(36√6 + 6^5/2 / 108×12)^2=6^n , then find the value of n?

[tex](\frac{36\sqrt{6}+6^{\frac{5}{2}}}{108\times12})^{2}=6^{n} \\ [/tex]


Thank you.....​

angle 3 = angle 6 = 60°

hope it helps...!!!

Answer:

m∠3 = 60°

m∠6 = 60°

Step-by-step explanation:

If a line intersects a set of parallel lines in the same plane at two distinct points, the alternate interior angles that are formed are congruent.  This is called the "Alternate Interior Angles Theorem".

As line p intersects the set of parallel lines m and n at two distinct points, then m∠3 = m∠6  and  m∠4 = m∠5

Given:

As m∠3 = m∠6, then:

⇒ 7x - 10 = 5x + 10

Add 10 to both sides:

⇒ 7x - 10 + 10 = 5x + 10 + 10

⇒ 7x = 5x + 20

Subtract 5x from both sides:

⇒ 7x - 5x = 5x + 20 - 5x

⇒ 2x = 20

Divide both sides by 2:

⇒ 2x ÷ 2 = 20 ÷ 2

⇒ x = 10

Now substitute the found value of x into one of the angle expressions:

m∠3 = 7(10) - 10

       = 70 - 10

       = 60°

As m∠3 = m∠6,  then m∠6 = 60°

Answer:

[tex]12\ gallons[/tex]

Step-by-step explanation:

Step 1:  Determine the unit rate

[tex]Miles / Gallons[/tex]

[tex]162\ miles / 9\ gallons[/tex]

[tex]18\ miles/gallon[/tex]

Step 2:  Determine the amount of gasoline used for 216 miles

[tex]216\ miles * (gallon / 18\ miles)[/tex]

[tex]12\ gallons[/tex]

Answer:  [tex]12\ gallons[/tex]

Answer:

12

Step-by-step explanation:

1. Figure out how many miles the car can go with one gallon of gasolline

162 ÷ 9 = 18

1 gallon = 18 miles

2. Figure out how many times 18 can go into 216

216 ÷ 18 = 12

12 gallons = 216 miles

*We do this because we know that every time the car drives 18 miles its uses another gallon of gas.

The car will use 12 gallons of gasoline to travel 216 miles.

Answer:

95th term

Step-by-step explanation:

the nth term of an AP is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 2 and d = a₂ - a₁ = 8 - 2 = 6 , then

[tex]a_{n}[/tex] = 2 + 6(n - 1) = 2 + 6n - 6 = 6n - 4

the 60th term is then

a₆₀ = 6(60) - 4 = 360 - 4 = 356

so 210 more than a₆₀ = 356 + 210 = 566

now equate [tex]a_{n}[/tex] to 566 and solve for n

6n - 4 = 566 ( add 4 to both sides )

6n = 570 ( divide both sides by 6 )

n = 95

Answer:

95th term.

Step-by-step explanation:

The sequence of 2, 8, 14, 20 . . . can be predicted by adding 6 to each successive term.  This can be written as 6n+2, where n starts at 0 for the first term.

n  Value  (6n+2)

0     2  

1      8

2     14

3     20

4     26

60   362

---

We want to know what term is 210 more than 362.  (362+ 210) = 572

We can solve by using the equation in reverse and solving for n:

(6n+2) = 572

6n = 570

n = 95

The 95th term (572) is greater than the 60th term (362) by 210.

Answer:

D

Step-by-step explanation:

First of all, "k" has nothing to do with determining vertical shrink/stretch, and therefore A and C can be eliminated from the choices. A shrink occurs with a fractional "a" value, so "a" must be greater than 1 in order for a vertical stretch to occur.

Answer:

y = [tex]\frac{1}{2}[/tex] x + 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

f(x) = - 2x + 1 ← is in slope- intercept form

with slope m = - 2

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-2}[/tex] = [tex]\frac{1}{2}[/tex] , then

y = [tex]\frac{1}{2}[/tex] x + c

the line crosses the y- axis at (0, 5 ) ⇒ c = 5

y = [tex]\frac{1}{2}[/tex] x + 5 ← equation of perpendicular line

The percentage shows that they were 28% more likely to come from Riverdale High school.

From the information given, the percentage of those from Rockport will be:

= 25/(25 + 44) × 100.

= 25/69 × 100

= 36.23%

The percentage of those from Riverdale will be:

= 44/(25 + 44) × 100.

= 44/69 × 100

= 63.77%

Therefore, the difference will be:

= 63.77% - 36.23%

= 28% approximately.

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Step-by-step explanation:

The question is not complete or correct

Answer:

S = 21

Step-by-step explanation:

21 - 19 = 2

Answer:

S=21

Step-by-step explanation: 21-19=2

Answer

B

Step-by-step explanation

Please give me brainlist.

Answer: t= Distance/Speed = 4/28= 1/7

Step-by-step explanation:

Speed is 28miles /hr

Distance = 4miles

Distance = Speed × time

Time(t) = Distance /Speed

Answer:

(3,7)

Step-by-step explanation:

First, substitute for y. Simplify.

2x+(x+4)=13

3x+4=13

3x=9

x=3

Input the value for x into either of the equations.

y=3+4

y=7

(3,7)

Hope this helps!

Answer:

E.

Step-by-step explanation:

Answer: (-12, -14), (-7, -4), (-1, 5), (0, -2), (3, 3), and (30, 5).

