Graph the equation.

Y= - 3/2x

The zero of the equation is 0. Since degree of denominator is greater than degree of numerator, therefore, the horizontal asymptote is y=0

The zero of the function is the point where the function is zero

Given the function below

f(x) = 4x/x-16

For the zeros

0 = 4x/x -16

4x = 0

x = 0

Hence the zero of the equation is 0

The vertical asymptote is the point where the denominator is zero

x - 16 = 0
x = 16

Since degree of denominator is greater than degree of numerator, therefore, the horizontal asymptote is y=0

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Answer:

[tex] {a}^{2} + 2ab + {b}^{2} [/tex]

Step-by-step explanation:

[tex](a + b) {}^{2} = (a + b)(a + b) = {a}^{2} + ab + ab + {b}^{2} = {a}^{2} + 2ab + {b}^{2} [/tex]

Hi!

___________________________________________________________

[tex]\rightsquigarrow\circ\boldsymbol{Answer}\circ\leftharpoonup[/tex]

a^2+2ab+b^2

[tex]\rightsquigarrow\circ\boldsymbol{Explanation}\circ\leftharpoonup[/tex]

Remember the rule for expanding a binomial squared.

[tex]\twoheadrightarrow\sf (a+b)^2=a^2+2ab+b^2[/tex]

So we square the first term, then multiply the product of the two terms times 2.

[tex]\twoheadrightarrow\sf a^2+2ab+b^2[/tex]

This is our answer.

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Hope that this helped! Best wishes.

[tex]\textsl{Reach far. Aim high. Dream big.}\\\boldsymbol{-Greetings!-}[/tex]

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The average rate of change for the height of the plant measured in centimeters per day between day 0 and day 20 is 1.32 cm per day.

The average height is the ratio of change in height of the plant and the time taken taken for that change.

Given is the height of a plant in centimeters is modeled as a function of time, in days.

For day 0, the height is 18cm and the height for day 20 is 42 cm, then the average height change is

height per day = 42 - 18/ 20 -0

height per day  = 1.2 cm/day

Thus, the average height of plant is  1.2 cm/day.

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Answer:

3.33, or 3 1/3

Step-by-step explanation:

Expected value:

[tex](9 \times \frac{2}{9} ) + (12 \times \frac{1}{9} ) = 2 + \frac{4}{3} = 2 + 1 \frac{1}{3} = 3 \frac{1}{3} [/tex]

Answer:

1,887,436,800

Step-by-step explanation:

f(t) = a·b^t

f (t) = number of cases at year t

a = starting value = 1800 in 1983

b = growth factor = 2

t = years since 1983 = 2003 - 1983 = 20

f(t) = 1800·(2)^20 =

1,887,436,800

wyzant

philip p

The equation in slope-intercept form is: y = -x + 5

The equation in point-slope form is: y - 3 = -1(x - 2)

Slope (m) = rise/run = -(2/2) = -1

Y-intercept (b) = 5 (where the line intercepts the y-axis)

Using a point, (2, 3) = (a, b) and m = -1, the equation in point-slope form is:

y - 3 = -1(x - 2)

Rewrite in slope-intercept form:

y - 3 = -x + 2

y = -x + 2 + 3

y = -x + 5

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i doooooooont knoooooooooooooooow iiiittttttttttttttttttttttt

Regarding conditional probabilities, the keyword is always given, as a previous event is considered to have happened.

Conditional probability is the probability of one event happening, considering a previous event. The formula is:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which:

The previous event having happened is represented by keyword given.

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The coordinate of point P that divides the line segment into 2 parts and 3 parts is (-5,5).

Let's call the point that divides the line segment point P.

Point P divides the line segment into a ratio of 2:3

The ratio of 2:3 means we are dividing the line segment into 2+3=5 equal parts.

The horizontal distance between the two coordinates is 5.

The vertical distance between the two coordinates is 10.

Dividing both vertical and horizontal distance into five equal parts, we have a horizontal distance of 1 and a vertical distance of 2.

Every time we move one unit to the left from point J and two units up, we are dividing the line segment into five equal parts as shown in the picture.

