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2 years ago

Can someone help me this is Algebra 2 thank you

Mathematics

1 answer:

ratelena [41]2 years ago

5 0

Answer:

Order of exponentiation can be swapped here, and the fractional power written as a root.

Step-by-step explanation:

The commutative property of multiplication and the rules of exponents apply.

<h3>Product of exponents</h3>

The rule is ...

(a^b)^c = a^(bc)

<h3>Application</h3>

The given expression can be rearranged to ...

$\left(3^\frac{1}{5}\right)^2=3^{\frac{1}{5}\cdot2}=3^{2\cdot\frac{1}{5}}=\left(3^2\right)^\frac{1}{5}\\\\=9^\frac{1}{5}=\boxed{\sqrt[5]{9}}$

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Write each of the following decimals in words.

Sergeeva-Olga [200]

A. nine hundredths

B. Thirty five hundredths

C. Seven Tenths

D. Three Thousandths

E. One Hundred Fourty five Thousandths

F. Fifty Nine Ten Thousandths

8 0

3 years ago

Find the vertex of the graph of the function.

lapo4ka [179]

Answer: The correct options are (1) (5,10), (2) (3,-3), (3) x = -1, (4) $y=(x+2)^2+3$ , (5) 21s and (6) 0, -1, and 5.

Explanation:

Te standard form of the parabola is,

$f(x)=a(x-h)^2+k$ .....(1)

Where, (h,k) is the vertex of the parabola.

(1)

The given equation is,

$f(x)=(x-5)^2+10$

Comparing this equation with equation (1),we get,

$h=5$ and $k=10$

Therefore, the vertex of the graph is (5,10) and the fourth option is correct.

(2)

The given equation is,

$f(x)=3x^2-18x+24$

$f(x)=3(x^2-6x)+24$

To make perfect square add $(\frac{b}{2a})^2$ , i.e., $9$ . Since there is factor 3 outside the parentheses, so subtract three times of 9.

$f(x)=3(x^2-6x+9)+24-3\times 9$

$f(x)=3(x-3)^2-3$

Comparing this equation with equation (1),we get,

$h=3$ and $k=-3$

Therefore, the vertex of the graph is (3,-3) and the fourth option is correct.

(3)

The given equation is

$f(x)=4x^2+8x+7$

$f(x)=4(x^2+2x)+7$

To make perfect square add $(\frac{b}{2a})^2$ , i.e., $1$ . Since there is factor 4 outside the parentheses, so subtract three times of 1.

$f(x)=4(x^2+2x+1)+7-4$

$f(x)=4(x+1)^2+3$

Comparing this equation with equation (1),we get,

$h=-1$ and $k=3$

The vertex of the equation is (-1,3) so the axis is x=-1 and the correct option is 2.

(4)

The given equation is,

$y=x^2+4x+7$

To make perfect square add $(\frac{b}{2a})^2$ , i.e., $2^2$ .

$f(x)=x^2+4x+4+7-4$

$f(x)=(x+2)^2+3$

Therefore, the correct option is 4.

(5)

The given equation is,

$h=-16t^2+672t$

It can be written as,

$h=-16(t^2-42t)$

It is a downward parabola. so the maximum height of the function is on its vertex.

The x coordinate of the vertex is,

$x=\frac{b}{2a}$

$x=\frac{42}{2}$

$x=21$

Therefore, after 21 seconds the projectile reach its maximum height and the correct option is first.

(6)

The given equation is,

$f(x)=3x^3-12x^2-15x$

$f(x)=3x(x^2-4x-5)$

Use factoring method to find the factors of the equation.

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

$f(x)=3x(x(x-5)+1(x-5))$

$f(x)=3x(x-5)(x+1)$

Equate each factor equal to 0.

$x=0,-1,5$

Therefore, the zeros of the given equation is 0, -1, 5 and the correct option is 2.

3 0

3 years ago

Please don't take this down, it's just an innocent question

hichkok12 [17]

Answer:

False

Step-by-step explanation:

You can only get a two by rolling 2 ones

you can get a three by rolling a 1 and 2

They both only have 1 option to roll on too. So the answer is false, with 2 die the probibility will be the same.

4 0

3 years ago

Usain Bolt of Jamaica set a world record in 2009 for the 200- meter dash with a time of 19.19 seconds. What was his average spee

kirill [66]

Answer:

His average speed was of 10.42 m/s

Step-by-step explanation:

We use the following relation to solve this question:

$v = \frac{d}{t}$

In which v is the velocity(in m/s), d is the distance(in meters), and t is the time, in seconds.

Usain Bolt of Jamaica set a world record in 2009 for the 200- meter dash with a time of 19.19 seconds.

This means that $d = 200, t = 19.19$

So his average speed was of:

$v = \frac{d}{t} = \frac{200}{19.19} = 10.42$

His average speed was of 10.42 m/s

6 0

3 years ago

Lisa gets paid $8 an hour for babysitting. She usually earns $60 to $70 each weekend, but last weekend she only earned $32. Whic

Harrizon [31]

C. Lisa's lower pay was caused by babysitting for fewer hours

5 0

3 years ago