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3 years ago

Solve for each System of Equation

Mathematics

2 answers:

weeeeeb [17]3 years ago

7 0

using substitution.

$\bf \begin{cases}5x-2y=4\\2x-y=1\end{cases}\\\\[-0.35em]\rule{34em}{0.25pt}\\\\\stackrel{\textit{solving the 2nd equation for \underline{y}}}{2x-y=1\implies 2x-1=\boxed{y}}~\hspace{5em}\stackrel{\textit{substituting the found \underline{y} in the 1st equation}}{5x-2\left( \boxed{2x-1} \right)=4}\\\\\\5x-4x+2=4\implies x=4-2\implies \blacktriangleright x = 2\blacktriangleleft$

$\bf \stackrel{\textit{now, we substitute the found \underline{x} in the 1st equation}}{5(2)-2y=4\implies 10-2y=4}\implies 10-4=2y\\\\\\6=2y\implies \cfrac{6}{2}=y\implies \blacktriangleright 3=y \blacktriangleleft\\\\[-0.35em]\rule{34em}{0.25pt}\\\\~\hfill (2,3)~\hfill$

SOVA2 [1]3 years ago

3 0

5x-2y=4 x=2 and y=3
2x-y=1 both x and y equals one

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Penelope determined the solutions of the quadratic function by completing the square. F(x) = 4x2 8x 1 –1 = 4x2 8x –1 = 4(x2 2x)

Ymorist [56]

By solving the quadratic equation using completing the square method we got that Penelope should have added 4 to both sides instead of adding 1.

<h3>What is quadratic equation ?</h3>

Any equation of the form $ax^2+bx+c=0$ where x is variable and a, b, and c are any real numbers where a ≠ 0 is called quadratic equation .

Given work of Penelope is

$\begin{aligned}&f(x)=4 x^{2}+8 x+1 \\&-1=4 x^{2}+8 x \\&-1=4\left(x^{2}+2 x\right) \\&-1+1=4\left(x^{2}+2 x+1\right) \\&0=4(x+2)^{2} \\&0=(x+2)^{2} \\&0=x+2 \\&-2=x\end{aligned}$

Now we can see that Penelope determined the solutions of the quadratic function by completing the square. so he must have been done as following

$\begin{aligned}&f(x)=4 x^{2}+8 x+1 \\&-1=4 x^{2}+8 x \\&-1=4\left(x^{2}+2 x\right) \\&-1+4=4\left(x^{2}+2 x+1\right) \\&3=4(x+2)^{2} \\&\frac{3}{4} =x+2)^{2} \\&\frac{\pm\sqrt3}{2} =x+2 \\&\frac{-2\pm\sqrt3}{2} =x\end{aligned}$

By solving the quadratic equation using completing the square method we got that Penelope should have added 4 to both sides instead of adding 1.

To learn more about quadratic equations visit : brainly.com/question/1214333

8 0

2 years ago

Use the graph to find the following.

Levart [38]

a) Local maximum values of g are: 0 and 3

b) The values at which g has local maximum are : -2 and 2

<h3>What is a maximum point?</h3>

A maximum point is the point at which the gradient of the curve changes from positive to negative.

Analysis:

The inverted v-curves all have maximum values and they are two.

The one at x = -2 and the one at x = 2 for in both cases their maximum values are y = 0 and y = 3 respectively.

Learn more about minimum and maximum points: brainly.com/question/14993153

#SPJ1

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2 years ago

Which fraction has a value that's equal to 7/8

S_A_V [24]

There's a bunch of them like if you simplify you could get 3/4.I'll give you some more.

Examples:14/16 21/24 28/32 and 35/40.

My brain was getting tired to think...but there's more.

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3 years ago

1. Grace was given the equation 2x + 20 = 15. She decides to add 10 to both sides of the equation. a.) Is that an acceptable mov

vlada-n [284]

9514 1404 393

Answer:

yes
2x +30 = 25

Step-by-step explanation:

Adding the same number to both sides of the equation is an acceptable move. The addition property of equality tells Grace that the value of the variable will remain unchanged by such a move.

Her new equation would be ...

2x +20 +10 = 15 +10

2x +30 = 25 . . . . the result of Grace's move

_____

<em>Additional comment</em>

There may be very good reasons why Grace would want to do that. If solving the equation is Grace's intent, that move would be counterproductive. For the purpose of solving the equation, it would be more productive to either subtract 20 from both sides, or divide both sides by 2. These steps would give, respectively, ...

2x = -5

x +10 = 7.5

6 0

3 years ago

If a bus leaves every 8 minutes and a other bus leaves every 10 how often will both buses leave at the same time

olga nikolaevna [1]

Answer:

i think its 10:00am

Step-by-step explanation:

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3 years ago