Mathematics High School

30 points! Numbers n, m, and k are natural numbers. Express as powers:
#1: 4^n*4^5
#2: 3^8*3^n
#3: 2^2n/2^n
#4: 2^3n/2^2n
Pictures of each question will also be attached.

30 Points! Numbers N, M, And K Are Natural Numbers. Express As Powers:#1: 4^n*4^5#2: 3^8*3^n#3: 2^2n/2^n#4:
30 Points! Numbers N, M, And K Are Natural Numbers. Express As Powers:#1: 4^n*4^5#2: 3^8*3^n#3: 2^2n/2^n#4:
30 Points! Numbers N, M, And K Are Natural Numbers. Express As Powers:#1: 4^n*4^5#2: 3^8*3^n#3: 2^2n/2^n#4:
30 Points! Numbers N, M, And K Are Natural Numbers. Express As Powers:#1: 4^n*4^5#2: 3^8*3^n#3: 2^2n/2^n#4:

Answers

Answer 1

The powers in this problem are expressed as follows:

1. 4^n x 4^5 = 4^(n + 5).

2. 3^8 x 3^n = 3^(8 + n).

3. 2^(2n)/2^n = 2^n

4. 2^(3n)/2^(2n) = 2^n

Exponents and multiplication

When two terms with the same base and different exponents are multiplied, we keep the base and add the exponents to find the product.

In the context of this problem, this is what we use for items 1 and 2, as follows:

1. 4^n x 4^5 = 4^(n + 5). -> Base 4, exponents n and 5, n + 5 = n + 5.

2. 3^8 x 3^n = 3^(8 + n). -> Base 3, exponents 8 and n, 8 + n = 8 + n.

Exponents and division

When two terms with the same base and different exponents are divided, we keep the base and subtract the exponents to find the quotient.

In the context of this problem, this is what we use for items 3 and 4, as follows:

3. 2^(2n)/2^n = 2^n -> Base 2, exponents 2n and n, 2n - n = n.

4. 2^(3n)/2^(2n) = 2^n -> Base 2, exponents 3n and 2n, 3n - 2n = n.

More can be learned about exponential rules at https://brainly.com/question/11761858

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Related Questions

Two trains start from Fort Worth traveling at the same speed. The trip for Train W takes 20 hours, while the trip for Train Z takes 25 hours. If the city Train Z is traveling to is 400 miles farther away than the city Train W is traveling to, how far will Train Z travel in total to reach its destination?

Answers

Answer:

= x/20=x+400/25

Distance traveled by Train W = 1600 miles

Distance traveled by Train Z = 2,000 miles

Step-by-step explanation:

Time taken for Train W to complete a trip = 20 hours

Time taken for Train Z to complete a trip = 25 hours

The city Train Z is traveling to is 400 miles farther away than the city Train W is traveling to.

both trains have same speeds and start from same location.

To find the distance in total each train travels.

Solution:

Let length of the trip of Train W be = xx miles

Speed of Train W can be given as :

⇒ \frac{Distance}{Time}

Time

Distance

⇒ \frac{x}{20}\ miles/h

20

x

miles/h

So, the length of the trip of Train Z will be = (x+400)(x+400) miles

Speed of Train Z can be given as :

⇒ \frac{Distance}{Time}

Time

Distance

⇒ \frac{x+400}{25}\ miles/h

25

x+400

miles/h

Since the speeds are same, so the equation to find xx can be given as:

⇒ \frac{x}{20}=\frac{x+400}{25}

20

x

=

25

x+400

Solving for xx

Multiplying both sides by 100 to remove fractions.

⇒ 100\times \frac{x}{20}=100\times \frac{x+400}{25}100×

20

x

=100×

25

x+400

⇒ 5x=4(x+400)5x=4(x+400)

Using distribution.

⇒ 5x=4x+16005x=4x+1600

Subtracting both sides by 4x4x

⇒ 5x-4x=4x-4x+16005x−4x=4x−4x+1600

⇒ x=1600x=1600

Thus, Distance traveled by Train W = 1600 miles

Distance traveled by Train Z = 1600+4001600+400 = 2,000 miles

Find the perimeter of the figure to the nearest hundredth.

Answers

Answer: 90.75 mm

Step-by-step explanation:

Given

The radius of the hemisphere is 16 mm

length of the inclined sides are 20 mm

The perimeter of the figure is the sum of the length of two inclined sides and a semi-circle circumference

[tex]\Rightarrow \text{Perimeter P=}\dfrac{2\pi r}{2}+2\times 20\\\\\Rightarrow P=\pi \times 16+40\\\Rightarrow P=50.75+40\\\Rightarrow P=90.75\ mm[/tex]

Which number could be included in Group B ​

Answers

Answer:

C

Step-by-step explanation:

Just did the test

what is the volume of the cube shown?

