Answer:
[tex]\frac{140}{3}, \frac{140}{3}, \frac{140}{3}[/tex]
Step-by-step explanation:
Let the numbers be [tex]x, y\ and\ z.[/tex]
Such that:
[tex]x + y + z = 140[/tex]
Make z the subject
[tex]z = 140 -x - y[/tex]
For their product to be maximum, we have:
[tex]f(x,y,z) = xyz[/tex]
Substitute [tex]z = 140 -x - y[/tex] in [tex]f(x,y,z) = xyz[/tex]
[tex]f(x,y) = xy(140 - x - y)[/tex]
Open bracket
[tex]f(x,y) = 140xy - x^2y - xy^2[/tex]
Differentiate w.r.t x and y
[tex]f_x=140y - 2xy - y^2[/tex]
[tex]f_y=140x - x^2 - 2xy[/tex]
Since the products are maximum, then [tex]f_x = f_y = 0[/tex]
For [tex]f_x=140y - 2xy - y^2[/tex]
[tex]140y - 2xy - y^2 = 0[/tex]
Factorize:
[tex]y(140 - 2x - y) = 0[/tex]
Split
[tex]y = 0\ or\ 140 - 2x - y = 0[/tex]
Make y the subject
[tex]y = 0\ or\ y = 140 - 2x[/tex]
For [tex]f_y=140x - x^2 - 2xy[/tex]
[tex]140x - x^2 - 2xy = 0[/tex]
---------------------------------------------------
Substitute y = 0
[tex]140x - x^2 -2x*0 = 0[/tex]
[tex]140x - x^2 = 0[/tex]
Factorize
[tex]x(140 - x)= 0[/tex]
[tex]x = 0\ or\ 140-x = 0[/tex]
[tex]x = 0\ or\ x = 140[/tex]
---------------------------------------------------
Substitute [tex]y = 140 - 2x[/tex]
[tex]140x - x^2 - 2xy = 0[/tex]
[tex]140x - x^2 - 2x(140 - 2x) = 0[/tex]
[tex]140x - x^2 - 280x + 4x^2 = 0[/tex]
Re-arrange
[tex]4x^2 -x^2 +140x - 280x = 0[/tex]
[tex]3x^2 -140x = 0[/tex]
Factor x out
[tex]x(3x - 140) = 0[/tex]
Divide through by x
[tex]3x - 140 = 0[/tex]
[tex]3x = 140[/tex]
[tex]x = \frac{140}{3}[/tex]
Recall that: [tex]y = 140 - 2x[/tex]
[tex]y = 140 - 2 * \frac{140}{3}[/tex]
[tex]y = 140 - \frac{280}{3}[/tex]
Take LCM
[tex]y = \frac{140*3-280}{3}[/tex]
[tex]y = \frac{140}{3}[/tex]
Recall that:
[tex]z = 140 -x - y[/tex]
[tex]z = 140 - \frac{140}{3} - \frac{140}{3}[/tex]
Take LCM
[tex]z = \frac{3 * 140- 140 - 140}{3}[/tex]
[tex]z = \frac{140}{3}[/tex]
Hence, the numbers are:
[tex]\frac{140}{3}, \frac{140}{3}, \frac{140}{3}[/tex]
Solve to x to the nearest foot
Answer:
x= 1325 ft (nearest foot)
Step-by-step explanation:
Please see the attached pictures for the full solution.
Daniel's car used 8 gallons to travel 136 miles. How many miles can the car go on one gallon of gas?
QUESTION: Daniel's car used 8 gallons to travel 136 miles. How many miles can the car go on one gallon of gas?
ANSWER: 17
Please help with 7
Will give brainlist
Answer:
y=3
x=5
Step-by-step explanation:
perfect right triangle
1-3-5
hypotneuse is always the longest and across the 90 degree angle
hope this helps :))
Kindred invested $38,976 into first company his investment decreased by 3.5% each years over the first 3 years. Which exponential decay model could use to determine the amount his investment will be worth if in continue to decrease at the same rate?
Answer:
35,025.08 x 0.965 ^ X = Y
Step-by-step explanation:
Given that Kindred invested $ 38,976 into First company, and his investment decreased by 3.5% each year over the first 3 years, to determine which exponential decay model could use to determine the amount his investment will be worth if it continues to decrease at the same rate the following calculation must be performed:
100 - 3.5 = 96.5
38,976 x 0.965 ^ 3 = 35,025.08
Thus, after 3 years of losses, the value of the account will be $ 35,025.08. In turn, if we wanted to determine the amount his investment will be worth if it continues to decrease at the same rate, the following equation should be applied:
35,025.08 x 0.965 ^ X = Y
In this case, X will be the number of years the investment has fallen, and Y will be the value of said investment after the years of decline.
find the squaret of 22
Answer:
the square root of 22 is 4.69
Step-by-step explanation:
Answer:
4.69041575982
Step-by-step explanation:
Suppose that point P is on a circle with radius r, and ray OP is rotating with angular speed o. Find each of the following for the given values ofr, w, and t r= 10 cm, 6 = radian per sec, t = 4 sec 6 radians (round to the nearest thousandths) a) What is the angle generated by P in time t? cm (round to the nearest thousandths) b) What is the distance traveled by P along the circle in time t? c) What is the linear speed of P? cm/sec (round to the nearest thousandths)
PLEASE HELP ME:
Strawberries cost $1.24 per pound. What is the cost for 3.16 pounds of strawberries?
