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4 years ago

Solve equation -3x + 5 = 2 (x - 2) + 1

2 answers:

6 0

simplify

−3x+5=2(x−2)+1

−3x+5=(2)(x)+(2)(−2)+1(Distribute)

−3x+5=2x+−4+1

−3x+5=(2x)+(−4+1)(Combine Like Terms)

−3x+5=2x+−3

−3x+5=2x−3

Subtract 2x from both sides.

−3x+5−2x=2x−3−2x

−5x+5=−3

Subtract 5 from both sides.

−5x+5−5=−3−5

−5x=−8

Divide both sides by -5.

−5x−5=−8−5

x=8/5

scoray [572]4 years ago

3 0

$-3x+5=2(x-2)+1\ \ \ |use\ distributive\ property:a(b-c)=ab-ac\\\\-3x+5=2(x)-2(2)+1\\\\-3x+5=2x-4+1\\\\-3x+5=2x-3\ \ \ \ |subtract\ 2x\ from\ both\ sides\\\\-5x+5=-3\ \ \ \ |subtract\ 5\ from\ both\ sides\\\\-5x=-8\ \ \ \ |divide\ both\ sides\ by\ (-5)\\\\\huge\boxed{x=\frac{8}{5}=\frac{5+3}{5}=\frac{5}{5}+\frac{3}{5}=1\frac{3}{5}}$

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What is a radius of a circle given by the equation x²-2x+8y-47=0

Zolol [24]

First, we are going to rewrite it as a parabola equation.
Rewrite.
$8y=-x^2+2x+47$
Divide by 8.
$y=-\frac{x^2}{8}+\frac{x}{4}+\frac{47}{8}$
Factor out coefficient.
$y=-\frac{1}{8}\left(x^2-2x\right)+\frac{47}{8}$
Then, we are going to convert x into square form.
$y=-\frac{1}{8}\left(x^2-2x+1\right)+\frac{1}{8}\cdot \:1+\frac{47}{8}$
Convert the whole expression into square form.
$y=-\frac{1}{8}\left(x-1\right)^2+\frac{1}{8}\cdot \:1+\frac{47}{8}$
Simplify.
$y=-\frac{1}{8}\left(x-1\right)^2+6$
Subtract 6 from both sides.
$y-6=-\frac{1}{8}\left(x-1\right)^2$
Divide by coefficient.
$-8\left(y-6\right)=\left(x-1\right)^2$
Rewrite in standard form.
$4\left(-2\right)\left(y-6\right)=\left(x-1\right)^2$

The radius of the circle will be -2. Also, no matter what the sign says, the radius has to always be positive.
Have a nice day! :)

7 0

3 years ago

Read 2 more answers

If a line with a slope of -2 crosses the y-axis at (0, 3), what is the equation of the line?

Karo-lina-s [1.5K]

Answer: Option D

$y +2x = 3$

Step-by-step explanation:

The equation of a line in the form of "slope-interception" has the following form:

$y = mx + b$

Where m is the slope of the line and b is the interception of the line with the y axis.

In this case we know that the line has a slope of -2. Then $m = -2$ .

We also know that the line intercepts the axis y at the point (0, 3) therefore we know that:

$b = 3$ .

Finally the equation of the line will be:

$y = -2x + 3$

If we add 2x on both sides of the equation we get:

$y +2x = 3$

The answer is the option D

5 0

4 years ago

A projectile is launched into the air. The function h(t) = –16t2 + 32t + 128 gives the height, h, in feet, of the projectile t s

Zinaida [17]

Answer:

t = 4 seconds

Step-by-step explanation:

The height of the projectile after it is launched is given by the function :

$h(t)=-16t^2+32t+128$

t is time in seconds

We need to find after how many seconds will the projectile land back on the ground. When it land, h(t)=0

So,

$-16t^2+32t+128=0$

The above is a quadratic equation. It can be solved by the formula as follows :

$t=\dfrac{-b\pm \sqrt{b^2-4ac} }{2a}$

Here, a = -16, b = 32 and c = 128

$t=\dfrac{-32\pm \sqrt{(32)^2-4\times (-16)(128)} }{2\times (-16)}\\\\t=\dfrac{-32+ \sqrt{(32)^2-4\times (-16)(128)} }{2\times (-16)}, \dfrac{-32\- \sqrt{(32)^2-4\times (-16)(128)} }{2\times (-16)}\\\\t=-2\ s\ \text{and}\ 4\ s$