Simplify the expression where possible. (r^3)^ -2

Answer:

c

Step-by-step explanation:

Answer:

-30

Step-by-step explanation:

The integers are the whole numbers and the opposite of the whole numbers.

That is {...,-3,-2,-1,0,1,2,3,...} is the set of integers.

If it is a number you count with or the opposite of a number you count with it or 0, then it is an integer.

So we need to solve the inequality [tex]-3 \le x+5 \le 8[/tex] first, and then just say all the integers included in that compound inequality. Last step is to add since it is asking for the sum of those integers.

Let's do this.

[tex]-3 \le x+5 \le 8[/tex]

Subtract 5 on all sides:

[tex]-3-5 \le x+5-5 \le 8-5[/tex]

Simplify all sides:

[tex]-8 \le x+0 \le 3[/tex]

[tex]-8 \le x \le 3[/tex]

This inequality includes all numbers between -8 and 3, and both include -8 and 3 because of the equal part on both of the inequality parts.

So we have -8,-7,-6,-5,-4,-3,-2,-1,0,1,2, and 3 are the integer solutions of this inequality.

Let's add them. I'm going to put opposites together because I know they will zero out.

So I have this:

-8+-7+-6+-5+-4+-3+-2+-1+0+1+2+3

-8+-7+-6+-5+-4+(-3+3)+(-2+2)+(-1+1)+0

-8+-7+-6+-5+-4+0       +0        +0     +0

-8+-7+-6+-5+-4

-(8+7+6+5+4)

-([8+7]+[6+5]+4)

-([15]+[11]+4)

-(15+11+4)

-([15+11]+4)

-([26]+4)

-(26+4)

-(30)

-30

Answer:

D

Step-by-step explanation:

Instead of going through each of the table, let's create one ourselves.

So, we have the piecewise function:

[tex]f(x)=-x+8,\text{ if } x<4\\f(x)=x, \text{ if } x\geq 4[/tex]

So, let's create a table of values starting with 2 and skipping the odd numbers until 12.

2:

For 2, since 2 is less than one, plug it into the first equation. Thus:

[tex]f(2)=-(2)+8=6[/tex]

So, the first value is (2,6).

For 4, since 4 is not less than 4 but rather equal to 4, use the second equation. Thus:

[tex]f(4)=(4)=4[/tex]

The second value is (4,4).

For 6, the same thing. 6 is greater than 4 so use the second equation:

[tex]f(6)=(6)=6[/tex]

So the third value is (6,6).

And this pattern will repeat. Therefore, our table of equations is:

x   |      y

2  |      6

4  |      4

6  |      6

8  |     8

10 |    10

12  |    12

The choice that represents this is D. D is the correct answer.

Answer:

its is a

Step-by-step explanatioits n:

The equation of the line will be y = (1/3)x + ( 11 / 3 ). The correct option is B.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

Let m be the slope of the line and c is the y-intercept of the line.

The equation of the line is given as,

y = mx + c

The product of the slopes of the perpendicular lines is equal to -1.

y = 3x – 2

m = 3

Then the slope of the perpendicular line will be -1 / 3. The equation of the line will be written as below:-

y = (-1 / 3)x + c

The line is passing through the point  (–2, 3). Then calculate the value of the constant.

3 = (-1 / 3 )2 + c

c = 11 / 3

The equation of the line will be:-

y = (-1/3)x + (11/ 3)

Therefore,  the equation of the line will be y = (1/3)x + ( 11 / 3 ). The correct option is B.

To know more about the equation of the line follow

https://brainly.com/question/18831322

#SPJ2

Answer:

7/15

Step-by-step explanation:

Well 4/5 - 1/3 = 12 / 15 - 5 / 15 which is equal to 7/15, but there aren't any expressions in your question.

Answer:

7/15

Step-by-step explanation:

4/5 - 1/3 = 12 / 15 - 5 / 15 = 7/15

Answer:

16

Step-by-step explanation:

Subtracting the 2 expressions

3b² - 8 - b(b² + b - 7) ← distribute parenthesis

= 3b² - 8 - (b³  + b² - 7b) ← distribute parenthesis by - 1

= 3b² - 8 - b³ - b² + 7b ← collect like terms

= - b³ + 2b² + 7b - 8 ← substitute b = - 3 into the expression

= - (- 3)³ + 2(- 3)² + 7(- 3) - 8

= - (- 27) + 2(9) - 21 - 8

= 27 + 18 - 21 - 8

= 16

Answer:

7/51

Step-by-step explanation:

Assuming that the marbles are drawn without replacement, the probability of the first marble being drawn is 7/(7+8+3) which is 7/18.

The probability of the second marble being red is 6/17, as there are 6 red marbles left and 17 marbles in the bag.

We then multiply 7/18 and 6/17, getting 7/51.

