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3 years ago

PLEASE HELP WITH MATH AND BEST GETS BRAINLIEST. PLEASE SHOW WORK.

Mathematics

2 answers:

leonid [27]3 years ago

4 0

Distribute
remember the -1 infront of the second set of partnhasees
a(b+c)=ab+ac
2(3/5x+3)=6/5x+6
-1(2/3x-1)=-2/3x+1
we now have
6/5x+6-2/3x+1
gropu like terms
6/5x-2/3x+6+1
add like terms
6/5x-2/3x+7
make bottom numbers same
6/5x times 3/3=18/15x
2/3x times 5/5=10/15x
18/15x-10/15x+7
8/15x+7
equivilent is 8/15x+7

Verizon [17]3 years ago

3 0

To solve this, we must multiply what's outside of the parentheses by what is inside.
For the first parenthetic set, we can see that we are multiplying the values by 2, so we do it this way:

$2( \frac{3}{5}x + 3) = (2 * \frac{3}{5}x) + (2 * 3) = \frac{6}{5}x + 6$

For the second part of the expression, we don't see any value, but we understand that there is a negative 1 that we don't see, because of the minus sign between the two parenthetic sets.
So we end up with this:

$- (\frac{2}{3}x - 1) = (-1 * \frac{2}{3}x) + (-1 * -1) = (\frac{-2}{3}x + 1)$

So, without parentheses, the expression looks like this:

$\frac{6}{5}x + 6 + \frac{-2}{3}x + 1$

Which could be further reduced to

$\frac{8}{15}x + 7$

Hope that helped! =)

You might be interested in

The polar coordinates of a point are 3π 4 and 7.00 m. What are its Cartesian coordinates (in m)? (x, y) = 6.06,−3.5 m

Keith_Richards [23]

Answer:

a) $\left(x,y\right)=\left(4.95,-4.95\right)$

b) $r\angle\theta = 7\angle0.5236\,\text{radians}$

Step-by-step explanation:

Polar coordinates are represented as: $r\angle\theta$ , where 'r' is the length (or magnitude) of the line, and ' $\theta$ ' is the angle measured from the positive x-axis.

in our case:

$7\angle\dfrac{3\pi}{4}$

to covert the polar to cartesian:

$x = r\cos{\theta}$

$y = r\sin{\theta}$

we can plug in our values:

$x = 7\cos{\dfrac{3\pi}{4}} = -7\dfrac{\sqrt{2}}{2}$

$y = 7\sin{\dfrac{3\pi}{4}} = 7\dfrac{\sqrt{2}}{2}$

the Cartesian coordinates are:

$\left(x,y\right)=\left(-7\dfrac{\sqrt{2}}{2},7\dfrac{\sqrt{2}}{2}\right)$

$\left(x,y\right)=\left(4.95,-4.95\right)$

(b) to convert (x,y) = (6.06,-3.5)

we'll use the pythagoras theorem to find 'r'

$r^2 = x^2+y^2$

$r^2 = (6.06)^2+(-3.5)^2$

$r = \sqrt{48.97} \approx 7$

the angle can be found by:

$\tan{\theta} = \dfrac{y}{x}$

$\tan{\theta} = \dfrac{3.5}{6.06}$

$\theta = \arctan{left(\dfrac{3.5}{6.06}\right)}$

$\theta = 0.5236 \text{radians}$

to convert radians to degrees:

$\theta = 0.5236 \times \dfrac{180}{\pi} \approx 30^\circ$

writing in polar coordinates:

$r\angle\theta = 7\angle30^\circ\,\,\text{OR}\,\,7\angle0.5236\,\text{radians}$

5 0

3 years ago

Write the slope-intercept form of the equation that passes through the point (-3, 5) and is perpendicular to the line y = 1/5x +

aleksley [76]

Answer:

Step-by-step explanation:

$\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\=========================$

$\text{We have}\ y=\dfrac{1}{5}x+10\to m_1=\dfrac{1}{5}\\\\\text{Therefore}\ m_2=-\dfrac{1}{\frac{1}{5}}=-5.\\\\\text{Put the value of a slope and the coordinates of the point (-3, 5)}\\\text{to the equation}\ y=mx+b:\\\\5=-5(-3)+b\\5=15+b\qquad\text{subtract 15 from both sides}\\-10=b\to b=-10\\\\\text{Finally:}\\\\y=-5x-10$