Missing part in the heading of the question:
"The force f (in pounds) required to push a sofa across the floor varies directly as the weight w (in pounds) of the sofa"
Answer:
F = 0.625 w
Explanation:
We are given that F in pounds varies directly with the weight of the sofa in pounds.
This means that:
F = kw
where:
F is the force
k is the constant of proportionality
w is the weight of the sofa
We are given that:
F is 100 pounds when w is 160 pounds
Substitute with these givens in the above equation to get the constant of proportionality k as follows:
F = kw
100 = 160k
k = 100 / 160
k = 0.625
This means that the equation describing the relation between the force and the weight of the sofa is:
F = 0.625 w
Hope this helps :)
Answer:
see the explanation
Step-by-step explanation:
we have
we know that
To cross multiply, start by multiplying the numerator of the left-hand fraction by the denominator of the right-hand fraction.
2(8)
Then, multiply the numerator of the right-hand fraction by the denominator of the left-hand fraction.
7(28)
Next, set the 2 products equal to each other.
2(8)=7(28)
Hi there! I can help you!
a. Okay. So we have to make a table for the amount of butterflies to total insects. Let's simplify the ratio. 36:100 simplifies to 9:25. We can use that ratio to make this table. Just multiply 25 by the amount it takes to get to 50 or 100, and multiply by the same amount at the top to find the amount of butterflies. If you do it correctly, your table should be as shown below in the image.
b. On that note, let's solve for the amount of butterflies in the conservatory. There are 450 total of them. Let's divide 450 by 100 to find the amount we will multiply by. 450/100 is 4.5. We will mutliply 36 by that amount to find the total amount of butterflies. 36 * 4.5 is 162. That's it. There are 162 butterflies in the conservatory.
Answer:
13 feet long
Step-by-step explanation:
This situation forms a right triangle, where the ladder is the hypotenuse, the distance away from the building is the short leg, and the height to the side of the building is the long leg.
Use the pythagorean theorem, and solve for c, the hypotenuse:
a² + b² = c²
5² + 12² = c²
25 + 144 = c²
169 = c²
13 = c
So, the ladder is 13 feet long
Answer:
missing element is 6
Step-by-step explanation:
Given
f(x) = x³ - 2 ( substitute x = 2 )
f(2) = 2³ - 2 = 8 - 2 = 6 ← missing element
ordered pair is (2, 6 )