3. The product of a rational number and an irrational number is always irrational except
when the rational number is 0.
Explain why

Answers

Answer 1

Answer:

This is because anything multiplied by zero is zero itself.

Step-by-step explanation:

Ex: Multiply

[tex] 2 \times \sqrt{2} [/tex]

Here 2 is rational and root. 2 is irrational.

Their product is

[tex]2 \sqrt{2} [/tex]

Which is irrational.

But if you have

[tex]0 \times \sqrt{2} [/tex]

Where 0 is rational and root .2 is irrational.

Their product is

[tex]0[/tex]

Whis is rational.

Hope this helps... :-)


Related Questions

A contractor purchases 7 dozen pairs of padded work gloves for ​$102.48. She incorrectly calculates the unit price as ​$14.64 per pair for the expense report. What is the correct unit​ price? What is the​ error?

Answers

Answer:

The correct unit price can be calculated by dividing the total price paid by 84 that was the number of pairs of padded work gloves that were bought:

$102.48/84=$1.22

The correct unit price is $1.22.

-The error is that the person calculated the unit price by dividing the total price paid by 7 but the statement indicates that the contractor purchased 7 dozen pairs, which means: 7*12= 84. According to this, the contractor purchased 84 pairs of padded work gloves.

The record high temperature in Alabama is 112f and the record low temperature is -27f. What is the difference between the highest and lowest temperature? A. 139 degrees B. 27 degrees C. 85 degrees D. 112 degrees

Answers

Answer:

(A) 139°

Step-by-step explanation:

What we are trying to find here is the distance between -27 and 112.

To do this, we have to think of it as a number line.

The distance from -27 to 0 is 27 units, and the distance from 0 to 112 is 112 units.

So the total distance is [tex]112+27=139[/tex]

Hope this helped!

midpoint of the segment with endpoints A(-5, -2) and B(-7, 6).

Answers

(-6,2)

Inbox me on fb for more help with math same name as my brainly

Answer:

(-6,2)

Step-by-step explanation:

A comfy jacket is normally $200. It is on sale for 40% off. What is the sale price?​

Answers

Answer:

120

Step-by-step explanation:

First find the discount

200 * 40%

200 * .40

80

Subtract the discount from the original price

200-80

120

The sale price is 120

Answer:

[tex]\huge \boxed{\mathrm{\$ \ 120}}[/tex]

Step-by-step explanation:

Calculating the discount on the jacket.

[tex]200 \cdot 40\% \\ \\ 200 \cdot 0.4 \\ \\ 80[/tex]

The discount on the jacket is $80.

Let’s find the sale price of the jacket.

[tex]\sf sale \ price = original \ price - discount.[/tex]

[tex]200-80 \\ \\ 120[/tex]

The sale price of the jacket is $120.

please help me on this

Answers

Answer:

Step-by-step explanation:

coordinate of O(2,1),Y(3,-2),T(-3,-3)

let the reflected points are O',Y',T'

distance of O from y=2 is 1 unit.

∴ ordinate of O' =1+2(1)=3

or O' is (2,3)

distance of Y from y=2 is2+2=4

ordinate of Y'=-2+2(4)=6

so coordinate of Y' is (3,6)

distance of T from y=2 is (2+3)=5

so ordinate of T' =-3+2(5)=7

coordinate of T' is(-3,7)

Which equation is equivalent to 7w – 1 = –15?

A: 1 - 7w = -15
B: 7w = -15 + 1
C: 7w = –15 – 1
D: 7w = 15 - 1

Answers

Answer:

i believe the answer is A

Step-by-step explanation:

(6x3 + 3x² + 3) + (2x - 5x + 1)
the sum is?

Answers

Answer:8x^3 + 3x^2 - 5x + 4 is the answer.

Step-by-step explanation:

(6x^3 + 3x² + 3) + (2x^3 - 5x + 1)

6x^3 + 2x^3 = 8x^3

3x^2 + 0 = 3x^2

-5x + 0 = -5x

3 + 1 = 4

8x^3 + 3x^2 - 5x + 4 is the answer because you have to put all the terms that were solved together. This will lead to 8x^3 + 3x^2 - 5x + 4. And, standard form is ax^2 + bx + c. So, 8x^3 + 3x^2 - 5x + 4 is the answer.

8x^3 + 3x^2 - 5x + 4

Hope this helped,

Kavitha

Answer:

= 8x³ + 3x² - 5x + 4

Step-by-step explanation:

(6x³ + 3x² + 3) + (2x³ - 5x + 1)

= 6x³ + 3x² + 3 + 2x³ - 5x + 1    remove parentheses

= 6x³ + 2x³ + 3x² - 5x + 1          group like terms

= 8x³ + 3x² - 5x + 3 + 1              add similar elements

= 8x³ + 3x² - 5x + 4

PLZ HELP ME 100 POINT AND BRAINEST Solve the Quadratic Equation X^2 = -8x -7
A. 7, -1
B. -1, -7
C. 8, 1
D. 7,1
E. -8, -1

Answers

Answer:

B

Introduction:

Given equation: [tex]x^2 = -8x -7[/tex]

To solve the quadratic equation, we will need to set one side of the equation equal to 0. This can be done by subtracting x² on both sides.

