How would you prove that the triangle below is equilateral?

A. Shows all angles to be congruent

B. Show all sides to be congruent

C. Show at least two sides to be congruent

D. Show two sides are of equal measure

Please help me with this I need help

Answer:

Step-by-step explanation:

Prove that for any natural number 3^(n+4)-3n is divisible by 16.

(I'm going to assume that you mean 3^(n+4)-3^n.)

1. We can break up 3^(n+4)-3n into 3^n * 3^4-3^n (by the rule a^b*a^c = a^b+c).

2. Solve to get 3^n * 81 - 3^n

3. Factor out the 3^n, and you'll get 3^n(81-1), and simplify: 3^n(80)

        You may notice that 80 is divisible by 16.

4. Rewrite what we got from the last step as: 3^n*5(16).

Hope this helped you!

The proof that any natural number n in (3ⁿ⁺⁴ - 3ⁿ) is divisible by 16 is; it was simplified to 3ⁿ × 5

We want to show that show that 3ⁿ⁺⁴ - 3ⁿ is divisible by 16.

This is; (3ⁿ⁺⁴ - 3ⁿ)/16

From laws of indices, we know that;

aᵐ⁺ⁿ = aᵐ × aⁿ.

Thus; 3ⁿ⁺⁴ can be expressed as 3ⁿ × 3⁴.

Thus; (3ⁿ⁺⁴ - 3ⁿ)/16 is;

((3ⁿ × 3⁴) - 3ⁿ) = 3ⁿ((81 - 1)/16)

3ⁿ(80/16) = 3ⁿ × 5

The expression has been fully simplified to show that any natural number n in (3ⁿ⁺⁴ - 3ⁿ) is divisible by 16.

Read more about proof of numbers at; https://brainly.com/question/10657323

Answer: 10 hours and 25 minutes.

Step-by-step explanation:

Multiply 25, 10, and 2 to find volume. Volume is 500 metres.

1 meter = 1000 litres. 500 * 1000 = 500,000 litres in volume.

500,000/ 800= 625 minutes.

625 minutes = 10 hours and 25 minutes

It take 10 hours and 25 minutes to fill the swimming pool.

The volume of a cuboid is given by the formula:

Volume = Length × Width × Depth

              = 25 m × 10 m × 2 m

              = 500 m³

Now, convert the rate of filling from liters per minute to cubic meters per minute:

1 m³ = 1000 liters

So, 800 liters per minute = 800/1000

                                           = 0.8 m³ per minute

Next, the time it will take to fill the pool:

Time (in minutes) = Volume / Rate of filling

                             = 500 m³ / 0.8 m³ per minute

                              = 625 minutes

Now, 1 hour = 60 minutes

625 minutes = 625 / 60

                     = 10 hours and 25 minutes

So, it take 10 hours and 25 minutes to fill the swimming pool.

Learn more about Volume here:

https://brainly.com/question/28058531

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Answer:

A: 12cm

B: 90 degrees

C: 60 degrees

Step-by-step explanation:

A. Measure of GH is 1/4 of perimeter of 48 cm

48/4=12

a is 12cm

B.  in a rhombus, diagonals are perpendicular,

FH and EG are perpendicular

So, angles EJF, GJF, GJH, and EJH are all right angles and equal 90 degrees

thus measure of angle EJF is 90 degrees

C.

First lets find the measure of EJF

Since all the inner angles of the triangle add up to 180 degrees,

we can make an equation:

60+90+x=180

150+x=180

x=30

angles EFJ and EHJ are congruent, since opposite angles in a rhombus are congruent,

Also, angles EHJ and GHJ are congruent since the diagonals in a rhomus are angle bisectors

Thus EHJ=30 and GHJ=30

30+30=60

EHG = 60

so answer is 60 degrees

Answer:

n=10

Step-by-step explanation:

22+18=40 40/4=10

Given

4n - 18 = 22

Add 18 to both sides:

(4n - 18) + 18 = 22 +18

4n = 40

Divide 4n to both sides

[tex]\frac{4n}{4}[/tex]=[tex]\frac{40}{4}[/tex]

n=10

Now if you have to you can substitute n into the original equation and see if they are equal to one another.

