If 2x + 5 = -25 and -3m - 6 = 48, what is the product of x and m?

The equation of a given circle in general form is x^2+y^2-8x+12y+27=0. Write the equation in standard form, (x-h)^2+(y-k)^2=r^2,

umka2103 [35]

Answer:

(x - 4)² + (y + 6)² = 5²

Step-by-step explanation:

rearrange the general equation as follows

collect the terms in x and y together and place the constant on the right side

x² - 8x + y² + 12y = - 27

add (half the coefficient of the x/y term)² to both sides

x² + 2(- 4)x + y² + 2(6)y = - 27

(x - 4)² + 16 + (y + 6)² + 36 = - 27 + 16 + 36

(x - 4)² + (y + 6)² = 25

(x - 4)² + (y + 6)² = 5² ← in standard form

7 0

3 years ago

Water fills a tank at a rate of 150 litres during the first hour, 350 litres during the second, 550 litres during the third and

Alborosie

Putting this as an arithmetic sequence gives:

$u_n = 150+200(n-1)$

The sum of the series = 16 x 7 x 7 = 784 m^3 = 784 000 L

The sum of an arithmetic series can be written as:

$S_n=n/2 [2a+(n-1)d] = 784 000
\\n/2[2(150)+(n-1)200] = 784 000
\\n[300+200(n-1)=1 568 000
\\300n+200n^2-200n = 1 568 000
\\200n^2+100n- 1 568 000 = 0
\\2n^2 +n- 15680 = 0

\\n= 88.2...,-88.7$

n has to be positive, so we get

n = <u>88.2 hours (3 s.f.)</u>

3 0

3 years ago

Read 2 more answers

PLEASE help i neeed help asap im willing to give u 100 or 40 points if u answer this correctly so please help answer them all

AURORKA [14]

Step-by-step explanation:

The hundredth place is the second number to the right of the decimal place (e.g., in ab.cd, where a, b, c, and d represent digits, the hundredth place is d).

When we round to the nearest hundredth, we remove all digits after the <em>thousandth</em> place. Then, if the thousandth place is 5 or greater, we remove it and add 0.01 (round up); if the thousandth place is 4 or lesser, we remove it (round down).

Thus:

50.30=50.30, as there is no thousandth place

50.20=50.20, same reasoning

56.90=56.90, same reasoning

49.50=49.50, same reasoning

51.10=51.10, same reasoning

30.00=30.00, same reasoning

5 0

3 years ago

Whate is answer of 36-[100÷5{60-32(8÷4-1)}]

svet-max [94.6K]

Answer:

$67\frac{23}{28}$

Step-by-step explanation:

$36-\left[100\div \:560-32\left(8\div \:4-1\right)\right]\\\\100\div \:560-32\left(8\div \:4-1\right)\\\\=100\div \:560-32\cdot \:1\\\\=\frac{100}{560}-32\cdot \:1\\\\=\frac{100}{560}-32\\\\=-\frac{891}{28}\\\\\\=36-\left(-\frac{891}{28}\right)\\\\36-\left(-\frac{891}{28}\right)\\\\=36+\frac{891}{28}\\\\\frac{36\cdot \:28}{28}+\frac{891}{28}\\\\\frac{36\cdot \:28+891}{28}\\\\=\frac{1899}{28}\\\\\\\frac{1899}{28}(1899\div28)=67\frac{23}{28}$

6 0

1 year ago

(7x4 + 2x3 - 3) – (4x2 - 9x + 2)

abruzzese [7]

Answer:

7x4+2x3-4x2-5

Step-by-step explanation:

We will start solving this question by opening the bracket first

So let's solve

(7x4+2x3-3)-(4x2-9x+2)

7x4+2x3-3-4x2+9x-2

Collect like terms

7x4+2x3-4x2-3-2

7x4+2x3-4x2-5

So the final answer is 7x4+2x3-4x2-5

4 0

3 years ago