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3 years ago

In the equation x^2+kx+54=0 one root is twice the other root find k

1 answer:

6 0

Let r be the lesser root and r^2 be the greater.......the sum of the roots = -b/a = -[-6] / 1 = 6

So we have that

r^2 + r = 6 → r^2 + r - 6 = 0

Factor

(r + 3) (r - 2) = 0

So r = -3 or r = 2

Then r^2 = 9 or r^2 =4

And the product of the roots = c/a = k/a = k

So....k = (-3)(9) = -27 or k = (2)(4) = 8

Check

x^2 - 6x - 27 = 0 factors as (x + 3)(x - 9) = 0 and the roots are -3 and 9

x^2 - 6x + 8 = 0 factors as (x -2) (x - 4) =0 and the roots are 2 and 4

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G(X)= 6X - 3<br> What is g-1 (9)

harkovskaia [24]

G(X)=6X-3
Y=6X-3
X=6Y-3
X+3=6Y
Y=(X+3)/6
G^-1(9)=(X+3)/6
G^-1(9)=(9+3)/6
G^-1(9)=2

6 0

3 years ago

Please tell me what the area formula and circumference formula is for a circle?

Whitepunk [10]

The formula for the Circumference of a circle is 2•Pi•R, or 2•Radius•3.14
This is to calculate the measurements around the circle.

The formula for the Area of a circle is Pi•R^2, or 3.14•R•R
This is to calculate the entire circle.

I hope this helps!

5 0

3 years ago

Jacob Lee is a frequent traveler between Los Angeles and San Diego. For the past month, he wrote down the flight times in minute

valkas [14]

Solution :

We know that

$H_0: \mu_1 = \mu_2=\mu_3$

$H_1 :$ At least one mean is different form the others (claim)

We need to find the critical values.

We know k = 3 , N = 35, α = 0.05

d.f.N = k - 1

= 3 - 1 = 2

d.f.D = N - k

= 35 - 3 = 32

SO the critical value is 3.295

The mean and the variance of each sample :

Goust Jet red Cloudtran

$\overline X_1 =50.5$ $\overline X_2 =50.07143$ $\overline X_3 =55.71429$

$s_1^2=19.96154$ $s_2^2=14.68681$ $s_3^2=36.57143$

The grand mean or the overall mean is(GM) :

$\overline X_{GM}=\frac{\sum \overline X}{N}$

$=\frac{51+51+...+49+49}{35}$

= 52.1714

The variance between the groups

$s_B^2=\frac{\sum n_i\left( \overline X_i - \overline X_{GM}\right)^2}{k-1}$

$=\frac{\left[14(50.5-52.1714)^2+14(52.07143-52.1714)^2+7(55.71426-52.1714)^2\right]}{3-1}$

$=\frac{127.1143}{2}$

= 63.55714

The Variance within the groups

$s_W^2=\frac{\sum(n_i-1)s_i^2}{\sum(n_i-1)}$

$=\frac{(14-1)19.96154+(14-1)14.68681+(7-1)36.57143}{(14-1)+(14-1)+(7-1)}$

$=\frac{669.8571}{32}$

= 20.93304

The F-test statistics value is :

$F=\frac{s_B^2}{s_W^2}$

$=\frac{63.55714}{20.93304}$

= 3.036212

Now since the 3.036 < 3.295, we do not reject the null hypothesis.

So there is no sufficient evidence to support the claim that there is a difference among the means.

The ANOVA table is :

Source Sum of squares d.f Mean square F

Between 127.1143 2 63.55714 3.036212

Within 669.8571 32 20.93304

Total 796.9714 34

3 0

2 years ago

Round the following number to four significant figures: 3.682417 *

Dovator [93]

Answer:

3.682

Step-by-step explanation:

We don't consider the decimal place or I should say comma so then we read from the first digit as long as it's not zero then until the fourth digit we look at the next digit if it's 5 or greater then we add 1 to the previous digit. And if the next digit is less than 5 then the digit won't change

7 0

2 years ago

If f(x) =1/x and g(x) = x - 2 what is f(g(x)) when X = 1

Fed [463]

Answer:

f(g(x)) = -1

Step-by-step explanation:

$f(x) = \frac{1}{x} \\ \\ g(x) = x - 2 \\ \\ \implies \: f(g(x)) = \frac{1}{x - 2} \\ \\ \implies \: f(g(1)) = \frac{1}{1 - 2} \\ \\ \implies \: f(g(1)) = \frac{1}{ - 1} \\ \\ \implies \: f(g(1)) = - 1$

8 0

1 year ago