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scoundrel [369]
3 years ago
9

Given the equation y − 3 = 1/2 (x + 6) in point-slope form, identify the equation of the same line in standard form. )

Mathematics
1 answer:
Doss [256]3 years ago
4 0

Answer:

a: x − 2y = −12

Step-by-step explanation:

the standard form of a line is is usually given as Ax + By = C, so just by deduction you can tell that the correct answer is a.

If you want to do the procedure it would be:

y − 3 = 1/2 (x + 6)

y − 3 = 1/2 x + 3

y - 1/2 x = 3 + 3

y - 1/2 x = 6

(y - 1/2 x = 6) * 2 to get rid of the fraction

2y - x = 12  rearrenge the terms

x - 2y = -12

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Whats the slope on the graph?
oee [108]

Answer:

-9/5 is the slope

Step-by-step explanation:

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6 0
2 years ago
Convert the Cartesian equation (x 2 + y 2)2 = 4(x 2 - y 2) to a polar equation.
SashulF [63]

<u>ANSWER</u>

{r}^{2}  = 4  \cos2\theta

<u>EXPLANATION</u>

The Cartesian equation is

{( {x}^{2}  +  {y}^{2} )}^{2}  = 4( {x}^{2} -  {y}^{2}  )

We substitute

x = r \cos( \theta)

y = r \sin( \theta)

and

{x}^{2}  +  {y}^{2}  =  {r}^{2}

This implies that

{( {r}^{2} )}^{2}  = 4(( { r \cos\theta)  }^{2} -  {(r \sin\theta) }^{2}  )

Let us evaluate the exponents to get:

{r}^{4}  = 4({  {r}^{2} \cos^{2}\theta } -   {r}^{2}  \sin^{2}\theta)

Factor the RHS to get:

{r}^{4}  = 4{r}^{2} ({   \cos^{2}\theta } -   \sin^{2}\theta)

Divide through by r²

{r}^{2}  = 4 ({   \cos^{2}\theta } -   \sin^{2}\theta)

Apply the double angle identity

\cos^{2}\theta -\sin^{2}\theta=  \cos(2 \theta)

The polar equation then becomes:

{r}^{2}  = 4  \cos2\theta

7 0
3 years ago
A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 48.0 and 58.
Yanka [14]

Answer: 0.025

Step-by-step explanation:

Given : A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between the interval [48.0 minutes, 58.0 minutes].

The probability density function :-

f(x)=\dfrac{1}{58-48}=\dfrac{1}{10}

Now, the probability that a given class period runs between 50.25 and 50.5 minutes is given by :-

\int^{50.5}_{50.25}\ f(x)\ dx\\\\=\int^{50.5}_{50.25}\ \dfrac{1}{10}\ dx\\\\=\dfrac{1}{10}|x|^{50.5}_{50.25}\\\\=\dfrac{1}{10}\ [50.5-50.25]=\dfrac{1}{10}\times(0.25)=0.025

Hence, the probability that a given class period runs between 50.25 and 50.5 minutes =0.025

Similarly , the probability of selecting a class that runs between 50.25 and 50.5 minutes = 0.025

5 0
3 years ago
Which relation is a function
Anon25 [30]
\{(\boxed{2};\ 3);\ (1;\ 5);\ (\boxed{2};\ 7)\}-NO\\\\\{(-1;\ 5);\ (-2;\ 6);\ (-3;\ 7)\}-YES\\\\\{(\boxed{11};\ 9);\ (\boxed{11};\ 5);\ (9;\ 3)\}-NO\\\\\{(\boxed{3};\ 8);\ (0;\ 8);\ (\boxed{3};\ -2)\}-NO
3 0
3 years ago
Seven apple women, possessing respectively 20, 40, 60, 80, 100, 120, and 140
Westkost [7]

Answer:

The amount each took home was 20 unit currency.

Step-by-step explanation:

We are given that Seven apple women, possessing respectively 20, 40, 60, 80, 100, 120, and 140  apples, went to market and sold all their apples at the same price, and each  received the same sum of money.

Formula  : a \times n + (n - 1), (a + b)\cdot n + (n - 2), (a + 2 \cdot b) \cdot n + (n - 3), (a + 3 \cdot b) \cdot n + (n - 4), (a + 4 \cdot b) \cdot n + (n - 5), (a + 5 \cdot b) \cdot n + (n - 6), (a + 6 \cdot b) \cdot n + (n - 7)

a \cdot n + (n - 1) = 20

(a + b) \cdot n + (n - 2)=40

(a + 2 \cdot b) \cdot n + (n - 3) = 60

(a + 3 \cdot b) \cdot n + (n - 4) = 80

(a + 4 \cdot b) \cdot n + (n - 5) = 100

(a + 5 \cdot b) \cdot n + (n - 6) = 120

(a + 6 \cdot b) \cdot n + (n - 7) = 140

On solving :

n = 7, a = 2, b = 3

So,

2 \times 7 + 6 = 20

5 \times 7 + 5=40

8 \times 7 + 4 = 60

11 \times 7 +  3 = 80

14 \times 7 + 2 = 100

17 \times 7 + 1 = 120

Based on market pricing if groups of apples are sold at 1 unit currency for 7, and extras are sold for 3 unit currency per extra 1, we have the amount :

2×1 + 6×3 = 20

5×1 + 5×3=20

8×1 + 4×3 = 20

11×1 +  3×3 = 20

14×1 + 2×3 = 20

17×1 + 1×3 = 20

20×1 = 20

Therefore, the amount each took home was 20 unit currency.

4 0
3 years ago
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