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uranmaximum [27]
3 years ago
15

Match the correct theorem or postulate with the correct statement.

Mathematics
1 answer:
Roman55 [17]3 years ago
4 0

1. Unique line postulate

Statement: Through any two points, there is exactly one line.

2. Line intersection postulate

Statement: If two lines intersect, then their intersection is exactly one point.

3. Segment addition postulate

Statement: If A, B and C are collinear and B is between A and C, then AB + BC = AC

4. Angle Addition postulate

Statement: If R is in interior of \angle PQS, then m \angle PQR + m \angle RQS = m \angle PQS.

5. Linear pair theorem

Statement: If two angles form a linear pair, then the angles are supplementary.

6. Congruent Complements theorem

Statement: If two angles are complementary to the same angle, then the angles are congruent.

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Sixty-five randomly selected car salespersons were asked the number of cars they generally sell in one week. Fourteen people ans
ss7ja [257]

Answer:

Step-by-step explanation:

From the information given:

We can compute the required calculations into a table as shown below.

\mathbf{Data \ value  }       \mathbf{ Frequency   } \mathbf{Relative  \ frequency}   \mathbf{Cumulative \  relative }

                                                                                              \mathbf{Frequency}

5                                     14                14/65 = 0.22                           14  

6                                     19                19/65 = 0.29               19+14 = 33

7                                      12                12/65 = 0.19               33+12 = 45

8                                       9                 9/65 = 0.14               45 + 9 = 54

9                                 <u>     11     </u>            11/65  = 0.17              54 + 11 = 65

                                        65

Note: that the relative frequency is determined by  dividing each value in the frequency by the total of the frequency.                        

8 0
3 years ago
Multiply. (2x2 + 4x - 3)(x2 - 2x + 5)
BigorU [14]
For a moment, let y=x^2-2x+5. Then by the distributive property,

(2x^2+4x-3)p=2x^2p+4xp-3p


Again by the distributive property,

2x^2p=2x^2(x^2-2x+5)=2x^4-4x^3+10x^2

4xp=4x(x^2-2x+5)=4x^3-8x^2+20x

-3p=-3(x^2-2x+5)=-3x^2+6x-15

Taking everything together, we get

(2x^2+4x-3)(x^2-2x+5)=(2x^4-4x^3+10x^2)+(4x^3-8x^2+20x)+(-3x^2+6x-15)
(2x^2+4x-3)(x^2-2x+5)=2x^4-x^2+26x-15
7 0
3 years ago
Read 2 more answers
Convert 25 miles into kilometres
Airida [17]

Answer:

1 miles= 1.609km

so, 25x1.609 = 40.225km

3 0
3 years ago
Tori devotes all of her income to the consumption of peanut butter and jelly. She has just discovered that at her current level
Schach [20]
The correct answer is option A
6 0
3 years ago
PYTHAGORAS THEROM AND TRIGONOMETRY RATIO​
marysya [2.9K]

Answer:

1) ΔACD is a right triangle at C

=> sin 32° = AC/15

⇔ AC = sin 32°.15 ≈ 7.9 (cm)

2) ΔABC is a right triangle at C, using Pythagoras theorem, we have:

AB² = AC² + BC²

⇔ AB² = 7.9² + 9.7² = 156.5

⇒ AB = 12.5 (cm)

3)  ΔABC is a right triangle at C

=> sin ∠BAC = BC/AB

⇔ sin ∠BAC = 9.7/12.5 = 0.776

⇒ ∠BAC ≈ 50.9°

4) ΔACD is a right triangle at C

=> cos 32° = CD/15

⇔ CD = cos32°.15

⇒ CD ≈ 12.72 (cm)

Step-by-step explanation:

7 0
3 years ago
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