The floor of a one-story building is 14 feet longer than it is wide. The building has 1715 square feet of floor space. Find the length l and width w of the floor.

Answer:

[tex]3x^{4}-4x^{3}-8x^{2}-35x-10[/tex]

Step-by-step explanation:

We have been given that Vanessa uses the expressions [tex]3x^2+5x+10[/tex] and [tex]x^2-3x-1[/tex] to represent the length and width of her patio.

To find the expression that represents the area of Vanessa's patio we will multiply the length of patio by width of patio as:

[tex](3x^2+5x+10)*(x^2-3x-1)[/tex]

Upon using distributive property [tex]a(b+c)=a*b+a*c[/tex] we will get,

[tex](3x^2*x^2)+(3x^2*-3x)+(3x^2*-1)+(5x*x^2)+(5x*-3x)+(5x*-1)+(10x^2)+(10*-3x)+(10*-1)[/tex]

Using exponent property [tex]a^b*a^c=a^{b+c}[/tex] we will get,

[tex](3x^{2+2})+(-9x^{2+1})+(-3x^2)+(5x^{1+2})+(-15x^{1+1})+(-5x)+(10x^2)+(-30x)+(-10)[/tex]

[tex](3x^{4})+(-9x^{3})+(-3x^2)+(5x^{3})+(-15x^{2})+(-5x)+(10x^2)+(-30x)+(-10)[/tex]

[tex]3x^{4}-9x^{3}-3x^2+5x^{3}-15x^{2}-5x+10x^2-30x-10[/tex]

Now let us combine like terms.

[tex]3x^{4}-9x^{3}+5x^{3}-3x^2-15x^{2}+10x^2-5x-30x-10[/tex]

[tex]3x^{4}-4x^{3}-8x^{2}-35x-10[/tex]    

Therefore, the expression [tex]3x^{4}-4x^{3}-8x^{2}-35x-10[/tex] represents the area of Vanessa's patio.

Answer: [tex]u=x^6[/tex]

Explanation:

A quadratic equation is an equation written in the form

[tex]au^2 + bu + c=0[/tex] (1)

where a,b,c are coefficients and where u is the variable.

Our original equation is:

[tex]4x^{12} - 5x^6 -14=0[/tex]

If we make the substitution [tex]u=x^6[/tex], we obtain

[tex]4u^2 -5u-14 =0[/tex]

Which corresponds to eq.(1), with coefficients a=4, b=-5, c=-14.

Answer:

The bar diagram is shown below. Number of peoples who are 18 or older is 163,776.

Step-by-step explanation:

Given information:

Total number of peoples in the city = 332,054

Number of peoples who are under 18 = 168,278

Number of peoples who are 18 or older is

[tex]332,054-168,278=163,776[/tex]

We need to draw a bar diagram.

In the bar diagram x axis represents the age and y-axis represents the number of peoples.

First bar represents the number of peoples who are under 18 i.e., 168,278.

Second bar represents the number of peoples who are 18 or older i.e., 163,776.

To determine the system of equations to which the ordered pair (3, –1) is a solution, we must find equations where substituting 'x' with 3 and 'y' with –1 produces true statements for both equations in the system.

The question pertains to finding the system of equations for which the ordered pair (3, –1) is a solution. To determine the correct system, we would need to identify equations that have both 'x' and 'y' variables. An ordered pair is composed of an 'x' coordinate and a 'y' coordinate, following the form (x, y). In this case, the 'x' value is 3, and the 'y' value is –1. If the ordered pair (3, –1) is a solution to a system of linear equations, it must satisfy both equations in the system. This means that when we substitute 'x' with 3 and 'y' with –1 into each equation, the equations should hold true.

For example, if we have a system of equations:

Substituting 'x' with 3 and 'y' with –1 into both equations, we get:

Since the ordered pair (3, –1) satisfies both equations, then (3, –1) is a solution to this system. To identify the system of equations the ordered pair belongs to, you would similarly test the pair in the given systems to see which one(s) it satisfies.

Joe's income was $40,200 in the 18th year.

To find the year in which Joe's income was $40,200, we need to determine the rate at which his income increases each year.

Given that his income increased by the same dollar amount each year, we can calculate the increase by subtracting his income in the first year from his income in the 11th year: $31,400 - $20,400 = $11,000.

Next, we can divide the increase in income by the number of years to find the increase per year: $11,000 ÷ 10 = $1,100.

Finally, to find the number of years it takes for his income to reach $40,200, we can divide the difference between $40,200 and $20,400 by the increase per year: ($40,200 - $20,400) ÷ $1,100 = 18.

Therefore, Joe's income was $40,200 in the 18th year.

Answer:

[tex](x^2 - x)[/tex] will always have an even value.

Step-by-step explanation:

We are given an integer x.

Let x be even, then it can be written in the form x = 2n, where n is an integer.

If we evaluate,

[tex](x^2 - x) = (2n)^2 - 2n = 4n^2 - 2n = 2(2n^2 - n)[/tex]

Thus, it have an even value.

If we take x to be an odd integer, then,it can be written in the form x = 2n+1, where n is an integer.

[tex](x^2 - x) = (2n+1)^2 - 2n = 4n^2 + 2n = 2(2n^2 + n)[/tex]

Thus, it have an even value.

Thus,

[tex](x^2 - x)[/tex] will always have an even value.

