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3 years ago

Express the interval in set-builder notation and graph the interval on a number line (-6.2]

Mathematics

1 answer:

zzz [600]3 years ago

7 0

Answer:

{ $x|-6$ }

The number line is attached.

Step-by-step explanation:

By definition Set-builder notation is a mathematical shorthand used to provide specific details about a set.

In this case, you have the following interval:

$(-6,2]$

You can obsseve that the left hand contains a parentheses, which means that -6 it is not included, then:

$-6$

The right hand contains a bracket, which means that 2 is included:

$\leq 2$

The inequality is:

$-6$

Therefore, in Set-builder notation this is:

{ $x|-6$ }

Observe the number line attached. Since -6 is not included, you must use an unfilled circle. Since 2 is included, you must use a filled circle.

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4. The red graph (1) is the graph of f(x) = log(x). Describe the transformation of the blue function (2) and write the equation

sergey [27]

Answer:

Function $f(x)$ is shifted 1 unit left and 1 unit up.

$f(x)\rightarrow f(x+1)+1$

Transformed function $f(x+1)+1=\log(x+1)+1$

Step-by-step explanation:

Given:

Red graph (Parent function):

$f(x)=\log(x)$

Blue graph (Transformed function)

From the graph we can see that the red graph is shifted 1 units left and 1 units up.

Translation Rules:

$f(x)\rightarrow f(x+c)$

If $c>0$ the function shifts $c$ units to the left.

If $c$ the function shifts $c$ units to the right.

$f(x)\rightarrow f(x)+c$

If $c>0$ the function shifts $c$ units to the up.

If $c$ the function shifts $c$ units to the down.

Applying the rules to $f(x)$

The transformation statement is thus given by:

$f(x)\rightarrow f(x+1)+1$

As function $f(x)$ is shifted 1 unit left and 1 unit up.

Transformed function is given by:

$f(x+1)+1=\log(x+1)+1$

5 0

3 years ago

Everything was marked down 30%. The oringinal price of a manatee hat was $18. What was the clearence price

valentinak56 [21]

.3 * 18 = 5.4. 18-5.4 = 12.6$

Or

.7 * 18 = 12.6$

5 0

3 years ago

The car you just bought keeps breaking down. The parts you need to buy cost $408.97. Your mechanic also charges $53 per hour for

DiKsa [7]

C. repair charge = 53 * hours of labor + 408.97

7 0

3 years ago

Read 2 more answers

-8 ( y + 4 ) = 10y + 4

maks197457 [2]

Let's solve your equation step-by-step.−8(y+4)=10y+4

Step 1: Simplify both sides of the equation.−8(y+4)=10y+4

Simplify: (−8)(y)+(−8)(4)=10y+4(Distribute)−8y+−32=10y+4−8y−32=10y+4

Step 2: Subtract 10y from both sides.−8y−32−10y=10y+4−10y−18y−32=4

Step 3: Add 32 to both sides.−18y−32+32=4+32−18y=36

Step 4: Divide both sides by -18.−18y−18=36−18y=−2

Answer:y=−2

Good luck mate :P

7 0

3 years ago

Read 2 more answers

To win the carnival game Ring Ding, you must toss a wooden ring onto a grid of rectangles so that it lands without touching any

guapka [62]

Answer:

5in x 10in

Step-by-step explanation:

Solution:

1. You have to assume that the ring will land on the board and as a result, just focus on one rectangle of the board since they are all the same size.

2. For the ring to land entirely inside the rectangle, the center of the ring needs to be 1.5 inches inside the border (radius is 1.5 inches), so the "winning rectangle" will have dimensions:

L = (x - 2(1.5)) = x - 3

w = (2x - 2(1.5)) = 2x-3.

3. Now, we will set up and solve our geometric probability equation. The winning rectangle's area of (x-3)*(2x-3) divided by the total rectangle's area of x*(2x) = 28%

(2x-3)*(x-3)/(2x^2) = .28

2x^2 - 9x + 9 = .56x^2

1.44x^2 - 9x + 9 = 0

4 . Now you can plug that in the quadratic formula and get the solutions x = 1.25 or 5. However, it cannot by 1.25 because that is too small of a dimension for the the circle with diameter of 3 to fit in, the answers has to be 5.

5. As a result, the dimensions of the rectangles are 5in x 10in.

6 0

3 years ago