Answers
Solution
- The coordinates of the points read from the graph given are:
A=(-2,3)
B=(0,6)
C=(5,4)
D=(3,-1)
E=(-1,-2)
- To find the perimeter, we can use the distance between two points formula to find the lengths of each side of the polygon after which we add them up.
- Thus, we have:
\(\begin{gathered} D=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}\text{ \lparen Distance between two points\rparen} \\ \\ AB=\sqrt{(6-3)^2+(0--2)^2} \\ AB=\sqrt{9+4}=\sqrt{13} \\ \\ BC=\sqrt{(6-4)^2+(0-5)^2} \\ BC=\sqrt{4+25}=\sqrt{29} \\ \\ CD=\sqrt{(4--1)^2+(5-3)^2} \\ CD=\sqrt{25+4}=\sqrt{29} \\ \\ DE=\sqrt{(-2--1)^2+(-1-3)^2} \\ DE=\sqrt{1+16}=\sqrt{17} \\ \\ AE=\sqrt{(3--2)^2+(-2--1)^2} \\ AE=\sqrt{25+1}=\sqrt{26} \end{gathered}\)- Thus, the Perimeter is
\(\begin{gathered} P=AB+BC+CD+DE+AE \\ P=\sqrt{13}+\sqrt{29}+\sqrt{29}+\sqrt{17}+\sqrt{26} \\ P=23.598006...\approx24units \end{gathered}\)- Thus the best approximation is 24.3 units (OPTION B)
Related Questions
Help me, please? I dont understand these
Answers
Choose 2 coordinates and pick one of the y values to subtract by the other and the same x value correlated with ur first y value u subtracted minus the other x value
The binomial (y-2) is a factor of y2 - 10y + 16. What is the other factor?
(-5)
(y + 5)
(y - 8)
(y + 8)
Answers
Answer:
(y-8)
Step-by-step explanation:
the other factor =
(y²-10y+16)/(y-2) =
(y-8) (y-2) /(y-2) =
eliminate (y-2),
we have (y-8)
The other factor of the given expression is y -8
Factors of a quadratic equationQuadratic equations are equations that has a leading degree of 2. Given the equation below
y^2 - 10y + 16.
Factorize
y^2 - 8y - 2y + 16
y(y-8) - 2(y - 8)
Group
(y-2)(y-8)
Hence the other factor of the given expression is y -8
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The radius of the base of a cylinder is expanding at a constant rate of 3 mm/min. If the height of
the cylinder is a constant 20 mm, find the rate at which the VOLUME of the cylinder is changing at the
moment when the radius of the base of the cylinder is 10 mm. Also find the rate at which the SURFACE
AREA of the cylinder is changing at this same moment.
(V = r²h, SA=2лrh+2rr²)
I’m getting 1800pi mm^3/min for volume and 360pi mm^2/min for surface area but I’m not sure if it’s correct
Answers
The rate at which the volume of the cylinder is changing is 600 mm^3/min, and the rate at which the surface area is changing is 240π mm^2/min.
To find the rate at which the volume and surface area of the cylinder are changing, we can use the given formulas for volume and surface area and differentiate them with respect to time. Let's calculate the rates at the moment when the radius of the base is 10 mm.
Given:
Radius rate of change: dr/dt = 3 mm/min
Height: h = 20 mm
Radius: r = 10 mm
Volume of the cylinder (V) = \(r^2h\)
Differentiating with respect to time (t), we have:
dV/dt = 2rh(dr/dt) + \(r^2\)(dh/dt)
Since the height of the cylinder is constant, dh/dt = 0.
Substituting the given values:
dV/dt = 2(10)(20)(3) + (10^2)(0)
dV/dt = 600 + 0
dV/dt = 600 mm^3/min
Therefore, the rate at which the volume of the cylinder is changing at the given moment is 600 mm^3/min.
Surface area of the cylinder (SA) = 2πrh + 2π\(r^2\)
Differentiating with respect to time (t), we have:
dSA/dt = 2πr(dh/dt) + 2πh(dr/dt) + 4πr(dr/dt)
Again, since the height of the cylinder is constant, dh/dt = 0.
Substituting the given values:
dSA/dt = 2π(10)(0) + 2π(20)(3) + 4π(10)(3)
dSA/dt = 0 + 120π + 120π
dSA/dt = 240π mm^2/min
Therefore, the rate at which the surface area of the cylinder is changing at the given moment is 240π mm^2/min.