Answers

Answer:

11 25/64

Step-by-step explanation:

you do 2 1/4 times itself 3 times.

please help!!

GE = ___ degrees

Answers

Answer:

90°

Step-by-step explanation:

NE=90° and NG=180° (<'s on a str. line)

NG=NE+GE

180°=90°-GE

GE=180°-90°

GE=90°

Which equation describes the relationship shown in the table?
Items Sold

A- p=2i
B- i=2p
C- p=i+5
D- i=p+5

Answers

Answer:

A

Step-by-step explanation:

i = items sold

p = profit

Based on the table, the profit is twice the number of items sold. Therefore the answer is A. Correct me if I'm wrong. I hope it helps.

El valor numérico de la expresión 〖P(y)=y〗^2-7y+10 para y=2 es: a. P(2)=9 b. P(2)=0 c. P(2)=-2 d. P(2)=-5

Answers

Answer:

Opción b, P(2) = 0

Step-by-step explanation:

Tenemos la expresión:

P(y) = y^2 - 7*y + 10

Para encontrar el valor P(2), simplemente debemos remplazar todas las "y" en la expresión de arriba por el valor 2, asi obtenemos:

P(2) = 2^2 - 7*2 + 10 = 4 - 14 + 10 = (4 - 14) + 10 = -10 + 10 = 0

P(2) = 0

La opción correcta es b.

The ratio of boys to girls in a gym class is 5:3. There are 27 girls in the class. How many boys are in the class?

Answers

Answer:

There are 45 boys in the gym class.

Step-by-step explanation:

Set up an equation:

Variable x = number of boys in the class

5/3 = x/27

Cross multiply:

5 × 27 = 3 × x

135 = 3x

Divide both sides by 3

45 = x

Check your work:

5/3 = 45/27

5 × 27 = 3 × 45

135 = 135

Correct!

who is correct
please answer ASAP!!! pls (:

Answers

Answer:Dwight is correct

Step-by-step explanation:

Solve for k.
8k = 24
k=

Answers

Answer:

K would equal 3

Step-by-step explanation:

8 x 3 = 24

Hope this helps :)

Answer:

k = 3

Step-by-step explanation:

Given:

8k = 24

Divide both sides by 8

8k / 8 = 24 / 8

k = 3

Check:

8k = 24

8(3) = 24

24 = 24

imagine paying attention in class

Answers

ikr smhhsjbddusbssddbd

The volume of a rectangular prism is 48 cubic centimeters. The volume of a similar rectangular prism is 6 cubic centimeters.
What is the scale factor for the rectangle?
a. 8
c. 4
b. 6
d. 2

Answers

The answer is a.) 8 6:48 = 1:8

|Calculate the midpoint (-5,5), K(-3,-2)

Answers

Answer:

(-4,1.5)

Step-by-step explanation:

Given :-

Two points (-5,5) and (-3,-2)

And we need to find out the midpoint of the two points. The midpoint of two points is given by the ,

[tex]:\implies[/tex] Midpoint =( x1+x2/2 , y1+y2/2)

[tex]:\implies[/tex] Midpoint =( -5-3/2 , 5-2/2)

[tex]:\implies[/tex] Midpoint =(-8/2,3/2)

[tex]:\implies[/tex] Midpoint = (-4 , 1.5)

Hence the midpoint of the two points is (-4,1.5) .
Explaination :

Here we would be using the midpoint formula to find the co-ordinates of the line segment joining the two given points.

Given points,

(-5,5) and (-3,-2)

★ Midpoint of two points:-

[tex]\boxed{ \sf{M \: = \: \dfrac{x_1 \: + \: x_2 }{2} \: , \: \dfrac{y_1 \: + \: y_2 }{2}}} \: \pink\bigstar[/tex]

★ We have :

x1 = -5 y1 = 5 x2= -3 y2 = -2

★ Putting the values :

Refer the attachment.Additional Information :

★ Centroid of a triangle :-

[tex]\boxed{ \sf{Centroid \: = \: \dfrac{x_1 \: + \: x_2 \: + \: x_3}{3} }} \: \pink\bigstar[/tex]

★ Distance Formula :-

[tex]\huge \large \boxed{\sf{{d \: = \: \sqrt{(x _{2} - x _{1}) {}^{2} \: + \: (y _{2} - y _{1}) {}^{2} }}}} \: \red\bigstar[/tex]

Preform the indecated operation 1/3x6/7

Answers

Answer:

0.257

Step-by-step explanation:

What is the area of this triangle? I need help!! pleaseee

Answers

Answer:72

Step-by-step explanation: 9x8 =72

What is the diameter of a cone with height 8 m and volume 150 pi m3 ?
A. 7.5 m
B. 5V3 m
o C. 7.573 m
D. 15 m

Answers

Answer:

V = pi*r^2*h

V = 150 m^3

h = 8 m

150 = pi*r^2*8

Solve for r (the radius) then multiply by 2 to obtain the diameter.Only, this is a cone, not a cylinder.

