All categories

2 years ago

Convert the following Standard Form equation to an equation in General For (x-7)^2 + (y + 3)^2 = 49

Mathematics

2 answers:

S_A_V [24]2 years ago

7 0

Answer:

x² + y² - 14x + 6y + 9 = 0

Step-by-step explanation:

the equation of a circle in general form is

x² + y² + 2gx + 2fy + c = 0

given

(x - 7)² + (y + 3)² = 49 ← expand factors using FOIL

x² - 14x + 49 + y² + 6y + 9 = 49 , that is

x² + y² - 14x + 6y + 58 = 49 ( subtract 49 from both sides )

x² + y²- 14x + 6y + 9 = 0 ← in general form

Harman [31]2 years ago

4 0

Answer:

x+y=11

Step-by-step explanation:

take the square root of both sides.

(x-7) + (y+3) = 7

collect like terms

x+y = 7+7-3

You might be interested in

Andy completes the square for the equation x2 + 6x - 8 = 0. Which of the following equations reveals the vertex of the parabola?

Stolb23 [73]

If the equation $x^2+6x-8$ has undergo completing the square, the answer would be:
$x^2+6x-8
$
$x^2+6x+9-8-9$
**In this example, since 6x is the middle term, what comes to my mind is the polynomial (x+3) because 2ab results into 6x. [from the special products lesson $(a+b)^2=a^2+2ab+b^2$ ]
$(x+3)^2 -17 = 0$
So if the equation is equal to y, then this equation's
$y+17=(x+3)^2$
The vertex would be on the point (-3, -17)

3 0

3 years ago

Read 2 more answers

2(2x+3)=3(3x+1)<br> Duýdhdhdjjdjdjđm

Vlada [557]

Answer:

Step-by-step explanation:

.......................

7 0

3 years ago

Read 2 more answers

Flow meters are installed in urban sewer systems to measure the flows through the pipes. In dry weatherconditions (no rain) the

ziro4ka [17]

Answer:

a) $\frac{(8)(30.23)^2}{20.09} \leq \sigma^2 \leq \frac{(8)(30.23)^2}{1.65}$

$363.90 \leq \sigma^2 \leq 4430.80$

Now we just take square root on both sides of the interval and we got:

$19.08 \leq \sigma \leq 66.56$

b) For this case we are 98% confidence that the true deviation for the population of interest is between 19.08 and 66.56

Step-by-step explanation:

423.6, 487.3, 453.2, 402.9, 483.0, 477.7, 442.3, 418.4, 459.0

Part a

The confidence interval for the population variance is given by the following formula:

$\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}$

On this case we need to find the sample standard deviation with the following formula:

$s=sqrt{\frac{\sum_{i=1}^8 (x_i -\bar x)^2}{n-1}}
And in order to find the sample mean we just need to use this formula:
[tex]\bar x =\frac{\sum_{i=1}^n x_i}{n}$

The sample deviation for this case is s=30.23

The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:

$df=n-1=9-1=8$

The Confidence interval is 0.98 or 98%, the value of $\alpha=0.02$ and $\alpha/2 =0.01$ , and the critical values are:

$\chi^2_{\alpha/2}=20.09$

$\chi^2_{1- \alpha/2}=1.65$

And replacing into the formula for the interval we got:

$\frac{(8)(30.23)^2}{20.09} \leq \sigma^2 \leq \frac{(8)(30.23)^2}{1.65}$

$363.90 \leq \sigma^2 \leq 4430.80$

Now we just take square root on both sides of the interval and we got:

$19.08 \leq \sigma \leq 66.56$

Part b

For this case we are 98% confidence that the true deviation for the population of interest is between 19.08 and 66.56

4 0

3 years ago

What is 2 gallons minus 5 quarts

MariettaO [177]

There are 4 quarts in a gallon.
In two gallons would be 8 quarts.

2 gallons - 5 quarts = 8 quarts - 5 quarts = 3 quarts.

Note: 3 quarts is 3/4 or .75 of a gallon.

6 0

3 years ago

Rosena bought an 8 pack of donuts. The donuts cost $28.00 all together. What is the unit rate for the donuts in dollars?

san4es73 [151]

Answer:

$3.50

Step-by-step explanation:

I hope this helps!

3 0

2 years ago

Read 2 more answers

Convert the following Standard Form equation to an equation in General For (x-7)^2 + (y + 3)^2 = 49​

Convert the following Standard Form equation to an equation in General For (x-7)^2 + (y + 3)^2 = 49