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shusha [124]
3 years ago
8

Mr. Smith is adding food coloring to water to create his own paint colors. He has 5 1/3 cups of water. to create a color, he nee

ds 2/3 cups of water. How many paint colors in all can Mr. Smith create if he uses all the cups of water he has?
Mathematics
2 answers:
serious [3.7K]3 years ago
6 0

8 Colors

If you make it an improper fraction it becomes 16/3 and 2/3, so now you can do 16/2, giving you 8 colors

galina1969 [7]3 years ago
5 0

Answer:

8 colors.

Step-by-step explanation:

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In a right triangle ABC, CD is an altitude, such that AD=BC. Find AC, if AB=3 cm, and CD= 2 cm.
konstantin123 [22]

Consider right triangle ΔABC with legs AC and BC and hypotenuse AB. Draw the altitude CD.

1. Theorem: The length of each leg of a right triangle is the geometric mean of the length of the hypotenuse and the length of the segment of the hypotenuse adjacent to that leg.

According to this theorem,

BC^2=BD\cdot AB.

Let BC=x cm, then AD=BC=x cm and BD=AB-AD=3-x cm. Then

x^2=(3-x)\cdot 3,\\ \\x^2=9-3x,\\ \\x^2+3x-9=0,\\ \\D=3^2-4\cdot (-9)=9+36=45,\\ \\\sqrt{D}=\sqrt{45}=3\sqrt{5},\\ \\x_1=\dfrac{-3-3\sqrt{5} }{2}0.

Take positive value x. You get

AD=BC=\dfrac{-3+3\sqrt{5} }{2}\ cm.

2. According to the previous theorem,

AC^2=AD\cdot AB.

Then

AC^2=\dfrac{-3+3\sqrt{5} }{2}\cdot 3=\dfrac{-9+9\sqrt{5} }{2},\\ \\AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.

Answer: AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.

This solution doesn't need CD=2 cm. Note that if AB=3cm and CD=2cm, then

CD^2=AD\cdot DB,\\ \\2^2=AD\cdot (3-AD),\\ \\AD^2-3AD+4=0,\\ \\D

This means that you cannot find solutions of this equation. Then CD≠2 cm.

8 0
3 years ago
Read 2 more answers
What's the value of<br><img src="https://tex.z-dn.net/?f=2%20%5Ctimes%20750%20%20%2B%200%20%7B%7D%5E%7B7%7D%20" id="TexFormula1"
Elina [12.6K]

Step-by-step explanation:

2×750=1500 + 0^7. ( 0×0×0×0×0×0×0=0)

So,

1500 Answer

7 0
2 years ago
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Help me please lol really need this<br> I gave 3 pics if you need to understand it better.
aalyn [17]

Answer:

-Bell-shaped, A bell shaped picture, shown below, usually presents a normal distribution

Step-by-step explanation:

-Hope this helps butter cup :)

7 0
3 years ago
The sum of two numbers is 52. The smaller number is 18 less than the larger number. What are the numbers?
ch4aika [34]

x + y = 52

x = y - 18

Adding,

2x + y = 52 + y - 18

2x = 34

x = 17

y = x + 18 = 35

Check: x+y = 17+35 = 52, good

Answer: 17 and 35

7 0
3 years ago
Is 5/8 grater than or equal to 11/16
dezoksy [38]

Answer:

Less than

Step-by-step explanation:

Although it wasn't an option, it is less than. In order to accurately compare then, you have to get the least common denominator. Using the least common multiple (2), you multiply 5/8 by 2 and end up with 10/16. Now 10 is less than 11, so the option is neither of those. 5/8 is less than 11/16.

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3 years ago
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