The function f(x) = x3 – 8x2 + x + 42 has zeros located at 7, –2, 3. Verify the zeros of f(x) and explain how you verified them. Describe the end behavior of the function.

The stages to utilize to construct a frequency distribution table utilizing Sturge's approximation are as follows:

The steps to create a frequency distribution table utilizing Sturge's approximation exist as follows;

Step 1: Estimate the range of the data:

This exists simply by finding the difference between the biggest and the least values.

Step 2: Decide on the inaccurate number of classes in which the provided data exist to be grouped. The formula for this is;

K = 1 + 3.322logN

where; K= Number of classes

logN = Logarithm of the whole number of observations.

Step 3: Specify the approximate class interval size:

This exists acquired by splitting the range of data by the number of classes and exists symbolized by h class interval size.

Step 4: Find the starting point:

The lower class limit should take care of the least value in the raw data.

Step 5: Determine the remaining class boundaries:

When you have reached the lowest class boundary, then you can count the class interval size to the lower class boundary to obtain the upper-class boundary.

Step 6: Circulate the data into separate classes.

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Answer:

[tex]2 {x}^{2} + 7xy - 15 {y}^{2} [/tex]

Step-by-step explanation:

We can use the rainbow expansion method to find the expression.

[tex](2x - 3y)(x + 5y) \\ = 2 {x}^{2} + 10xy - 3xy - 15 {y}^{2} \\ = 2 {x}^{2} + 7xy - 15 {y}^{2} [/tex]

The answer is |-4 - 1|.

If you solve this absolute value, the answer would be 5 and if you look at the number line, the distance between the two dots is 5 units.

|-4 - 1| --> |-5| --> 5

in an absolute value, there are no negative numbers so the -5 becomes 5.

Answer:

68?

Step-by-step explanation:

multiples of 5 end in 5 or 0

_ _ _

last digit has 2 choices ( 5 and 0 )

1,3,5,7,9 are odd

so tens digit has 5 choices but we see that 5 is repeated so we split into more cases

when last digit is 0, tens digit has 5 choices then hundreds digit has 8 choices so 1*5*8=40

when last digit is 5, tens digit has 4 choices and hundreds digit has 7 choices (0 can't be first digit) 1*4*7=28

40+28=68

Answer:

[tex]-3(x-2)^2+5[/tex]

Step-by-step explanation:

First we can factor a -3 from the [tex]x^2[/tex] term and the [tex]x[/tex] term to get [tex]-3(x^2-4x)-7[/tex].

Then we want the stuff in the parentheses to have the form of [tex](x+b)^2[/tex], or equivalently, [tex](x^2+2b+b^2)[/tex] . So we can let [tex]2b = -4[/tex]. By solving it, we get [tex]b = -4/2 = -2[/tex]. Then our [tex]b^2[/tex] term should be [tex]b^2 = (-2)^2 = 4[/tex].

In order to make our [tex]b^2[/tex] term appear in the parentheses, we need to add and subtract our [tex]b^2[/tex] term, so we get [tex]-3(x^2 - 4x + 4 - 4) -7[/tex].

What we to keep inside our parentheses is [tex](x^2 - 4x + 4)[/tex] , so we can factor the [tex]-4[/tex] out of parentheses to get [tex]-3(x^2-4x+4-4)-7 = -3(x^2-4x+4)+(-3)(-4) - 7 = -3(x^2 - 4x + 4) + 12 - 7 = -3(x^2 - 4x + 4) + 5[/tex]

Finally, plugging  [tex]b = -2[/tex]  that we computed earlier into the equation [tex](x^2+2b+b^2) = (x+b)^2[/tex], we get  [tex](x^2 - 4x + 4) = (x-2)^2[/tex].

So we have [tex]-3(x^2-4x+4)+5 = -3(x-2)^2+5[/tex].

In summary, the procedure is

[tex]-3x^2+12x-7 \\= &-3(x^2-4x) -7 \\= &-3(x^2-4x+4-4)-7 \\= -3(x^2-4x+4) + (-3)(-4)-7\\=-3(x^2-4x+4)+12-7\\= -3(x^2-4x+4)+5 \\= -3(x-2)^2+5[/tex]

Answer: $51156

Step-by-step explanation:

a = b x p%

how much will the price increase

a = 49,000 x 4.4%

= 49,000 x 0.044

= $2156

price of next model

49,000 + 2156 = $51156

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

To prove two lines parallel, we need to check if the two angles involving the lines acts as some angle pair with defininte property.

In the given figure,

( by Alternate Exterior angle pair )

Hence, the two lines are parallel.

