The three positive numbers whose sum is 27 will be 14, 1, and 12.
What is the number?A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.
Suppose the three positive numbers are x, y and z.
If the summation of numbers is 27.
⇒ x + y + z = 27 --- (1)
⇒ z = 27 - x - y
Suppose the square sum of the number be S.
∴ S = x² + y² + z²
⇒ S = x²+ y² + (27 - x - y)² --- (2)
We will optimize the function, partially differentiating it with respect to x and y, and setting dS/dx = 0 to get the minimum value of S.
2x + 2(27- x - y)(-1) = 0
2x - 54 + 2x + 2y = 0
4x + 2y - 54 = 0
y = 27 - 2x --- (3)
Differentiate partially with respect to y as
2y + 2(27 - x - y)(-1) = 0
2y - 54 + 2x + 2y = 0
4y + 2x - 54 = 0
x = 54 - 2y --- (4)
Substitute the value of y = 27 - 2x in the equation (4),
x = 12 - 2(27 - 2x)
x = 12 - 54 + 4x
4x - x = 54 - 12
3x = 42
⇒ x = 14
By substituting x = 14 in equation (3)
y =2(14) - 27
y = 28 - 27
⇒ y = 1
Substitute the values of x and y in equation (1),
14 + (1) + z = 27
z = -14+27-1
z= 12
Thus, the three positive numbers whose sum is 27 will be 14, 1, and 12.
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There is a pair of parallel sides in the following shape. 9, 4, and 5. What is the area of the shape?
Answer:
28
Step-by-step explanation:
The formula for trapezoid area is [(b1+b2)/2]h where the b's are the bases and the h is the height. Plugging the values in, you get 28. Have a good day!
Mate I’ve got it! 28 is our answer.
A sport jacket that cost the retailer$25 is marked up$10. Write as a fraction the mark up compared to the cost
Answer:
2/5
Step-by-step explanation:
markup / cost = 10 /25 = 2/5
The prices of commodities X,Y,Z are respectively x, y, z, rupees per unit. Mr. A purchases 4 units of Z and sells 3 units of X and 5 units of Y. Mr. B purchases 3 units of Y and sells 2 units of X and 1 units of Z. Mr. C purchases 1 units of X and sells 4 units of Y and 6 units of Z.in this process A and C earn Rs. 6000 and Rs. 13000 respectively. While B neither lose nor gain. Find the prices per unit of the three commodities by using appropriate method.
please help me!!
Answer:
[tex](x,y,z)=(1477, 1464, 1437)[/tex]
Step-by-step explanation:
Consider the selling of the units positive earning and the purchasing of the units negative earning.
Case-1:Mr. A purchases 4 units of Z and sells 3 units of X and 5 units of YMr.A earns Rs6000So, the equation would be
[tex]3x + 5y - 4z = 6000[/tex]
Case-2:Mr. B purchases 3 units of Y and sells 2 units of X and 1 units of ZMr B neither lose nor gain meaning he has made 0₹hence,
[tex]2x - 3y + z = 0[/tex]
Case-3:Mr. C purchases 1 units of X and sells 4 units of Y and 6 units of ZMr.C earns 13000₹therefore,
[tex] - x + 4y + 6z = 13000[/tex]
Thus our system of equations is
[tex]\begin{cases}3x + 5y - 4z = 6000\\2x - 3y + z = 0\\ - x + 4y + 6z = 13000\end{cases}[/tex]
Solving the system of equations:
we will consider elimination method to solve the system of equations. To do so ,separate the equation in two parts which yields:
[tex]\begin{cases}3x + 5y - 4z = 6000\\2x - 3y + z = 0\end{cases}\\\begin{cases}2x - 3y + z = 0\\ - x + 4y + 6z = 13000\end{cases}[/tex]
Now solve the equation accordingly:
[tex]\implies\begin{cases}11x-7y=6000\\-13x+22y=13000\end{cases}[/tex]
Solving the equation for x and y yields:
[tex]\implies\begin{cases}x= \dfrac{223000}{151}\\\\y= \dfrac{221000}{151}\end{cases}[/tex]
plug in the value of x and y into 2x - 3y + z = 0 and simplify to get z. hence,
[tex]\implies z= \dfrac{217000}{151} [/tex]
Therefore,the prices of commodities X,Y,Z are respectively approximately 1477, 1464, 1437
A cup of hot water is left out to cool. The water is currently 19°C above room temperature. If the heat difference decreases by 5% every minute, what will the difference be in 13 minutes?