The recursive formula is an = a_(n-1) +4.

The correct option is (D).

A recursive formula refers to a formula that defines each term of a sequence using the preceding term(s). The recursive formulas define the following parameters:

The recursive formula to find the nth term of an arithmetic sequence is:

an = an-1 + d for n ≥ 2

where

an is the nth term of a A.P.

d is the common difference.

Given:

14, 18, 22, 26, 30, …

a1=14

and, d= 18-14

d=4

a2= a1 + 4

a2 = 14+4= 18

Similarly, going this way

an = a_(n-1) +4

Hence, the recursive formula is an = a_(n-1) +4

Learn more about recursive function here:

https://brainly.com/question/23896867

#SPJ2

Answer:

2.99x + 12.99y = 43.92

Step-by-step explanation:

Here, x represents the number of pairs of socks purchased, and let y represents the number of blouses purchased.

Since, the cost of each pair of socks is $ 2.99 and the cost of a blouse is $ 12.99,

Thus, the total cost of x pairs of socks and y blouses = ( 2.99x + 12.99y ) dollars,

According to the question,

Total cost is $43.92,

⇒ 2.99x + 12.99y = 43.92

Which is the required equation.

To calculate Frederick's approximate savings if he paid off the loan early, subtract the total amount he would pay if the loan continued for the full term from the original loan amount. The monthly payment amount can be calculated using the compound interest formula. By multiplying the monthly payment by the number of payments, you can find the total amount paid over 20 years. Subtracting this from the original loan amount gives you the approximate savings.

To calculate the approximate amount Frederick would save if he paid off the loan early, we need to find the total amount he would pay if he continued making monthly payments for the full 20 years and subtract the total amount he would pay if he paid off the loan early.

1. First, find the monthly interest rate by dividing the annual interest rate by 12:

i = 0.022 / 12 = 0.00183

2. Next, calculate the monthly payment using the compound interest formula:

P = (r * PV) / (1 - (1 + r)^(-n))

Where P is the monthly payment, r is the monthly interest rate, PV is the loan amount, and n is the number of monthly payments.

3. Substitute the values into the formula:

P = (0.00183 * $70,000) / (1 - (1 + 0.00183)^(-240))

4. Solve for P to find the monthly payment amount:

P ~ $520.63

5. To find the total amount paid over 20 years, multiply the monthly payment by the number of payments:

Total amount paid = $520.63 * 240 = $124,950.98

6. To find the approximate amount saved if the loan is paid off early, subtract the total amount paid from the original loan amount:

Approximate savings = $70,000 - $124,950.98 = -$54,950.98

https://brainly.com/question/40972120

#SPJ11

Final answer:

Frederick would save approximately $34,692.80 if he paid off the loan early.

Explanation:

To calculate the amount Frederick would save if he paid off the loan early, we need to determine the total cost of the loan and compare it to the amount he would pay if he paid it off in a shorter time period.

First, we need to calculate the monthly payment using the formula:

Monthly Payment = Loan Amount * (Monthly Interest Rate / (1 - (1 + Monthly Interest Rate)^(-Total Number of Payments)))

Substituting the values, we have:

Loan Amount = $70,000

Monthly Interest Rate = 2.2% / 12 = 0.1833%

Total Number of Payments = 20 * 12 = 240

Plugging the values into the formula, we get:

Monthly Payment = $70,000 * (0.1833% / (1 - (1 + 0.1833%)^(-240)))

Calculating this equation gives us a monthly payment of approximately $436.22.

Next, we calculate the total cost of the loan by multiplying the monthly payment by the total number of payments:

Total Cost = Monthly Payment * Total Number of Payments

Plugging in the values, we get:

Total Cost = $436.22 * 240

Calculating this equation gives us a total cost of approximately $104,692.80.

If Frederick paid off the loan early, he would save the difference between the total cost and the original loan amount, which is $104,692.80 - $70,000 = $34,692.80.

divide cost by number of bottles

7/28 = 0.25 per bottle

check 28 * 0.25 = 7.00 

Final answer:

After 30 seconds, she will be 150 meters away.

Explanation:

To calculate how far the friend will be after 30 seconds on her bike, we must assume a constant velocity since no acceleration is mentioned. Given that she is 15 meters away after 3 seconds, we can calculate her velocity using the formula v = d/t, where v is velocity, d is distance, and t is time.

First, we find her velocity:

v = 15 m / 3 s = 5 m/s

Now that we have her velocity, we can calculate how far she will be after 30 seconds:

Distance = Velocity × Time = 5 m/s × 30 s = 150 m

Therefore, after 30 seconds, she will be 150 meters away.

Final answer:

Yes, if four points are collinear, they are also coplanar, as they lie on the same straight line and therefore exist in the same plane.

Explanation:

If four points are collinear, this implies that they lie on the same straight line. By definition, a straight line is a one-dimensional figure and hence exists within any given plane. Therefore, four collinear points must also be coplanar, existing on the same plane. In three-dimensional geometry, the concept of coplanarity can be evaluated using a determinant. If this determinant equals zero, it indicates that the four points lie within the same plane.

Moreover, lines and planes in three-dimensional space can be represented by equations, and by combining these into a system of equations, one can ascertain the geometric relationships between the points in question.

Answer:

associative property

Step-by-step explanation: