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11.03.2020

Describe all numbers x that are at a distance of 4 from the number 9. Express this using absolute value notation.

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24.06.2023, solved by verified expert

Ranjana Bhatt

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|x - 9| = 4

Step-by-step explanation:

All numbers x that are at a distance of 4 fro the number 9

Given two numbers a and B, the absolute distance between them is written as :

|a - b| = c

Hence all numbers x at distance of x from 9

|x - 9| = 4

{x : |x - 9| = 4}

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Mathematics

Describe all numbers x that are at a distance of 4 from the number 9. Express this using absolute value notation.

Step-by-step answer

P Answered by PhD

|x - 9| = 4

Step-by-step explanation:

All numbers x that are at a distance of 4 fro the number 9

Given two numbers a and B, the absolute distance between them is written as :

|a - b| = c

Hence all numbers x at distance of x from 9

|x - 9| = 4

{x : |x - 9| = 4}

Mathematics

Evaluate the expression if x = −4, y = 10, z = −9. Expression: x - y - z *

Step-by-step answer

P Answered by PhD

Step-by-step explanation:

-4 - 10 + 9 = -14 + 9 = -5

Mathematics

Evaluate the expression if x = −4, y = 10, z = −9. Expression: x - y - z *

Step-by-step answer

P Answered by PhD

Step-by-step explanation:

-4 - 10 + 9 = -14 + 9 = -5

Mathematics

Evaluate the expression if x = -4, y = 10, z = -9 Expression: -5x - z + y

Step-by-step answer

P Answered by PhD

-5x - z + y = 39

Step-by-step explanation:

Evaluate the expression if x = -4, y = 10, z = -9 Expression: -5x - z + y

Mathematics

Consider the following expression and the simplified expression. Expression Simplified Expression 3 x squared + 5 y squared box + 3 box + 4 y squared + 6 9 x squared minus y squared + 9 Which terms could be in the boxes to make the expressions equivalent? Positive 6 x squared and Negative 6 y squared Positive 6 x squared and Negative 10 y squared Positive 9 x squared and Negative 10 y squared Positive 9 x squared and Negative 6 y squared

Step-by-step answer

P Answered by PhD

The correct answer is:

$+6x^{2}\\-9y^2$

Step-by-step explanation:

We are given the term:

$3x^{2} +5y^{2} [\text{ \ }] +3 [\text{ \ }] +4y^{2} +6 = 9x^{2} -y^{2} +9$

We have to fill in to the empty spaces such that the above equation gets satisfied.

First of all, let us simplify the LHS (Left Hand Side):

$3x^{2} +5y^{2} [\text{ \ }] +3 [\text{ \ }] +4y^{2} +6\\\Rightarrow 3x^{2} +5y^{2} +4y^{2} [\text{ \ }] [\text{ \ }] +6 +3\\\Rightarrow 3x^{2} +9y^{2} [\text{ \ }] [\text{ \ }] +9$

Now, let us equate the LHS and RHS (Right Hand Side):

$\Rightarrow 3x^{2} +9y^{2} [\text{ \ }] [\text{ \ }] +9 = 9x^{2} -y^{2} +9$

Equating the coefficients of $x^{2}\ and\ y^{2}$ in LHS and RHS:

One box will have value = $9x^{2} -3x^{2} =+6x^{2}$

Other box will have value = $-y^{2} -9y^{2} =-10y^{2}$

The correct answer is:

$+6x^{2}\\-9y^2$

So, if we fill the boxes with above values, the expression will be simplified as given.

Mathematics

Me i ll fail math 20 points question 1(multiple choice worth 4 points) (06.02) which of these is the algebraic expression for the verbal expression five times the difference of a number and six? 5(x − 6) x − 5 ⋅ 6 6(x − 5) 5 ⋅ x − 6 question 2(multiple choice worth 3 points) (06.02) which of these is the algebraic expression for nine less than some number? fraction 9 over k fraction k over 9 9 − k k − 9 question 3(multiple choice worth 3 points) (06.02) which of these is the algebraic expression for five more than the product of ten and some number?

Step-by-step answer

P Answered by PhD

1.a. 5(x-6)

2.d= k-9

3.c. 10 x+5

4.c.The quotient of some number and six.

