Their sum plus their product has a maximum potential value of 420.
Given that the product of the two positive numbers and their sum is 39.
The highest feasible value of the total of their products must be determined.
Let's tackle this issue step-by-step:
Assume x and y are the two positive integers.
The product's sum is xy, while the two integers' sum is x + y.
The answer to the issue is 39, which is the product of the two integer sums and their sum.
[tex]\mathrm{xy + (x + y) = 39}[/tex]
We need to maximize the value of to discover the biggest feasible value of the product of their sum and their product [tex]\mathrm {(x + y) \times xy}[/tex].
Now, we can proceed to solve the equation:
[tex]\mathrm {xy + x + y = 39}[/tex]
To make it easier to solve, we can use a technique called "completing the square":
Add 1 to both sides of the equation (1 is added to "complete the square" on the left side):
[tex]\mathrm {xy + x + y + 1 = 39 + 1}[/tex]
Rearrange the terms on the left side to form a perfect square trinomial:
[tex]\mathrm{(x + 1)(y + 1) = 40}}[/tex]
[tex]\mathrm{(x + 1)(y + 1) = 2 \times 2 \times 2 \times 5 }}[/tex]
Now, we want to maximize the value of [tex]\mathrm {(x + y) \times xy}[/tex], which is equal to [tex]\mathrm{(x + 1)(y + 1) + 1}[/tex]
Finding the two positive numbers (x and y) whose sum is as close as feasible to the square root of 40, or around 6.3246, is necessary to maximize this value.
The two positive integers whose sum is closest to 6.3246 are 5 and 7, as 5 + 7 = 12, and their product is 5 × 7 = 35.
Finally, [tex]\mathrm {(x + y) \times xy}[/tex]
= [tex](5 + 7) \times 5 \times 7[/tex]
= 12 × 35
= 420
So, the largest possible value is 420.
Learn more about Positive Integers click;
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please do them all please
Answer:
7(3 + 3x) = 21x + 21
2d + 10(4d +4 + 2a) = 20a + 42d + 40
3t + 2x + x = 3t + 3x
5(r + 12) - 25 = 5r + 35
18s + 12rs + 10r - 2rs = 10rs + 10r + 18s
s(12 - 4) + 2 = 8s + 2
w(15 - 3) + 2 + 7w = 19w + 2
Step-by-step explanation:
Find the slope between (1,-19) and (-2,7)
Answer:
m= -26/3
Step-by-step explanation:
I used an app called "M a t h w a y " (with no spaces) you should use it
it is very helpful!
10.
Describe the graph of the equation x = 7. Is the equation a function?
horizontal line; no
horizontal line; yes
vertical line; yes
vertical line; no
Answer:
The answer is Vertical Line; Yes
Step-by-step explanation:
The answer is Vertical Line; Yes. This is because all equations that are "X =" will always be vertical.
x=7 represents the equation of a function which is a vertical line
You are renting a car for the day. There is a daily fee of $25 and a charge of $0.10 per mile. Your budget allows a maximum total cost of $50. How many miles can you travel on this budget?
Answer:
250 miles
Step-by-step explanation:
daily charge: $25
per mile: $0.10
budget: $50
50-25=25
25 divided by 0.10 = 250
you can travel 250 miles on this budget
Yo i need help refer to picture
Step-by-step explanation:
AA: Two pairs of corresponding angles are equal.
ASA (Angle-Side-Angle)ASA: Two pairs of corresponding angles and the corresponding sides between them are equal. hope this helps you. means similarity would be equal.. I cannot read your paragraphs that well they are too small but I hope this helps you just got to find which paragraph it shows that they AA and AAS a are similar to each other by being equal
The number sentence 4×6 = 6×4 is an example of what property?
Answer:
Multiplication property of equality
Step-by-step explanation:
ZB
Round your answer to the nearest hundredth.
B
?
9
A
4
Answer:
∠ B ≈ 26.39°
Step-by-step explanation:
Using the sine ratio in the right triangle
sinB = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{AC}{AB}[/tex] = [tex]\frac{4}{9}[/tex] , then
∠ B = [tex]sin^{-1}[/tex] ([tex]\frac{4}{9}[/tex] ) ≈ 26.39° ( to the nearest hundredth )
Which property is demonstrated in the equation 0 x 35 = 0?
