All categories

4 years ago

1. Simplify the expression and explain each step: 4(3x+2)-2.

2 answers:

6 0

1. 4 (3x+2)-2
distribute the 4 to 3x and 2
12x+8-2
combine like terms: 8-2
12x+6
answer: 12x+6

2. 20b - 16
/ \ / \
10 2 8 2
/ \ / \
5 2 4 2
/ \
2 2
answer: 5×2×2×b+2×2×2×2

Lera25 [3.4K]4 years ago

5 0

The correct answers are:

12x+6; and 4(5b-4).

Explanation:

For the first question, we first use the distributive property. It states that we multiply everything within parentheses by the term outside parentheses:

4(3x+2)-2 = 4(3x)+4(2)-2 = 12x+8-2

Combine like terms:

12x+(8-2) = 12x+6

For the second question, we first find the GCF. To do this, find the prime factorization of 20 and 16:

20 = 4*5

4 = 2*2

20 = 2*2*5

16 = 4*4

4 = 2*2

16 = 2*2*2*2

For the GCF, we take the common factors; these are 2*2 = 4. This makes 4 the GCF.

Factoring 4 out of 20b, we have 5b; factoring 4 out of -16 gives us -4. This gives us 4(5b-4).

You might be interested in

Line 1: 2x-3y>12

nata0808 [166]

Answer:

The graph of this line i.e. $2x-3y>12$ should be BELOW the DOTTED line as $y$ involves < symbol.
The graph of this line i.e. $y>-2x+5$ should be ABOVE the DOTTED line as it involves > symbol.
The correct graph for line 1 and line 2 is shown in attached figure.

Step-by-step explanation:

If the inequality involves < or >, then the graph of the equation involves a dotted line.
If the inequality involves ≤ or ≥, then the graph of the equation involves a solid line.

Considering the line 1

$2x-3y>12$

Solving line 1

$2x-3y>12$

$-3y>12-2x$

$3y$

$y$

As $y$ involves < symbol, so the graph of this line should be BELOW the DOTTED line.

But, as you can see that there is an error in the graph. As the graph of $y$ is being shown ABOVE the SOLID line.

Therefore, the graph of this line i.e. $y$ should be BELOW the DOTTED line as it involves < symbol.

Considering the line 2

$y>-2x+5$

As $y>-2x+5$ involves > symbol, so the graph of this line should be ABOVE the DOTTED line.

But, as you can see that there is an error in the graph. As the graph of $y>-2x+5$ is being shown ABOVE the SOLID line.

Therefore, the graph of this line i.e. $y>-2x+5$ should be ABOVE the DOTTED line as it involves > symbol.

The correct graph for line 1 i.e. $2x-3y>12$ and line 2 i.e. $y>-2x+5$ is shown in attached figure.

From the attached graph, it is shown that only (5, -2) satisfies the both inequalities. So, (5, -2) is the correct solution for the given inequalities.

Solution Verification:

Putting (5, -2) in line 1 and line 2

For line 1:

2x - 3y > 12 ⇒ 2(5) - 3(-2) > 12 ⇒ 10 + 6 > 12 ⇒ 16 > 12 which is true.

For line 2:

y > -2x + 5 ⇒ -2 > -2(5) + 5 ⇒ -2 > -10 + 5 ⇒ -2 > -5 which is true.

So, (5, -2) is IN the solution for line 1 and line 2

Putting (-1, -1) in line 1 and line 2

For line 1:

2x - 3y > 12 ⇒ 2(-1) - 3(-1) > 12 ⇒ -2 + 3 > 12 ⇒ 1 > 12 which is false.

For line 2:

y > -2x + 5 ⇒ -1 > -2(-1) + 5 ⇒ -1 > 2 + 5 ⇒ -1 > 7 which is false.

So, (-1, -1) is NOT in the solution for line 1 and line 2

Putting (0, 5) in line 1 and line 2

For line 1:

2x - 3y > 12 ⇒ 2(0) - 3(5) > 12 ⇒ 0 - 15 > 12 ⇒ -15 > 12 which is false.