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x squared plus 2x factorised
Answers
Answer:
x(x+2)
Step-by-step explanation:
Answer x(x+2)
Step-by-step explanation:
Question 7
Jorge earned 91, 84, 87 on his first three out of four Algebra tests. He wants to get an
average of 90 in the class. What should he make on his last test to achieve this goal?
Answers
To earn an average score of 90, the score on the fourth test needs to be 98.
What is average?The core value of a set of data is expressed mathematically as the average of a list of data. It is defined mathematically as the ratio between the total number of units in the list and the sum of all the data. The term "mean" in statistics also refers to the average of a particular set of numerical data.
Given the score of the first three tests as:
91, 84, 87.
The average is given by the following formula:
Average = Sum of scores ÷ total number of tests
Let us suppose the score of fourth test as x.
Given that A = 90:
90 = (91 + 84 + 87 + x) ÷ 4
x = 98
Hence, the score on the fourth test must be equal to 98, to get an average score of 90.
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length of a rectangle with a width of 10 and an area of 150 meters
Answers
We know that the area of a rectangle is given by the formula A = l × w, where A is the area, l is the length, and w is the width.
In this case, we are given that the width is 10 meters and the area is 150 square meters. So, we can plug in these values into the formula to find the length:
150 = l × 10
Dividing both sides by 10, we get:
15 = l
Therefore, the length of the rectangle is 15 meters.
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The number line shows four points. Which point represents the approximate location of V12?
A) point A
B). point B
C) point C
D) point D
Answers
Answer:
point A
Step-by-step explanation:
Answer:c
Step-by-step explanation:
please answer this question
Answers
Let p(t) be the number attendees and t be the ticket price measured in units of 10s of rupees. When the price is t = 7 (i.e. Rs70), there were p(7) = 300 people in attendance.
For each unit increase in t (i.e. for each Rs10 increase in price), p(t) is expected to fall by 20, so that
p(t + 1) = p(t) - 20
Solve for p(t). Suppose t ≥ 7. By substitution,
p(t + 1) = (p(t - 1) - 20) - 20 = p(t - 1) - 2×20
p(t + 1) = (p(t - 2) - 20) - 2×20 = p(t - 2) - 3×20
p(t + 1) = (p(t - 3) - 20) - 3×20 = p(t - 3) - 4×20
and so on, down to
p(t + 1) = p(7) - (t - 6)×20 = 420 - 20t
or
p(t) = 420 - 20 (t - 1) = 440 - 20t
With t = price per ticket (Rs/ticket) and p(t) = number of attendees = number of tickets sold, it follows that the income made from ticket sales for some fixed ticket price t would be t×p(t). If one plots p(t) in the coordinate plane, the price that maximizes income and number of attendees is such that the area of a rectangle inscribed by the line p(t) and the coordinate axes is maximized.
Let A(t) be the area of this rectangle, so
A(t) = t p(t) = 440t - 20t²
Without using calculus, complete the square:
A(t) = 440t - 20t² = 2420 - 20 (t - 11)²
This is the equation of a parabola with vertex at (11, 2420), so the optiml ticket price is Rs11, and at this price the drama club can expect an income of Rs2420.
With calculus, differentiate A with respect to t and find the critical points:
A'(t) = 440 - 40t = 0 ⇒ 11 - t = 0 ⇒ t = 11
Differentiate A again and check the sign of the second derivative at this critical point:
A''(t) = -40 ⇒ A''(11) = -40 < 0
which indicates a local maximum at t = 11 of A(11) = 2420.
The population of a herd of deer is represented by the function A(t)=210(1.11)t , where t is given in years. To the nearest whole number, what will the herd population be after 4 years?
Answers
By Compound interest, 318.7947861 will the herd population be after 4 years.
What does compound interest mean ?
When you earn interest on your interest earnings as well as the money you have saved, this is known as compound interest. As an illustration, if you put $1,000 in an account that offers 1% yearly interest, you will receive $10 in interest after a year.
Compound interest allows you to earn 1 percent on $1,010 in Year Two, which equates to $10.10 in interest payments for the year. This is possible because interest is added to the principle in Year Two.
A(t)= \(210(1.11)^{t}\)
after 4 years , t = 4
a(4) = 210 (1.11)⁴
a(4) = 210 * 1.51807041
a(4) = 318.7947861
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what is the slope of the line -3y=12x+6
Answers
Answer:
Step-by-step explanation:
uhh
A market woman purchased a number of plates for GH 150.00. Four of the plates
4
got broken while transporting them to her shop. By selling the remaining plates at a
profitof GH€ 1.00 on each, she made a total profit of GH€ 6.00. How many
plates did she purchase?
Answers
Answer: 160 plates.
