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3 years ago

using a single graph paper and the same axes draw the graph of the following equation x-y+1=0 and 3x+2y=12

Mathematics

1 answer:

Mashcka [7]3 years ago

4 0

Answer:

See attachment

Step-by-step explanation:

We want to graph the following equation:

x-y+1=0

and

3x+2y=12

For the first equation: x-y+1=0

When x=0, we have 0-y+1=0---->y=1

We plot the point (0,1)

When y=0, we have x-0+1=0---->x=-1

We plot (-1,0)

We draw a straight line through these two points to get the graph of this line.

For the second equation: 3x+2y=12

When x=0,y=6. So we plot (0,6)

When y=0, x=4, So we plot (4,0)

We draw another straight line through them to obtain the graph in the attachment.

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Write an equation for the cubic polynomial function whose graph has zeroes at 2, 3, and 5.

TiliK225 [7]

we know that

For a polynomial, if x=a is a zero of the function, then (x−a) is a factor of the function. The term multiplicity, refers to the number of times that its associated factor appears in the polynomial.

In this problem

If the cubic polynomial function has zeroes at 2, 3, and 5

then

the factors are

$(x-2)\\ (x-3)\\ (x-5)$

Part a) Can any of the roots have multiplicity?

The answer is No

If a cubic polynomial function has three different zeroes

then

the multiplicity of each factor is one

For instance, the cubic polynomial function has the zeroes

$x=2\\ x=3\\ x=5$

each occurring once.

Part b) How can you find a function that has these roots?

To find the cubic polynomial function multiply the factors and equate to zero

$(x-2)*(x-3)*(x-5)=0\\ (x^{2} -3x-2x+6)*(x-5)=0\\ (x^{2} -5x+6)*(x-5)=0\\ x^{3} -5x^{2} -5x^{2} +25x+6x-30=0\\ x^{3}-10x^{2} +31x-30=0$

therefore

the answer Part b) is

the cubic polynomial function is equal to

$x^{3}-10x^{2} +31x-30=0$

7 0

2 years ago

Read 2 more answers

1.) Find the value of the discriminant and the the number of real solutions of

ruslelena [56]

Hi there!

When we have an equation standard form...
$a {x}^{2} + bx + c = 0$
...the formula of the discriminant is
D = b^2 - 4ac

When
D > 0 we have two real solutions
D = 0 we have one real solutions
D < 0 we don't have real solutions

1.) Find the value of the discriminant and the the number of real solutions of
x^2-8x+7=0

Plug in the values from the equation into the formula of the discriminant

$( - 8) {}^{2} - 4 \times 1 \times 7 = 64 - 28 = 36$

D > 0 and therefore we have two real solutions.

2.) Find the value of the discriminant and the number of real solutions of
2x^2+4x+2=0

Again, plug in the values from the equation into the formula of the discriminant.

${4}^{2} - 4 \times 2 \times 2 = 16 - 16 = 0$

D = 0 and therefore we have one real solution.

~ Hope this helps you.

4 0

2 years ago

Read 2 more answers

Which equation can be used to find x, the length of the hypotenuse of the right triangle? A triangle has side lengths 18, 24, x.

natima [27]

Answer:

A triangle has side lengths 18, 24, x.

18 + 24 = x

18 squared + 24 = x

(18 + 24) squared = x squared

18 squared + 24 squared = x squared

Step-by-step explanation: