What is the value of x?

x+58=6x+58=6

Enter your answer in the box in simplest form.
x =

Answer:

Domain is {x| 1<=x <5}

Step-by-step explanation:

The graph of the piecewise function f(x) is shown.

In the given graph of piecewise function

Domain is the set of x values for which the function is defined

first graph is from x= 1 to 3, 3 is excluded

second graph is from x= 3 to 5, 5 is excluded

So the graph of x values is from x=1 to 5 ( 5 excluded because we have open circle at 5)

Domain is {x| 1<=x <5}

Answer : [tex] 5m^4n^3[/tex]  and [tex] 15m^2n^2[/tex]

Greatest common factor of  [tex] 5m^2n^2 [/tex]

If we are able to factor out [tex] 5m^2n^2 [/tex] from each option then that would be our answer.

Lets check with each options

(a)[tex] m^5n^5 [/tex], we cannot take out 5.

(b)[tex] 5m^4n^3 [/tex], We can take out common factor and it can be written as [tex] 5m^4n^3=5m^2n^2(m^2n) [/tex]

(c) [tex] 10m^4n [/tex], we cannot take out n^2 because we have only 'n'

(d) [tex] 15m^2n^2[/tex], We can take out common factor and it can be written as [tex] 15m^2n^2=5m^2n^2(3) [/tex]

(e) [tex] 24m^3n^4 [/tex], we  cannot take out 5 because we have 24

So answer is (b)  and (d)

Answer:

the graph is stretched horizontally to 1/3 the original width

Step-by-step explanation:

the graph is also reflected and translated but those are rigid transformations and this is asking about the non rig transformations

Final answer:

To calculate the total charges for the cable installation, multiply the hourly rate of $30.00 by the 8.5 hours spent ($255.00) and add the $50.00 service charge, resulting in total charges of $305.00.

Explanation:

The task requires us to calculate the total charges based on the cable installer's hourly rate and a service charge. The installer charges $30.00 per hour and there's an additional $50.00 service charge. To find the total cost for 8.5 hours of work, we multiply the hourly rate by the number of hours and then add the service charge.

Calculation: Total charges = (Hourly rate × Number of hours) + Service charge = ($30.00 × 8.5 hours) + $50.00

Step 1: Calculate the hourly charge
Hourly charge = $30.00 × 8.5 = $255.00

Step 2: Add the service charge
Total charges = $255.00 + $50.00 = $305.00

The total charges for the cable installation service will be $305.00.

Answer:

[tex]6x^2,3xy,4z[/tex]

Step-by-step explanation:

We are given that an expression

[tex]6x^2+3xy+4z[/tex]

We have to find the variable terms in the given expression.

Variable term: The term which contains variable is called variable term.

Constant term:The term which does not contain variable is called constant term.

To find the variable terms we will find the terms which contains variable.

We can see that in the given expression

There are three terms which contain variables.

Hence, the variable terms are

[tex]6x^2,3xy,4z[/tex]

Answer:

a)  2 red lights

b) SD = 1.26

c) mean = 10, SD = 1.26

Step-by-step explanation:

a) The number of red lights she expects to hit by day can be gotten by calculating the mean of the distribution.

[tex]E(X) = \sum xP(x)[/tex]

[tex]E(X) = (0*0.05) + (1*0.25) + (2*0.35) + (3*0.15) + (4*0.15) + (5*0.15)\\E(X) = 2.25[/tex]

Since the number of lights cannot be a decimal, she expects to hit 2 lights each day

b)

Variance, [tex]V(X) = \sum(x- \mu)^{2} P(x)[/tex]

[tex]V(X) = [(0-2.25)^{2}*0.05] + [(1-2.25)^{2}*0.25] + [(2-2.25)^{2}*0.35] + [(3-2.25)^{2}*0.15] + [(4-2.25)^{2}*0.15] + [(5-2.25)^{2}*0.05][/tex]

V(X) = 0.253 + 0.391 + 0.022 + 0.084 + 0.459 + 0.378

V(X) = 1.587

Standard Deviation, [tex]SD = \sqrt{V(X)}[/tex]

[tex]SD = \sqrt{1.587}[/tex]

SD = 1.26

c) In a 5 day work week, the commuter is expected to hit an average of 5* 2 red lights, i.e. mean = number of red lights hit per day * number of days

mean = 2 * 5

mean = 10

The standard deviation will not change, SD = 1.26

Answer:

9

Step-by-step explanation:

Answer:

[tex]p(x)=-0.0005x+29[/tex]

Step-by-step explanation:

It is given that a baseball team plays in a stadium that holds 51,000 spectators.

Let x be the attendance and p be the price.

With ticket prices at $10, the average attendance had been 38,000. When ticket prices were lowered to $8, the average attendance rose to 42,000.  

Assuming that the demand function is linear. It means, the demand line passes through the points (38000,10) and (42000,8).

The equation of line is

[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

[tex]y-10=\dfrac{8-10}{42000-38000}(x-38000)[/tex]

[tex]y-10=\dfrac{-2}{4000}(x-38000)[/tex]

[tex]y-10=-0.0005(x-38000)[/tex]

[tex]y-10=-0.0005x-0.0005(-38000)[/tex]

[tex]y-10=-0.0005x+19[/tex]

[tex]y=-0.0005x+19+10[/tex]

[tex]y=-0.0005x+29[/tex]

Substitute y=p(x).

