A maintenance warranty for solar heaters cost $50 a month plus a one time $15 processing fee. Complete the table to determine the total cost for different number of months.

[tex]\large\underline{\sf{Solution-}}[/tex]

First equation is

[tex]\rm \longmapsto\:(x - a)(y - b) = (x - 2a)\bigg(y -\dfrac{b}{2}\bigg) [/tex]

can be further simplified to

[tex]\rm \longmapsto\:xy - bx - ay + ab = xy - \dfrac{bx}{2} - 2ay + ab[/tex]

[tex]\rm \longmapsto\: - bx - ay = - \dfrac{bx}{2} - 2ay [/tex]

[tex]\rm \longmapsto\: - bx + \dfrac{bx}{2} = - 2ay + ay[/tex]

[tex]\rm \longmapsto\: - \dfrac{bx}{2} = - ay[/tex]

[tex]\rm \longmapsto\: \dfrac{bx}{2} = ay[/tex]

[tex]\rm \longmapsto\:bx = 2ay[/tex]

[tex]\rm:\longmapsto \:\boxed{\tt{ bx - 2ay = 0}} - - - - (1)[/tex]

Second equation is

[tex]\rm \longmapsto\:x\bigg(x + \dfrac{1}{2b} \bigg) + y \bigg(y + \dfrac{a}{2}\bigg) - 2xy = 5 + {(x - y)}^{2} [/tex]

[tex]\rm \longmapsto\: {x}^{2} + \dfrac{x}{2b} + {y}^{2} + \dfrac{ay}{2} - 2xy = 5 + {x}^{2} + {y}^{2} - 2xy[/tex]

[tex]\rm \longmapsto\: \dfrac{x}{2b} + \dfrac{ay}{2} = 5[/tex]

[tex]\rm \longmapsto\: \dfrac{x + aby}{2b} = 5[/tex]

[tex]\rm :\longmapsto\:\boxed{\tt{ x + aby = 10b}} - - - (2)[/tex]

So, we have two equations in simplest form as

[tex]\rm \longmapsto\:bx - 2ay = 0 [/tex]

and

[tex]\rm \longmapsto\:x + aby = 10b[/tex]

Now, Consider

[tex]\rm \longmapsto\:\dfrac{a_1}{a_2} = \dfrac{b}{1} = b[/tex]

[tex]\rm \longmapsto\:\dfrac{b_1}{b_2} = \dfrac{ - 2a}{ab} = - \dfrac{2}{b} [/tex]

[tex]\bf\implies \:\dfrac{a_1}{a_2} \: \ne \: \dfrac{b_1}{b_2} [/tex]

This implies, System of equations is consistent having unique solution.

So, The student is correct as lines are intersecting.

So, option (b) is correct.

Answer:

$300

Step-by-step explanation:

Diane's interest rate on the loan is approximately 8.43%.

Let's determine Diane's interest rate step by step.

1. First, we need to understand the formula for simple interest:

  Simple Interest (SI) = Principal (P) × Rate (R) × Time (T)

  where:

  P = Principal amount (initial loan amount)

  R = Interest rate (unknown, what we want to find)

  T = Time period in years

2. We have the following information from the problem:

  P = $3000 (Principal amount)

  SI = $253 (Total interest paid)

  T = 11 months

3. However, to use the formula, we need to convert the time from months to years. Since 1 year has 12 months, we can write:

  T = 11 months ÷ 12 months/year

     ≈ 0.917 years

4. Now, let's rearrange the formula to solve for the interest rate (R):

  R = SI / (P × T)

  Substituting the given values:

  R = $253 / ($3000 × 0.917) ≈ 0.0925

5. Finally, we need to convert the interest rate from a decimal to a percentage:

  R = 0.0925 × 100 ≈ 8.43%

So, Diane's interest rate on the loan is approximately 8.43%.

In summary, to find the interest rate, we used the simple interest formula and rearranged it to solve for the rate. We converted the time from months to years before calculating the interest rate. The result is approximately 8.43% interest rate, indicating the percentage of the principal that Diane had to pay as interest over 11 months.

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Answer:

1/5

Step-by-step explanation:

Answer:

Step-by-step explanation:

yes cdrj

ejkfkj

ennejw

Answer:

Step-by-step explanation:

solution 1:

570 not man = 15% (cause 100% - 85%)

15% = 570

100% = w (for "whole package")

15w = 100 * 570

15w = 57000

w = 57000 / 15

w = 3800

solution 2:

15% = 570

85 = m (for "men)

15m = 570 * 85

15m = 48450

m = 48450 / 15

m = 3230

100% = 85% + 15%

100% = b (for "buch of people")

b = 3230 + 570

b = 3800

The probability of 1 number showing up out of 20 is 1/20

The probability of 3 different numbers showing up would be 3/20

Answer: 3/20

Answer:

fsuu vvv

Step-by-step explanation:

gdcytzvnvdezcghiyyk for giving biscuits vicbeddings vicbeddings vicbeddings

Step-by-step explanation:

g(x) is a polynomial. It doesn't contain a rational degree with the variable as the denominator, negative eexponents, or irrational coeffecienfs, and no rational exponents as a degree.

