pls help this due before 11:59​

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:

The histogram is attached

Step-by-step explanation:

The histogram attached shows the points scored in each game, where total number of games are 20

Histogram is made by the following details:

X-Axis: Game No.

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20)

Y-Axis: Total points scored in that game.

(24,49,28,50,34,51,36,52,36,52,40,62,41,67,43,68,43,73,48,79)

Different colors are used for each much so that it is easy to differentiate among them.

Answer:

- 8x² - 40x - 50

Step-by-step explanation:

Begin by evaluating the inside, that is g(f(x))

Substitute x = f(x) into g(x), that is

g(f(x))

= g(2x + 5)

= (2x + 5)² ← expand using FOIL

= 4x² + 20x + 25

Now substitute x = 4x² + 20x + 25 into h(x)

h(4x² + 20x + 25)

= - 2(4x² + 20x + 25) ← distribute parenthesis by - 2

= - 8x² - 40x - 50

Thus

h(g(f(x))) = - 8x² - 40x - 50

Answer:

Step-by-step explanation:

[tex]\sqrt{-2}=\sqrt{2}i\\\\\sqrt{-18}=\sqrt{2*3*3}i=3\sqrt{2}i\\\\\sqrt{-2}+\sqrt{-18}= \sqrt{2}i+3\sqrt{2}i\\ =(1+3)\sqrt{2}i\\\\=4\sqrt{2}i[/tex]

Answer:

h=14

Step-by-step explanation:

3/4*1/4=3/16

21/32/(3/16)=14

Answer:

h=25

Step-by-step explanation:

Answer:

X=42

Step-by-step explanation:

AB and BC make a right angle

So, 24°+x+24° =90°

48°+x=90°

X=90°-48°

X=42

______________________________

a. 42 degree.

b.i. q=135 degree( being vertically opposite angles)

j=135 degree( being corresponding angles)

b.ii. 225

a. 24+X+24=90[ sum of complementary angles]

or, 48+X=90

or,X= 90-48

X=42 degree

b.i. q=135 degree( being vertically opposite angles)

Vertically angles are always equal to each other.

j=135 degree( being corresponding angles)

Corresponding angles are always equal to each other.

b.ii. p+135=180[ sum of angle in straight line]

or,p= 180-135

p=45 degree.

q= 135 degree[ being vertically opposite angles]

r=p[being vertically opposite angles]

r=45 degree

Now,

p+q+r

= 45+135+45

=225 degree

Hope it helps

Good luck on your assignment

__________________________________

Answer:

[tex]xy=30-109i+30i^2[/tex]

Step-by-step explanation:

If x=(10-3i) and y=(3-10i), then xy=

[tex](10-3i)(3-10i)=[/tex]

Using the FOIL method:

First: [tex]30[/tex]

Outer: [tex]-100i[/tex]

Inner: [tex]-9i[/tex]

Last: [tex]30i^2[/tex]

[tex]30-100i-9i+30i^2=\\30-109i+30i^2[/tex]

[tex]xy=30-109i+30i^2[/tex]

Answers:

Perimeter=6 units

Area=0 units ^2

please see the attached picture for full solution

hope it helps

Good luck on your assignment

The one on the far left

Answer:

Yes.

Step-by-step explanation:

Apples needed             =130

apples in the kitchen    =68

130-68= 62 to complete for all the students

1 (3 dozens x 12) = 36 apples x 2= 72

68 +72=140 apples available for all the students

Answer:

Yes

Step-by-step explanation:

The reason for this is because 1 dozen is 12. And the schools bought 6 dozens of apples. If you multiply 36 by 2 you get 72. Then if you add 72+68 you get 140 apples, but the school only needed 130 apples. So yes the school has enough apples for grade 2.

Hope it helps

Answer:

At least 11: x≥11  ; At most 11:x≤11 ; More than11: x>11 ; Fewer than 11: x<11; Strictly between 3 and 11 : 3 < x < 11  ; Between 3 and 11: 3≤x≤11  ; Inclusive no more than 3: x≤3

Step-by-step explanation:

At least means that the number can't be lower than 11 (11 included)

At least means that the number can't be higher than 11 (11 included)

More means that the number must be higher than 11 ( 11 not included)

Fewer than means that the number must be lower than 11 ( 11 not included)

"Strictly between" means excluding the endpoints

Including endpoints.

