How do I solve 5/9x+ 6=10?, №18010361, 04.04.2022 20:17

Mathematics

How do I solve 5/9x+ 6=10?

Step-by-step answer

P Answered by Specialist

x = 36/5, 7 1/5, or 7.2 (all same, just in different form)

Step-by-step explanation:

Step 1: Subtract 6 from both sides.

$\frac{5}{9}x+6-6=10-6$ $\frac{5}{9}x=4$

Step 2: Multiply both sides by 9/5.

$\frac{5}{9}x*\frac{9}{5} =4*\frac{9}{5}$ x = 36/5, 7 1/5, or 7.2

Have a lovely rest of your day/night, and good luck with your assignments! ♡

Mathematics

Rewrite 2x^6-9x^5+4x^2-5/x^3-5 in the form q(x)+r(x)/b(x) what is q(x)? a- 2x^9-9x^8-10x^6+49x^5-5x^3-20x^2+25 b-2x^6-9x^5+4x^2-5 c-2x^3-9x^2+4x-5 d-2x^3-9x^2+10

Step-by-step answer

P Answered by PhD

25

Hello,

(2x^6-9x^5+4x^2-5)|x^3-5
-(2x^6-10x^3 ) | 2x^3 -9x^2 +10

-9x^5 +10x^3 +4x^2-5
-(-9x^5+45x^2)

10x^3-41x^2-5
-(10x^3-50)

-41x²+45

Answer D

Mathematics

Rewrite 2x^6-9x^5+4x^2-5/x^3-5 in the form q(x)+r(x)/b(x) what is q(x)? a- 2x^9-9x^8-10x^6+49x^5-5x^3-20x^2+25 b-2x^6-9x^5+4x^2-5 c-2x^3-9x^2+4x-5 d-2x^3-9x^2+10

Step-by-step answer

P Answered by PhD

25

Hello,

(2x^6-9x^5+4x^2-5)|x^3-5
-(2x^6-10x^3 ) | 2x^3 -9x^2 +10

-9x^5 +10x^3 +4x^2-5
-(-9x^5+45x^2)

10x^3-41x^2-5
-(10x^3-50)

-41x²+45

Answer D

Mathematics

What is the sum or difference? 1. 2x^4 - 8x^4 (a). -6x^8 (b). -6x^4 (c). -16x^4 (d). -16x^8 what is the sum or difference? 2. 6y^5 - 9y^5 (a). -3y^10 (b). 15y^5 (c). -54y^5 (d). -3y^5 3. write the polynomial in standard form. then name the polynomial based on its degree and number of terms. 6 - 12x + 13x^2 - 4x^2 (a). 9x^2 - 12x; quadratic binomial (b). 9x^2 - 12x + 6; quadratic trinomial (c). -3x^2 + 6; quadratic binomial (d). 9x^2 - 12x - 6; cubic trinomial 4. a biologist studied the populations of common guppies and endler s guppies over a 6-year

Step-by-step answer

P Answered by Specialist

10

1. Ans: Option (B) -6x^4

Explanation:
Given: 2x^4 - 8x^4

Take the common out:
=> x^4(2 - 8)

Hence: =>

[/tex] (Option B)

2. Ans: Option (D) -3y^5

Explanation:
Given: 6y^5 - 9y^5

Take the common term(s) out:
=> y^5(6-9)

Hence: =>

(Option D)

3. Ans: Option (B) 9x^2 - 12x + 6

quadratic trinomial

Explanation:
Given: 6 - 12x + 13x^2 - 4x^2

The standard form of polynomial function must have the highest powered value at the start, then the second highest and so on.

=> 13x^2 - 4x^2 - 12x + 6

=>

(Option B)

4. Ans: Option (C) 7.3x^2 + 0.8x + 1.3

Explanation:
In order to find the total number of Common and Endler's guppies, you need to add both Common and Endler's guppies' polynomials, as follows:

Common guppies: 3.1x^2 +6.0x + 0.3

Endler's guppies: 4.2x^2 - 5.2x + 1.0

(add both)
-----------------------------------------------------------------
Total number: 7.3x^2 +0.8x + 1.3

-----------------------------------------------------------------
Hence the ans is Option(C) 7.3x^2 + 0.8x + 1.3

5. Ans: Option (D) $2x^2(133 - 18 \pi )$

Explanation:
First let's find the total area of the yard:
Total Area of the Yard = 14x * 19x = 266x^2

Now the area of the circular fountain:
Area of the Circular Fountain = $\pi r^2$
Since, r=6x
Therefore,
Area of the Circular Fountain = $\pi (6x)^2 = 36 \pi x^2$

Now the final Area of the yard would be:
Final area of the Yard = Total Area of the Yard - Area of the Circular Fountain
Final area of the Yard = 266x^2

- $36 \pi x^2$
=> Final area of the Yard = $2x^2(133 - 18 \pi)$ (Option D)

6. Ans: Option (A) 56x^2

Explanation:
First let's find the total area of the lot:
Total Area of the lot= 6x * 10x = 60x^2

