Solve the inequality and write the solution set using both set-builder notation and interval notation. -3a-15≤-2a+6

Answers

Answer 1

Answer:

Answer:

Set builder notation: {a | a ≥ -21}

Interval notation: [-21, ∞)

Step-by-step explanation:

A set represents a collection of things, objects, or numbers. A set builder notation is in the form y = {x | x is an odd number between 8 and 10}, which means y contains all the odd numbers between 8 and 10.

Interval notation is a way to define a set of numbers between a lower limit and an upper limit using end-point values. for example (8, 20) means numbers between 8 and 20.

Given -3a-15≤-2a+6; solving :

-3a - 15 ≤ -2a + 6

-3a + 2a ≤ 6 + 15

-a ≤ 21

dividing through by -1:

a ≥ -21

The solution is:

Set builder notation: {a | a ≥ -21}

Interval notation: [-21, ∞)

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The perimeter of a rectangle is 38m. The length is 3m more than times the width. Find the length and the width of the rectangle.

Answers

Answer:

Width = 4.75

Step-by-step explanation:

Step 1:

P = 2 ( L + W )

Step 2:

38 = 2 ( 3w + w )

Step 3:

38 = 6w + 2w

Step 4:

38 = 8w

Answer:

4.75 = w

Hope This Helps :)

The music you hear when listening to a magnetic cassette tape is the result of the magnetic tape passing over magnetic heads, which read the magnetic information on the tape. The length of time a tape will play depends on the length of the tape and the operating speed of the tape player. The formula is T = L S , where T is the time in seconds, L is the length of the tape in inches, and S is the operating speed in inches per second. How long a tape does a police officer need to record a 3-minute confession at an operating speed of 4 1 2 inches per second?

Answers

Using the given formula T = LS

And given the time is 3 minutes (3 x 60 = 180 seconds)and the speed is 4-1/2 inches per second:

180 = L x 4-1/2

Solve for L by dividing both sides by 4-1/2:

L = 180 / 4-1/2

L = 40

The length should be 40 inches.

A square is a figure with four sides of equal length and four right anglesa)conditional statement
b)postulate
c)definition
d)conjecture

Answers

The statement given in the statement is the definition of square.

What is a square?

A square is closed, two-dimensional shape with 4 equal sides and all the internal angles are right angles.

How to find which is the best statement?

In the question it is given that A square is a figure with four sides of equal length and four right angles.

So this is nothing but the definition of square .

So the correct answer is definition

Find more about "Squares" here: brainly.com/question/25092270

#SPJ2

Answer:

c) definition

Step-by-step explanation:

given f(7)=4, f'(7)=10, g(7)=-1, g'(7)=8, find the values of the following: 1. (fg)'(7) = 2. (f/g)'(7) =

Answers

By the product rule,

$(fg)'=f'g+fg'$

so that

$(fg)'(7)=f'(7)g(7)+f(7)g'(7)=10\cdot(-1)+4\cdot8=22$

By the quotient rule,

$\left(\frac fg\right)'=(f'g-fg')/(g^2)$

so that

$\left(\frac fg\right)'(7)=(f'(7)g(7)-f(7)g'(7))/(g(7)^2)=(10\cdot(-1)-4\cdot8)/((-1)^2)=-42$

What is the sum of prime numbers between 40 and 56

Answers

Answer:

184

Step-by-step explanation:

The prime numbers between 40 and 56 are 41, 43, 47, and 53.

Add the prime numbers.

41 + 43 + 47 + 53

= 184

Answer:

184

Step-by-step explanation:

Prime numbers between 40 and 56: 41, 43, 47, 53.

41+43+47+53=

84+47+53=

131+53=

184

What expression is equivalent to this equation?

Answers

Answer:

I think it’s d

Step-by-step explanation:

Answer: the right bottom corner

HOPE THIS HELPS !!

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