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2x - y = 8<br> y= x-3<br> Use substitution method

uranmaximum [27]

Answer:

Slope = 0.222/2.000 = 0.111

x-intercept = -3/1 = -3.00000

y-intercept = 3/9 = 1/3 = 0.33333

Step-by-step explanation:

Step 1 :

Equation of a Straight Line

1.1 Solve x-9y+3 = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line x-9y+3 = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 1/3 so this line "cuts" the y axis at y= 0.33333

y-intercept = 3/9 = 1/3 = 0.33333

Calculate the X-Intercept :

When y = 0 the value of x is -3/1 Our line therefore "cuts" the x axis at x=-3.00000

x-intercept = -3/1 = -3.00000

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 0.333 and for x=2.000, the value of y is 0.556. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 0.556 - 0.333 = 0.222 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

Slope = 0.222/2.000 = 0.111

Geometric figure: Straight Line

Slope = 0.222/2.000 = 0.111

x-intercept = -3/1 = -3.00000

y-intercept = 3/9 = 1/3 = 0.33333

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3 0

3 years ago

Does anyone know this

Arturiano [62]

Answer:

C

Step-by-step explanation:

Option C is the correct answer.

8 0

3 years ago

The sugar content of the syrup in canned peaches is normally distributed. A random sample of n = 10 cans yields a sample standar

Serggg [28]

Answer:

The 95% confidence interval is given by:

3.30<σ<8.76

Step-by-step explanation:

1) Data given and notation

s=4.798 represent the sample standard deviation

$\bar x$ represent the sample mean

n=10 the sample size

Confidence=95% or 0.95

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population mean or variance lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

The Chi Square distribution is the distribution of the sum of squared standard normal deviates .

2) Calculating the confidence interval

The confidence interval for the population variance is given by the following formula:

$\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}$

The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:

$df=n-1=10-1=9$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a tabel to find the critical values.