[tex]p(x)=-0.0005x+29[/tex]

Therefore, the demand function is [tex]p(x)=-0.0005x+29[/tex].

Final answer:

For the function f(x) = (sinx)/x to be continuous at x = 0, the value of k must be 1, which is the limit of the function as x approaches 0.

Explanation:

The student is asking about the continuity of a given function at x = 0. To determine what the value of k must be for the function f(x) = (sinx)/x when x is approaching 0, we need to look at the limit of the function as x approaches 0.

Although the function is not defined at x = 0 due to division by zero, we know that the limit of (sin x)/x as x approaches 0 is 1. This can be proven using L'Hospital's rule or the squeezing theorem. Hence, for the function to be continuous at x = 0, the value of k must also be 1.

the solution to the system of equation is (5, -T

From equation 1;

x = -1 - 3y

Substitute x = -1-3y into equation 2

x + y = 3

-1-3y + y = 3

-1 -2y = 3

-2y = 4

y = -2

Since x + y = 3

x = 3 + 2

x = 5

Hence the solution to the system of equation is (5, -2)

Answer:

The value of the equation for [tex]d_2[/tex] is [tex]d_2=\frac{2A}{d_1}[/tex].

Step-by-step explanation:

Consider the provided equation.

[tex]A=\frac{1}{2}d_1d_2[/tex]  

We need to solve the equation for [tex]d_2[/tex].

Multiply both the sides by 2.

[tex]2A=2\times \frac{1}{2}d_1d_2[/tex]

[tex]2A=d_1d_2[/tex]

Divide both sides by [tex]d_1[/tex].

[tex]\frac{2A}{d_1}=\frac{d_1d_2}{d_1}[/tex]

[tex]d_2=\frac{2A}{d_1}[/tex]

Hence, the value of the equation for [tex]d_2[/tex]is [tex]d_2=\frac{2A}{d_1}[/tex].

Answer:

Answer is option c

Step-by-step explanation:

Given that the cost, c(x), for a taxi ride is given by c(x) = 2x + 4.00, where x is the number of minutes.

We find that whenever 1 minute increases cost increases by 2 dollars.

Hence rate of change of cost with respect to minute of taxi ride = 2 dollas

i.e. this is of the form y=mx+b where

m =2 is the slope or rate of change and

b = 4 is the fixed charge even for 0 minute.

Thus option C is right

A function is denoted as y = f (x), where x is the argument or input of the function. This means that from  f(6) follows that x= 6, and to get the answer we should replace x with 6.

f(6)=6^2÷ 3 + 6= 36÷ 3 + 6= 12+6= 18

f(6)=18

Answer:

The value of f(6) is, 18

Step-by-step explanation:

Given the function:

[tex]f(x) = x^2 \div 3+ x[/tex]               .....[1]

We have to find the value of [tex]f(6)[/tex].

Put x = 6 in [1] we have;

[tex]f(6) = 6^2 \div 3+ 6[/tex]

⇒[tex]f(6) = 36 \div 3 +6[/tex]

⇒[tex]f(6) = \frac{36}{3}+6[/tex]

Simplify:

[tex]f(6) = 12 +6 = 18[/tex]

Therefore, the value of f(6) is, 18

So basically the answer would be 86%

The simplified form of each expression is as follows:

[tex]A. \( 729 \times 33 \) simplifies to \( 3^6 \times 33 \) B. \( 3 \times 33 \) simplifies to \( 3 \times 3 \times 11 \) or \( 3^2 \times 11 \). C. \( 729 \times 29 \) simplifies to \( 3^6 \times 29 \). D. \( 3 \times 29 \) simplifies to \( 3 \times 29 \).[/tex]

To simplify these expressions, we recognize that 729 is a power of 3, specifically [tex]\( 3^6 \)[/tex], and that 33 and 29 are prime numbers. Therefore, we can express each product in terms of its prime factors.

A. For the expression [tex]\( 729 \times 33 \)[/tex] , we know that 729 is [tex]\( 3^6 \)[/tex] and 33 is a prime number. Thus, the simplified form is [tex]\( 3^6 \times 33 \)[/tex].

[tex]B. For the expression \( 3 \times 33 \), we can further break down 33 into \( 3 \times 11 \), since 33 is the product of these two prime numbers. Therefore, the simplified form is \( 3^2 \times 11 \) or \( 3 \times 3 \times 11 \).[/tex]

[tex]C. For the expression \( 729 \times 29 \), similar to expression A, 729 is \( 3^6 \) and 29 is a prime number. Hence, the simplified form is \( 3^6 \times 29 \).[/tex]

[tex]D. For the expression \( 3 \times 29 \), both 3 and 29 are prime numbers, so the expression is already in its simplest form and cannot be simplified further. Thus, the simplified form remains \( 3 \times 29 \).[/tex]In summary, the simplified forms are:

[tex]A. \( 3^6 \times 33 \) B. \( 3^2 \times 11 \) or \( 3 \times 3 \times 11 \) C. \( 3^6 \times 29 \) D. \( 3 \times 29 \)[/tex]

Answer:

D. $15061.98

Step-by-step explanation:

In order to calculate the proceeds we will using the following computation:

Principal + {Principal * Discounted rate * Frequency of a year on Maturity Date}

15,000 + {15,000 * 5% * (30/365)}

Hence, the proceeds of note would be $15,061.98