Answer:
Step-by-step explanation:
Given
Required
The value of k
From the attached graph, line f(x) is shifted up 7 times to match g(x).
This implies that:
Compare: and
The gradient of the function is constant s the independent variable (x) varies The graph passes through the origin. That is to say when x = 0, y = 0. Clearly A and D pass through the origin, and the gradient is constant because they are linear functions, so they are direct variations. The graph of 1/x does not have a constant gradient, so any stretch of this graph (to y = k/x for some constant k) will similarly not be direct variation. Indeed there is a special name for this function, inverse proportion/variation. It appears both B and C are inverse proportion, however if I interpret B as y = (2/5)x instead, it is actually linear. I believe the answer is C. Hope I helped!
Let's call the two numbers x and y. The first sentence, one is 6 less than twice another, translates to
We also know the sum of their squares:
So, we have the following system:
We can use the expression for x in terms of y from the first equation to turn the second equation into something involving y alone:
Expand the square:
Subtract 680 from both sides:
Using the quadratic equation
we find the two solutions
Since we know that both numbers are integer we can only accept the second solution. It yields the following x value:
Answer:
Gold
Step-by-step explanation:
<em>Casandra finds a treasure chest packed with metallic coins. The chest has a volume of 0.25 cubic meters. The coins have a combined mass of 4825 kg. Hoping to find gold, she calculates the density to determine the metal of the coins.</em>
<em>What kind of metal are the coins made of?</em>
<em>Bronze (8700 kg per cubic meter)</em>
<em>Silver (10500 kg per cubic meter)</em>
<em>Lead (11300 kg per cubic meter)</em>
<em>Gold (19300 kg per cubic meter)</em>
<em />
Density is mass per volume:
D = M / V
D = (4825 kg) / (0.25 m³)
D = 19,300 kg/m³
The coins must be made of gold.
