Answer:
For the pen to be as large as possible, the length the farmer should choose for the third side should be 20.52 feet
Step-by-step explanation:
The length of one side of the right triangle = 14 feet
The length of the other side = 15 feet
Therefore, the length of the third side can be one of the following side lengths;
[tex]S_{3,1} = \sqrt{14^2 + 15^2} = \sqrt{421} = 20.52 \ feet[/tex]
[tex]S_{3,2} = \sqrt{15^2 - 14^2} = \sqrt{29} = 5.39 \ feet[/tex]
The possible lengths of the third side of the triangle are;
Third side = 20.52 feet and
Third side = 5.39 feet
b. For the area of the pen to be as large as possible, we have;
With third side = 20.52 feet, area of the pen = 0.5 × 15 × 14 = 105 ft²
With third side = 5.39 feet, area of the pen = 0.5 × 5.39 × 14 = 37.7 ft²
Therefore, for the pen to be as large as possible, the farmer should choose 20.52 feet as he third side.
Answer:
a. c ≈ 20.5 ft (first possibility)
b ≈ 5.4 ft(other possibility)
b. The farmer should choose the side that has 20.5 ft for the third side because it provide more larger area as needed by the farmer.
Step-by-step explanation:
The pen the farmer wants to build is a right angle triangle. one side of the triangle is 14 ft while another side is 15 ft.
A right angle triangle has opposite side, adjacent side and an hypotenuse which is the longest side.
a. To the nearest tenth of a foot, find all possible lengths for the third side of the triangle.
Pythagoras theorem can be used to solve any sides of the triangle when given 2 sides.
We are not told which side is the hypotenuse or the adjacent or the opposites side. Therefore , the possible length for the third side can be computed using Pythagoras theorem.
c² = a² + b²
c = hypotenuse
while a and b can be any of opposite or adjacent sides. The first possible length can be when both sides are the legs of the triangle (no hypotenuse)
c² = 14² + 15²
c² = 196 + 225
c² = 421
c= √421
c = 20.5182845287
c ≈ 20.5 ft (first possibility)
The other possibility of the third side is when the hypotenuse is Known and one other side(either adjacent or opposite). We can use only 15 since it should be the longest side.
c² = a² + b²
c² - a² = b²
15² - 14² = b²
225 - 196 = b²
b² = 29
b = √29
b = 5.38516480713
b ≈ 5.4 ft(other possibility)
b. The farmer wants the area of the pen to be as large as possible. What length should he choose for the third side? Justify your answer.
The two scenarios are as follows
First area
area = 1/2 × base × height
area = 1/2 × 14 × 15 = 210/2 = 105 ft²
Second area
area = 1/2 × base × height
area = 1/2 × 5.4 × 14 = 75.6/2 = 37.8 ft²
The farmer should choose the side that has 20.5 ft for the third side because it provide more larger area as needed by the farmer.
Solve the following system. x squared / 25 + y squared / 100 = 1 x squared + y squared = 25
Answer :
[tex] \frac{1}{100} (4 {x}^{2} + {y}^{2} )[/tex] [tex] \frac{dy}{dx} = \frac{ - x}{y} [/tex]y is equal to the product of 3 and x divided by 9; x = -6 What is the output?
Answer:
Out put would be - 2
Step-by-step explanation:
[tex]y = 3x \div 9 \\ y = \frac{3x}{9} \\ y = \frac{x}{3} \\ plug \: x = - 6 \\ y = \frac{ - 6}{3} \\ \huge \purple{ \boxed{ y = - 2}}[/tex]
sum interior of polygon help!
Answer:
180
Step-by-step explanation:
Kite ABCD is translated (x − 2, y + 3) and then rotated 90° about the origin in the counterclockwise direction. Complete the table to show the locations of A″, B″, C″, and D″ after both transformations. I need help
Answer:
A' (-4, - 7), B' (-5, -4), C' (-4, -3), D' (-3, -4)
Step-by-step explanation:
Rule of rotation about the origin at an angle of 90° in the counterclockwise direction:
The stated value of (x, y) after performing the translation are switched or interchanged, with x used as the y coordinate value and the negative value of y used as the x coordinate value. That is ;
(x, y) - - - -> (-y, x)
Solving the problem above:
Applying translation: (x-2, y+3), then rotating about the origin at 90° in the counterclockwise direction.
