All categories

3 years ago

If the sum of a number and eight is doubled, the result is three less than the number. Find the number.

Mathematics

1 answer:

nydimaria [60]3 years ago

8 0

Answer:

n = -19

Step-by-step explanation:

2(n+8) = n - 3

2n + 16 = n - 3

2n = n - 19

n = - 19

You might be interested in

The first shipping by company charges a fee of $20 to ship a medium box, plus an additional $1 per pound. A second company charg

viktelen [127]

Answer:

Total cost=$25

Step-by-step explanation:

We can derive two expressions as follows;

Total cost for the First shipping company=Medium box charges+total additional charges

where;

Medium box charges=$20

Total additional charges=Charges per pound×number of additional pounds (n)

Total additional charges=1×n=n

replacing;

Total cost for the First shipping company=20+n....equation 1

Total cost for the second shipping company=Medium box charges+total additional charges

where;

Medium box charges=$15

Total additional charges=Charges per pound×number of additional pounds (n)

Total additional charges=2×n=2 n

replacing;

Total cost for the First shipping company=15+2 n....equation 2

Equating equation 1 and equation 2

15+2 n=20+n

2 n-n=20-15

n=5

Replace the value for n in equation 2

Total cost for the First shipping company=15+2 n....equation 2

Total cost=15+(2×5)=$25

7 0

4 years ago

How do you find the area of a regular polygon?

weqwewe [10]

Each of the triangles are equal in base length, height, and area. Remember the formula for the area of a triangle. The area of any triangle is 1/2 times the length of the base (which, in the polygon, is the length of a side) multiplied by the height (which is the same as the apothem in regular polygon)

8 0

3 years ago

To find the quotient of 3 divided by one-sixth, multiply 3 by

a_sh-v [17]

Answer:

You have to multiply 3 x 6.

Step-by-step explanation:

$3/\frac{1}{6} \\Flip\\3*\frac{6}{1} \\3*6$

Hope this helped! :)

6 0

3 years ago

Read 2 more answers

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:

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

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

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

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

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