A. symmetric
B. property of zero
c. associative
d. commutative
Answer:
Step-by-step explanation:
the property of zero,
multiplication property of zero
An isosceles triangle includes two 72°
angles. Which equation could be used to
find the measure of the third angle?
A X + 72 = 180
B X = 180 - 72
C 72-X= 180
D 180 - 2(72) = X
I don't understand the options but I will explain it to u!
Step-by-step explanation:
An Isosceles triangle has two equal sides that means , In this question it is given that there are two 72°angles so,
72+72+x =180
(Transpose)
x = 180-(72+72)
x = 180-(144)
Therefore, x= 36
In an isosceles triangle, two sides are equal and their opposite angles are also equal. Then the correct option is D.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
An isosceles triangle includes two 72° angles.
In an isosceles triangle, two sides are equal and their opposite angles are also equal.
And the sum of the angles of the triangle is 180°.
Let the third angle be x. Then we have
72° + 72° + x = 180°
180° - 2(72°) = x
Thus, the correct option is D.
More about the triangle link is given below.
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Please answer! I will give brainliest, it would make my day :-)
Write a formula for the given measure. Let P represent the perimeter in inches, and w represent width in inches. Identify which variable depends on which in the formula.
the perimeter of a rectangle with a length of 5 inches
P=
Step-by-step explanation:
p = perimeter
w = width
let the length be l
as we know that
perimeter of rectangle (p).= 2(l+ w)
p = 2 ( 5+w)
p = 10 + 2w
so here variable p is dependent on the value of w.
hope this will be helpful to you .plz mark my answer as brainlist plzzzz if you find it useful.☺️.
Greg invested $6000 in a bond with a yearly interest of 4%. His total interest on his investment was $1200. What was the length of the investment
Answer:
5 years
Step-by-step explanation:
First, converting R percent to r a decimal
r = R/100 = 4%/100 = 0.04 per year,
then, solving our equation
t = 1200 / ( 6000 × 0.04 ) = 5
t = 5 years
The time required to
accumulate simple interest of $ 1,200.00
from a principal of $ 6,000.00
at an interest rate of 4% per year
is 5 years.
Jorge builds a rectangular prism that has a volume of 42 cubic inches. Which of the following could be Jorge’s prism? (4 points)
Group of answer choices
A rectangular prism with a height of five inches, length of five inches, and a width of five inches.
A rectangular prism with a height of five inches, length of four inches, and a width of four inches.
A rectangular prism with a height of two inches, length of seven inches, and a width of three inches.
A rectangular prism with a height of six inches, length of three inches, and a width of two inches.
Answer: A rectangular prism with a height of two inches, length of seven inches, and a width of three inches.
Step-by-step explanation:
Multiply the dimensions given, then select the one that matches Jorge's required 42 in³
5×5×5 = 125
5×4×4 = 80
2×7×3 = 42
6×3×2 = 36
Answer:
A
Step-by-step explanation:
60 people attend a game night everyone chooses to play chess a two player game or cribbage a four player game all 60 people are playing chess or cribbage if there were 8 games of cribbage played how many games of chess was played
Answer:
there were 14 games of chess
Answer:
14 games of chess
Step-by-step explanation:
f(x)=6, what is x? HELP ANSWER FAST!!!!!!
Answer:
x = 6 / f
Step-by-step explanation:
Write your question here (Keep it simple and clear to get the best answer)a sum of 1,5000.00 in the ratio 5:3
Answer:
Ratio 5 = 9375
Ratio 3 = 5625
Step-by-step explanation:
Write your question here (Keep it simple and clear to get the best answer)
a sum of 1,5000.00 in the ratio 5:3
The ratio is given as:
5:3
Total Proportion = 5+3 = 8
For ratio 5
= 5/8 × 15000
= 9375
For ratio 3
= 3/8 × 15000
= 5625
The temperature in Lukeville is -13 ºC. The temperature in Metroburg is 12 ºC. How many degrees warmer is the temperature in Metroburg?