[tex] \qquad \large \sf {Conclusion} : [/tex]

Answer: 55.2 in

Step-by-step explanation:

1ft = 12 in

41.4/9 = 4.6 ft

4.6 x 12 = 55.2 in

The Lateral area of the cube = 900 in.²

The Surface area of the cube = 1,350 in.².

A cube's lateral area is the area covered by the lateral surfaces of the cube shape. The formula for the lateral area of a cube is given as: LA = 4a², where:

a = edge length of cube.

The surface area of a cube is the total area of all its 6 surfaces. The formula for finding the surface area of a cube is: 6a², where:

a = edge length of cube.

Edge length of cube (a) = 15 in.

Lateral area = 4a² = 4(15²)

Lateral area = 4(225)

Lateral area of the cube = 900 in.²

Surface area = 6a² = 6(15²)

Surface area = 6(225)

Surface area of the cube = 1,350 in.².

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The volume of the rectangular box is the product of the base area and the height 3x - 1

The given parameters are:

Length = 3x + 4

Width = 3x

Height = 3x - 1

The base area of the rectangular box is calculated as

Base area = Length * Width

Substitute the known values in the above equation

Base area = 3x(3x + 4)

This means that the volume of the rectangular box is the product of the base area and the height 3x - 1

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The addition of the polynomials x⁴ - 3x + 1, 4x² - 2x + 8, x³ - 9 in descending powers of x is x⁴ + x³ + 4x² - 5x.

Adding the polynomial

(x⁴ - 3x + 1) + (4x² - 2x + 8) + (x³ - 9)

= x⁴ - 3x + 1 + 4x² - 2x + 8 + x³ - 9

= x⁴ + x³ + 4x² - 3x - 2x + 1 + 8 - 9

= x⁴ + x³ + 4x² - 5x

Therefore, the addition of the polynomials x⁴ - 3x + 1, 4x² - 2x + 8, x³ - 9 in descending powers of x is x⁴ + x³ + 4x² - 5x.

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Answer:

Step-by-step explanation:

2^0 is less than or equal to 1!, because 1<= 1

if 2^n <= (n+1)!, we wish to show that 2^(n+1) <= (n+2)!, since

(n+2)! = (n+1)! * (n+2), and (n+1)!>= 2^n, then we want to prove that n+2<=2, which is always true for n>=0

Marketing-oriented firms focus more on what the market needs above every other aspects.

Marketing-oriented firms can be described as firms that major in identifying the needs and wants of customers and then creating specific products that are designed to meet the wants of such customers. One of the important elements of marketing-oriented firms is to ensure there is a demand for whatever products or services they offer.

Some examples of marketing-oriented firms are:

A product-oriented firm focus more resources on and focus on researching and developing quality products rather than focusing more on the market to discover the wants of customers.

Sales-oriented firm tend to focus more on developing its sales force that will promote their products and services.

Marketing-oriented firms stand out and are different from the other two types of firms because they focus more on what the market needs above every other aspects.

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The equation for the horizontal asymptote will be y = -2.

Since the degree of the numerator and denominator of f(x) is the same both being 1, therefore horizontal asymptote exists and is given by:

y = Leading coefficient of numerator of f(x) / Leading coefficient of denominator of f(x)

= y = -2/1

= y = -2

The vertical asymptote will be f(x) = -2x / (x + 3). To find the vertical asymptote we will equate the denominator of f(x) = 0

= x + 3 = 0

= x = -3

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The voltage of the circuit is 8 + i .  Option C

From the information given, we have that;

E = IZ

Where;

We have that;

I = 3 + 2i

Z = 2 - i

Substitute into the formula

E = IZ

E = ( 3 + 2i) ( 2 - i)

Making the product of complex numbers we have:

E = ( 3 × 2 - i ) + ( 4i - 2i²)

E = ( 6 - 3i ) + ( 4i - 2 ( -1) )

E = ( 6 + 2) + ( 4 - 3 ) i

E = 8 + i

Thus, the voltage of the circuit is 8 + i .  Option C

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Answer:

It's C

Step-by-step explanation:

The solution to 1 - cos(6x) is 2sin²(x).

Hence, option B) 2sin²(x) is the correct answer.

Given that; 1 - cos(6x) = ?

First, we rewrite using trig identity

1 - cos(2 × 3x)

Using the double angle identity, { cos2(x) = 1 - 2sin²(x) }

1 - ( 1 - 2sin²(x) )

Eliminate the parentheses

1 - 1 + 2sin²(x)

2sin²(x)

The solution to 1 - cos(6x) is 2sin²(x).

Hence, option B) 2sin²(x) is the correct answer.