Now the area of the stadium:
Area of the stadium = 1x * 4x = 4x^2

Now the final Area of the lot would be:
Final area of the lot= Total Area of the lot - Area of the stadium
Final area of the lot= 60x^2

-

=> Final area of the lot = 56x^2

(Option A)

-i

Mathematics

What is the sum or difference? 1. 2x^4 - 8x^4 (a). -6x^8 (b). -6x^4 (c). -16x^4 (d). -16x^8 what is the sum or difference? 2. 6y^5 - 9y^5 (a). -3y^10 (b). 15y^5 (c). -54y^5 (d). -3y^5 3. write the polynomial in standard form. then name the polynomial based on its degree and number of terms. 6 - 12x + 13x^2 - 4x^2 (a). 9x^2 - 12x; quadratic binomial (b). 9x^2 - 12x + 6; quadratic trinomial (c). -3x^2 + 6; quadratic binomial (d). 9x^2 - 12x - 6; cubic trinomial 4. a biologist studied the populations of common guppies and endler s guppies over a 6-year

Step-by-step answer

P Answered by Specialist

10

1. Ans: Option (B) -6x^4

Explanation:
Given: 2x^4 - 8x^4

Take the common out:
=> x^4(2 - 8)

Hence: =>

[/tex] (Option B)

2. Ans: Option (D) -3y^5

Explanation:
Given: 6y^5 - 9y^5

Take the common term(s) out:
=> y^5(6-9)

Hence: =>

(Option D)

3. Ans: Option (B) 9x^2 - 12x + 6

quadratic trinomial

Explanation:
Given: 6 - 12x + 13x^2 - 4x^2

The standard form of polynomial function must have the highest powered value at the start, then the second highest and so on.

=> 13x^2 - 4x^2 - 12x + 6

=>

(Option B)

4. Ans: Option (C) 7.3x^2 + 0.8x + 1.3

Explanation:
In order to find the total number of Common and Endler's guppies, you need to add both Common and Endler's guppies' polynomials, as follows:

Common guppies: 3.1x^2 +6.0x + 0.3

Endler's guppies: 4.2x^2 - 5.2x + 1.0

(add both)
-----------------------------------------------------------------
Total number: 7.3x^2 +0.8x + 1.3

-----------------------------------------------------------------
Hence the ans is Option(C) 7.3x^2 + 0.8x + 1.3

5. Ans: Option (D) $2x^2(133 - 18 \pi )$

Explanation:
First let's find the total area of the yard:
Total Area of the Yard = 14x * 19x = 266x^2

Now the area of the circular fountain:
Area of the Circular Fountain = $\pi r^2$
Since, r=6x
Therefore,
Area of the Circular Fountain = $\pi (6x)^2 = 36 \pi x^2$

Now the final Area of the yard would be:
Final area of the Yard = Total Area of the Yard - Area of the Circular Fountain
Final area of the Yard = 266x^2

- $36 \pi x^2$
=> Final area of the Yard = $2x^2(133 - 18 \pi)$ (Option D)

6. Ans: Option (A) 56x^2

Explanation:
First let's find the total area of the lot:
Total Area of the lot= 6x * 10x = 60x^2

Now the area of the stadium:
Area of the stadium = 1x * 4x = 4x^2

Now the final Area of the lot would be:
Final area of the lot= Total Area of the lot - Area of the stadium
Final area of the lot= 60x^2

-

=> Final area of the lot = 56x^2

(Option A)

-i

Mathematics

Consider the sequence of steps to solve the equation: 2(x − 4) + 6x = 9x − 10 given ⇒ 2(x − 4) + 6x = 9x − 10 step 1 ⇒ 2x − 8 + 6x = 9x − 10 step 2 ⇒ 2x + 6x − 8 = 9x − 10 step 3 ⇒ 8x − 8 = 9x − 10 step 4 ⇒ 8x − 8x − 8 = 9x − 8x − 10 step 5 ⇒ 0 − 8 = x − 10 step 6 ⇒ −8 = x − 10 step 7 ⇒ −8 + 10 = x − 10 + 10 step 8 ⇒ 2 = x + 0 step 9 ⇒ 2 = x which step in solving this equation is justified by the commutative property of addition? a) step 1 ⇒ 2x − 8 + 6x = 9x − 10 b) step 2 ⇒ 2x + 6x − 8 = 9x − 10 c) step 3 ⇒ 8x − 8 = 9x − 10 d) step 4 ⇒ 8x − 8x

Step-by-step answer

P Answered by PhD

8

Option B i.e. step 2 is the correct answer.

Step-by-step explanation:

The simplest example of Commutative Property of Addition is as follows:

4 + 2 = 2 + 4

So, in Commutative Property of Addition, we can interchange the position of two or more terms which are in summation operation.

Now, in step 2, we have written

if 2x − 8 + 6x = 9x − 10

then we can write

2x + 6x − 8 = 9x − 10

Therefore, we have interchanged the position of - 8 and 6x in this step 2.

Hence, option B i.e. step 2 is the correct answer.

