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Kobotan [32]
2 years ago
10

Q2.a) Is the equality √a^4 = a valid for all values of a? Explain.​

Mathematics
1 answer:
allochka39001 [22]2 years ago
7 0

Answer:

The equality is only true for a = 0\ and\ 1, not for all values

Step-by-step explanation:

Given

(\sqrt a)^4 = a

Required

Determine if it is valid

(\sqrt a)^4 = a

Evaluate the exponent

(a^\frac{1}{2})^4 = a

a^\frac{1*4}{2} = a

a^2 = a

Rewrite as:

a^2 - a = 0

Factorize

a(a- 1) = 0

a =0\ or\ a - 1 = 0

a =0\ or\ a = 1

<em>The equality is only true for </em>a = 0\ and\ 1<em>, not for all values</em>

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15xy - 4 + 2xy -7xy - 1​
Eduardwww [97]

Answer:

10xy-5

Step-by-step explanation:

15xy-4+2xy-7xy-1 is the given expression.

I assume the directions say to simplify.

Group the xy terms together and group the constants together.

15xy+2xy-7xy-4-1

This is a demonstration of the commutative property.

Now I will use the distributive property to rewrite the first 3 terms as a multiplication:

(15+2-7)xy-5

10xy-5

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3 years ago
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Step-by-step explanation:

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3 years ago
After a dreary day of rain, the sun peeks through the clouds and a rainbow forms. You notice the rainbow is the shape of a parab
Gekata [30.6K]

We can answer the first part of the question not taking intersecting function into account. The domain of y=-x^{2}+36 is all the numbers, x∈(-∞, +∞) and the range is y∈(-∞, 36]. We can observe these results with the help of a graph, as well. Since we are talking about the rainbow, the values above the ground level will make sense. In this case, we will take into account the range as it changes between 0 and 36, included and the domain between -6 and 6. Here (0;36) is the y-intercept and (-6;0) and (6;0) are the x-intercepts of the parabola.


Since in our problem, the linear function that intersects parabola is not given, we have to provide it by ourselves according to the conditions of the problem. It could be any line intersecting parabola in two points. One important point is that the y-intercept has to be no more than 36. Considering these conditions, we can set our linear function to be y=0.5x+5. We can observe the points that we included in the table (they have been given with orange dots in the graph and the table is attached below). We can see that the values of the function (values of y) are positive. Indeed, we are discussing the part of the rainbow above the ground level.


The system of equations with linear and quadratic functions has got two solutions and we can observe that result from the graph. The solutions are (-5.823; 2.088) and (5.323; 7.662). The solutions are the intersection points.

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3 years ago
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Katena32 [7]
The answer looks like it's A.
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3 years ago
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