The perimeter of the isosceles triangle will be P(x) = x√2 + 2x.
A polygon with three sides is known as a triangle. The angles of a triangle add up to form 180° and the sum of all sides of a triangle is known as the perimeter. In an isosceles triangle, the two sides are equal and their opposite angle too. In an isosceles triangle, the hypotenuse side of the triangle can be written as h(x) = x√2. The combined length comes out to be L(x) = 2x. Using this information the perimeter of the triangle comes out to be,
P(x) = h(x) + L(x).
P(x) = x√2 + 2x
Hence the perimeter of the triangle comes out to be P(x) = x√2 + 2x
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a box with an open top and a square base is to be constructed to contain 4000 cubic inches. find the dimension that will require the minimum amount of material to construct the box.
The dimension of the box will be (40 inch × 40 inch × 10 inch).
How to determine the maximum and minimum values of an expression using differentiation?
Any given expression can have both minimum and maximum outcomes for any number in a real world scenario, which can be determined using differentiation; first order differentiation when equated to zero reveals the value that will solute to produce the maximum or minimum and then the upon differentiating the obtained expression again and then substituting the variable in acceptable positions, if the outcome is a positive number then the obtained number in first differentiation suggests a minimum value of the given expression.
Given, the volume of the box described = 4000 inch³
Let the dimension of the base of the box be = 'a' inch × 'a' inch = a² inch²
Therefore, height of the box = (4000 inch³)/(a² inch²) = (4000/a²) inch
Total surface area of the described box = S = a² + [4a×(4000/a²)]
= [a² + 16000/a] inch
For the limiting values of S, dS/da = 0 ⇒ d[a² + 16000/a]/da = 0
⇒ 2a - [16000/a²] = 0 ⇒ 2a = 16000/a² ⇒ a³ = 8000 ⇒ a = ∛8000 = 20
Therefore, the value of a is 20 inch.
Thus, height of the box = 4000/a² = 4000/400 = 10 inch
For S to have the minimum limited value, d²S/da² > 0 for a = 20 inch, which is satisfied by the available value of S.
∴ The minimal surface area = a² + 16000/a = 400 + (16000/400)
= 440 inch²
We are aware that the least amount of material will be needed to build the box when its overall surface area is the smallest.
Thus, to minimize the amount of material in consideration, the dimension of the box will be (40 inch × 40 inch × 10 inch).
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Owners of a recreation area are filling a small pond with water. They are adding water at a rate of 25 liters per minute. There are 700 liters in the pond to start.
Let W represent the amount of water in the pond (in liters), and let T represent the number of minutes that water has been added. Write an equation relating W to T, and then graph your equation using the axes below.
An equation relating W to T is given by W = 700 + 25T. Also, a graph of this linear equation is shown in the image attached below.
How to write an equation relating W to T?In order to write an equation relating W to T, we would define the variables that represents the amount of water in the pond (in liters) and the number of minutes this water has been added as follows:
Let the variable W represent the amount of water in the pond (in liters).Let the variable T represent the number of minutes that water has been added.The initial volume of water is given by:
700
The volume of water added to this pool would be given by:
25T
Therefore, the total volume of water added to this pool is given by:
W = 700 + 25T
Next, we would determine the points for the graph of this equation:
At T = 0, we have:
W = 700 + 25(0)
W = 700 ⇒ (0, 700)
At T = 1, we have:
W = 700 + 25(1)
W = 725 ⇒ (1, 725)
At T = 2, we have:
W = 700 + 25(2)
W = 750 ⇒ (2, 750)
At T = 3, we have:
W = 700 + 25(3)
W = 775 ⇒ (3, 775)
At T = 4, we have:
W = 700 + 25(4)
W = 800 ⇒ (4, 800)
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Evaluate the expression when g = 4 and h = 6.
h+7g
a sum of money was shareed between aziz and ahmad in the ratio of 4:7. aziz reeceived 21 dollars less than ahmad. find the total sum of money shareed by both of them
The total sum of money is 77 dollars .
Let the total sum of money be x .