A =(-5, 1) = (-5 - 2, 1 + 3) = (-7, 4)
(-7, 4) - - -> A' = (-4, - 7)
B =(-2, 2) = (-2 - 2, 2 + 3) =(-4, 5)
(-4, 5)- - -> B' = (-5, -4)
C =(-1, 1) = (-1 - 2, 1 + 3) = (-3, 4)
(-3, 4) - - -> C' = (-4, -3)
D =(-2, 0) = (-2 - 2, 0+3) =(-4, 3)
(-4, 3)- - -> D' = (-3, -4)
Answer:
the other guy is correct.
Step-by-step explanation:
Point S(6,-2) is translated 3 units left.What would be the coordinates of the resulting point,S’?
Answer:
S'(3,-2)
Step-by-step explanation:
I need help I keep getting it wrong
Find the area of the triangle and multiply by the length of the prism.
Area = 1/2 x 8x3 = 12 square yds.
Volume = 12 x 6 = 72 cubic yards.
Se sabe que el 20% de todas las personas a quienes se administra cierto medicamento se siente muy mal en 2 minutos; encuentra la probabilidad de que entre 14 personas a las que se les administra este medicamento: a) A lo sumo 2 se sientan muy mal en dos minutos b) Por lo menos 5 se sientan muy mal en dos minutos c) De 2 a 4 se sientan muy mal en dos minutos
Answer:
a) 0.4481
b) 0.1298
c) 0.6722
Step-by-step explanation:
English Translation
It is known that 20% of all people given a certain medicine feel very bad in 2 minutes; Find the probability that among 14 people who are given this medicine:
a) At most 2 feel very bad in two minutes
b) At least 5 feel very bad in two minutes
c) From 2 to 4 they feel very bad in two minutes
Solution
This is a binomial distribution problem
A binomial experiment is one in which the probability of success doesn't change with every run or number of trials.
It usually consists of a number of runs/trials with only two possible outcomes, a success or a failure.
The outcome of each trial/run of a binomial experiment is independent of one another.
Binomial distribution function is represented by
P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ
n = total number of sample spaces = 14
x = Number of successes required
p = probability of success = probability of feeling bad after taking the medicine = 20% = 0.20
q = probability of failure = probability of NOT feeling bad after taking the medicine = 1 - 0.20 = 0.80
a) At most 2 feel very bad in two minutes
P(X ≤ 2) = P(X=0) + P(X=1) + P(X=2)
= 0.04398046511 + 0.15393162789 + 0.25013889532 = 0.44805098832 = 0.4481
b) At least 5 feel very bad in two minutes
P(X ≥ 5) = 1 - P(X < 5) = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4)]
= 1 - [0.04398046511 + 0.15393162789 + 0.25013889532 + 0.25013889532 + 0.17197049053] = 0.12983962583 = 0.1298
c) From 2 to 4 they feel very bad in two minutes
P(2 ≤ X ≤ 4) = P(X=2) + P(X=3) + P(X=4)
= 0.25013889532 + 0.25013889532 + 0.17197049053 = 0.6722482811 = 0.6722
Hope this Helps!!!
9. Determine the equation of a line that passes though the points (3,-4) and (6,2). [
Answer:
y=2x-10
Step-by-step explanation:
First of all, remember what the equation of a line is:
y = mx+b
Where:
m is the slope, and
b is the y-intercept
First, let's find what m is, the slope of the line...
The slope of a line is a measure of how fast the line "goes up" or "goes down". A large slope means the line goes up or down really fast (a very steep line). Small slopes means the line isn't very steep. A slope of zero means the line has no steepness at all; it is perfectly horizontal.
For lines like these, the slope is always defined as "the change in y over the change in x" or, in equation form:
So what we need now are the two points you gave that the line passes through. Let's call the first point you gave, (3,-4), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=3 and y1=-4.
Also, let's call the second point you gave, (6,2), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=6 and y2=2.