Answer:
The difference will be 0.65 °C above room temperature after 13 minutes.
The difference in temperature in 13 minutes will be 6.65° C.
What is an expression?The expression is defined as the relations of the numbers and the variables combined together to form the equation by the use of mathematical algebraic symbols like equal greater than or less than.
Given that a cup of hot water is placed on the counter to cool. The temperature of the water is currently 19°C above room temperature. If the temperature difference falls by 5% every minute.
The heat difference will be calculated as:-
Total decrease = 13 x 5 = 65%
[tex]H = 19\times\dfrac{100-65}{100}[/tex]
[tex]H = 19\times \dfrac{35}{100}[/tex]
H = 19 x 0.35
H = 6.65°
Therefore, the temperature will be 6.65°.
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The population standard deviation for the heights of dogs, in inches is 3,7 inches. If we want to be 95% confident that the sample mean is within 2 inches of the true population mean, what is the minimum sample size that can be taken?
the difference between any two square consecutive number is 20. find the number ?
Answer:
hi. this is the way
Step-by-step explanation:
this is the process of doing it. hope you like it
Answer:
hey can you help me to do homework
Box A contains only 20-cent coins and Box B contains only 50-cent coins. The number of coins in Box A is twice the number of coins in Box B. The amount of money in Box B is $1.60 more than the amount of money in Box A. How many 20-cent coins are there in Box A?
Answer: C
Step by Step Explanation:
20¢ 50¢ Box A : Box B Diff Box B -- Box A 2 : 1 0.50--0.40 = $1.600.20 * 2 : 0.50 0.104 = 1.600.40¢ u = 1.60 ------16, 0.40¢ Coins Box A 0.1032, 0.20¢ Coins Box A u = 16 The answer choice is C
(1) 8
(2) 16
(3) 32
(4) 48
Answer:
find out and discuss drawbacks that campaigners should avoid in order to run a successful social media campaign against human rights violations
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answer:
x=18
Step-by-step explanation:
In this question we can use the Geometric mean of leg theorem
The theorem states that the hypotenuse/leg 2 = leg 2/part 2
In this problem, leg 2 is x+18, the hypotenuse is 72, and part 2 is x.
Plugging the given values in, we get
72/x+18=x+18/x
We can then simplify it.
(x+18)^2=72x
x^2+36x+324=72x
x^2-36x+324=0
That is equal to (x-18)^2
So, x=18
Heather drove 265 miles using 10 gallons of gas. At this rate, how many gallons of gas would she need to drive 424 miles?
Answer:
Step-by-step explanation:
Next bit of info that we have is 424 miles. Miles go on the numerator, and gallons, which we will call "x" will go on the denominator. It should be set up like this: 265/10 = 424/x Once you cross multiply you should get 265x=4240. Divide 265 by both sides and the answer is 16 gallons. Sorry if its wrong
Write an equation of the line that passes through (-4, 1) and is parallel to the
line y - 3 = 2(x + 7).
Answer:
y-1=2(x+4) or y=2x+9
Step-by-step explanation:
y - 3 = 2(x + 7)
y=mx+b
m=2
(x1,y1) -> (-4, 1)
(y−y1)=m(x−x1)
plug in
y-1=2(x+4)
y-1=2x+8
y=2x+9
test:
(1)=2(-4)+9
1=-8+9
1=1
Hoy do you write 75% as a fraction
Step-by-step explanation:
[tex] = \frac{75}{100} \\ [/tex]
[tex] = \frac{75 \div 5}{100 \div 5} \\ [/tex]
[tex] = \frac{15 \div 5}{20 \div 5} \\ [/tex]
[tex] = \frac{3}{4} \\ [/tex]
surface area of a rectangular prism that has 12 5 3
Answer:
The surface area of a rectangular prism calculator gives us the answer: A = 2*1* w+2*1*h+2*w *h = 2*8 ft 6 ft + 2*8 ft* 5 ft + 2*6 ft * 5 ft = 236 ft².