⇒ Aziz's share = 4x / 11
Ahmad's share = 7x / 11
Given : Aziz received 21 dollars less than Ahmad
⇒ 4x / 11 = ( 7x / 11 ) - 21
Solving the above linear equation in one variable ,
( 7x - 4x ) / 11 = 21 ( taking like terms together )
3x = 21 * 11
x = 7 * 11
x = 77
Aziz's share = ( 4 / 11 ) * 77 = 28
Ahmad's share = ( 7 / 11 ) * 77 = 49
Total Sum of money = 28 + 49 = 77 dollars .
Hence , the total sum of money = 77 dollars .
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you are about to roll 2 fair six-sided dice, hoping to get a double. (a double is when both dice show the same value on top). which double will occur the least often?
you are about to roll 2 fair six-sided dice, hoping to get a double. (a double is when both dice show the same value on top). Each double will occur once with the probability of 1/36
The sample space for the event of rolling 2 fair six-sided dice is :
S={ (1, 1),(1, 2),(1,3),(1,4),(1,5),(1,6),(2,1)........., (6,5),(6,6) } , So in total for the outcome, we get a total of 36 pairs, with the probability of getting an event as 1/36, now the situation given to us is the vent of getting a double.So the event space for getting a double while rolling 2 dice is E = { (1, 1),(2, 2),(3,3),(4,4),(5,5),(6,6) } , the outcome will be 6 pairs, so the probability for each double pair to come out when we roll the 2 dice is: 1/36 and the probability of getting the least double from the 6 pairs of double is: 1/6
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Line g has an equation of y= 1 3 x–1. Parallel to line g is line h, which passes through the point (10,2). What is the equation of line h?
need answer ASAP
find the domain and range of the function !! NEED NOW
Answer:
Domain = { -2 , 0 , 2 , 4 }
Range = { 3 }
Step-by-step explanation:
Domain is the x-values that the Function have and Range is the y-values that the Function have corresponding to these x-values
Since the x-values for the Function attached are -2 , 0 , 2 , 4
and the y-values for the Function is 3
Then the Domain = { -2 , 0 , 2 , 4 }
and the Range = { 3 }
Glad to Help
50 POINTS!! NEED HELP
Drag each label to the correct location on the image.
Identify which equations have one solution, infinitely many solutions, or no solution.
Answer:
the label are marked by numbers
Find the slope (rate of change) of a line that passes through (-2,-3) and (1, 1).
We have coordinates (-2, -3) and (1, 1)
To find: Slope of a line that passes through these two coordinates
Let (-2, -3) be (x₁ , y₁) and (1, 1) be (x₂, y₂)
We will use the formula of Slope :
m = y₂ - y₁ / x₂ - x₁
Where 'm' stands for slope
m = 1 - (-3) / 1 - (-2)
m = 1 + 3 / 1 + 2
m = 4 / 3
The slope of the line is 4/3
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Given that £1 = $1.62
how much is $405 in £
Answer:
£250
Step-by-step explanation:
Divide $405 by $1.62 which is 250.
Multiply that by £1 which is £250.
sin(2x)cos(7x) - cos(2x)sin(7x)= -0.1
Answer:
sin(2x)cos(7x) - cos(2x)sin(7x)= -0.1
(2x-5)(x+2) write the area as a product and a sum
Answer:
2x^2 -x -10 is the answer as a product
3x-3 as a sum
Step-by-step explanation:
Assuming (2x-5)(x+2)=0
Let's distribute.
(2x^2+4x)(-5x-10)=0
Then combine like terms
2x^2 -x -10 is the answer as a product
3x-3 as a sum
Which expression shows the distance you would travel from the gym to your science class in this hallway?
The expression that shows the distance you would drive from the gym to the office along this road is b.|-6|+|4|
What is a Distance ?Distance is a numerical or qualitative measurement of the distance between two objects or points. Distance is defined as an object's total movement without regard for direction. The distance can be defined as how much ground an object has covered regardless of its starting or ending point.
To find the distance between two points in a number line we do the absolute value of the points subtracted. That is if we need to find the distance between point a and point b in a number line we do |a-b|.
Now, the Gym is at point -6 in the number line and the office is at point 4 in the number line, then the distance from -6 to 4 is |-6-4| = |-10| = 10.
Now, option a is |-6+4| ≠ |-6-4|.
The option b is |-6|+|4| = 6+4 = 10 =|-6-4|. Then, option b is correct.
Option c is -6+4 ≠ |-6-4|.
The option d is -|6|+|4| = -6+4 ≠ |-6-4|.
Then, the correct answer is b.
The complete question is given below.
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Complete question
Which expression shows the distance you would drive from the gym to the office along this road?
a.|-6 + 4|
b.|-6|+|4|
c.-6+4
d.-|6|+|4|
there are more than 200 pages but fewer than 800 in my book. all thre digits of my number are the same. the number is divisible by 9. how many pages sre in my book
Answer:777
Step-by-step explanation: I do not care
There are 333 pages are in my book.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
There are more than 200 pages but fewer than 800 in my book.
And, All the digits of my number are the same and the number is divisible by 9.
Now,
Let a number with three same digit = xxx
So, We get;
200 < xxx < 800
Since, the number is divisible by 9.
So, By the rule of the number divide by 9, we get;
x + x + x = 9k
3x = 9k
for k = 1;
x = 3
Thus, Number of pages = 333
Therefore,
There are 333 pages are in my book.
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Use either long division or synthetic division to solve:
(2i^4 +-6i³+-25i² +31i+-30)/(i +-5)
Answer:
[tex]\textsf{Quotient}: \quad 2i^3+4i^2-5i+6[/tex]
[tex]\textsf{Simplified Quotient}: \quad 2-7i[/tex]
Step-by-step explanation:
Long division method
Divide the first term of the dividend by the first term of the divisor, and put that in the answer.Multiply the divisor by that answer, put that below the dividend.Subtract to create a new dividend.Repeat.Given rational expression:
[tex]\dfrac{2i^4-6i^3-25i^2 +31i-30}{i -5}[/tex]
Solve using long division:
[tex]\large \begin{array}{r}2i^3+4i^2-5i+6\phantom{)}\\i-5{\overline{\smash{\big)}\,2i^4-6i^3-25i^2 +31i-30\phantom{)}}}\\{-~\phantom{(}\underline{(2i^4-10i^3)\phantom{-b00000000000.)}}\\4i^3-25i^2+31i-30\phantom{)}\\-~\phantom{()}\underline{(4i^3-20i^2)\phantom{))))))))))))}}\\-5i^2+31i-30\phantom{)}\\-~\phantom{()}\underline{(-5i^2+25i)\phantom{........}}\\6i-30\phantom{)}\\-~\phantom{()}\underline{(6i-30)\phantom{}}\\0\phantom{)}\end{array}[/tex]
Therefore, the quotient is:
[tex]2i^3+4i^2-5i+6[/tex]
Imaginary number rule
[tex]i^2=-1[/tex]
Simplify the quotient:
[tex]\implies 2i^3+4i^2-5i+6[/tex]
[tex]\implies 2i^3+4(-1)-5i+6[/tex]
[tex]\implies 2i^3-4-5i+6[/tex]
[tex]\implies 2i^3-5i-4+6[/tex]
[tex]\implies i(2i^2-5)+2[/tex]
[tex]\implies i(2(-1)-5)+2[/tex]
[tex]\implies-7i+2[/tex]
[tex]\implies 2-7i[/tex]
which of the following is part of the solution of the system?
y-x<=-5, y-2x>-5
a) (0,1)
b) (-1,-6)
Answer:
Neither of them are solutions unless you had a typo in the question.
Step-by-step explanation:
1) plug in the known values into both of the equations
First Coordinate:
y-x[tex]\leq[/tex]-5
(1)-(0)[tex]\leq[/tex]-5
1[tex]\leq[/tex]-5 which is not true.
In this case, we do not need to plug in (0,1) into both of the equations because the coordinate cannot be a solution unless the coordinate works in BOTH of the equations.
Second Coordinate:
1) y-x[tex]\leq[/tex]-5
(-6)-(-1)[tex]\leq[/tex]-5
(-6)+1[tex]\leq[/tex]-5 --> It becomes a +1 because two negatives make a positive
-5 [tex]\leq[/tex]-5 - -> which means this is true because -5 is less than or equal to -5
2) y-2x>-5
(-6)-2(-1)>-5
-6(2)>-5
-12>-5 NOT TRUE
ANSWER: Neither of them are solutions unless you had a typo in the question.
Express 2x=3y-7 in the form of ax+by+c=0 write the values
The final answer of the given quadratic equation is 2x - 3y + 7= 0.
What is the quadratic equation?
