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3 years ago

PLEASE HELP! Which of the following is the best definition of a Linear pair of angles?

Mathematics

2 answers:

galina1969 [7]3 years ago

8 0

A pair of angles with a common vertex and sides that are opposite rays

lord [1]3 years ago

6 0

Answer:

Option A is correct.

A linear pair of angles whose measure sum to 180 degree and share a common ray

Step-by-step explanation:

Linear pair of angles states that it is formed when two lines intersect as shown in the figure given below,

Two angles are said to be linear pair of angles if they are adjacent angles formed by two intersecting lines.

Then, the measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees.

Therefore, A linear pair of angles whose measure sum to 180 degree and share a common ray.

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The triangles are similar. What is the value of x?

jok3333 [9.3K]

Given that the two triangles are similar:
$\frac{7}{28}$ = $\frac{25}{6x + 28}$
$\frac{1}{4}$ = $\frac{25}{6x + 28}$
6x + 28 = 4 x 25
6x + 28 = 100
6x = 100 - 28
6x = 72
x = 12

8 0

3 years ago

Read 2 more answers

A proportional relationship is represented by the equation 2x = 18y. IF y = kx, where k is the constant of proportionality, find

ddd [48]

2x=18y
divide 2
x=9y
9y=x
divide by 9
y=1/9x

k=1/9

3 0

3 years ago

Please help! Will give Brainliest!!!!!!!!!!!!

Ahat [919]

Answer:

for the first answer the second option is correct and 8 will go in the box and for the second question the second option is correct and 40 will go in the box.

3 0

2 years ago

For each of 2 ≤ n ≤ 5, compute c(n, 0) + c(n, 2) + ⋅⋅⋅ + c(n, 2k), where 2k is largest even integer ≤ n, and compute c(n, 1) + c

Ksivusya [100]

Denote $C(n,m)=\dbinom nm$ . Then

$n=2\implies\displaystyle\binom20+\binom22=1+1=2$
$n=3\implies\displaystyle\binom30+\binom32=1+3=4$
$n=4\implies\displaystyle\binom40+\binom42+\binom44=1+6+1=8$
$n=5\implies\displaystyle\binom50+\binom52+\binom54=1+10+5=16$

In general, it would appear that

$\displaystyle\sum_{k=0}^{2\lfloor\frac n2\rfloor}\binom n{2k}=2^{n-1}$

On the other hand,

$n=2\implies\displaystyle\binom21=2$
$n=3\implies\displaystyle\binom31+\binom33=3+1=4$
$n=4\implies\displaystyle\binom41+\binom43=4+4=8$
$n=5\implies\displaystyle\binom51+\binom53+\binom55=5+10+1=16$

so that in general, we also get

$\displaystyle\sum_{k=0}^{2\lfloor\frac{n-1}2\rfloor+1}\binom n{2k+1}=2^{n-1}$

7 0

3 years ago

There are two polygons. The larger one has three times as many sides as the smaller one.

dlinn [17]

Answer:

Step-by-step explanation:

There are two polygons. The larger one has three times as many sides as the smaller one. Its angle sum is four times as big. How many sides does the smaller polygon have? (Need full solution)?

“Three times as many sides” means the larger polygon has a multiple of 3 sides. 3 is the fewest sides any polygon can have, so it has not less than 9 sides.

Its angle sum is four times the smaller one’s. This applies to interior angles.

A triangle’s sum is 180. A square’s is 360. A pentagon’s is 540. Any sum will be a multiple of 180, and equal to the number of sides minus two, then multiplied by 180.

A hexagon has 6 sides, so 4×180=720 degrees sum. That part fits the triangle, but we know that can’t be the answer because 3×3=9.

So start at 9.

7×180÷4 can’t be a multiple of 180. What we need is a multiple of 3 which is 2 greater than a multiple of 4.

18 fits that description.

The 18-gon’s interior sum is 16×180=2880, divide that by 4 to get 720, which is the hexagon’s sum.

18÷6=3, so we have a solution. The smaller polygon can be a hexagon.

We should check the next one though. Multiples of 3: 21, 24, 27, 30, 33, 36, 39, 42 (every 4th multiple of 3 will be 2 more than a multiple of 4).

So the 30-gon:

28×180=5040

5040÷4=1260

1260÷180=7

7+2=9

9×3=27

Off by 3.

The 42-gon:

((((((42–2)×180)÷4)÷180)+2)×3)=36

Off by 6. It will keep getting farther away, so we have a unique solution.

6 0

2 years ago