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Nina [5.8K]
3 years ago
11

Twice the sum of a number and 4 is less than 12

Mathematics
1 answer:
Allisa [31]3 years ago
3 0
To find the number you can set up a small equation (x being the number) and solve for x.
It can be written as 2 ( x + 4) < 12
Solve for x to find the number.
2 ( x + 4) < 12
Distribute the 2
2x+8<12
Subtract 8 on both sides
2x<4
Divide by 2 on both sides
x<2

Therefore the number is any number less than 2

~I hope this helps!~
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PLEASE HELP
valina [46]

Answer:

Step-by-step explanation:

You have 3 unknowns: a, b, and c.  It's our job to find them algebraically.  I'm going to start with the point where x = 0 and y = 7.  You'll see why in a minute.  Filling in the standard form of a quadratic

y=ax^2+bx+c  using (0, 7):

7=a(0)^2+b(0)+c  gives you that c = 7.  We will use that value now when we write the next 2 equations.  Now the point (-2, 19):

19=a(-2)^2+b(-2)+7  and

19=4a-2b+7 so

12 = 4a - 2b

Now for the next point (-1, 12):

12=a(-1)^2+b(-1)+7  and

12=a-b+7  so

5 = a - b

Now we have a system of equations (the 2 bold font equations) that we will solve by elimination:

 12  =  4a  -  2b

  5  =   a   -    b

Multiply the bottom equation by -4 to get a new system:

 12  =  4a  -  2b

-20  = -4a  +  4b

Add those together to get rid of the a terms and end up with

-8 = 2b so

b = -4

Now we can sub in -4 for b to solve for a.  I'm using the second bold type equation to do this:

5 = a - (-4) and

5 = a + 4 so

a = 1 and the equation for the quadratic function is

y=x^2-4x+7

7 0
3 years ago
What happens to the distance between each billiard ball during this rigid<br><br> transformation?
Delicious77 [7]

The question is incomplete. Here is the complete question.

To set up a game of billiards, the first player moves the balls contained within a triangular rack as shown. What happens to the distance between each billiard during this rigid transformation?

A. The distance remains constant throughout the transformation.

B. The distance decreases at the start and increases after all motion stops.

C. The distance stays the same at the start but decreasesexactly when motion ends.

D. The distance increases at the start and then decreases as the rack gets further from the player.

Answer: A. The distance remains constant throughout the transformation.

Step-by-step explanation: In a <u>rigid</u> <u>motion</u>, all moving points in the plane are moving in way such tha:

1)  relative distance between them stays the same and

2) relative position of the points stays the same

There are four types of rigid motions: translation, rotation, reflexion and glide reflection.

<u>Translation</u>: every point or object is moved by the same amount and in the same direction;

<u>Rotation</u>: the object rotates by the same amount around a fixed point;

<u>Reflexion</u>: the object exchange points from one side of a line with points on the other side of the line at the same distance from the line;

<u>Glide</u> <u>Reflection</u>: is a mirror reflection followed by a translation parallel to the mirror.

In the game of billiards, because all the balls are inside the triangular rack, the distance, and also the position, between them stays the same, limited by the rack. Since they are moving by the same amount in the same direction, the rigid transformation is a translation.

Therefore, the distance of the balls in the triangular rack remains constant throughout the transformation.

6 0
3 years ago
Which is the quotient of 396 divided by 12
Anton [14]
To find the quotient, divide 396 by 12.
396/12= 33
5 0
3 years ago
Read 2 more answers
Can someone help me on problem 2<br> Please ?
Elza [17]

Answer:

x=48

Step-by-step explanation:

48/4=12

please mark brainiest

thank you

7 0
2 years ago
Read 2 more answers
3 What is the y-intercept of the line with the equation Y = 1/2 - x - 3?
PSYCHO15rus [73]

Answer:

<h2>a. -3</h2>

Step-by-step explanation:

Given Equation :

y =  \frac{1}{2} x - 3

Which is in slope intercept form :

y = mx + b

Where :

m = slope

b = y-intercept.

Thus , in the given Equation , the y-intercept is -3

8 0
3 years ago
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