Consider the function . find the vertical asymptote(s) of f(x). x = 0, –9 x = –9 x = 0, 9 x = 9

Considering the dot plot, it is found that the tallest conifer is 3.25 inches taller than the shortest conifer.

It shows, with dots, the number of times that each of the measures appears in a data-set.

Researching this problem on the internet, and finding the dot plot, we have that:

The difference is:

9.5 - 6.25 = 3.25 inches.

Hence the tallest conifer is 3.25 inches taller than the shortest conifer.

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Using proportions, it is found that 68 more people prefer vanilla than do strawberry.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

Researching this problem on the internet, it is found that, out of 400 people:

Hence the amounts are:

The difference is:

140 - 72 = 68.

68 more people prefer vanilla than do strawberry.

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To estimate that table given in Option (4) will define the quadratic relationship.

Therefore, the table of Option (5) will describe the quadratic relationship.

By estimating the second difference, if the second difference in a table exists equivalent, the table will define the quadratic relationship.

In the given option, we estimate that table given in Option (4) will define the quadratic relationship.

x       y      I st difference       II nd difference

0      4           -                               -

1      -4      -4 - (4) = -8                    -  

2     -4      -4 - (-4) = 0                0 - (-8) = 8

3      4       4 - (-4) = 8                 8 - 0 = 8

The second difference between the terms in y exists exactly as 8.

Therefore, the table of Option (4) means the quadratic relationship.

Similarly, in Option (5) we will estimate the second distinction of y terms.

x        y             I st difference       II nd difference

0      -4                     -                          -

1       -8               -8 - (-4) = -4              -

2     -10             -10 - (-8) = -2      -2 - (-4) = 2  

3     -10             -10 - (-10) = 0       0 - (-2) = 2

Here the second difference exists identical to 2.

Therefore, the table of Option (5) will describe the quadratic relationship.

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Step-by-step explanation:

1st : Vector translation.

a vector -8j ( 0 , -8 ) helped translate (x , y) => (x , y - 8)

2nd : rotation.

The only rotation that results in (-x , -y) is pi rotation.

formula : (x , y -8) => ( xcos(pi) - ysin(pi) , xsin(pi) + ycos(pi) )

substitute x & y-8 into x & y respectively of the formula above.

The value of integration of y=16-[tex]x^{2}[/tex] from x=-1 to x=1 is 94/3.

Given the equation y=16-[tex]x^{2}[/tex] and the limit of the integral be x=-1,x=1.

We are required to find the value of integration of y=16-[tex]x^{2}[/tex] from x=-1 to x=1.

Equation is relationship between two or more variables that are expressed in equal to form.Equation of two variables look like ax+by=c.It may be linear equation, quadratic equation, or many more depending on the power of variable.

Integration is basically opposite of differentiation.

y=16-[tex]x^{2}[/tex]

Find the integration of 16-[tex]x^{2}[/tex].

=16x-[tex]x^{3}/3[/tex]

Now find the value of integration from x=-1 to x=1.

=16(1)-[tex](1)^{3}/3[/tex]-16(-1)-[tex](-1)^{3}/3[/tex]

=16(1)-1/3+16-1/3

=32-2/3

=(96-2)/3

=94/3

Hence the value of integration of y=16-[tex]x^{2}[/tex] from x=-1 to x=1 is 94/3.

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0.0016

reduce expression if possible by canceling the common factors

Answer:

4/9

Step-by-step explanation:

.44444.. = 4/9

0.nnnnnnnn.... = n/9

0.mnmnmnmnmn.... = mn/99

and so on

Using proportions, the value of y is of 100º.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

In a circle, the measure of an arc is twice the measure of it's equivalent internal angle. The internal angle is of 50º, hence the measure of the arc, given by y, is found as follows:

y = 2 x 50º = 100º.

