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3 years ago

8

What is the gmc of 84, 56

1 answer:

kati45 [8]3 years ago

8 0

28. hope this helps!

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What is the equation of the line that passes through (-2,3) and is parallel to 2x+3y=6?

Vsevolod [243]

Answer:

<h2>2x + 3y = 5</h2>

Step-by-step explanation:

$\bold{METHOD\ 1:}$

The slope-intercept form of an equation of a line:

$y=mx+b$

<em>m</em><em> - slope</em>

<em>b</em><em> - y-intercept</em>

Let $k:y=m_1x+b_1,\ l:y=m_2x+b_2$

then

$l\ \parallel\ k\iff m_1=m_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}$

We have the equation of a line:

$2x+3y=6$

Convert to the slope-intercept form:

$2x+3y=6$ <em>subtract 2x from both sides</em>

$3y=-2x+6$ <em>divide both sides by 3</em>

$y=-\dfrac{2}{3}x+2\to m_1=-\dfrac{2}{3}$

therefore the slope is $m_2=-\dfrac{2}{3}$

Put the value of the slope and the coordinates of the point (-2, 3) to the equation of a line:

$3=-\dfrac{2}{3}(-2)+b$

$3=\dfrac{4}{3}+b$ <em>subtract 4/3 from both sides</em>

$\dfrac{9}{3}-\dfrac{4}{3}=b\to b=\dfrac{5}{3}$

Finally:

$y=-\dfrac{2}{3}x+\dfrac{5}{3}$

Convert to the standard form (Ax + By = C):

$y=-\dfrac{2}{3}x+\dfrac{5}{3}$ <em>multiply both sides by 3</em>

$3y=-2x+5$ <em>add 2x to both sides</em>

$2x+3y=5$

$\bold{METHOD\ 2:}$

Let $k:A_1x+B_1y=C_1,\ l:A_2x+B_2y=C_2$ .

Lines <em>k</em> and <em>l</em> are parallel iff

$A_1=A_2\ \wedge\ B_1=B_2\to\dfrac{A_2}{A_1}=\dfrac{B_2}{B_1}$

We have the equation:

$2x+3y=6\to A_1=2,\ B_1=3$

then the equation of a line parallel to given lines has the equation:

$2x+3y=C$

Put the coordinates of the point (-2, 3) to the equation:

$C=2(-2)+3(3)\\\\C=-4+9\\\\C=5$

Finally:

$2x+3y=5$

4 0

3 years ago

What is the solution set for -4x-10 ≤ 2?

SashulF [63]

Answer:

x≥−3

Step-by-step explanation:

Let's solve your inequality step-by-step.

−4x−10≤2

Step 1: Add 10 to both sides.

−4x−10+10≤2+10

−4x≤12

Step 2: Divide both sides by -4.

−4x /−4 ≤ 12 /−4

= x≥−3

<h3><em><u>brainliest please?</u></em></h3>

5 0

3 years ago

Read 2 more answers

Mr. Jones will cut 6 identical loaves of bread into pieces that are 1/4 loaf

r-ruslan [8.4K]

Answer B. 24
Each loaf of bread is divided into 4 slices
And there are 6 loaves of bread
6 x 4 =24
24 pieces

8 0

3 years ago

The roots of x2 − ( ) + 34 are 5 ± 3i.

Angelina_Jolie [31]

Use quadratic formula
if you had ax^2+bx+c=0, then
x= $\frac{-b+/- \sqrt{b^{2}-4ac} }{2a}$
a=1
b=?
c=34
subsitute
$\frac{-b+/- \sqrt{b^{2}-4(1)(34)} }{2(1)}$ =5+/-3i
$\frac{-b+/- \sqrt{b^{2}-136} }{2}$ =5+/-3i
make 5+/-3 into fraction over 2,(10+/-6i)/2
$\frac{-b+/- \sqrt{b^{2}-136} }{2}$ =(10+/-6i)/2
multiply both sides by 2
$-b+/- \sqrt{b^{2}-136}$ =10+/-6i
we conclude that -b=10
b=-10

ok so equaton is
x^2-10x+34

5 0

4 years ago

Read 2 more answers

Plzzzz I need the answer

Free_Kalibri [48]

Answer: 5

Step-by-step explanation:

5 0

3 years ago