your Answer will be:
3
Solve the following equations
3y-6x=48
y=3x+11
Answer:
See below
Step-by-step explanation:
a). 3y-6x=48
soln
or, 3xy=48
or, xy=48÷3
or, xy=32,,
b). y=3x+11
soln
or, y=13x
or, xy=13,,
A company wishes to manufacture a box with a volume of 20 cubic feet that is open on top and is twice as long as it is wide. Find the width of the box that can be produced using the minimum amount of material.
Answer:
2.47 feet
Step-by-step explanation:
Let l, b, and h be the length, width, and height of the box.
As the length is twice the width, so l=2b ...(i)
The volume of the box is 20 cubic feet, so
lbh=20
(2b)bh=20 [by using (i)]
[tex]h=\frac {20}{2b^2} \\\\h= \frac {10}{b^2} ...(ii)[/tex]
The material required= surface area, S, of the open box
S= lb+2bh+2lh
By using equation (i) and (ii), we have
[tex]S= 2b(b)+2b\times \frac {10}{b^2} +2(2b)\times \frac {10}{b^2}[/tex]
[tex]S= 2b^2+ \frac {20}{b} + \frac {40}{b} \\\\S= 2b^2+ \frac {60}{b} \cdots(i)[/tex]
Now, we have the surface area, S, as the function of width, b.
Differentiate S with respect to b then equate it to zero to get the extremum values, as
[tex]\frac {dS}{db}=0 \\\\\frac {d}{db}(2b^2 +60/b)=0 \\\\4b-\frac{-60}{b^2}=0 \\\\4b=\frac{60}{b^2} \\\\b^3=\frac{60}{4} \\\\b=(15)^{1/3}[/tex]
b=2.47 feet.
Now, by second differentiation, checking the nature of extremum value.
[tex]\frac {d^2S}{db^2}=4+\frac {120}{b^3}[/tex]
For [tex]b>0, \frac {d^2S}{db^2} >0[/tex]
So, the width of the box, b=2.47, is the minima for the area, S(b).
Hence, the width of the box that can be produced using the minimum amount of material is 2.47 feet.
A day can be evenly divided into 86,400 periods of 1 second; 43,200 periods of each 2 seconds; or in many other ways. In total, how many ways are there to divide a day into periods of seconds, where and are positive integers
Answer:
96 ways
Step-by-step explanation:
Given
[tex]Day = 86400\ seconds[/tex]
Required
Ways to divide it into period of seconds
What this question implies is to determine the total number of factors of 86400
To start with, we determine the prime factorization of 86400
To do this, we continually divide 86400 by 2; when it can not be further divided, we divide by 3, then 7, then 11...
[tex]86400/2 = 43200[/tex]
[tex]43200/2=21600[/tex]
[tex]21600/2=10800[/tex]
[tex]10800/2=5400[/tex]
[tex]5400/2= 2700[/tex]
[tex]2700/2 = 1350[/tex]
[tex]1350/2=675[/tex]
[tex]675/3=225[/tex]
[tex]225/3=75[/tex]
[tex]75/3=25[/tex]
[tex]25/5=5[/tex]
[tex]5/5 = 1[/tex]
This implies that:
[tex]86400 = 2^7 * 3^3 * 5^2[/tex]
The number of factors d is the solved by:
[tex]d = (a+1)*(b+1) *(c+1)[/tex]
Where
[tex]n = 2^a * 3^b * 5^c[/tex]
By comparison:
[tex]a = 7[/tex]
[tex]b = 3[/tex]
[tex]c=2[/tex]
So:
[tex]d = (7+1)*(3+1) *(2+1)[/tex]
[tex]d = 8*4 *3[/tex]
[tex]d = 96[/tex]
Hence, there are 96 total ways
what is the simplified form of 4x - 7 + x - 10
Answer:5x-17
Step-by-step explanation:
4x - 7 + x -10 = 0
4x + x - 7 - 10 = 0
5x - 17 = 0
5x = 17
x = 17/5
Given the function f (x) = -2x -5, determine the value of f (-3). Please helpp
Answer: if you see my picture that the answer for your question
Step-by-step explanation: hope this help
In the adjoining figure, if XY = XZ and YA = AZ, write
down the relation between XA and YZ.