Step-by-step explanation: The following image should help you with your question if you're still confused.

Hope this helps! :)

Done!

Answer:

Step-by-step explanation:

Remark

If the trinomial is going to factor, it must factor as 5 and 1 paired with 3 and 1 as both 5 and 3 do not factor any further. They are prime numbers.

Let's try this:

(5x  +   1) ( 1x + 3)

Both factors must contain an + otherwise something in the given equation would be - when the factors are expanded.

It looks like this works. 5 * 3x + 1x = 16x

Answer:

1008

Step-by-step explanation:

If 4/5 of eighth graders, or 80%, are enrolled with class, there are still 20% of students that didn't study. That means you add 168, the 20%,  and you'll get 1008.

Answer:

3.4 yards cubed

Step-by-step explanation:

Volume is length x width x height

Length 2 4/5, Width 2, Height 3/5 so 2 4/5 x 2 x 3/5

It looks like they want the answer in decimal form, so you can convert the fractions into decimals.

For the length 2 4/5,  you divide the 4 by 5 to get a decimal of .8 so now it's 2.8

For the height of 3/5, you divide the 3/5 & get .6

Now it's 2.8 x 2 x .6 = 3.36 yards cubed which could get rounded up to 3.4 yards cubed

Answer:

1/3

Step-by-step explanation:

Slope is rise over run.

Pick a point and count how many steps up and how many steps to the right you need to make to get to the next point. That's how you find slope.

Answer:

2x²+2x+5

Step-by-step explanation:

Since the area of a square is a² (where a is the length of one of its sides) we'll have:

(x—1)(x—1)+(x+2)(x+2) = (x²—2x+1)+(x²+4x+4) = 2x²+2x+5

So write the answer as: 2, 2 and 5

Answer:

It’s D

Step-by-step explanation:

Answer:

Step-by-step explanation:

It mentions the new line is perpendicular to the original line.

It also mentions it passes through the point (3, -1).

Using point-slope form of equation,

Answer:

500.00    equal

5 × 10      not equal

5 × 10²      equal

50.05     not equal

500.500      not equal

Answer: area

Step-by-step explanation:

        Area is solved with L * W

        Volume is solved with L * W * H

        Using these formulas we can see that area uses 2-dimensions, the length and the width, while volume uses 3.

Answer:

Area.

Step-by-step explanation:

2 dimentional spaces have only area, and no volume. Volume describes the amount of space within the container

This is the answer of your question

Answer

See in pic

Step-by-step explanation:

Step-by-step explanation:

1.

that creates a right-angled triangle :

the string is the Hypotenuse (the baseline, which is the side opposite of the 90° angle).

the invisible "line" from the kite straight down to the ground is one leg. and we need that length.

and the invisible "line" on the ground between the point where Brian is standing, and the point, where the : line: coming down from the kite hits the ground, is the second leg.

the angle between both legs is 90°.

so, we use the law of sine :

a/sin(A) = b/sin(B) = c/sin(C)

where the sides and the associated angles are always opposite of each other.

in our case, the Hypotenuse (the string) is opposite of 90°.

and the angle opposite of the kite height line is the designated angle of elevation at the point, where Brian is standing : 70°.

so, we have here

65/sin(90) = height/sin(70)

height = 65×sin(70)/sin(90)

sin(90) = 1

height = 65×sin(70) = 61.08002035... m

2.

another right-angled triangle.

what is not clear to me : what does "distance from plane to building" mean ?

is it really the line of sight from the plane in the air to the building in the ground ? which is the Hypotenuse of that triangle.

or is it the ground distance (from the point where the height line hits the ground to the building) ? which is also the air distance (parallel line to the ground distance up in the air with the plane).

remember, the sum of all angles in a triangle is always 180°.

per law of sine we have

height/ sin(28) = line of sight / sin(90) =

= air (or ground) distance / sin(180-28-90)

1200/sin(28) = line of sight / 1 =

= air distance / sin(62)

line of sight (if that is what we need) =

= 1200/sin(28) = 2,556.065362... m

air distance = 1200×sin(62)/sin(28) = 2,256.871758... m

3.

another right-angled triangle.

the Hypotenuse is the line of sight from the point 12 ft away in the ground to the top of the pole.

the ground distance (12 ft) is one leg.

the pole (and its height) is the second leg.

so, we have our law of sine

height/sin(53) = line of sight / sin(90) =

= ground distance / sin(180-53-90)

we need the height, so

height/sin(53) = ground distance / sin(37)

height = 12×sin(53)/sin(37) = 15.92453786... ft

add the degrees 90 and 25 which gives 115° and subtract to give 65°

I am subtracting by 180 because angle on a straight line is 180 hope this helps

Answer: y is 155⁰ X is 65⁰

Step-by-step explanation: y = 180⁰ - 25⁰

X = 180⁰ - (90 + 25) = 180 - 115= 65

Straight line triangle is 180

Total angle in a triangle 180

Answer:

9.4

Step-by-step explanation:

I used r=C/2π as the formula

The horizontal distance that's traveled by the golf ball based on the velocity given is 138.56feet.

From the information given, the golf ball has been hit off of the tee at an angle of elevation of 30 degrees and an initial velocity of 160 ft/sec.

The distance will be:

= 160 × cos30°

=160 × 0.866

= 138.56 feet

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