Question

1. what is the value of x in the solution to this system of equations? 3x - 5y = 22 y = -5x + 32 f. -6.5 g. 0.5 h. 6.5 j. -0.5 7. a construction manager is monitoring the progress of the build of a new house. the scatter - plot and table show the number of months since the start of the build and the percentage of the house still left to build. a linear function can be used to model this relationship. which function best models the data? a y = -13.5x + 97.8 b y = -13.5x + 7.3 c y = 97.8x - 13.5 d y = 7.3x - 97.8

Explanation:

Question 6

Step1: Substitute y - equation into x - equation

Substitute $y=-5x + 32$ into $3x-5y=22$. We get $3x-5(-5x + 32)=22$.

Step2: Expand the equation

$3x + 25x-160=22$.

Step3: Combine like - terms

$28x-160 = 22$.

Step4: Add 160 to both sides

$28x=22 + 160$, so $28x=182$.

Step5: Solve for x

$x=\frac{182}{28}=6.5$.

Question 7

Step1: Recall the slope - intercept form

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

Step2: Calculate the slope (approximate)

Using two points $(0,100)$ and $(1,86)$, the slope $m=\frac{86 - 100}{1-0}=-14$ (approx). Looking at the options, the slope of option A is $-13.5$ which is close.

Step3: Check the y - intercept

When $x = 0$, the y - value from the table is 100. In option A, when $x = 0$, $y=97.8$ which is also a reasonable approximation considering the data may not be perfectly linear. So the function $y=-13.5x + 97.8$ best models the data.

Answer:

G. 0.5