.

If the result of 155-128 wasn't a perfect cube number, then you'd have to try the next largest power of 2 (which is 64) and work your way down the list.

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

Or you could work with the list of perfect cubes

1, 8, 27, 64, 125, 216, ...

Each value is of the form x^3 where x is a whole number.

Let's pick the largest perfect cube that is under 155, and subtract it

155-125 = 30 which isn't a power of 2 (refer to the list above)

Then try 155-64 = 91 which isn't a power of 2 either

Keep moving down the list until reaching 155-27 = 128 which is a power of 2 since 2^7 = 128

Answer:

option number 3

Step-by-step explanation:

day 3 = 1000 sales

day 6 = 2000 sales

day 9 = 3000 sales

Two positive integers whose product is 24,999,999 are 4999 and 5001

Given

The product of two numbers should be 24,999,999.

The positive difference should be small

There are many ways to obtain those two numbers but an easiest way would be taking the square root of the given number and making decision by trial and error.

This may take few iterations but this is the optimal way to solve.

Square root of 24,999,999 is 4999.99

Hence try multiplying a number less than and a number equal to 4999.99.

Eventually we will reach to a conclusion 4999 x 5001 whose product is 24,999,999.

The difference of the numbers is 5001 - 4999 = 2

Hence the positive difference is small.

Hence the two numbers are 4999, 5001.

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Answer:

  18 m/s²

Step-by-step explanation:

You want Dean's acceleration when his speed changes from 10 m/s to 100 m/s in 5 seconds.

Acceleration is the rate of change of velocity, the change in velocity divided by the corresponding change in time:

  a = ∆v/∆t

  a = (100 m/s -10 m/s)/(5 s) = (90 m/s)/(5 s) = 18 m/s²

Dean's acceleration is 18 m/s².

__

Additional comment

Both velocity and acceleration are vector quantities. They have both magnitude and direction.

We assume the given speeds are in the same direction, so the direction of the velocity vector does not change. The acceleration is in that same direction.

The simple interest Lori would pay if the loan was not amortized and the entire loan was paid at the end of 3 years is $ 1,350.

It is given in the question that:-

Principal = $15,000

Time period = 3 years

Interest rate = 3 %

Total interest paid by Lori, if the loan was amortized = $ 704.

We have to find the simple interest Lori would pay if the loan was not amortized and the entire loan was paid at the end of 3 years.

We know that,

Simple interest = (Principal*Rate*Time)/100

Hence,

Simple interest = (15000*3*3)/100 = $ 1350.

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Answer:

552.8

Step-by-step explanation:

16584/8=2073

2073*0.8=1658.4

1658.4*8=13267.2

13267.2/24=552.8

A potential advertiser for marketing purpose, after performing a test at 0.05 level of significance fails to reject the null hypothesis leads to the conclusion that there is not sufficient evidence at the 0.05 level of significance to say that the percentage is less than 68%.

Hypothesis testing refers to a statistical inference approach used to determine if the available data sufficiently support a particular hypothesis. Hypothesis testing enable researchers to make probabilistic statements about population parameters. In the given case, the null and alternative hypothesis regarding the publisher’s claim state:

The null hypothesis stated that the 68% or more of the readers own a Rolls Royce. H0: p ≥ 0.68

The alternate hypothesis states that less than 68% of the readers own a Rolls Royce. H1: p < 0.68

As the advertiser failed to reject the null hypothesis, it was accepted and thus, 68% or more of the readers own a Rolls Royce. It is concluded that there is not sufficient evidence at the 0.05 level of significance to say that the percentage is less than 68%.

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Answer:

Suppose every object in the domain has only one image in the codomain, then the mapping is a function. Otherwise, it is not a functions

Looking at the given mapping:

-2 is mapped to both 1 and 3

0 is mapped to -3

1 is mapped to 4

3 is mapped to 1

Because -2 has more than one image, it disqualifies the mapping from being a function.

Answer:

4 pounds with a membership

29 pounds without

i just added both because i didnt know if you meant 58 extra dollars after bbuying membership or not

Step-by-step explanation:

58 -50(membership fee)=8

16 divide by 8=2

16$=8 pounds

8$=4 pounds

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

without membership you could buy 29 pounds of apples

58 divide by 16=3.625

3.625 x 8=29

Answer:

A = 34

B = 29.4

C = 58.8

D = 34

Answer:$9.72

Step-by-step explanation: 48.60 DIVIDED BY 5 EQUALS 9.72

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