Answer:
XAㅗYZ
XA is perpendicular to YZ
HOPE THIS WILL HELP YOU..!
Write an equation passing through the point in perpendicular to the given line.
Please solve both!
Thank you!
Answer:
10. y=-4x+3
12. y=[tex]\frac{1}{2}[/tex]x+3
Step-by-step explanation:
In order for a line to be perpendicular to another, their slopes must be opposite reciprocals.
1. Put the given equations into slope-intercept form. (y=mx+b)
2. Identify the opposite reciprocal of the original equations. (#10: -4 & #12: [tex]\frac{1}{2}[/tex])
3. Plug your given coords and opposite reciprocals into point-slope formula (y-y₁=m(x-x₁)) and simplify the expression to get your equation of the line.
a standard six-sided die is rolled. what is the probability that the value of the second die is higher than the first
Answer:
The probability that the value of the second die is higher than the first
[tex]P(E) = \frac{15}{36} = \frac{5}{12}[/tex]
Step-by-step explanation:
Explanation:-
In a single throw with two dice total number of sums = 6 X 6 = 36
Let 'E' be the event of the second die is higher than the first
Total number of cases
= {( 1,1), (1,2 )( 1,3), (1,4) , (1,5) ,(1,6)
( 2,1), (2,2 )( 2,3), (2,4) , (2,5),(2,6)
( 3,1), (3,2 )( 3,3), (3,4) , (3,5),(3,6)
( 4,1), (4,2 )( 4,3), (4,4) , (4,5),(4,6)
( 5,1), (5,2 )( 5,3), (5,4) , (5,5),(5,6)
( 6,1), (6,2 )( 6,3), (6,4) , (6,5),(6,6)}
The favourable cases
n(E) = {(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)} = 15
The probability that the value of the second die is higher than the first
[tex]P(E) = \frac{15}{36} = \frac{5}{12}[/tex]
Ricky draws a square . He claims that any rotation about the center of the square that is a multiple of 30 degrees will carry the square onto itself . Which statement best describes Ricky's claim ?
Answer:
Option (a)
Step-by-step explanation:
This question is incomplete without statements; find the statements as followed,
a). Ricky's claim is incorrect since not all rotations that carry a square onto itself are multiples of 30 degrees.
b). Ricky's claim is incorrect since not all rotations that are multiples of 30 degrees carry a square onto itself.
c). Ricky's claim is correct since any rotation that carries a square onto itself is a multiple of 30 degrees.
d). Ricky's claim is correct since any rotation that is a multiple of 30 degrees carries a square onto itself.
Square ABCD will map onto itself when point A comes to B, C or D by a rotation about the center E with a multiple of measure of angle AEB.
m∠AEB = 90° [Diagonals of a square intersect each other at 90°]
In simpler words, if square ABCD is rotated 90° or it's multiple about the center E, square will overlap itself.
Therefore, Option (a) is correct.
A florist can order roses in bunches of 12 and lilies in bunches of 8. Last month she ordered the same number of roses and lilies. If she ordered no more than 100 of each kind of flower, how many bunches of each could she have ordered? Find all the possible combinations.
Answer:
2 bunches of roses and 3 bunches of lilies.
4 bunches of roses and 6 bunches of lilies.
Step-by-step explanation:
Given that:
Roses come in a bunch of 12 flowers and
Lilies come in a bunch of 8 flowers
Number of roses ordered is equal to the number of lilies ordered.
Total number of flowers ordered are lesser than 100.
To find:
The possible number of combinations such that equal number of flowers are bought.
Solution:
Here, we need to find the Least Common Multiple.
[tex]12 = \underline{2 \times 2} \times 3[/tex]
[tex]8 = \underline{2 \times 2} \times 2[/tex]
LCM = [tex]2\times 2 \times 3 \times 2 = 24[/tex]
Therefore, we need to find the number of bunches such that number of flowers of each type bought are equal to LCM or multiples of LCM.
i.e.
24, 48, 72, 96 ....
