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3 years ago

The two parallelograms in the figure are similar. What is the value of x?

Mathematics

2 answers:

puteri [66]3 years ago

5 0

Answer:

The answer is D, 30.4

Step-by-step explanation:

Because the two parallelograms are similar, the relationship between the sides of them are directly proportional.

So:

$\frac{9}{8} =\frac{x}{27}$

Cross multiply

8x = 243

÷8 both sides

x = 30.375 ≈ 30.4

The answer is D, 30.4

12345 [234]3 years ago

3 0

ANSWER

D. 30.4

EXPLANATION

The two parallelograms are similar, therefore the corresponding sides must be in the same proportion:

$\frac{x}{9} = \frac{27}{8}$

Multiply both sides of the equation by 8. This implies that,

$x = \frac{27}{8} \times 9$

$x = 30.375$

Rounding to the nearest tenth gives us:

$x = 30.4 \: units$

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Step-by-step explanation:

cd being the longer segment is equal to 2/3s of 15.

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2 years ago

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A roast turkey is taken from an oven when its temperature has reached 185 degrees F and is placed on a table in a room where the

Vedmedyk [2.9K]

(a) Using Newton's Law of Cooling, $\dfrac{dT}{dt} = k(T - T_s)$ , we have $\dfrac{dT}{dt} = k(T - 75)$ where T is temperature after T minutes.
Separate by dividing both sides by T - 75 to get $\dfrac{dT}{T - 75} = k dt$ . Integrate both sides to get $\ln|T - 75| = kt + C$ .

Since $T(0) = 185$ , we solve for C:
$|185 - 75| = k(0) + C\ \Rightarrow\ C = \ln 110$
So we get $\ln|T - 75| = kt + \ln 110$ . Use T(30) = 150 to solve for k:
$\ln| 150 - 75 | = 30k + \ln 110\ \Rightarrow\ \ln 75 - \ln 110= 30k \Rightarrow \\ k= \frac{1}{30}\ln (75/110) = \frac{1}{30}\ln(15/22)$

So

$\ln|T - 75| = kt + \ln 110 \Rightarrow |T - 75| = e^{kt + \ln110} \Rightarrow \\ \\
|T - 75| = 110e^{kt} \Rightarrow T - 75 = \pm110e^{(1/30)\ln(15/22)t} \Rightarrow \\
T = 75 \pm110e^{(1/30)\ln(15/22)t}$

But choose Positive because T > 75. Temp of turkey can't go under.

$T(t) = 75 + 110e^{(1/30)\ln(15/22)t} \\
T(45) = 75 + 110e^{(1/30)\ln(15/22)(45)} = 136.929 \approx 137{}^{\circ}F$

(b)

$T(t) = 75 + 110e^{(1/30)\ln(15/22)t} = 75 + 110(15/22)^{t/30} \\
100 = 75 + 110(15/22)^{t/30} \\
25 = 110(15/22)^{t/30} 
\frac{25}{110} = (15/22)^{t/30} \\
\ln(25/110) / ln(15/22) = t/30 \\
t = 30\ln(25/110) / ln(15/22) \approx 116\ \mathrm{min}$

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4 0

2 years ago

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Shkiper50 [21]

Answer:

$x=1$

Step-by-step explanation:

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7 0

2 years ago

Please help me with this! I will appreciate the help :)

dexar [7]

Answer:

Step-by-step explanation:

I'm pretty sure it's D

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2 years ago