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horrorfan [7]
3 years ago
12

Daniel wants to prove that the interior angles of any triangle sum to 180°. He draws a line through one vertex parallel to the o

pposite side, and then he labels all the angles formed.
Drag a reason to match each statement in Daniel's proof in the table below.

Mathematics
1 answer:
Serggg [28]3 years ago
4 0

Alternate interior angles theorem.

<u>Step-by-step explanation:</u>

By using the definition of Alternate Interior Angles theorem, we can say that If a transversal cuts any two parallel lines, then those pairs of alternate interior angles are seems to be  congruent.

So in the given triangle,

∠4 ≅ ∠2

∠5 ≅ ∠3

Sum of all the angles in a triangle = 180°

∠1 + ∠2 + ∠3 = 180°

Since from the above congruence, we can write that

∠1 + ∠4 + ∠5 = 180°

Hence proved.

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From a box containing 10 cards numbered 1 to 10, four cards are drawn together. The probability that their sum is even is 21 21
ankoles [38]

Answer:

Step-by-step explanation:

We know that between 1 to 10 there are 5 even and 5 odd numbers.

We could get 4 even cards , 4 odd cards or 2 odd and 2 even cards

Let´s check all this combinations

Case 1: When all 4 numbers are even:  

We are going to take 4 of the 5 even numbers in the box so we have

5C4=5

Case 2: When all 4 numbers are odd:  

We are going to take 4 of the 5 odd numbers in the box, so we have

5C4=5

Case 3: When 2 are even and 2 are odd:

We are giong to take 2 from 5 even and odd cards in the box so we have

 

5C2 * 5C2

Remember that we obtain the probability from

\frac{Number-of-favourable-Outcome}{Total-number-of-outcomes}

So we have the number of favourable outcomes but we need the Total cases for drawing four cards, so we have that:  

We are taking 4 of the 10 cards:

10C_4=210

Hence we have that the probability that their sum is even

\frac{5+5+100}{210}=\frac{11}{21}

8 0
3 years ago
A rectangular plant holder is 8 inches long 7 1/2 inches wide and 5 inches high. How much potting soil can the planter hold
Lesechka [4]

Answer:

300

Step-by-step explanation:

8 \times 7 \frac{1}{2}  \times 5 \times = 300

5 0
3 years ago
Read 2 more answers
A function f() is graphed on the coordinate plane.
Mkey [24]

Answer:

i dont know but some one will help freeee points

Step-by-step explanation:

7 0
2 years ago
85% of what number is 10.2
Free_Kalibri [48]

<em>Answer:</em>

<em>n = 12</em>

<em>Step-by-step explanation:</em>

<em>85%×n = 10.2</em>

<em>85n/100 = 10.2</em>

<em>85n = 1020</em>

<em>n = 1020 : 85</em>

<em>n = 12</em>

7 0
4 years ago
Y=-1/2x+10x what is the height of the arch at the turning point
lozanna [386]

your equation is linear, so there isn't any arch

6 0
3 years ago
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