Can anyone please help me?

7x + y = 13<br> 4x – 4y = -20

aalyn [17]

Answer: (x,y) = (1,6)

Step-by-step explanation:

5 0

3 years ago

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Write and equation of the translated or rotated graph in general form (picture below)

WINSTONCH [101]

Answer:

The answer is hyperbola; (x')² - (y')² - 16 = 0 ⇒ answer (a)

Step-by-step explanation:

* At first lets talk about the general form of the conic equation

- Ax² + Bxy + Cy² + Dx + Ey + F = 0

∵ B² - 4AC < 0 , if a conic exists, it will be either a circle or an ellipse.

∵ B² - 4AC = 0 , if a conic exists, it will be a parabola.

∵ B² - 4AC > 0 , if a conic exists, it will be a hyperbola.

* Now we will study our equation:

xy = -8

∵ A = 0 , B = 1 , C = 0

∴ B² - 4 AC = (1)² - 4(0)(0) = 1 > 0

∴ B² - 4AC > 0

∴ The graph is hyperbola

* The equation xy = -8

∵ We have term xy that means we rotated the graph about

the origin by angle Ф

∵ Ф = π/4

∴ We rotated the x-axis and the y-axis by angle π/4

* That means the point (x' , y') it was point (x , y)

- Where x' = xcosФ - ysinФ and y' = xsinФ + ycosФ

∴ x' = xcos(π/4) - ysin(π/4) , y' = xsin(π/4) + ycos(π/4)

∴ x' = x/√2 - y/√2 = (x - y)/√2

∴ y' = x/√2 + y/√2 = (x + y)/√2

* Lets substitute x' and y' in the 1st answer

∵ (x')² - (y')² - 16 = 0

∴ $(\frac{x-y}{\sqrt{2}})^{2}-(\frac{x+y}{\sqrt{2}})^{2}=$

( $\frac{x^{2}-2xy+y^{2}}{2})-(\frac{x^{2}+2xy+y^{2}}{2})-16=0$

* Lets open the bracket

∴ $\frac{x^{2}-2xy+y^{2}-x^{2}-2xy-y^{2}}{2}-16=0$

* Lets add the like terms

∴ $\frac{-4xy}{2}-16=0$

* Simplify the fraction

∴ -2xy - 16 = 0

* Divide the equation by -2

∴ xy + 8 = 0

∴ xy = -8 ⇒ our equation

∴ Answer (a) is our answer

∴ The answer is hyperbola; (x')² - (y')² - 16 = 0

* Look at the graph:

- The black is the equation (x')² - (y')² - 16 = 0

- The purple is the equation xy = -8

- The red line is x'

- The blue line is y'

6 0

3 years ago

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An item is priced at $13.24. If the sales tax is 5%, what does the item cost including sales tax?

cestrela7 [59]

B would be correct cause 5 percent would be .66

8 0

3 years ago

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The values of 60, 62, and 84 were common to both samples. The three values are identified as outliers with respect to the age-gr

postnew [5]

Answer:

Only 60 is an identified outlier

Step-by-step explanation:

Given

<u>Age group: 40 to 50</u>

$Min = 60$ $Q_1 = 70$ $Median= 73$

$Q_3 = 76$ $Max = 85$

<u>Conditions for outlier</u>

$Value > Q_3 + 1.5 * IQR$

$Value < Q_1 - 1.5 * IQR$

<em>See attachment for complete question</em>

<u>Required</u>

Which of 60, 62 and 84 is an outlier of age grout 40 to 50 years

First, calculate the IQR of group 40 to 50.

This is calculated as:

$IQR = Q_3 - Q_1$

Where:

$Q_3 = 76$ and $Q_1 = 70$

So:

$IQR = 76 - 70$

$IQR = 6$

<em>Next, is to test the outlier conditions on each value (i.e. 60, 62 and 84)</em>

<u></u>

<u>Testing 60</u>

<u>Condition 1</u>

$Value > Q_3 + 1.5 * IQR$

$60 > 76 + 1.5 * 6$

$60 > 76 + 9$

$60 > 85$ --- False

<u>Condition 2</u>

$Value < Q_1 - 1.5 * IQR$

$60 < 70 - 1.5 * 6$

$60 < 70 - 9$

$60 < 61$ --- True

<em>Because one of the conditions is true, then 60 is an outlier of group 40 - 50 years</em>

<u>Testing 62</u>

<u>Condition 1</u>

$Value > Q_3 + 1.5 * IQR$

$62> 76 + 1.5 * 6$

$62 > 76 + 9$

$62 > 85$ --- False

<u>Condition 2</u>

$Value < Q_1 - 1.5 * IQR$

$62 < 70 - 1.5 * 6$

$62 < 70 - 9$

$62 < 61$ --- False

<em>Because both conditions are false, then 62 is not an outlier of group 40 - 50 years</em>

<u>Testing 84</u>

<u>Condition 1</u>

$Value > Q_3 + 1.5 * IQR$

$84> 76 + 1.5 * 6$

$84 > 76 + 9$

$84 > 85$ --- False

<u>Condition 2</u>

$Value < Q_1 - 1.5 * IQR$

$84 < 70 - 1.5 * 6$

$84 < 70 - 9$

$84 < 61$ --- False

<em>Because both conditions are false, then 84 is not an outlier of group 40 - 50 years</em>

5 0

3 years ago

Please please help ASAP! Classify each angle!

Olenka [21]

Answer:

<h3> Acute Angles: ∠TLS, ∠SLT, ∠ULR</h3><h3> Right Angles: ---------</h3><h3> Obtuse Angles: ∠RLT, ∠SLU, ∠ULS,</h3><h3> Straight Angles: ∠RLS, ∠TLU </h3><h3> Not angles: ∠TRL </h3>

Step-by-step explanation:

The lines intersect at point L, so all angles have a vertex (middle letter) L so there is no angle TRL

Straight angle is a line with dot-vertex, so the straight angles are ∠RLS and ∠TLU.

∠TLS is less than 90° then it is acute angle (∠SLT is the same angle). ∠ULR is vertex angle to ∠TLS, so it's also acute angle.

Two angles adding to straight angle mean that they are both right angles or one is acute and the second is obtuse. ∠TLS is acute so ∠RLT is obtuse (they adding to ∠RLS) and ∠SLU is obtuse (they adding to ∠TLU). ∠ULS is the same angle as ∠SLU.

8 0

3 years ago