PLEASE HELP

A) What is the y-intercept of y = 3x ?<br> (b) What is the slope of y = -x - 2 ?

JulijaS [17]

Answer:Q. How would you write the equation with a slope of 2/3 and a y-intercept of -3. answer choices. y=3/2x+3. y=2/3-3. y=2/3x-3. y=2/3x+3. Tags: Question 11.

Step-by-step explanation:

THATS IT I THINK sorry caps

5 0

3 years ago

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Harold wrote this equation to model the level of water in a pool over time. The variable x represents time in hours. f(x) = 3,50

lina2011 [118]

Answer:

The water level is falling.

The initial level of water in the pool was 3,500 units

The water was 2,600 units high after 4 hours.

Step-by-step explanation:

The given function that models the water level is

$f(x)=3,500-225x$

where $x$ represents time in hours.

The function represents a straight line that has slope $m=-225$

Since the slope is negative, it means the water level is falling.

The initial level of water in the pool can found when we put $x=0$ into the function.

$f(0)=3,500-225(0)$

$f(0)=3,500$ , hence the initial level is 3,500.

To determine the level of water in the pool after 14 hours, we put $x=14$ into the equation to get;

$f(14)=3,500-225(14)$

$f(14)=3,500-3150$

$f(14)=350$

To determine the water level after 4 hours we put $x=4$

$f(4)=3,500-225(4)$

$f(4)=3,500-900$

$f(14)=2,600$

4 0

3 years ago

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Determine the formula for the nth term of the sequence:<br>-2,1,7,25,79,...

rodikova [14]

A plausible guess might be that the sequence is formed by a degree-4* polynomial,

$x_n = a n^4 + b n^3 + c n^2 + d n + e$

From the given known values of the sequence, we have

$\begin{cases}a+b+c+d+e = -2 \\ 16 a + 8 b + 4 c + 2 d + e = 1 \\ 81 a + 27 b + 9 c + 3 d + e = 7 \\ 256 a + 64 b + 16 c + 4 d + e = 25 \\ 625 a + 125 b + 25 c + 5 d + e = 79\end{cases}$

Solving the system yields coefficients

$a=\dfrac58, b=-\dfrac{19}4, c=\dfrac{115}8, d = -\dfrac{65}4, e=4$

so that the n-th term in the sequence might be

$\displaystyle x_n = \boxed{\frac{5 n^4}{8}-\frac{19 n^3}{4}+\frac{115 n^2}{8}-\frac{65 n}{4}+4}$

Then the next few terms in the sequence could very well be

$\{-2, 1, 7, 25, 79, 208, 466, 922, 1660, 2779, \ldots\}$

It would be much easier to confirm this had the given sequence provided just one more term...

* Why degree-4? This rests on the assumption that the higher-order forward differences of $\{x_n\}$ eventually form a constant sequence. But we only have enough information to find one term in the sequence of 4th-order differences. Denote the k-th-order forward differences of $\{x_n\}$ by $\Delta^{k}\{x_n\}$ . Then

• 1st-order differences:

$\Delta\{x_n\} = \{1-(-2), 7-1, 25-7, 79-25,\ldots\} = \{3,6,18,54,\ldots\}$

• 2nd-order differences:

$\Delta^2\{x_n\} = \{6-3,18-6,54-18,\ldots\} = \{3,12,36,\ldots\}$

• 3rd-order differences:

$\Delta^3\{x_n\} = \{12-3, 36-12,\ldots\} = \{9,24,\ldots\}$

• 4th-order differences:

$\Delta^4\{x_n\} = \{24-9,\ldots\} = \{15,\ldots\}$

From here I made the assumption that $\Delta^4\{x_n\}$ is the constant sequence {15, 15, 15, …}. This implies $\Delta^3\{x_n\}$ forms an arithmetic/linear sequence, which implies $\Delta^2\{x_n\}$ forms a quadratic sequence, and so on up $\{x_n\}$ forming a quartic sequence. Then we can use the method of undetermined coefficients to find it.