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3 years ago

What is the slope of the line shown?

Mathematics

1 answer:

Olin [163]3 years ago

4 0

By using two arbitrary points on the line, we can find the slope using the slope formula:

$\frac{y.2 - y.1}{x.2 - x.1} = m$

We'll use the points (0, 4) and (5, 1) for this.

1 - 4 / 5 - 0

-3 / 5

The slope of the line is -3/5.

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Find the length of HD

mel-nik [20]

Answer:

11 units

Step-by-step explanation:

HPO and DPI are similar triangles

HP/DP = PO/PI

HP/9 = 6/27

HP = 9×6/27

HP = 2

HD = HP + PD

HD = 2 + 9 = 11

7 0

3 years ago

Describe the transformation.

Lesechka [4]

Answer:

g(x) = 1/3 (x - 12) .. vertical compression with factor 1/3 from f(x-4)

Step-by-step explanation:

*f(x) = x - 8 ... horizontal translation right 8 units from parent function f(x)=x

f(x-4) = (x-4) - 8 = x - 12 .... horizontal translation right 4 units from f(x)=x-8

g(x) = 1/3 (x - 12) .. vertical compression with factor 1/3 from f(x-4)

4 0

3 years ago

Save

nikklg [1K]

Answer:

9 years i think

Step-by-step explanation:

3 0

4 years ago

3 Simplify:1/4 (15 – 6) +3 : 12 A. 2 B. 3 C. 41 D. 5 7 12

zalisa [80]

Answer: 5.25 or 5.5 [see note]

Step-by-step explanation:

1/4 (15 – 6) +3 [I'm not clear what is meant by the " : 12," so I left it out.]

1/4 (9) +3

9/4 + 3

2.25 + 3 = 5.25

===

If it is supposed to read

1/4 (15 – 6) +3/12

Then it would be

5.25 + 0.25 = 5.5

4 0

3 years ago

A certain system can experience three different types of defects. Let Ai (i = 1,2,3) denote the event that the system has a defe

andreev551 [17]

Answer:

(a) 0.5000

(b) 0.0833

((d) 0.9500

Step-by-step explanation:

Given that the following probabilities;

P(A1) = 0.12; P(A2) = 0.08,

P(A3) = 0.05; P(A1 ∪ A2) = 0.14, P(A1 ∪ A3) = 0.14,

P(A2 ∪ A3) = 0.11,

P(A1 ∩ A2 ∩ A3) = 0.01

(a) we want to find P(A2/A1).

P(A2/A1) = P(A1nA2)/P(A1)..........a

So we need to find P(A1nA2)

P(A1 ∪ A2)= P(A1) + P(A2) - P(A1nA2)

P(A1nA2) =P(A1) + P(A2) - P(A1 ∪ A2)

P(A1nA2) = 0.12 + 0.08 - 0.14

P(A1nA2) = 0.20- 0.14

P(A1nA2 )= 0.060

P(A2/A1) = 0.06/0.12

= 0.5000. (Ans)

(b) The required probability is: P(A2∩A3/A1) =[P(A2∩A3)∩P(A1)] /P(A1).........b

But [P(A2nA3)nP(A1)] = P(A1∩A2∩ A3)

P(A2∩A3/A1) = 0.01/0.12

P(A2∩A3/A1) = 0.0833 (Ans)

(Pr. of A1 defect) + (Pr. of A2 defect) + (Pr. of A3 defect)........c

Pr = 0.12 + 0.08 + 0.05

Pr = 0.2500 (And)

(d) The required probability is given by:

Pr[(A3)' /(A1∩A2)] = Pr[(A3)'nPr(A1∩A2)] /Pr(A1∩A2)]

Pr(A3)’ = 1 - Pr(A3) = 1 -0.05

Pr(A3)'/(A1∩A2)= (0.95×0.06)/(0.06)

Pr(A3)'/(A1∩A2 )= 0.95(Ans)......d

7 0

3 years ago