Factor out the greatest common factor<br> 15x^2-21x<br> ^=exponent

20 Point!

ludmilkaskok [199]

determinant: $\sqrt{b^2-4ac}$

(a) $x^2+4x+5=0\\D=4^2-4\cdot1\cdot5={-4}\\D$

D<0 means there are no real roots. there are two complex roots with imaginary components.

(b) D=16+20=36>0

D>0 means there are two real roots

(c) D = 20^2-4*4*25 = 0

D=0 means there is one real root with multiplicity 2

7 0

3 years ago

Determining Whether a Difference Is Statistically

SCORPION-xisa [38]

Using the z-distribution, it is found that:

The 95% confidence interval is of -1.38 to 1.38.

The value of the sample mean difference is of 1.74, which falls outside the 95% confidence interval.

<h3>What is the z-distribution confidence interval?</h3>

The confidence interval is:

$\overline{x} \pm zs$

In which:

$\overline{x}$ is the difference between the population means.

s is the standard error.

In this problem, we have a 95% confidence level, hence $\alpha = 0.95$ , z is the value of Z that has a p-value of $\frac{1+0.95}{2} = 0.975$ , so the critical value is z = 1.96.

The estimate and the standard error are given by:

$\overline{x} = 0, s = 0.69$

Hence the bounds of the interval are given by:

$\overline{x} - zs = 0 - 1.96(0.69) = -1.38$

$\overline{x} + zs = 0 + 1.96(0.69) = 1.38$

1.74 is outside the interval, hence:

The 95% confidence interval is of -1.38 to 1.38.

The value of the sample mean difference is of 1.74, which falls outside the 95% confidence interval.

More can be learned about the z-distribution at brainly.com/question/25890103

#SPJ2

6 0

2 years ago

(Algebra 2)<br><br> Find the inverse of f(x) and its domain.

elixir [45]

Let f(x)=y
f^-1(x)=x
y=1/(x+5) - 1
y+1=1/(x+5)
(x+5)=1/(y+1)
x=1/(y+1)-5
f^-1(x)=1/(x+1) -5

denominator cannot equals to zero
x+1≠0
x≠-1

answer
B

4 0

2 years ago

Angie and Becky each completed a separate proof to show that the measures of vertical angles AKG and HKB are equal. Who complete

Helga [31]

Answer:

Becky, because her justification for the second statement should be "definition of supplementary angles" rather than "angle addition postulate."

Step-by-step explanation:

Becky completed the proof incorrectly because her justification for the second statement is not totally correct.

Angle addition postulate does not really apply here, as the sum of 2 angles may not give you exactly 180°.

However, the second statement, m<AKG + m<GKB = 180° and m<GKB + m<HKB = 180°, can be justified by the "Definition of Supplementary Angles".

The sum of supplementary angles = 180°.

Therefore, Becky completed the proof incorrectly.

6 0

3 years ago

Gabriella is building a garden that is 3.6 m long by 7.77 m wide. What is the area of her garden?

attashe74 [19]

Answer: 27.97 m^2

Explanation:
Area = Length x Width
Area = 3.6m x 7.77m
Area = 27.97 m^2

7 0

2 years ago

Factor out the greatest common factor 15x^2-21x ^=exponent