4n - 18 = 22

4(10) - 18 = 22

40 - 18 = 22

22 = 22

With this being done n = 10

Answer:

4/5, 3/4, 0.72, 0.70, %65.5

Step-by-step explanation:

65.5/100=0.655

Answer:

3t² - Q / 5t

Step-by-step explanation:

Q = 3t² - 5th        collect like terms (separate 5th from the rest of the equation)

5th = 3t² - Q                                                                      (divide both sides by 5t)

h = 3t² - Q / 5t

If this helped please mark me as brainliest

Answer:

20

Step-by-step explanation:

1.75 x 6 = 10.5

10.5 + 9.5 = 20

Answer:

20 is the answer im 100% sure ask me for a picture if u want my work shown

Step-by-step explanation:

Answer:

The answer is B.

Step-by-step explanation:

Just took the quiz on A P E X .

Answer:

41.47

Step-by-step explanation:

So to find the price after the discount, multiply 48 by 0.8

38.4

To find the amount after tax, multiply by 1.08

41.472 ≈ 41.47

Answer:

$41.47

Step-by-step explanation:

Original price: $48.00

Discount: 20%

20% of $48 = 20% * $48 = 0.20 * $48 = $9.60

Price after 20% discount = $48.00 - $9.60 = $38.40

Tax: 8%

8% of $38.40 = 0.08 * $38.40 = $3.07

Price after tax: $38.40 + $3.07 = $41.47

Answer: $41.47

________________________________

Hey!!

Solution,

(5r+2)(3r-4)

= 5r(3r-4)+2(3r-4)

= 15r^2-20r+6r-8

= 15r^2-14r-8

So the right answer is 15 r squared minus 14 r minus 8

Hope it helps

Good luck on your assignment

_________________________________

Answer:

15 r squared minus 14 r minus 8

Step-by-step explanation:

from my understanding that what I think it is :) have an awesome day!!!!!!

________________________________

5y-3y+12

=2y+12

So the new expression becomes 2y+12

hope it helps

Good luck on your assignment

________________________________

Answer:

2y+12

Step-by-step explanation:

Answer: C  12

Step-by-step explanation:

ALL possible outcomes

1 tails

2 tails

3 tails

4 tails

5 tails

6 tails

1 Heads

2 Heads

3 Heads

4 Heads

5 Heads

6 Heads

so its 12 total outcomes

Answer:

12

Step-by-step explanation:

go ask edge

uquzas prguntale ea otroi

Using the normal distribution, it is found that the minimum average wait time is of 192 seconds.

------------------

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]0.675 = \frac{X - 185}{11}[/tex]

[tex]X - 185 = 11(0.675)[/tex]

[tex]X = 192[/tex]

The minimum wait time is of 192 seconds.

A similar problem is given at https://brainly.com/question/7001627

Answer:

2/13

Step-by-step explanation:

So firstly, know that there are 13 cards in the deck (3 + 6 + 4).

Therefore, the probability of drawing a green is 4/13.

After you draw the green card, there will be 12 cards left. Therefore, the probability of drawing a purple card next is 6/12.

To find compound probability, multiply the probabilities of the two separate events happening together:

4/13 * 6/12

= 2/13

Hope this helps! Please contact me if you have any questions :)

Answer: A. (-1,-10)

The x-coordinate of the vertex can be calculated using [tex]x=-\frac{b}{2a}[/tex].

According to the equation given a = 1, and b = 2.

[tex]x=-\frac{b}{2a} =-\frac{2}{2(1)}=-\frac{2}{2} =-1[/tex]

The y-coordinate of the vertex can be calculated by subbing in the x-value from the previous equation (x = -1) for x, and solving for y.

[tex]y=x^{2}+2x-9=(-1)^{2}+2(-1)-9=1-2-9=-10[/tex]

∴ the vertex is (-1,-10).

Answer:

Step-by-step explanation:

The given function is

[tex]f(x)=(x-1)(x+7)[/tex]

Zeroes of the function are

[tex](x-1)(x+7)=0[/tex]

[tex]x=-7,1[/tex]

It means, f(x) intersect x-axis at x=-7 and x=1.

Mid value of -7 and 1 is the x-coordinate of the vertex.

[tex]\dfrac{-7+1}{2}=-3[/tex]

At x=-3,

[tex]f(-3)=(-3-1)(-3+7)=(-4)(4)=-16[/tex]

So, the vertex of the function is at (-3,-16).

The given function can be written as

[tex]f(x)=x^2+7x-x-7[/tex]

[tex]f(x)=x^2+6x-7[/tex]

Here leading coefficient is negative, it means it is an upward parabola.

