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Amiraneli [1.4K]
3 years ago
7

A square has a perimeter of 32 and one vertex at (6,8). what could be the location of another vertex of this shape?

Mathematics
2 answers:
lukranit [14]3 years ago
8 0

Answer:

6,5

Step-by-step explanation:

qwelly [4]3 years ago
6 0

Answer:

(6,0),(-2,8),(-2,0)

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Classify each conic section and write its equations in standard form. Show work.
svp [43]

Answer:

The conic is ellipse of equation (x - 1)²/22 + (y + 4)²/44 = 1

Step-by-step explanation:

* Lets revise how to identify the type of the conic  

- Rewrite the equation in the general form,  

 Ax² + Bxy + Cy² + Dx + Ey + F = 0  

- Identify the values of A and C from the general form.  

- If A and C are nonzero, have the same sign, and are not equal  

 to each other, then the graph is an ellipse.  

- If A and C are equal and nonzero and have the same sign, then  

 the graph is a circle  

- If A and C are nonzero and have opposite signs, and are not equal  

then the graph is a hyperbola.  

- If either A or C is zero, then the graph is a parabola  

* Now lets solve the problem

The equation is 4x² + 2y² - 8x + 16y - 52 = 0

∴ A = 4 and C = 2 ⇒ same sign and different values

∴ The equation is ellipse

* The standard form of the ellipse is

  (x - h)²/a² + (y - k)²/b² = 1

- Lets try to make this form from the general form

- Group terms that contain the same variable, and move the

  constant to the opposite side of the equation

∴ (4x² - 8x) + (2y² + 16y) = 52

- Factorize the coefficients of the squared terms

∴ 4(x² - 2x) + 2(y² + 8y) = 52

- Complete the square for x and y

# To make completing square

- Divide the coefficient  of x (or y) by 2 and then square the answer

- Add and subtract this square number and form the bracket of

 the completing the square

# 2 ÷ 2 = 1 ⇒ (1)² = 1 ⇒ add and subtract 1

∴ 4[(x² - 2x + 1) - 1] = 4(x² - 2x + 1) - 4

- Rewrite as perfect squares ⇒ 4(x -1)² - 4

# 8 ÷ 2 = 4 ⇒ (4)² = 16 ⇒ add and subtract 16

∴ 2[(y² + 8y + 16) - 16] = 2(y² + 8y + 16)² - 32

- Rewrite as perfect squares ⇒ 2(y + 4)² - 32

∴ 4(x - 1)² - 4 + 2(y + 4)² - 32 = 52

∴ 4(x - 1)² - 4 + 2(y + 4)² = 32 + 4 + 52

∴ 4(x - 1)² + 2(y + 4)² = 88 ⇒ divide all terms by 88

∴ (x - 1)²/22 + (y + 4)²/44 = 1

8 0
2 years ago
For the parent function y=√x what effect does a value of k = -3 have on the graph?
luda_lava [24]

Answer:

Vertical shift of 3 units down ⇒ last answer

Step-by-step explanation:

* Lets revise the translation of a function

- If the function f(x) translated horizontally to the right  

 by h units, then the new function g(x) = f(x - h)

- If the function f(x) translated horizontally to the left  

 by h units, then the new function g(x) = f(x + h)

- If the function f(x) translated vertically up  

 by k units, then the new function g(x) = f(x) + k

- If the function f(x) translated vertically down  

 by k units, then the new function g(x) = f(x) – k

* Lets solve the problem

∵ The parent function y = √x

∵ There is a translation by k = -3

- From the rules above k is for the vertical translation

∵ k = -3

- That means the parent function translated 3 units down

∴ The value of k = -3 makes the graph of the parent function translated

   3 units down

- For more understand look to the attached graph

# y = √x ⇒ the red graph

# y = √x - 3 ⇒ the blue graph

4 0
3 years ago
Evaluate the following using<br> powers of ten rules.<br> 104)1.042
Alinara [238K]

Answer:

0.0001042

Step-by-step explanation:

Power of tens rule states that if the denominator of a fraction has the positive power of 10, decimal in the numerator will be shifted to the left by the same number of places as exponent.

10⁴) 1.042 = \frac{1.042}{10^4}

In the denominator of the given fraction, exponent of 10 = +4

So the decimal in numerator will be shifted left by 4 places.

\frac{1.042}{10^4}=0.0001042

Therefore, answer is 0.0001042

5 0
2 years ago
{8x [1+(20-6)]}÷ 1/2=
IceJOKER [234]
You would do 20-6 which = 14. + 1 =15. times 8= 120 then divide that by 1/2 =  240 if you do 120 divided by .5 in a calculator thats what you get. i hope that helps you

7 0
3 years ago
From a boat ont he lake, the angle of elevation to the top of a cliff is 11° 50'. If the base of the cliff is 1568 feet from the
Marizza181 [45]

Answer:

328 feet

Step-by-step explanation:

From a boat ont he lake, the angle of elevation to the top of a cliff is 11° 50'. If the base of the cliff is 1568 feet from the boat, how high is the cliff (to the nearest foot)

Step 1

Note that

that 11°50' is just 11 degrees and 50 minutes

60 minutes = 1 degree,

thus 50 minutes = x degree

50/60 degrees

= 0.83°

Hence: 11°50' = 11.83°.

Step 2

We solve using Trigonometric function of tan

tan theta = Opposite/Adjacent

theta = 11.83°

Adjacent = 1568 feet

Opposite = Height of the cliff = x

tan 11.83° = x/1568

Cross Multiply

x = tan 11.83 × 1568

x = 328.429195 feet

Approximately = 328 feet

The height of the cliff is 328 feet

8 0
3 years ago
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