A restaurant has two pastry ovens. When both ovens are used, it takes about 3 hours to bake the bread needed for one day. When only the large oven is used, it takes about 4 hours to bake the bread for one day. Approximately how long would it take to bake the bread for one day if only the small oven were used? 

If x² = y³ , for what value of z does =    ?

Answer:

z= 2

Step-by-step explanation:

To solve the question given, we will follow the steps below;

=     -----------------------------------------------------------------(1)

but   applying the law of indices mᵃᵇ = (mᵃ)ᵇ

then

 =

replace    by    in equation (1)

=  

=     --------------------------------------------------------------------(2)

but  from the question x² = y³

replace y³ by x²  in equation (2)

=  

=  

=  

3z = 6

divide both-side of the equation by 3

3z/3 = 6/3

On the left-hand side of the equation, 3 at the numerator will cancel-out 3  at the denominator leaving us with just z while on the right-hand side of the equation 6 will be divided by 3

z= 2

Answer: vertex:  ( 2, –10   &   axis of symmetry: x = 2.

What is axis of symmetry ?

Axial symmetry is symmetry around an axis; an object is axially symmetric if its appearance is unchanged if rotated around an axis.

here, we have,

given that,

y = -2x² + 8x - 18

now,

x = -b/2a => -8/2(-2) => -8/-4 => 2

x = 2

now, we get,

Substitute 2 in for x in y = -2x² + 8x - 18

y = -2(2)² + 8(2) - 18

=> -2(4) + 16 - 18

=> -8 - 2

=> -10

i.e. y = -10

(x, y) = (2, -10)

so, we get,

Vertex: (2, -10)

Axis of Symmetry: x = 2

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Answer:

vertex:  ( 2, –10)

axis of symmetry: x = 2

Step-by-step explanation:

y = -2x² + 8x - 18

x = -b/2a => -8/2(-2) => -8/-4 => 2

x = 2

Substitute 2 in for x in y = -2x² + 8x - 18

y = -2(2)² + 8(2) - 18 => -2(4) + 16 - 18 => -8 - 2 => -10

y = -10

(x, y) = (2, -10)

Vertex: (2, -10)

Axis of Symmetry: x = 2