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lina2011 [118]
3 years ago
5

Simplify the expression.

Mathematics
1 answer:
mr Goodwill [35]3 years ago
5 0

Answer:

x^{\frac{1}{2}}

Step-by-step explanation:

we have

(x^{\frac{1}{6}})^{3}

Applying the rule power

(b^{n})^{m}=b^{n*m}

(x^{\frac{1}{6}})^{3}=(x^{\frac{1}{6}*3})=x^{\frac{3}{6}}

Simplify

x^{\frac{1}{2}}

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Write an equation for a quadratic function that has x intercepts (-3, 0) and (5, 0)
Blizzard [7]

Answer:

One possible equation is f(x) = (x + 3)\, (x - 5), which is equivalent to f(x) = x^{2} - 2\, x - 15.

Step-by-step explanation:

The factor theorem states that if x = x_{0}  (where x_{0} is a constant) is a root of a function, (x - x_{0}) would be a factor of that function.

The question states that (-3,\, 0) and (5,\, 0) are x-intercepts of this function. In other words, x = -3 and x = 5 would both set the value of this quadratic function to 0. Thus, x = -3\! and x = 5\! would be two roots of this function.

By the factor theorem, (x - (-3)) and (x - 5) would be two factors of this function.

Because the function in this question is quadratic, (x - (-3)) and (x - 5) would be the only two factors of this function. In other words, for some constant a (a \ne 0):

f(x) = a\, (x - (-3))\, (x - 5).

Simplify to obtain:

f(x) = a\, (x + 3)\, (x - 5).

Expand this expression to obtain:

f(x) = a\, (x^{2} - 2\, x - 15).

(Quadratic functions are polynomials of degree two. If this function has any factor other than (x - (-3)) and (x - 5), expanding the expression would give a polynomial of degree at least three- not quadratic.)

Every non-zero value of a corresponds to a distinct quadratic function with x-intercepts (-3,\, 0) and (5,\, 0). For example, with a = 1:

f(x) = (x + 3)\, (x - 5), or equivalently,

f(x) = x^{2} - 2\, x - 15.

6 0
2 years ago
If 10x+6y=7 is a true equation, what would be the value of 6(10x+6y)?
aleksandr82 [10.1K]

Answer:

42

Step-by-step explanation:

We know that 10x + 6y = 7, and so

6(10x + 6y) = 6(7) = 42

8 0
3 years ago
Katherine has $140 in the bank and is saving $6 per week. Abbie has $462 in the bank, but is spending at a rate of $10 per week.
AveGali [126]
Let x be the number of weeks for this financial situation. The amount that Katherine will have at the end of x weeks is 140 + 6x. On the other hand, with the spending that she is doing, Abbie will have 462 - 10x after x weeks. Equating the two,
                                     140 + 6x = 462 - 10x
Thus, the answer is letter B. 
3 0
3 years ago
Read 2 more answers
***TEN POINTS*** Answer the questions. Deals with functions.
forsale [732]

Answer:

f(x) = 250x + 1300

hope this helped and brainliest please (im only ~90 percent sure though, don’t give me brainliest if wrong)

5 0
3 years ago
Read 2 more answers
Help me please!!!<br><br> ASAP!!
Leno4ka [110]

Answer:

Hello with the simplified expression the answer is 2

Step-by-step explanation:

7 0
2 years ago
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