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fredd [130]
3 years ago
6

Julia can finish a 20-mile bike ride in 1.2 hours. Katie can finish the same bike ride in 1.6 hours. To the nearest tenth of a m

ile, how much faster does Julia ride than Katie?
Mathematics
1 answer:
Brums [2.3K]3 years ago
4 0

Answer:

Step-by-step explanation:

julia : 20 miles in 1.2 hrs = (20/1.2) = 16.67 miles per hr

katie : 20 miles in 1.6 hrs = (20 / 1.6) = 12.5 miles per hr

how much faster does julia ride then katie...

16.67 - 12.5 = 4.17 rounds to 4.2 miles per hr faster <==

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1-69.
timofeeve [1]

The question above was not written properly

Complete Question

Lacey and Haley are rewriting expressions in an equivalent, simpler form.

a. Haley simplified x³⋅ x² and got

x⁵

Lacey simplified x³ + x² and got the same result! However, their teacher told them that only one simplification is correct. Who simplified correctly and how do you know?

b. Haley simplifies 3⁵⋅ 4⁵ and gets the result 12^10, but Lacey is not sure.

Is Haley correct? Be sure to justify your answer.

Answer:

a) Haley is correct, Lacey simplified wrongly.

b) Haley is incorrect

Step-by-step explanation:

a. Haley simplified x³⋅ x² and got

x⁵

Lacey simplified x³ + x² and got the same result! However, their teacher told them that only one simplification is correct. Who simplified correctly and how do you know?

For Question a, when it comes to simplifying algebraic expression that has to do with powers, there are certain rules that should be followed.

For example

x^a × x^b = x^(a + b)

For Haley, she simplified x³⋅ x² and got

x⁵

She is correct because this follows the product rule of powers or exponents above

= x³⋅ x² = x³+² = x⁵

For Lacey she is wrong because:

x³ + x² ≠ x⁵

x³ + x² when simplified as quadratic equation = x²(x + 1)

b. Haley simplifies 3⁵⋅ 4⁵ and gets the result 12^10, but Lacey is not sure.

Is Haley correct? Be sure to justify your answer.

For question b, when we have two distinct or different numbers with the same power(exponents) the rule states that:

x^a × y^a = (x × y)^a = (xy)^a

Haley is simplified wrongly. She did not apply the rule above

Haley simplified 3⁵⋅ 4⁵ = (3 × 4) ⁵+⁵

= 12^10, this is wrong.

The correct answer according to the rule =

3⁵⋅ 4⁵ = (3 × 4) ⁵ = 12⁵

Therefore,

3⁵⋅ 4⁵ ≠ 12^10

3⁵⋅ 4⁵ = 12⁵

Haley is wrong.

3 0
3 years ago
Simplify quantity 1 over 36 minus 1 over x squared all over 1 over 6 plus 1 over x.
Ne4ueva [31]
 <span>[ (1 / 36) - (1 / x²) ] / [ (1 / 6) + (1 / x) ] 

[ (x² - 36) / 36x² ] / [ (x + 6) / 6x ] 

</span>remember that<span>: 
x² - 36 = (x + 6)(x - 6) 

so

[ (x+6)(x-6) / 36x² ] / [ (x + 6) / 6x ] 


[ (x+6)(x-6) / 36x² ] * [ 6x / (x + 6) ] 


6x / 36x² = 1 / 6x 


[ (x+6)(x-6) / 6x ] * [ 1 / (x+6) ] -------------------- > </span>(x - 6) / 6x<span>

The answer is </span>(x - 6) / 6x<span>

</span>
7 0
3 years ago
|3x-7| + 7 = 9 What is the first solution?<br><br> Plzzz help
posledela

Answer:

  • 3 and 5/3

Step-by-step explanation:

<u>Solving in steps:</u>

  • |3x-7| + 7 = 9
  • |3x-7|  = 2

<u>1. If 3x - 7 > 0</u>

  • 3x - 7 = 2
  • 3x = 9
  • x = 3

<u>2.  If 3x - 7 < 0</u>

  • 3x - 7 = -2
  • 3x = 5
  • x = 5/3
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\frac{11x}{11y} =\frac{x}{y}
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What is the solution set of the compound inequality 3.5x - 10&gt; -3 and 8x -9 &lt;39
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I need to answer two questions in order to ask a question. sorry that i’m stupid and have no idea how to do this
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