Inclusive includes number 3 (less or equal)

Feel free to ask for more if needed or if you did not understand something.  

Answer: 13

Step-by-step explanation: 15-2=13

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:

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:

x=2.4650

Step-by-step explanation:

I assume that you mean [tex]3^x=15[/tex]

so let s use the ln() function

[tex]ln(3^x)= xln(3)=ln(15)[/tex]

so x = ln(15)/ln(3)

x = 2.4650

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

Answer:

In Quadrant I or III

Step-by-step explanation:

We know if the sign was not showing closed inequality facing other way

xy < 0 would be in the 2nd or 4th quadrant.

If xy = 0  then either xy or both are on the x or y axis

But if xy>0 then they are in quadrant I or III

If xy>0, then the points of P(x,y) lies in Quadrant I and III

According to the given condition;

This means that the product of x and y is a positive number.

Hence, either both x and y-coordinates are positive or are both negative

Hence, only points in the Quadrant I have positive x and y coordinates Or Quadrant III in which case all x and y values are negative.

Read more on Cartesian plane;

https://brainly.com/question/14325342

Answer:

w<0 or w>9

Step-by-step explanation:

2

w

+3>

29

w

3w+2

w

>

29

w

Let's find the critical points of the inequality.

3w+2

w

=

29

w

3w+2=29(Multiply both sides by w)

3w2+2w=29w(Multiply both sides by w)

3w2+2w−29w=29w−29w(Subtract 29w from both sides)

3w2−27w=0

3w(w−9)=0(Factor left side of equation)

3w=0 or w−9=0(Set factors equal to 0)

Answer:

Explanation:

2

w

+

3

>

29

w

First take LCM

2

+

3

w

>

29

w

Now you can remove the denominator(LCM) because it is on both sides.

So, we get

2 + 3w > 29

3w > 27

w>9

In this way, we get the answer.

Step-by-step explanation:

Could you show the given circle please?

Answer: The answer is C.

Step-by-step explanation: I just did it

Answer:

8 1/8

Step-by-step explanation:

2 4/8 plus 5 5/8

4/8 because it equals to 1/2

Answer:

8 1/8

Step-by-step explanation:

2 1/2+ 5 5/8

2 4/8 + 5 5/8

7 9/8

8 1/8

Answer:

2,4,5

Step-by-step explanation:

Do not repeat numbers, u need to put them in order from least to greatest, and range is for the y

Answer:

f(3π/4) = -π

A = π

b = 2

Step-by-step explanation:

Given that the function follows the form: f(x) = A sin(bx), then f(0) = 0. Given that the period is π, then at x = π/4 the function reaches a maimum, at x = π/2, f(x) = 0, and at x = 3π/4, f(x) reaches a minimum, which have to be π*(-1) = -π

Given the general equation: f(x) = A sin(bx), its period is calculated as:

period = 2π/b

which is equal to π, then:

2π/b = π

b = 2

Replacing x = π/4 into the equation of the function, we get:

A sin(2(π/4)) = π

A sin(π/2) = π

A = π

Answer:

x = 3 will be the answer.

Step-by-step explanation:

From right triangle ABC,

By applying Sine rule,

Sin45° = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex] = [tex]\frac{BC}{AC}[/tex]

    [tex]\frac{1}{\sqrt{2}}[/tex]  = [tex]\frac{BC}{6\sqrt{2}}[/tex]

BC = 6 units

Now from right triangle BCD,

By applying Cosine rule,

Cos60° = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex] = [tex]\frac{BD}{BC}[/tex]

[tex]\frac{1}{2}=\frac{x}{6}[/tex]

x = [tex]\frac{6}{2}[/tex]

x = 3

Answer:

The surface area of the pyramid is 208 units²

Step-by-step explanation:

Luckily, since this is a square pyramid, we only need to find two numbers. These two numbers are the area of the base and the area of one triangular side. After we find them, we need to add them all together.

