How many ways to make 80 cent

Determine the discriminant for the given equation x^2+4x+5=0. Then describe the roots(how many and what type).

Fed [463]

Discriminant = b^2 - 4ac, where a, b and c come from the form of the quadratic equation as ax^2 + bx + c

Discriminant = (4)^2 - 4(1)(5)
= 16 - 20
= -4

-4 < 0, therefor there are no roots

(If the discriminant = 0, then there is one root
If the discriminant > 0, there are two roots, and if it is a perfect square (eg. 4, 9, 16, etc.) then there are two rational roots
If the discriminant < 0, there are no roots)

3 0

4 years ago

Find the slope and y-intercept of 3y - 4x = 39

Alexus [3.1K]

<h2>Greetings!</h2><h3>Firstly, the slope is found by rearranging the formula:</h3>

3y = 4x + 39

y = $\frac{4x}{3}$ + $\frac{39}{3}$

When x is 0, y = 0(x) + $\frac{39}{3}$ , so the y intercept is $\frac{39}{3}$

<h3>Next, the slope is simply the number in front of the x, </h3>

So $\frac{4x}{3}$ can be rearranged to $\frac{4}{3}x$ , so the slope would be $\frac{4}{3}$ .

<h2>Hope this helps!</h2>

3 0

3 years ago

Read 2 more answers

I have four bills that need to be paid this week. The electric bill is 182.17 the water bill is 92.55 the cell phone bill is 225

tangare [24]

The answer would be 200 + 200 +200+100 = 700

7 0

3 years ago

Read 2 more answers

Which solid has a greater volume?

Lady_Fox [76]

Answer:

C

Step-by-step explanation:

The volume of a cone is given by $V=\frac{1}{3}\pi r^2h$

The volume of a cylinder is given by $V=\pi r^2 h$

<em>Where h is the height and r is the radius</em>

The first figure is a cone with height 6 and radius 5, we can put it into the formula and find the volume:

$\frac{1}{3}\pi r^2 h\\\frac{1}{3}\pi (5)^2 (6)\\=157.08$

The second figure is a cylinder with height 50 and radius 1, we can put it into the formula and find the volume:

$\pi r^2 h\\\pi (1)^2 (50)\\=157.08$

We can see that they are equal. So answer choice C is right.

5 0

3 years ago

Which expression is equivalent to *picture attached*

DiKsa [7]

Answer:

The correct option is;

$4 \left (\dfrac{50 (50+1) (2\times 50+1)}{6} \right ) +3 \left (\dfrac{50(51) }{2} \right )$

Step-by-step explanation:

The given expression is presented as follows;

$\sum\limits _{n = 1}^{50}n\times \left (4\cdot n + 3 \right )$

Which can be expanded into the following form;

$\sum\limits _{n = 1}^{50} \left (4\cdot n^2 + 3 \cdot n\right ) = 4 \times \sum\limits _{n = 1}^{50} \left n^2 + 3 \times\sum\limits _{n = 1}^{50} n$

From which we have;

$\sum\limits _{k = 1}^{n} \left k^2 = \dfrac{n \times (n+1) \times(2n+1)}{6}$

$\sum\limits _{k = 1}^{n} \left k = \dfrac{n \times (n+1) }{2}$

Therefore, substituting the value of n = 50 we have;

$\sum\limits _{n = 1}^{50} \left k^2 = \dfrac{50 \times (50+1) \times(2\cdot 50+1)}{6}$

$\sum\limits _{k = 1}^{50} \left k = \dfrac{50 \times (50+1) }{2}$

Which gives;

$4 \times \sum\limits _{n = 1}^{50} \left n^2 = 4 \times \dfrac{n \times (n+1) \times(2n+1)}{6} = 4 \times \dfrac{50 \times (50+1) \times(2 \times 50+1)}{6}$

$3 \times\sum\limits _{n = 1}^{50} n = 3 \times \dfrac{n \times (n+1) }{2} = 3 \times \dfrac{50 \times (51) }{2}$

$\sum\limits _{n = 1}^{50}n\times \left (4\cdot n + 3 \right ) = 4 \times \dfrac{50 \times (50+1) \times(2\times 50+1)}{6} +3 \times \dfrac{50 \times (51) }{2}$

Therefore, we have;

$4 \left (\dfrac{50 (50+1) (2\times 50+1)}{6} \right ) +3 \left (\dfrac{50(51) }{2} \right )$ .

4 0

3 years ago