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guajiro [1.7K]
2 years ago
15

3. Serena is the manager of the coffee shop. The amount of money she earns is represented by the equation = 21ℎ, where ℎ is the

number of hours Serena works, and is the amount of money she earns. How much more money does Serena make an hour than Gabe?
Mathematics
2 answers:
spin [16.1K]2 years ago
7 0
I don't think this can be answered without any information on Gabe
WARRIOR [948]2 years ago
5 0
Since Gabe is earning 13.50 dollars an hour, we can just subtract 13.50 from 21 to get the amount Serena gets more.

Serena is currently getting paid $7.50 more per hour.
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andrey2020 [161]

First observe that if a+b>0,

(a + b)^2 = a^2 + 2ab + b^2 \\\\ \implies a + b = \sqrt{a^2 + 2ab + b^2} = \sqrt{a^2 + ab + b(a + b)} \\\\ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b(a+b)}} \\\\ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b(a+b)}}} \\\\ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{\cdots}}}}

Let a=0 and b=x. It follows that

a+b = x = \sqrt{x \sqrt{x \sqrt{x \sqrt{\cdots}}}}

Now let b=1, so a^2+a=4x. Solving for a,

a^2 + a - 4x = 0 \implies a = \dfrac{-1 + \sqrt{1+16x}}2

which means

a+b = \dfrac{1 + \sqrt{1+16x}}2 = \sqrt{4x + \sqrt{4x + \sqrt{4x + \sqrt{\cdots}}}}

Now solve for x.

x = \dfrac{1 + \sqrt{1 + 16x}}2 \\\\ 2x = 1 + \sqrt{1 + 16x} \\\\ 2x - 1 = \sqrt{1 + 16x} \\\\ (2x-1)^2 = \left(\sqrt{1 + 16x}\right)^2

(note that we assume 2x-1\ge0)

4x^2 - 4x + 1 = 1 + 16x \\\\ 4x^2 - 20x = 0 \\\\ 4x (x - 5) = 0 \\\\ 4x = 0 \text{ or } x - 5 = 0 \\\\ \implies x = 0 \text{ or } \boxed{x = 5}

(we omit x=0 since 2\cdot0-1=-1\ge0 is not true)

3 0
1 year ago
How many terms are in the expression<br><br> a3 + 3a2b - 4b - 11b + 7<br><br> 5<br> 6<br> 4<br> 7
Contact [7]

Answer:

there are 5 terms!

Step-by-step explanation:

trust me

6 0
2 years ago
What is an equivalent expression for (x + 7)(x + 1).
kakasveta [241]

Answer:

x2−8x 7

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Please explain step by step for 0.67÷0.3=?
pentagon [3]
Multiply each of the numbers by a ten to a power that they both become whole numbers.

0.67 * 10^2 = 67
0.3 * 10^2 = 30

Divide as usual.

67 / 30 = 2 \frac{1}{3}

So, the answer is 2 1/3.
3 0
3 years ago
Evaluate 48×15^2-5^2×2×24 by using factorisation and algebraic identities.
nikklg [1K]

Step-by-step explanation:

9600

This is your answer

4 0
2 years ago
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