Answer:
[tex]S(x) = x + \frac{1}{x}[/tex] --- Objective function
Interval = [tex]\{x:x=1\}[/tex]
Step-by-step explanation:
Given
Represent the number with x
The required sum can be represented as:
[tex]x + \frac{1}{x}[/tex]
Hence, the objective function is:
[tex]S(x) = x + \frac{1}{x}[/tex]
To get the the interval, we start by differentiating w.r.t x
Using first principle, this gives:
[tex]S'(x) = 1 - \frac{1}{x^2}[/tex]
Equate S'(x) to 0 in order to solve for x
[tex]0 = 1 - \frac{1}{x^2}[/tex]
Subtract 1 from both sides
[tex]0 -1 = 1 -1 - \frac{1}{x^2}[/tex]
[tex]-1 = - \frac{1}{x^2}[/tex]
Multiply both sides by -1
[tex]1 = \frac{1}{x^2}[/tex]
Cross Multiply
[tex]x^2 * 1 = 1[/tex]
[tex]x^2 = 1[/tex]
Take positive square root of both sides because x is positive
[tex]\sqrt{x^2} = \sqrt{1[/tex]
[tex]x = 1[/tex]
Representing x using interval notation, we have
Interval = [tex]\{x:x=1\}[/tex]
To get the smallest sum, we substitute 1 for x in [tex]S(x) = x + \frac{1}{x}[/tex]
[tex]S(1) = 1 + \frac{1}{1}[/tex]
[tex]S(1) = 1 + 1[/tex]
[tex]S(1) = 2[/tex]
Hence, the smallest sum is 2
Mr. Brown bought some books at a book sale, including 4 paperback books. 20% of all the books he bought were paperbacks. How many books did Mr. Brown buy in all?
Answer:
20 books
Step-by-step explanation:
20% is 1/5 of 100% so the other 4/5 would be 4 times 5 which equals 20 books it total
Answer:
Mr. Brown bought 20 books.
Step-by-step explanation:
20% times 5 would be 100%. Since Mr. Brown bought 4 books, and that was 20% of all the books he bought, you would have to multiply the number of paper back books by 5 to get the answer of 100% of all books he bought, which would be 20. This problem would look like this 20(5) = 4(5), 100% = 20 books.
PLZ HELP ME WITH THIS ITS DUE SOON AND IDK HOW TO DO IT :(
Answer:
Is it everything or which ones particularly?
Translate the sentence into an equation.
Three times the sum of a number and 5 equals 9.
Use the variable c for the unknown number.
Answer:
3×c+5=9
Step-by-step explanation:
thats the answer ig
Answer:
3*(c+5)=9
Step-by-step explanation:
Tamela's school day is 6 hours. Yesterday, she had a doctor appointment and she missed 1/6 of her school day. How many school hours did she miss
during her doctor appointment? Express your answer in simplest form.
Answer:
1 hour
Step-by-step explanation:
Equation: 6 hours × 1/6 hours = 1 hour
If there are 6 hours and Tamela missed 1/6, that means she missed 1 hour of school.
There are 4 trucks for every 5 cars in a parking lot. How many trucks and cars
could be in the parking lot?
A 64 trucks and 80 cars
B 72 trucks and 73 cars
C 84 trucks and 100 cars
D 96 trucks and 110 cars
Answer:
The answer is A.
Step-by-step explanation:
I hope this helps!
what is c(4+3c)-0.75(c+3) simplified
Write the equation of the line through (6, 1) and perpendicular to x+2y−12=0.
what is the 8th term of the following sequence?
3/25, 3/5, 3, 5
Answer:
The 8th term of the following sequence is 9375.
Step-by-step explanation:
Given the sequence
3/25, 3/5, 3, 15
As we know that a geometric sequence has a constant ratio and is defined by:
[tex]\:a_n=a_0\cdot r^{n-1}[/tex]
so
[tex]\frac{3}{25},\:\frac{3}{5},\:3,\:15[/tex]
[tex]\frac{\frac{3}{5}}{\frac{3}{25}}=5,\:\quad \frac{3}{\frac{3}{5}}=5,\:\quad \frac{15}{3}=5[/tex]
As the ratio 'r' is the same.
so
[tex]r=5[/tex]
As the first element of the sequence is
[tex]a_1=\frac{3}{25}[/tex]
Therefore, the nth term is computed by
[tex]\:a_n=a_0\cdot r^{n-1}[/tex]
[tex]a_n=\frac{3}{25}\cdot \:5^{n-1}[/tex]
Putting n = 8 to determine the 8th term.