-1 ºC
1 ºC
25 ºC
-25 ºC
Answer:
25
Step-by-step explanation:
1. Make an equation: 12-(-13).
2. Solve the equation. Since there are 2 negative signs (one to the right of 12 and another to the left of 13) they can cancel each other out and they turn into an addition sign. Then, you get 12+13. You can easily solve that and you will get the answer of 25 degrees.
Name three sets of collinear points:
Possible answers:
T,U,andS
T,U and V
V,U and Q
R,V and X
W,X and Q
R,S and U
what is six and eight seven thousandths as a decimal
Answer:
6.087
Step-by-step explanation:
0.000
^ones
^tenths
^hundredths
^thousandths
Mr. Lowe had to replace the fluid in his tractor tire. The tire needed 73
gallons of fluid at $1.95 per gallon. About what did it cost to replace the
needed fluid? *
Answer:
$142.35
Step-by-step explanation:
The graph shows two lines, A and B.
у
6
A
B
5
4
3
2
1
-X
0
1
2
3
4
5
6
Part A: How many solutions does the pair of equations for lines A and B have? Explain your answer. (5
Part B: What is the solution to the equations of lines A and B? Explain your answer. (5 points)
3(2t + 5) = 5t + 25
What does t equal
Answer:
t = 10
(Hope this helps! Btw, I am the first to answer. Brainliest pls!)
Answer:
hello! :) have a good day!
t = 10
Business woman Maya spends 1⁄4 hours a day on her cell phone. Her husband Larry spends 3⁄16 hours a day on his cell phone. What is the total time spent on the phone between the couple per day?
Answer:
45 minutes, or 3/4 hours
Answer:
the 3/4 is wrong this is how it was explained in the answer screen
Step-by-step explanation:
The correct answer is:
Create Equal Denominators
1⁄4 × 4⁄4 = 4⁄16
Total Time Spent
4⁄16 + 3⁄16 = 7⁄16 hours in a day
please answer correctly and quickly all question
Answer:
Step-by-step explanation:
1. 8=2x+4
8-4=2x
4=2x
x=2
2. 2x+3=9
2x=9-3
2x=6
x=3
3. 6y=54
y=54/6
y=9
5. 3= x/2
x=6
Answer:
8=2x+4
4=2x
2=x
2x+3=9
2x=6
x=3
6y=54
I'm not sure about question #4
3=x/2
6=x
can someone please help me again, i suck at math..
Answer:
18.55 - 1.75= 16.8
16.8/12= 1.4 oz
Answer- 1.4 oz
Step-by-step explanation:
Sorry if this is wrong, I suck at math, too.
How do I solve this?
Answer:
sin (330)
csc (60)
cos (390)
Step-by-step explanation:
Solve the trigonometric equation by isolating the function and then taking the inverse. Use the period to find the full set of all solutions
8 x ÷ 4 = 100 What is the value of x in the equation?
5
A. 5
B. 25
C. 50
D. 200
Answer:
Hi there. I had put a comment replying to your question as I didn't see any place that I could answer. If you still need it, then the answer was
C. 50
Step-by-step explanation:
8 * 50 = 400
400 / 4 = 100
In any way possible, I hope this helps you! Have a great day!
how to solve 15x^3/4
Answer:
3
Simplify —
4
Equation at the end of step
1
:
3
15x • —
4
STEP
2
:
Final result :
45x
———
4
Step-by-step explanation:
Answer:
Well...without the x I know it is 843.75 but I don't know the fraction of it so sorry! I try my best to help people!
The difference of a number and seven
Answer: x-7
Step-by-step explanation:
Answer:
x -- 7
Step-by-step explanation:
Jonathan had $40 in his bank account. He withdrew $12 and deposited $4. How much is in his bank account now?
Answer:
he 32 is what he got in bank now an hope this help.
Step-by-step explanation:
I think it’s 2 over 1 but I’m not sure??
Answer:
it is 2/1
Step-by-step explanation: