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never [62]
2 years ago
14

PLEASE HELP TIMED TEST

Mathematics
1 answer:
Paraphin [41]2 years ago
5 0

Answer:

8

Step-by-step explanation:

How many more unit tiles must be added to the function

f(x)=x²-6x+1 in order to complete the square?

The easier, but usually not viable way: If we look at how many more tiles need to be added, we can see that each smaller sides is 1 unit. Thus, we need 8 more tiles to complete the square.

However, this is just an educated guess. If we didn't have a diagram or it was drawn badly, we would be wrong. Let's solve it algebraically.

Note:

completing the square is changing a quadratic equation (the format is

ax² + bx + c = 0)into a(x - d)² + e = 0. (an example of this is (a + b)² or (a - b)²)

This may be confusing, but look at an example:

x² + 4x + 4 = (x + 2)²

Also note that, (a - b)² = a² - 2ab + b²

If we substitute a = x, then we get:

x² - 2bx + b².

Now, all we need to do is find b.

If we know that 2bx = 6x, then we can divide both sides by 2x and get an answer of

2bx = 6x

b = 3.

Thus, b is 3.

Remember, to complete the square, we need to find b², which is

3² = 9.

Then, because they already give us a "1", we just need to add 9-1 = 8 more units.

Just in case, let's check the answer.

If we add 8 to the problem, we get:

x² - 6x + 1 + 8 =

x² - 6x + 9

As you can see, this follows the a² - 2ab + b² format, so we can factor it.

x² - 6x + 9 = (x - 3)²

This is a completed square. Thus, we need to add 8 more unit tiles.

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Joe and grace are baking cookies they need a total of 2 cups of sugar for the recipe joe has 11/10 cups of sugar and grace has 3
DanielleElmas [232]

Answer:

Step-by-step explanation:

Total amount of sugar needed to bake the cookies is 2 cups. Amount of sugar that Joe has is 11/10 cups of sugar. Amount of sugar that Grace has is 3/4 cups of sugar.

The total amount of sugar that Joe and Grace have won't be enough to bake the cake because the total of 11/10 cups and 3/4 cups is below 2 cups

6 0
3 years ago
A triangular bookself has a base of 10 inches,12 inches and 18 inches. Will the bookself fit in the corner of a square living ro
melisa1 [442]

Answer:

No, if fit means that the sides of the book case need to be flush with the wall, which means that the sides of the bookcase are touching the wall and the bookcase fits perfectly in that spot

Step-by-step explanation:

A square room will have corners that meause 90°, so we need to see if any of the vertices of the bookcase measure 90°.  All right triangles have a 90° in them, so we can use Pythagorean Theorem to solve this.

 Pythagorean Theorem is  a² + b² = c²,    where a and b are the legs, and c is the hypotenuse.  Since the hypotenuse is always the longest side, for our bookshelf, 10 and 12 are the legs, and 18 would be the hypotenuse if it is a right triangle.   Plug the values in to see if the equation is true or false

10² + 12² = 18²

  100 + 144 = 324

     244 ≠ 324   so the bookcase does not form a right angle, and won't fit in the corner of the room

4 0
3 years ago
Please help: <br><br> 12x^4(-5/6x^3y^2)<br><br> If possible, include steps<br><br> Thanks.
tangare [24]
---------------------------------------------------------------------------------------
Question
---------------------------------------------------------------------------------------
12x^4(- \frac{5}{6} x^3y^2)

---------------------------------------------------------------------------------------
Multiply the constant: 12 x (-5/6)
---------------------------------------------------------------------------------------
-10x^4( x^3y^2)

---------------------------------------------------------------------------------------
Multiply the x (we add the power together when we multiply)
---------------------------------------------------------------------------------------
-10x^7y^2

---------------------------------------------------------------------------------------
Answer: -10x⁷y²
---------------------------------------------------------------------------------------
4 0
2 years ago
Answer question worth 25 points plz help!
Ilya [14]

Answer:

B

Step-by-step explanation:

6 0
2 years ago
What is the answer to this
Xelga [282]
Lateral area of triangular prism = (a+b+c)h where a, b and c are the sides of the triangular base, h is the height.

LA= (a+b+c)h=
a=4
b=6
c=?
c=9
h=8

c=√6²+4²=√80 or approximately 9

you should get An Area= (4+6+√80)8

LA= 80+8√80


4 0
3 years ago
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