[tex]a_8=5^7\cdot \frac{3}{25}[/tex]
[tex]a_8=\frac{3\cdot \:5^7}{25}[/tex]
[tex]=\frac{5^7\cdot \:3}{5^2}[/tex]
[tex]=5^5\cdot \:3[/tex]
[tex]=9375[/tex]
Therefore, the 8th term of the following sequence is 9375.
Convert 52 centimetres to millimeters.
Answer:
Step-by-step explanation:
1 cm = 10mm
52cm = 52 x 10 = 520mm
What equation is graphed in this figure?
y−4=−13(x+2)
y−3=13(x+1)
y+2=−3(x−1)
y−5=3(x−1)
Number graph ranging from negative four to four on the x and y axes. A line is drawn on the graph that passes through begin ordered pair negative one comma four end ordered pair and begin ordered pair one comma negative two end ordered pair
Answer:
C. [tex] y + 2 = -3(x - 1) [/tex]
Step-by-step explanation:
All we need to create an equation of the given graph is a point on the line (x1, y1) and the slope (m) of the line.
Thus, equation of in point-slope form is given as [tex] y - y_1 = m(x - x_1) [/tex].
Finding the slope (m) of the line of the graph given, using points (0, 1) and (1, -2).
[tex] m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-2 - 1}{1 - 0} = \frac{-3}{1} = -3 [/tex]
Substitute (x1, y1) = (1, -2) and m = -3 into [tex] y - y_1 = m(x - x_1) [/tex]
[tex] y - (-2) = -3(x - 1) [/tex]
[tex] y + 2 = -3(x - 1) [/tex]
The answer is C.
A 10-pound sack of flour costs $8. whats the cost per pound
Answer:
Your answer is 1.25 stay safe ❤.
Step-by-step explanation:
10÷8 = 1.25
Answer:
0.8
Step-by-step explanation:
8 / 10 = 0.8
please help me fast.
Answer:
A
Step-by-step explanation:
A
Need help ASAP ! Determine whether the following polygons are similar.
Answer:
they are not similar because you can't multiply both sides given by the same number to get the second polygon
Answer:
NO THEY arent
Step-by-step explanation:
if you were to multiply both, you wouldnt get the same answer also the scale factor isnt the same.
True or False: Rosa has a beginning balance of $4,750 in her Checking account. After
depositing a paycheck (p), she then writes 3 checks (c), withdraw money from an ATM (a),
then gets refunded some money (r). Write an Algebraic Expression that models the
situation.
Is this the correct expression?
$4,750 + p - 3c - a +r
Answer:
true
Step-by-step explanation:
Select the image set that matches the ratio 4:2
its the second option since there are 4 circles and 2 oval things.
hope this helps!! :)
Rewrite the fraction with a denominator of 12.
5/6
Explain how to get it
Answer:
50
Step-by-step explanation:
let <LPM be x
60+70+x=180 (sum of angle in triangle is 180)
x=50
<LPM=<KPN (being vertically opposite angle)
<KPN= 50
Answer:
Angle NPK° = 50°Step-by-step explanation:
in triangle MPL
60 + 70 +AngleMPL=180(Angle sum property)
Angle MPL = 180 -60-70 = 50°
Angle NPK = AngleMPL
Angle NPK = 50°
The coordinates of point A on a grld are (-3,-2), Point A is reflected across the y-axls to obtain point B. The coordinates of point B are
-2).
Answer:
The coordinates of the image of B(-3, -2) is B'(3, -2).
Step-by-step explanation:
We know that when a point (x, y) is reflected across the y-axis, the y-coordinate remains the same, and then the x-coordinate becomes negative.i.e.
Thus, the image of P(x, y) is P' (-x, y).Given the point
B(-3, -2)Hence, the image of B(-3, -2):
(-x, y) → (-(-3), -2) = (3, -2)Therefore, the coordinates of the image of B(-3, -2) is B'(3, -2).
The area of the basketball court under the goal is 179.25 square feet. If the cost of
the flooring for the basketball court is $8 per square foot, how much will the flooring
under the goal cost?
Dollars
Answer:
I think its $1,434
Step-by-step explanation:
Because each its 8 dollars per square foot. I multiply 179.25 to get 1,434
Good luck!!!
Answer:
1434
Step-by-step explanation:
If the cost of the flooring for the court is 8 per square foot. Multiply the area of the court under the goal by the cost per square foot Because each its 8 dollars per square foot. I multiply 179.25 to get 1,434
What is the y-coordinate of the point (6,8)?
Answer:
y-coordinate = 8
Step-by-step explanation:
(6 , 8)
x-coordinate = 6
y-coordinate = 8
Answer: 8
Step-by-step explanation: (X,Y)
Enter the ordered pair for point A in the boxes
Answer:
x= 1.5 y= 2.5
Step-by-step explanation:
(-1.5,2.5) is the ordered pair for point A.
