Write the following inequality in slope-intercept form. −6x + 2y ≤ 42

Answer:

  The product of an odd number of negative factors is negative.

Step-by-step explanation:

The factor -1 can be factored from any negative number. Then the product of some number of negative numbers is the product of that number of positive numbers and -1 raised to that power.

An even power of -1 is 1.

An odd power of -1 is -1. So, the product of an odd number of negative factors is negative.

_____

Examples

_____

Comment on this result

This is helpful to remember when considering the solutions to polynomial inequalities. Once the factored form of the polynomial is found, the solution will depend on the signs of the factors. For example, consider ...

  (x +4)(x -2)(x -3) < 0

The zeros of these factors are -4, 2, 3. At each of these values of x, the sign of one of the factors will change. For x<-4, all three factors are negative, so the inequality is true. For -4<x<2, only two of the factors are negative, so the inequality is false. For 2<x<3, one of the factors is negative, so the inequality is again true. For 3<x, all factors are positive, so the inequality is false. Then the solution is (x < -4) ∪ (2 < x < 3).

See the graph for a plot of this polynomial and the solution to the inequality.

Answer:

1 : 5

Step-by-step explanation:

The amount of tip I would leave for the waiter is  $24.89

A tip is a form of payment that is given to someone who renders a service. The amount of tip that was given is a percentage of the total bill at the restaurant.

The value of the tip can be determined by multiplying the percentage of tip by the total bill at the restaurant

Value of the tip = percentage tip x total bill at the restaurant

20% x  $24.89

0.2 x  $24.89 = $4.98

A similar question was solved here: https://brainly.com/question/15258234?referrer=searchResults

Answer:

C. His friend's house, grocery store, and his home.

Step-by-step explanation:

Triangle Proportionality Theorem-

If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.

So if the line joining the park, bus stop and friend's house, grocery store will be parallel, Stephen can use triangle proportionality theorem.

When two lines are crossed by another line i.e the transversal, the angles in matching corners are called corresponding angles. And when the corresponding angles are equal then the two lines are parallel.

The corresponding angle of the angle between the park, the bus stop, and his home is the angle between his friend's house, grocery store, and his home.

Therefore, he needs to measure that angle.

On the second day, Andrea will still win by 0.026 seconds and the other girl will be at 99.75 meters on the track.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, Andrea and Sula ran a race on a track that was 100 meters long.

Let us assume that Andrea completed the 100m race in 10 secs.

∴  Andrea's speed is (100/10) = 10m/sec.

Also given that Sula was exactly 5 meters behind her.

∴ In 10 secs she completed 95 meters, and her speed is

= (95/10) = 9.5m/sec.

The next day they ran another race and Andrea agreed to start 5 meters behind the starting line and both the girls run at the same speed,

∴  Andrea has to run 105 meters, so she'll complete the race in

(105/10) secs.

= 10.5 secs.

Sula has to run only 100 meters, so the time needed for her to complete is,

= (100/9.5) secs.

= 10.526 seconds.

So, on the next day, Andrea will win again by (10.526 - 10.5) secs

= 0.26 secs.

∴ When the winner crosses the finish line the other girl will be,

(10.5×9.5) meters = 99.75 meters on the track.

learn more about the unitary method here :

https://brainly.com/question/21648365

#SPJ2

Answer : The given polynomial equation can have 0,2 or 4 complex roots.

Explanation:-

Given polynomial equation is [tex]3x^5-2x+1=0[/tex] which is a polynomial of degree 5.

We know that the complex roots always occur in pair ,therefore the number of complex roots in any polynomial must be an even number but less than equal  to the degree of polynomial.

Thus, the given polynomial equation has 4 complex roots.

Answer:

The polynomial equation have 4 complex roots.

Step-by-step explanation:

We are given a polynomial equation as:

[tex]3x^5-2x+1=0[/tex]

clearly the polynomial equation is a equation of degree 5 hence, the polynomial equation has atmost 5 roots.

