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3 years ago

It took 7 hours to mow four equal-size lawns. At that rate, how many lawns could be mowed in 35 hours?

Mathematics

1 answer:

NISA [10]3 years ago

7 0

Answer: 20 lawns could be mowed in 35 hours.

Step-by-step explanation: Lets write a ratio to represent this problem. The ratio 7:4 states that for every 7 hours you will mow 4 lawns.

Now we have to figure out how many lawns we will mow in 35 hours. Simply keep adding 7 to the left side of the ratio and 4 to the right side.

7:4

14:8

21:12

28:16

35:20

So in 35 hours, 20 lawns will be mowed.

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Two cars start out together from the same place. they travel in opposite directions, with one of them traveling 5 miles per hou

Mashutka [201]

Annotation
General formula for distance-time-velocity relationship is as following
d = v × t
The velocity of the first car will be v₁, the time is 2 hours, the distance will be d₁.
The velocity of the second car will be v₂, the time is 2 hours, the distance will be d₂.

One of them traveling 5 miles per hour faster than the others. That means the velocity of the first car is 5 miles per hour more than the velocity of the second car.
v₁ = v₂ + 5 (first equation)

The distance of the two cars after two hours will be 262 miles apart. Because they go to opposite direction, we could write it as below.
d₁ + d₂ = 262 (second equation)

Plug the d-v-t relationship to the second equation
d₁ + d₂ = 262
v₁ × t + v₂ × t = 262
v₁ × 2 + v₂ × 2 = 262
2v₁ + 2v₂ = 262

Plug the v₁ as (v₂+5) from the first equation
2v₁ + 2v₂ = 262
2(v₂ + 5) + 2v₂ = 262
2v₂ + 10 + 2v₂ = 262
4v₂ + 10 = 262
4v₂ = 252
v₂ = 252/4
v₂ = 63
The second car is 63 mph fast.

Find the velocity of the first car, use the first equation
v₁ = v₂ + 5
v₁ = 63 + 5
v₁ = 68
The first car is 68 mph fast.

Answer
$\boxed{\boxed{ v_{1}=68mph} }$
$\boxed{\boxed{ v_{2}=63mph} }$

7 0

3 years ago

Find a current example of a linear optimization model used in your industry. Describe the industry's needs, including any unique

marishachu [46]

Answer:

Follows are the explanation to the given question:

Step-by-step explanation:

Its determination of inventory amounts for various products. Its demand is an excellent illustration of a dynamic optimization model used in my businesses. Throughout this case, its store has restrictions within this room are limited. There are only 100 bottles of beverages to be sold, for instance, so there is a market restriction that no one can sell upwards of 50 plastic cups, 30 power beverages, and 40 nutritional cokes. Throughout this situation, these goods, even the maximum quantity supplied is 30, 18, and 28. The profit for each unit is $1, $1.4, and $0.8, etc. With each form of soft drink to also be calculated, a linear extra value is thus necessary.

5 0

3 years ago

Please solve this problem

asambeis [7]

Answer:

(4) 0

Step-by-step explanation:

Given:

cos²27°×cos²34°×...×cos²167 = ?

Looking at the angles measures, they form series of:

27, 34, 41, ..., 167

This is AP with the first term of 27 and common difference of 7

We can see one of the terms of this AP is 90

27+9*7 = 27 + 63 = 90

Since cos 90° = 0 ⇒ cos²90° = 0 and therefore given series equals to zero as one of the terms of multiplication is zero.

So correct answer choice is Option 4) 0

8 0

3 years ago

HURRYY!!!!! Which algebraic expression means “three more than a number squared”? 2 n + 3 2 n minus 3 n squared + 3 n squared min

stiv31 [10]

Answer: (n+3)^2

Step-by-step explanation:

This is the answer lol

7 0

3 years ago

Find an equation for the line perpendicular to 2x+ 6y = 30 and goes through the point (6,2)

Mashutka [201]

Answer:

y = 3x - 16

Step-by-step explanation:

We are asked to find the equation of the line perpendicular to 2x + 6y = 30

We can use two formulas for this question, either

y = mx + c. Or

y - y_1 = m(x - x_1)

Step 1: calculate the slope

From the equation given

2x + 6y = 30

Make y the subject of the formula

6y = 30 - 2x

6y = -2x + 30

Divide both sides by 6, to get y

6y/6 = ( -2x + 30)/6

y = (-2x + 30)/6

Separate them in order to get the slope

y = -2x/6 + 30/6

y = -1x/3 + 5

y = -x/3 + 5

Slope = -1/3

Step 2:

Note: if two lines are perpendicular to the other, both are negative reciprocal of each other

Perpendicular slope = 3/1

Substitute the slope into the equation

y = mx + c

y = 3x + c

Step 3: substitute the point into the equation

( 6,2)

x = 6

y = 2

2 = 3(6) + c

2 = 18 + c

Make the c the subject

2 - 18 =c

c = 2 - 18

c = -16

Step 4: sub the value of c into the equation

y = 3x + c

y = 3x - 16

The equation of the line is

y = 3x - 16

If you try out the other formula, u will get the same answer

5 0

3 years ago