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11Alexandr11 [23.1K]
3 years ago
11

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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Which point on the graph shows the amount of water in the bucket after 1 second? Hint: Type your answer in the form (x coordinat
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):

0=m(0)+b

It follows that b=0

The equation now takes the form:

w=mt

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)}

6 0
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)=2​x

​​  vertically:

The domain, (−∞,∞) remains unchanged.

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

The y-intercept shifts down 3 units to (0,−2).

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

The range becomes (−3,∞).

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Answer:

C

Step-by-step explanation:

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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

x^{2}=2x+8

Step-by-step explanation:

Let

x -----> the number

we know that

The equation that represented the problem is equal to

x^{2}=2x+8

x^{2}-2x-8=0

Solve the quadratic equation by graphing

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

From the graph, we have the following ordered pairs

(x,y) = (0,270) and (1.5,80)

Given that:

y = ab^x

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ab^0=270

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Substitute 270 for a

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Divide both sides by 270

b^{1.5} = 0.2963

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<h3>(b) The factor at which the medicine decreased in the first half hour, and the first hour</h3>

In (a), we have:

The decay factor (b) to be 0.44

This represents the factor at which the medicine decreased throughout.

Hence, the medicine decrease in the first half hour, and the first hour at a factor of 0.44

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In (a), we have:

a= 270

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