For line 2:

y > -2x + 5 ⇒ 5 > -2(0) + 5 ⇒ 5 > 0 + 5 ⇒ 5 > 5 which is false.

So, (0, 5) is NOT in the solution for line 1 and line 2

Keywords: inequality, solution, graph, dotted line, solid line

Learn more about inequality solution from brainly.com/question/12036085

#learnwithBrainly

4 0

4 years ago

Evaluate this expression 33+(-5)-(-70)-26

SVETLANKA909090 [29]

Answer:

Step-by-step explanation:

33 + (-5) - (-70) - 26

33 - 5 + 70 - 26

- and - = +

- and + = -

+ and - = -

33 -5 = 28

28 + 70 = 108

108 - 26 = 82

8 0

3 years ago

PLEASE HELP!!!!! 3, 8, 13, 18, 23, .... The recursive formula for this sequence is:

rodikova [14]

Answer:

a₈ = 37

Step-by-step explanation:

The given arithmetic sequence is: 3, 8, 13, 18, 23, . . .

The recursive formula for the sequence is: $a_n = a_{n - 1} + 5$

Here, $a_n$ represents the $n^{th}$ of the sequence.

And, $a_{n - 1}$ represents the $(n - 1)^{th}$ of the sequence.

'+5' denotes that '5' is added to the $(n - 1)^{th}$ term to get the $n^{th}$ term. In other words, the difference between two consecutive numbers in the sequence is 5.

Now, we are asked to find a₈ i.e., n =8.

Substituting in the recursive formula we get: a₈ = a₍₈₋ ₁₎ + 5 = a₇ + 5.

So, to determine a₈ we need to know a₇. From the sequence we see that a₅ = 23.

⇒ a₆ = 23 + 5 = 28.

⇒ a₇ = 28 + 5 = 32.

⇒ a₈ = 32 + 5 = 37.

Therefore, the $8^{th}$ term of the sequence is 37.

8 0

3 years ago

What is Xavier’s available lot coverage?

slavikrds [6]

Answer:

Step-by-step explanation:

<h3>At first:</h3>

Given,

Back of lot of the trapezoid = 175

Front of lot of the trapezoid = 185

Length of lot of the trapezoid = 100

Therefore, 

Area of the trapezoid

$= \frac{a + b}{2} c$

[On putting the values]

$= \frac{175 + 185}{2} \times 100$

[On Simplification]

= 360 × 50

[On multiplying]

= 18000

Hence,

We got the Total Area as 18000.

As per given equation,

$\frac{40}{100} = \frac{x}{total \: area}$
To find the value of x

Solution ,

$= > \frac{40}{100} = \frac{x}{total \: area}$

[On putting Total Area = 18000]

$= > \frac{40}{100} = \frac{x}{18000}$

[On cross multiplication]

=> 40 × 18000 = 100 × x

[On Simplification ]

=> 720000 = 100x

[On dividing both sides with 100]

$= > \frac{720000}{100} = \frac{100x}{100}$

[On Simplification ]

=> x = 7200

Hence,

Xavier's avaliable lot coverage (x) = 7200 (Ans)

7 0

3 years ago

Mariko has an 80: 1 scale drawing of the floor plan of her house. On the floor plan

Ivan

Answer:

16,771.56 square feet.

Step-by-step explanation:

In order to get to the result we will need to use the scale and the numbers that are provided of the dimensions of the room.

The dimensions of the room on the floor plan are 17.8 inches by 21.2 inches. We first need to multiply these numbers with the scale:

17.8 x 80 = 1,424

21.2 x 80 = 1,696

Now that we got the real measures we need to multiply these two values in order to get to a result as in how many square inches is the room:

1,424 x 1696 = 2,425,104

Now we need to convert the square inches into square feet to get to the final result:

1 ft² = 144 in²

2,425,104 / 144 = 16,771.56

So we have a result of 16,771.56 square feet.

4 0

3 years ago