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4 years ago

Help??!?! I honestly forgot

Mathematics

2 answers:

dmitriy555 [2]4 years ago

8 0

Commutative property of addition

stealth61 [152]4 years ago

3 0

I think its D distributive property

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H-4/j=k for help <br> Please

krek1111 [17]

Do you need to solve for a certain variable?

4 0

3 years ago

I need so.e help with this

Flauer [41]

Answer:

(3,7) is not a solution

Step-by-step explanation:

You fill in the values x=3 and y=7 in both equations and see if you end up with something that is true.

-5·3 - 2·7 = 23 is not true, because it simplifies to -29 = 23

no need to look further, but if you would, the second equation is also false:

3 + 4·7 = -19 is also not true.

The real solution by the way is (-3, -4).

3 0

3 years ago

Use Cramer Rule to solve the following system: 8x−5y=70 and 9x+7y=3

nlexa [21]

Answer:

$(x,y) = (5,-6)$

Step-by-step explanation:

$\underline{\textbf{Determinant of a matrix.}}\\\\\text{For a}~ 2 \times 2 ~ \text{matrix,}\\\\\begin{vmatrix} a_1&a_2\\b_1&b_2 \end{vmatrix} = a_1b_2 - a_2b_1\\\\\\\text{For a}~ 3 \times 3 ~ \text{matrix,}\\\\\begin{vmatrix} a_1&a_2&a_3\\ b_1&b_2&b_3\\ c_1&c_2&c_3 \end{vmatrix} = a_1\begin{vmatrix} b_2&b_3\\c_2&c_3 \end{vmatrix} - a_2 \begin{vmatrix} b_1&b_3\\c_1&c_3 \end{vmatrix}+ a_3 \begin{vmatrix} b_1&b_2\\c_1&c_2 \end{vmatrix}\\\\\\$

$~~~~~~~~~~~~~~~~~~=a_1(b_2c_3-b_3c_2) -a_2(b_1c_3-b_3c_1) +a_3(b_1c_2-b_2c_1)$

$\underline{\textbf{Cramer's Rule to solve a system of two equations.}}\\\\\text{Consider the system of two equations:}\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a_1x + b_1 y= c_1\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a_2x +b_2 y = c_2\\\\\text{Here,}\\\\x = \dfrac{D_x}{D}= \dfrac{\begin{vmatrix} c_1&b_1\\c_2&b_2 \end{vmatrix}}{\begin{vmatrix} a_1&b_1\\a_2&b_2 \end{vmatrix}}\\\\\\ y= \dfrac{D_y}{D}= \dfrac{\begin{vmatrix} a_1&c_1\\a_2&c_2 \end{vmatrix}}{\begin{vmatrix} a_1&b_1\\a_2&b_2 \end{vmatrix}}\\\\$

$\underline{\textbf{Solution:}}\\\\~~~~~~~~~~~~~~~~~~~~~~~8x-5y = 70~~~~~~...(i)\\\\~~~~~~~~~~~~~~~~~~~~~~~9x +7y = 3~~~~~~~...(ii)\\\\\text{Applying Cramer's rule:}\\\\x = \dfrac{D_x}{D}\\\\\\~~=\dfrac{\begin{vmatrix} 70& -5 \\3&7 \end{vmatrix}}{\begin{vmatrix} 8& -5\\ 9& 7\end{vmatrix}}\\\\\\~~=\dfrac{70(7) -(-5)(3)}{(8)(7)-(-5)(9)}\\\\\\~~=\dfrac{490+15}{56+45}\\\\\\~~=\dfrac{505}{101}\\\\\\~~=5$

$y = \dfrac{D_y}{D}\\\\\\~~=\dfrac{\begin{vmatrix} 8& 70 \\9&3 \end{vmatrix}}{\begin{vmatrix} 8& -5\\ 9& 7\end{vmatrix}}\\\\\\~~=\dfrac{(8)(3) -(70)(9)}{(8)(7)-(-5)(9)}\\\\\\~~=\dfrac{24-630}{56+45}\\\\\\~~=-\dfrac{606}{101}\\\\\\~~=-6$

$\textbf{Hence, the solution to the system of equation is}~ (x,y) = (5,-6)$

7 0

2 years ago

Use the given information to determine the exact trigonometric value.

pashok25 [27]

Answer: $\bold{a.\quad -\dfrac{2\sqrt{6}}{5}}$

<u>Step-by-step explanation:</u>

$sin\theta=\dfrac{y}{h}\implies y=-1, h=5\\\\\\\text{Use Pythagorean Theorem to find x:}\\x^2 + y^2 = h^2\\x^2 + (-1)^2=5^2\\x^2+1=25\\x^2=24\\x=\sqrt{24}\\x=2\sqrt{6}$

$\text{Since }\theta\text{ is between }\pi\text{ and }\dfrac{3\pi}{2} \text{ (Quadrant III)},\text{ then x and y are negative.}\\\implies x=-2\sqrt{6}\\\\\\cos\theta = \dfrac{x}{h}\quad =\boxed{-\dfrac{2\sqrt{6}}{5}}$

5 0

4 years ago

A sample of weights of defensive tackles on Big 10 football teams are: Johnson, 202 pounds; Patrick, 215 pounds; Junior, 207 pou

ExtremeBDS [4]

Answer:

the sample standard deviation is 4.926 pounds

Step-by-step explanation:

the sample standard deviation s is defined as

s =√[ 1/(n-1) ∑ ( x- m)²] for x=1 to x=n

where

n= sample size = 10

x= weights of defensive tackles

m= sample mean

m= 1/n ∑ x* for x=1 to x=n

then

m= 1/10 (202 + 215... +208) = 209.66 pounds

thus

s =√[ 1/(10-1) ∑ ( x- m)²] = √[ 1/(10-1) [ ( 202 - 209.66 )² + ( 215 - 209.66 )² + ( 28 - 209.66 )² ] ] = 4.926 pounds

then the sample standard deviation is 4.926 pounds

4 0

3 years ago