5.a.The quotient of three times some number and five

6.b. x^5

Step-by-step explanation:

1.We are given that verbal expression ''five times the difference of a number and six''

We have to find its algebraic expression

Let x be the number

Difference of x and 6=x-6

We are multiplying difference of x and 6 by 5

Then we get

5(x-6)

Option a is true

2.Verbal expression ''nine less than some number ''

Let k be the some number

Nine less than some number k

= k-9

Option d is true.

3.Five more than the product of ten and some number .

Let x be the some number

Product of 10 and some number x

Then we get 10 x

Now, 5 more than the product of 10 and x

Then, we get an algebraic expression

10 x+5

Hence, option c is true.

4.Given algebraic expression

Fraction with variable x in numerator and 6 in the denominator .

We have to find its verbal expression

The quotient of some number and six.

Hence, option c is true.

5.We are given that an algebraic expression

$3x\div5$

We have to find its verbal expression

The quotient of three times some number and five

Where x is some number in algebraic expression.

Hence, option a is true.

6.We are given that verbal expression

''Some number to the power of 5''

We have to find the algebraic expression

Let x be the some number

Then , the algebraic expression

x^5

Hence, option b is true.

Mathematics

Step-by-step answer

P Answered by PhD

1.a. 5(x-6)

2.d= k-9

3.c. 10 x+5

4.c.The quotient of some number and six.

5.a.The quotient of three times some number and five

6.b. x^5

Step-by-step explanation:

1.We are given that verbal expression ''five times the difference of a number and six''

We have to find its algebraic expression

Let x be the number

Difference of x and 6=x-6

We are multiplying difference of x and 6 by 5

Then we get

5(x-6)

Option a is true

2.Verbal expression ''nine less than some number ''

Let k be the some number

Nine less than some number k

= k-9

Option d is true.

3.Five more than the product of ten and some number .

Let x be the some number

Product of 10 and some number x

Then we get 10 x

Now, 5 more than the product of 10 and x

Then, we get an algebraic expression

10 x+5

Hence, option c is true.

4.Given algebraic expression

Fraction with variable x in numerator and 6 in the denominator .

We have to find its verbal expression

The quotient of some number and six.

Hence, option c is true.

5.We are given that an algebraic expression

$3x\div5$

We have to find its verbal expression

The quotient of three times some number and five

Where x is some number in algebraic expression.

Hence, option a is true.

6.We are given that verbal expression

''Some number to the power of 5''

We have to find the algebraic expression

Let x be the some number

Then , the algebraic expression

x^5

Hence, option b is true.

Mathematics

Given f(x) = 2x² + 8x – 4 and g(x) = -5x + 6, find (f – g)(x) or f(x) – g(x) a. 7x² + 8x – 10 b. 2x² + 13x – 10 c. 2x² + 3x + 2 d. 2x² - 6x +10 2. given f(x) = 3x – 5 and g(x) = x + 2, find f(x) * g(x) or (f*g)(x) a. 4x - 3 b. 4x² - 3x - 10 c. 3x² + x - 10 d. 3x² - x + 10 3. given f(x) = x³ and g(x) = 4x + 3, find g(f(3)) a. 108 b. 405 c. 3,375 d. 111 4. given f(x) = 3x – 9 and g(x) = x – 4 what is the value of g(f( a. 2 b. 6 c. 9 d. -4 5. which expression is equal to f(x) + g(x) given f(x) = x² + 10 and g(x) = x – 3 ? a. 2x² + 7 b. 7x² + x - 3

Step-by-step answer

P Answered by PhD

wow!

those are a lot of questions!

Mathematics

Step-by-step answer

P Answered by PhD

wow!

those are a lot of questions!

Mathematics

Mickey simplified the expression below. He then checked his work by substituting 4 for x. He noticed his two values were not equal. What was Mickey s error when simplifying? Expression Simplified Expression 2 x squared minus 4 x minus 9 minus x squared + 2 x + 3 x squared minus 6 x minus 6 Mickey should have added –4 and 2 when combining the coefficients of the x terms. Mickey should have added 2 and 1 when combining the x squared terms. Mickey should have added 9 and 3 when combining the constant terms. Mickey should have added –4 and –1 when

Step-by-step answer

P Answered by Specialist

Mickey should have added –4 and 2 when combining the coefficients of the x terms.

Step-by-step explanation:

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Describe all numbers x that are at a distance of 4 from the number 9. Express this using absolute value notation.

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