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diamong [38]
3 years ago
7

Allison and her children went into a bakery where they sell donuts for $2 each and cookies for $1 each. Allison has $20 to spend

and must buy at least 11 donuts and cookies altogether. If x represents the number of donuts purchased and y represents the number of cookies purchased, write and solve a system of inequalities graphically and determine one possible solution.
Mathematics
1 answer:
KATRIN_1 [288]3 years ago
8 0

Answer:

if donuts are 2 for each and cookies for 1 each it could be

X x 2 and X x 1

one equation could be 4 donuts for 2$ and 7 cookies for 1$

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Newton's law of cooling states that the temperature of an object changes at a rate proportional to the difference between its te
Aleonysh [2.5K]

Answer:

t=5.18 minute

Step-by-step explanation:

Using Newton's law of cooling

\frac{dT}{dt}=-k(T-T_{s})

T is temperature of a cup of coffee at any time t T_{s}, is the temperature of the surrounding and k is a constant of proportionality in this negative because temperature is decreasing.

T(0)=190\\T(1)=170\\T_{s}=66

\frac{dT}{dt}=-k(T-T_{s})\\\frac{dT}{(T-T_{s})}=-k*dt\\\int\limits {\frac{1}{T-T_{s} } } \, dT=-\int\limits {k} \, dt\\ln(T-T_{s})=k*t+C\\e*ln(T-T_{s})=e^{k*t+C} \\T-T_{s}=e^{k*t}*e^{C}\\e^{C}=C\\T-T_{s}=e^{k*t}*C\\T=T_{s}+e^{k*t}*C

To find constant knowing the time and the temperature the first step of the change of energy in cup of coffee

T=T_{s} +e^{-k*t}*C\\ C=190-66=124\\170=66+124*e^{-k*2}\\ 170-66=124*e^{-k*2}\\ln(\frac{104}{124})=ln*e^{-k*2}\\-0.175=-k*2\\k=0.08794

Now using the constant of decreasing can find the time to be a 145 temperature the cup of coffee

145=66+124*e^{-k*t} \\145-66=124*^{-0.087*t}

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4 0
3 years ago
Given that El bisects ZCEA, which statements must be
Alexxx [7]

Question: Given that BE bisects ∠CEA, which statements must be true? Select THREE options.

(See attachment below for the figure)

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m∠CEB = 2(m∠CEA)

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Answer:

m∠CEA = 90°

∠CEF is a straight angle.

∠AEF is a right angle

Step-by-step explanation:

Line AE is perpendicular to line CF, which is a straight line. This creates two right angles, <CEA and <AEF.

Angle on a straight line = 180°. Therefore, m<CEA + m<AEF = m<CEF. Each right angle measures 90°.

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m∠CEA = 90°

∠CEF is a straight angle.

∠AEF is a right angle

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2 years ago
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