First, the base:

Since it's a square, we can just do 8 · 8 and get 64. Now we have one of the two needed numbers.

Second, one of the triangles:

To start, we multiply the base (8) by the height (9) giving us 72. After we divide that by 2, we have the area of the triangle, which is 36. Now we have the second number down. Now we can...

Finally, add them all together:

Now that we have the area of the base (64) and one of our triangles (36), we need to add them together. We add the base once and the triangle four times (because there are four triangles) to get the total surface area. Our expression looks like this:

64 + 36 + 36 + 36 + 36

After doing some simplifying, we get our final number, 208.

The surface area of the pyramid is 208 units²

The surface area of the regular pyramid in the diagram is 208 units².

The surface area of the pyramid = Sum of area of the triangular faces + Area of the square base.

Surface area of the pyramid = 2bh + b²

Where b is the base

and h is the perpendicular height of each triangular faces

In the given diagram,

b = 8

h = 9

∴ Surface area of the pyramid = 2×8×9 + 8²

Surface area of the pyramid =  144 + 64

Surface area of the pyramid = 208 units²

Hence, the surface area of the regular pyramid in the diagram is 208 units².

Learn more on Calculating area of Pyramid here: brainly.com/question/22744289

#SPJ7

Answer:

40cm^2

Step-by-step explanation:

A=a+b/2×h

A=6+10/2*5

A=16cm/2*5cm

A=8cm*5cm

A=40cm^2

Answer:

To me the triangles in #6 appear to be the same shape as the first triangle in #7(EFG) with different lengths on the sides. But not much else is the same. I mean they are all triangles but the shape of the second triangle in #7(XYZ) isn't the same as either of the triangles in #6.

I hope that made sense to you!

Hope this helped! Have a great day! :)

Answer:

Answer is 16 ft.

The answer is rounded to the nearest tenth place.

Step-by-step explanation:

[tex]given \: that \: \\ diameter \: of \: circle \: = 5 \: ft \\ then \: radius \: = \frac{5}{2} \: ft \\ we \: know \: that \\ circumferece = 2\pi \: r \\ on \: substiuting \: r= \frac{5}{2} \: ft \ \\ in \: formula \\ circumferece = 2\pi \times \frac{5}{2} \\ = 5\pi \\ substiuting \: \pi = 3.14 \\ = 5(3.14) \\ = 15.7079 \\ = 15.708 \\ when \: it \: is \: rounded \: off \: to \: nearest \: tenth \\ we \: get \: 16 \: ft\: as \: the \: answer.[/tex]

HAVE A NICE DAY!

THANKS FOR GIVING ME THE OPPORTUNITY TO ANSWER YOUR QUESTION.

The circumference of the circle having a diameter of 5 ft will be 15.7 ft.

The easiest way to find the perimeter for any shape is to add up the lengths of all the sides, but a circle only has one side, so that isn't possible. If you don't know its circumference, you also don't know the length of that side.

Fortunately, we can use a formula that uses other properties of a circle to find its circumference. In fact, there are two different formulas for circumference we can use and they look like this:

C = 2πr

Here the diameter of the giver circle is 5 ft so the radii will be 2.5 ft

By putting the value of radius in the formula we get

[tex]C=2\pi r[/tex]

[tex]C=2\pi \times 2.5=15.7\ ft[/tex]

Hence the circumference of the circle having a diameter of 5 ft will be 15.7 ft.

To know more about circumference follow

https://brainly.com/question/20489969

Answer:

It should be 5:10 or 5 people not wearing sneakers and 10 not wearing a blue shirt

Step-by-step explanation:

Well it quite simple 1st you have the total which is 40

next you look at the rest, 15 people wearing sneakers plus the 5 waering sneakers and blue shirt. now you have 15.

next you have 10 people wearing but shirts. if you add the numbers you have now you get this: 15+10=25.

Now that you have 25 you can just add numbers to get 25(in that case 10 and 5). whats how you get 5:10

hope this helps (barry_ary)

Answer:

10

Step-by-step explanation:

15+10= 25

25+5=30

40-30=10

10 people are not wearing sneakers and

blue shirts

Answer:

B

Step-by-step explanation: