x = 8 and y = 8 are the two positive numbers whose sum is 16 and the sum of the squares is minimum.
According to the question,
The two numbers are positive and the sum of the two numbers is 16 and the sum of the squares of the two numbers is the minimum.
Now to solve the question we will consider,
x and y are the two numbers, such that x > 0 and y > 0
Sum of the numbers : x + y = 16
Sum of squares of the numbers: S = x²+ y²
x + y = 16 y = (16 - x)
Assume, S = x² + y²
S = x² + (16 - x)²
Now we will differentiate with respect to x
dS/dx = 2x+ 2(16-x)(-1)
2x-2(16-x)=0
2x-32+2x=0
4x-32=0
4x=32
x=32/4
x=8
As x > 0, x = 8
d²S/dx² = d/dx [2x+ 2(16-x)(-1)]
d²S/dx² = d/dx (2x) - 2 d/dx (16-x)
d²S/dx² = 2 - 2[0-1]
d²S/dx² = 4
Now when x=8
d²S/dx² = 4 ≥0
Therefore, the function S = sum of the squares of the two numbers is minimum at x = 8.
y = 16-8 = 8
Therefore, x = 8 and y = 8 are the two positive numbers whose sum is 16 and the sum of the squares is minimum.
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Estimate a 25% tip on a bill of 68.37$ by first rounding the bill amount to the nearest ten dollars.
Answer:
20 dollar tip (rounded) assuming the bill is 68.37
Step-by-step explanation:
just multiply 68.37 by 0.25, and you get 17.09 or 20 dollars rounded to TENS place.
suppose that the radius is expanding at a rate of 0.6 inches per second. how fast is the volume changing when the radius is 2.3 inches? use at least 5 decimal places in your answer.
Using the theories of Application of derivative,we got that 59.11221inches³/sec is rate of volume changing when the radius is 2.3 inches.
We are given rate of change of radius (dr/dt)=0.6inches
We know very well that volume of sphere is given by (4/3)πr³
where r is the radius of the sphere.
Now, differentiating the volume with respect to radius, we get
=>dV/dr=4πr²
=>dV/dt=(dv/dr)·(dr/dt)
=>dV/dt=4πr².(dr/dt)
We are given that dr/dt=0.6inches/sec
So, dV/dt=4πr²·(0.6)
Now, putting values of r=2.3
dV/dt=4π(2.3)²×(0.6)
=>dV/dt=4×3.14×2.3×2.3×0.6
=>dV/dt=59.11221inches³/sec
Hence, if we suppose suppose that the radius is expanding at a rate of 0.6 inches per second, the volume is changing at the rate of 59.11221inches³/sec when the radius is 2.3 inches.
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Multiply (4.21 x 10-9) (7.8 x 1015). Write the final answer in scientific notation.
O 3.2838 x 107
O 32.838 x 106
O3.2838 x 10-134
O 32.838 x 10-135
4.21 x 10-9) (7.8 x 1015) = 32.838 * 10^6" ; the correct option is second.
What is multiplication ? In mathematics, multiplication is a way of finding the product of two or more numbers. This is one of the basic arithmetic operations that we use in our daily life. The main application can be seen in the multiplication table. In arithmetic, multiplication of two numbers represents the repeated addition of one number to another. These numbers include integers, natural numbers, whole numbers, fractions, and so on. Multiplying m by n means that m is added to itself n times, or vice versa. Multiplication in mathematics (denoted by an 'x') is an arithmetic operation separate from addition, subtraction, and division. Elementary school students learn the four arithmetic operations on their own and learn how to solve multiplication problems quickly and easily. Multiplication is the process of taking the product of two or more numbers. Multiplication of numbers such as 'a' and 'b' is given as 'a' multiplied by 'b'. In mathematics, the basic description of multiplication is the repeated addition of one number to another. Multiplying single-digit numbers is easy. However, multiplying numbers with two or more digits is a difficult and time-consuming task. Numbers can be multiplied in any order. (3x4 = 4x3)If you want to multiply the number by a multiple of 10, enter the number of zeros equal to the multiple of 10 next to the multiplier (for example, 6 x 100 = 600).When multiplying three numbers, multiply by the smaller number first to do the math quickly, then multiply by the third number.If the multiplication involves numbers with two or three digits, write those numbers in extended form and then multiply. (for example.:45 × 9 = (40 + 5) × 9 = 40 × 9 + 5 × 9 = 360 + 45 = 405)Calculation4.21 * 10 ^ -9 * 7.8 * 10 ^ 15 = 32.838 * 10^6
so the correct option is second
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graph the system of inequalities shown i need this quick
x>1
y>x
Answer:
Graph
Step-by-step explanation:
graph the line x=1 (vertical line passing through point (1,0))with a dotted line and shade everything to the right of the line. Then graph the line y=x (line with slope 1 passing through origin) with a dotted line, shading everything above the line.
