4 - 2y + 8 = -6 solve for y

Given the system<br><br> y > -2<br><br> x + y < 4

katen-ka-za [31]

1. Points that lie on the intersection area of the inequalities are solutions.

For example (0,2), (-4,4), (2,-1), (-8,0) and all others which lie in this area.

2 Not solutions are points that are on the lines (because we have signs > and <, not ≤ and ≥), or on the areas that are not intercepted. For example, (6,2), (2,2), (2,-4),(-6,-2).

7 0

2 years ago

Determine an equation for the right bisector of the line segment with endpoints J(-5,3) and K(3,-2)

Norma-Jean [14]

Answer:

$y=1.6x+2.1$

Step-by-step explanation:

we know that

The right bisector of the line segment JK is a perpendicular line to the segment JK that pass through the midpoint of segment JK

step 1

Find the midpoint JK

The formula to calculate the midpoint between two points is equal to

$M(\frac{x1+x2}{2},\frac{y1+y2}{2})$

we have

$J(-5,3),K(3,-2)$

substitute the values

$M(\frac{-5+3}{2},\frac{3-2}{2})$

$M(\frac{-2}{2},\frac{1}{2})$

$M(-1,\frac{1}{2})$

step 2

Find the slope JK

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have

$J(-5,3),K(3,-2)$

substitute

$m=\frac{-2-3}{3+5}$

$m=\frac{-5}{8}$

$m=-\frac{5}{8}$

step 3

Find the slope of the line perpendicular to the segment JK

we know that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of the slopes is equal to -1)

$m_1*m_2=-1$

we have

$m_1=-\frac{5}{8}$ ----> slope of segment JK

Find m_2

substitute

$(-\frac{5}{8})*m_2=-1$

$m_2=\frac{8}{5}$

step 4

Find the equation for the right bisector of the line segment JK

The equation in point slope form is equal to

$y-y1=m(x-x1)$

we have

$m=\frac{8}{5}$

$point\ M(-1,\frac{1}{2})$

substitute

$y-\frac{1}{2}=\frac{8}{5}(x+1)$

Convert to slope intercept form

isolate the variable y

$y-\frac{1}{2}=\frac{8}{5}x+\frac{8}{5}$

$y=\frac{8}{5}x+\frac{8}{5}+\frac{1}{2}$

$y=\frac{8}{5}x+\frac{21}{10}$

$y=1.6x+2.1$

7 0

3 years ago

TheSolution to the equation is ??

spayn [35]

Answer:

X = 1

Step-by-step explanation:

2x^2 + x - 1 = 2

2x^2 + x - 3 = 0

2x^2 + 3x -2x - 3 = 0

x(2x+3) -1 ( 2x+3) = 0

(x-1) (2x+3) = 0

x-1=0

x=1

2x+3=0

2x=-3

x=-3/2.

5 0

3 years ago

Remi is building a triangular wooden shelving unit. The base measures 30 cm and the slant sides measure 18 cm and 24 cm. He want

tresset_1 [31]

Answer:

Remi needs 15 cm of wood to be cut for the shelf.

Step-by-step explanation:

We have drawn the triangle for your reference.

Now Given:

Base measure (BC) =30 cm

Slant height (AB) = 24 cm

Slant height (AC) = 18 cm

Also Given horizontal shelf halfway between the base and the top.

In the triangle drawn horizontal shelf is denoted by DE.

We need to find the measure of DE.

Now we know that horizontal shelf halfway between the base and the top.

Hence by Midpoint theorem which states that;

"The segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side."

$DE=\frac{1}{2}\times BC$

Substituting the value we get;

$DE = \frac{1}{2}\times 30 =15\ cm$

Hence Remi needs 15 cm of wood to be cut for the shelf.

5 0

2 years ago

Kara and Sonny went to see a movie at the local theater.

CaHeK987 [17]

Answer:

popcorn=4$

soft drink=4.5$

Step-by-step explanation:

if we used omitting method:

1-we multiply (p+s=8.5) by (-2) so we could get rid of (s) and be leftover with (p)

so: (-2p-2s= -17)

2- we subtract this equation from (p+2s=13) and the result will be (-p= -4)

3- divide them by (-1) and the result is (p=4)

4-(p+s=8.5) ,substitute (p) with (4) and make it go to the other side with negative sign and the result of (s) is (8.5-4=4.5)

if we used substituting method:

1-(p+s=8.50), we will make (s) go to the other side with negative sign so the result is (p=8.50-s)

2-(p+2s=13.00), substitute (p) with (8.50-s):

(8.50-s+2s=13)

3- make (8.50) go to the other side with negative sign:

(s=13-8.50=4.5) and then you could get (p)

8 0

3 years ago