Now we find the roots of the equation by it's graph.

we could clearly see that the graph ofthe function passes through the point (-1,0). hence -1 is the root of the polynomial equation, other than this point the graph does not touches or pass through the x-axis.

Hence, the other four roots of the polynomial equation are complex.

Hence, the polynomial equation has 4 complex roots.

Answer:

13.57

Step-by-step explanation:

We have been given an equation [tex]v=-1385n+18,790[/tex], which represents the value of a car. We are asked to find the n-intercept of our given equation.

We know that the n-intercept will be at [tex]v=0[/tex].

[tex]0=-1385n+18,790[/tex]

Subtracting 18,790 from both sides of our equation we will get,

[tex]0-18,790=-1385n+18,790-18,790[/tex]

[tex]-18,790=-1385n[/tex]

Now, we will divide both sides of our equation by [tex]-1385[/tex].

[tex]\frac{-18,790}{-1385}=\frac{-1385n}{-1385}[/tex]

[tex]13.566787=n[/tex]

[tex]n\approx 13.57[/tex]

Therefore, the n-intercept of our given graph is approximately 13.57.

Answer:

B. Positive correlation

Step-by-step explanation:

Positive correlation is nothing but when the values of x increase, the corresponding y values are also increase.

When we look at the scatter plot, when x increase, the y also increase.

Therefore, it is a positive correlation.

Hope this will helpful.

Thank you.

The measure of angle m∠3 would be 60°.

The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.

Given;

g ∥ h, m∠1 = (4x + 36)°,

m∠2 = (3x – 3)°.

m∠2 = m∠3 ( alternate interoir angle)

we know that

m∠1 + m∠2 = 180

4x + 36 + 3x – 3 = 180

7x + 33 = 180

7x = 147

x = 21

Substituting

m∠2 = 3x – 3

m∠2 = 3(21) - 3

m∠2 = 63 - 3

m∠2= 60

Therefore, m∠3 = m∠2 = 60

Hence, The measure of angle m∠3 would be 60°.

Learn more about the triangles;

https://brainly.com/question/2773823

#SPJ5

Answer:  The correct option is (a) [tex]2x^2+3x-5.[/tex]

Step-by-step explanation:  We are given to find the quotient in the following division :

[tex]Q=\dfrac{2x^3-3x^2-14x+15}{x-3}.[/tex]

To find the quotient, first we will try to factorize the numerator and then we will try to divide by the denominator.

We have

[tex]Q\\\\\\=\dfrac{2x^3-3x^2-14x+15}{x-3}\\\\\\=\dfrac{2x(x-3)+3x(x-3)-5(x-3)}{x-3}\\\\\\=\dfrac{(x-3)(2x^2+3x-5)}{(x-3)}\\\\=2x^2+3x-5.[/tex]

Thus, the required coefficient is [tex]2x^2+3x-5.[/tex]

Option (a) is CORRECT.

To find angle PQR in a parallelogram, we can use the Exterior Angle Theorem. By subtracting the measures of the other two angles in triangle QRS from 180 degrees, we find that angle PQR is 70 degrees.

To find the measure of angle PQR, we can use the fact that opposite angles in a parallelogram are congruent. This means that angle PQR is equal to angle STQ. Since STQ is an exterior angle of triangle QRS, we can use the Exterior Angle Theorem to find its measure by subtracting the measures of the other two angles in the triangle from 180 degrees.

Given that angle QRS is 110 degrees, we can find angle STQ by subtracting the measures of angles QRS and QSR from 180 degrees:

angle STQ = 180 - (110 + 180) = -110 degrees

However, angles cannot have negative measures, so we need to find the equivalent positive measure. Adding 180 degrees to -110 degrees gives us angle STQ = 70 degrees. Therefore, angle PQR is also equal to 70 degrees.

https://brainly.com/question/31116104

#SPJ3

Answer:

give the other person brainly

its A

Step-by-step explanation: