All categories

3 years ago

The difference between the roots of the quadratic equation x2 -14x +q =0 is 6. Find q

Mathematics

1 answer:

Irina-Kira [14]3 years ago

3 0

9514 1404 393

Answer:

q = 40

Step-by-step explanation:

When the quadratic has roots p and r, it can be factored as ...

(x -p)(x -r) = x² -(p+r)x +pr

So, the sum of the roots is 14, and their difference is 6. This lets us find the roots from ...

p + r = 14

p - r = 6

2p = 20 . . . add the two equations

p = 10

r = 14 -p = 4

The value of interest is then ...

q = pr = (10)(4)

q = 40

The graph shows the roots to be 4 and 10, as we found.

You might be interested in

Which expression should you simplify to find the 90% confidence interval,

bogdanovich [222]

Answer:

$0.45 - 1.96\sqrt{\frac{0.45(1-0.45)}{36}}=0.2870.45 + 1.96\sqrt{\frac{0.45(1-0.45)}{36}}=0.613$

we can conclude at 95% of confidence that the true proportion of interest for this case is between 0.287 and 0.613

Step-by-step explanation:

The estimated proportion of interest is $\hat p=0.45$

We need to find a critical value for the confidence interval using the normla standard distributon. For this case we have 95% of confidence, then the significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ .

And the critical value is: $z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

The confidence interval for the true population proportion is interest is given by this formula:

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

Replacing the values provided we got:

$0.45 - 1.96\sqrt{\frac{0.45(1-0.45)}{36}}=0.287\\\\0.45 + 1.96\sqrt{\frac{0.45(1-0.45)}{36}}=0.613$

And we can conclude at 95% of confidence that the true proportion of interest for this case is between 0.287 and 0.613

5 0

3 years ago

calculate the scale factor of abc to def enter answer as a whole number or as a fraction into lowest terms

SVETLANKA909090 [29]

Answer:

Scale is 1/6

Step-by-step explanation:

Since all sides and angles are identical these are congruent triangles

3 ways to solve:

Scale Factor = DE / AB = 12/72 = 1/6

Scale Factor = DF/AC = 7/42 = 1/6

Scale Factor = EF/CB = 11/66 = 1/6

3 0

4 years ago

Find the quotient 4 / (2/5)=

sweet-ann [11.9K]

Answer:

it will be 10

Step-by-step explanation:

4 0

3 years ago

Michelle tried to solve an equation step by step. \begin{aligned} t-\dfrac35&=\dfrac45\\\\ t-\dfrac35+\dfrac35&=\dfrac45

valentinak56 [21]

Answer:

Step 2

Step-by-step explanation:

Michelle's step in trying to solve the equation is given below:

$\begin{aligned} t-\dfrac35&=\dfrac45\\\\ t-\dfrac35+\dfrac35&=\dfrac45+\dfrac35&\green{\text{Step } 1}\\\\ t&=1&\blue{\text{Step } 2} \end{aligned}$

Michelle made a mistake in Step 2.

The right hand side of Step 1: $\dfrac45+\dfrac35\neq 1$

Rather, the correct sum is:

$\dfrac45+\dfrac35=\dfrac75\\\\=1\dfrac25$

5 0

3 years ago

The population of a city has decreased by 35% since it was last measured. If the current population is 9100 , what was the previ

Alina [70]

The previous population was 14000.

Explanation

The population decreased by 35% since the last measurement. So the current population is less than the previous population.

current population=9100

previous population =x

current population is 35% less than the previous population x

$9100=x*(100-35)/100\\9100=(x*65)/100\\x=(100*9100)/65=14000$

The previous population was 14000.

4 0

3 years ago