The coordinate of point P that divides the line segment into 2 parts and 3 parts is (-5,5).

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Answer:

(u + [tex]\frac{65}{2}[/tex] )²

Step-by-step explanation:

u² + 65u

to complete the square

add ( half the coefficient of the u- term )²

= u² + 2([tex]\frac{65}{2}[/tex] )u + [tex]\frac{4225}{4}[/tex]

= (u + [tex]\frac{65}{2}[/tex] )²

Answer:

According to the graph, g(x) is stretched by what seems to be 5, so g(x) is (x^2) / 25. (Square the stretching/compressing factor so 5^2 became 25). We also divide x^2 by this because it is being stretched. You multiply if it's being compressed.

You can check this by plugging 5 for x and trying to get 1.

g(x) = x^2 / 25

g(5) = 5^2 / 25 --> 25/25

g(5) = 1

g(x) = (x^2)/25

Answer:

a computer is an electronic device,which input data/instruction,store and processes it and produces output in the desired from

A percentage is a way to describe a part of a whole. The relative change from last year to this year is 3.7%.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

28.6% of city employees ride the bus to work, therefore, the final value is 28.6. While Last year, 29.7% of city employees rode the bus to work, therefore, the initial value is 29.7.

Since relative change means change with respect to some value. Thus, the relative value with respect to last year is,

Relative value = (29.7-28.6)/29.7 = 0.037 = 3.7%

Hence, the relative change from last year to this year is 3.7%.

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Answer:

Or if you don't want any rounding it will be 115.38461538461

Answer:

The length of the side BC is 6 units.

Step-by-step explanation:

Rectangle ABCD

Coordinates of Point A,B,C,D

[tex]A = ( 5 , 5)B = (7, 5)C = (7 , -1)D = (5 , -1)[/tex]

As we are asked to find the length of side BC, we'll apply the Distance formula on side BC

BC = [tex]\sqrt{(7_ {-} 7)^{2} +(-1 {-} 5)^{2}}[/tex]

     = [tex]\sqrt{(0)^{2} +(-6)^{2}}[/tex]

     = [tex]\sqrt{ 36}[/tex]

     = [tex]6[/tex]

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|2x + 5| ≤ 11

x = 3

2(3) + 5

6 + 5

11 ≤ 11

The solution for the x in the inequality |2x + 5| ≤ 11 is {-8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3}

Inequality shows relation between two expression which are not equal to each others.

The given inequality is,

|2x + 5| ≤ 11

To find the solution for the x, solve the inequality,

|2x + 5| ≤ 11

-11 ≤ 2x + 5 ≤ 11

Subtract 5 from whole the expression,

-11 - 5 ≤ 2x + 5 - 5 ≤ 11 - 5

-16 ≤ 2x ≤ 6

-8 ≤ x ≤ 3

The value of x for the given inequality varies from -8 to 3.

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Answer:

The mid-point is (9,-9/2)

Step-by-step explanation:

You would use the mid-point formula for this

[tex](\frac{x_{2} +x_{1} }{2} , \frac{y_{2}+y_{1} }{2} )[/tex]

if you plug that in it is ([tex]\frac{13-2}{2}, \frac{-7+5}{2}[/tex])

resulting in (11/2,-2/2) = (11/2,-1)

Multiplying the linear expressions, the correct sequence is given as follows:

They are multiplied applying the distributive property, in which all the terms are multiplied and the like terms are combined.

Hence:

5x(-3 -7x)

(5x)(-3) + (5x)(-7x)

-15x - 35x²

Hence the last option is correct.

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Answer: C

Step-by-step explanation:

[tex]a^{b} \times a^{c}=a^{b+c}[/tex], so [tex]4^{-5} \times 4^{8}=4^{-5+8}=4^{3}[/tex].

