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katrin [286]
3 years ago
14

If x and y are positive integers such that 5x+3y=100, what is the greatest possible value of xy? please include steps. Thank you

!
Mathematics
1 answer:
natulia [17]3 years ago
6 0

Answer:

The greatest possible value of xy is 165.

Step-by-step explanation:

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Find the length of the line PA.
Diano4ka-milaya [45]

RO divides the rectangle into two congruent right triangles.

The area of the one triangle is equal half area of the rectangle.

Calculate the area of rectangle:

A_R=lw\\l=12,\ w=5\\\\A_R=12\cdot5=60

The area of right triangle:

A_T=\dfrac{1}{2}A_R\to A_T=\dfrac{1}{2}\cdot60=30

Use the Pythagorean theorem to calculate the length of RO:

|RO|^2=5^2+12^2\\\\|RO|^2=25+144\\\\|RO|^2=169\to|RO|=\sqrt{169}\to|RO|=13

The formula of an area of this right triangle is:

A_T=\dfrac{1}{2}|RO||PA|

Therefore we have the equation:

\dfrac{1}{2}(13)|PA|=30\qquad|\cdot2\\\\13|PA|=60\quad|:13\\\\|PA|=\dfrac{60}{13}\\\\|PA|\approx4.62

8 0
3 years ago
A person is working at a constant rate. If he produces 15 details in 8 hours, how long does he need to work to produce 18 detail
Kryger [21]
15=8
15÷3=5
Answer is 20
8 0
3 years ago
Consider the circles A, B, C, and D. SOMEONE PLEASE HELP ASAPPPP THANKS!!!
Zepler [3.9K]

Answer:

a= d and b= b

Step-by-step explanation:

circumference falls hand and hand with diameter and radius

a has a circumference of about 301 inches

b is about 62 inches

c is about 75 inches

d is about 314

8 0
2 years ago
Read 2 more answers
What is the operation symbol if the question is like this.<br> 52=8___(4___5)___20
stepan [7]

Answer:

52= 8×(4+5)-20

so I guess it's correct

7 0
3 years ago
What is 859 under a thousand as a mixed number?
Semmy [17]
To convert the improper fraction \frac{1000}{859} into a mixed number, you first want to divide the numerator (1000) by the denominator (859):
1000 \div 859 = 1 R141

The quotient, which is 1, will be your whole number part of your mixed number. The remainder, 141, will become the numerator of the fraction part of your mixed number. The original denominator of your improper fraction, 859, is still the denominator of your mixed number. So your mixed number form of your improper fraction is:
\frac{1000}{859} = 1 \frac{141}{859}

Your answer is 1 \frac{141}{859}

6 0
2 years ago
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