Find the value of the missing coefficient a in the equation y = a(x - 3)(x + 5) if the graph goes through the point (1, -6)

Mathematics

2 answers:

erik [133]3 years ago

6 0

Answer:

missing coffecient is 8

Iteru [2.4K]3 years ago

3 0

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

y-(a*(x-3)*(x+5))=0

STEP
1
:
Equation at the end of step 1

y - (a • (x - 3) • (x + 5)) = 0
STEP
2
:
Equation at the end of step 2

y - a • (x - 3) • (x + 5) = 0
STEP
3
:
Equation at the end of step 3

y - ax2 - 2ax + 15a = 0
STEP
4
:

Solving a Single Variable Equation:

4.1 Solve y-ax2-2ax+15a = 0

In this type of equations, having more than one variable (unknown), you have to specify for which variable you want the equation solved.

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$n=\frac{0.5(1-0.5)}{(\frac{0.04}{1.64})^2}=420.25$

And rounded up we have that n=421

Step-by-step explanation:

We know that the sample proportion have the following distribution:

$\hat p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by $\alpha=1-0.90=0.1$ and $\alpha/2 =0.05$ . And the critical value would be given by:

$z_{\alpha/2}=-1.64, z_{1-\alpha/2}=1.64$

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.04$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

We assume that a prior estimation for p would be $\hat p =0.5$ since we don't have any other info provided. And replacing into equation (b) the values from part a we got: