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3 years ago

Solve the system of linear equations by graphing. y = x +2 y = -x -4 The solution is

Mathematics

2 answers:

Mnenie [13.5K]3 years ago

8 0

Answer:

Solution: (-3,-1)

7nadin3 [17]3 years ago

7 0

Answer:

x = -3

Step-by-step explanation:

x + 2 and -x-4 is equal, because they are both y

we want to move the variables to one side and the numbers to the other side

x+x = 2x, and -4-2 = -6

so 2x = -6

and x = -3

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What happens to a number when you multiply by 1000? Why does this happen?

Elis [28]

Answer:

the number will get 1000 times larger than its original number or 3 zeroes will be added in the last place of the number

Step-by-step explanation:

let's say x=5,

if we multiply 5 by 1000 it becomes 5000 (it is 1000 times more or larger than its orignal number and 3 zeroes are added in 5000).

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2 years ago

Who can answer the 3x+2y=-6 for the intercepts and to graph it ?? I'm so lost

ELEN [110]

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put (0,3) and (2,0) as points on the graph

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3 years ago

Liam has 9/10 gallon of paint for painting the bird houses he sells at the craft fair each birdhouse requires 1/20 gallon of pai

Rina8888 [55]

So to get the fractions easier to understand you need to put them on the same level you are on. So change the 9/10 gallons to 18/20 ( this makes them easier to deal with the 1/20)
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2 years ago

X^2(x^2+3x+2)plzz help me

agasfer [191]

The zeros for this function are -2, -1 and a double root of 0.

You can find this by first factoring the polynomial on the inside of the parenthesis. Polynomials like this can be factored by looking for two numbers that multiply to the constant (2) and add up to the second coefficient (3). The numbers 2 and 1 satisfy both of those needs and thus can be used as the numbers in a factoring.

x^2(x^2 + 3x + 2)

x^2(x + 2)(x + 1)

Now to find the zeros, we set each part equal to 0. You may want to split the x^2 into two separate x's for this purpose.

(x)(x)(x + 2)(x + 1)

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8 0

3 years ago

Read 2 more answers

Use vectors to find the interior angles of the triangle with the given vertices. (Enter your answers as a comma-separated list.

aleksandr82 [10.1K]

Answer:

23.20°, 71.57°, 85.24°

Step-by-step explanation:

The angle between two vectors can be found by making use of the definition of the dot product. The computed angle is the angle between the vectors when they are placed tail-to-tail.

<h3>setup</h3>

vector definition

The second attachment shows the given points plotted as A, B, C in the order given. In the diagram, the vectors a, b, c are defined as BA, CB, AC, respectively. That is, the vector a is ...

a = A -B = (-6, -9) -(2, 7) = (-6-2, -9-7) = (-8, -16)

The vectors are defined in counterclockwise order around the triangle, though that makes no difference to the calculation.

dot product definition

The definition of the dot product of vectors A and B is ...

A·B = |A|×|B|×cos(θ) . . . . . where θ is the angle between the vectors

Solving for the angle, we find it to be ...

$\theta=\arccos\left(\dfrac{\vec{A}\cdot\vec{B}}{|\vec{A}|\,|\vec{B}|}\right)$

<h3>computation</h3>

Because of the way the vectors in this solution are defined, the angle between any given pair of vectors will be an exterior angle of the triangle. In order to find the measure of the interior angle, we must reverse one of the vectors. That is, the dot product used in our computation will be the opposite of the dot product of the vectors we have found.

The spreadsheet shown in the first attachment does the necessary computations.

Each vector is the difference of successive points. (x1 -x2, y1 -y2)
Each dot product shown is the opposite of the dot product of successive vectors. -(x1x2 +y1y2)
The magnitude is computed in the usual way: the root of the sum of the squares of the components of the vector. √(x²+y²)
The cosine is the dot product of successive vectors, divided by each of the vector magnitudes.
The spreadsheet shows the angle in degrees, having converted it from the radian value produced by the ACOS function.

As a check, the spreadsheet shows the sum of the angle values. (The rounded values add up to 180.01°.)

The interior angles of the triangle are 23.20°, 71.57°, 85.24°.

_____

Additional comment

Another way to find the interior angles from coordinates is to consider the slope of each side of the triangle as being the tangent of the angle it makes with the x-axis. The difference of these angles can be used to find the interior angles of the triangle. Less work is involved because there is no dot-product or magnitude computation.

7 0

2 years ago