The only option that is equal to this is C

The domain of a function f(x)/m(x) = 1/√x(x² - 4) is (0, ∞) - {0, 2, -2} for other function is shown in the solution.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have:

f(x) =  1/√x

m(x) = x² - 4

Domain of f(x)/m(x):

f(x)/m(x) = (1/√x)/(x² - 4)

f(x)/m(x) = 1/√x(x² - 4)

The denominator cannot be zero:

√x(x² - 4) ≠ 0

x(x - 2)(x+2) ≠ 0

x ≠ 0, 2, -2

and x > 0

Domain of f(x)/m(x) is:   (0, ∞) - {0, 2, -2} or [tex]\:\left(0,\:2\right)\cup \left(2,\:\infty \:\right)[/tex]

Domain of f(m(x)):

f(m(x)) = 1/√(x² - 4)

x² - 4 > 0

Domain: [tex]\rm \left(-\infty \:,\:-2\right)\cup \left(2,\:\infty \:\right)[/tex]

Domain of m(f(x)):

= ((1/√x)² - 4)

Domain: [tex]\:\left(0,\:\infty \:\right)[/tex]

Thus, the domain of a function f(x)/m(x) = 1/√x(x² - 4) is (0, ∞) - {0, 2, -2} for other function is shown in the solution.

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Supply and demand can help consumers make informed decisions about their purchases, anticipate price fluctuations, and stay up to date with market trends.

We have to give that,

To find supply and demand affect on consumers.

Supply and demand have a significant impact on consumers.

When the demand for a product or service is high and the supply is limited, it can lead to higher prices.

On the other hand, when there is high supply and low demand, prices tend to be lower.

For consumers, this means that when the demand for a product is high, they may have to pay more or face limited availability.

Conversely, when the demand is low, consumers may find discounted prices or special promotions.

Supply and demand dynamics also influence the choices available to consumers.

For example, if the demand for a particular type of product increases, companies may introduce new variations or brands to meet consumer preferences.

This can lead to a broader range of options for consumers to choose from.

In summary, understanding supply and demand can help consumers make informed decisions about their purchases, anticipate price fluctuations, and stay up to date with market trends.

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Step-by-step explanation:

Answer:

23.1 years  (nearest tenth)

Step-by-step explanation:

Compound Interest Formula

[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]

where:

Given:

Substitute the given values into the formula and solve for t:

[tex]\implies \sf 1200=600\left(1+\dfrac{0.03}{12}\right)^{12t}[/tex]

[tex]\implies \sf 1200=600\left(1.0025\right)^{12t}[/tex]

[tex]\implies \sf \dfrac{1200}{600}=\left(1.0025\right)^{12t}[/tex]

[tex]\implies \sf 2=\left(1.0025\right)^{12t}[/tex]

Take natural logs:

[tex]\implies \sf \ln 2=\ln \left(1.0025\right)^{12t}[/tex]

[tex]\implies \sf \ln 2=12t\ln \left(1.0025\right)[/tex]

[tex]\implies t=\dfrac{ \ln 2}{12 \ln (1.0025)}[/tex]

[tex]\implies t=23.13377513...[/tex]

[tex]\implies t=23.1\: \sf years \:\:(nearest\:tenth)[/tex]

The money will double in value in approximately [tex]\boxed{\sf 23.1}[/tex] years.

Used formula

[tex]\boxed{\sf A=P(1+\dfrac{r}{n})^{nt}}[/tex]

[tex]\\ \implies \sf 1200=600\left(1.0025\right)^{12t}[/tex]

[tex]\\ \implies \sf \dfrac{1200}{600}=\left(1.0025\right)^{12t}[/tex]

[tex]\\ \implies \sf 2=\left(1.0025\right)^{12t}[/tex]

[tex]\implies \sf \ln 2=\ln \left(1.0025\right)^{12t}[/tex]

[tex]\\ \implies \sf \ln 2=12t\ln \left(1.0025\right)[/tex]

[tex]\\ \implies t=\dfrac{ \ln 2}{12 \ln (1.0025)}[/tex]

[tex]\\ \implies t=23.1years[/tex]

Answer:

9:12

Step-by-step explanation:

since the others are multiples of 2:3

but 9:12 is not a multiple

Answer:

2

Step-by-step explanation: