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balu736 [363]
3 years ago
6

Find the number of real number solutions for the equation. x^2+5x+7=0

Mathematics
1 answer:
koban [17]3 years ago
7 0

Given a quadratic equation ax^2+bx+c=0, we define the discriminant as

\Delta = b^2-4ac

The number of real solutions of the equation depend on the sign of \Delta:

  • If \Delta>0 the equation has two solutions
  • If \Delta=0 the equation has one double solution
  • If \Delta the equation has no real solutions

In this case, we have

\Delta = 25-28=-3

And so this equation has no real solutions.

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Someone please help me with number 8.
vichka [17]

Measurement of angle DEF would equal 180 because 71 plus 109 is 180

3 0
2 years ago
A rectangle has its base on the x axis and its upper two vertices on the parabola y = 9 − x2. (a) Draw a graph of this problem.
gtnhenbr [62]

Answer:

  • (a) see attached
  • (b) width: 2x; height: y = 9-x²
  • (c) A=2x(9-x²) . . . 0 ≤ x ≤ 3
  • (d) dA/dx = -6x² +18; x=±√3
  • (e) 12√3 units²

Step-by-step explanation:

(a) The attachment shows the graph of the parabola in blue. It also shows an inscribed rectangle in black.

(b) The upper right point of the rectangle is shown in the attachment as (x, y). The dimension y is the height of the rectangle. The x-dimension is half the width of the rectangle, which is symmetrical about the y-axis. Hence the width is 2x.

(c) As with any rectangle, the area is the product of length and width:

... A = (2x)(9 -x²) . . . . . the attachment shows a graph of this

... A = -2x³ +18x . . . . . expanded form suitable for differentiation

A suitable domain for A is where both x and A are non-negative: 0 ≤ x ≤ 3.

(d) The derivative of A with respect to x is ...

... A' = -6x² +18

This is defined everywhere, so the critical values will be where A' = 0.

... 0 = -6x² +18

... 3 = x² . . . . . . . divide by -6, add 3

... √3 = x . . . . . . . -√3 is also a solution, but is not in the domain of A

(e) The rectangle will have its largest area where x=√3. That area is ...

... A = 2x(9 -x²) = 2√3(9 -(√3)²) = 2√3(6)

... A = 12√3 . . . . square units . . . . ≈ 20.785 units²

7 0
3 years ago
lavonne sold 4 times as many raffle tickets as kenneth. lavonne sold 56 raffle tickets.How many tickets kenneth sold?
Fofino [41]
Its 56 times 4 = 224
8 0
3 years ago
Read 2 more answers
The volume of a cube is 27 cubic meters.<br> What is its surface area, in square meters?
stiks02 [169]

Step-by-step explanation:

the volume of a cube is

side³.

since the volume is 27 m³, the individual side lengths are then the cubic root of 27 = 3 m.

the surface area is 6 squares of 3×3 = 9m², so in total

9 × 6 = 54 m²

8 0
2 years ago
Which of the following quartic functions has x=-1 and x=-2 as its only two real zeros
Brums [2.3K]
Quartic is 4th degree
the factors of an equation with roots r1,r2 is
(x-r1)(x-r2)
4th degree
it could be
(x-r1)¹(x-r2)³ or
(x-r1)²(x-r2)² or
(x-r1)³(x-r2)¹


roots or zeroes at x=-1 and x=-2
(x-(-1)) and (x-(-2))
(x+1) and (x+2)

the function could be factored into
(x+1)¹(x+2)³ or
(x+1)²(x+2)² or
(x+1)³(x+2)¹

expanded would be
x⁴+7x³+18x²+20x+9 or
x⁴+6x³+13x²+12x+4 or
x⁴+5x³+9x²+7x+2
one of those is the answer

4 0
3 years ago
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