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Firdavs [7]
2 years ago
13

PLEASEEE HELP !! in two the three sentences, explain how you would find the line of symmetry for the parabola whose equation is

Mathematics
1 answer:
Arada [10]2 years ago
5 0

Answer:

<em>Axis of symmetry line  is parallel to y- axis</em>

Equation of the parabola <em> ( x - ( -2 ))² =  (y - 12 )   </em>

Step-by-step explanation:

<u><em>Explanation</em></u>:-

Given equation is y = x²+4 x+16

                            y =  x²+2 (2 ) x + (2)² - (2)² + 16

                           y   = ( x + 2 )² + 12

                         ( x + 2 )² = y - 12

                        <em> ( x - ( -2 ))² =  (y - 12 )   </em>

                         ( x- h)² = 4 a ( y - k)

            <em> Center (h ,k) = ( -2 , 12)</em>

<em>              Here   4 a  = 1 </em>

                          <em>  a = 1/4</em>

<em>Focus  S = ( h , K +a) = ( -2 , 12 + 0.25) = ( -2 , 12.25)</em>

<em>Axis of symmetry line  is parallel to y- axis</em>

                           

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According to the Rational Root Theorem, what are all the potential rational roots of f(x) = 5x3 – 7x + 11?
iogann1982 [59]

ANSWER

\pm1,\pm11,\pm \frac{1}{5} \pm \frac{11}{5}

EXPLANATION

The given function is;

f(x) = 5 {x}^{2}  - 7x + 11

The constant term is 11.

The coefficient of the leading term is 5.

The factors of 11 are ±1,±11

The factors of 5 are ±1,±5

According to the Rational roots Theorem,

the potential roots are obtained by expressing the factors of the constant term over the coefficient of the leading term.

\pm1,\pm11,\pm \frac{1}{5} \pm \frac{11}{5}

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Answer:

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Find m∠DEC (the picture is not drawn to scale).
pochemuha

Answer:

M∠DEC equals 123º.

Step-by-step explanation:

The sum of a triangle's three angles always equal 180º. The exterior angle, x, equals the two non-adjacent interior angles.

180 - {(x - 45)+(x - 12)} = m∠DEC

m∠DEC + x = 180

<u>(x - 45) + (x - 12) = x</u>

Solving for x:

(x - 45) + (x - 12) = x

x - 45 + x - 12 = x                             Remove parenthesis

2x - 57 = x                                       Combine like terms

2x = x + 57                                      Add 57 to both sides

<u>x = 57</u><u>                                             Subtract x from both sides</u>

Finding m∠D:

x - 45 = ?

<u>57 - 45 = </u><u>12º                                          </u>

Finding m∠C:

x - 12 = ?

<u>57 - 12 = </u><u>45º                                           </u>

<em>** </em><em>(Checking x: 12 + 45 = 57) </em><em>**</em>

<em>Finding </em>m∠DEC:

AC is a straight line, and because straight lines are equivalent to 180º, we subtract 57 from 180:

180 - 57 = 123º

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❤<em>A.W.E.</em><u><em>S.W.A.N.</em></u>❤

8 0
3 years ago
A triangular pyramid is formed from three right triangles as shown below.
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Formula of the Pythagorus Theorem :  

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The value of AD is 54 and the value of AC is 90:

54² + CD² = 90²

Solve for CD:

54² + CD² = 90²

CD² = 90² - 54²

CD² = 5184

CD = √5184

CD = 72

ΔADC is also a right angle triangle, we will use the Pythagorus Theorem to find the length BD.

Formula of the Pythagorus Theorem :  

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The value of CD is 72 and the value of BC is 97:

BD² + 72² = 97²

Solve for BD:

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BD² = 4225

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Answer: The length of BD is 65 units.

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