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3 years ago

7 meters/20 minutes= x cm/2 hours

Mathematics

1 answer:

meriva3 years ago

4 0

Answer:4,200

Step-by-step explanation:

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GalinKa [24]

Answer: umm

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2 years ago

How can we determine a slope?

zimovet [89]

slope formula: y2-y1/x2-x1

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3 years ago

How to find the derivative of e^3㏑(x²)

vovikov84 [41]

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7 0

3 years ago

PLEASE HELP NOW!!

Rufina [12.5K]

1. Carl's constant rate of speed is the slope of the straight line graph.

This straight line passes through: (0,0), (5,1), (10,2) etc

We can use the slope formula with any two points to find the slope of this line.

The slope formula is $m=\frac{y_2-y_1}{x_2-x_1}$ .

Let $(x_1,y_1)=(0,0)$ and $(x_2,y_2)=(5,1)$

Then $m=\frac{1-0}{5-0}$ , $\implies m=\frac{1}{5}$ .

Carl's speed is $\frac{1}{5}$ miles per minute.

But we must leave our answer in miles per hour

Hence Carl's speed is $\frac{1}{5}\times 60=12$ miles per hour

After 2 hours, Carl will travel $12\times 2=24$ miles.

2. The given line has equation $-4x+y=10$

We write this in slope-intercept form by solving for y.

$\implies y=4x+10$

This is in the form $y=mx+c$ , where $m=4$ is the slope.

When x=3, $y=4(3)+10$

$\implies y=12+10=22$

When x=3, y=22

3. The given straight line graph that models the situation passes through:

(0,0) and (20,30).

The slope of this line is $\frac{Rise}{Run}=\frac{300}{20}=15$

Therefore the rate is $ 15 per ticket.

If the theater sells 150 tickets, the earnings will be: $150\times 15=2,250$ dollars.

7 0

3 years ago

Solve (4x+y^5)^7 using binomial theorem

sweet [91]

Step-by-step explanation:

$\text{The binomial theorem:}\\\\(a+b)^n = \sum\limits_{k=0}^n {n \choose k}a^{n-k}b^k\\\\{n \choose k}=\dfrac{n!}{k!(n-k)!}$

$\text{We have}\ (4x+y^5)^7\Rightarrow a=4x,\ b=y^5,\ n=7.\\\\\text{Substitute:}\\\\(4x+y^5)^7={7\choose 0}(4x)^{7-0}(y^5)^0+{7\choose 1}(4x)^{7-1}(y^5)^1+{7\choose 2}(4x)^{7-2}(y^5)^2\\\\+{7\choose 3}(4x)^{7-3}(y^5)^3+{7\choose 4}(4x)^{7-4}(y^5)^4+{7\choose 5}(4x)^{7-5}(y^5)^5\\\\+{7\choose 6}(4x)^{7-6}(y^5)^6+{7\choose 7}(4x)^{7-7}(y^5)^7\\\\=(1)(4x)^7(y^5)^0+(7)(4x)^6(y^5)^1+(21)(4x)^5(y^5)^2+(35)(4x)^4(y^5)^3\\\\+(35)(4x)^3(y^5)^4+(21)(4x)^2(y^5)^5+(7)(4x)^1(y^5)^6+(1)(4x)^0(y^5)^7$

$=16384x^7+28672x^6+21504x^5y^{10}+8960x^4y^{15}\\\\+2240x^3y^{20}+336x^2y^{25}+28xy^{30}+y^{35}$

$\text{Used}\\\\(a^n)^m=a^{nm}\\\\a^0=1$

3 0

3 years ago