(4√7 + √3) (√7 - 2√3)
Solve by multiplying and simplifying radical expression
How many solutions does the following equation have? -9(x+6)=−9x+108
Answer:
2 or 3 im not sure but choes 2
Step-by-step explanation:
If a right angle triangle has a hypotenuse of length 13 units and a leg of length 7 units, what would
be the length of the other leg?
OA) 13 units
OB) √120 units
OC) 7 units
OD) √102 units
Answer:
the square root of 120
Step-by-step explanation:
a^2+b^2=c^2
a^2+7^2=13^2
a^2+49=169
a^2=120
a= the square root of 120
The variance statistic is an unbiased estimator of the population variance.
O False
O True
Evaluate the function.
f(x) = -x^2+3
Find f(-2)
Answer:
Step-by-step explanation:
f(x)= -(-2)^2 + 3 = -4 + 3 = -1
Please Help - Find the Volume
I know the answer is 1982.0 ft³. However, I don't know how to get to that answer. I keep getting 2112ft³.
Answer:
1982 ft^3 ( rounded)
Step-by-step explanation:
The cube bottom is 12 x 12 x 12 = 1728
The pyramid top is 1/3 ( 12*12) * sqrt 28 = 253.99
added together = ~ 1982
( you have to use the HEIGHT of the pyramid for the volume calculation V = 1/3 * base area * height height = sqrt (28) )
Answer:
1,982 ft³
Step-by-step explanation:
Solving
Volume of rectangular prism (below)
lbh12 x 12 x 12144 x 121728 ft³Volume of square pyramid
1/3Bh1/3 x 144 x √2848 x 5.29253.92Total Volume : 1728 + 253.92 = 1,981.92 ft³ ≅ 1,982 ft³
find the diffrence between x+5 and 2x+3
Answer:
-x + 2
Step-by-step explanation:
collect the like terms of x and 2x . So subtract 1-2 = -1
so 1x - 2x = -1x or -x . Then just subtract 5-3 and you have your answer
The radius of a circle is 9 feet. What is the Area and the circumference of the circle?
Answer:
area is 254.34 circumference is 56.52
Step-by-step explanation:
To find the area you need to follow the formula r^2(pi)
so it would be 9x9x3.14 which is 254.34
to find circumference you need to find diameter which is double the radius (9x2) so the diameter is 18
To find circumference to need to do radius x pi
18x3.14 is 56.52
A rectangluar pyramid of height 8 mi
measuring 4 mi and 6 mi along the base.
Answer:
A rectangluar pyramid of height 8 mi measuring 8 mi and 10 mi along the base. 213.33 mi³ 3) A cone with diameter 18 mi and a height of 18 mi. 1526.81 mi³ 4) A sphere with a diameter of 16 cm. 2144.66 cm³ 5) A pyramid 11 yd tall with a right triangle for a base with side lengths 6 yd, 8 yd, and 10 yd. 88 yd³
Step-by-step explanation:
hope this helps if not let me know
Simplify.........................
[tex] \sqrt{50} \times \sqrt{20} \times \sqrt{100} [/tex]
Answer:
316.03
Step-by-step explanation:
[tex] \hookrightarrow \sf \sqrt{50} \times \sqrt{20} \times \sqrt{100} [/tex]
[tex]\hookrightarrow \sf 7.07 \times 4.47 \times 10[/tex]
[tex]\hookrightarrow \sf 316.03[/tex]
Therefore, [tex] \rm \sqrt{50} \times \sqrt{20} \times \sqrt{100} [/tex] ≈ 316.03
The playground pictured here is having rubber flooring installed to help protect children against injuries from falls. If the cost, including installation, is $8.00 per square foot, what is the total cost of installing the surface?
Answer:
$6,672
Step-by-step explanation:
Area of Playground
Area (rectangle) + 2 x Area (semicircle)26 x 20 + 2 x 3.14 x 10² x 1/2520 + 314834 square feetCost
$8.00 per square feet$8 x 834$6,672Answer:
Using π: $6,673.27 (nearest cent)
Using π = 3.14: $6,672
Step-by-step explanation:
Separate the figure into a rectangle and two semicircles.