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The equivalent expression to [tex](k o h)(x)[/tex]is [tex]\frac{1}{5 + x}[/tex]

Therefore  [tex](k o h)(x) = \frac{1}{5 + x}[/tex]

Given that the functions h is defined by h(x)=5+x

and k is defined by k (x) = [tex]\frac{1}{x}[/tex]

To find the composition of k and h that is: (k o h) (x)

Therefore

k (h(x)) = k (5+x)

k (h(x)) = [tex]\frac{1}{5+ x}[/tex]

The equivalent expression to is [tex]\frac{1}{5+ x}[/tex]

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The correctly matched quadratic functions are given as follows:

Quadratics are polynomial equations of the second degree, which means that they contain at least one squared term.

Quadratic equations are another name for it. The quadratic equation has the following general form: ax2 + bx + c = 0.

Recall that:
f(x) - a (x -c) (x - d)

where

Part A) First graph

We are given to know

The solutions or zeros of the first graph are

x=-1 and x=3

The parabola open up, so the leading coefficient a is positive, the function therefore, is equal to

The vertex is equal to the point (1, -4)

Substitute and solve for a

-4 = a(1-3)(1+1)

-4 = a(-2)(2)

a = 1

Hence, the function is equal to f(x) = (x-3) (x + 1)

Part B) Second Graph

We are also given to know that

The solutions or zeros of the first graph are

x=-3 and x=1

The parabola open down, so the leading coefficient a is negative

The function is equal to f(x) = a (x-1)(x+3)

Find the value of the coefficient a

The vertex is equal to the point (-1,8)

to solve for a, we must substitute:

8 = a(-1-1) (-1+3)

8 = a(-2)(2)

a = -2

Hence, the function is equal to: f(x) = -2 (x - 1) ( x + 3)

Part C)

We are given to know that the solutions or zeros of the first graph are

x=-2 and x=6

The parabola open up, so the leading coefficient a is positive

The function is equal to f(x)  = a(x-6) (x+2).

Find the value of the coefficient a

The vertex is equal to the point (2,-8)

We substitute and solve for a:

-8 = a(2-6) (2+2)

-8 = a(-4)(4)

a = 0.5

Hence, the function is equal to f(x) = 0.5(x - 6) (x + 2)

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By working with percentages, we will see that they served 56 salmon filets.

Here we know that the restaurant served 70 specials in total, such that 80% of these were salmon filets.

So we just need to calculate what is the 80% of 70.

This is just given by:

70*(80%/100%) = 70*0.8 = 56

This means that they served 56 salmons filet.

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By substitution, the value of x and y are 1 and 1 respectively.

3 / 8 x + 1 /3  y = 17 / 24

x + 7y = 8

x = 8 - 7y

Let's substitute the value of x in equation(ii)

3 / 8(8 - 7y) + 1 / 3 y = 17 / 24

3 - 21 / 8 y + 1 / 3 y = 17 / 24

1 / 3 y - 21 / 8 y = 17 / 24 - 3

8y - 63y/24 =  17 - 72/ 24

-55y / 24 = -55 / 24

cross multiply

-1320y = -1320

divide both sides by -1320

y = -1320 / -1320

y = 1

Hence,

x + 7(1) = 8

x = 8 - 7

x = 1

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Answer:

Connect the arcs to make a perpendicular bisector

The first one , the second one ,the fourth one are true.

What is a commutative property in math?

This law simply states that with addition and multiplication of numbers, you can change the order of the numbers in the problem and it will not affect the answer.

1)  x + y = y + x  = a + c (b +  d ) i                                      true

2) ( xy )z = x (yz) = (a + bi)(c + di)( f + gi)                           true

3) x - y = a + bi - ( c - di ) = a - c + ( b- d )i

    y - x = c + di - ( a+bi) = c-a +(d-b)i                                  false

4) (x + y ) + z = x + ( y + z ) = a + c +f + (b +d + g)i                 true

5) (x - y ) - z = a + bi - ( c + di) - ( f + gi)

                    = a - c . f + ( b- d - g) i

         x - ( y - z ) = a + bi - ( c + di - f - gi )

                          = a - c + f + ( b - d + g ) i

{ put the hypothesis into the equation and get the proof }

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The profit is Rs.4800.

When, in a transaction, the selling price is greater than the cost price, it means we earn a profit. It is calculated with the help of the formula: Profit = Selling price - Cost price.

