All categories

4 years ago

Which of the statements about the following quadratic equation is true?

Mathematics

2 answers:

anzhelika [568]4 years ago

6 0

Answer:

Its A) the discriminant is greater than zero, so there are two real roots.

Step-by-step explanation:

Sedaia [141]4 years ago

3 0

After manipulating above equation we get, 2x^2 - 7x - 8= 0. Discriminant= b^2 - 4ac = (-7)^2 - 4(2)(-8) = 113>0. So there are 2 real roots :)

You might be interested in

HELP PLEASE URGENT NEED REALLY PLEASE GUYS

aliina [53]

Answer:

4x+2

Step-by-step explanation:

4 0

3 years ago

element X is a radioactive isotope such that every 21 years, its mass decreases by half. Given that the initial mass of a sample

pashok25 [27]

Answer:

The percentage rate of decay per year is of 3.25%.

The function showing the mass of the sample remaining after t is $A(t) = 80(0.9675)^t$

Step-by-step explanation:

Equation for decay of substance:

The equation that models the amount of a decaying substance after t years is given by:

$A(t) = A(0)(1-r)^t$

In which A(0) is the initial amount and r is the decay rate, as a decimal.

Every 21 years, its mass decreases by half.

This means that $A(21) = 0.5A(0)$ . We use this to find r, the percentage rate of decay per year.

$A(t) = A(0)(1-r)^t$

$0.5A(0) = A(0)(1-r)^{21}$

$(1-r)^{21} = 0.5$

$\sqrt[21]{(1-r)^{21}} = \sqrt[21]{0.5}$

$1 - r = 0.5^{\frac{1}{21}}$

$1 - r = 0.9675$

$r = 1 - 0.9675 = 0.0325$

The percentage rate of decay per year is of 3.25%.

Given that the initial mass of a sample of Element X is 80 grams.

This means that $A(0) = 80$

The equation is:

$A(t) = A(0)(1-r)^t$

$A(t) = 80(1-0.0325)^t$

$A(t) = 80(0.9675)^t$

The function showing the mass of the sample remaining after t is $A(t) = 80(0.9675)^t$

8 0

3 years ago

Read 2 more answers

Help help needed for composition of function

dimulka [17.4K]

Answer:

$\circledast \ \ f\circ f\left( x\right) = x$

$\circledast \ \ g\circ g\left( x\right) =4x - 21$

Step-by-step explanation:

$f(x)=\frac{5}{2x}$

g(x) = 2x - 7

==============

$f\circ f\left( x\right) =\frac{5}{2\left( f\left( x\right) \right) }$

$=\frac{5}{2\left( \frac{5}{2x} \right) }$

$=\frac{5}{\left( \frac{5}{x} \right) }$

$=5\times\frac{x}{5}$

$=x$

_____________

$g\circ g\left( x\right) =2(g(x)) - 7$

= 2(2x - 7) - 7

= 4x - 14 - 7

= 4x - 23

3 0

2 years ago

Given the cosine equation y = 2cos(4x) - 1, What is the midline?

pogonyaev

Answer:

$y = 2 \cos(4x) - 1 \\ when \: y = 0 \\ \cos(4x) = \frac{1}{2} \\ 4x = 60 \\ x = 15 \\ when \: x = 0 \\ y = 2 - 1 = 1 \\ intercepts = > (15, \: 0) \: and \: (0, \: 1) \\ midpoints : ( \frac{15 + 0}{2} , \: \frac{0 + 1}{2} ) \\ = (7.5, \: 0.5) \\ gradient = \frac{1 - 0}{0 - 15} \\ = - \frac{1}{15} \\ y = mx + c \\ at \: (7.5, \: 0.5) \\ 0.5 = - \frac{1}{15} \times 7.5 + c \\ 0.5 = - 0.5 + c \\ c = 1 \\ \therefore \: y = - \frac{1}{15} x + 1 \\ = > 15y = - x + 15$

6 0

3 years ago

•How do you use the distance formula and slope formula to classify a triangle?

trasher [3.6K]

To classify the angle of a triangle (acute, obtuse, or right), you can use slope formula to see if the slopes are perpendicular. If so, it is a right triangle. The distance formula can be applied to figure out whether the triangle is isosceles, equilateral, or scalene. if the triangle is isosceles, then two of the sides will be the same length and one side will be of a different length. If the triangle is equilateral, then all sides will be of the same length. If the triangle is scalene, then all side will be of different lengths.

6 0

4 years ago