Find the value of the expression (2x − 12) + (xy-10) for x = 8 and y = 2.
-
O-8
O 6
O-10
02o
The required value of the expression (2x − 12) + (1/2 xy - 10) for x = 8 and y = 2 is 2. Option D is correct.
First, let us understand the algebraic expression and how is it formed:
A multitude of strategies is used to build algebraic expressions utilizing variables and constants. It is a term-based mathematical expression that comprises variables, constants, and algebraic operations such as addition, subtraction, and so on.
We are given:
(2x − 12) + (1/2 xy - 10)
We need to find the value of the given expression for x = 8 and y = 2.
Substitute the values of x and y in the given expression, we will get;
(2 * 8 − 12) + (1/2 * 8 * 2 - 10)
= (16 − 12) + (8 - 10)
= 4 + (-2)
= 4 - 2
= 2
So, the obtained value is 2.
Thus, the required value of the expression (2x − 12) + (1/2 xy - 10) for x = 8 and y = 2 is 2. Option D is correct.
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8.7+x/1.1 = 7 solve for x
The solution of this Algebraic Equation is -1.0
What is an Algebraic Equation?
An algebraic equation is a mathematical statement which establishes two expressions equal to each other. An algebraic equation is generally composed of a variable, coefficients, and constants.
Solution:
According to the question,
the algebraic equation given is,
(8.7 + x)/1.1 = 7
By cross multiplying
8.7 + x = 7.7
x = -1.0
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Suppose a certain baseball diamond is a square 60 feet on a side. The pitching rubber is located 40.5 feet from home plate on a line joining home plate and second
base.
(a) How far is it from the pitching rubber to first base?
(b) How far is it from the pitching rubber to second base?
(c) If a pitcher faces home plate, through what angle does he need to turn to face first base?
(a) The distance from the pitching rubber to first base is about feet.
(Round to two decimal places as needed.)
(b) The distance from the pitching rubber to second base is about feet.
(Round to two decimal places as needed.)
(c) He needs to turn about to his left.
(Round to one decimal place as needed.)
Answer: 41.7 feet from pitcher to 1st
13.2 feet from pitcher to 2nd
58 degrees to turn from home to 1st
distance from pitcher to the line from home to 1st is 57.5(sin45) = 57.5(.707) = 40.66
construct a right triangle with legs 40.66 and 50-40.66 = 9.34. then sum the legs' squares, and take the square root to get 41.72 feet
distance from home to 2nd = hypotenuse of a right triangle with sides 50 and 50, and angle of 45 degrees
50^2 + 50^2 = 2(2500) = 5000. sqr5000= 70.71, subtract 57.5. 70.71-57.5= 13.21 feet from pitcher to 2nd
Step-by-step explanation:
There are 50 tudent in cla. Boy make up 20% of the cla. 60% of the boy wear glae. How many boy in the cla wear glae?
The boys in the class that wear glae are 6 people.
The boys in the class that wear glae can be calculated as follows:
First we should calculate how many boys there are in the class. We can calculate it by multiplying the percent of the boys to the total students.
Boys in the class = [tex]\frac{20}{100} X 50[/tex] = 10 people.
Thus, we can calculate the boys who wear the glae by multiplying the percent of the boys wearing glae of the boys in the class.
Boys wear glae = [tex]\frac{60}{100} X 10[/tex] = 6 people.