Given that,

S.P =$6000

C.P = $6000

If, 1$ = Rs.115.4 (in cost price)

  1$ = Rs.116.20 (in selling price)

Then,

C.P =  Rs. 115.40×6000

S.P = Rs.  116.20×6000

Then,

Profit = S.P-C.P

         =  116.20×6000 -115.40×6000

         =  (116.20-115.40)×6000

         = 0.80×6000

         =  Rs.4800

Hence, The profit is Rs.4800.

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The new mixture exists 56.5% peanuts.

The first batch of 9 lb of mixed nuts possesses 40% peanuts.

This means the quantity of peanuts exists:

9 [tex]*[/tex] 40/100 = 3.6 lb

The second batch of 9 lb of mixed nuts possesses 73% peanuts.

This means the quantity of peanuts exists:

9 [tex]*[/tex] 73/100 = 6.57 lb

The total quantity of peanuts in the mix exists

3.6 lb + 6.57 lb = 10.17 lb

There exist 9 lb + 9 lb = 18 lb of mix.

Therefore, the percent of peanuts in the mix exists:

10.17 / 18 [tex]*[/tex] 100 = 56.5%

The new mixture exists 56.5% peanuts.

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Answer:

2√(133)

Step-by-step explanation:

Triangle 1 = 8, 12, ?

triangle 2 = 18, x, ?

we have to find value of x which is a hypotenuse

a² + b² = c²

8² + 12² = 64 + 144 = √208 = 14.4222051019

x = 14.4222051019² + 18²

= 208 + 324

= 532

x = √532 = 2√(133)

Answer:

There are two solutions:  
x = 0, y = -3  Point (0, -3)
x = 3, y = -6  Point (3, 6)

The solutions are at the intersections of the two individual graphs corresponding to each of the two equations (see attached figure)

Step-by-step explanation:

Use a graphing calculator or tool to plot each equation. The point of intersection of the two is the solution to the system of equations. See attached image

Algebraically

The first equation must be equal to the second equation for a unique value of y and x

[tex]y = x^2 - 3 = 3x -3\\x^2 - 3 = 3x - 3[/tex]

Subtract 3x - 3 from both sides giving

[tex]x^2 - 3 - (3x -3) = 0\\x^2 -3 -3x + 3 = 0\\x^2 - 3x = 0\\[/tex]

Factoring out x we get
[tex]x(x-3) = 0[/tex]

This means that x = 0 and also
x -3 = 0, or x = 3

Substituting for x = 0 in y = 3x-3 gives
y = 3.0 - 3 = -3
So x= 0, y = -3 is one solution (0,-3)

Substituting for x = 3 in the same equation gives
y = 3(3) - 3 = 6
So x = 3, y = 6 is another solution (3, 6)

Answer:

  24 m depth

Step-by-step explanation:

The quadratic function modeling depth will have zeros at x=1 and x=12, the distances in meters from the boat where the diver is at the surface.

The factored form of a quadratic function can be written as ...

  y = a(x -p)(x -q)

where p and q are zeros of the function. The value 'a' is a vertical scale factor.

Here, we are given y=0 at the surface, at points where x=1 and x=12. This means the function can be written as ...

  y = a(x -1)(x -12)

To find the value of 'a', we can use the maximum depth value. That depth will be halfway between the function zeros, at x = (1+12)/2 = 6.5

  -30.25 = a(6.5 -1)(6.5 -12)

  30.25 = 5.5²·a = 30.25a   ⇒   a=1

Then the function modeling the diver's depth in meters is ...

  y = (x -1)(x -12)

And the depth at x=4 will be ...

  y = (4 -1)(4 -12) = 3(-8) = -24 . . . . meters

The diver's depth is 24 meters when she is 4 m away from the boat.

Based on the information given about the temperature, Daniela made her error on step 3 because it says: "Find the ratio of the differences of the means compared to the mean absolute deviation.

From the information given, it van be seen that Daniela recorded the low temperatures during the school day last week and this week and her results are shown in the table.

Here, she didn't find the difference between the today and last week means. She just put the mean as a whole.

