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3 years ago

Solve the following: (1 point) x + 3y = 9 3x − 3y = −13

Mathematics

1 answer:

sp2606 [1]3 years ago

7 0

Answer:

Step-by-step explanation:

Add the equations in order to solve for the first variable. Plug this value into the other equations in order to solve for the remaining variables.

Point Form:

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Equation Form:

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A grocer mixes peanuts that cost $1.41 per pound and walnuts that cost $2.61 per pound to make 100 pounds of a mixture that cost

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w = 60 lb (amt. of walnuts needed)

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3 years ago

Shanika makes 2800 milliliter of chicken soup for dinner party. She needs 3.5 liters. How many more milliliter a does shaninka n

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3 years ago

Find the slope of the line drawn below

Marysya12 [62]

Answer:

slope is undefined

Step-by-step explanation:

Calculate the slope m using the slope formula

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

with (x₁, y₁ ) = (1, 2) and (x₂, y₂ ) = (1, - 3)

m = $\frac{-3-2}{1-1}$ = $\frac{-5}{0}$

Since division by zero is undefined then the slope of the line is undefined

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3 years ago

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

Different hotels in a certain area are randomly selected, and their ratings and prices were obtained online. Using technology, w

Savatey [412]

Answer:

a. $y= 130x + 350 + \epsilon$

b. The symbol y-bar represents the average price of hotels in the area

Step-by-step explanation:

a. The regression line equation is given by:

$y=\alpha x + \beta + \epsilon$

Where Alpha represents the slope, Beta represents the intercept with the Y axis, and epsilon represents the random component of the model. Thus,

$\alpha = 130$ y $\beta = 350$ Obtaining:

$y= 130x + 350 + \epsilon$ .

b. In a simple linear regression model the value of y-bar represents the average of all values of y observed. Thus, since y represents the prices of the hotels, then y-bar is the average price of hotels in the area.

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3 years ago