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lara [203]
3 years ago
11

After 10 weeks of work, bob has $1200. After 15 weeks of work Bob has $1800. After 20 weeks of work Bob has $2400. Write the fir

s four terms of a sequence that represents this situation. Writ and equation to model the situation
Mathematics
1 answer:
lozanna [386]3 years ago
7 0

Answer:

1200,1800,2400,3000

5x = 600x

Step-by-step explanation:

The first four terms would be

1200,1800,2400,3000

As we can see that

After 10 weeks of work bob has $1200

After 15 weeks of work, bob has $1,800

So the more the weeks would be, the more the earnings it is

And, the difference of the earnings is

= $1,800 -$1,200

= $600

The equation would be

5x = 600x

So if we assume x = 1

So

5 = 600

if we assume x = 2

So

10 = 1200

and so on

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Serga [27]

\bf \textit{exponential form of a logarithm} \\\\ \log_a b=y \implies a^y= b\qquad\qquad a^y= b\implies \log_a b=y \\\\\\ \begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} ~\hspace{7em} \begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ log_a a^x = x\qquad \qquad \stackrel{\textit{we'll use this one}}{a^{log_a x}=x} \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}

\bf \log_2(x-1)=\log_8(x^3-2x^2-2x+5) \\\\\\ \log_2(x-1)=\log_{2^3}(x^3-2x^2-2x+5) \\\\\\ \log_{2^3}(x^3-2x^2-2x+5)=\log_2(x-1) \\\\\\ \stackrel{\textit{writing this in exponential notation}}{(2^3)^{\log_2(x-1)}=x^3-2x^2-2x+5}\implies (2)^{3\log_2(x-1)}=x^3-2x^2-2x+5

\bf (2)^{\log_2[(x-1)^3]}=x^3-2x^2-2x+5\implies \stackrel{\textit{using the cancellation rule}}{(x-1)^3=x^3-2x^2-2x+5} \\\\\\ \stackrel{\textit{expanding the left-side}}{x^3-3x^2+3x-1}=x^3-2x^2-2x+5\implies 0=x^2-5x+6 \\\\\\ 0=(x-3)(x-2)\implies x= \begin{cases} 3\\ 2 \end{cases}

5 0
3 years ago
The equation of a parabola is y=x^2-10x+27. Write the equation in vertex form
azamat

Answer:

\large \boxed{y = (x - 5)^{2} + 2 }

Step-by-step explanation:

y = x² - 10x + 27

y = ax² + bx + c

This is the general form of the equation for a parabola.

We must convert it to the vertex form

y = (x - h)² + k, where (h,k) are the coordinates of the vertex.

We can do this by completing the square.

\begin{array}{rcll}y & = & x^{2} - 10x + 27 & \\y - 27 & = & x^{2} - 10x & \text{Subtracted 27 from each side}\\y - 27&= & x^{2} - 10x + 25 - 25 & \text{Added and subtracted (b/2)}^{2}\\y - 27&= & (x - 5)^{2} - 25 & \text{Wrote the first three terms as the square of a binomial}\\y& = & \mathbf{(x - 5)^{2} + 2} & \text{Added 27 to each side}\\\end{array}\\\text{The vertex form of the parabola is $\large \boxed{\mathbf{y = (x - 5)^{2} + 2 }}$}The figure below shows that your parabola has its vertex at (5,2).

4 0
4 years ago
Please help me!
OLEGan [10]
You need to find 7 1/2% of $29.95.
To do that, just multiply the percent by the number.

7 1/2% * $29.95 =

= 7.5% * $29.95

= 0.075 * $29.95

= $2.24625

The answer is $2.25
7 0
4 years ago
Which is NOT true regarding the hypotenuse? *
Usimov [2.4K]

Answer:

It helps form the right angle = FALSE

Step-by-step explanation:

The legs form the angle

6 0
3 years ago
The sum of two numbers is 51 and the difference is 27. What are the numbers?
Bezzdna [24]

Answer:

26

Step-by-step explanation:

50-20=30+1=31-7=26

5 0
3 years ago
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