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3 years ago

* Unions are important in today's economy because they

Mathematics

1 answer:

DedPeter [7]3 years ago

7 0

Step-by-step explanation:

Unions are important because they help set the standards for education, skill levels, wages, working conditions, and quality of life for workers. Union-negotiated wages and benefits are generally superior to what non-union workers receive. Most union contracts provide far more protections than state and federal laws.

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Best tip for Maths test to figure out challenging problems

padilas [110]

First solve the easier questions which can be solved in very low time.
Drop out the harder questions for last.
After completing the easier questions take your time to complete harder ones.
Stay away from unsolvable questions

3 0

3 years ago

Part 4: Identify the vertex, focus and directrix of each. Then sketch the graph.

Nezavi [6.7K]

Answer: 1) Vertex: (6, -2) Focus: (6, -7/4) Directrix: y = -9/4

2) Vertex: (-2, -1) Focus: (-7/4, -1) Directrix: x = -9/4

<u>Step-by-step explanation:</u>

Rewrite the equation in vertex format y = a(x - h)² + k or x = a(y - k)² + h by completing the square. Divide the b-value by 2 and square it - add that value to both sides of the equation.

(h, k) is the vertex
p is the distance from the vertex to the focus
-p is the distance from the vertex to the directrix

$\bullet\quad a=\dfrac{1}{4p}$

1) y = x² - 12x + 34

$y-34=x^2-12x\\\\y-34+\bigg(\dfrac{-12}{2}\bigg)^2=x^2-12x+\bigg(\dfrac{-12}{2}\bigg)^2\\\\\\y-34+36=(x-6)^2\\\\y+2=(x-6)^2\\\\y=(x-6)^2-2\qquad \rightarrow \qquad a=1\quad (h,k)=(6,-2)\\$

$a=\dfrac{1}{4p}\quad \rightarrow \quad 1=\dfrac{1}{4p}\quad \rightarrow \quad p=\dfrac{1}{4}\\\\\\\text{Focus = Vertex + p}\\.\qquad \quad =\dfrac{-8}{4}+\dfrac{1}{4}\\\\.\qquad \quad =-\dfrac{7}{4}\quad \rightarrow \quad\text{Focus}=\bigg(6,-\dfrac{7}{4}\bigg)\\\\\\\text{Directrix: y= Vertex - p}\\.\qquad \qquad y=\dfrac{-8}{4}-\dfrac{1}{4}\\\\.\qquad \qquad y=-\dfrac{9}{4}$

*******************************************************************************************

2) x = y² + 2y - 1

$x+1=y^2+2y\\\\x+1+\bigg(\dfrac{2}{2}\bigg)^2=y^2+2y+\bigg(\dfrac{2}{2}\bigg)^2\\\\\\x+1+1=(y+1)^2\\\\x+2=(y+1)^2\\\\x=(y+1)^2-2\qquad \rightarrow \qquad a=1\quad (h,k)=(-2,-1)\\$

$a=\dfrac{1}{4p}\quad \rightarrow \quad 1=\dfrac{1}{4p}\quad \rightarrow \quad p=\dfrac{1}{4}\\\\\\\text{Focus = Vertex + p}\\.\qquad \quad =\dfrac{-8}{4}+\dfrac{1}{4}\\\\.\qquad \quad =-\dfrac{7}{4}\quad \rightarrow \quad\text{Focus}=\bigg(-\dfrac{7}{4},-1\bigg)\\\\\\\text{Directrix: x= Vertex - p}\\.\qquad \qquad y=\dfrac{-8}{4}-\dfrac{1}{4}\\\\.\qquad \qquad x=-\dfrac{9}{4}$

4 0

3 years ago

How many solutions are there to the equation below? 4(x-5)=4x-24

blondinia [14]

It is a linear equation so there can be 1 solution, 0 solutions, or infinite solutions

4(x-5)=4x-24

distribute

4x -20 = 4x-24

subtract 4x from each side

-20 = -24

no solutions

6 0

3 years ago

Read 2 more answers

Simplify this expression;<br>3(2x+7)

Advocard [28]

Answer:

6x+21 (Maybe)

Are you doing the buddy method, how is your teacher wanting to do this, When you respond I might have the correct answer

(buddy method) Multiply the 2x and 7 by the 3 giving you 6x+21 and then that's it you cant do anything else but I don't know if that's how you're teacher wants it done.

5 0

3 years ago

Read 2 more answers

There are 161 calories in 28 grams you eat 9 cashews totaling 12 grams. How many cashews are in one serving

makkiz [27]

Answer:

For every 4 grams there are 3 cashews.

12g=9. So that means there are 18 cashews in 24 grams. And like we said, there are 3 cashews in every 4 grams. So there are 21 cashews for 161 cals, equating to 28g.

5 0

3 years ago