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VLD [36.1K]
2 years ago
10

Simplify the following exponential expressions:

Mathematics
2 answers:
slava [35]2 years ago
8 0
30y 1# 24x^7 2# 105m^7 3#.
zhannawk [14.2K]2 years ago
5 0

Answer:

See below

Step-by-step explanation:

1. \: 6 {y}^{3}  \times 5 {y}^{6}  \\  = 6 \times 5 \times  {y}^{3 + 6}   \\ = 30 {y}^{9}  \\  \\ 2. \: 8 {x}^{5}  \times 3 {x}^{2}   \\ = 8 \times 3 \times  {x}^{5 + 2}   \\ = 24 {x}^{7}  \\  \\ 3. \: 7m^4  \times  3m  \times  5m^2  \\ = 105 {m}^{4 + 1 + 2}   \\ = 105 {m}^{7}  \\  \\ 4. \: 10d^7  \times  5d^0 \\  = 10 \times 5 \times  {d}^{7 + 0}  \\  = 50 {d}^{7}

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C. $128

Step-by-step explanation:

320 x 0.5 = 160

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2 years ago
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In Problems 23–30, use the given zero to find the remaining zeros of each function
Talja [164]

Answer:

x =  2i, x = -2i and x = 4 are the roots of given polynomial.

Step-by-step explanation:

We are given the following expression in the question:

f(x) = x^3 - 4x^2+ 4x - 16

One of the zeroes of the above polynomial is 2i, that is :

f(x) = x^3 - 4x^2+ 4x - 16\\f(2i) = (2i)^3 - 4(2i)^2+ 4(2i) - 16\\= -8i+ 16+8i-16 = 0

Thus, we can write

(x-2i)\text{ is a factor of polynomial }x^3 - 4x^2 + 4x - 16

Now, we check if -2i is a root of the given polynomial:

f(x) = x^3 - 4x^2+ 4x - 16\\f(-2i) = (-2i)^3 - 4(-2i)^2+ 4(-2i) - 16\\= 8i+ 16-8i-16 = 0

Thus, we can write

(x+2i)\text{ is a factor of polynomial }x^3 - 4x^2 + 4x - 16

Therefore,

(x-2i)(x+2i)\text{ is a factor of polynomial }x^3 - 4x^2 + 4x - 16\\(x^2 + 4)\text{ is a factor of polynomial }x^3 - 4x^2 + 4x - 16

Dividing the given polynomial:

\displaystyle\frac{x^3 - 4x^2 + 4x - 16}{x^2+4} = x -4

Thus,

(x-4)\text{ is a factor of polynomial }x^3 - 4x^2 + 4x - 16

X = 4 is a root of the given polynomial.

f(x) = x^3 - 4x^2+ 4x - 16\\f(4) = (4)^3 - 4(4)^2+ 4(4) - 16\\= 64-64+16-16 = 0

Thus, 2i, -2i and 4 are the roots of given polynomial.

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3 years ago
Find the length of XY
Pachacha [2.7K]

Since this is a right triangle, you can use the pythagorean theorem, leg^2+leg^2=hypotenuse^2, to find XY. Since we know that 15 and 17 are our legs and that XY is the hypotenuse, we can solve it as such:

15^2+17^2=XY^2\\ 225+289=XY^2\\ 514=XY^2\\ \sqrt{514}=XY

In short, XY is √514, or 22.67 rounded to the hundreths, units long.

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