Mathematics, 24.06.2019 09:30 dannaasc5475

Which systems of equations have no real number solutions? check all that apply. y = x2 + 4x + 7 and y = 2 y = x2 – 2 and y = x + 5 y = –x2 – 3 and y = 9 + 2x y = –3x – 6 and y = 2x2 – 7x y = x2 and y = 10 – 8x

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Answer from: estherboocx

QUESTION 1

The first system is

$y = {x}^{2} + 4x + 7$

and

y = 2

Let us equate the two system to obtain,

${x}^{2} + 4x + 7 = 2$

Let us rewrite in general quadratic format to get

${x}^{2} + 4x + 7 - 2 = 0$

${x}^{2} + 4x + 5 = 0$

This implies that,

a=1,b=4, c=5

We now find the discriminant,

D=b^2-4ac

D=4^2-4(1)(5) = - 4

Since the discriminant is negative, the system has no real number solution.

QUESTION 2

The second system is

$y = {x}^{2} - 2$

and

y = x + 5

We equate the two system to obtain,

${x}^{2} - 2 = x + 5$

This implies that,

${x}^{2} - x - 2 - 5= 0$

${x}^{2} - x - 7 = 0$

a=1,b=-1,c=-7

$D = {b}^{2} - 4ac$

We substitute the values to obtain,

$D = {( - 1)}^{2} - 4(1)( - 7) = 29$

Since the discriminant is positive, the system has real number solutions.

QUESTION 3

The given system is

$y = - {x}^{2} - 3$

y = 9 + 2x

Equate the system to get,

$- {x}^{2} - 3 = 9 + 2x$

Rewrite in general quadratic format

$- {x}^{2} - 2x - 3 - 9= 0$

$- {x}^{2} - 2x - 12= 0$

Divide through by -1 to get,

${x}^{2} + 2x + 12 = 0$

a=1,b=2,c=12

Using the discriminant we obtain,

$D= {2}^{2} - 4(1)(12) = - 44$

Since the discriminant is negative the system has no real number solution.

QUESTION 4

The given system is,

y = - 3x - 6

and

$y = 2 {x}^{2} - 7x$

Equate the two equations to get,

$2 {x}^{2} - 7x = - 3x - 6$

Rewrite in general quadratic format, to obtain,

$2 {x}^{2} - 7x + 3x + 6 = 0$

$2 {x}^{2} - 4x + 6 = 0$

Divide through by 2 to obtain,

${x}^{2} - 2x + 3= 0$

This implies that,

a=1, b=-2,c=3

We calculate the discriminant to obtain,

$D= {( - 2)}^{2} - 4(1)(3) = - 8$

Since the discriminant is negative the system has no real number solution.

QUESTION 5

The given system is

$y = {x}^{2}$

and

y = 10 -8 x

Equate the two equations to get,

${x}^{2} = 10 - 8x$

Rewrite in general quadratic format to obtain,

${x}^{2} + 8x - 10 = 0$

a=1,b=8,c=-10

We now calculate the discriminant to get,

$D= {8}^{2} - 4(1)( - 10) =104$

Since the discriminant is positive the system has real number solutions.

Answer from: Quest

circle area = pi * radius^2

if diameter = 10 then radius = 5

circle area = pi * 5^2

circle area = pi * 25

circle area = 78.5398163397 square units

step-by-step explanation:

Answer from: Quest

a, b, c, d are correct.

step-by-step explanation:

we have g(x) = 3 $\sqrt{x}$ and are required to find which option is a translation of g(x).

now, 'translation' is a transformation which means to shift the function in any direction and the general form of translation is g(x) + k, where k is any real number.

so, according to the options we see that all are correct as they satisfy the general form of translation.

also, it can be seen from the graph below that the function g(x) = 3 $\sqrt{x}$ is shifted from its position in all the four options.

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Which systems of equations have no real number solutions? check all that apply. y = x2 + 4x + 7 and...