Question

lesson (eng) lección (esp)
2 - 6. a tile pattern has five tiles in figure 0 and adds seven tiles in each new figure. write a linear equation that represents this pattern. 2 - 6 hw etool homework help
2 - 7. benjamin is taking algebra 1 and is stuck on the problem shown below. examine his work so far and help him by showing and explaining the remaining steps. homework help
original problem: simplify (3a^(-2)b)^3.
he knows that (3a^(-2)b)^3=(3a^(-2)b)(3a^(-2)b)(3a^(-2)b). now what?
2 - 8. examine the function h(x) defined at right. then estimate the values below. homework help
a. h(1)
b. h(3)
c. x when h(x)=0
d. h(-1)
e. h(-4)
2 - 9. calculate the value of each of the following expressions. homework help
a. \frac{6\cdot7^2}{3 + 8}+11
b. 5^{(1 + 2)}+8 - 6
c. \sqrt{3^2+4^2}-5
2 - 10. examine the diagram at right. based on the information in the diagram, which angles can you determine the measures of? copy the diagram on your paper and determine the measures of only those angles that you can justify. homework help

Explanation:

2 - 6

Step1: Identify the slope - intercept form

The linear equation is of the form $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept.

Step2: Determine the values of $m$ and $b$

The initial number of tiles (when Figure number $x = 0$) is $b=5$. The number of tiles added each new figure is the slope $m = 7$.

Step3: Write the linear equation

The linear equation is $y=7x + 5$, where $y$ is the number of tiles and $x$ is the figure number.

Step1: Apply the power - of - a - product rule

$(3a^{-2}b)^3=3^3\times(a^{-2})^3\times b^3$
Since $3^3 = 27$, $(a^{-2})^3=a^{-6}$ (using the power - of - a - power rule $(a^m)^n=a^{mn}$), we have $27a^{-6}b^3$.

Step2: Rewrite with positive exponents

Using the rule $a^{-n}=\frac{1}{a^n}$, we get $\frac{27b^3}{a^6}$.

Step1: Find $h(1)$

Locate $x = 1$ on the x - axis and read the corresponding y - value on the graph of $h(x)$.

Step2: Find $h(3)$

Locate $x = 3$ on the x - axis and read the corresponding y - value on the graph of $h(x)$.

Step3: Find $x$ when $h(x)=0$

Find the x - values where the graph of $h(x)$ intersects the x - axis.

Step4: Find $h(-1)$

Locate $x=-1$ on the x - axis and read the corresponding y - value on the graph of $h(x)$.

Step5: Find $h(-4)$

Locate $x = - 4$ on the x - axis and read the corresponding y - value on the graph of $h(x)$.

Answer:

$y = 7x+5$

2 - 7