Area of a rectangle = width × length
= 20 ft × 26 ft
= 520 ft²
Area of a semicircle = 1/2 π r²
= 1/2 π · 10²
= 50π ft²
⇒ Total area = area of rectangle + (2 × area of semicircle)
= 520 + (2 × 50π)
= (520 + 100π) ft²
⇒ Total cost = area × cost
= (520 + 100π) × $8
= $6,673.27 (nearest cent)
**using π = 3.14**
Total cost = (520 + 100 × 3.14) × $8 = $6,672
7th Grade Math:
A library keeps track of the number of overdue items at the end of each month.
* At the end of April, there were x overdue items.
* At the end of May, the number of overdue items was 3% less than the number of overdue items at the end of April.
The expression x - 0.03x represents the number of overdue items at the end of May. Which sentence best explains how to simplify the expression that represents the number of overdue items at the end of May?
A. Combine x and 0.03x, since they are like terms, by cancelling out the x.
B. Combine c and 0.03x, since they are like terms, by subtracting 1 - 0.03 to find the new coefficient.
C. Factor out an x, since it appears in both terms, leaving 1 in the first term and 0.03x in the second term.
D. Factor out an x, since it appears in both terms, eliminating the first term and leaving 0.03 in the second term.
Answer:
(Mostly) C. Or D
Step-by-step explanation:
Because you first have to factor out the equation by factoring the x . The this will leave you with the terms. Hopefully This Helps.
Can someone help me please
Answer:
7⅞
Step-by-step explanation:
NO.OF HATS TO BE MADE= 9
YARD OF YARN NEEDED TO MAKE EACH HAT= 7/8
THEN,
TOTAL YARDS OF YARN= 9*7/8
= 63/8
Given to write answer in mixed form= 7⅞
ThankYouPlease mark me as brainliest
Find the perimeter of the figure below
Answer:
60 ft.
Step-by-step explanation:
The missing side length would be 6 ft.
14-8=6
Add up all the sides: 14+16+6+9+8+7=60
Hence, the perimeter is 60 ft.
Hope this helps!
Pythagorean Theorem
you leave your house and drive 12 miles north , then turn left and drive 9 miles west . How far are you from your hours ? I NEED HELP WILL MARK YOU BRAINLIEST IF ANSWERED CORRECTLY IF YOU DO NOT KNOW THE ANSWER DONT REPLY TO THIS THREAD
Answer:
15 miles far from your house.
Step-by-step explanation:
By using Pythagorean Theorem
H² = P² + B²
=> 12² + 9² = H²
=> 144 + 81 = H²
=> 225 = H²
=> √225 = H
=> 15 = H
4. Which point is incorrectly labeled? Explain. A(0.1) B(0.5) C(0.75)
Answer:
C
Step-by-step explanation:
It should be .7. Count each mark as .1 and this should be clear.
30 points
A. Transform F using the rule (x, y) → (-x, y)
B. Describe the transformation precisely.
C. Does the transformation result in a a congruent figure?
Answer:
A: You plot these points (-3,4) (-3,6) (-5,6) (-7,4)
B: The transformation would be described as a reflection over the y axis
C: The transformation does result in a congruent figure because the shape doesn't change in size or shape and in length or width
Step-by-step explanation:
So our plots from the figure are: (3,4) (3,6) (5,6) (7,4)
So using the rule (x, y) → (-x, y) are new points would be:
(-3,4)
(-3,6)
(-5,6)
(-7,4)
This rule (x, y) → (-x, y) is used for the type of transformation that is a reflection but over the y axis.
PLEASE HELP ME ASAP IM LOSING POINTS
Let's solve this problem step-by-step:
1. Let's put this in a fraction format:
6834 ÷ 17 = [tex]\frac{6834}{17}[/tex]
2. Now we know 6834 = 6800 + 34
⇒ so:
[tex]\frac{6834}{17} =\frac{6800+34}{17} =\frac{6800}{17} +\frac{34}{17}[/tex]
3. Now let's convert the fractions to denominators
[tex]\frac{6800}{17} +\frac{34}{17} =[/tex] (6800 ÷ 17) + (34 ÷ 17)
Let's check:
6834 ÷ 17 = 402(6800 ÷ 17) + (34 ÷ 17) = (400) + (2) = 400 + 2 = 402
Answer: (6800 ÷ 17) + (34 ÷ 17) or Choice (C)