MATHEMATICS HIGH SCHOOL

When a bill is not paid by the due date, a late fee is added each month until the bill is paid. The values in the table represent the total amount due, in dollars, for each month that a payment remains overdue.Months | Total due
2 300
5 375
10 500
Using x for the number of months overdue and y for the total amount due, in dollars, construct a linear function that describes the relationship between the number of months the bill is overdue and the total amount due. Enter the equation of the function in the box

Answers

Answer 1

Answer:

The total amount due, in dollars, is an illustration of a linear function

The equation of the function is $y = 25x + 250$

Represent the month with x, and the total due with y.

Start by calculating the slope (m) using:

$m = (y_2 -y_1)/(x_2 -x_1)$

So, we have:

$m = (375 - 300)/(5 - 2)$

Simplify

$m = (75)/(3)$

Divide 75 by 3

$m = 25$

The linear equation is then calculated as:

$y = m(x - x_1) + y_1$

So, we have:

$y = 25(x - 2) + 300$

Open bracket

$y = 25x - 50 + 300$

Add 300 to -50

$y = 25x + 250$

Hence, the equation of the function is $y = 25x + 250$

Read more about linear equations at:

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For the missing term in the geometric sequence, Find the possiblefor the missing term in the geometric sequence, Find the possible values.4, ?, 1/36

Answers

Use property of geometric sequence:

$4,x,(1)/(36)\n \n (x)/(4)=((1)/(36))/(x)\n \n x^2=4.(1)/(36)\n \n x^2=(1)/(9)\n \n x=\pm (1)/(9)\n \n \boxed{x=\pm (1)/(3)}$

Equation 5d + 8 = 14 + 3d has o

Answers

Answer:

d = 3

Step-by-step explanation:

Isolate the variable, d. Note the equal sign, what you do to one side, you do to the other. Subtract 8 and 3d from both sides:

5d (-3d) + 8 (-8) = 14 (-8) + 3d (-3d)

5d - 3d = 14 - 8

2d = 6

Divide 2 from both sides:

(2d)/2 = (6)/2

d = 6/2

d = 3

d = 3 is your answer.

ANSWER:d=3 im thinking.

EXPLANATION

What is the value of z in the equation 3z - 7 = 14?

Answers

1st add 7 to both sides : 3z = 21, 2nd divide both sides with 3: z = 7

Find the value of x , if log₂ [log₅ (log₃x)] = 0

Answers

$\log_2 (\log_5( \log_3x)) = 0\n D:x>0 \wedge \log_3x>0 \wedge \log_5(\log_3x)>0\n D:x>0\wedge x>1 \wedge\log_3x>1\n D:x>1 \wedge x>3\n D:x>3\n \log_5(\log_3x)=1\n \log_3x=5\n x=3^5\n x=243$

What is the area of a circular wading pool with a radius of 50cm

Answers

An area of a circle is calculated by the formula pi(3.14) x radius^2 (squared)

This mean that you would have to type pi x 50^2 (squared) into your calculator which would equal 7853.98. Then round it up to equal 7854cm^2

Answer: D. 7854.0 cm^2

Step-by-step explanation:

A 19-foot piece of string is cut into two pieces so that the longer piece is 4 feet longer than twice the shorter piece. If the shorter piece is x feet long find the lengths of both peices

Answers

here,
let the longer piece be y and shorter piece be x
now,
according to the question,
x+y=19 .............................equation (1)
y=4+2x ...............................equation (2)

from equation 1
x+y=19
x+4+2x=19 substituting the value of y from equation 2
3x=19-4
x=(19-4)/3
x=5

now
substituting value of x in equation (2)
y=4+2(5)
y=4+10
y=14

so , the longer piece is 14 foot and the shorter piece is 5 foot

Final answer:

The shorter piece of string is 5 feet long and the longer piece is 14 feet long. These lengths were determined by setting up and solving an equation based on the given facts.

Explanation:

In this problem, we need to find the lengths of two sections of a 19-foot piece of stringthat was split such that the longer piece is 4 feet longer than twice the length of the shorter one. Let's denote the length of the shorter piece as 'x'. Thus, the longer piece of string is 2x+4 (twice the length of the shorter piece, plus an additional 4 feet).

Next, we set up an equation based on the information given: the sum of the lengths of the shorter and the longer sections of string equals 19 feet, so x + (2x+4) = 19. Simplify the equation to 3x + 4 = 19, subtract 4 from both sides to give 3x = 15, and then divide by 3 to solve for x, the length of the shorter piece, which is 5 feet. Therefore, the longer piece, by substituting x=5 in 2x+4, is 14 feet.

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