Mathematics

Consider the sequence of steps to solve the equation: 2(x − 4) + 6x = 9x − 10 given ⇒ 2(x − 4) + 6x = 9x − 10 step 1 ⇒ 2x − 8 + 6x = 9x − 10 step 2 ⇒ 2x + 6x − 8 = 9x − 10 step 3 ⇒ 8x − 8 = 9x − 10 step 4 ⇒ 8x − 8x − 8 = 9x − 8x − 10 step 5 ⇒ 0 − 8 = x − 10 step 6 ⇒ −8 = x − 10 step 7 ⇒ −8 + 10 = x − 10 + 10 step 8 ⇒ 2 = x + 0 step 9 ⇒ 2 = x which step in solving this equation is justified by the commutative property of addition? a) step 1 ⇒ 2x − 8 + 6x = 9x − 10 b) step 2 ⇒ 2x + 6x − 8 = 9x − 10 c) step 3 ⇒ 8x − 8 = 9x − 10 d) step 4 ⇒ 8x − 8x

Step-by-step answer

P Answered by PhD

8

Option B i.e. step 2 is the correct answer.

Step-by-step explanation:

The simplest example of Commutative Property of Addition is as follows:

4 + 2 = 2 + 4

So, in Commutative Property of Addition, we can interchange the position of two or more terms which are in summation operation.

Now, in step 2, we have written

if 2x − 8 + 6x = 9x − 10

then we can write

2x + 6x − 8 = 9x − 10

Therefore, we have interchanged the position of - 8 and 6x in this step 2.

Hence, option B i.e. step 2 is the correct answer.

Mathematics

Consider the sequence of steps to solve the equation: 2(x − 4) + 6x = 9x − 10 given ⇒ 2(x − 4) + 6x = 9x − 10 step 1 ⇒ 2x − 8 + 6x = 9x − 10 step 2 ⇒ 2x + 6x − 8 = 9x − 10 step 3 ⇒ 8x − 8 = 9x − 10 step 4 ⇒ 8x − 8x − 8 = 9x − 8x − 10 step 5 ⇒ 0 − 8 = x − 10 step 6 ⇒ −8 = x − 10 step 7 ⇒ −8 + 10 = x − 10 + 10 step 8 ⇒ 2 = x + 0 step 9 ⇒ 2 = x which step in solving this equation is justified by the distributive property? a) step 1 ⇒ 2x − 8 + 6x = 9x − 10 b) step 2 ⇒ 2x + 6x − 8 = 9x − 10 c) step 3 ⇒ 8x − 8 = 9x − 10 d) step 4 ⇒ 8x − 8x − 8 = 9x −

Step-by-step answer

P Answered by Specialist

5

Step 1

Step-by-step explanation:

You distributed the 2 in 2(x-4) to get 2x-8

Mathematics

Consider the sequence of steps to solve the equation: 2(x − 4) + 5x = 9x − 10 given ⇒ 2(x − 4) + 6x = 9x − 10 step 1 ⇒ 2x − 8 + 6x = 9x − 10 step 2 ⇒ 2x + 6x − 8 = 9x − 10 step 3 ⇒ 8x − 8 = 9x − 10 step 4 ⇒ 8x − 8x − 8 = 9x − 8x − 10 step 5 ⇒ 0 − 8 = x − 10 step 6 ⇒ −8 = x − 10 step 7 ⇒ −8 + 10 = x − 10 + 10 step 8 ⇒ 2 = x + 0 step 9 ⇒ 2 = x which step in solving this equation is justified by combining like terms? a) step 1 ⇒ 2x − 8 + 6x = 9x − 10 b) step 2 ⇒ 2x + 6x − 8 = 9x − 10 c) step 3 ⇒ 8x − 8 = 9x − 10 d) step 4 ⇒ 8x − 8x − 8 = 9x − 8x −

Step-by-step answer

P Answered by PhD

6

The like terms 2x and 6x of Step 2 are combined in Step 3:

... C) Step 3 ⇒ 8x -8 = 9x -10

Mathematics

5) consider the sequence of steps to solve the equation: 2(x − 4) + 5x = 9x − 10 given ⇒ 2(x − 4) + 6x = 9x − 10 step 1 ⇒ 2x − 8 + 6x = 9x − 10 step 2 ⇒ 2x + 6x − 8 = 9x − 10 step 3 ⇒ 8x − 8 = 9x − 10 step 4 ⇒ 8x − 8x − 8 = 9x − 8x − 10 step 5 ⇒ 0 − 8 = x − 10 step 6 ⇒ −8 = x − 10 step 7 ⇒ −8 + 10 = x − 10 + 10 step 8 ⇒ 2 = x + 0 step 9 ⇒ 2 = x which step in solving this equation is justified by the addition property of equality?

Step-by-step answer

P Answered by Master

13

The answer to this question is Step 7.
Step 7 ⇒ −8 + 10 = x − 10 + 10
This is where 10 is being added to both sides. It is not Step 4 as that uses the Subtraction Property of Equality (which can be proved true by taking the addition of a negative number).

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