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2 years ago

Solve for x. Enter your answer in interval notation using grouping symbols. x2 + x < 20

Mathematics

2 answers:

Rus_ich [418]2 years ago

6 0

Answer:

x<18

Step-by-step explanation:

2+x<20

Karo-lina-s [1.5K]2 years ago

3 0

Answer:

(-5, 4)

Step-by-step explanation:

x^2 + x < 20 can be rewritten as a quadratic in standard form: x^2 + x - 20 < 0. Recognize that the graph of x^2 + x - 20 is that of a parabola that opens up. Because the y-intercept (0, -20) is below the x-axis, we know for certain tht the graph intersects the x-axis in two places. Our job is to determine the two horizontal intercepts, which in turn determine the solution set.

x^2 + x - 20 = 0 factors as follows: (x + 5)(x - 4) = 0, whose roots are -5 and 4.

These two roots form 3 intervals: (-infinity, -5), (-5, 4) and (4, infinity). We now must identify on which intervals x^2 + x - 20 is less than 0 (that is, on which intervals the graph is below the x-axis). Choose three test values for x: the first could be -6 (which is in the set (-infinity, -5) ); x^2 + x - 20 is + there, and so the graph is above the x-axis and x^2 + x - 20 is positive. Reject this.

Next, test x = 0; x^2 + x - 20 is negative there, meaning that x^2 + x - 20 < 0 and that x^2 + x < 20. Thus, the solution is (-5, 4). It can be shown that x^2 + x - 20 is positive again for x-values within the interval (4, infinity).

Evaluating

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S - 1/3 equals 4/9 so S equals what?

bekas [8.4K]

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5 0

3 years ago

Evaluate the function. f(x) = 3x² – x Find f(10)

kirill [66]

Answer:

Step-by-step explanation:

<u>Function Evaluation</u>

Given a function f(x) as an explicit expression, finding f(x=a) implies substituting the value of x by a in every instance it occurs.

We are given the function:

$f(x)=3x^2-x$

It's required to find f(10). We replace the x for 10:

$f(10)=3*10^2-10$

Operating:

$f(10)=3*100-10$

$f(10)=300-10$

$f(10)=290$

Thus, f(10)=290

4 0

3 years ago

Use the equation P(A or B)= P(B)-P(A and B) to find the missing value below.

Anvisha [2.4K]

Answer:

$P(B) = \frac{7}{8}$

Step-by-step explanation:

Given

P(A or B)= P(B)-P(A and B)

P(A)=1/3

P(A and B)=1/8

P(A or B)= 3/4

Required

Find P(B)

To find P(B), all we need to do is to substitute values of P(A or B) and P(A and B) in the given equation.

This goes thus;

P(A or B) = P(B) - P(A and B) becomes

$\frac{3}{4} = P(B) - \frac{1}{8}$

Make P(B) the subject of formula

$P(B) = \frac{3}{4} + \frac{1}{8}$

Take L.C.M

$P(B) = \frac{6 + 1}{8}$

Add fractions

$P(B) = \frac{7}{8}$

From the workings above, the value of P(B) using the given equation is $\frac{7}{8}$

6 0

3 years ago

Need help here plss

Ierofanga [76]

Two linear equations can have no solutions, exactly one solution or infinitely many solutions. There will be no solution if the lines are parallel on a graph. There will be exactly one solution if the lines intersect each other on a single point. And finally, there will be infinite solutions if the lines overlap each other perfectly.

A single line however has infinite ordered pair solutions as the line travels infinitely in both directions on the coordinate plane. For example, using the equation y=3x, for any real value of x, we will get a real value for y.

Linear inequalities with two variables have infinitely many solutions. We can use the inequality y>3x as an example. For any real value of x, we will get a real value for y.

I hope this helps!

6 0

3 years ago

2. In a recent survey conducted by the International Nanny Association, 4,176 nannies were placed in a job in a given year. Only

Natali [406]

Answer:

There is a 0.57% probability that a randomly selected nanny who was placed during the last year is a male nanny (a "mannie").

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this problem, we have that:

Desired outcomes:

The number of male nannies selected. 24 of the nannies placed were men. So the number of desired outcomes is 24.

Total outcomes:

The number of nannies selected. 4,176 nannies were placed in a job in a given year. So the number of total outcomes 4176.

Find the probability that a randomly selected nanny who was placed during the last year is a male nanny (a "mannie").

$P = \frac{24}{4176} = 0.0057$

There is a 0.57% probability that a randomly selected nanny who was placed during the last year is a male nanny (a "mannie").

3 0

3 years ago