Hence, The boys in the class that wear glae are 6 people.
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Which expression represents the phrase? “The product of 8 and the quotient of 6 and and w.”
Answer:
B
Step-by-step explanation:
product means multiplication and quotient is division , then
product of 8 and the quotient of 6 and w is
8 ([tex]\frac{6}{w}[/tex] )
Meshea sold 12 dresses in 120 minutes at this rate how many hours will it take her to sell 144 dresses
Answer: 144 dresses in 1440 minutes.
Step-by-step explanation:
Divide 144 and 12 you get 12. So you multiply 12 and 120 and you get 1440.
The rate is 120min/12dresses. Let's simplify it.
12/120 = 10min/1dress (or just 10)
Lets use this rate for 144 dresses
10 x 144 = 1140
It will take 1440 minutes to sell 144 dresses.
A shop sells tins of paint in 2 litre and 5 litre cans. The manager checks the amount of paint he
has in stock, and finds that there are 500 cans altogether. These cans hold a total of 1420 litres of
paint. By forming and solving a pair of simultaneous equations, find the number of each size of
can in stock.
Answer:
360 of 2 liter cans and 140 of 5 liter cansStep-by-step explanation:
Let the number of 2 liter cans be x and 5 liter cans be y.
Number of cans:
x + y = 500Amount of paint:
2x + 5y = 1420Solve the system by elimination, double the first equation and subtract from the second one:
2x + 5y - 2x - 2y = 1420 - 2*5003y = 420y = 420/3y = 140Find x:
x + 140 = 500x = 500 - 140x = 360Please answer this question
Answer:
x=9
y=-5
Or
(9,-5)
Step-by-step explanation:
-x+y=-14
+x. +x
y=x-14
2x-3(x-14)=33
2x-3x+42=33
-x+42=33
-42. -42
-x=-9
/-1. /-1
x=9
-(9)+y=-14
+9. +9
y=-5
Hopes this helps please mark brainliest
You are given that a conditional is false and its hypothesis true. Determine whether the conclusion is true or false.
Answer:
The conclusion is false.
Step-by-step explanation:
If the conclusion is false, then the whole conditional is false even if the hypothesis is true.
Put the following equation of a line into slope-intercept form, simplifying all fractions. 9y−3x= −54
The equation of the line into slope-intercept form is y = x/3 - 6
What are linear equations?Linear equations are equations that have constant average rates of change.
Note that the constant average rates of change can also be regarded as the slope or the gradient
How to put the equation of a line into slope-intercept form?From the question, we have the following equation that can be used in our computation:
9y−3x= −54
Rewrite properly
This gives
9y - 3x = -54
Divide through the equation by 3
So, we have the following representation
9y/3 - 3x/3 = -54/3
Evaluate
3y - x = -18
To rewrite as slope-intercept form is to make y the subject
So, we have
3y = x - 18
Divide through the equation by 3
So, we have the following representation
y = x/3 - 6
Hence, the equation is y = x/3 - 6
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lisa receives a salarry of rs 9500 per month plus a commision of 10 % on all sales. For te month of December, she earns rs 14000. find her total sales in december
Total earning = Salary + 10% of sales
According to question, we have
14000 = 9500 + 10% of sales
4500 = 0.1 sales
sales = 4500*10 = 45000
So, her total sales was Rs 45000
Write the equation in standard form using integers
(no fractions or decimals): y= -2/3 x-1
standard form for a linear equation means
• all coefficients must be integers, no fractions
• only the constant on the right-hand-side
• all variables on the left-hand-side, sorted
• "x" must not have a negative coefficient
[tex]y=-\cfrac{2}{3}x-1\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3(y)=3\left( -\cfrac{2}{3}x-1 \right)} \\\\\\ 3y=-2x-3\implies {\Large \begin{array}{llll} 2x+3y=-3 \end{array}}[/tex]
From Monday to Thursday the debts of a snowdrift changed by -8 inches. From Thursday to Friday, the depth changed by half as much. What is the oh angle in the depth of the snowdrift from Monday to Friday?
The depth of snowdrift changed from Thursdays to Friday by -4 inches
The change of depth of snowdrift from Monday to Thursday = -8 inches
From Thursday to Friday, the depth changed by half as much
The equation is the mathematical statement that shows the relationship between two expression with and equal sign. The equation may consist of variables, numbers and arithmetic operators
Then the equation will be
The change of depth of snowdrift from Thursday to Friday = -8 /2
Here we have to use the division
Divide the terms
The change of depth of snowdrift from Thursday to Friday = -4 inches
Hence, depth of snowdrift changed from Thursdays to Friday by -4 inches
The complete question is :
From Monday to Thursday, the depth of a snowdrift changed by -8 inches. From Thursday to Friday, the depth changed by half as much. What is the change in the depth of the snowdrift from Thursday to Friday?
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the rectangular floor of a classroom is 30 feet in length and 20 in width. A scale drawing
of the floor has a length of 15 inches. what is the area in square inches, of the floor in the scale drawing
Answer: 150 square inches
Step-by-step explanation:
Set up the proportional ratios (convert feet to inches first):
30 ft = 360 inches (there are 12 inches in 1 foot)
20 ft = 240 inches (I'm assuming there is an error in the question and the width is 20 ft, NOT 20 inches!)
360/15 = 240/x
x is the width of the scaled down rectangle
solve for x:
360x = 3600
x = 10 in
Now calculate Area = length x width
A = 15 x 10 = 150 square inches
5 cards are drawn from a standard deck without replacement. What is the probability that at least one of the cards drawn is a 3? Express your answer as a fraction or a decimal number rounded to four decimal places.
The probability that at least one of the cards drawn is a 3 is 1/5 0r 0.2000.
What is probability?
Probability shows the likelihood of an event happening. It can be calculated by dividing the number of outcomes of an event by the total number of possible outcomes or sample space. Probability is equal to '1' when the event is certain to occur. i.e P =1. It is less than '1' when it is not likely to occur. i.e P< 1
Probability P=no. outcomes/total no. of the possible outcomes
From the question;
No. of total no of cards =5
The probability the card drawn is a 3 =1/5
=0.2000
Therefore the probability that at least one of the cards drawn is a 3 is 1/5 0r 0.2000.
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Ninety five percent of students in statistics scored between 62 pts and 90 pts. Assuming this data is normally distributed, what are the mean and standard deviation?.
The mean is 76 and the standard deviation is 7.
What is mean and standard deviation?
The standard deviation in statistics is a measurement of how much a group of values can vary or be dispersed. A low standard deviation suggests that values are often close to the set's mean, whereas a large standard deviation suggests that values are dispersed over a wider range.
In mathematics, particularly in statistics, there are various types of means. Each mean summarizes a particular set of data, frequently to help determine the overall significance of a particular data set.
Let, 95% of students in statistics scored between 62 and 90 points.
Here,
Mean = [tex]\frac{62+90}{2} = \frac{152}{2} = 76[/tex]
And the standard deviation is,
SD = [tex]\frac{90-76}{2}= \frac{14}{2} = 7[/tex]
Hence, the mean is 76 and the standard deviation is 7.
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Can anyone please help me with this? I don't get it.
Answer:
739
Step-by-step explanation:
2217 (weight) / 3 ( # of blocks)
Help me solve this please
Step-by-step explanation:
let's use the law of sine :
a/sin(A) = b/sin(B) = c/sin(C)
so,
5.4/sin(K/2) = 12.3/sin(M1)
8.2/sin(K/2) = x/sin(M2)
M1 + M2 = 180 (as complementary angles or linear pair)
M2 = 180 - M1
sin(K/2) = 5.4×sin(M1)/12.3
sin(K/2) = 8.2×sin(M2)/x
therefore
5.4×sin(M1)/12.3 = 8.2×sin(180 - M1)/x
since sin(a) = sin(180 - a)
5.4×sin(M1)/12.3 = 8.2×sin(M1)/x
and then
5.4/12.3 = 8.2/x
x×5.4 = 8.2×12.3
x = 8.2×12.3/5.4 = 18.67777777... ≈ 18.7
Step-by-step explanation:Step-by-step explanation:
let's use the law of sine :
a/sin(A) = b/sin(B) = c/sin(C)
so,
5.4/sin(K/2) = 12.3/sin(M1)
8.2/sin(K/2) = x/sin(M2)
M1 + M2 = 180 (as complementary angles or linear pair)
M2 = 180 - M1
a train is 2500m long crosses a platform whose length is 1900 meters in 40 seconds . if a dog is running at the speed of 6 m\s in the direction of the train and the train is 936 meters away from the dog , then how much time will the train catch up with the dog
The train will catch up with the dog in 1.996 seconds
How to determine how much time it will take the train to catch upThe problem is solved using the formula for speed which is
distance / time
speed of the train = length of track / time
= 1900 / 40
= 475 m/s
speed of the dog is given to be 6 m/s
The relative velocity = 475 - 6 = 469 m/s
The time to catch up is calculated using relative velocity
469 * time = 936 meters
time = 936 / 469
= 1.996 seconds
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A 2-pint bucket of paint costs $11.08. What is the price per cup?