Answer:

5√8, 14.025, 40/3, √170

Step-by-step explanation:

Step 1: Evaluate √170

√170 = 13.0384

Step 2: Evaluate 5√8

5√8 = 14.1421

Step 3: Evaluate 40/3

40/3 = 13.333

Step 4: Align greatest to least

14.1421 > 14.025 > 13.333 > 13.0384

Step 5: Revert

5√8, 14.025, 40/3, √170

Answer:

I = BLv/R

Step-by-step explanation:

V = BLv

V = IR

Since both right sides are equal to V, set the right sides equal to each other.

IR = BLv

I = BLv/R

Answer:

You can buy a maximum number of 11 boxes

Step-by-step explanation:

The first step is to calculate the number of boxes that you can afford with the $150 without the discount. This can simply be done by dividing $150 by $15

= 10 boxes.

The next step is to calculate the effect of the discount on the total of $150. The $25 discount will increase your average sum to $175.  This extra $ 25  can afford you one more box. bringing the total number of boxes to 11.

You can buy a maximum number of 11 boxes

Answer:

Q1. y = 5 Q2.  (√2 - √3)/2

Step-by-step explanation:

Q1

√12 - √147 + y√3 = 0

Taking -√147 and √12 to the right hand side, we have

y√3 = √147 - √12

y√3 = √(3 × 49) - √(3 × 4)

y√3 = √3 × √49 - √3 × √4

y√3 = √3 × 7 - √3 × 2

y√3 = 7√3 - 2√3

y√3 = 5√3

Dividing both sides by √3, we have

y√3/√3 = 5√3/√3

y = 5

Q2

Sin45° - Cos30°

Since Sin45° = √2/2 and Cos 30° = √3/2

Substituting these values into the equation, we have

Sin45° - Cos30° = √2/2 - √3/2

Taking L.C.M of both factors, we have

Sin45° - Cos30° = (√2 - √3)/2

Answer:

Step-by-step explanation:

[tex]4a-3\left(4-a\right)\\\\\mathrm{Expand}\:-3\left(4-a\right):\quad -12+3a\\\\=4a-12+3a\\\\\mathrm{Simplify}\:4a-12+3a:\quad 7a-12\\\\\mathrm{Simplify}\:4a-12+3a:\quad 7a-12\\\\=7a-12[/tex]

Answer:

Step-by-step explanation:

Given three functions 3x⁴, 15x³and 21x², the greatest common factor is the greatest value that can divide through the three functions at the same time.

To get this GCF, let us divide each functions into simplest form

3x⁴ = (3 *x * x) * x * x

15x³ = 5 * (3 * x * x) * x

21x² = 7 * (3 * x * x)

It can be seen that the product in parenthesis is common to the three functions given on expanding them, hence the greatest common factor of the three functions is 3 * x * x = 3x²

Answer:

[tex]\frac{3*(8e-4f-1)}{8}[/tex]

I hope this helps. Sorry for a late response. I used

tiger-algebra.com

PEACE!☘️

Answer:

M^4

Step-by-step explanation:

Here use product law which state- same base power should add

M^7-3

M^4

Answer:

A. 6 to the Second Power.

Step-by-step explanation:

Hope it Helped!

Answer:

First one

Step-by-step explanation:

If you mean 2 to the sixth power, then it's for sure the first one.

Answer:

2^6

Step-by-step explanation:

Answer:

(C) Division Property of Equality

Step-by-step explanation:

Looking at the equation [tex]2y=18[/tex], we see that if we want to isolate y, we need to divide it by 2 - because we're multiplying it by 2, and 2 times a number divided by 2 is just the number.

The Division Property of Equality states that if we have an equation, [tex]a=b[/tex], then [tex]a\div c = b\div c[/tex].

So, that means [tex]2y\div 2[/tex] will be equal to [tex]18 \div 2[/tex], which is 9.

Hope this helped!

Answer:

C. Division Property of Equality

Step-by-step explanation:

The equation is

2y = 18

The answer is of the form

y = a number

Now, we have 2y. We want y alone. 2y means 2 multiplied by y. Since we want y alone, to undo the multiplication of 2 and y, we need to use division. We need to divide 2y by 2. Then we also need to divide the right side by 2. Since we are using division, the answer is:

C. Division Property of Equality

Answer:

Step-by-step explanation:

[tex]2\frac{1}{3}*\frac{3}{14}=\frac{7}{3}*\frac{3}{14}=\frac{1}{2}\\\\[/tex]

option 1)one- half

  1/2

Option 3) Seven-thirds times three fourteenths

[tex]\frac{7}{3}*\frac{3}{14}=\frac{1}{2}\\\\[/tex]

Option 5) 21/42

[tex]\frac{21}{42}=\frac{1}{2}[/tex]

Answer:

10.25

Step-by-step explanation:

Answer:

the answer would be 10.25

Answer:

It sooo D

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer:

B. 5,7,12 is what I got.

Answers:

A. Commutative Property of Multiplication

D. Commutative Property of Addition

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

Explanation:

The commutative property of multiplication is the idea we can multiply two numbers in any order. The rule is x*y = y*x

An example would be 2*3 = 3*2 since both sides result in 6.