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Answer:

Yes

Step-by-step explanation:

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side or largest side. So, 7+6 = 13 which is greater than 9

Answer:

Yes, triangle with sides 6, 7 ,9 can be formed.

Step-by-step explanation:

The sum of any two sides of the triangle should be greater than the third side. If so, triangle can be formed.

6 + 7 = 13  >  9

7+ 9 = 16    > 6

6 +9 = 15   > 7

The equation for the trajectories orthogonal to the family of functions of the form 5 · x² - 2 · y² = C is equal to (1 / 5) · ㏑ x + (1 / 2) · ㏑ y = C.

In this problem we have a family of functions in implicit form, that is, a function of the form f(x, y, c) = 0. The equation of a orthogonal trajectory is always perpendicular to a particular form of a equation. First, we determine the first derivative of the given expression:

5 · x² - 2 · y² = C

10 · x - 4 · y · y' = 0

4 · y · y' = 10 · x

y' = (10 · x) / (4 · y)

y' = (5 · x) / (2 · y)

If f(x, y) = (5 · x) / (2 · y), then the differential equation for the orthogonal trajectories related to the family of functions is:

y' = - 1 / f(x, y)

y' = - (2 · y) / (5 · x)

dy / (2 · y) = - dx / (5 · x)

By indefinite integration we get the following solution to the ordinary differential equation:

(1 / 2) · ㏑ y = - (1 / 5) · ㏑ x + C

(1 / 5) · ㏑ x + (1 / 2) · ㏑ y = C

The equation for the trajectories orthogonal to the family of functions of the form 5 · x² - 2 · y² = C is equal to (1 / 5) · ㏑ x + (1 / 2) · ㏑ y = C.

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Answer:

x-1 gave ggs is it correct

Answer:

160 cm × 120 cm

Step-by-step explanation:

this means 1 cm turns into 20 cm.

so, 8 cm × 6 cm becomes

8×20 = 160 cm × 6×20 = 120 cm

-0.81 has negative direction and o.81 is the magnitude, 0.40 has  positive direction and 0.40 is the magnitude, 0.15 positive direction and 0.15 is the magnitude, -0.08 has negative direction and 0.08 is the magnitude and 0.29 has positive direction and 0.29 is the magnitude

A quantity having direction as well as magnitude, especially as determining the position of one point in space relative to another.

-0.81

Minus zero point eight one has negative direction and o.81 is the magnitude

0.40

zero point four zero has positive direction and 0.40 is the magnitude

0.15

Zero point one five has positive direction and 0.15 is the magnitude

-0.08

Minus zero point zero eight has negative direction and 0.08 is the magnitude

0.29

Zero point two nine has positive direction and 0.29 is the magnitude

Hence -0.81 has negative negative direction and o.81 is the magnitude, 0.40 has  positive direction and 0.40 is the magnitude, 0.15 positive direction and 0.15 is the magnitude, -0.08 has negative direction and 0.08 is the magnitude and 0.29 has positive direction and 0.29 is the magnitude

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Answer:

t = 21

Step-by-step explanation:

The ball strikes the groujd when h = 0.

[tex]-3.2t^2 + 54.4t+268.8=0 \\ \\ 32t^2 - 544t-2688=0 \\ \\ t^2 - 17t-84=0 \\ \\ (t-21)(t+4)=0 \\ \\ t=-4, 21[/tex]

Since time must be positive, t = 21.

Answer:

2 1/8

Step-by-step explanation:

I counted from 29 to 31 and then saw that for 29 it was 3/8 and for 31 it was 2/8 so i knew that the answer would be 2 1/8

Answer:

Joey needs 9 boxes.

Step-by-step explanation:

You will use the fact that a dozen is 12 cookies. You're trying to find how many dozen are in 100.

Something like:

12b = 100

or if you're studying inequalities:

12b >= 100

Divide by 12 to solve. See image. Interpret the results. See image.

Answer: [tex]x=-5[/tex]

Step-by-step explanation:

[tex]x+5=0 \implies x=-5[/tex]

Step-by-step explanation:

1 kilogram (kg) = 1000 grams (g)

as "kilo" means 1000.

b = a × c / 1000

it is simple : we have "c" square meters. as we need to apply "a" grams per square meter, we need to multiply both numbers to know how many grams we need for that many square meters. hence a × c.

and to get kg, we need to divide this number of grams by 1000.

that's it.

a. Recall that in polar coordinates, we can parameterize [tex]x=r\cos(\theta)[/tex] and [tex]y=r\sin(\theta)[/tex]. So, doing as the hint suggests, we have

[tex]r = 6\cos(\theta) + 8 \sin(\theta)[/tex]

[tex]\implies r^2 = 6r\cos(\theta) + 8r\sin(\theta)[/tex]

