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topjm [15]
4 years ago
8

Alaine has 1 gallon of paint. She is going to pour it into a paint tray that measures 10 inches wide, 12 inches long, and 5 cm d

eep.
(1 gallon = 231 in3, 1 inch = 2.54 cm)

Which of the following scenarios will happen?
a. The paint will not fill the tray by 369 cm3.
b. The paint will not fill the tray by 5.22 in3.
c. The paint will fill the tray exactly.
d. The paint will overfill the tray by 5.22 in3
Mathematics
1 answer:
Damm [24]4 years ago
6 0
If Alaine has 1 gallon of paint, and she pours it into a paint tray that measures 10"w, 12"L, and 3cm deep, the paint tray will not fill the tray by 5.22 in3. 
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OlgaM077 [116]
We know that
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y=ax²+bx+c
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(-b/2a,(1-D)/4a)
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D=(-1)²-4*(1/4)*3-----> D=1-3---> D=-2
therefore
x coordinate of the focus
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3 years ago
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8. In right triangle LMN shown below, altitude MK is drawn to LN from M. IF LM = 12 and LK =10, then
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The length of the KN is 4.4

Step-by-step explanation:

We know from Pythagoras theorem  

In a right angle ΔLMN  

Base² + perpendicular² = hypotenuse ²

From the properties of triangle we also know that altitudes are ⊥ on the sides they fall.

Hence ∠LKM = ∠NKM = 90 °

Given values-

LM=12

LK=10

Let KN be “s”

⇒LN= LK + KN

⇒LN= 10+x        eq 1

Coming to the Δ LKM

⇒LK²+MK²= LM²

⇒MK²= 12²-10²

⇒MK²= 44           eq 2

Now in Δ MKN

⇒MK²+ KN²= MN²

⇒44+s²= MN²       eq 3

In Δ LMN

⇒LM²+MN²= LN²

Using the values of MN² and LN² from the previous equations

⇒12² + 44+s²= (10+s) ²

⇒144+44+s²= 100+s²+20s

⇒188+s²= 100+s²+20s    cancelling the common term “s²”

⇒20s= 188-100

∴ s= 4.4

Hence the value of KN is 4.4  

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