Therefore, Daniela made her error on step 3 because it says: "Find the ratio of the differences of the means compared to the mean absolute deviation. This was the error.

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Answer:

200,075

Step-by-step explanation:

90 times 2.5 = 225

225 divided by 3 = 75

75 + 200,000 = 200,075

Answer: 200075

Step-by-step explanation:

90 * 2.5 = 225

225 / 3 = 75

75 + 200,000 = 200,075

Answer: H

Step-by-step explanation:

[tex]9(-3)=-27[/tex], which is an integer.

Her business will break even when she contains sold 1740 bottles of her lotion.

Given: She invests $15,225 in equipment to manufacture and package her lotion each bottle costs $3.25 to manufacture and sells for $12.

"Break even" occurs when Revenue = Costs.

($12/bottle)x = $15225 + ($3.25)x

Simplifying the above equation, we get

$8.75x = $15225

Diving both sides of the equation by 8.75, we get

$8.75x/8.75 = $15225/8.75

x = 1740 bottles

Therefore, the value of x = 1740 bottles.

Her business will break even when she contains sold 1740 bottles of her lotion.

Therefore, the correct answer is option b. 1740 bottles.

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The solution of the given logarithmic equation is x = 28.1

Here we have the logarithmic equation:

4*ln(x - 8) = 12

And we want to solve this for x.

Remember the relations:

[tex]ln(e^x) = x\\e^{ln(x)} = x[/tex]

First, we divide both sides by 4:

[tex]ln(x - 8) = 12/4 = 3[/tex]

Then, if we apply the exponential equation to both sides of our equation, we get:

[tex]e^{ln(x - 8)} = e^{3}\\\\x - 8 = e^3\\\\x = e^3 + 8 = 28.1[/tex]

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Step-by-step explanation:

x^2 +4x +4 -7 is

y=x^2+4x-3

Answer: g(x)=(x+2)²-4.

Step-by-step explanation:

g(x)=f(x)+3

g(x)=(x+2)²-7+3

g(x)=(x+2)²-4.

The values that exist two standard deviations above and below the mean are 681 and 265.

The given parameters exist:

Mean = 473

Standard deviation =104

The values above and below the mean exist calculated utilizing:

[tex]$x=\bar{x} \pm n \sigma$[/tex]

In this case n = 2.

So, we have, [tex]$x=\bar{x} \pm 2 \sigma$[/tex]

The value above is:

x = 473 + 2 [tex]*[/tex] 104 = 681

The value below is:

x = 473 - 2 [tex]*[/tex] 104 = 265

Therefore, the values that exist two standard deviations above and below the mean are 681 and 265.

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Answer:

cot x

Step-by-step explanation:

using the identities

csc x = [tex]\frac{1}{sinx}[/tex]

sin([tex]\frac{\pi }{2}[/tex] - x) = cos x

then

csc x × sin ([tex]\frac{\pi }{2}[/tex] - x)

= [tex]\frac{1}{sinx}[/tex] × cosx

= [tex]\frac{cosx}{sinx}[/tex]

= cot x

Using the normal distribution, it is found that:

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for this problem are given, respectively, by:

[tex]\mu = 83, \sigma = 6[/tex]

The proportion of students, with a grade of at least 70 is one subtracted by the p-value of Z when X = 70, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{70 - 83}{6}[/tex]

Z = -2.17

Z = -2.17 has a p-value of 0.015.

1 - 0.015 = 0.985 = 98.5% of students have at least a 70.

The proportion of students, with a grade of at least 80 is one subtracted by the p-value of Z when X = 80, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{80 - 83}{6}[/tex]

Z = -0.5

Z = -0.5 has a p-value of 0.3085.

1 - 0.3085 = 0.6915 = 69.15% of students have an 80 or above.

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Explanation:

To go from gallons to fluid ounces (abbreviation fl oz), we multiply by 128

For example, 2 gallons becomes 2*128 = 256 fl oz as shown in the table.

Another example: 3 gallons = 3*128 = 384 fl oz.

Therefore, 6 gallons would be 6*128 = 768 fl oz.

To go in reverse, from fl oz to gallons, we divide by 128.