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3 years ago

Find the discriminant and determine the number of real roots for each equation. Show steps.

Mathematics

1 answer:

Leni [432]3 years ago

7 0

Answer:

discriminant: 4; number of real roots: 2

Step-by-step explanation:

The coefficients a, b and c of this quadratic are {-3, -2, 0}.

Thus, the discriminant b^2 - 4ac is (-2)^2 - 4(-3)(0), or 4.

Because the discriminant is positive, this quadratic has two real, unequal roots.

-3p^2 - 2p can be factored as follows: -p(3p + 2). If we set this expression equal to zero, we can find the roots: {-2/3, 0}

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The line y = 2x-5 cuts the x and y axes at point A and B respectively.

neonofarm [45]

To find the coordinates of points A and B, go to Desmos and graph the given equation.

The word gradient means slope.

The slope is the coefficient of x in the equation. See it?

The gradient is 2.

8 0

3 years ago

64% of US adults have very little confidence in newspapers you randomly select 10 US adults find the probability that the number

9966 [12]

Answer:

A) 0.1636

B) 0.7292

C) 0.0305

Step-by-step explanation:

This is a binomial probability distribution question that follows;

P(X = x) = nCx × p^(x) × q^(n - x)

In this case, p = 64% = 0.64

q = 1 - p = 1 - 0.64 = 0.36

Thus;

A) P(exactly 5) = P(5) = 10C5 × 0.64^(5) × 0.36^(10 - 5) = 0.1636

B) P(at least 6) = P(x ≥ 6) = P(6) + P(7) + P(8) + P(9) + P(10)

P(6) = 10C6 × (0.64^(6)) × (0.36^(10 - 6)) = 0.2424

P(7) = 10C7 × (0.64^(7)) × (0.36^(10 - 7)) = 0.2462

P(8) = 10C8 × (0.64^(8)) × (0.36^(10 - 8)) = 0.1642

P(9) = 10C9 × (0.64^(9)) × (0.36^(10 - 9)) = 0.0649

P(10) = 10C10 × (0.64^(10)) × (0.36^(10 - 10)) = 0.0115

Thus;

P(x ≥ 6) = 0.2424 + 0.2462 + 0.1642 + 0.0649 + 0.0115

P(x ≥ 6) = 0.7292

C) P(x < 4) = P(0) + P(1) + P(2) + P(3)

From online binomial probability calculator, we have;

P(x < 4) = 0.0305

5 0

3 years ago

Find the equation of the line passing through the point (2, -4) that is parallel to the line y=3x+2

castortr0y [4]

Answer <u>(assuming it can be put in point-slope format)</u>:

$y + 4 = 3(x-2)$

Step-by-step explanation:

You can write an equation of a line when knowing its slope and a line it passes through using point slope formula, $y-y_1 = m (x-x_1)$ .

1) First, find the slope of the equation. We know it has to be parallel to y = 3x + 2. Lines that are parallel have the same slope, thus the slope of y = 3x + 2 is the slope of the answer as well. y = 3x + 2 is in slope-intercept format, or $y = mx + b$ . The coefficient of the x term, or $m$ , represents the slope - so, the slope must be 3.

2) Now, use point-slope formula, $y-y_1 = m (x-x_1)$ , to write the equation. Substitute $m$ , $x_1$ , and $y_1$ for real values.

The $m$ represents the slope, so substitute 3 for $m$ . The $x_1$ and $y_1$ represent the x and y values of a point the line crosses through. The line crosses through (2, -4), so substitute 2 for $x_1$ and -4 for $y_1$ . This gives the following answer:

$y - (-4) = 3 (x-(2))\\y + 4 = 3(x-2)$

3 0

3 years ago

Can you help me solve this?

antiseptic1488 [7]

The required composite value f(g(-8) is 28

A composite function is a function inside another function. Given the following functions

f(x) = x² - 3x - 12

g(x) = -x - 12

Required composite function is f(g(-8))

First we need to get f(g(x))

f(g(x)) = f(-x-12)

f(-x-12) = (-x-12)² - 3x - 12

Expand

f(-x-12) = x² +24x + 144 - 3x - 12

f(-x-12) = x² +21x + 132

f(g(x)) = x² +21x + 132

Substitute x = -8 into the result

f(g(-8)) = (-8)² +21(-8) + 132

f(g(-8)) = 64 - 168 + 132

f(g(-8)) = 28

Hence the required composite value f(g(-8) is 28

Learn more here : brainly.com/question/3256461

8 0

3 years ago

Garney picks 72 apples every 6 minutes, How long would it take to pick 1440 apples

Harlamova29_29 [7]

Answer:

120 minutes or 2 hours

Step-by-step explanation:

72/6=1440/x cross multiply

8640/72 = x

x = 120

3 0

3 years ago

Read 2 more answers