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AysviL [449]
3 years ago
13

Express in completed square form x 2 + 6x + 20

Mathematics
1 answer:
podryga [215]3 years ago
7 0

Answer:

(x + 3)² + 11

Step-by-step explanation:

Given

x² + 6x + 20

To complete the square

add/subtract ( half the coefficient of the x- term )² to x² + 6x

x² + 2(3)x + 9 - 9 + 20

= (x + 3)² + 11

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The coordinates of A, B, and C in the diagram are A(p,4), B(6,1), and C(9,q). Which equation correctly relates p and q?
Temka [501]

ANSWER

p  + q= 7

EXPLANATION

We determine the slope of each line using the slope formula;

m =  \frac{y_2-y_1}{x_2-x_1}

The slope of BC is

=  \frac{ q - 1}{9 - 6}

\frac{ q - 1}{3}

The slope of AB is

= \frac{1 - 4}{6 - p}

=  - \frac{3}{6 - p}

The two lines are perpendicular so the product of their slopes is -1.

- \frac{3}{6 - p}   \times \frac{ q - 1}{3}  =  - 1

This implies that,

\frac{q - 1}{6 - p}  =  1

q - 1=6 - p

q + p = 6 + 1

p  + q= 7

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4 0
2 years ago
Read 2 more answers
Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 5; B: the numbers add to 2
labwork [276]

Answer:

Part 1

A = {5}

B = {(1,1)}

C = {(2,1), (2,3), (2,4), (2,5), (2,6), (1,2), (3,2), (4,2), (5,2), (6,2)}

D =  {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (3,1), (3,2), (3,3), (3,4), (3,6), (4,1), (4,2), (4,3), (4,5), (4,6), (5,1), (5,2), (5,4), (5,5), (5,6), (6,1), (6,3), (6,4), (6,5), (6,6)}

Part 2

35

Step-by-step explanation:

Part 1

We use brakets for indicate that the elements belong to a event.

In each event, the first member of each parentheses belong to dice red and the second belong to green dice.

We consider in each event all elements that accomplish the condition.

Part 2

When we combinate pair with the two dice obtain 36 pairs (6*6, six possible results in the red dice and six possible results in the green dice), now we look for all of them that do not add 2.

(1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)

4 0
3 years ago
Two objects are moving along separate linear paths where each path is described by postion, d, and time, t. The variable d is me
fiasKO [112]
Linear equation:  d = m t + b
If the graph of the position of the second object is parallel to d = 2.5 t +2.2, than m = 2.5
t = 0, d = 1
1 = 2.5 · 0 + b
b = 1
Answer: A ) d = 2.5 t + 1
3 0
3 years ago
Read 2 more answers
The half-life of Carbon-14 is 5730 years. Suppose a fossil is found with 50% of Carbon-14 as compared to a living sample. How ol
melisa1 [442]
The answer is C. Because it takes 5730 years for half of a sample of carbon-14 atoms to decay. It says that 50% of the carbon atoms have decayed so that means that 5730 years have elapsed for that fossil.

I hope that helps.
4 0
2 years ago
What is the x-coordinate of the solution to the system?<br> { 2x-3y= -27<br> -3x+2y= 23
UkoKoshka [18]

Answer:

x = 41 and y = 76

Step-by-step explanation:


4 0
2 years ago
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