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Liono4ka [1.6K]
3 years ago
6

The regular price of a basketball is $25.During a recent sale, it was marked down by $7. Use a proportion to find the percent di

scount.
Mathematics
2 answers:
nikklg [1K]3 years ago
8 0
25-7=18
18/25=x/100
the scale factor is 4
multiply 18*4
72%
malfutka [58]3 years ago
5 0
The equation is part/whole = percent/100. Percent is unknown so it will be a variable, and it was marked down by 7 dollars so subtract : 25-7=18 now let's see our equation : 18/25 = x/100 Now solve : make sure 18/25 is simplified. (It all ready is) Now trade off : 18•100=25•x=1,800=25x (Divide by 25 on both sides and get) : 72=x. It was 72% off. Hoped I helped!
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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
A video game awards 25 points for defeating a monster and 85 additional points for getting to the end of a stage.
Vilka [71]

Answer:

p=25m+85

Step-by-step explanation:

..............................

7 0
3 years ago
The best answer gets brainliest
faltersainse [42]

Answer:

ok?

Step-by-step explanation:

Sure friend what do you need help with? I will help you

7 0
3 years ago
Read 2 more answers
What number line shows the solution of -5x + 10 > -15
andrezito [222]

Answer:

-65 will be the answer I think it will helpful to you

Step-by-step explanation:

I think this is answer

8 0
2 years ago
Please Help me with this question!!
kipiarov [429]

Answer:

Third one one

(1 x^8/ 2^2y^5)^3

Step-by-step explanation:

Quotient of power: a^m/a^n = a^(m-n)

[(x^3y^-2) /(2^2x^-5y^3)]^3 = (x^8/ 2^2y^5)^3

So. It's third option

3 0
3 years ago
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