f(x) and f(a) isn't a polynomial. It contain a irrational coeffceint like pi. So it not a polynomial. And they both have a rational exponet as a degree

Answer:

[tex]y = mx + c \\ m = 1 \\ c = 8 \\ y = 1x + 8 \\ y = x + 8[/tex]

Given :-

To find :-

Solution :-

We know that ,

On substituting ,

Answer:

Step-by-step explanation:

2. 3 × 12 = 3 × 2 × 6 = 3 × 2 × 2 × 3

3. 4 × 9 = 2 × 2 × 3 × 3

4. 6 × 6 = 2 × 3 × 2 × 3

please give me a brainliest answer

Step-by-step explanation:

2. 36 = 3 × 12 = 3 × 2 × 6 = 3 × 2 × 2 × 3

3. 36 = 4 × 9 = 2 × 2 × 3 × 3

4. 36 = 6 × 6 = 2 × 3 × 2 × 3

Answer:

irrational numbers integers

Answer:Message me for full answer

Step-by-step explanation:

Answer:

Mr. Pandya's class has 12 boys and 18 girls.

Mr. Chapman's class has 5 girls and 25 boys.

Step-by-step explanation:

Answer:

I hope this helped. Look throught the pictures

Step-by-step explanation:

Answer:

Part A: 0<x<9

Part B: The y-intercept 3 represents how big the fish was when she first started her study.

Part C: The average rate of change from m=2 to m=8 is 2.09, and it represents the growth of the species of fish.

I don't know about Part C, but I hope this helps!

Answer:

I'm not entirely sure what the question is but every thing under 12.5 is closer to 12, everything 12.5 and upwards like 12.87 would be closer to 13

Using a geometric sequence, it is found that after 3 rounds, 8 teams are left.

In a geometric series, the quotient between consecutive terms is always the same, and it is called common ratio q.

The general equation of a geometric series is given by:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

In this problem:

The number of teams after 3 rounds is the 4th term of sequence, as the first is the initial number(0 rounds), thus:

[tex]a_n = a_1q^{n-1}[/tex]

[tex]a_4 = 64\left(\frac{1}{2}\right)^{4-1}[/tex]

[tex]a_4 = 8[/tex]

After 3 rounds, 8 teams are left.

A similar problem is given at https://brainly.com/question/25317689

Given the function, f(x) = 3x + 6, we can solve for f(a), f(a + h) and [tex]\frac{(f(a + h) - f(a)) }{h}[/tex] by substituting their values into f(x) = 3x + 6. We will have the following:

[tex]\mathbf{f(a) = 3a + 6}\\\\\mathbf{f(a + h) = 3a + 3h + 6}\\\\\mathbf{\frac{(f(a + h) - f(a)) }{h} = 6}[/tex]

Given:

We are told to find:

1. Find f(a):

f(a) = 3(a) + 6

f(a) = 3a + 6

2. Find f(a + h):

f(a + h) = 3(a + h) + 6

f(a + h) = 3a + 3h + 6

3. Find [tex]\frac{(f(a + h) - f(a)) }{h}[/tex]:

Thus:

[tex]\frac{((3a + 3h + 6) - (3a + 6)) }{h}\\\\\frac{(3a + 3h + 6 - 3a - 6) }{h}\\\\[/tex]

[tex]\frac{(3a - 3a + 3h + 6 - 6) }{h}\\\\= \frac{3h }{h}\\\\\mathbf{= 3}[/tex]

Therefore, given the function, f(x) = 3x + 6, we can solve for f(a), f(a + h) and [tex]\frac{(f(a + h) - f(a)) }{h}[/tex] by substituting their values into f(x) = 3x + 6. We will have the following:

[tex]\mathbf{f(a) = 3a + 6}\\\\\mathbf{f(a + h) = 3a + 3h + 6}\\\\\mathbf{\frac{(f(a + h) - f(a)) }{h} = 6}[/tex]

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Answer:

the answer is 7.2 cm

Step-by-step explanation:

14^2 is 196

12^2 is 144

196 - 144 = 52

square root of 52 = 7.2

also i did FLVS & got it right lol

Answer:

c

Step-by-step explanation:

Answer

yc(T)=y"+y'-6y=0

Step-by-step explanation:

BTW,,

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Answer:

pls mark my brainliest because you didn't wriitten coorect question

Step-by-step explanation:

Answer:

x = 1 3/5

Step-by-step explanation:

distribute.

-2.5*4x + (-2.5*-4) = -6

-10x +10 = -6

subtract 10 on both sides

-10x = -6 -10

divide by -10

x = -16/-10

x = 1 3/5

Answer:

Step-by-step explanation:

Answer:

11.28 Divided by 4.7 equals 2.4.

Step-by-step explanation:

It's just simple division. Glad I could help though!

Answer:

2.4

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

If the first number (in this case, behind the decimal) is 5 or more, you round up. If it is 4 or less, you round down. since 2 and 1 are less than 4, you round down making them both 0. Then, you round up making the answer 6. I hope this makes sense! I wasn't entirely sure how to explain this.

Answer:

2^2 * 3^2

Step-by-step explanation:

2 * 2 * 3 * 3

We are multiplying 2 twos and we are multiplying 2 threes 3^2

The base is the number and the exponent is the number of the times

2^2 * 3^2