Now, just plug the numbers into the formula for m above, like this:
m=
2 - -4
6 - 3
or...
m=
6
3
or...
m=2
So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:
1. Find a. The length of side
b. The Apothum
c. The area of the regular polygon inscribed in a circle of radius r= 13 cm of hexagon,
2. The side length of inscribed regular polygon is 10 unit long. Find the area of hexagon.
3. The area of inscribed regular hexagon is 18 V3 cm2. Find
8. The radius
b. The side length
c. The Apothum
d. The perimeter
4. If a regular polygon of 12 sides with radius units long is given. What is its area?
please help guys i dont understand
Teena's calculator is broken and does not have key 9 that works! With this broken calculator she found out the value of (-35) x 99. Explain your reasoning carefully and clearly
Answer:
(-35) * (100 - 1)
Step-by-step explanation:
She was able to find the value of (-35) * 99 without using the missing 9 button on her calculator.
The easiest way to do this is to replace 99 with another set of numbers that has the same value as 99.
(100 - 1) has the same value as 99. So, Teena can replace 99 with (100 - 1):
(-35) * (100 - 1)
It will yield the desired result.
A taxi cab charges $1.75 for the flat fee and $0.25 for each mile. Write an in equality to determine how many miles Eddie can travel if he has $15 to spend. A. $1.75 + $0.25x ≤ $15 B. $1.75 + $0.25x ≥ $15 C. $0.25 + $1.75x ≤ $15 D. $0.25 + $1.75x ≥ $15
Answer:
A. $1.75 + $0.25x ≤ $15
Step-by-step explanation:
This is because if Eddie has 15 dollars, he can only use 15 dollars or less. So in this case, the inequality would have to be less than or equal to 15 dollars.
Eddie travel $1.75 + $0.25x ≤ $15 miles when he has $15 to spend.
Option A is the correct option.
Here,
Amount of flat fee of taxi cab = $1.75
Amount of charge for each miles = $0.25
The amount Eddie has to spent = $15
We have to find inequality relationship.
What is inequality?
The relationship between two values that are not equal is defined by inequalities.
Now,
Amount of flat fee of taxi cab = $1.75
Amount of charge for each miles = $0.25
The amount Eddie has to spent = $15
Let Eddie travel x miles.
Therefore, the total charge of taxi cab = $1.75 + 0.25x
And this amount should not exceed the $15 as it is the only amount Eddie has.
Hence the inequality relationship be,
$1.75 + 0.25x ≤ $15.
Option A is the correct option.
To visit more about inequality visit:
https://brainly.com/question/11613554
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the ratio of zinc to copper is 3:19,
if theres 741 copper how much zinc is there?
Answer:
117
Step-by-step explanation:
For every 3 zinc there would be 19 copper, and for every 19 copper there would be 3 zinc. There are 741 copper, so there would be 741 * 3 / 19 zinc, which turns out to be 117 zinc.
what role do binomial factors (like (x+3) and (x-2) ) have in algebra.
Answer: Binomial factors are polynomial factors that have exactly two terms. Binomial factors are interesting because binomials are easy to solve, and the roots of the binomial factors are the same as the roots of the polynomial. Factoring a polynomial is the first step to finding its roots.
Find the value of this expression if X=-7
Answer:
-9
Step-by-step explanation:
[tex](-7)^{2}[/tex] = 49
when you have a negative number to any power make sure you plug it in correctly into the calculator.
[tex]\frac{49+5}{-7+1}[/tex] = [tex]\frac{54}{-6}[/tex]
54÷-6= -9
I hope this helps
Answer:
[tex]-9[/tex]
Step-by-step explanation:
[tex]\frac{x^2+5}{x+1}[/tex]
If [tex]x=-7[/tex] then:
[tex]\frac{-7^2+5}{-7+1} =\\\\\frac{49+5}{-6} =\\\\\frac{54}{-6} =\\\\-9[/tex]
The expression equals [tex]-9[/tex] if [tex]x=-7[/tex]
HELP
According to the Rational Root Theorem, Negative 2/5 is a potential rational root of which function?
f(x) = 4x4 – 7x2 + x + 25
f(x) = 9x4 – 7x2 + x + 10
f(x) = 10x4 – 7x2 + x + 9
f(x) = 25x4 – 7x2 + x + 4
Answer: Answer is f(x) = 25x4 - 7x2 + x + 4
Step-by-step explanation:
Answer:
d on edg
Step-by-step explanation:
Find the missing side. Leave your answer in simplest radical form.
