Lucia bought a table and some chairs at a furniture store. The equation that models this situation is y = 40x + 55, where y is the amount of money she spent and x is the number of chairs she bought. What does the y-intercept mean in this situation?

A. She paid $40 for each chair.

B. She paid $55 for the table.

C. She paid $40 for the table.

D. She paid $55 for each chair.

Answer:

it is the distance of a circle

Step-by-step explanation:

So basically the answer would be 86%

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:

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].

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

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:

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

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].

Answer:

9

Step-by-step explanation:

Answer : The north middle school have fewer than 750 students.

Step-by-step explanation:

Let the number of students in south middle school be, x

and the number of students in north middle school be, y

Given:

Number students in south middle school = x = 750

and,

North middle school has 13/15 times as many students as South. That means,

[tex]y=\frac{13}{15}\times x[/tex]   ........(1)

Now put the value of 'x' in expression 1, we get:

[tex]y=\frac{13}{15}\times 750[/tex]

[tex]y=650[/tex]

Thus, number of students in north middle school = y = 650

From this we conclude that north middle school have fewer than 750 students.

Hence, the north middle school have fewer than 750 students.

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)

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)

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.

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

Explanation of how to expand and simplify the given quadratic expression Hence answer is 4a²x² + abx² + 1/4b²x²,

Solve the equation: (2ax + 1/2 bx)²

Expanding the given expression:

(2ax + 1/2 bx)²

= (2ax)² + (2ax) (1/2 bx) + (1/2 bx)²

= 4a²x² + 2abx² + 1/4b²x²

= 4a²x² + abx² + 1/4b²x²

Answer: 4a²x² + abx² + 1/4b²x²

By the principle of mathematical induction, we have shown that for all positive integers n, n^3 + 2n is divisible by 3.

Proof by Induction: n^3 + 2n is divisible by 3 for all positive integers n.

Base Case:

For n = 1, n^3 + 2n = 1^3 + 2(1) = 3, which is divisible by 3.

Induction Hypothesis:

Assume that for some positive integer k, k^3 + 2k is divisible by 3. We can write this as: k^3 + 2k = 3m, where m is an integer.

Induction Step:

We need to show that (k + 1)^3 + 2(k + 1) is divisible by 3. Expanding the expression:

(k + 1)^3 + 2(k + 1) = k^3 + 3k^2 + 3k + 1 + 2k + 2

= (k^3 + 2k) + (3k^2 + 3k + 3)

Substituting the induction hypothesis:

= 3m + 3(k^2 + k + 1)

= 3(m + k^2 + k + 1)

Since k^2 + k + 1 is an integer (sum of three integers), and m is an integer, their sum (m + k^2 + k + 1) is also an integer. Therefore, (k + 1)^3 + 2(k + 1) is divisible by 3.