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3 years ago

Graph the equations to solve the system

Mathematics

1 answer:

wlad13 [49]3 years ago

6 0

Answer:

This system has one solution (-1,1)

Step-by-step explanation:

The attached picture shows the solutions for the system

If we equalize the eq. obtain the following

-x=2x+3

From we obtain that x= -1

Using the first equation y=-x, we obtain that y=1

so (-1,1)

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Georgia [21]

IT is c i checked using all the steps

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3 years ago

Help please i am stuck on what to do

nikklg [1K]

Answer:

These are confusing Beth , b/c you have to remember that they will add to 100%

Step-by-step explanation:

green = 3* yellow

100% = green + yellow + 35% + 25%

100% = 3* yellow + yellow +60%

40% = 4* yellow

10% = yellow

30% = green

there are 14 purples in the bag , which is 35% of total

14/.35 = 40

there are a total of 40 pins

4 are yellow (10% of 40 or 40* 0.1)

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3 years ago

A parabola has a focus of F(2, -0.5) and a directrix of y=-1.5 P(x,y) represents any point on the parabola, while D(x, -1.5) rep

prohojiy [21]

The sketch of the parabola is attached below

We have the focus $(a,b) = (2, -0.5)$
The point $P(x,y)$
The directrix, c at $y=-1.5$

The steps to find the equation of the parabola are as follows

Step 1
Find the distance between the focus and the point P using Pythagoras. We have two coordinates; $(2, -0.5)$ and $(x,y)$ .
We need the vertical and horizontal distances to find the hypotenuse (the diagram is shown in the second diagram).
The distance between the focus and point P is given by
$\sqrt{ (x-a)^{2}+ (y-b)^{2} }$

Step 2
Find the distance between the point P to the directrix $c$ . It is a vertical distance between y and c, expressed as $y-c$

Step 3
The equation of parabola is then given as
$\sqrt{ (x-a)^{2}+ (y-b)^{2} }$ = $y-c$
$(x-a)^{2}+ (y-b)^{2}= (y-c)^{2}$ ⇒ substituting a, b and c
$(x-2)^{2}+ (y--0.5)^{2} = (y--1.5)^{2}$
$(x-2)^{2}+ (y+0.5)^{2}= (y+1.5)^{2}$ ⇒Rearranging and making $y$ the subject gives

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

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3 years ago

Travis wants to solve a quadratic equation. Since his equation cannot be factored, Travis has to graph the equation and approxim

SOVA2 [1]

Answer:

The correct answer is B.

Step-by-step explanation:

In order to find this, calculate out the discriminant for each of the following equations. If the discriminant is a perfect square, then it can be factored.

Discriminant = b^2 - 4ac

The only of the equations that does not yield a perfect square is B. The work for it is done below for you.

Discriminant = b^2 - 4ac

Discriminant = 7^2 - 4(2)(-5)

Discriminant = 49 + 40

Discriminant = 89

Since 89 is not a perfect square, we cannot factor this.

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3 years ago

Read 2 more answers

Two airplanes leave an airport at the same time, flying in the same direction. One plane is flying at twice the speed of the oth

Vsevolod [243]

Answer:

The slower plane has a speed of 450 km/h and the faster one has a speed of 900 km/h.

Step-by-step explanation:

Two planes:

The first one's speed is x

The second is y.

One plane is flying at twice the speed of the other.

I will say that y = 2x.

Two airplanes leave an airport at the same time, flying in the same direction

Same direction, so their relative speed is the subtraction of their speeds. 2x - x = x.

Means that after 1 hour, they will be x miles apart.

If after 4 hours they are 1800 km apart, find the speed of each plane

After 1 hour, x km apart. After 4, 1800. So

1 hour - x km apart

4 hours - 1800 km apart

4x = 1800

x = 1800/4

x = 450

2x = 2*450 = 900

The slower plane has a speed of 450 km/h and the faster one has a speed of 900 km/h.

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3 years ago