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4 years ago

Where does the graph of y=2x2-x-3 cross as the x-axis?

1 answer:

6 0

This can be determined by finding the x-intercept. In doing so, we let y=0 to find the value of x.

y= 2x^2 -x -3
[0 = 2x^2 -x-3]÷2
0 = x^2 -1/2 x - 3/2

Complete the squares:

1/16 + 3/2 = x^2 - 1/2x + 1/16
25/16 = (x -1/4)^2
sqrt (25/16) = x - 1/4
+/- 5/4 = x - 1/4

Thus,
x = 1/4 + 5/4 = 3/2
x = 1/4 - 5/4 = -1

Thus, the graph crosses at x = 3/2 and x = -1.

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Consider the polynomial f(x) = 5x4+ 3x2+ x + 19. How many complex solutions does the polynomial have?

antiseptic1488 [7]

Answer:

there are 4 complex solutions
3 real zeros and 2 complex zeros

Step-by-step explanation:

1. Descarte's rule of signs tells you there are 0 positive real roots and 0 or 2 negative real roots. (for positive x, signs are ++++ so have no changes; for negative x, signs are ++-+, so have 2 changes.) A graph shows no real roots.

2. There are 3 sign changes in the given polynomial, so 3 or 1 positive real roots. When the sign of x is changed, there are 2 sign changes, so 0 or 2 negative real roots. A graph shows 2 negative and one positive real root (for a total of 3), so the remaining 2 roots are complex.

5 0

3 years ago

The volume of a rectangular prism is 948.6 m3. The prism has a base that is 3.1 m by 5.1 m. Find the height of the prism.

saveliy_v [14]

Just divide 948.6 m^3 by 3.1 m and 5.1 m to get 60 m

6 0

4 years ago

What is x + 5 equals 10

Wittaler [7]

x+5= 10

move +5 to the other side

sign changes from +5 to -5

x+5-5= 10-5

x= 10-5

x= 5

Answer:

x= 5

7 0

3 years ago

Barbara has a goal to read 45 minutes every day.

Masteriza [31]

Do 45 times 360 and you will get d as your answer
i hope this helped

5 0

3 years ago

Read 2 more answers

We take a milk carton from the refrigerator and put it on the table at room temperature. We assume that the temperature of the c

Kisachek [45]

We can solve this problem using separation of variables.

Then apply the initial conditions

EXPLANATION

We were given the first order differential equation

$\frac{dT}{dt}=k(T-a)$

We now separate the time and the temperature variables as follows,

$\frac{dT}{T-a}=kdt$

Integrating both sides of the differential equation, we obtain;

$ln(T-a)=kt +c$

This natural logarithmic equation can be rewritten as;

$T-a=e^{kt +c}$

Applying the laws of exponents, we obtain,

$T-a=e^{kt}\times e^{c}$

$T-a=e^{c}e^{kt}$

We were given the initial conditions,

$T(0)=4$

Let us apply this condition to obtain;

$4-20=e^{c}e^{k(0)}$

$-16=e^{c}$

Now our equation, becomes

$T-a=-16e^{kt}$

or

$T=a-16e^{kt}$

When we substitute a=20,
we obtain,

$T=20-16e^{kt}$

b) We were also given that,

$T(5)=8$

Let us apply this condition again to find k.

$8=20-16e^{5k}$

This implied

$-12=-16e^{5k}$

$\frac{-12}{-16}=e^{5k}$

$\frac{3}{4}=e^{5k}$

We take logarithm to base e of both sides,

$ln(\frac{3}{4})=5k$

This implies that,

$\frac{ln(\frac{3}{4})}{5}=k$

$k=-0.2877$

After 15 minutes, the temperature will be,

$T=20-16e^{-0.2877\times 15}$

$T=20-0.21376$

$T=19.786$

After 15 minutes, the temperature is approximately 20°C

6 0

3 years ago