Find the lowest common denominator and solve

A large ice chest holds 62 liters of water. A smaller chest holds 4/5 as much water

dedylja [7]

Answer:

Step-by-step explanation:

Since a large ice chest holds the water = 62 liters

And smaller chest holds the water = $\frac{4}{5}$ of the larger ice chest

= $\frac{4}{5}\times 62$

= $\frac{248}{5}$ liters

Therefore, fraction that represents the amount of ice water in the smaller ice chest will have 0 in the first box, 248 in the numerator and 5 in the denominator.

$0\frac{248}{5}$

6 0

2 years ago

A farmer is estimating the surface area of his barn to find how much paint he needs to buy. One part of the barn is triangular a

Nady [450]

We know the triangle is an isosceles triangle. So, we use the Pythagorean Theorem.

a^2+b^2=c^2

The c would be 22, because it's the longest edge. Now find a or b. They are the same, that is how you find the two sides of the triangle for part A.

To find the area of the triangle, the forumla is a=hb/2

Plug in the numbers for that formula and the answer would be found for part B.

I hope I helped.

7 0

2 years ago

Felipe planted some seeds for a science project. One of his plants grew 6 2/7 inches in the first week, and then it grew 5 11/14

MatroZZZ [7]

Answer:

The plant grew $12\frac{1}{14}$ inches

Step-by-step explanation:

Operations with Fractions

Felipe planted seeds for a science project. One of the plants grew 6 2/7 inches in the first week and 5 11/14 inches in the second week.

We are required to find the total growth during the two weeks. We have to find the sum of:

$6\frac{2}{7}+5\frac{11}{14}$

Let's convert both fractions to improper form:

$6\frac{2}{7}+5\frac{11}{14}=6+\frac{2}{7}+5+\frac{11}{14}$

Adding the integers:

$6\frac{2}{7}+5\frac{11}{14}=11+\frac{2}{7}+\frac{11}{14}$

Now we find the LCM of 7 and 14 is 14, thus:

$6\frac{2}{7}+5\frac{11}{14}=11+\frac{4}{14}+\frac{11}{14}$

$6\frac{2}{7}+5\frac{11}{14}=11+\frac{15}{14}=11+\frac{14+1}{14}$

$6\frac{2}{7}+5\frac{11}{14}=11+1+\frac{1}{14}$

$6\frac{2}{7}+5\frac{11}{14}=12+\frac{1}{14}$

Rewriting as a mixed number:

The plant grew $12\frac{1}{14}$ inches

8 0

2 years ago

David proved the Law of Cosines with reference to ∆ABC using a different method. Arrange the steps of his proof in the correct s

AURORKA [14]

Answer: We can arrange the steps with help of below explanation.

Step-by-step explanation:

Here ABC is a triangle,

Draw a perpendicular from BD to side AC ( construction)

where $D\in AC$

In the right triangle BCD, from the definition of cosine:

cos C =CD/ BC

CD= a cos C

Subtracting this from the side b, we see that

DA= b-acos C

In the triangle BCD, from the definition of sine:

sin C =BD / a

BD = a sin C

In the triangle ADB, applying the Pythagorean Theorem

$c^2 =BD^2 +DA^2$

Substituting for BD and DA from (2) and (3)

$c^2 =(asinC)^2 +(b-acosC)^2$

⇒ $c^2 =a^2sin ^2C+b^2-2ab cosC+a^2 cos ^2C$ ( On simplification)

⇒ $c^2 =a^2sin ^2C+a^2 cos ^2C+b^2-2abcos C$

⇒ $c^2=a^2(sin^2C+cos^2C) +b^2-2abcosC$

⇒ $c^2 = a^2+b^2-2abcosC$ (because, $sin^2\theta+cos^2\theta =1$ )

3 0

2 years ago

A private plane is traveling due east at a rate of 160 mph. A south wind is blowing 30 mph. What is the actual velocity of the p

photoshop1234 [79]

The resultant velocity of the plane is the sum of the two velocity vectors which are perpendicular to each other. See the attached figure.

The magnitude of the resultant velocity is

$\sqrt{160^2+30^2}= \sqrt{26500}=162.79 \;mph$ .

The approximate value of the actual velocity of the plane is $163 \;mph$ . Correct choice is (D).

8 0

2 years ago