V = 1/3 pi r^2 h

Diameter of the cone is 15 m. So, option D is correct.

What is meant by solid shape ?

Solid shapes are defined as the three-dimensional objects that are described by the three dimensions length, breadth and height.

Here,

Volume of the cone is given by,

 V = 150[tex]\pi[/tex] m³

Height of the cone, h = 8 m

We know, the equation for the volume of a cone is,

V = 1/3[tex]\pi[/tex]r²h

where r is the radius and h is the height of the cone.

So,

(1/3) [tex]\pi[/tex]r²h = 150[tex]\pi[/tex]

r²x 8 = 3 x 150 = 450

r² = 450/8

r² = 56.25

r = 7.5 m

Therefore, diameter of the cone,

d = 2r

d = 2 x 7.5

d = 15 m

Hence,

Diameter of the cone is 15 m.

To learn more about solid shapes, click:

https://brainly.com/question/22731242

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"Woohoo! The school carnival is here! You think about all the fun carnival games that you love to play every year. Then you remember that some of the probability concepts you learned about in math class could help you here. Time to play!"

Answers

Answer:

14

Step-by-step explanation:

Is the relationship linear,exponential, or neither ?

Answers

ANSWER:

B

Step-by-step explanation:

Find the area of a circle having a circumference of 34pi Round to the nearest tenth. Use 3.14 for pi.

Answers

Answer:

the answer is 76.5

Step-by-step explanation:

Area formula= A= π r^2

Circumference formula= 2 π r

A holiday park is digging a swimming pool.
The volume of earth to be removed is 120m^3.
A mechanical digger can remove 0.15m^3 of earth with each scoop.
a) How many scoops will be needed to remove all the earth?
Please it’s urgent!

Answers

I think it’s A
Hope this helps:)

What is the measure, in degrees, of angle x?

Answers

Answer:

121°

Step-by-step explanation:

they're basically the same

Answer:

121°

Step-by-step explanation:

Theorem of vertical angles state that the opposite angles formed by two intersecting lines are congruent.

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

What is the diameter of the circle

Answers

Answer:

8.4 is the answer and the circumference is 26.4

Ill give brainliest - please help ASAP

WITH THE WORK THO PLEASE?

Answers

Answer:

Solution given:

5.

we have.

11x=½(16x+16+50)

22x=16x+66

22x-16x=66

6x=66

x=66/6

x=11

6.

118°=½(6x-11+181)

236=6x+170

6x=236-170

x=66/6

x=11°

What is the sum of all interior angles of a regular hexagon? A. 120° B. 360° C. 540° D. 720°

Answers

d-720

because 120x6 =720

GIVING BRAINLIEST -23 points-
URGENT HELP ME PLEASE!!!

Answers

Answer:

See a sides are equal so your answer is 8.2 in.

Ram is 20 years older than Sam. In 5 years, Ram will be twice old as Sam .Find their present ages.

Answers

Answer:

Sam is 15 years old and Ram is 35.

in five years Sam will be 20 and Ram will be 40, which is twice as old in age.

Sam=x Ram=x+20 in 5 years they will be Sam=x+5. Ram=x+20+5=x+25 also Ram will be twice old as sam so Ram=2Sam. X+25=2(x+5). X+25=2x+10. X=15 so sam will be 15 years old and Ram 2•15=30

What is the value of the expression 6 3/4 ( - 11.5) ? Explain why your answer is positive or negative.

Answers

Answer:

-77.625

Step-by-step explanation:

Covert 6 3/4 Mix it with decimal Which is 6.75,

then calculate Times this 6.75 by (-11.5). and we will get

- 77.625 ( Answer)

what is f(-1) for the function given?
f(x)=x^2-3x+8

Answers

Answer: 12

Work is provided in the image I attached

So you go to the store one day with 50$ to spend. You wanna buy some apples and some pears. The apples are 5$ per pack (3 in each pack) and the pears are 3$ each pack (4 in each pack.) you end up buying 5 packs each fruit. How much money do you have left over?

Answers

Answer:

10$

Step-by-step explanation:

Answer:

$10

Step-by-step explanation:

Honestly, who eats that much fruit? but okay, we'll start with finding how much money she spent, and apples will go first:

So this is basically dealing with rates, so you just gotta multiply:

5 x 5 = 25

So you spent an unnecessary $25 on apples, now let's go to pears:

3 x 5 = 15

So you spent $15 on pears, now we combine those two:

25 + 15 = 40

So you spent $40 on fruit

So now we want to know how much money we have left, so we're gonna subtract:

50 - 40 = 10

So you have $10 left over

hope this helps:)

Helpppppppppppppppppp
Pppppo

Answers

Answer:

(2 * L)+(2 * W)

Step-by-step explanation:

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