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In ∆ABC,

As, we have :

So, By angle sum property of triangle :

∠A + ∠B + ∠C = 180°

[tex] \tt : \implies 60\degree + 60\degree + \angle C = 180\degree[/tex]

[tex] \tt : \implies 120\degree + \angle C = 180\degree[/tex]

[tex] \tt : \implies \angle C = 180\degree - 120\degree[/tex]

[tex] \tt : \implies \angle C = 60\degree[/tex]

Now, we have :

As, all angles are of same length, therefore it is a equilateral triangle.

We know that sides of equilateral triangle are equal.

[tex] \tt : \implies AB = BC = AC[/tex]

Now, we have BC = 12 units.

Hence, all sides are of 12 units.

Now, we know that area of equilateral triangle is :

[tex] \large \underline{\boxed{\bf{Area_{(equilateral \: triangle)} = \dfrac{\sqrt{3}}{4} side^{2}}}}[/tex]

[tex] \tt : \implies Area = \dfrac{\sqrt{3}}{4} \times (12 \: units)^{2}[/tex]

[tex] \tt : \implies Area = \dfrac{\sqrt{3}}{\cancel{4}} \times \cancel{144} \: units^{2}[/tex]

[tex] \tt : \implies Area = \sqrt{3} \times 36 \: units^{2}[/tex]

[tex] \tt : \implies Area = 36\sqrt{3} units^{2}[/tex]

So, Area of given triangle is 36√3 units².

Given:

The  function that represents how the amount of fuel changes as a function of distance flown is

[tex]f(x)=-0.9x+665[/tex]

where x represents miles flown, and f(x) represents the amount of fuel remaining.

To find:

The rate of change for this scenario.

Solution:

The slope intercept form of a linear function is

[tex]y=mx+b[/tex]        ...(i)

Where, m is the slope or rate of change and b is the y-intercept.

We have,

[tex]f(x)=-0.9x+665[/tex]        ...(ii)

On comparing (i) and (ii), we get

[tex]m=-0.9[/tex]

Therefore, the rate of change for this scenario is -0.9. It means, the amount of fuel in the airplane is decreasing by 0.9 gallons per mile.

Answer:

The answer is

[tex]y = - 7[/tex]

Answer:

y = -7

Step-by-step explanation:

Hey :)

y = mx + b

*m is equal to the slope...

y = (0)x + b

Plug in the point you have...

-7 = (0) (5) + b

-7 = 0 + b

-7 = b

y = (0)x - 7

y = -7

Ignore the (0)x because anything multiplied by 0 is 0 so there's no point in having 0x in your equation.

Answer: y = -7

Hope this helps :)

26 I think (i'm not sure please correct me.)

Answer:

Step-by-step explanation:

Arcs in the circle sum to 360°

Answer:

x = 20

Step-by-step explanation:

Each line creates a 180° angle on each side of it. Since these lines intersect, they have congruent angles. This means that these two quantities can be set equal to each other.

3x + 50 = 6x - 10

Solve by combining like-terms and isolating x. Move the 3x to the right by subtracting it from both sides.

50 = 3x - 10

Move the 10 to the left by adding it to both sides.

60 = 3x

Divide the 3 from both sides to isolate the x.

x = 20

Furthermore, this can be checked by plugging in 20 to x and seeing if the expression is true.

3(20) + 50 = 6(20) - 10

110 = 110

Answer:

Hey!

0.309<0.32<0.35<0.4

hope this helps you

The numbers in order of size start with the smallest can be done as 0.309 < 0.32 < 0.35 < 0.40.

The decimal numeral system is the most widely used system for representing both integer and non-integer values. It is the Hindu-Arabic numeral system's expansion to non-integer numbers. Decimal notation is the method of representing numbers in the decimal system.

The given number can be arranged from smallest to largest can be arranged as shown below. Therefore, we can write,

0.309 < 0.32 < 0.35 < 0.40

Hence, the numbers in order of size start with the smallest can be done as 0.309 < 0.32 < 0.35 < 0.40.

Learn more about Decimal Numbers here:

https://brainly.com/question/4708407

#SPJ2

Answer:

0.16

Step-by-step explanation:

9514 1404 393

Answer:

  D)  infinitely many

Step-by-step explanation:

There are infinitely many points on any portion of the number line. The shading on the graph indicates all numbers less than or equal to 8 are solutions. There are infinitely many such numbers.

Answer:

12 i think

Step-by-step explanation:

Answer:

314,880

Step-by-step explanation:

If the population decreases by 1.6% per year, this means the population is 98.4% of the population of the previous year. What this means is we can multiply the current population, 320,000, by 98.4/100, as 98.4/100 is equivalent to 98.4%. This gets us 314,880.

Answer:

314880

Step-by-step explanation:

Answer:

the answer is 256

Step-by-step explanation:

Answer:

5 + i

Step-by-step explanation:

Answer:

5+i is the answer

Step-by-step explanation:

cause 6-4=2-7=5+i