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3 years ago

8

lena's house casts a shadow that is 14 feet long at the same time that lena casts a shaodw that is 3.5 feet long if lena is 4.5

feet tall how tall is hr house?

1 answer:

aleksandrvk [35]3 years ago

4 0

The house is 18 ft tall

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Joe can cut and split a cord of firewood in 3 fewer hours than Dwight can. When they work together, it takes them 2 hours. How

aalyn [17]

Answer:

Dwight will take 6 hours to finish the job alone and Joe will take 3 hours to finish the job alone.

Step-by-step explanation:

Let us assume the time taken by Dwight to split a cord of firewood = K hrs

So, the per hour rate of Dwight = $(\frac{1}{K})$

As, Joe uses 3 LESS hours then Dwight.

So, the time taken by Joe to split a cord of firewood = (K- 3) hrs

So, the per hour rate of Joe = $(\frac{1}{K-3})$

Now, when both of them wok together, it takes them 2 hours.

So, the per hour rate of BOTH of them = $(\frac{1}{2})$

⇒ Per hour rate of ( Dwight + Joe) = $(\frac{1}{2} )$

$\implies (\frac{1}{K}) + (\frac{1}{K-3}) = (\frac{1}{2})$

Now, solving for the value of K , we get:

$(\frac{1}{K}) + (\frac{1}{K-3}) = (\frac{1}{2})\\\implies \frac{(K-3) + K}{K (K-3)} = (\frac{1}{2})\\\implies 2(2K -3) = K^2 - 3K\\\implies k^2 - 3K -4K +6 = 0\\\implies K^2 - 7K + 6= 0\\\implies K^2 - 6K - K + 6= 0\\\implies K(K-6) -1(K - 6)= 0\\\implies (K-6)(K-1) = 0$

Implies either K = 6 Or K = 1

But if K = 1, (K-3) = 1- 3 = -2 hours would be A CONTRADICTION.

⇒ K = 6 hours

Hence, Dwight will take 6 hours to finish the job alone and Joe will take (k-3) = (6-3) = 3 hours to finish the job alone.

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2 years ago

grants plans to a factory enough water from 22 gallons in a 16% ammonia solution to make a 24% solution which equation can be us

Andreyy89

16/22=24/x

x=33

then subtract

33-22=11

11 galons should be taken out

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3 years ago

Find a Cartesian equation for the curve and identify it. r=8tanxsecx

ANTONII [103]

R = 8 tan(x) sec(x)

In order to solve this, we are going to use the following:
r = sqrt(x^2 + y^2) //but in this case, we don't need this.
tan(x) = Y / X
X = r cos(x)
Y = r sin(x)

<span>(r cos x)^2 = 8(r sin x)</span>

x^2 = 8y

3 0

3 years ago

Meg conducted a survey of four school cafeterias to find the number of students who like sandwiches for lunch. The results of he

Natasha_Volkova [10]

C. 38.46% To get your answer you divide the number of students who liked sandwiches by total number of students in the cafeteria. Example: 10/26=.3846 which is 38.46%

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3 years ago

Read 2 more answers

Please help me with this

shutvik [7]

Answer:

1) 151.29 | 2) 413 km | 3) 75 cm

Step-by-step explanation:

1) 12.3 x 12.3 = 151.29 in

2) 17.5 x 23.6 = 413 km

3) 15 x 5 = 75 cm

4 0

2 years ago