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3 years ago

How would you graph the solution set of x - 6 < - 3?

Mathematics

1 answer:

melomori [17]3 years ago

5 0

Move all terms not containing x to the right side of the inequality. You should get x<3

This is what your line should look like. The circle will be open because the is not line under the less than sign. And it will be going toward the left because it is less than greater than is graphed to the right.

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I don’t know how to do this

stich3 [128]

To check for continuity at the edges of each piece, you need to consider the limit as $x$ approaches the edges. For example,

$g(x)=\begin{cases}2x+5&\text{for }x\le-3\\x^2-10&\text{for }x>-3\end{cases}$

has two pieces, $2x+5$ and $x^2-10$ , both of which are continuous by themselves on the provided intervals. In order for $g$ to be continuous everywhere, we need to have

$\displaystyle\lim_{x\to-3^-}g(x)=\lim_{x\to-3^+}g(x)=g(-3)$

By definition of $g$ , we have $g(-3)=2(-3)+5=-1$ , and the limits are

$\displaystyle\lim_{x\to-3^-}g(x)=\lim_{x\to-3}(2x+5)=-1$

$\displaystyle\lim_{x\to-3^+}g(x)=\lim_{x\to-3}(x^2-10)=-1$

The limits match, so $g$ is continuous.

For the others: Each of the individual pieces of $f,h$ are continuous functions on their domains, so you just need to check the value of each piece at the edge of each subinterval.

4 0

3 years ago

I had a summer job cooking two items at a bbq place. I sell burgers for $9.00 and sell chicken sandwiches for $11.25. Because I

pishuonlain [190]

Answer:

He sold 180 chicken sandwiches and 150 burguers.

Step-by-step explanation:

Since 330 items were sold, then the amount of burguers and chicken sandwiches sold must be equal to this value. From this information we have:

burguers + sandwiches = 330

We know that each burguer cost $9 and each chicken sandwich cost $11.25 and that we made a total of $3,375. So we have:

9*burguers + 11.25*sandwiches = 3,375

From the first equation we have:

burguers = 330 - sandwiches

Applying it on the second equation:

9*(330 - sandwiches) + 11.25*sandwiches = 3,375

2,970 - 9*sandwiches + 11.25*sandwiches = 3,375

2.25*sandwiches = 3,375 - 2,970

2.25*sandwiches = 405

sandwiches = 405/2.25 = 180

So,

burguers = 330 - 180 = 150

He sold 180 chicken sandwiches and 150 burguers.

8 0

2 years ago

Use the zero product property to find the solutions to the equation 6x^2 – 5x = 56.

frez [133]

Answer:

x = 7/2 or x = -8/3

Step-by-step explanation:

Solve for x over the real numbers:

6 x^2 - 5 x = 56

Divide both sides by 6:

x^2 - (5 x)/6 = 28/3

Add 25/144 to both sides:

x^2 - (5 x)/6 + 25/144 = 1369/144

Write the left hand side as a square:

(x - 5/12)^2 = 1369/144

Take the square root of both sides:

x - 5/12 = 37/12 or x - 5/12 = -37/12

Add 5/12 to both sides:

x = 7/2 or x - 5/12 = -37/12

Add 5/12 to both sides:

Answer: x = 7/2 or x = -8/3

8 0

3 years ago

Read 2 more answers

Calculate the slope.please help due in 2 hours

sergejj [24]

Answer:

Slope = 4

Step-by-step explanation:

Use any two pairs from the table of values, say (0, 3) and (2, 11).

Slope = ∆y/∆x

Slope = $\frac{11 - 3}{2 - 0}$

Slope = $\frac{8}{2}$

Slope = 4

3 0

2 years ago

The diagonal AC is drawn in parallelogram ABCD Which method can NOT be used to prove that AABC is congruent to ACDA?

diamong [38]

Answer:

B SSA

Step-by-step explanation:

Geometric proofs can be used to show that the two triangles are congruent using ASA, SAS and SSS.

However, there is no such thing as SSA in geometry because an angle and two sides can not show congruence of triangles. This is so because the angle is not an included angle.

5 0

3 years ago