Answer:
[tex] \sqrt{19} \: units[/tex]
Step-by-step explanation:
Given is a right angled triangle in which x represents the hypotenuse.
Therefore, by Pythagoras theorem:
[tex]x = \sqrt{( { \sqrt{10} })^{2} + {3}^{2} } \\ \\ = \sqrt{10 + 9} \\ \\ = \sqrt{19} \: units \\ [/tex]
What percentage of 220 is 130?
Answer:
59.09%
Step-by-step explanation:
You find it through the following formula:
Part divided by whole times 100.
Substitute it and you get the answer:
130 / 220 times 100 = 59.09
Q 1: There are n boxes in a large bag and m toys in each box. What is the total number of toys in the bag? Q 2 :The length of a rectangle is given by x + 2 and its width is equal to 3. Give a simplified expression of the area of this rectangle.
Answer:
Q1: n*m
Q2: A = 3x+6
Step-by-step explanation:
Q1: The total number of toys in the bag is given by the number of boxes (n) in the bag multiplied by the number of toys in each box (m):
[tex]T = n*m=nm[/tex]
Q2: The area of a rectangle is given by the product of its height by its length:
[tex]A = (x+2)*3\\A=3x+6[/tex]
The area of this rectangle is given by the expression A = 3x+6.
Lin’s family has completed 70% of a trip. They have traveled 35 miles. How far is the trip?
Answer:
The trip is 45 and 1/2 miles long
Step-by-step explanation:
Can someone please help me please please
Answer:
AA similarity postulate
Step-by-step explanation:
B and D are corresponding angles who both have measures of 50 degrees, which makes one pair of angles for this postulate. The other pair are ACB and ECD, because they are vertical angles and therefore congruent. Since when two angles in two triangles are the same, the third must be the same as well, these triangles must be similar. Hope this helps!
(PLZ NEED HELP) The doubling time of a bacterial population is 10 minutes. After 80 minutes, the bacterial population was 80000. _____
Using your rounded answer for the initial population above (do not round your growth rate), find the size of the bacterial population after 5 hours.____
Answer:
Initial population = 313
Population after 5 hours = [tex]3.36 \times 10^{11}[/tex]
Step-by-step explanation:
Let initial population = [tex]x[/tex]
It is given that population gets doubled every 10 minutes.
Population after 10 minutes = [tex]2x[/tex]
Population after 20 minutes = [tex]2^{2} x[/tex]
:
:
Population after 80 minutes = [tex]2^{8} x[/tex] and it is given as 80000.
[tex]\Rightarrow 2^{8} x = 80000\\\Rightarrow x = \dfrac{80000}{256}\\\Rightarrow x = 313[/tex]
So, initial population is 312.5 = ~313
To find, population after 5 hours i.e. 5 [tex]\times[/tex] 60 = 300 minutes
Population after 300 minutes =
[tex]2^{30} x\\\Rightarrow 2^{30} \times 313\\\Rightarrow 3.36 \times 10^{11}[/tex]
So, the answers are:
Initial population = 313
Population after 5 hours = [tex]3.36 \times 10^{11}[/tex]
Can someone please help me?
A baseball team won 9 games, which was 60% of the total number of games the team played. How many total games did the team play?
Answer:
They Played 15 games total
Step-by-step explanation:
Make ratios:
9:60 %
x:100 %
Cross multiply: 60 times x =60x and 9x100= 900 = 60x=900
Divide to get x: 60x/60=900/60
x=15
They Played 15 games total
Please mark brainliest and have a awesome day
Here is a rectangle ABCD the length of the rectangle is increased by 10% The width of the rectangle is increased by 5% Find the percentage increase in the perimeter of the rectangle
Answer:
7.5 % increase
Step-by-step explanation:
So,first we know that Square is also a special type of Rectangle,
so consider a Square with side 100 unit ,
Initially, After increament in side
Length = 100 unit -(increases by 10% ,So 110% of 100) NEW length = 110 unit
width = 100 unit (increases by 5% ,So 105% of 100) NEW width = 105
initially, Perimeter of Rectangle = 2 x (L + B) = 2 x (100 +100)
= 400 unit
After increment in length and width
Perimeter of New Rectangle = 2 x (L + B) = 2 x (110 +105)
= 430 unit
So we can clearly see that there is an increase of 30 unit in perimeter from initial.
Therefore ,% increase in perimeter will be
(final perimeter - initial perimeter)/initial perimeter x 100
= (430 - 400)/400 x 100
= 7.5 % increase
Answer:
increased by 8%
Step-by-step explanation:
Please help! Correct answer only!
For a fundraiser, there is a raffle with 100 tickets. One ticket will win a $150 prize, and the rest will win nothing. If you have a ticket, what is the expected payoff?
$ ___
Answer:
Expected Payoff ⇒ $ 1.50 ; Type in 1.50
Step-by-step explanation:
Considering that 1 out of the 100 tickets will have a probability of winning a 150 dollar prize, take a proportionality into account;
[tex]100 - Number of Tickets,\\1 - Number of Tickets You Can Enter,\\\\1 / 100 - Probability of Winning,\\$ 150 - Money Won,\\\\Proportionality - 1 / 100 = x / 150, where x - " Expected Payoff "\\\\1 / 100 = x / 150,\\100 * x = 150,\\\\Conclusion ; x = 1.5 dollars[/tex]
Thus, Solution ; Expected Payoff ⇒ $ 1.50
A cube fits perfectly in a sphere. If the cube has a side length of 10cm, what is the volume of the sphere? Round your answer to the nearest hundredth (2 decimal places) or leave your answer in Pi form
Answer:
500 /3 pi cm^3
Step-by-step explanation:
The side length of the cube is 10 cm, so the diameter of the sphere is 10 cm
That means the radius is
r =d/2 =10/2 = 5 cm
The volume of a sphere is
V = 4/3 pi r^3
= 4/3 pi (5)^3
= 500 /3 pi cm^3
Answer:
Your correct answer is 500/3 cm^3
I will show you how and tell you why it is 500/3 cm^3 down below:
Explanation:
The side length of the cube is 10 cm therefore, the diameter of the sphere is 10 cm so, the radius is 5 cm:
r = d/2 = 10/2 = 5 cm
and right here I will show you the volume of the sphere:
v = 4/3 r^3
= 4/3 (5)^3
= 500/3 cm^3
Showing these results, you can see that the answer is 500 /3 cm^3
what is the ratio of 2 hours and 115 minutes
HELP MARK AS BRAINLIST
Answer: Area for trapezoid= 1/2(4+5×1)=4.5 m
Area of triangle= Iam not exactly sure
hope this helped you a bit
Step-by-step explanation:
What type of transformation has taken place in the picture shown?
10
D
В
-10
-5
0
5
10
C'
-B-5
A!
-101
O translation
O rotation
O reflection
O dilation
Answer:
Reflection and translation.Step-by-step explanation:
The picture shows the preimage ABCD and the image A'B'C'D'.
Notice that both images are at the same distance from the x-axis, which implies a reflection across the x-axis. Them, the image was translated 1 units to the left.
Therefore, the right answers are reflection and translation.
please help me, with full explanation!!!!
Answer:
9.54 cm
Step-by-step explanation:
In triangle ABD, AD is the hypotenuse (longest side)
We know that according to Pythagoras theorem,
a^2+b^2=c^2
In the figure, c (10cm) and a (5cm) is given. So,
(5)^2 + b^2 = 100
25+b^2 = 100
b^2 = 75
So b is √75 = 8.66
Therefore BD is 8.66 cm
Now even BDC is a triangle
In it, the hypotenuse is missing but we know the value of other sides
so, in Pythagorean theorem,
a=4 (CD)
b=8.66 (BD)
c=x
Therefore,
(4)^2 + (8.66)^2 = x^2
16+74.99= x^2
x^2 = 90.99
x= 9.54 cm
Hope this helps!
