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3 years ago

Which is equivalent to (2x^2y)(8x^3y^3)?

Mathematics

2 answers:

polet [3.4K]3 years ago

8 0

Answer: A

Step-by-step explanation: In order to answer this you need to understand the rules of exponents. Whenever you multiply two terms with the same base or variable you add the powers together. For example, 4x*2x = 8x^2 or x^4*x^2 = x^6. Any term with a negative exponent is equivalent to its reciprocal. For example x^-2 = 1/x^2.

Knowing this we expand this equation by multiplying. (2x^-2y) * (8x^-3y^-3) = 16x^-5y^-2. We now move the variables with negative exponents to the bottom. Giving us 16/(x^5y^2).

Fittoniya [83]3 years ago

3 0

4y =88 is your answer

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Given f(x)=2x^2+3x-5 for what values of x is f(x) positive

kow [346]

Answer:

The function f(x) is positive in the interval (-≠,-2.5) ∪ (1,∞)

Step-by-step explanation:

we have

$f(x)=2x^{2}+3x-5$

This is a vertical parabola open upward (the leading coefficient is positive)

The vertex is a minimum

The coordinates of the vertex is the point (h,k)

step 1

Find the vertex of the quadratic function

Factor the leading coefficient 2

$f(x)=2(x^{2}+\frac{3}{2}x)-5$

Complete the square

$f(x)=2(x^{2}+\frac{3}{2}x+\frac{9}{16})-5-\frac{9}{8}$

$f(x)=2(x^{2}+\frac{3}{2}x+\frac{9}{16})-\frac{49}{8}$

Rewrite as perfect squares

$f(x)=2(x+\frac{3}{4})^{2}-\frac{49}{8}$

The vertex is the point (-\frac{3}{4},-\frac{49}{8})

step 2

Find the x-intercepts (values of x when the value of f(x) is equal to zero)

For f(x)=0

$2(x+\frac{3}{4})^{2}-\frac{49}{8}=0$

$2(x+\frac{3}{4})^{2}=\frac{49}{8}$

$(x+\frac{3}{4})^{2}=\frac{49}{16}$

take the square root both sides

$x+\frac{3}{4}=\pm\frac{7}{4}$

$x=-\frac{3}{4}\pm\frac{7}{4}$

$x_1=-\frac{3}{4}+\frac{7}{4}=1$

$x_2=-\frac{3}{4}-\frac{7}{4}=-2.5$

therefore

The function f(x) is negative in the interval (-2.5,1)

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6 0

4 years ago

The sum of 14 ad a number is 17

Fiesta28 [93]

Answer:

x = 3

Step-by-step explanation:

The sum of 14 ad a number is 17

The sum of 14 and a number (represented by x)

14 + x

is 17

= 17

The sum of 14 and a number is 17

14 + x = 17

Now, let's solve this.

14 + x = 17

-14 -14

x = 3

6 0

3 years ago