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-BARSIC- [3]
3 years ago
8

it takes 1/2 of a box of nails to build a bird house if you wanted to build 5 bird houses how many boxes would you need​

Mathematics
1 answer:
dedylja [7]3 years ago
7 0

Answer:

You would need 2.5

Step-by-step explanation:

You can use a porportion to solve.

\frac{.5}{1} = \frac{x}{5} (cross multiply and solve)

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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
Evaluate the expression -434 + (-1.5)2
lorasvet [3.4K]

Answer: -437

Step-by-step explanation:

5 0
3 years ago
12. Find m?1 if m?2 = 35° in parallelogram ABCD. A. 55° B. 35° C. 75° D. 40°
brilliants [131]

Answer: A

Step-by-step explanation: Complementary angles must add up to 90 degrees.

8 0
2 years ago
Determine the rate: 6,000 miles in 3 hours
zmey [24]

Answer:

6,000:3

Step-by-step explanation:

6 0
2 years ago
Can someone pls help, I know this is kind of a lot but I’ve been stuck on this for a while now.
Greeley [361]

9514 1404 393

Answer:

  (a, b, c) = (-0.425595, 11.7321, 2.16667)

  f(x) = -0.425595x² +11.7321x +2.16667

  f(1) ≈ 13.5

Step-by-step explanation:

A suitable tool makes short work of this. Most spreadsheets and graphing calculators will do quadratic regression. All you have to do is enter the data and make use of the appropriate built-in functions.

Desmos will do least-squares fitting of almost any function you want to use as a model. It tells you ...

  a = -0.425595

  b = 11.7321

  c = 2.16667

so

  f(x) = -0.425595x² +11.7321x +2.16667

and f(1) ≈ 13.5

_____

<em>Additional comment</em>

Note that a quadratic function doesn't model the data very well if you're trying to extrapolate to times outside the original domain.

3 0
2 years ago
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