Here, two types of flowers are there.
Therefore, 24 of each type, total 48 flowers i.e. 2 bunches of roses and 3 bunches of lilies.
48 of each type, total 96 flowers i.e. 4 bunches of roses and 6 bunches of lilies.
Total possible combinations:
2 bunches of roses and 3 bunches of lilies.
4 bunches of roses and 6 bunches of lilies.
need help finding answer
Step-by-step explanation:
Triangle XYZ is isosceles.
Since Angle Y = 90°, Angle Z = (180° - 90°)/2 = 45°.
Please help I'll mark brainliest
Answer:
I would say for almonds next to the number 2 put $21.98 and for dried apricots next to $26.25 put 3 pounds and then see which one is more expensive.
Step-by-step explanation:
Apricots is less expensive than Almonds.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
2 pounds almonds cost = 21.98
So, cost of 1 pounds cost = 21.98/2= 10.99
and, 3 pounds apricots cost= 26.25
So, cost of 1 pounds cost = 26.25/3 = 8.75
Hence, Apricots is less expensive than Almonds.
The complete Table is
Almonds Dried Apricots
Cost Weight Cost Weight
21.98 2 26.25 3
10.99 1 8.75 1
Learn more about unitary method here:
https://brainly.com/question/22056199
#SPJ5
Find the value of X. round to the nearest tenth
There is no equation, what is the equation?
Answer:
what is the equation
Step-by-step explanation:
Liam bought 2 vintage movie posters, 2 rock posters, and 1 rap poster. He applied a $35 gift card to the total purchase and a 1/2-off coupon to the rap poster. Write and evaluate a numerical expression to show how much Liam paid for the posters.
Vintage Movie: $28.50
B Movie: $18.25
Rock: $29.75
Rap: $19.50
Answer:
the vintage movie posters and the 2 rock posters could be priced the same, $8.
8 x 4 = 32.
the rap poster could be $6, but with the half-off coupon it comes to $3
32 + 3 = 35
assuming the gift card covers the total cost, this reasoning is correct.
Step-by-step explanation:
29+8 = 8 +29 is = 4+2 or 4 x 2
Answer: it 5 cuh
Step-by-step explanation:
Which number line best shows how to solve -4- (-8)
Answer:
A
Step-by-step explanation:
For this specific question its B but If you get another order of answers its is the on that goes down to -4 then gets 8 units higher leaving it at 4.
how does the graph of y=|x|+ 4 compare to the graph of the parent function y=|x|?
Answer:
Please check the explanation and attached graph.
Step-by-step explanation:
Given the parent function
y = |x|
In order to translate the absolute function y = |x| vertically, we can use the function
g(x) = f(x) + h
when h > 0, the graph of g(x) translated h units up.
Given that the image function
y=|x|+4
It is clear that h = 4. Since 4 > 0, thus the graph y=|x|+4 translated '4' units up.
The graph of both parent and translated function is attache below.
In the graph,
The blue line represents the parent function y=|x|.
The red line represents the image function y=|x| + 4.
It is clear from the graph that the y=|x| + 4 translated '4' units up.
Please check the attached graph.
Which expression is equivalent-3(6x+7)+4(7x+2)
Answer: are there choices?
Step-by-step explanation:
In the liner equation shown which variable represent the output values
Y=
MX + b
Answer:
b=−mx+y
Step-by-step explanation:
I doesn’t really make sense to me need some help
Answer: x= 15
Step-by-step explanation: So to prove these two lines A and B are congruent the angles must line up which mean rules of complimentary, Supplementary and alternating angles apply. For angles 2 and 4 due to our alternating angles rule they add up to equal 180 so in math
2x+10+4x+80 = 180 or 6x+90=180 where x = 15
on the first day of your garage sale, you earn 12x+9 dollars. The next day you earn 22x dollars. Is it possible that you earned the same amount each day? Explain.
Set the two expressions equal to one another and solve for x
22x = 12x+9
22x-12x = 9
10x = 9
x = 9/10
x = 0.9
Assuming x is the number of items sold, then it is not possible to have the same amount earned for the two days. This is because we cannot sell 0.9 of an item. So it appears it is not possible to earn the same amount each day.
