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3 years ago

What is the image point of (-6,-9)(−6,−9) after a translation left 1 unit and down 5 units?

Mathematics

1 answer:

Anna [14]3 years ago

7 0

Answer:

(-7,-4)

Step-by-step explanation:

-6-1=-7

-9-(-5)=-4

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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

3 years ago

3x+1+5x=7+15+7x what is x?

LenKa [72]

Answer: x=21

Step-by-step explanation:

To solve for x you must first combine you like terms on each side of the equal sign. So you problem will become 8x+1=22+7x. Then get your x on one side and your numbers on the other by taking the one away from the right side and 1 away from 22. Then take away 7 from the left side to cancel it out. Then take 7x away from 8x to leave you with x. making your answer x=21

3 0

3 years ago

Read 2 more answers

WILL GIVE BRAINLIEST!

soldi70 [24.7K]

Honestly just use desmos or mathyway

7 0

3 years ago

Is the difference of 1.48-0.25 less or greater than one

adoni [48]

it is going to be greater than 1

4 0

4 years ago

This is the graph of y = sin(x). Does anyone know the second part?

Alborosie

Answer:

The resulting graph is $y = 5\cdot \sin x$ .

Step-by-step explanation:

The resulting function is of the form:

$y = A\cdot \sin x + k$

Where:

$x$ - Independent variable, dimensionless.

$y$ - Dependent variable, dimensionless.

$A$ - Amplitude, dimensionless.

$k$ - Midpoint value, dimensionless.

The sine function is bounded, between -1 and 1, and must be multiplied by a stretch factor. That is: $A > 0$ . According to the graph, the function is bounded between 5 ( $y_{max}$ ) and -5 ( $y_{min}$ ), and the midpoint value ( $k$ ) is 0. The amplitude is determined by the following calculation:

$A = \frac{y_{max}-y_{min}}{2}$

If $y_{min} = -5$ and $y_{max} = 5$ , then:

$A = 5$

The resulting graph is $y = 5\cdot \sin x$ .

6 0

3 years ago