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WARRIOR [948]
3 years ago
8

Is -¼ + 2 ¼y + 2 - y equivalent to y + 2 ?

Mathematics
1 answer:
Juliette [100K]3 years ago
5 0

Answer: No

Step-by-step explanation:

-\frac{1}{4}+2\frac{1}{4}y+2-y=y+2

(-\frac{1}{4}+2)+(2\frac{1}{4}y-y)=y+2\\

(\frac{(-1)+(4)(2)}{4})+(\frac{9}{4}y-y)=y+2

(\frac{-1+8}{4})+(\frac{(9)(1)-(4)(1)}{4} )y=y+2

(\frac{7}{4})+(\frac{9-4}{4} )y=y+2

(\frac{7}{4})+(\frac{5}{4})y=y+2

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Solve the following using Substitution method<br> 2x – 5y = -13<br><br> 3x + 4y = 15
Digiron [165]

\huge \boxed{\mathfrak{Question} \downarrow}

Solve the following using Substitution method

2x – 5y = -13

3x + 4y = 15

\large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}

\left. \begin{array}  { l  }  { 2 x - 5 y = - 13 } \\ { 3 x + 4 y = 15 } \end{array} \right.

  • To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.

2x-5y=-13, \: 3x+4y=15

  • Choose one of the equations and solve it for x by isolating x on the left-hand side of the equal sign. I'm choosing the 1st equation for now.

2x-5y=-13

  • Add 5y to both sides of the equation.

2x=5y-13

  • Divide both sides by 2.

x=\frac{1}{2}\left(5y-13\right)  \\

  • Multiply \frac{1}{2}\\ times 5y - 13.

x=\frac{5}{2}y-\frac{13}{2}  \\

  • Substitute \frac{5y-13}{2}\\ for x in the other equation, 3x + 4y = 15.

3\left(\frac{5}{2}y-\frac{13}{2}\right)+4y=15  \\

  • Multiply 3 times \frac{5y-13}{2}\\.

\frac{15}{2}y-\frac{39}{2}+4y=15  \\

  • Add \frac{15y}{2} \\ to 4y.

\frac{23}{2}y-\frac{39}{2}=15  \\

  • Add \frac{39}{2}\\ to both sides of the equation.

\frac{23}{2}y=\frac{69}{2}  \\

  • Divide both sides of the equation by 23/2, which is the same as multiplying both sides by the reciprocal of the fraction.

\large \underline{ \underline{ \sf \: y=3 }}

  • Substitute 3 for y in x=\frac{5}{2}y-\frac{13}{2}\\. Because the resulting equation contains only one variable, you can solve for x directly.

x=\frac{5}{2}\times 3-\frac{13}{2}  \\

  • Multiply 5/2 times 3.

x=\frac{15-13}{2}  \\

  • Add -\frac{13}{2}\\ to \frac{15}{2}\\ by finding a common denominator and adding the numerators. Then reduce the fraction to its lowest terms if possible.

\large\underline{ \underline{ \sf \: x=1 }}

  • The system is now solved. The value of x & y will be 1 & 3 respectively.

\huge\boxed{  \boxed{\bf \: x=1, \: y=3 }}

8 0
2 years ago
If George is 33 1/3% richer than Pete, than Pete is what percent poorer than George?
OleMash [197]

Answer:

25%

Step-by-step explanation:

George is 33\frac{1}{3}% (\frac{100}{3}%) richer than Pete. Let Pete's percentage of wealth be 100%.

Thus George percentage of wealth = 100% + \frac{100}{3}%

                                                           = \frac{400}{3}%

                                                           = 133\frac{1}{3}%

Pete's percent poorer than George can be determined by;

                                                           = (\frac{100}{3}) ÷ (\frac{400}{3} ) × 100

                                                           = (\frac{100}{3}) × \frac{3}{400} ×100

                                                           = 0.25 × 100

                                                           = 25%

Pete is 25% poorer than George.

3 0
3 years ago
What types of solutions does 6x^2 - 20x + 1 have?​
elena55 [62]

Answer:

2 real solutions

Step-by-step explanation:

We can use the determinant, which says that for a quadratic of the form ax² + bx + c, we can determine what kind of solutions it has by looking at the determinant of the form:

b² - 4ac

If b² - 4ac > 0, then there are 2 real solutions. If b² - 4ac = 0, then there is 1 real solution. If b² - 4ac < 0, then there are 2 imaginary solutions.

Here, a = 6, b = -20, and c = 1. So, plug these into the determinant formula:

b² - 4ac

(-20)² - 4 * 6 * 1 = 400 - 24 = 376

Since 376 is clearly greater than 0, we know this quadratic has 2 real solutions.

<em>~ an aesthetics lover</em>

3 0
2 years ago
What is the value of y
guajiro [1.7K]

Answer:

<h2>              y = 5.6</h2>

Step-by-step explanation:

From Thales' theorem:

                                        \dfrac y7\ =\ \dfrac45\\\\y=\dfrac45\cdot7\\\\y = \dfrac{28}5\\\\y = 5.6

5 0
3 years ago
F(x)=x^2(x+3)^2 <br><br> How do I find the roots of this equation?
Genrish500 [490]
= x^2 ( x+3 ) (x+3)
= set equal to 0

X^2= 0
X=0

X+3=0
X=-3


Answer is -3 and 0
6 0
2 years ago
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