So, we conclude that

1. The graph is increasing on the interval x > -3.

2. The graph is decreasing on the interval x < -3.

3. The graph is positive only on the intervals where x <-7 and where x > 1.

4. The graph is negative only on the intervals where -7 < x < 1.

Therefore, the correct options are 2, 3 and 4.

Answer:

THE CORRECT ANSWERS ARE 2,3,4!

Step-by-step explanation:

TOOK THE TEST ON EDGE

The gradient of the blue line which shown in the graph and passes from the point (3,0) and (-1,2) is -1/2.

The gradient of a line is the difference in the height of the y coordinates and the difference in the width of the coordinates. It can be calculated with the following formula.

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Here, (x1,y1) and (x2,y2) are the coordinates of two points lies on the line.

In the given graph, the blue line passes through the point (3,0) and the form the point (-1,2). Thus, the gradient of the line is,

[tex]m=\dfrac{2-0}{-1-3}\\m=\dfrac{2}{-4}\\m=-\dfrac{1}{2}[/tex]

Thus, the gradient of the blue line which shown in the graph and passes from the point (3,0) and (-1,2) is -1/2.

Learn more about the gradient of a line here;

https://brainly.com/question/11693181

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Answer: Even

Step-by-step explanation:

This graph has been translated up by one unit but is still symmetrical about the y axis.

A simple proof would be to check if  f(x) = f(-x). If it does, then it is even.

To check for an odd function, check if f(-x) = -f(x). If it does, then it is even.

To check for neither, f(-x) will not equal -f(x)

Answer:

Step-by-step explanation:

Multiply by the reciprocal of 3/4. That is 4/3

[tex]\frac{11}{1} *\frac{4}{3} =\frac{44}{3}[/tex]

2 doesnt go into 44, but it does go into 42. It goes into 42 fourteen times. Then there is 2/3rds leftover

[tex]\frac{44}{3} ,14\frac{2}{3}[/tex] are both equivalent

Answer: 3.2 seconds

Step-by-step explanation:

Time = Distance / speed

= 2000 / 625

= 3.2 seconds

Answer:

Solve each equation for x. 1) x – 15 = 24 => x = 39 2) 18 = −6 + x => x = 24 3) 19 — X = 8 => x = 11 4) x – 22 = 24 => x = 46 5) 24 — X = 17 => x = 7 6) 16 — X = 3 ...

Step-by-step explanation:

Answer:

31.2 dm

Step-by-step explanation:

Podemos calcular a hipotenusa do triángulo empregando a regra de Pitágoras:

[tex]h^2 = a^2 + b^2[/tex]

onde h = hipotenusa

a = unha perna do triángulo

b = outra perna do triángulo

Polo tanto:

[tex]h^2 = 20^2 + 24^2\\\\h^2 = 400 + 576\\\\h^2 = 976\\\\h = \sqrt{976}\\ \\h = 31.2 dm[/tex]

A hipotenusa é de 31,2 dm

Answer:

see below

Step-by-step explanation:

The blue graphs had 2 real solutions since it crosses the x axis twice

The yellow graph has no real solutions since it does no cross the x axis

The red graph has one solutions since it touches the x axis

Answer:

3/4

Step-by-step explanation:

There are 12 marbles in the bag

9 marbles are not blue

P(not blue) = marbles that are not blue / total marbles

                   = 9/12 = 3/4

Answer:

C

Step-by-step explanation:

5a+ 18 < -27

Subtract 18 from each side

5a+18-18 < -27-18

5a < -45

Divide each side by 5

5a/5 < -45/5

a < -9

Open circle at 9, line doing to the left

Answer:

Step-by-step explanation:

(6, -4) ; (-4,-4)

[tex]Distance=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1}^{2})}\\\\ =\sqrt{(-4-6)^{2}+(-4-[-4])^{2}} \\\\=\sqrt{(-10)^{2}+(-4+4)^{2}} \\\\=\sqrt{100+0}\\\\ =\sqrt{100}\\\\[/tex]

= 10 units

Answer:

x = 75

Step-by-step explanation:

X and 105 are supplementary angles so they add to 180

x+105 = 180

Subtract 105 from each side

x = 180-105

x= 75

Answer:

Inverse Property

Step-by-step explanation:

This property is inverse property with respect to addition.

E.g.

If x=y and z= -y

Then,

x+z = 0

its basically d on edg :)