All categories

3 years ago

Compute the value of the discriminant and give the number of real solutions of the quadratic equation. -4x^2+3x+1=0

1 answer:

5 0

-4x^2+3x+1=0
D = b² - 4ac = 3² - 4 * (-4) * 1 = 9 + 16 = 25
D>0 ⇒ this equation has two solutions.

You might be interested in

Find the inverse function. f (x)=1/2x+6

Lana71 [14]

The inverse of this function is f(x) = 2x - 12.

You can find the inverse of any function by switching the f(x) and x values in the equation. Then you can solve for the new f(x) value. The result is your inverse function. The work for this one is below.

f(x) = 1/2x + 6 ----> switch f(x) and x

x = 1/2f(x) + 6 ----> subtract 6

x - 6 = 1/2f(x) ----> multiply by 2

2x - 12 = f(x) ----> change the order for consistency.

f(x) = 2x - 12

7 0

3 years ago

Use the alternative form of the dot product to find u · v.

vodka [1.7K]

Answer:

Step-by-step explanation:

u = 45

v = 30

Angle between them, θ = 5π / 6 = 150°

(a) The formula for the dot product is given by

$\overrightarrow{u}.\overrightarrow{v}= u v Cos\theta$

$\overrightarrow{u}.\overrightarrow{v}= 45 \times 30 \times Cos150$

$\overrightarrow{u}.\overrightarrow{v}= -1169.13$

(b) $\overrightarrow{u}=Cos\frac{\pi }{3}\widehat{i}+Sin\frac{\pi }{3}\widehat{j}$

$\overrightarrow{u}=0.5\widehat{i}+0.866\widehat{j}$

$\overrightarrow{v}=Cos\frac{2\pi }{3}\widehat{i}+Sin\frac{2\pi }{3}\widehat{j}$

$\overrightarrow{v}=-0.707\widehat{i}+0.707\widehat{j}$

Let the angle between them is θ

The formula in terms of the dot product is given by

$Cos\theta =\frac{\overrightarrow{u}.\overrightarrow{v}}{u v}$

$u=\sqrt{0.5^{2}+0.866^{2}}=1$

$v=\sqrt{-0.707^{2}+0.707^{2}}=1$

$Cos\theta =\frac{0.5 \times (-0.707) + 0.866 \times 0.707)}{1\times 1}$

$Cos\theta=0.2587$

θ = 75°

$u=\sqrt{1^{2}+4^{2}+8^{2}}=9$

$Cos\alpha =\frac{1}{9}$

$Cos\beta =\frac{4}{9}$

$Cos\gamma =\frac{8}{9}$

7 0

4 years ago

Find the length of the missing side (nearest tenth). 25 yd 37 yd

Ket [755]

Answer:

27.3 yards

Step-by-step explanation:

Since this triangle is a right triangle, this can be solved using the equation:

a^2 + b^2 = c^2

c^2 is the side opposite to the right angle (37)

So, you need to change the equation to where it is set equal to b^2.

Subtract a^2 on both sides.

b^2 = c^2 - a^2

Now, plug in the numbers you have.

b^2 = 37^2 - 25^2

Simplify.

b^2 = 1369 - 625

b^2 = 744

Now, to find b, take the square root of 744.

√744 = 27.3

8 0

3 years ago

Read 2 more answers

Which of the following statements follows from (x - 3)2 = 5?

Leokris [45]

I think the answer should be A correct me if I’m wrong tho

6 0

3 years ago

Read 2 more answers

Which function represents the number if seats in a theater with n rows?

Diano4ka-milaya [45]

The number of seats in the theater can be calculated by multiplying the number of seats in each row by the number of rows. In this item, we are not given the number of seats present in each row. For the purpose of representation in this item, we let S be the number of seats in each row such that the total number of seats,

Total number of seats = (number of rows)(number of seat / row)
Total number of seats = nS = Sn

5 0

4 years ago