Answer:
$3.92
Step-by-step explanation:
1.24 x 3.16 = 3.9184
Rounding it off to two decimal places:
$3.92
(1) The tuition T for one year at a college can be approximated by the equation T = 1/8 + 9 where x is the year since 2000, and T is tuition in thousands of dollars. Use this equation to estimate the tuition for one year at this college in 2020.
Answer:
Step-by-step explanation:
I’m assuming you meant to write
T = ⅛x + 9
T = ⅛(20) + 9 = 11.5
The required estimate of tuition for one year at the college in 2020 is $11500
Given,
The tuition T for one year at a college can be approximated by the equation.
T = 1/8x + 9 - - - - - - (1)
where x is the year since 2000, and T is tuition in thousands of dollars.
Tuition fee in the year 2020 to be calcuate.
Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
The expression is given, since 2000
so the change in years
x = 2020 - 2000
x = 20
Put this x in equation 1
T = 20/8 + 9
T = 2.5 + 9
T = 11.5
SInce t is in thousand so Tuition fee = $11,500.
Thus, the required estimate of tuition for one year at the college in 2020 is $11500
Learn more about function here:
brainly.com/question/21145944
#SPJ2
Help me pls & thanksss
Answer:
135 degrees.
Step-by-step explanation:
Assuming that it is a regular octagon, you can use the formula (n-2) (180) divided by n. n = sides. Therefore, (8-2) (180) divided by 8, which is 135.
Answer:
135 degrees
Step-by-step explanation:
(just took that test!!)
(Asher)
Can someone solve this for x and y
Answer:
[tex]y = 6\\\\x = 6\sqrt{2}\\x=8.485[/tex]
Step-by-step explanation:
The base-angles converse theorem states that in a triangle where two angles are congruent, the sides opposite the congruent angles are congruent. One can apply this theorem to the given triangle, and thus, y = 6, because of the base angles converse theorem.
It is also given that the given triangle is a right triangle, therefore, the isosceles triangle with a right angle theorem is applicable. This theorem states that in a right triangle (a triangle with a right angle), that is isosceles (two sides are congruent), the third side (non-congruent side) is equal to the length of the two congruent sides times the square root of (2). Hence, x = [tex]6\sqrt{2}[/tex], in the decimal form that is 8.485.
I need help fast. I will give brainliest. GEOMETRY
Answer:
Step-by-step explanation:
The two triangles are similar dues to the ASA therom, so we can relate the sides to one another. That means that
13x=11x-4
2x=-4
x=-0.5
PLEASE SOMEONE HELP ME PLEASE :(
Answer:
1 and 5= corresponding angles.
4 and 2=vertical opposite angle
3 and 6=co interior angle.
5 and 8=linear pair.
5 and 3= alternate interior angle
2 and 8=alternate exterior angle.
Answer:
Ezzzz i got u lol
Step-by-step explanation:
1 and 5 are corresponding
4 and 2 are vertical angles
3 and 6 are same side interior
5 and 8 are Consecutive interior
5 and 3 are alt interior
2 and 8 are alt exterior
Brainliest is much apreciated Hope i helped u
Solve for x
3(4x-1)+9-x=2x+8+9x
Answer: no solution
Step-by-step explanation:
Please help and thank you:)
Answer:
Its C
Step-by-step explanation:
Since the x is being multiplied by the 12, not being added or divided or substracted
How many digits does the smallest repeating block in the decimal expansion of 7/9 contain?
Applying the division of 7 by 9, it is found that the smallest repeating block in the decimal expansion of 7/9 contains 1 digit.
The decimal expansion of 7/9 represents the division of 7 by 9.
The integer part is 0, as 7 < 9.The decimal part is given by the result of 70 divided by 9, which is 7.7777....The repeating block is 7777777....As the only repeating digit is 1, it is found that the smallest repeating block in the decimal expansion of 7/9 contains 1 digit.
You can learn more about division at https://brainly.com/question/13150694
A deli shop sells sandwiches for $4.85 each, including tax. The shop received a total of $63.05 from the sales of sandwiches one afternoon. Write and solve an equation that can be used to determine the number of sandwiches, x, sold by the sandwich shop that afternoon.