[tex]\implies x^2 - x^2= -8x -7 - x^2[/tex]

[tex]\implies 0= -8x -7 - x^2[/tex]

To further simplify, we can factor -1 from the expression on the R.H.S. Then, we can cancel the -1 since there is a 0 on the other side.

[tex]\implies 0= -1(8x + 7 + x^2)[/tex]

[tex]\implies 0= 8x + 7 + x^2 = x^2 + 8x + 7[/tex]

Finally, factor the expression on the right hand side.

Factoring a quadratic equation can be done in 2 ways.

1) Splitting method

In this method, we split the middle term into two suitable terms. The suitable terms must follow two conditions.

The product of the suitable terms must be equal to the product of the first and last terms of the expression. The sum of the suitable terms must be equal the middle term.

Then, we factor the first two terms of the expression and the last two terms of the expression. Eventually, we will get a common expression. So, we can further factorize to get a product of two expressions.

However, this method follows a condition. If the middle term cannot be split into two suitable terms, then the second method should be followed to determine a solution. 2) The Quadratic Formula

In this method, we will compare our equation with the standard form equation to determine the a, b, and c variables. Then, we plug the variables into the formula and simplify to get the roots (solutions).

[tex]\text{Quadratic Formula:} \ \dfrac{-b\ \± \sqrt{b^{2} - 4ac} }{2a}[/tex]

We can use any method to solve for the roots. First, let us check whether the middle term could be split into two suitable terms such that those terms could meet the criteria stated above.

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

Solving for x using the splitting method

We can see that 8x is the middle term and it can be split into the sum of 7x and x. The product of the (middle term) coefficients is 7. The product of the coefficients (first and last terms) is also 7. Since both products match, we can use the splitting method to factorize the expression.

[tex]\implies 0= x^2 + 8x+ 7[/tex]

[tex]\implies 0= x^2 + x + 7x+ 7[/tex]

Now, factor the first two terms and the last two terms separately.

[tex]\implies 0= x^2 + x + 7x+ 7[/tex]

[tex]\implies 0= x(x + 1) + 7(x+ 1)[/tex]

We can see a common expression. Finally, let us factor the common expression to get a product of two expressions.

[tex]\implies 0= (x + 7)(x + 1)[/tex]

Since the factorized expression equals to 0, we can set each expression (inside the parentheses) equal to 0.

[tex]\implies x + 7 = 0; x + 1 = 0[/tex]

[tex]\implies x = -7; x = -1[/tex]

Solving for x using the Quadratic formula

Now, let us try to solve using the Quadratic formula.

[tex]0= x^2 + 8x+ 7[/tex]

Tip: Standard form: 0 = ax² + bx + c

Comparing both equations will allow us to determine the a, b, c variables.

⇒ a = 1; b = 8; c = 7

Now, let us plug these values into the quadratic formula and simplify.

[tex]\implies \dfrac{-b\ \± \sqrt{b^{2} - 4ac} }{2a}[/tex]

[tex]\implies \dfrac{-8\ \± \sqrt{8^{2} - 4(1)(7)} }{2(1)}[/tex]

[tex]\implies \dfrac{-8\ \± \sqrt{64 - 28} }{2}[/tex]

[tex]\implies \dfrac{-8\ \± \sqrt{36}}{2} = \dfrac{-8\± 6}{2} = \dfrac{-8 + 6}{2},\ \dfrac{-8 - 6}{2} = \dfrac{-2}{2} ,\ \dfrac{-14}{2} = -1 , -7 \ \text{(B)}[/tex]

Therefore, in both methods, the answer is -1, -7 (B).

Learn more about quadratic formula: brainly.com/question/22364785

Learn more about splitting method: brainly.com/question/13874704

In each expression below identify the coefficient constant and variable

Answers

Answer:

The expression is missing in the question.

The expression is 4x +450

The variable is x and the coefficient is 4

Step-by-step explanation:

In an expression, a variable is a quantity which is not fixed value and can be of any arbitrary value. A variable is the unknown in the expression. In any expression, the variable are represented by alphabets such as a, b, c, x, y or z etc.

The numeric quantity which lies in the front of a variable is known as a coefficient. It can be any numeric values. For example, 9x --- here 9 is the coefficient of variable x, 4x -- here 4 is the coefficient.

If the first differences of a sequence are a constant -7 and the third term is 22, find the first 5 terms of the sequence.

Answers

Answer:

36, 29, 22, 15, 8

Step-by-step explanation:

Step 1: State known information

First difference is -7

Third term of the sequence is 22

Step 2: Find first 5 terms

You just need to add and subtract 7 to 22 and the answer 5 times

1. 36 +7

2. 29 +7

3. 22 <- We know 22 is the 3rd term

4. 15 -7

5. 8 -7

Therefore the first 5 terms of the sequence is 36, 29, 22, 15, 8

what is the slope of the line shown below? (1,-4) (2,2)

Answers

Your question has been heard loud and clear.

Slope formula when two points are given= y2-y1/x2-x1

Here y2= 2

X2=2

Y1= -4

X1= -1

= 2-(-4)/2-(-1)= 2

Slope of line= 2

Thank you.

Answer:

[tex]\huge \boxed{\mathrm{B. \ 2}}[/tex]

Step-by-step explanation:

The line crosses two points.

The two points are (-1, -4) and (2, 2).

The slope of a line can be found through two points.

[tex]\displaystyle \sf slope = \frac{rise}{run}[/tex]

[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]y_2=2 \\ y_1 = -4 \\ x_2=2 \\ x_1=-1[/tex]

Plug in the values and evaluate.

[tex]\displaystyle m=\frac{2-(-4)}{2-(-1)}[/tex]

[tex]\displaystyle m=\frac{2+4}{2+1}[/tex]

[tex]\displaystyle m=\frac{6}{3}[/tex]

[tex]m=2[/tex]

The slope of the line is 2.

Pls help answer ASAP I will give Brainlyist

Answers

Answer:

Letter B because it is less than. < is less than

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

c < 27.50

The sign < means less than.

Plug the numbers in and you've got:

The cost is less than $27.50

Good luck mate :)

What equation represents a population of 300 animals at the crease and an annual rate of 23%

Answers

Answer:

300 + 69x

Step-by-step explanation:

Given initial population of animals = 300 animals

If the population increases by 23% annualy, yearly increment will be expressed as:

Yearly increment = 23% of 300

Yearly increment = 0.23*300

Yearly increment for = 69

Let the total number of years of be x

Increment after x years = 69x

Increase in population of animals after x years with an annual rate of 23% = Initial population + Increment after x years

= 300 + 69x

Hence, the equation represents a population of 300 animals at the increase and an annual rate of 23% is expressed as 300 + 69x

Graph the function and its parent function. Then describe the
transformation.
g(x) = 1/3x^2

Answers

Answer: find the answer in the explanation

Step-by-step explanation:

Given the function and its parent function, to describe the

transformation of g(x) = 1/3x^2

First sketch the graph of the parent function which is g(x) = x^2

For every value of x, g(x) will take the value it would have had at kx, that is, the graph of g(x) = x^2 is stretched by a factor of 1/3 in the x - direction.

Find the attached files for the graph and solution

A rectangle is 10 inches smaller than it is wide. The perimeter of the rectangle is 80 inches. Find the length and the width of the rectangle.​

Answers

Answer:

l = 15 and w = 25

Step-by-step explanation:

[tex]l - w = - 10[/tex]

[tex]l + w = 40[/tex]

Adding both equations

[tex]2l = 30[/tex]

[tex]l = 15[/tex]

subtracting both equation

[tex]2w = 50[/tex]

[tex]w = 25[/tex]

Hope it helps..........

BRAINLIEST PLEASE

Answer:

Length=30 Width=10

Step-by-step explanation:

You have —1 ounce of whole wheat grains. How many more ounces do you need to 8
make the recipe?

Answers

idek

-=-=-=--=-==-=-=-=-=-=-=-=-=-=-=-===========-----------------==============================================------------------------------------------------------====================================-----------==================--===================================--------------------------------------------------==========--------------------========----------------------------------------------------================-------------=====-=-=-=-=-==-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

what is the difference between -8 to the power of 2 and (-8) to the power of 2?

Answers

Answer:

0

because -8 powered 2 and -8 powered 2 is same. 64-64=0

Step-by-step explanation:

8. Laurenpacksanorderofblocksin 2 crates and 7 stacks. How many blocks does Lauren pack?

Answers

Answer:

14

Step-by-step explanation:

(multiply 2by7)

2×7

=14

I need help on this problem. (-5)^5/(-5)^-6

Answers

Answer: (-5)¹¹ of (-5)^11

Step-by-step explanation:

Since the base of the two exponents are teh same at -5, we can subtract the exponents.

5-(-6)=11

Now, we know that the new exponent will be 11, with the base staying the same.

Figure A is a scale image of Figure B.
27
Figure A
Figure B
45
35
What is the value of x?

Answers

Greetings from Brasil...

According to the statement, one figure is scaled in relation to another, so we can apply similarity to polygons.....

So

BIG/small = BIG/small

or

small/BIG = small/BIG

27/X = 45/35

OR

35/45 = X/27

27/X = 45/35

45X = 27·35

45X = 945

X = 945/45

X = 21

solve the equation -3+(1) −3+(1)

Answers

Answer:

-4

Step-by-step explanation:

you can just plug this into a calculator.

OR you could take -3+1 and get -2 and then subtract that from 2 (-3+1=2) and then you get -4

Answer:

-4

Step-by-step explanation:

-3 + (+1)= -2

2(-3 + (+1)) = -4

What is the value of
3 - x if x = 6?

Answers

Answer:

-3

Step-by-step explanation:

3-x if x=6

3-6

-3

Hope this helps ;) ❤❤❤

Answer: -3

Step-by-step explanation: In this case, we are given that x = 6.

So we have 3 - 6 which is -3.

Read the table. 1/2 = 2 gallons 1 = 4 gallons 1 1/2 = 6 gallons. If this goes on. how much gallons is 6 1/2?

Answers

Answer:

24 1/2

Step-by-step explanation:

Every 1/2 is 2 gallons.

1/2 x 2 gallons = 4 gallons.

The whole number in 6 1/2 is 6.

1 x 6 = 6.

Now, we multiply 6 by 4 because each 1 = 4 gallons.

6 x 4 = 24.

There is still an 1/2 left in 6 1/2.

You add that.

Your answer is 24 1/2.

Hope this helps you!

Find m∠PQR. A. 81 B. 90 C. 77 D. 72

Answers

Answer: D. 72

Work Shown:

Angle PQR = (far arc - near arc)/2

Angle PQR = ( (major arc PR) - (minor arc PR) )/2

Angle PQR = ( (2x+252) - (2x+108) )/2

Angle PQR = 144/2

Angle PQR = 72

Notice how we didn't need to find the value of x at all.

Evaluate the expression when x = 5 and z= 7.
5z +x
Simplify your answer as much as possible.

Answers

40
Reason 5(7)+(5)=40

Answer:

12

Step-by-step explanation:

We are given the expression:

[tex]\frac{5z+x^2}{x}[/tex]

and asked to evaluate when x= 5 and z=7. Therefore, we must substitute 5 for x and z for 7.

[tex]\frac{(5(7)+(5)^2)}{5}[/tex]

Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

First, evaluate the exponent.

(5)²= 5*5= 25

[tex]\frac{(5(7)+25)}{5}[/tex]

Next, multiply 5 and 7.

5*7=35

[tex]\frac{(35+25)}{5}[/tex]

Next, add 35 and 25.

25+25=60

[tex]\frac{60}{5}[/tex]

Finally, divide 60 by 5.

[tex]12[/tex]

The expression (5z+x²)/x when x=5 and z=7 is 12.

The area of a compact disc is 78.53 square centimeters. What is the radius of the disc? Use pi = 3.14

Answers

Answer:

r = 5 cm

Step-by-step explanation:

A = πr²

78.53 = (3.14)r²

divide by 3.14

25 = r²

r = ±5

r = 5

Show that the statement is true. If DF has endpoints D(-1,8) and E(3,-2), then the midpoint M of DE lies
I
in Quadrant I.
The midpoint M is
and the y-coordinate is (select)
). M lies in (select)
since the x-coordinate is (select) v

Answers

please help me with my homework

Riley is preheating her oven before using it to bake. The initial temperature of the oven is 65° and the temperature will increase at a rate of 10° per minute after being turned on. What is the temperature of the oven 6 minutes after being turned on? What is the temperature of the oven t minutes after being turned on? ​

Answers

Answer:

After 6 minutes, the oven temperature will be: [tex]125^o[/tex]

Step-by-step explanation:

If the increase in temperature is [tex]10^o[/tex] per minute, then in 6 minutes, the increase in temperature would be [tex]6\,*\,10^o=60^o[/tex], therefore, since the initial temperature of the oven was [tex]65^o[/tex], its temperature after 6 minutes would be:

[tex]65^o+60^o=125^o[/tex]

step by step explanation pls?

Answers

Answer:

x = 34

Step-by-step explanation:

x/3  - 7/3 = 9

Combine like terms

(x-7)/3 = 9

Multiply each side by 3

(x-7)/3 * 3 = 9*3

x-7 = 27

Add 7 to each side

x-7+7 = 27+7

x = 34

A dealer sold a painting for $800. She made a profit of 25% on the price she paid for it. Calculate the price she paid for the painting.

Answers

She paid $640 for the painting

Step-by-step explanation:

her selling price SP = 800

CP+25%of CP = 800

1.25CP=800

CP=640

Answer:

$640

Step-by-step explanation:

paint sold for $800

profit 25%

the price she paid for the painting = $800 / 1.25 = $640

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