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3 years ago

Solve for x. Use the completing the squares method. Round decimals to the nearest tenth. 2x2+16x=−18 (

1 answer:

7 0

To solve by completing square method we proceed as follows:
2x^2+16x=-18
dividing through by 2 we get:
x^2+8x=-9
but
c=(-b/2a)^2
c=(-8/2)=16
hence
x^2+8x+16=-9+16
x^2+8x+16=7
(x+4)(x+4)=7
(x+4)^2=7
thus getting the square root of both sides
x+4=+/-√7
x=-4+/-√7
x=

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Assume that y varies inversely with x. If y=1/3 when x=1/2, find y when x=1/4.

LenKa [72]

Answer:

y = $\frac{2}{3}$

Step-by-step explanation:

Given that y varies inversely with x then the equation relating them is

y = $\frac{k}{x}$ ← k is the constant of variation

To find k use the condition y = $\frac{1}{3}$ when x = $\frac{1}{2}$ , thus

$\frac{1}{3}$ = $\frac{k}{\frac{1}{2} }$ = 2k ( divide both sides by 2 )

k = $\frac{1}{6}$

y = $\frac{1}{6x}$ ← equation of variation

When x = $\frac{1}{4}$ , then

y = $\frac{1}{6(\frac{1}{4}) }$ = $\frac{1}{\frac{3}{2} }$ = $\frac{2}{3}$

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Read 2 more answers

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lakkis [162]

Answer:

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Step-by-step explanation:

Given expression

3 tenths- 3 twentieth

⇒

$=\frac{3}{10} -\frac{3}{20} \\=\frac{6}{20} -\frac{3}{20}\\=\frac{6-3}{20} \\=\frac{3}{20} \\=0.15$

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3 years ago

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2 years ago

Which graph represents the solution to the given system ? Y=- 6X - 2Y +2=- 6X

Nonamiya [84]

Answer: The graph is attached.

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

$y=mx+b$

Where "m" is the slope and "b" is the y-intercept.

Given the first equation:

$y=- 6x - 2$

You can identify that:

$m=-6\\b=-2$

By definition, the line intersects the x-axis when $y=0$ . Then, subsituting this value into the equation and solving for "x", you get that the x-intercept is:

$0=- 6x - 2\\\\2=-6x\\\\x=-\frac{1}{3}\\\\x=-0.333$

Now you can graph it.

Solve for "y" from the second equation:

$y +2=- 6x\\\\y=-6x-2$

You can identify that:

$m=-6\\b=-2$

Notice that the slopes and the y-intercepts of the first line and the second line are equal; this means that they are exactly the same line and the System of equations has<u> Infinitely many solutions.</u>

See the graph attached.

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3 years ago