I Only need to do questions 22 and 24
20/12=15/x find x plz help
Answer:
[tex]x = 9[/tex]
Step-by-step explanation:
To find x, we first have to solve the equation given in the question:
[tex]\frac{20}{12} = \frac{15}{x}[/tex]
[tex]20x = 15 \cdot 12[/tex]
[tex]x = \frac{180}{20}[/tex]
[tex]x = 9[/tex]
Therefore, x = 9.
Hope this helped!
Answer:
x=9
Step-by-step explanation:
We have: [tex]\frac{20}{12}[/tex]=[tex]\frac{15}{x}[/tex]
First, we can simplify 20/12 by 4
[tex]\frac{5}{3}[/tex]=[tex]\frac{15}{x}[/tex]
this is a proportion, so we can cross multiply (multiply 5 by x and 3 by 15)
5x=45
divide by 5
x=9
Hope this helps!
Find the number z, if 1 4/11 of z is 45. pls help!
Answer:
z = 33
Step-by-step explanation:
[tex]1 \frac{4}{11} \times z = 45 \\ \\ \frac{1 \times 11 + 4}{11} \times z = 45 \\ \\\frac{11 + 4}{11} \times z = 45 \\ \\\frac{15}{11} \times z = 45\\ \\z = \cancel{ 45} \: \: \red{ \bold{3}} \times \frac{11}{ \cancel{15}} \\ \\ z = 3 \times 11 \\ \\ z = 33[/tex]
Find the highest common factor (HCF) of 90 and 48.
Answer:
The answer is 6
Step-by-step explanation:
The highest common factor between the numbers is 6.
What is the greatest common factor?The greatest common factor is the largest positive number which can be divided into given numbers evenly.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the two numbers are 90 and 48. The highest common factor will be calculated as,
90 = 2 x 3 x 3 x 5
48= 2x2x2x2x3
The common numbers are 2 x 3 = 6
Therefore, the highest common factor between the numbers is 6.
To know more about the greatest common factor follow
https://brainly.com/question/219464
#SPJ2
What is the sum of −6
−6
and its opposite?
A. −12
−12
B. −6
−6
C. 0
D. 6
6
Answer:a
Step-by-step explanation:
PLEASE HELP ME ASAP!! ILL GIVE YOU POINTS AND BRAINLIEST IF YOU ANSWER ALL 3 TRUE OR FALSE QUESTIONS CORRECTLY.
A) Slope=8 True or False?
B) Unit Rate= $8/hour True or False?
C) The equation of this relationship is y= 1/8x True or False?
Answer:
True, True, False.
Step-by-step explanation:
A) Rise/Run is 8/1
B) 8 dollars are earned every hour
C) Correct equation is y=8x
find the value of angle x
pls answer
Answer:
110
Step-by-step explanation:
lets assume y is the angle next to x which should complete to form a 360.
50 + 25 + 35 + y = 360
y = 250
x + y = 360
x + 250 = 360
x = 110
Answer:
110
Step-by-step explanation:
lets assume y is the angle next to x which should complete to from a 360.
50 + 25 + 35 + y = 360
y = 250
x + y = 360
x + 250 = 360
x = 110
Henri brought a swim suit at a cost of $8. Which statements are true regarding the cost of the suit? Select three options.
If the selling price is marked up by 25 percent, the new price will be $10.
If the selling price is marked up by 40 percent, the new price will be $7.50.
If the selling price is marked up by 55 percent, the new price will be $5.50.
If the selling price is marked up by 70 percent, the new price will be $13.60.
If the selling price is marked up by 75 percent, the new price will be $14.
Answer:
the first forth and fifth answers are correct.
Step-by-step explanation:
8 times 1.25 = 10
8 time 1.70 = 13.60
8 times 1.75 = 14
A water bottle cost $9.45. Sales tax is 7%. What is the total cost?
Answer:
$10.11
Step-by-step explanation:
Answer:
10.11
Step-by-step explanation:
7% of 9.45 is 0.66, and 9.45 + 0.66 = 10.11, so the answer is 10.11