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3 years ago

Graph the solution to the following system of inequalities in the coordinate plane.

Mathematics

1 answer:

Goshia [24]3 years ago

4 0

Answer:

see below

Step-by-step explanation:

The first equation is in slope-intercept form, so you can see that the boundary line has a slope of -2 and goes through the point (x, y) = (0, -4). Since the comparison is "<", the line is dashed and shading is below it.

The second equation is that of a vertical boundary line at x=-3. It is solid, because the comparison includes the "equal" case. Shading is to the right of it, where x values are greater than -3.

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1.This circle is centered at the origin and contains the points two units away. Write the equation for this circle.

denis-greek [22]

Answer:

1. The location of the center of the given circle = The origin (0, 0)

The given points on the circumference of the circle = (1, √3), and (0, -2)

The general form of the equation of a circle, is presented as follows

(x - h)² + (y - k)² = r²

Where;

(h, k) = The coordinates of the center of the circle

r = The radius of the circle

∴ (h, k) = (0, 0)

The radius of the given equation is the distance from the center (0, 0) to either the point (0, -2) or (1, √3)

The distance from the center (0, 0) to the point (0, -2), which are points on the same ordinate, r = y₂ - y₁

∴ r = 0 - (-2) = 2

r = 2

The equation of the circle is therefore;

(x - 0)² + (y - 0)² = 2²

∴ x² + y² = 2²

2. When x = 1, and y = √3, we have;

(1 - 0)² + (√3 - 0)² = 1 + 3 = 4 = 2²

When x = 0, and y = -2, we have;

(0 - 0)² + ((-2) - 0)² = (-2)² = 4 = 2²

Therefore, the points shown on the circle (1, √3), and (0, -2) satisfy the equation of the circle, x² + y² = 2² and are solutions to the equation of the circle

Step-by-step explanation:

3 0

2 years ago

A commuter has $245 in his computer savings account.This account changes by $-15 each week he buys a ticket.In one period,the ac

Levart [38]

He needs $395, cuz he already had $5, and 15×20=300. subtract the 5 from 300.

3 0

3 years ago

Can someone please solve this with steps

EastWind [94]

(x+10)+(3x-5)+x=5x+5

5x-5=180

+5 +5

5x=185

185/5=37

37=x

6 0

3 years ago

Please give me the correct answers

UkoKoshka [18]

Answer:

blue question mark = –

Step-by-step explanation:

6(2x -1) uses the distributive property, which means that both 2x and -1 are multiplied by 6 when expanding the brackets.

6(2x - 1)

= (6 x 2x) + (6 x -1)

= 12x - 6

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3 years ago

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Ms.Brown flight left at 9:20 a.m Her plane landed 1 hour ane 23 min later. What time did her plane land?

Aliun [14]

You have to count add 83 minuets to 9:20

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3 years ago

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