Step-by-step explanation:
The woman bought N plates for GH€ 150.00
4 of the plates where broken, so she has N - 4 plates to sell.
She sold each one of the N - 4 plates for GH€ 1, then after all the N- 4 plates were sold, the total money that she has is:
(N - 4)*GH€1 = GH€ (N - 4)
And the total profit (profit is the difference between the final amount of money that she gets, and the initial payment) is GH€ 6, then we have that:
GH€ (N - 4) - GH€ 150.00 = GH€ 6
ignoring the units, we have:
N - 4 - 150 = 6.
N = 6 + 154 = 160.
She bought 160 plates.
How many fluid ounces are there in 2.5 liters?
Using dimensional analysis
Answers
In 2.5 liters we have 84.535 fluid ounces.
(1 liter is equal to 33.814 fluid ounces)
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
We know, 1 liter is equal to 33.814 fluid ounces.
Now, To convert liters to fluid ounces we have multiply the number of liters by the unit value of fluid ounces which is,
= 2.5×33.814 fluid ounces.
= 84.535 fluid ounces.
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Which theorem shows that △ ABC ≅ △ def?
Answers
By the SSS Congruence Theorem, △ABC ≅ △DEF.
What does a math congruent mean?
Congruent refers to having precisely the same form and size. Even after the forms have been flipped, turned, or rotated, the shape and size ought to remain constant.
What is the SSS rule?
According to the SSS rule, two triangles are said to be congruent if all three sides of one triangle are equal to the corresponding three sides of the second triangle.
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con 16 barras de mantequilla se prepararon 20 postres ?que fraccion del total de mantequilla corresponde a cada postre
Answers
De ahí que la fracción de la mantequilla total que corresponde a cada postre sea 1/4
Si con 16 barras de mantequilla se prepararon 20 postres, esto se puede expresar como:
16 pegatinas = 20 postres
Para obtener la fracción del total de mantequilla que corresponde a cada postre, podemos escribir;
x = 1 postre
Divide ambas expresiones
16 / x = 20/1
20 veces = 16 * 1
20x = 16
x = 16/20
x = 4/5
De ahí que la fracción de la mantequilla total que corresponde a cada postre sea 1/4
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graph y+2=2(x+3). What is the x intercept?
x intercept :
Answers
The given equation is y + 2 = 2(x + 3) and the x-intercept is -2.
To find the x-intercept of the equation y + 2 = 2(x + 3), we need to set y equal to zero and solve for x. The x-intercept occurs when the value of y is zero, meaning the graph crosses the x-axis.
Let's substitute y with 0 in the equation:
0 + 2 = 2(x + 3)
Simplifying the equation:
2 = 2(x + 3)
Dividing both sides by 2:
1 = x + 3
Subtracting 3 from both sides:
-2 = x
The x-intercept is -2. This means that the graph of the equation y + 2 = 2(x + 3) crosses the x-axis at the point (-2, 0).
The x-intercept represents the value of x where the graph intersects or crosses the x-axis. In this case, it occurs when x is equal to -2, and the y-value is zero.
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(x+26=y) and (y-12=z) if x+y+z=71 solve for x
Answers
Answer:
\(\mathsf{x = \frac{31}{3}}\)
Step-by-step explanation:
\(\textsf {Given :}\)
\(\implies \mathsf {x + 26 = y}\)
\(\implies \mathsf {y - 12 = z}\)
\(\implies \mathsf{x + y + z = 71}\)
\(\textsf {Substitute for y and z in the 3rd equation :}\)
\(\implies \mathsf {x + x + 26 + y - 12 = 71}\)
\(\implies \mathsf {2x + 14 + x + 26 = 71}\)
\(\implies \mathsf {3x + 40 = 71}\)
\(\implies \mathsf {3x = 31}\)
\(\implies \mathsf {x = \frac{31}{3}}\)
The cost to rent a moving yan for a day is an initial cost of $29 plus $0.35 per mile driven, Find a function to model the cast of the moving van rental
based on the initial cost and miles driven
Answers
Hello!
miles driven = x
the initial cost = 29
f(x) = 29 + 0.35x
Father is 30 years older than his son. If the sum of their ages is 50 years, find their ages.
Answers
The age of father and son is 40 years and 10 years respectively.