Any equation in algebra that can be written in standard form as where x is an unknown and a, b, and c denote known numbers, where a 0 is a quadratic equation.
We have,
2x = 3y - 7
Converting the given equation in the form of ax + by + c = 0, we get
2x - 3y + 7= 0
Hence, the final answer of the quadratic equation is 2x - 3y + 7= 0.
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a federal report indicated that 13% of children under age 6 live in poverty in massachusetts, an increase over previous years. how large a sample is needed to estimate the true proportion of children under age 6 living in poverty in massachusetts within 2% with 99% confidence? round the intermediate calculations to three decimal places and round up your final answer to the next whole number.
Using the concepts of statistics, we got that 2004 is the sample size needed to estimate the true proportion of children under age 6 living in poverty in Massachusetts within 2% with 99% confidence.
The number of observations used to calculate estimates for the certain population is known as the sample size. The sample size was actually determined by drawing from the population. Sampling is a practice of choosing a portion of a population from which to draw conclusions about the characteristics of a entire population. A subset of the population is chosen for analysis based on the number of entities in it.
We have Margin of error(E)=0.02,
Significance level([tex]\alpha[/tex])=0.01
Proportion(p)=0.13
Therefore, q is defined by =1-p
=> q =1-0.13
=>q=0.87
So, the Z-score is 2.582
Now, we know that sample size(S) is given by
=>S =[ [ [Z²×p×(1-p)] / e²] / [1+(Z²×p×(1-p)/e²)] ]
=>S=[ [ ( 2.582)²×0.13×0.87/(0.02)²] / [1 + [(2.582)²×0.13×0.87] / (0.02)²]
=>S= ([0.754/0.0004] / [1+(0.754/0.0004)])×1000
=>S=([885.01] / [1+1885.01]) × 1000
=>S=(0.200351)×1000
=>S=2003.51=2004 (approx)
Hence, a federal report indicated that 13% of children under age 6 live in poverty in Massachusetts, an increase over previous years in that case size of sample which is needed to estimate the true proportion of children under age 6 living in poverty in Massachusetts within 2% with 99% confidence is 2004.
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The length and width of a rectangle are consecutive integers. The perimeter of the
rectangle is 54 centimeters. Find the length and width of the rectangle.
Answer:
length = 13 cm , width = 14 cm
Step-by-step explanation:
let the length be n , then the width is n + 1
the perimeter (P) of a rectangle is calculated as
P = 2(l + w) ← l is the length and w the width
given P = 54 , then
2(n + n + 1) = 54 ( divide both sides by 2 )
2n + 1 = 27 ( subtract 1 from both sides )
2n = 26 ( divide both sides by 2 )
n = 13
n + 1 = 13 + 1 = 14
so, length = 13 cm and width = 14 cm
There are 185 marbles in a bag. 40% of the marbles are blue and the rest are of other colours.
a. Find the percentage of marbles that are not blue.
b. Find the number of marbles that are not blue
Step-by-step explanation:
There are 185 marbles in a bag. 40% of the marbles are blue and the rest are of other colours.
a. Find the percentage of marbles that are not blue.
100% - 40% = 60%
b. Find the number of marbles that are not blue.
60% = 0.6
0.6 * 185 = 111 marbles
How many terms are in the given expression?5x - 2
The number of terms in the expression 5x - 2 is 2
What is number of terms in a mathematical expression ?The number of terms in an expression or equation refers to the values separated by a mathematical operator. A mathematical operator could be
AdditionSubtractionMultiplicationDivision and so onThe terms can be like terms or unlike terms
The two terms given is separated by the subtraction operator and are both unlike terms
The first term 5x consist of
coefficient = 5variable = xThe second term is just a constant which is 2
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Mikaela purchased a paddleboard originally priced at $899. If all merchandise was on sale for 40% off and the state tax rate is 7.25%, what is the total amount
that Mikaela spent on the paddleboard?
Total amount that Mikaela spent on the paddleboard is 578.5065.
How to calculate total amount spent on the paddleboard?According to given data,
original price = 899$ and 40% off.
state tax rate is 7.25%.
Solution:-
Applying formula,
⇒ 899 × (7.25% + 1) × (1 - 40%)
⇒ 899 × 1.0725 × 0.6
⇒ 578.5065.
Total amount that Mikaela spent on the paddleboard is 578.5065.