What is Coordinate System?A coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.
We have to find the ordered pair of point A.
As we observe the given graph.
The points A lies in the second quadrant.
The x axis value in second quadrant will be in negative.
The y value in second quadrant is positive.
The point A is 2.5 units away from the x axis and -1.5 units from the y axis.
So the ordered pair of A is (-1.5,2.5)
Hence, (-1.5,2.5) is the ordered pair for point A.
To learn more on Coordinate system click:
https://brainly.com/question/4726772
#SPJ6
You are traveling in a car. Your speed is 50 miles per hour. What is your speed in feet per minute?
Answer:
4399.98 ft per min
Step-by-step explanation:
Divide 50 mi by 60 min = 0.83333Multiply this by 5280 = 4399.9824 ft per minWhich of the following would be the most accurate equation for the scatter plot?
find the value of x of given figure and solve this question step by step plzz help question number D
Answer:
The value of x is 15 cm
Step-by-step explanation:
#(d)
In Δ BDC
∵ ∠D is a right angle
∴ BC is the hypotenuse
∴ BD and DC are the legs of the right angle
→ By using Pythagoras Theorem
∵ (BC)² = (BD)² + (DC)²
∵ BD = 10 cm
∵ DC = 2√11 cm
→ Substitute them in the equation above
∴ (BC)² = (10)² +(2√11)² = 100 + 44 = 144
→ Take √ for both sides
∴ BC = 12 cm
In Δ ABC
∵ ∠B is a right angle
∴ AC is the hypotenuse
∴ AB and BC are the legs of the right angle
→ By using Pythagoras Theorem
∵ (AC)² = (AB)² + (BC)²
∵ AB = 9 cm
∵ BC = 12 cm
∵ AC = x
→ Substitute them in the equation above
∴ x² = (9)² +(12)² = 81 + 144 = 225
→ Take √ for both sides
∴ x = 15 cm
∴ The value of x is 15 cm
Please help. The topic is angles. Anything you know helps
Answer:
all of them except straight and reflex
Step-by-step explanation:
when angles are supplementary it means that they add up to 180
an acute angle is supplementary to an obtuse angle
an obtuse angle is supplementary to an acute angle
a right angle is supplementary to a right angle
but a reflex angle is over 180 so it's not supplementary to anything
and a straight angle is already 180 so it has no supplements either
please help me, make sure to tell me the answer, why it is the answer, and how it is the answer
Answer:
Step One
Calculate the area of both the skating area and the spectator area.
Area = L * W
L = 4x
W = 4x
Area = 4x * 4x
Area = 16x^2
Step Two.
Find the radius of the semicircle. R = radius
From the diagram
R = The full length - the length given in the red shaded area.
R = 4x - 2x
R = 2x
Step Three
Find the area of the semicircle.
Area of a full circle = pi R^2
Area of a 1/2 circle = [tex]\frac{\pi *(2x)^2}{2}[/tex]
Area of a 1/2 circle = [tex]\frac{\pi *4*x^2}{2}[/tex]
Area of a 1/2 circle = [tex]\frac{\pi *2*x^2}{}[/tex]
Notice that the 2 in the denominator cancels in part with the 4 in the numerator.
Step Four
Find the area of the shaded area
Area of the shaded Area = Whole Area - Area of the Semi Circle.
Area of the shaded Area = 16x² - [tex]\frac{\pi *2*x^2}{}[/tex]
The answer is the upper right corner choice I think
Find the value of X.
Answer:
x=16
Step-by-step explanation:
(4x+2)+(x+8)=90
5x+10=90
5x=80
x=16
Which of the following is a description of the data with a correlation coefficient of 0.1?
2)
Un ómnibus interprovincial parte de Lima a Huacho cada 30 minutos y otro sale cada 45 minutos. ¿Cada cuántos minutos salen juntos?
Answer:
The leave together every 90 minutes
Step-by-step explanation:
The leave together every 90 minutes:
bus A : 30 + 30 + 30 = 90
bus B : 45 + 45 = 90
Number 3 plz really need help.
Answer:
40ft^2
Step-by-step explanation:
Hello There!
In this problem since we know that these are similar triangles we can set up a ratio in order to solve for the missing leg lenght, and then the areas.
This can be done by using the ratios and solving for x:
[tex]\frac{8ft}{12ft}[/tex] x [tex]\frac{4ft}{x}[/tex]
After this is done we find that the missing leg on the larger triangle is equal to roughly 6. With this in mind we find the area of the two triangles by multiplying the legs and dividing by 2, respectively.
The larger triangle will have an area of 72ft^2
the smaller triangle will have an area of 32ft^2
in order to find the difference in area we will simply subtract the two and find that the difference is equal to 40ft^2
Hope this helps
-HM