What is Algebra?Algebra is the branch of mathematics that helps in the representation of problems or situations in the form of mathematical expressions. It involves variables like x, y, z, and mathematical operations like addition, subtraction, multiplication, and division to form a meaningful mathematical expression. All the branches of mathematics such as trigonometry, calculus, coordinate geometry, involve the use of algebra. One simple example of an expression in algebra is 2x + 4 = 8.
given:
Father is 30 years older than his son.
sum of their ages= 50 years
let the age of son is x
age of father= x+ 30
Now,
x + x + 30= 50
2x = 20
x= 10
hence, age of father is 40 and age of son is 10 years.
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Use the limit definition of the derivative to find the slope of the tangent line to the curve f(x) = 7x ^ 2 + 2x + 3 at x = 1
Answers
Answer:
16
Step-by-step explanation:
Step 1: Write down the function \(f(x)=7x^2+2x+3.\)
Step 2: Write down the limit definition of the derivative:
\(f'(x)= lim_{h0} \frac{f(x+h)=f(x)}{h} .\)
Step 3: Substitute the function \(f(x)\) into the limit definition:
\(f'(x)=lim_{h0} \frac{(7(x+h)^2+2(x+h)+3)-(7x^2+2x+3)}{h}.\)
Step 4: Simplify the expression inside the limit:
\(f'(x)=lim_{h0}\frac{7x^2+14xh+7h^2+2x+2h+3-7x^2-2x-3}{h} .\)
Step 5: Combine like terms:
\(f'(x)=lim_{h0} \frac{14xh+7h^2+2h}{h} .\)
Step 6: Factor out an \(h\) from the numerator:
\(f'(x)=lim_{h0} \frac{h(14x+7h+2h}{h} .\)
Step 7: Cancel out the \(h\) in the numerator and denominator:
\(f'(x)=lim_{h0}(14x+7h+2).\)
Step 8: Evaluate the limit as \(h\) approaches 0:
\(f'(x)=14x+2.\)
Step 9: Substitute \(x=1\) into the derivative:
\(f'(1)=14(1)+2=14+2=16.\)
The Slope of the tangent line to the curve \(f(x)=7x^2+2x+3\) at \(x=1\) would be \(16.\)
Find the equation of a line that passes through the point (2,-5) and is perpendicular to the y-axis. Do not put any spaces in your answer.
Answers
Answer:
y=-5
Step-by-step explanation:
Equation of the line
Lines can be expressed in several forms. The slope-intercept form of the line is:
y = mx + b
Where m is the slope of the line and m is the y-intercept.
If the line is perpendicular to the y-axis, then it's a horizontal line. Horizontal lines have slope m=0, thus, the equation is:
y = b
To find the value of b, just substitute the given point:
-5=b
The equation of the line is:
y=-5
Q6)Define the term 'Molar mass'. State its unit of measurement.
What is a ‘Mole’? Write the value for avogadro’s number
Answers
Answer:
The molar mass of a chemical compound is defined as the ratio between the mass and the amount of substance of any sample of said compound.
unit of measurement: g/mol.
A mole is the amount of substance that contains as many elementary entities as there are atoms in 12g of carbon-12.
Avogadro's number= 6.02*10^23 particles.
Consider the function.
f(x)=2log5(x−2)+1
On what interval is the function positive?
Enter your answer in the box. Round to the nearest hundredth.
Answers
2log5(x−2)+1 > 0
2log5(x−2) > -1
log5(x−2) > -1/2
x - 2 > 5^(-1/2)
x - 2 > 0.4472
x > 2.4472
Therefore, the function is positive when x is greater than 2.4472.
The interval on which the function is positive is (2.45, infinity).
Solve equation
176 =-4(4 + 6m)
Answers
to solve for m
distribute into parentheses
176 = -16 - 24m
get m on one side
176 + 16 = -24m
192 = -24m
divide by -24
-8 = m
m = -8
1. A crash repair bill comes to $1380.00. How much is 10% of
the bill? What is the final bill once 10% is taken off?
2. A person buys a new fan belt, a new alternator, and a new water pump for their car. The total comes to $170.50. What is 20% of the total? How much is the final total once the 20% is taken off?
Answers
Answer:
1. 10% of the bill is $138. The final bill once 10% is taken off is $1242.
2. 20% of the total is $34.10. The final total once the 20% is taken off is $136.4
Step-by-step explanation:
1. A crash repair bill comes to $1380.00. How much is 10% of the bill? What is the final bill once 10% is taken off?
To find how much is 10% of the bill, we multiply the bill by 0.1
0.1*1380 = 138
10% of the bill is $138.
To find the final bill, we subtract the initial bill by 10%.
1380 - 138 = 1242
The final bill once 10% is taken off is $1242.
2. A person buys a new fan belt, a new alternator, and a new water pump for their car. The total comes to $170.50. What is 20% of the total? How much is the final total once the 20% is taken off?
Same logic as above.
0.2*170.50 = 34.1
20% of the total is $34.10.
170.50 - 34.1 = 136.4
The final total once the 20% is taken off is $136.4
A local orchestra is holding a charity concert concert at the community center. Each adult ticket $12, and child ticket costs $8. The organizers of the event hope to raise no less than $2,500, and the community center can seat up to 280 people. This graph and system in inequalities represent this situation, where x represents the number of adult tickets and y represents the number of child tickets. 12x + 8y> 2,500. X + y < 280
Answers
The answer is (180,80)
To solve this problem, we have to plot the graph, using a tool. This question relates to an inequality and graphical method is a reliable approach to solve inequality problem.
InequalityThe given question is an inequality situation where we are asked to use graph to solve.
The data given are
adult ticket = $12child ticket = $8Total amount raised = $2500Total number of people = 280The inequality for this problem is given is as
\(12x + 8y > 2500\\x + y < 280\)
Kindly find the attached image as the graph and solution to this problem.
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i suck with these type of problems please help
Answers
Answer:
Step-by-step explanation:
\(tan \ 64 =\dfrac{opposite \ side}{adjacent \ side}\\\\2.05=\dfrac{x}{11}\\\\2.05*11=x\\\\\\x = 22.55\)
Eduardo buys a sandwich and a drink.
Use mental math to find the amount of
change he gets from $10.00
Answers
Answer:
Eduardo will get $4.03
Step-by-step explanation:
To solve this problem, first add 4.99 and 0.98 together, remember to line up the decimals
4.99
+ 0.98
-------------
5.97
Now take 5.97 from 10.00
first you can't take 7 from 0 so you take 1 from the tens place making 10.00 into 9.9 10, now you can take 7 from 10 which equals 3. Into the tenths place you can take 9 from 9 which is a 0. Lastly 9 - 5 is 4, adding the decimal back you get
10.00
- 05.97
--------------
$ 4.03
What percent of 240 is 132? pls I need it now
Answers
Answer:
55%
Step-by-step explanation:
Answer:
55%
132 is 55% of 240
Step-by-step explanation:
The vertices of figure PQRS are translated to form figure P'Q'R'S'. Select all the statements that describe the two figures. Q S R P' S' Q' 'R
the anawer choices are : A. P Q R S is the preimage of PQRS, B. the two figures are congruent, C. the two figures are in different positions , but have the same orientation, D. the two figures are in different positions and have oppsoite orientation , E. corresponding angles and sides of the figures have the same measures.
Answers
The true statements are:
(B) Both figures are congurent.
(C) The two figures have the same orientation but different positions.
(E) Corresponding angles and sides have the same measures.
What is orientation?In geometry, how an item is positioned in the space it occupies—such as a line, plane, or rigid body—is described in terms of its orientation, angular position, attitude, bearing, and direction.
It refers more particularly to the fictitious rotation required to shift an object from a reference placement to its present location.
To get to the current positioning, a rotation might not be sufficient.
It could be required to include a fictitious translation known as the object's location (or position, or linear position).
Together, the position and orientation completely explain where the object is situated in space.
Therefore, the true statements are:
(B) Both figures are congurent.
(C) The two figures have the same orientation but different positions.
(E) Corresponding angles and sides have the same measures.
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Which expression is equivalent to 2.1 raised to the fifth power divided by 0.9 raised to the fourth power all raised to the third power?
2.33
2.1 raised to the fifteenth power divided by 0.9 raised to the twelfth power
2.1 raised to the eighth power divided by 0.9 raised to the seventh power
2.315
Answers
The expression that is equivalent to 2.1 raised to the fifth power divided by 0.9 raised to the fourth power all raised to the third power is; A: 2.1 raised to the fifteenth power divided by 0.9 raised to the twelfth power
How to solve exponents problems?We want to find the expression that is equivalent to 2.1 raised to the fifth power divided by 0.9 raised to the fourth power all raised to the third power.
This can be written as;
(2.1⁵/0.9⁴)³
Now according to laws of exponents;
(a²)³ = a^(2 * 3) = a^(6)
Thus;
(2.1⁵/0.9⁴)³ = [(2.1)⁵*³]/(0.9)⁴*³
= 2.1¹⁵/0.9¹²
Thus, the expression that is equivalent to 2.1 raised to the fifth power divided by 0.9 raised to the fourth power all raised to the third power is; A: 2.1 raised to the fifteenth power divided by 0.9 raised to the twelfth power
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Answer:
B
Step-by-step explanation: