Answer:
The minimum value for 
is 
.
Step-by-step explanation:
Given function is
We need to find the maximum value or the minimum value for the function.
Now, differentiate w.r.t 
.
Now, we will equate 
to find critical point.
Plug this critical point in to the function we get,
Also, 
which is positive, We have minimum value.
So, the minimum value for is .
Answer: 4500 grams
Step-by-step explanation: 1 kilogram is 1,000 grams, so 4 kilograms is 4,000 grams, and half a kilogram is 500 grams. So, 4000 + 500 = 4,500
Answer:
8.5$
Step-by-step explanation:
85 diveded by 10 is 8.5$.
Let's go through the choices one by one
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Choice A
If all sides are congruent, then this figure is a rhombus (by definition). If all angles are congruent, then we have a rectangle. Combine the properties of a rhombus with the properties of a rectangle and we have a square.
In terms of "algebra", you can think
rhombus+rectangle = square
Or you can draw out a venn diagram. One circle represents the set of all rhombuses; another circle represents the set of all rectangles. The overlapping region is the set of all squares. The overlapping region is inside both circles at the same time.
So we can rule out choice A. This guarantees we have a square when we want something that isn't a guarantee.
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Choice B
If we had a parallelogram with perpendicular diagonals, then we can prove that we have a rhombus (all four sides congruent). However, we don't know anything about the four angles of this parallelogram. Are they congruent? We don't know. So we can't prove this figure is a rectangle. The best we can say is that it's a rhombus. It may or may not be a rectangle. There isn't enough info about the rectangle & square part.
This is why choice B is the answer. We have some info, but not enough to be guaranteed everytime.
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Choice C
This is a repeat of choice A. Having "all right angles" is the same as saying "all angles congruent". This is because "right angle" is the same as saying "90 degrees". So we can rule out choice C for identical reasons as we did with choice A.
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Choice D
As mentioned before in choice A, if we know that a quadrilateral is a rectangle and a rhombus at the same time, then the figure is also a square. This is always true, so we are guaranteed to have a square. We can cross choice D off the list.
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Once again, the final answer is choice B
<h2>Answer:
y = - ¹/₂ x OR y - 1 = - ¹/₂ (x + 2) </h2>
<h3>Step-by-step explanation: </h3>
For us to write the equation for this line, we need to (1) find the slope of the line, and (2) use one of the points to write an equation:
The question gives us two points, (-2, 1) and (-8, 4), from which we can find the slope and later the equation of the line.
<u>Finding the Slope </u>
The slope of the line (m) = (y₂ - y₁) ÷ (x₂ - x₁)
= (4 - 1) ÷ (-8 - (-2))
= - ¹/₂
<u>Finding the Equation</u>
We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line:
⇒ y - 1 = - ¹/₂ (x - (-2))
∴ y - 1 = - ¹/₂ (x + 2)
we could also transform this into the slope-intercept form ( y = mx + c)
since y - 1 = - ¹/₂ (x + 2)
⇒ y = - ¹/₂ x
<em>To test my answer, I have included a Desmos Graph that I graphed using the information provided in the question and my answer.</em>
