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Bezzdna [24]
2 years ago
13

Find the product with the exponent in simplest form.

Mathematics
1 answer:
nordsb [41]2 years ago
7 0

Answer:

x = 7 , y = 12

Step-by-step explanation:

using the rule of exponents

a^{m} × a^{n} = a^{(m+n)}

consider left side

6^{\frac{1}{3} } × 6^{\frac{1}{4} }

= 6^{(\frac{1}{3}+\frac{1}{4})  }

= 6^{(\frac{4}{12}+\frac{3}{12})  }

= 6^{\frac{7}{12} } = 6^{\frac{x}{y} } , comparing exponents , then

x = 7 and y = 12

You might be interested in
The polynomial $f(x)$ has degree 3. If $f(-1) = 15$, $f(0)= 0$, $f(1) = -5$, and $f(2) = 12$, then what are the $x$-intercepts o
Alex_Xolod [135]

Your calculator's cubic regression function can tell you the equation is

... f(x) = 2x³ + 5x² -12x = x(x +4)(2x-3)

The x-intercepts are -4, 0, +1.5.

_____

If you want to solve this "by hand", you can first of all recognize that since there is an x-intercept at 0, the cubic will only have three coefficients. That is, you can write the equation as

... f(x) = ax³ + bx² + cx

Substituting the given points (except (0, 0)) gives three linear equations in a, b, c.

... -a +b -c = 15 . . . . . for x=-1

... a + b + c = -5 . . . . for x=1

... 8a +4b +2c = 12 . . for x=2

adding the first two equations gives 2b=10, or b=5. Now, you can reduce the system to

... a + c = -10

... 4a +c = -4

Subtracting the first of these equations from the second gives 3a=6, or a=2. That tells you c=-12 (from a+c=10).

Then your equation is

... f(x) = x(2x² +5x -12)

Factoring by any of the usual techniques, or graphing, or using the quadratic formula will tell you the zeros (x-intercepts) are as above.

_____

Since the input values are sequential, you can also develop the function from differences of the output values. Those are 15, 0, -5, 12. First differences are -15, -5, +17. Second differences are +10, +22. The third difference is 12. Using the first of these differences in appropriate places in the interpolating polynomial formula, we have

... f(x) = 15 + (x+1)(-15 + (x)/2·(10 + (x-1)/3·(12))) = 2x³ +5x² -12x . . . . as above

4 0
2 years ago
Farmer Jonson is putting together vegetable baskets. He has 270 carrots and 180 beets. What is the largest number of baskets he
Nostrana [21]
Factors of 180:

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180.


Factors of 270:

1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270.


What are the factors of both 270 and 180?

1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90.

Which one of these would give us the greatest amount of baskets possible?

Answer: 90 baskets.

I hope this helped you! c:
4 0
3 years ago
Need help for question 3! 98 points and brainliest!
Softa [21]

1: $68

2: 45(5)=225

-TTL

6 0
3 years ago
Read 2 more answers
5x +y=8
makvit [3.9K]
Take away the bottom equation from the top so the y’s cancel out
3x = -24
x therefore = -8
and put x back into the equation to find out y
2(-8) + y= 32
-16 + y =32
y= 48
6 0
2 years ago
Solve the system of equations for the variables: x+2y-z=3 x+y-2z= -1
8_murik_8 [283]

Answer:

z=0

x= -5

y=4

Step-by-step explanation:

Check the attachment please

Hope this helps :)

4 0
3 years ago
Read 2 more answers
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