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3 years ago

Solve the system of linear operations

Mathematics

1 answer:

zhenek [66]3 years ago

7 0

Answer:

$\boxed{(-2,1)}$

Step-by-step explanation:

$\left \{ {{5x+2y=-8} \atop {x+4y=2}} \right.$

I'll be solving this system of equations using the elimination method since the x and y values are neatly lined up.

I want to get a pair of x's or y's that cancel out, and it looks like the easiest way to start would be by multiplying the first equation by -2 (the y's will cancel).

I chose to multiply the first equation by -2 instead of multiplying the second equation by 5 because -2 is a smaller number and easier to multiply by.

$-2\times(5x+2y=-8)$

Distribute -2 inside the parentheses. Now you've got:

$\left \{ {{-10x-4y=16} \atop {x+4y=2}} \right.$

Add up the equations from top to bottom.

-10x plus x is -9x, the -4y and 4y cancel out, and 16 plus 2 is 18. Make this one single equation.

$-9x=18$

Divide both sides by -9.

$x=-2$

Substitute this value of x into the second equation (less to do with the x since it has no coefficient which means no multiplying).

$(-2)+4y=2$

Add 2 to both sides.

$4y=4$

Divide both sides by 4.

$y=1$

The final answer is $x=-2, ~y=1$ .

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the basketball team sold t shirts and hats as a fundrasier they sold a total of 23 items and made a profit of 246 the made a pro

Gnesinka [82]

s - the number of the t-shirts;

h - the number of hats:

The system of equations:

s + h = 23

10 s + 12 h = 246

--------------------------

s = 23 - h

10 * ( 23 - h ) + 12 h = 246

230 - 10 h + 12 h = 246

2 h = 246 - 230

2 h = 16

h = 16 : 2

h= 8

s = 23 - 8

s = 15

Answer: The basketball team sold 15 t-shirts and 8 hats.

mark me as brainliest answer

6 0

3 years ago

Consider the parabola given by the equation: f(x) = 4x² - 6x - 8 Find the following for this parabola: A) The vertex: Preview B)

jeyben [28]

Answer:

The vertex: $(\frac{3}{4},-\frac{41}{4} )$

The vertical intercept is: $y=-8$

The coordinates of the two intercepts of the parabola are $(\frac{3+\sqrt{41} }{4} , 0)$ and $(\frac{3-\sqrt{41} }{4} , 0)$

Step-by-step explanation:

To find the vertex of the parabola $4x^2-6x-8$ you need to:

1. Find the coefficients a, b, and c of the parabola equation

$a=4, b=-6, \:and \:c=-8$

2. You can apply this formula to find x-coordinate of the vertex

$x=-\frac{b}{2a}$ , so

$x=-\frac{-6}{2\cdot 4}\\x=\frac{3}{4}$

3. To find the y-coordinate of the vertex you use the parabola equation and x-coordinate of the vertex ( $f(-\frac{b}{2a})=a(-\frac{b}{2a})^2+b(-\frac{b}{2a})+c$ )

$f(-\frac{b}{2a})=a(-\frac{b}{2a})^2+b(-\frac{b}{2a})+c\\f(\frac{3}{4})=4\cdot (\frac{3}{4})^2-6\cdot (\frac{3}{4})-8\\y=\frac{-41}{4}$

To find the vertical intercept you need to evaluate x = 0 into the parabola equation

$f(x)=4x^2-6x-8\\f(0)=4(0)^2-6\cdot 0-0\\f(0)=-8$

To find the coordinates of the two intercepts of the parabola you need to solve the parabola by completing the square

$\mathrm{Add\:}8\mathrm{\:to\:both\:sides}$

$x^2-6x-8+8=0+8$

$\mathrm{Simplify}$

$4x^2-6x=8$

$\mathrm{Divide\:both\:sides\:by\:}4$

$\frac{4x^2-6x}{4}=\frac{8}{4}\\x^2-\frac{3x}{2}=2$

$\mathrm{Write\:equation\:in\:the\:form:\:\:}x^2+2ax+a^2=\left(x+a\right)^2$

$x^2-\frac{3x}{2}+\left(-\frac{3}{4}\right)^2=2+\left(-\frac{3}{4}\right)^2\\x^2-\frac{3x}{2}+\left(-\frac{3}{4}\right)^2=\frac{41}{16}$

$\left(x-\frac{3}{4}\right)^2=\frac{41}{16}$

$\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=\sqrt{a},\:-\sqrt{a}$

$x_1=\frac{\sqrt{41}+3}{4},\:x_2=\frac{-\sqrt{41}+3}{4}$

4 0

3 years ago

According to the diagram below, which similarity statements are true? Check all that apply.

goldenfox [79]

Ddddddddddddddddddddddddd

8 0

3 years ago

A rectangular room has a n actual length of 6 meters and a width of 4 meters. The scale for a drawing is 1 cm = 2 meters. What i

jonny [76]

Answer:

the answer is this seems to be a trick question because you have to divide 6 meters by two to get 3 cm and the four also gets divided by 2 cm and that is how i got the aanswer d

Step-by-step explanation:

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3 years ago

Go step by step to reduce the radical. The square root of 96

lakkis [162]

Answer:

Step-by-step explanation:

We want to reduce the radical. In order to do that, we want to find the factors of 96 that are square numbers

The factors of 96 are:

$1, 96, 2, 48, 3, 32, 4, 24, 6, 16...$

16 is a square number, so we can rewrite

$\sqrt{96} = \sqrt{16*6} = \sqrt{16} * \sqrt{6} = 4\sqrt{6}$

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3 years ago