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zysi [14]
3 years ago
6

When lines are parallel...

Mathematics
1 answer:
Otrada [13]3 years ago
3 0

Answer:

1) Congruent

2) Supplementary

3) Congruent

4) Congruent

Step-by-step explanation:

1) The Alternate Interior Angles Theorem states that, when two parallel lines are cut by a transversal , the resulting alternate interior angles are congruent .

2) Formally, we can say that if two lines are parallel, then consecutive interior angles are supplementary. We refer to this as the consecutive interior angles postulate.

3) When the lines are parallel, the corresponding angles are congruent . When two lines are cut by a transversal, the pairs of angles on one side of the transversal and inside the two lines are called the consecutive interior angles.

4) The Alternate Exterior Angles Theorem states that, when two parallel lines are cut by a transversal , the resulting alternate exterior angles are congruent.

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The area of the front side of the toy building is 1 square foot. The real building's
Brilliant_brown [7]
The ratio or the relationship of the toy to the large building is one foot to every 400 feet so in mathematical terms it’s shown as a ratio like this... 400:1 and since they are asking about the real building as the primary reason for the ratio it’s number goes first because they are enquiring about it’s relationship to the small one.(which is worded weirdly so I think they are trying to get you messed up)
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6 0
3 years ago
Find the explicit formula that produces the given sequence. <br> 3/2, 3/4, 3/8, 3/16,...
lara [203]
\frac{3}{2};\ \frac{3}{4};\ \frac{3}{8};\ \frac{3}{16};\ ...\\\\a_1=\frac{3}{2}\\\\a_2=\frac{3}{4}=\frac{3}{2}\cdot\frac{1}{2}\\\\a_3=\frac{3}{8}=\frac{3}{4}\cdot\frac{1}{2}=\frac{3}{2}\cdot\left(\frac{1}{2}\right)^2\\\\a_4=\frac{3}{16}=\frac{3}{8}\cdot\frac{1}{2}=\frac{3}{2}\cdot\left(\frac{1}{2}\right)^3\\\vdots
a_n=\frac{3}{2}\cdot\left(\frac{1}{2}\right)^{n-1}=\frac{3}{2}\cdot\left(\frac{1}{2}\right)^{-1}\cdot\left(\frac{1}{2}\right)^n=\frac{3}{2}\cdot2\cdot\left(\frac{1}{2}\right)^n=3\cdot\left(\frac{1}{2}\right)^n
7 0
3 years ago
Julio bought a total of 20 medium and large pumpkins. If he spent $53 and bought 6 more large pumpkins as medium pumpkins, how m
Tatiana [17]
20 medium and large pumpkins

m ... number of medium pumpkins
l ... number of large pumpkins

20 = m + l
20 = m + (m + 6)
20 = 2 * m + 6
2 * m = 20 - 6
2 * m = 14
m = 7 medium pumpkins

l = 20 - 7 = 13 large pumpkins

Result: Julio bought 13 large pumpkins.
5 0
3 years ago
Two triangles have side lengths 3,4,5 and 6,____10, respectively. The triangles are similar to each other.
Sergeu [11.5K]

Answer:

8

Step-by-step explanation:

3,4,5 and 6,_,10 are similar. what do you notice between the two? 6 is twice of 3. 10 is twice of 5. so then 4 would be half of 8.

hope i helped ;)

8 0
3 years ago
7. The points P(2, -3), Q(3, -2) and R(8, z) are
Hatshy [7]

Answer:

z = 3

Step-by-step explanation:

Since the points are collinear then the slopes between the points are equal.

Calculate the slope m using the slope formula

m = \frac{y_{2}-y_{1}  }{x_{2}-x_{1}  }

with (x₁, y₁ ) = P (2, - 3) and (x₂, y₂ ) = Q (3, - 2)

m = \frac{-2+3}{3-2} = 1

Repeat with

(x₁, y₁ ) = Q (3, - 2) and (x₂, y₂ ) = R (8, z )

m = \frac{z+2}{8-3} = \frac{z+2}{5} , then

\frac{z+2}{5} = 1 ( multiply both sides by 5 )

z + 2 = 5 ( subtract 2 from both sides )

z = 3

4 0
3 years ago
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