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prisoha [69]
3 years ago
6

During his vacation, Dalyn rents a small boat from a rental service that charges a flat fee of $30 plus $10 per hour (including

taxes). The total charge comes to $90. Which equation can be used to calculate the number of hours, x, that Dalyn rents the boat?
Mathematics
1 answer:
Helga [31]3 years ago
3 0
What’s they answers question then
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What is the coefficient of x2y3 in the expansion of (2x + y)5?
Zigmanuir [339]

Option C:

The coefficient of x^{2} y^{3} is 40.

Solution:

Given expression:

(2 x+y)^{5}

Using binomial theorem:

(a+b)^{n}=\sum_{i=0}^{n}\left(\begin{array}{l}n \\i\end{array}\right) a^{(n-i)} b^{i}

Here a=2 x, b=y

Substitute in the binomial formula, we get

(2x+y)^5=\sum_{i=0}^{5}\left(\begin{array}{l}5 \\i\end{array}\right)(2 x)^{(5-i)} y^{i}

Now to expand the summation, substitute i = 0, 1, 2, 3, 4 and 5.

$=\frac{5 !}{0 !(5-0) !}(2 x)^{5} y^{0}+\frac{5 !}{1 !(5-1) !}(2 x)^{4} y^{1}+\frac{5 !}{2 !(5-2) !}(2 x)^{3} y^{2}+\frac{5 !}{3 !(5-3) !}(2 x)^{2} y^{3}

                                                            $+\frac{5 !}{4 !(5-4) !}(2 x)^{1} y^{4}+\frac{5 !}{5 !(5-5) !}(2 x)^{0} y^{5}

Let us solve the term one by one.

$\frac{5 !}{0 !(5-0) !}(2 x)^{5} y^{0}=32 x^{5}

$\frac{5 !}{1 !(5-1) !}(2 x)^{4} y^{1} = 80 x^{4} y

$\frac{5 !}{2 !(5-2) !}(2 x)^{3} y^{2}= 80 x^{3} y^{2}

$\frac{5 !}{3 !(5-3) !}(2 x)^{2} y^{3}= 40 x^{2} y^{3}

$\frac{5 !}{4 !(5-4) !}(2 x)^{1} y^{4}= 10 x y^{4}

$\frac{5 !}{5 !(5-5) !}(2 x)^{0} y^{5}=y^{5}

Substitute these into the above expansion.

(2x+y)^5=32 x^{5}+80 x^{4} y+80 x^{3} y^{2}+40 x^{2} y^{3}+10 x y^{4}+y^{5}

The coefficient of x^{2} y^{3} is 40.

Option C is the correct answer.

5 0
3 years ago
Which explanation can be used to derive the formula for the circumference of a circle?
Gelneren [198K]

Answer: The answer is the first explanation.


Step-by-step explanation:  We are given five different options and we are to select which explanation is correct to derive the formula for a circumference of a circle.

Let 'C' be the circumference and 'd' be the diameter of a circle. Now, we will write the ratio of the circumference to the diameter as

\dfrac{\textup{C}}{\textup{d}}.

Also, we know that

\dfrac{\textup{C}}{\textup{d}}=\pi.

And diameter of a circle is twice the radius, so

d=2r.

Therefore,

\dfrac{\textup{C}}{2\textup{r}}=\pi\\\\\Rightarrow \textup{C}=2\pi \textup{r}.

This is the formula for the circumference of a circle. Since this explanation matches exactly with the first option, so the correct option is

(a). Find the relationship between the circumference and the diameter by dividing the length of the circumference and length of the diameter. Use this quotient to set up an equation to showing the ratio of the circumference over the diameter equals to π . Then rearrange the equation to solve for the circumference. Substitute 2 times the radius for the diameter.


8 0
3 years ago
SOMEONE HELP ME WITH THISS
Katen [24]

Answer:

/_ 12 is the angle of depression from the firefighter to the second story window.

Step-by-step explanation:

Hope it helps!

<em>#CarryOnLearning</em><em> </em>

7 0
2 years ago
Read 2 more answers
Find the circumference of the circle in terms of pi? [30]
son4ous [18]

Answer:

60π

Step-by-step explanation:

If the circle has radius of 30 units, substitute r=30 into the formula C = 2πr.

C = 2π(30)

C = 60π

3 0
3 years ago
Read 2 more answers
Which polynomial represents twice the sum of -5x^2-x+6 and 7x^2+x-1?
elena-14-01-66 [18.8K]

The polynomial that represent twice the sum of -5x^{2} - x +6 and 7x^{2} + x -1 is : 4x^{2}+10

<h3>What is a polynomial?</h3>

A polynomial is any  algebraic expression that has the least value of the power of  its variable as 2.

When the highest value of the polynomial is 2, it is a called a quadratic expression.

Analysis:

2( -5x^{2} -x +6 + 7x^{2} +x -1)

2( 2x^{2} + 5) =

4x^{2} + 10

In conclusion, the polynomial that represents the above  expressions is 4x^{2} + 10

Learn more about polynomials: brainly.com/question/2833285

#SPJ1

7 0
2 years ago
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