The floor of a canyon has an elevation of −14.5−14.5 feet. Erosion causes the elevation to change by −1.5−1.5 feet per year. How many years will it take for the canyon floor to have an elevation of −31−31 feet?

To solve the equation 5x(x+6) = -50 by completing the square, we first isolate the quadratic term and then add the square of half the coefficient of x to both sides of the equation. Taking the square root gives us the solution x = -3 + i and x = -3 - i.

To solve the equation by completing the square, we first need to isolate the quadratic term on one side of the equation. So, let's distribute the 5x to get 5x^2 + 30x = -50. Next, we move the constant term to the other side and divide the equation throughout by the leading coefficient to get x^2 + 6x + 10 = 0.

Now, we can complete the square by adding the square of half the coefficient of x (which is 3) to both sides of the equation. This gives us (x + 3)^2 + 10 - 9 = 0, which simplifies to (x + 3)^2 + 1 = 0.

Taking the square root of both sides, we get x + 3 = ±√(-1), which means x = -3 ± i. Hence, the solution to the equation is x = -3 + i and x = -3 - i.

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Answer:

48

Step-by-step explanation:

Answer:

The correct option is C.

Step-by-step explanation:

It is given that gross pay is a function of the number of hours that you work.

Let y represents the gross pay and x represents the number of hours. So, the value of x and y can be negative.

Hourly wage = $8 per hour.

The weekly gross pay function is

[tex]y=8x[/tex]              .... (1)

Domain is the set of inputs and ranges is the set of outputs.

It is given that you work 40 hours per week. It means the value of x lies between 0 to 40.

Domain = [0,8]

Substitute x=40 in equation (1), to find the gross pay when number of hours is 40.

[tex]y=8(40)=320[/tex]

Range = [0,320]

The practical domain is 0 through 40. The practical range is 0 through 320.

Therefore the correct option is C.

The practical domain for the function representing gross pay is the range of hours worked, 0 to 40 hours. The practical range is the corresponding gross pay, from $0 to $320, based on an $8 per hour wage for up to 40 hours of work. So correct answer  is option C.

To determine the practical domain and range of the function that represents your gross pay based on an hourly wage of $8 per hour, we must consider the possible number of hours you can work in a week and the corresponding earnings. Given that you work 40 hours per week, the practical domain (which represents the number of hours worked) would be any value from 0 to 40 hours, since you cannot work negative hours and we're assuming a standard full-time workweek.

The practical range (which represents the gross pay) is calculated by multiplying the number of hours worked by the hourly wage. Therefore, the range would be 0 (if you work 0 hours) to $320 (if you work 40 hours), because 40 hours times $8 per hour equals $320.

So, the correct answer from the given options is Option C.

Practical domain: 0 through 40.

Practical range: 0 through 320.

6/7 because if you divide 30/35 by 5 it will leave at 6/7

its not d its the +2 one

The correct equation for the distance Tran drove at a constant speed of 55 mph is B. d = 55t.

In this equation:

"d" represents the distance in miles that Tran drove.

"t" represents the time in hours.

So, the distance "d" is equal to Tran's constant speed of 55 mph multiplied by the time "t" in hours, which is why the equation is written as d = 55t.

Option D is not the correct equation because it has the variables and constants in the wrong order.

The correct order is distance (d) on the left side of the equation, followed by the constant speed (55) and then the time (t) on the right side of the equation.

for such more question on distance

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Answer:

205000

Step-by-step explanation:

Given :  253,495 - 48,617

To Find : What is rounding and estimate

Solution:

To Estimate a difference by rounding.

1 ) Round each term that will be subtracted

2 )Subtract the rounded numbers

Round off of 253,495 = 253000

Round off of 48,617 = 48000

So,  253000 - 48000 = 205000

Hence The rounding and estimate 253,495 - 48,617= 205000

3.2(2.3) - 4.8

Simplify.

(3.2 × 2.3) - 4.8

Simplify.

(7.36) - 4.8

Simplify.

2.56

Hope this helped. :)

The least common denominator of 5/6 and 7/9 is 18. This results in equivalent fractions of 15/18 for 5/6 and 14/18 for 7/9.

To find the least common denominator (LCD) of the fractions 5/6 and 7/9, we first find the least common multiple (LCM) of the two denominators, 6 and 9. The LCM of 6 and 9 is 18.

Next, we convert each fraction to an equivalent fraction with the LCD as the new denominator. We multiply the numerator and denominator of 5/6 by 3 to get 15/18. Similarly, we multiply numerator and denominator of 7/9 by 2 to obtain 14/18.

So the fractions 5/6 and 7/9, when written with their LCD, are 15/18 and 14/18, respectively.

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The number of music lessons must a member and a non-member take so the cost for each is the same will be 15.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

PEMDAS rule means the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

It costs $150 to be a member of a music club. A member of the club pays $5 per music lesson. A nonmember pays $15 per music lesson.

Let x be the number of music. Then the equation is given as,

15x = 5x + 150

Simplify the equation, then we have

15x - 5x = 150

10x = 150

x = 15

The number of music lessons must a member and a non-member take so the cost for each is the same will be 15.

More about the Algebra link is given below.

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Joe was given  $329 for an overnight trip because he drove a distance of 220 miles

Given Data

The Mathematical relation for this scenario is

Total amount = Amount Receive+ 0.7*Distance driven

let the distance driven be x

Substituting our given data into the relation we have

329= 175+ 0.7*x

329-175 = 0.7x

154 = 0.7x

divide both sides by 0.7

x = 154/0.7

x = 220miles

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The correct option is d. 8 oz. can of juice is most convenient to meet this requirement.

First, let's convert 240 milliliters to ounces because the answer choices are in ounces.

1 milliliter is approximately equal to 0.0338 ounces.

So, 240 milliliters is approximately \( 240 \times 0.0338 \) ounces, which is about 8.112 ounces.

Now, let's examine the options:

a. 5 oz. can of juice: Not enough juice. It's less than the required 8.112 ounces.

b. 4 oz. can of juice: Not enough juice. It's less than the required 8.112 ounces.

c. 12 oz. can of juice: More than enough juice. It's more than the required 8.112 ounces.

d. 8 oz. can of juice: Exactly the amount needed. It matches the required 8.112 ounces, which is the closest to the calculated amount of 8.112 ounces.

Therefore, the 8 oz. can of juice is the most convenient option to meet the requirement of having 240 milliliters of juice every 2 hours.

By setting up a proportion based on the similar triangles created by the streetlight and the building, we can find that Melanie is standing 48 feet away from the building.

To solve the problem of determining how far Melanie is standing from the building using the shadows, we can use similar triangles. We are given a 25-foot streetlight that casts a 20-foot shadow and a 60-foot tall building. The goal is to find the length of the shadow cast by the building, which will tell us how far Melanie is from the building.

By setting up a proportion based on the similar triangles, we have:

Therefore, Melanie is standing 48 feet away from the building.