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3 years ago

Evaluate the expression. 12 + 3 • 8

Mathematics

2 answers:

Olenka [21]3 years ago

5 0

Answer:

Step-by-step explanation:

3*8=24

24+12= 36

Gnesinka [82]3 years ago

5 0

Answer:

Step-by-step explanation:

When evaluating an expression, you must take PEMDAS into account. PEMDAS stands for:

Parenthesis

Exponents

Multiplication

Division

Addition

Subtraction

You follow these steps, for example, in this expression we don't have any parenthesis or exponents, leaving us to do multiplication first instead of addition:

12 + 24

Now, all you have to do is add these two together:

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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

The United States govermoment produced about 10.25 billion pennies in one year. How is 10.25 billion written in scientific notat

Margarita [4]

<span>In scientific notiation the number is noted as a number between 1 and 10 times 10 to whatever power is necessary to equal the original number so it needs to be 1.025 x 10^10 instead of 10.25.</span>

4 0

3 years ago

Read 2 more answers

I need some help!! plss

3241004551 [841]

Answer:

250

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

Can someone solve this

Pani-rosa [81]

Answer:

m=5

c=-7

Step-by-step explanation:

m is slope

c is the intercept on the y axis

Mark me brainliest pls

3 0

3 years ago

Ruth has a savings account at a bank that charges a $3.50 fee for every month her balance falls below $1,500. Her account has $1

borishaifa [10]

Answer:

1304.5 balance after 5 months

Step-by-step explanation:

first you subtract 400 from 1722 to find the balance she will have which is 1322. then you must multiply 3.5 x 5= 17.50. now subtract 17.50 from 1322 and you get her balance after 5 months

7 0

3 years ago