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2 years ago

Solve -2a-5>3. which graph shows the solutions?

Mathematics

1 answer:

Flura [38]2 years ago

8 0

Answer:

see explanation

Step-by-step explanation:

Given

- 2a - 5 > 3 ( add 5 to both sides )

- 2a > 8

Divide both sides by - 2, reversing the direction of the inequality sign as a consequence of dividing by a negative quantity

a < - 4

Since a is less than we require an open circle at - 4 on the number line.

Since less than the arrow head is pointing to the left, that is

Graph A, the top graph illustrates the solution

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What is the coefficient of x2y3 in the expansion of (2x + y)5?

Zigmanuir [339]

Option C:

The coefficient of $x^{2} y^{3}$ is 40.

Solution:

Given expression:

$(2 x+y)^{5}$

Using binomial theorem:

$(a+b)^{n}=\sum_{i=0}^{n}\left(\begin{array}{l}n \\i\end{array}\right) a^{(n-i)} b^{i}$

Here $a=2 x, b=y$

Substitute in the binomial formula, we get

$(2x+y)^5=\sum_{i=0}^{5}\left(\begin{array}{l}5 \\i\end{array}\right)(2 x)^{(5-i)} y^{i}$

Now to expand the summation, substitute i = 0, 1, 2, 3, 4 and 5.

$$=\frac{5 !}{0 !(5-0) !}(2 x)^{5} y^{0}+\frac{5 !}{1 !(5-1) !}(2 x)^{4} y^{1}+\frac{5 !}{2 !(5-2) !}(2 x)^{3} y^{2}+\frac{5 !}{3 !(5-3) !}(2 x)^{2} y^{3}$

$$+\frac{5 !}{4 !(5-4) !}(2 x)^{1} y^{4}+\frac{5 !}{5 !(5-5) !}(2 x)^{0} y^{5}$

Let us solve the term one by one.

$$\frac{5 !}{0 !(5-0) !}(2 x)^{5} y^{0}=32 x^{5}$

$$\frac{5 !}{1 !(5-1) !}(2 x)^{4} y^{1} = 80 x^{4} y$

$$\frac{5 !}{2 !(5-2) !}(2 x)^{3} y^{2}= 80 x^{3} y^{2}$

$$\frac{5 !}{3 !(5-3) !}(2 x)^{2} y^{3}= 40 x^{2} y^{3}$

$$\frac{5 !}{4 !(5-4) !}(2 x)^{1} y^{4}= 10 x y^{4}$

$$\frac{5 !}{5 !(5-5) !}(2 x)^{0} y^{5}=y^{5}$

Substitute these into the above expansion.

$(2x+y)^5=32 x^{5}+80 x^{4} y+80 x^{3} y^{2}+40 x^{2} y^{3}+10 x y^{4}+y^{5}$

The coefficient of $x^{2} y^{3}$ is 40.

Option C is the correct answer.

5 0

2 years ago

What is the area of a parallelogram that has a base of 6 centimeters and a height of 4 millimeters?

qwelly [4]

Answer:

(A)24 cm2

Step-by-step explanation:

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2 years ago

A medicine instructs you to take 1 pill every 3.5 hours, and comes with 4 pills. How long will it last.?

Harlamova29_29 [7]

Answer:

14 hours

Step-by-step explanation:

If you need to take 1 pill every 3.5 hours then this suggest that the effects of 1 pill lasts for 3.5 hours.

Therefore, if you take 4 pills then they will last: 4 x 3.5 = 14 hours

4 0

2 years ago

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Match each expression written in standard form to the equivalent expression in factored form

den301095 [7]

Answer:

1. 15x^7y^2 + 4x^3 => x^3(15x^4y^2 + 4)

2. 15x^7y^2 + 3x => 3x(5x^6y^2 + 1)

3. 15x^7y^2 + 6xy => 3xy(5x^6y + 2)

4. 15x^7 + 10y^2 => 5(3x^7 + 2y^2)

Step-by-step explanation:

To obtain the answer to the question, first let us factorise each expression. This is illustrated below:

1. 15x^7y^2 + 4x^3

Common factor is x^3, therefore the expression is written as:

x^3(15x^4y^2 + 4)

2. 15x^7y^2 + 3x

Common factor is 3x, therefore the expression is written as:

3x(5x^6y^2 + 1)

3. 15x^7y^2 + 6xy

Common factor is 3xy, therefore the expression is written as:

3xy(5x^6y + 2)

4. 15x^7 + 10y^2

Common factor is 5, therefore the expression can be written as:

5(3x^7 + 2y^2)

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3 years ago

Mrs. Shelly paid $3 for 6 muffins and Mrs. Kloske paid $9 for 18 muffins. Is the amount Mrs. Kloske and Mrs. Shelly paid equival

Mrac [35]

Yes, because you can multiply $3 by 3 to get $9 and 6 muffins by 3 to get 9 muffins.

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2 years ago

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Solve -2a-5>3. which graph shows the solutions?​

Solve -2a-5>3. which graph shows the solutions?