Answer:
13 sandwiches were sold
Step-by-step explanation:
Is the volume of congruent figures for same
Answer:
Yes, the volume of congruent figures are the same.
Step-by-step explanation:
They are the same shape and size
True or false?
All quadrilaterals are also rhombuses.
Answer:
It's false
All quadrilaterals are also rhombus, False
Answer:
The answer is true. A rhombus is a quadrilateral that has four sides that are equal. This definition can also be applied for a square.
Step-by-step explanation:
4x + 112° Find x.
9x + 72°
Answer:x = 8 Step-by-step explanation:4x + 112 = 9x + 72-112 -1124x = 9x - 40-9x -9x-5x = -40----- -------- -5 -5x = 8
Explanation;
the answer is 5x=8
I WILL MARK BRAINLIST
The "Converse of the Pythagorean Theorem" states that if the sum of the square of the legs is = to the square of the hypotenuse then the triangle is a right triangle
TRUE
FALSE
Answer:
its true
Step-by-step explanation:
CAN YOU PLEASE MARK ME BRAINLIEST THANK YOU AND HAVE A NICE DAY!
a point on the edge of a flywheel with the radius of 14 cm is rotating at a rate of 14 radians per second. what is the linear speed of a point on its rim in centimeters per minute
Preston writes 3 songs in 2 days, working 7 hours each day. He spends the same amount of time on each song. How long does he spend on each song?
Answer:
Step-by-step explanation:
In 2 days he spends 2*7 = 14 hours total
He divides the number of hours on each song evenly
14 /3 = 4 2/3 hours on each song.
What is 2/3 of an hour?
2/3 * 60 = 120 / 3 = 40 minutes
Total time spent on each song 4 hours and 40 minutes
Answer:
3 songs =2 days working only 7 hour =7×2=14 hour
1 song =14/3hour.=4.6 hour
he spends 4.6 hour on each song
MP is the angle bisector of
Answer: ∠LMN
Step-by-step explanation: Since ∠LMN is a right angle
Can you please help me :) you are supposed to use a^2+ b^2 =c^2 format I will mark brainliest
13 is x
144+25=169
169 is 13 squared
In ΔRST, the measure of ∠T=90°, TR = 1.8 feet, and RS = 8.7 feet. Find the measure of ∠S to the nearest tenth of a degree.
Answer:it’s 11.9
Step-by-step explanation:
HURRY PLEASE HELP! GIVING BRAINLIEST!!
Ms. Federman graded 5 papers in 40 minutes. At this rate, how many minutes will it take her to grade 30 papers?
Answer:
240 minutes
Step-by-step explanation:
If it's 40 minutes for just 5 papers, we need to figure how many minutes it would take to grade just 1. So you have to divide 40 by 5 which is 8. Then 8 time 30 which is 240.
Three radar sets, operating independently, are set to detect any aircraft flying through a certain area. Each set has a probability of 0.03 of failing to detect a plane in its area. Consider one of the radar sets. What is the probability that it will correctly detect exactly three aircraft before it fails to detect one, if aircraft arrivals are independent single events occurring at different times?
Answer:
[tex]Probability = 0.00002619[/tex]
Step-by-step explanation:
Given
Let d represents the event that a radar detects an aircraft.
So:
[tex]P(d) = 0.03[/tex]
Required: Determine the probability that a radar detects three before it fails to detect 1.
This event is represented as: d d d d'
And the probability is calculated as thus:
[tex]Probability = P(d) * P(d) * P(d) * P(d')[/tex]
Using complement rule:
[tex]Probability = P(d) * P(d) * P(d) * (1 - P(d))[/tex]
So, we have:
[tex]Probability = 0.03 * 0.03 * 0.03 * (1 - 0.03)[/tex]
[tex]Probability = 0.03 * 0.03 * 0.03 * 0.97[/tex]
[tex]Probability = 0.00002619[/tex]
#
A four group with 22 people in his getting rooms in a more to sny in to the
night. No more than 3 people can stay in each room. How many terms will
they need?
Answer:
To find the answer you will have to divide 22 by 3 so 7 with 1 person left over so you round up and there will be 8 rooms needed.
Hope I helped :)
Hey guys I need some help with this problem; Will mark brainliest :)
Answer:
The red one
Step-by-step explanation:
Branlies plz Thank you!! :)
Answer:
65 pi, the closest one is 204.1 in^2
Step-by-step explanation:
This question is asking a surface area for a cylindrical bowl with top is empty, so you need to find one circle base and one rectangular side, as the hight is 4in, and wide is 10 inch, use the wide to find the circumference of the rectangular side, which is C = pi*d = 10 pi. Then the area for the rectangular side is A = 40 pi, and the area for the circle is A = pi*r^2 = (10/2)^2 * pi = 25 pi. Then add them together get Total area = 40 pi + 25pi = 65 pi or 65 * 3.14 = 204.1 in^2