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Nitella [24]
3 years ago
10

BRAINLIEST TO BEST ANSWER!!!!

Mathematics
1 answer:
Thepotemich [5.8K]3 years ago
5 0
The equation would be y = -(3/4)x+1
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Find two positive integers such that the sum of the first number and four times the second number is 1000, and the product of th
vladimir2022 [97]

Answer:

The two numbers are:

x = 500

y = 125

Step-by-step explanation:

We want to find two numbers x and y, such that:

x + 4*y = 1000

f(x, y) = x*y is maximum.

From the first equation, we can isolate one of the variables to get

x = 1000 - 4y

now we can replace it in f(x, y):

x*y = (1000 - 4*y)*y  = 1000*y - 4*y^2

So now we want to maximize the function:

f(y) =- 4*y^2 + 1000*y

where y must be an integer.

Notice that this is a quadratic equation with a negative leading coefficient (so the arms of the graph will open downwards), thus, the maximum will be at the vertex.

Remember that for a general quadratic equation:

y = a*x^2 + bx + c

the x-value of the vertex is:

x = -b/(2*a)

so, in the case of:

f(y) =- 4*y^2 + 1000*y

the y-value of the vertex will be:

y = -1000/(2*-4) = 1000/8 = 125

So we found the value of y.

now we can use the equation:

x = 1000 - 4*y

x = 1000 - 4*125 = 1000 - 500 = 500

x = 500

Then the two numbers are:

x =500

y = 125

6 0
2 years ago
A bicycle shop advertised all mountain bikes priced at a 1/3 discount. If the original cost of the bikes is $327, what is the ne
nataly862011 [7]
Answer- B


Explanation- 327 divided by 3 would be 109 and a 109 + 109 would equal 218 and 218 would be 2/3 of 327
3 0
2 years ago
In the diagram below, RA is parallel to ET, and RT is 21 units long. Find the length of ST
pav-90 [236]

Answer:

ST = 12 units

Step-by-step explanation:

As RA is parallel to ET, the angle in R is equal to the angle in T, and the angle in A is equal to the angle in E, so the triangle RAS is similar to the triangle SET.

If RT is 21 units, we have that RS + ST = 21 -> RS = 21 - ST

Using a rule of three with the sides of the triangle (as they are proportional), we have:

RS / ST = AR / ET

(21 - ST) / ST = 6 / 8

4 * (21 - ST) = 3*ST

84 - 4*ST = 3*ST

7*ST = 84

ST = 12 units

5 0
3 years ago
A ball is dropped from a height of 10 feet and returns to a height that is one half of the height from which it fell
Alexandra [31]

Answer:

5ft

Step-by-step explanation:

5 0
3 years ago
Help help help please please
Vsevolod [243]
The answer is 10 miles
3 0
2 years ago
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