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Black_prince [1.1K]
3 years ago
10

Determine whether ABCD is a parallelogram The vertices are A(-2,3) , B(3,2), C(2,-1) and D(-3,0)

Mathematics
1 answer:
iogann1982 [59]3 years ago
3 0

Answer:

Yes, this is a parallelogram

Step-by-step explanation:

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A metallurgist needs to make 12.4 lb. of an 10) alloy containing 50% gold. He is going to melt and combine one metal that is 60%
sergeinik [125]
Now, let's say, we add "x" lbs of the 60% gold alloy, so..  how much gold is in it?  well, is just 60%, so (60/100) * x, or 0.6x.

likewise, if we use "y" lbs of the 40% alloy, how much gold is in it?  well, 40% of y, or (40/100) * y, or 0.4y.

now, whatever "x" and "y" are, their sum must be 12.4 lbs.

we also know that the gold amount in each added up, must equal that of the 50% resulting alloy.

\bf \begin{array}{lccclll}
&\stackrel{lbs}{amount}&\stackrel{gold~\%}{quantity}&\stackrel{gold}{quantity}\\
&------&------&------\\
\textit{60\% alloy}&x&0.6&0.6x\\
\textit{40\% alloy}&y&0.4&0.4y\\
------&------&------&------\\
\textit{50\% alloy}&12.4&0.50&6.2
\end{array}

\bf \begin{cases}
x+y=12.4\implies \boxed{y}=12.4-x\\
0.6x+0.4y=6.2\\
-------------\\
0.6x+0.4\left( \boxed{12.4-x} \right)=6.2
\end{cases}
\\\\\\
0.6x-0.4x+4.96=6.2\implies 0.2x=1.24\implies x=\cfrac{1.24}{0.2}
\\\\\\
x=\stackrel{lbs}{6.2}

how much of the 40% alloy?  well, y = 12.4 - x.
5 0
4 years ago
Help!, i honestly forgot this lol
jeka94

Answer:

A

Step-by-step explanation:

8 0
3 years ago
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Guidelines for the amount of supplementary nitrogen needed to grow winter wheat depend on the amount of nitrogen in the soil​ (a
Ierofanga [76]

The net profit or income for case A and case B based on the information will be $9250 and $9500 respectively.

<h3>How to compute the net profit?</h3>

Case A:

Based on the information, the price of fertilizer will be:

= 0.25 × 100 × 50

= $1250

Price of wheat = 3.50 × 50 × 50

= $10500

Net profit = $10500 - $1250

= $9250

Case B:

Price of fertilizer will be:

= 0.50 × 70 × 50

= $1750

Price of wheat = 4.50 × 50 × 50

= $11250

Net profit = $11250 - $1750

= $9500

Therefore, the net profit or income for case A and case B based on the information will be $9250 and $9500 respectively.

Learn more about net income on:

brainly.com/question/15530787

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3 0
2 years ago
Hallie bikes 1 5/8 km before lunch and 6 1/4 km after lunch. How much farther does Hallie bike after lunch than before lunch? Ex
EleoNora [17]

Answer:

4 \frac{5}{8} km

Step-by-step explanation:

To find how much farther Hallie biked after lunch compared to the amount she biked before lunch, we can subtract the amounts:

6 \frac{1}{4}-1\frac{5}{8}

However, we can only subtract fractions that have the same denominator, so we need to convert \frac{1}{4} to a fraction with a denominator of 8:

\frac{1}{4}=\frac{2}{8}

Now, we can't subtract 2 from 8, so we need to 'borrow' from the 6 to make the fraction larger:

6\frac{2}{8}=5\frac{10}{8}

Now subtract: 5\frac{10}{8}-1\frac{5}{8}=4\frac{5}{8}

4 0
3 years ago
How do i solve for x and what is the answer
kiruha [24]

Answer:

(4+8)(4) = (x) 3

Step-by-step explanation:

The picture shows two secants intersecting at a point outside the circle.  A beautiful pattern for this is:  along each secant, the product (multiply) the <em>entire</em> secant by the <em>outside</em> part is the same.

(entire secant)(outside part) = (entire secant)(ouside part)

(4+8)(4) = (x)(3)

4 0
3 years ago
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