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pickupchik [31]
1 year ago
6

Emily and her family are planning to fly to Italy over the summer. If they fly out from LAX, the distance of the trip will be 6,

343 miles. If the time to travel 6,343 miles is 9 hours, what is the speed,that the plane traveled at ?
Mathematics
1 answer:
Iteru [2.4K]1 year ago
8 0

The speed is the ratio between the distance and the time:

s=\frac{d}{t}

Data:

d=6343miles

t=9h

s=\frac{6343\text{miles}}{9h}=704.77\frac{miles}{h}Then, the plane traveled at a speed of 704.77 miles per hour.

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Polynomial expressions with matching​
yuradex [85]

Answer:

The difference of 27x³ and 8y³ → [3x - 2y][9x² + 6xy + 4y²]

The difference of 27x³ and 64y³ → [3x - 4y][9x² + 12xy + 16y²]

The sum of 27x³ and 64y³ → [3x + 4y][9x² - 12xy + 16y²]

The sum of 27x³ and 8y³ → [3x + 2y][9x² - 6xy + 4y²]

Step-by-step explanation:

For the first two, we use the Difference of Cubes [(a³ - b³)(a² + 2ab + b²)] first by taking the cube root of the given expression to get our first factor[s]:

\displaystyle 3x - 2y = \sqrt[3]{27x^3 - 8y^3} \\ 3x - 4y = \sqrt[3]{27x^3 - 64y^3}

Then, use the acronym of SOAP {whether the next operations symbols will be negative or positive [SAME (your cube-rooted factor has an IDENTICAL OPERATION SYMBOL as your given expression), OPPOSITE (the first sign in your second factor in the second set of parentheses will be the opposite of what the sign in your given expression, which will be a plus sign), ALWAYS POSITIVE (the last sign in your second factor in the second set of parentheses will ALWAYS stay positive NO MATTER WHAT)]} to get the second factor:

Given: 27x³ - 64y³

[3x - 4y][9x² + 12xy + 16y²]

↑ ↑ ↑

same as opposite ALWAYS POSITIVE

given of given

Given: 27x³ - 8y³

[3x - 2y][9x² + 6xy + 4y²]

↑ ↑ ↘

same as opposite ALWAYS POSITIVE

given of given

Now, for the last two, we use the Sum of Cubes [(a³ + b³)(a² - 2ab + b²)] first by taking the cube root of the given expression to get our first factor[s]:

\displaystyle 3x + 2y = \sqrt[3]{27x^3 + 8y^3} \\ 3x + 4y = \sqrt[3]{27x^3 + 64y^3}

Then, use the acronym of SOAP {whether the next operations symbols will be negative or positive [SAME (your cube-rooted factor has an IDENTICAL OPERATION SYMBOL as your given expression), OPPOSITE (the first sign in your second factor in the second set of parentheses will be the opposite of what the sign is in your given expression, which will be a minus sign), ALWAYS POSITIVE (the last sign in your second factor in the second set of parentheses will ALWAYS stay positive NO MATTER WHAT)]} to get the second factor:

Given: 27x³ + 64y³

[3x + 4y][9x² - 12xy + 16y²]

↑ ↑ ↘

same as opposite ALWAYS POSITIVE

given of given

Given: 27x³ + 8y³

[3x + 2y][9x² - 6xy + 4y²]

↑ ↑ ↘

same as opposite ALWAYS POSITIVE

given of given

I am delighted to assist you anytime!

* As you can see, when using the <em>Difference\Sum of Cubes</em>, SOAP can vary depending on how an expression is given to you. They resemble each other though.

6 0
3 years ago
I have 3/5 of work and i complete 1/5 how much is left
9966 [12]
I hope this helps you




3/5-1/5=2/5
5 0
3 years ago
-4^6•4^2/4^4<br><br> Simplify
elena-14-01-66 [18.8K]

Answer:

-4^{4}

Step-by-step explanation:

Reduce the expression -4^2×4^2

Calcualte the product and you get -4^4

If you want the alternative form is will be -256

Hope this helpsʕ•ᴥ•ʔ

6 0
3 years ago
14 more than the prouduct of the three and nine
Varvara68 [4.7K]
41
3 times 9 is 27
27+14=41
5 0
3 years ago
Read 2 more answers
Find the area of the shaded figure. Give answer in decimal to the hundredth place.
Firdavs [7]

Answer:

13.5

Step-by-step explanation:

72/(16/3)

6 0
3 years ago
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