The figure is a parallelogram. m

State the value of the discriminant. Then determine the number of real roots of the equation. n(7n + 8) = –10

Viktor [21]

Answer:

a. -216, 0 real roots

Step-by-step explanation:

The discriminant of ...

ax² + bx + c = 0

is ...

d = b² -4ac

When we put your equation into the standard form shown above, we get ...

7n² +8n +10 = 0

Then we can identify a=7, b=8, c=10. The discriminant is then ...

d = 8² - 4·7·10 = 64 -280 = -216

___

The interpretation of the discriminant is ...

< 0; no real roots (2 complex roots)
= 0; one real root (multiplicity 2)
> 0; 2 real roots

Your discriminant is -216, so there are 0 real roots.

7 0

3 years ago

what is the different in the number of solutions between a system of equations and a system of inequalities?

KiRa [710]

A system of equations has at least one point in common in the solution (unless it is a special case)

A system of inequalities has regions of common solutions. (always an infinite number of solutions)

5 0

4 years ago

The domain of f(x) is the set of all real values except 7, and the domain of g(x) is the set of all real values except –3. Which

allochka39001 [22]

Answer:

The last is the correct option

"all real values except x not-equals 7 and the x for which f (x) not-equals negative 3"

Step-by-step explanation:

Domain and Range of Functions

Given the function f(x), the domain of f is the set of all the values that x can take such f(x) exists. The range of f is the set of all the values that f takes.

We have a problem where we have to find the domain of a composite function. Let's recall that being f and g real functions, then

$g\circ f=g(f(x))$

is the composite function of f and g.

We know the domain of f is the set of all real values except 7, and the domain of g is the set of all real values except –3.

Since f is the innermost function, the domain of the composite function is directly restricted by the domain of f. So, x cannot be 7.

Now, g takes f as its independent variable, and we know the domain of g excludes -3. It can be found that f(x) cannot be -3 because it will cause g not to exist.

Thus, the domain of $g\circ f$ is

All real numbers except x=7 and those where f(x)=-3

The last is the correct option

8 0

3 years ago

Solve the equation, x^2+3x+1=0, using the quadratic formula.

kari74 [83]

Answer:

x = (-3±√5)/2

Step-by-step explanation:

Matching the given equation to the pattern ...

... ax² +bx +c = 0

we see that a=1, b=3, c=1.

The solution to the above pattern is given by the quadratic formula ...

... x = (-b±√(b²-4ac))/(2a)

Substituting the values of a, b, c that we found, the formula gives ...

... x = (-3±√(3²-4·1·1))/(2·1)

... x = (-3±√5)/2

7 0

4 years ago

What is the simplified value of the expression below?

slavikrds [6]

Answer:

I dont know the experssion but I will give you steps to figure it out!

Step-by-step explanation:

Before you evaluate an algebraic expression, you need to simplify it. This will make all your calculations much easier. Here are the basic steps to follow to simplify an algebraic expression:

remove parentheses by multiplying factors

use exponent rules to remove parentheses in terms with exponents

combine like terms by adding coefficients

combine the constants

When simplifying an expression, the first thing to look for is whether you can clear any parentheses. Often, you can use the distributive property to clear parentheses, by multiplying the factors times the terms inside the parentheses. In this expression, we can use the distributive property to get rid of the first two sets of parentheses.

Now we can get rid of the parentheses in the term with the exponents by using the exponent rules we learned earlier. When a term with an exponent is raised to a power, we multiply the exponents For example, (x2)2 becomes x4.

The next step in simplifying is to look for like terms and combine them. The terms 5x and 15x are like terms, because they have the same variable raised to the same power

Finally, we look for any constants that we can combine.

Now our expression is simplified. Just one more thing -- usually we write an algebraic expression in a certain order. We start with the terms that have the largest exponents and work our way down to the constants. Using the commutative property of addition, we can rearrange the terms and put this expression in correct order, like this.

8 0

3 years ago