The same applies to 3*(2+c) because it can be written as (2+c)*3. Simply flip the two factors 3 and (2+c).

--------------------

A similar idea is the commutative property of addition. This rule says that we can add two numbers in any order we want.

x+y = y+x

An example would be 7+9 = 9+7 because both sums result in 16

Using this rule, we can rewrite 2+c as c+2

Therefore 3(2+c) is the same as 3(c+2)

--------------------

We can't use any associative properties because we would need to have 3 terms being either added or 3 terms being multiplied, for associative rules to apply.

For instance 1+(2+3) = (1+2)+3 is an example of the associative property of addition. An example of the associative property of multiplication would be 3(7*9) = (3*7)*9

Answer:

(12, 10, -12)

x = 12

y = 10

z = -12

Step-by-step explanation:

Let's start by picking a variable to eliminate from the three equations, since "z" is at the end, let's go with "z".

Next we'll eliminate z from two of the equations by adding them together so:

(x+y+z=10) + (-2x-2y-z=-32)

you'll get: -x-y=-22

Next we'll eliminate z from the remaining equation in the same way so:

(-2x-2y-z=-32) + (3x-2y+2z=-8)

you'll get: -x-6y=-72

We now have two new equations:

-x-y=-22

-x-6y=-72

From these let's eliminate another variable, let's go with "x" and since both "x" are negative we'll multiply one of the equations by the negative sign of the other equation so we'll end up with one positive x and one negative x, which looks like this:

-x-y=-22

x+6y=72

and when we add these two equations we get:

5y=50

Finally we can solve for y:

y=10

With the known value of y we can use y to plug into the other equations and solve for the x and z variables to get x=12, y=10, z=-12

Answer:

Step-by-step explanation:

hello :

the area is : (3x+4y)²cm²    when :x=4 and y=1, the area is : (3(4)+4(1))²cm² =16²cm2=256cm²

Answer:

8b+2

Step-by-step explanation:

Combine Like Terms:

=−b+2+9b

=(−b+9b)+(2)

=8b+2

Answer:

multiplying the length and the width.

Step-by-step explanation:

To find the area of a rectangle, multiply its height by its width.

For a square you only need to find the length of one of the sides then multiply this by itself to find the area.

Answer:  see proof below

Step-by-step explanation:

Use the Triple Angle Identity: sin 3A = 3sinA - 4sin³A

[tex]\text{Given:}\quad \sin\bigg(\dfrac{\theta}{3}\bigg)=\dfrac{1}{2}\bigg(m+\dfrac{1}{m}\bigg)[/tex]

Proof LHS → RHS

LHS:                                 sin Ф

Let A = Ф/3                     sin 3A

Triple Angle Identity:     3sinA - 4sin³A

Substitute Ф/3 = A:         3sin(Ф/3) - 4sin³(Ф/3)

Substitute sin(Ф/3):         [tex]3\bigg(\dfrac{1}{2}\bigg(m+\dfrac{1}{m}\bigg)\bigg)-4\bigg(\dfrac{1}{2}\bigg(m+\dfrac{1}{m}\bigg)\bigg)^3[/tex]

[tex]\text{Simplify:}\qquad \qquad \dfrac{3m}{2}+\dfrac{3}{2m}-4\bigg(\dfrac{1}{8}\bigg(m^3+3m+\dfrac{3}{m}+\dfrac{1}{m^3}\bigg)\bigg)\\\\.\qquad \qquad \qquad =\dfrac{3m}{2}+\dfrac{3}{2m}-\dfrac{m^3}{2}-\dfrac{3m}{2}-\dfrac{3}{2m}-\dfrac{1}{2m^3}\\\\.\qquad \qquad \qquad =-\dfrac{m^3}{2}-\dfrac{1}{2m^3}\\\\\text{Factor:}\qquad \qquad -\dfrac{1}{2}\bigg(m^3+\dfrac{1}{m^3}\bigg)[/tex]

[tex]\text{LHS = RHS:}\quad -\dfrac{1}{2}\bigg(m^3+\dfrac{1}{m^3}\bigg)=-\dfrac{1}{2}\bigg(m^3+\dfrac{1}{m^3}\bigg)\quad \checkmark\\[/tex]

Answer:

-42

Step-by-step explanation:

negative * negative = positive

positive * negative = negative

negative * positive = negative

(-6)(-7)(-1) =

= 42(-1)

= -42

Answer:

-42

Step-by-step explanation:

negative * negative = positive

positive * negative = negative

negative * positive = negative

(-6)(-7)(-1) =

= 42(-1)

= -42