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If someone could please answer all 3 points (20 points)
The missing parts of the table for the function are 49, 1 and 49 respectively
How to complete the missing parts of the table?
An exponential function is a type of function which involves exponents. A simple exponential function is of the form y = bˣ
Given: the exponential function y = (1/7)ˣ
In order to find the missing parts, we have to substitute the relevant values into the function. Thus:
For x = -2:
y = (1/7)ˣ
Substitute x = -2 into the function:
y = (1/7)⁻² = 49
For x = 0:
y = (1/7)ˣ
Substitute x = 0 into the function:
y = (1/7)⁰ = 1
For x = 2:
y = (1/7)ˣ
Substitute x = 2 into the function:
y = (1/7)² = 1/49
The missing part is 49
Therefore, the missing parts of the table are 49, 1 and 49 respectively
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Factorise completely:
Answer:
2xy(8x + 5)
Step-by-step explanation:
16x²y + 10xy ← factor out 2xy from each term
= 2xy(8x + 5)
on a map, 3/4 inch corresponds to an actual distance of 4 miles. how many square miles of actual area does a 3.5-inches-by-10-inches region of the map represent?
The actual area represented by 3.5-inches-by-10-inches on map is 995.5 miles.
As the measure of 3/4 inch is provided, working out the calculation for 1 inch.
3/4 inch = 4 miles
1 inch = (4×4)/3
1 inch = 16/3
1 inch = 5.33 miles
Now, the actual area of the region = 3.5 × 10
The actual area of the region = 35 inches²
Converting the area in square miles
The actual area of the region = 35 × (5.33)²
Taking square on Right Hand Side of the equation
The actual area of the region = 35 × 28.4
Performing multiplication on Right Hand Side of the equation
The actual area of the region = 995.5 square miles
Thus, the actual area of the region is 995.5 square miles.
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The triangles shown below must be congruent.
A. True
• B. False
Answer:
true
Step-by-step explanation:
Answer:
True
Step-by-step explanation:
Omar compro 3.5k de cebolla a 8.90 el kilo. Cuanto pago por las cebollas
The amount that Omar will pay when he bought 3.5k of onions are 8.90 per kilo is $31.15.
What is money?From the information given, Omah wants to know the total amount that he will pay for the onions. It's important to know the cost for each kilogram of onion and then multiply it but the number of kilograms that are bought.
In this case, Omar bought 3.5k of onions are 8.90 per kilo.
The amount that Omar will pay for the onions will be:
= Number of kilograms × Cost per kg
= 3.5 × 8.90
= $31.15
In conclusion, the amount is $31.15.
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hi please help me..this is a multiple choice
Answer:
Step-by-step explanation:
A and D are the answers that I would pick
Answer:
B and C
Step-by-step explanation:
- 1 / -3 = 1/3, we know negative divide by a negative number = positive
- -1/3 = 1/3, we know negative times negative = positive
Write a linear function f with the values ƒ (0) = -3 and ƒ (7) = 11.
The linear function with f values f(0) = -3 and f(7) = 11 is f(x) = 2x - 3
What is a Linear Function?linear function is defined as a function that has either one or two variables without exponents. It is a function that graphs to the straight line. In case, if the function contains more variables, then the variables should be constant, or it might be the known variables for the function to remain it in the same linear function condition.
if f(0) = -3, it means at x = 0, f(x) = -3
and if f(7) = 11, it means at x = 7, f(x) = 11
So the Linear equation that will yield these results is f(x) = 2x - 3
In conclusion, the Linear function is f(x) = 2x - 3
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Graph the points of the given function with the x-values x=−4 , x = 0, and x = 5. f(x)=−2x+4−−−−√
The graph is attached and the table of value of the graph is as follows
x y
-4 12
0 4
5 -6
How to get the table of valuesThe function y = −2x + 4 is a linear function and will have a straight line graph
The table of values is gotten form the equation y = −2x + 4
solving for x = -4,
y = −2 * -4 + 4 = 12
solving for x = 0
y = −2 * 0 + 4 = 4
solving for x = 5,
y = −2 * 5 + 4 = -6
x y
-4 12
0 4
5 -6
The graph is plotted by finding the points in the table in the Cartesian plane and joining the points together
Other values are solved for in similar step
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Answer:Here is your answer
Step-by-step explanation: