All categories

2 years ago

Simplify 2^4 x 2^3/ 2^5 x 2^4 leaving your answer in index form.

Mathematics

1 answer:

DanielleElmas [232]2 years ago

8 0

Answer:

2^-2

Step-by-step explanation:

When multiplying indices or exponents with the same base number, you can add the powers:

2^4 x 2³ = 2^7 (4 + 3 = 7)

2^5 x 2^4 = 2^9 (5 + 4 = 9)

When dividing indices or exponents with the same base number, you can subtract the powers:

2^7 ÷ 2^9 = 2^-2 (7 - 9 = -2)

You might be interested in

A bag contains 3 red marbles, 2 blue marbles, and 5 green marbles. What is the probability of selecting a red marble, replacing

RUDIKE [14]

Answer:

3/20

Step-by-step explanation:

The total number of marbles is

3 red marbles+ 2 blue marbles+ 5 green marbles = 10 marbles

P(1st marble is red) = red marbles/total

=3/10

We replace the marble so there are still 10 marbles in the bag

P(2nd marble is green) = green marbles/total

=5/10 = 1/2

P(1st red, 2nd green) = P(1st marble is red) * P(2nd marble is green)

=3/10 *1/2

=3/20

8 0

3 years ago

Can someone help please

yanalaym [24]

Step-by-step explanation:

a) The volume of the prism is

$V = (n^2 - 1)×(n^2 - 1)×(5n)$

$\:\:\:\:= (n^4 - 2n^2 + 1)(5n)$

$\:\:\:\:=5n^5 - 10n^3 + 5n$

b) If the dimensions L of the prism are tripled, the new volume will be

$V' = (3L)^3 = 27L^3 = 27V$

so it will increase by a factor of 27.

7 0

2 years ago

Help? please and thank you

11111nata11111 [884]

Answer:

first one

relationship between base and perpendicular is

given by tan angle

tan x=P/h

remember perpendicular is opposite side of taken angle

tan x=13/8

<x=tàn-¹(13/8)=58.39°

for second one

relationship between base and hypotenuse is given by cos angle

cos G=b/h

cos G=24/32

<G=cos-¹(24/32)=41.4 is your answer

8 0

3 years ago

Write an equation of the line that is:

Marysya12 [62]

$a)\\y=4x+1\\a=4\\new\ y=bx+c\\if\ parallel a=b\\y=4x+c\\substituting\point\ (2,3)\\3=4*2+c\\c=-5\\y=4x-5\\b)\\2y-6x=9\\2y=6x+9\\y=3x+4,5\\a=3\\new\ y=bx+c\\if\ parallel a=b\\y=3x+c\\substituting\ point\ (-2,1)\\1=4*(-2)+c\\c=9\\y=3x+9\\ c)\\y=4x+3\\a=4\\new\ y=bx+c\\if\ parallel a=b\\y=4x+c\\c=-3\\y=4x-3\\e)\\2y-4x=8\\2y=4x+8\\y=2x+4\\a= 2 \\new\y=bx+c\\if\ perpendicular b=-1/a\\y=- \frac{1}{2} x+c\\point(6,-6)\\-6=-1/2*6+c\\c=-3\\y=-1/2x-3\\f)\\2y-5x=15\\2y=5x+15\\y=\frac{5}{2}x+\frac{15}{2}$

4 0

3 years ago

Scarlett is working two summer jobs, making $13 per hour landscaping and making $8 per hour clearing tables. In a given week, sh

dolphi86 [110]

Answer:

The graph in the attached figure

Step-by-step explanation:

Let

x ----> the number of hours landscaping

y ----> the number of hours clearing tables

we know that

she can work a maximum of 12 total

$x+y\leq 12$ ----> inequality A

she must earn a minimum of $120

$13x+8y\geq 120$ ----> inequality B

Solve the system of inequalities by graphing

The solution is the triangular shaded area

see the attached figure

Remember that

If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities (the ordered pair lie in the shaded area of the solution set)

One possible solution is the point (10,1)

The point (10,1) lie in the shaded area

That means

The number of hours landscaping is 10 and the number of hours clearing tables is 1

5 0

3 years ago