Solve for x: x to the negative 3rd power is equal to 27 over 64

Answers

Answer 1

Answer: Remember what a negative exponent means ... it's just a positive exponent
in the denominator of a fraction. 'x' to negative 3rd power is the same as 1/x³ .

1/x³ = 27/64

Take the reciprocal of each side:

x³ = 64/27

x= ∛64/27 = ∛64 / ∛27.

64 is the perfect cube of 4.
27 is the perfect cube of 3.

x = 4/3 .

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Solve the compound inequality. y - 3 > 5 OR y + 3 < -2

Answers

Answer: y < -5 or y > 8

Step-by-step explanation:

$y-3>5\quad \text{or}\quad y+3<-2\n\underline{\ \ \ +3}\ \underline{\ +3}\qquad \underline{\quad \ \ -3}\ \underline{\ \ \ -3}\ny\quad \ \ >8\quad \text{or}\quad y\quad \ \ <-5$

Graph: ←---------o -1 8 o------------→

Interval Notation: (-∞, -5) ∪ (8, ∞)

Given the general identity tan X =sin X/cos X , which equation relating the acute angles, A and C, of a right ∆ABC is true?A. tan A = sin A/sin C
B. cos A = tan (90-A)/sin (90-C)
C. sin C = cos A/tan C
D. cos A = tan C
E. sin C = cos (90-C)/tan A

Answers

First, note that $m\angle A+m\angle C=90^(\circ).$ Then

$m\angle A=90^(\circ)-m\angle C \text{ and } m\angle C=90^(\circ)-m\angle A.$

Consider all options:

$\tan A=(\sin A)/(\sin C)$

By the definition,

$\tan A=(BC)/(AB),\n \n\sin A=(BC)/(AC),\n \n\sin C=(AB)/(AC).$

Now

$(\sin A)/(\sin C)=((BC)/(AC))/((AB)/(AC))=(BC)/(AB)=\tan A.$

Option A is true.

$\cos A=(\tan (90^(\circ)-A))/(\sin (90^(\circ)-C)).$

By the definition,

$\cos A=(AB)/(AC),\n \n\tan (90^(\circ)-A)=(\sin(90^(\circ)-A))/(\cos(90^(\circ)-A))=(\sin C)/(\cos C)=((AB)/(AC))/((BC)/(AC))=(AB)/(BC),\n \n\sin (90^(\circ)-C)=\sin A=(BC)/(AC).$

Then

$(\tan (90^(\circ)-A))/(\sin (90^(\circ)-C))=((AB)/(BC))/((BC)/(AC))=(AB\cdot AC)/(BC^2)\neq (AB)/(AC).$

Option B is false.

$\sin C = (\cos A)/(\tan C).$

By the definition,

$\sin C=(AB)/(AC),\n \n\cos A=(AB)/(AC),\n \n\tan C=(AB)/(BC).$

Now

$(\cos A)/(\tan C)=((AB)/(AC))/((AB)/(BC))=(BC)/(AC)\neq \sin C.$

Option C is false.

$\cos A=\tan C.$

By the definition,

$\cos A=(AB)/(AC),\n \n\tan C=(AB)/(BC).$

As you can see $\cos A\neq \tan C$ and option D is not true.

$\sin C = (\cos(90^(\circ)-C))/(\tan A).$

By the definition,

$\sin C=(AB)/(AC),\n \n\cos (90^(\circ)-C)=\cos A=(AB)/(AC),\n \n\tan A=(BC)/(AB).$

Then

$(\cos(90^(\circ)-C))/(\tan A)=((AB)/(AC))/((BC)/(AB))=(AB^2)/(AC\cdot BC)\neq \sin C.$

This option is false.

The right anwer is option A.
tan A = sin A / sin C
sin C = sin A / tan A = sin A / (sin A / cos A) = cos A
sin C = cos A

Brendon sells tires at the local auto parts store. He told a customer that the tire width for a new tire was 21.5 centimeters. Which of the following describes the tire width for the new tire? Help please thank you!!!

Answers

Answer:

215 mm

Step-by-step explanation:

1 cm = 10 mm

21.5 cm * (10 mm)/(1 cm) = 215 mm

Answer: 215 mm

I need help here please..! I took a picture of the Multi -Step equations..!

Answers

There are 8 problems in the picture. What you need is for someone to give you
some tips and solve one or two of them.
Giving you a bunch of answers and nothing else does NOT help you.

Here are my tips to you:

A). You're always trying to find the number that the unknown letter must be equal to,
in order to make the equation a true statement. That's the solution to the equation,
and the 'answer' to the problem.

B). Always do what you have to do in order to get the letter all by itself on one side.

C). Whatever you do to one side of the equation, you must do to the other side.

==========================================

Examples, from the picture:

#3: 8x - 2 = -9 + 7x What can you do to get the 'x' all alone on one side?

Subtract 7x from each side: x - 2 = -9

Add 2 to each side: x = -7
===========================================
#2: 6 = 1 - 2n + 5

Combine the 1 and the +5 on the right side: 6 = 6 - 2n

What can you do to get the 'n' all alone on one side?

Subtract 6 from each side: 0 = - 2n

Divide each side by -2 : 0 = n
===========================================
#5: 4m - 4 = 4m

Subtract 4m from each side: - 4 = 0

There is no number for 'm' that can make -4 equal to zero.
So this equation has no solution.
(That's OK. Not every equation must have a solution.)

What is the area of the whole rectangle