[tex]\implies \boxed{x^2 + y^2 = 6x + 8y}[/tex]

b. By completing the square, we get

[tex]x^2 + y^2 = 6x + 8y[/tex]

[tex]x^2 - 6x + y^2 - 8y = 0[/tex]

[tex]x^2 - 6x + 9 + y^2 - 8y + 16 = 25[/tex]

[tex](x-3)^2 + (y-4)^2 = 5^2[/tex]

which is the equation of the circle centered at (3, 4) with radius 5. Thus the area bounded by [tex]C[/tex] is [tex]\pi\cdot5^2 = \boxed{25\pi}[/tex].

c. This is made easier if you can consult a plot (attached). In the first quadrant, we have [tex]0\le\theta\le\frac\pi2[/tex], while the radial coordinate [tex]r[/tex] runs uninterrupted from the origin [tex]r=0[/tex] to the circle [tex]r=6\cos(\theta)+8\sin(\theta)[/tex]. So the area is

[tex]\displaystyle \int_0^{\pi/2} \int_0^{6\cos(\theta) + 8\sin(\theta)} r\,dr\,d\theta = \boxed{\frac12 \int_0^{\pi/2} \left(6\cos(\theta) + 8\sin(\theta)\right)^2 \, d\theta}[/tex]

d. Evaluate the integral.

[tex]\displaystyle \frac12 \int_0^{\pi/2} \left(36\cos^2(\theta) + 96\sin(\theta)\cos(\theta) + 64 \sin^2(\theta)\right) \, d\theta[/tex]

Simplify the integrand with the help of the identities

[tex]\cos^2(x) + \sin^2(x) = 1[/tex]

[tex]\sin(x)\cos(x) = \dfrac12 \sin(2x)[/tex]

[tex]\sin^2(x) = \dfrac{1 - \cos(2x)}2[/tex]

[tex]\displaystyle \frac12 \int_0^{\pi/2} \left(50 + 48\sin(2\theta) - 14 \cos(2\theta)\right) \, d\theta[/tex]

The rest is easy. You should end up with

[tex]\displaystyle \frac12 \int_0^{\pi/2} \left(6\cos(\theta) + 8\sin(\theta)\right)^2 \, d\theta = \boxed{24 + \frac{25\pi}2}[/tex]

a) The Cartesian equation that described curve C is x² + y² = 6 · x + 8 · y.

b) The area inside C is A = π · 5² = 25π square units.

c) The integral that computed the area inside curve C within the first quadrant is A = (1 / 2)∫ (6 · cos θ + 8 · sin θ)² dθ, for θ ∈ [0, 0.5π].

d) The integral evaluated at the given limits is equal to an area of 20.139π square units.

In this question we find a polar equation in explicit form. a) To find the equivalent form in rectangular coordinates, we must apply the following substitutions x = r · cos θ, y = r · sin θ:

r = 6 · cos θ + 8 · sin θ

r² = 6 · r · cos θ + 8 · r · sin θ

x² + y² = 6 · x + 8 · y       (1)

The Cartesian equation that described curve C is x² + y² = 6 · x + 8 · y.

b) Perhaps the equation represents a conic section, possibly a circunference. To prove this assumption, we must apply algebraic handling until standard form is obtained:

x² - 6 · x + y² - 8 · y = 0

x² - 6 · x + 9 + y² - 8 · y + 16 = 25

(x - 3)² + (y - 4)² = 5²          (1b)

Which indicates a circumference centered at point (h, k) = (3, 4) and with a radius of 5 units. By the area formula for a circle we find that the area inside C is A = π · 5² = 25π square units.

c) The polar form of the area integral is presented herein:

A = ∫ ∫ r dr dθ, for r ∈ [0, r(θ)] and θ ∈ [0, 0.5π]  

A = (1 / 2)∫ [r(θ)]² dθ, for θ ∈ [0, 0.5π]  

A = (1 / 2)∫ (6 · cos θ + 8 · sin θ)² dθ, for θ ∈ [0, 0.5π]  

The integral that computed the area inside curve C within the first quadrant is A = (1 / 2)∫ (6 · cos θ + 8 · sin θ)² dθ, for θ ∈ [0, 0.5π].

d) By algebraic handling, trigonometric formulas and integral properties:

A = 25 ∫ dθ  + 24 ∫ sin 2θ dθ - 14 ∫ cos 2θ dθ, for θ ∈ [0, 0.5π]  

A = 25 · θ - 12 · cos 2θ - 7 · sin 2θ, for θ ∈ [0, 0.5π]  

A = 20.139π

The integral evaluated at the given limits is equal to an area of 20.139π square units.  

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