Factor the polynomial 6b^2-17b+10

Answers

Answer 1

Answer: $6b ^ 2-17b +10 \n \n\Delta = b^(2)-4ac = (-17)^(2)-4*6*10=289-240=49\n \nx_(1)=(-b-√(\Delta ))/(2a) =(17- √(49))/(2*6)=(17-7)/(12)= (10)/(12)=(5)/(6)\n \nx_(2)=(-b+√(\Delta ))/(2a) =(17+ √(49))/(2*6)=(17+7)/(12)= (24)/(12)=2 \n \n Answer : \ x=(5)/(6) \ \ or \ \ x=2$

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The variables x and y are directly proportional, and y = 2when x = 3. What is the value of y when x = 9 ?

Answers

Direct proportionality:
$y=kx$
k - the constant of proportionality

$y=2 \hbox{ when } x=3 \n \Downarrow \ny=kx \n 2=3k \nk=(2)/(3) \n \ny=? \hbox{ when } x=9 \n\Downarrow \ny=kx \n y=(2)/(3) * 9 \ny=2 * 3\ny=6 \n \n\boxed{y=6 \hbox{ when } x=9}$

Y=4x-7 make x the subject of the equation

Answers

Step-by-step explanation:

y=4x-7

y+7=4x

x=y+7

hope it helps.

Explain how unwrapping a present is used as an analogy for solving an equation. How do you "unwrap" with an equation?...?

Answers

Here is an analogy comparing between unwrapping a present and unwrapping an equation. Both actions do require following a process. You cannot just skip one step in order to arrive at the answer. Just like unwrapping a present, you need to do it in order. First, you take off the ribbon, then you start to unwrap the wrapper until you see the actual gift. On the other hand, when you are unwrapping an equation, you also follow a certain step. You are given a certain formula and values. What you need to do next is to substitute, do the solution, until it is simplified. And lastly, there you have it. You can now see the actual answer. Hope this answer helps.

Final answer:

Solving an equation is likened to unwrapping a present because in both cases, you aim to uncover what's within by dealing with the outer layers systematically. Through an inverse process, you isolate the equation's variable and solve for it, just as the step-by-step unwrapping of layers reveals the gift within the package.

Explanation:

Unwrapping a present is a great way to understand the process of solving an equation. If you consider the equation itself as being 'wrapped' in different operations such as multiplication, division, addition, and subtraction, you can begin to 'unwrap' it by systematically dealing with these operations in reverse from the order of operations. This would be like when you unpack the present by undoing the tape, then the paper, then the box, or whatever other layers might be present.

To use a direct example, let's consider the equation 3x + 7 = 22. You start unwrapping by isolating for the term with the variable. This means you handle the operation that does not involve the variable first. So, subtract 7 from both sides of the equation to get 3x = 15. Next, you handle the multiplication operation by dividing both sides by 3 and solving for x, which would be 5 in this case. Just like unwrapping a present, we aim to get to the 'inside' or the root of the equation.

Learn more about Solving Equations here:

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Find the volume of the cylinder in terms of Pi.
h = 6 and r = 3

Answers

The volume of the cylinder that has 6 as its height and 3 as its radius would be 54π or 169.71 square unit. This is solve using the formula of volume of cylinder which is equal to π times squared of radius times the height. Substituting the value, it would equal to π(3²)(6) or 54π.

What is the solution to 3!

Answers

3! =3 x 2 x 1 = 6

Y!= Y x (y-1) x ... x 1=

$3!=2\cdot3=6$

Suppose the juice boxes go on sale for $1.79 for the eight 4.23-ouncejuice boxes, and the cider goes on sale for $6.50 per gallon. Does this
change your decision? Why or why not?

Answers

Yes it does shegehehehavueheuwbuehwhwb

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