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2 years ago

Three copies of a triangle were rotated and positioned as shown. Which statement is always true about the angles in the figure?

1 answer:

6 0

After a thorough research, there exists the same question with the following choices and the image link:
https://static.k12.com/calms_media/media/1560500_1561000/1560892/1/97202a8cba8d842585e08726b9a1a3262....

A. The sum of m∠1, m∠2, and m∠3 is 90°.
B. m∠1 + m∠2 + m∠3 = 180° 
C. Angle 1 and angle 3 form a straight angle 
D Angle 1, angle 2, and angle 3 all have the same measure.

The correct answer is letter B. m∠1 + m∠2 + m∠3 = 180° . The sum of interior angles of a triangle is 180 degrees.

You might be interested in

Use the rectangle to find x and y

sineoko [7]

Y=11 x=13
It’s a rectangle so each angle equals 90
1
Angle 1 + angle 2 =90
5y+2y+13=90
7y=77
y=11
Th diagnose of a rectangle bisect so 8x-16=5x+23
3x=39
X=13

8 0

2 years ago

For the polynomial shown below find f(1). f(x)=3x^4-x^2+4x-2

Feliz [49]

Answer:

f(1)=4

Step-by-step explanation:

f(1)=3(1)^4-(1)^2+4(1)-2

f(1)=3(1)-1+4-2

f(1)=3-1+4-2

f(1)=4

6 0

3 years ago

Statistics show that about 42% of Americans voted in the previous national election. If three Americans are randomly selected, w

MrRa [10]

Answer:

19.51% probability that none of them voted in the last election

Step-by-step explanation:

For each American, there are only two possible outcomes. Either they voted in the previous national election, or they did not. The probability of an American voting in the previous election is independent of other Americans. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

42% of Americans voted in the previous national election.

This means that $p = 0.42$

Three Americans are randomly selected

This means that $n = 3$

What is the probability that none of them voted in the last election

This is P(X = 0).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{3,0}.(0.42)^{0}.(0.58)^{3} = 0.1951$

19.51% probability that none of them voted in the last election

6 0

2 years ago

Amelia wants to paint three walls in her family room. Two walls are 26 feet long by 9 feet wide. The other wall is 18 feet long

sattari [20]

Given:
Wall 1 & 2 : 26 ft by 9 ft
Wall 3 : 18 ft by 9 ft

Area 1 : 26 ft x 9 ft = 234 ft²
Area 2 : 26 ft x 9 ft = 234 ft²
Area 3 : 18 ft x 9 ft = 162 ft²

Total Area : 234 ft² + 234 ft² + 162 ft² = 630 ft²

1 Gallon = 250 ft²

630 ft² ÷ 250 ft² per gallon = 2.52 gallons

6 0

3 years ago

Which of the following pairs of functions are inverses of each other?

AnnyKZ [126]

Answer:

Step-by-step explanation:

Rearrange each function to solve for x.

Switch x and y,

The resulting equation is the inverse function.

f(x) = y = 5+x

x = y-5

y = x-5

f⁻¹(x) = x-5

g(x) = 5-x ≠ f⁻¹(x)

g(x) is not the inverse of f(x).

:::::

f(x) = y = 2x-9

x = (y+9)/2

y = (x+9)/2

f⁻¹(x) = (x+9)/2

g(x) = (x+9)/2 = f⁻¹(x)

g(x) is the inverse of f(x).

:::::

f(x) = y = 2/x - 6

x = 2/(y+6)

y = 2/(x+6)

f⁻¹(x) = 2/(x+6)

g(x) = (x+6)/2 ≠ f⁻¹(x)

:::::

f(x) = y = x/3 + 4

x = 3y - 12

y = 3x - 12

f⁻¹(x) = 3x - 12

g(x) = 3x - 4 ≠ f⁻¹(x)

g(x) is not the inverse of f(x).

4 0

2 years ago