The price per cup for a 2-pint bucket of paint costs $11.08 is $2.77.
How to calculate the price per cup?It should be noted that 1 pint = 2 cup
In this case, 2-pint bucket will be:
= (2 × 2)
= 4 cups.
Therefore, 4 cups cost $11.08.
The price per cup will be:
= Total cost / Number of cups
= $11.08 / 4
= $2.77
The price is $2.77.
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24) The cost in millions of dollars for a company to manufacture x thousand automobiles is given by
the function C(x) = 3x^2 - 30x + 200. Find the number of automobiles that must be produced to
minimize the cost.
A) 15 thousand automobiles
C) 5 thousand automobiles
B) 125 thousand automobiles
D) 10 thousand automobiles
For minima,
C'(x) = 0
6x-30 = 0
x = 5
If C"(x) >0, then minima
So, C"(x) = 6 > 0
So, for x = 5 , thr value of C(x) will be minimum.
Option C is correct
Write the equation for the following graph
Answer:
y = 4x - 6
Step-by-step explanation:
linear equation:
y = mx + b
1. find the slope m
first select two point
im gonna take point 1 (-1,-7) and point 2 (3,9)
m = (y2-y1)/(x2-x1)
m = (9-(-7))/(3-(-1)) = 16/4 = 4
2. find b
first select a point
im gonna reuse point 2 (3,9)
y = mx + b
9 = 5(3) + b
9 = 15 + b
b = 9 - 15 = -6
3. keep x y, substitute m,b to linear equation
y = 4x - 6
Maria is renting kayaks from a local shop that charges a $10 fee, plus an hourly rate of $7. 50. For how long can maria rent the kayak if she pays a total of $70?.
Answer:
8 hours
Step-by-step explanation:
We can use an algebraic equation to solve this problem.
7.5x + 10 = 70
7.5x + 10 (-10) = 70 (-10)
7.5x (/7.5)= 60 (/7.5)
x = 8
Determine the function below that has a domain of a 2-4.
A f(x)=√x-1-4
B f(x)=1-√√x+4
f(x)=1+√x-4
D f(x)=√-4+x−1
12 Cookies
4 kids are trying to share amongst themselves 12 cookies. How many does each kid get? Write a story to describe the situation.
A number is raised to the third power, then subtracted from 15 to get 7. What is the number squared?
Answer:
4
Step-by-step explanation:
Let x be the unknown number.
[tex]\begin{aligned}&\textsf{A number is raised to the third power}: & x^3&\\&\textsf{Subtracted from 15}: & 15-x^3&\\&\textsf{To get 7}: & 15-x^3&=7\end{aligned}[/tex]
Solve the found equation for x:
[tex]\begin{aligned}&\textsf{Given}: & 15-x^3&=7\\&\textsf{Subtract $15$ from both sides}: & -x^3&=-8\\&\textsf{Divide both sides by $-1$}: & x^3&=8\\&\textsf{Rewrite $8$ as $2^3$}: &x^3&=2^3\\&\textsf{Cube root both sides}: & x&=2\end{aligned}[/tex]
Therefore, the number squared is:
[tex]\implies x^2=2^2=4[/tex]