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3 years ago

Simplify

Mathematics

2 answers:

Marta_Voda [28]3 years ago

6 0

Answer:

x⁸y³

Step-by-step explanation:

x⁵ ÷ y² × x³ × y⁵

It will be easier to solve this problem if you first rearrange the expression to associate like terms.

(x⁵ × x³) × (y⁵ ÷ y²)

Now, you can use the rules of exponents: When multiplying, you add exponents; when dividing, you subtract exponents.

x⁵ × x³ = x⁵⁺³ = x⁸

y⁵ ÷ y² = y⁵⁻² = y³

Thus,

(x⁵ × x³) × (y⁵ ÷ y²) = x⁸y³

jeka57 [31]3 years ago

4 0

$\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ x^5\div y^2\times x^3\times y^5\implies \cfrac{x^5}{y^2}\cdot x^3\cdot y^5\implies x^5\cdot y^{-2}\cdot x^3\cdot y^5 \\\\\\ x^{5+3}y^{-2+5}\implies x^8y^3$

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Taya2010 [7]

Answer:

$\displaystyle \left(1,\frac{5}{12}\right)$

Step-by-step explanation:

<u>Graphs</u>

The graph shows the amount of water in gallons as a function of time in seconds.

We are required to find the amount of water in the bucked after 1 second. Since the graph does not show an exact location for t=1, we must find the equation of the line.

Two points are clear on the graph: (0,0) (12,5). This gives us the necessary information to find the equation of the line, which has the form:

$w=mt+b$

Where w is the amount of water in the bucket, t is the time, and m and b are two constants to be determined.

Using the point (0,0):

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Using the point (12,5):

$5=m(12)$

We find m:

$\displaystyle m=\frac{5}{12}$

The final equation is:

$\displaystyle w=\frac{5}{12}\cdot t$

Substituting t=1:

$\displaystyle w(1)=\frac{5}{12}\cdot (1)=\frac{5}{12}$

The bucket has 5/12 gallons of water at t=1 second. Expressing the answer as an ordered pair:

$\boxed{\displaystyle \left(1,\frac{5}{12}\right)}$

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3 years ago

Let f(x) be an exponential functionWhich transformations to the graph of f(x) would describe e - f(x - 3) ?

gayaneshka [121]

Look at the graph below carefully

Observe the results of shifting ={2}^{x}f(x)=2x

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The domain, (−∞,∞) remains unchanged.

When the function is shifted up 3 units to ={2}^{x}+3g(x)=2x +3:

The y-intercept shifts up 3 units to (0,4).

The asymptote shifts up 3 units to y=3y=3.

The range becomes (3,∞).

When the function is shifted down 3 units to ={2}^{x}-3h(x)=2 x −3:

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The asymptote also shifts down 3 units to y=-3y=−3.

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2 years ago

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jenyasd209 [6]

Answer:

Step-by-step explanation:

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3 years ago

Write an equation for each problem. The square of a number is 8 more than twice the number.

avanturin [10]

Answer:

The equation is equal to

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Step-by-step explanation:

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3 years ago

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<h3>(a) The factor at which the medicine decreased, in 1.5 hour</h3>

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Read more about exponential equations at:

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2 years ago