Answers
Answer:
500 < c < 1,700
Step-by-step explanation:
Related Questions
What is an equation of the line that passes through the points (2, 1) and (3, -4)?
Answers
Answer:
huh Step-by-step explanation:
its really hard
Answer:
y = -x - 1
Step-by-step explanation:
(y - y1)/(x - x1) = (y1 - y2)/(x1 - x2)
(y - 4)/(x - (-3)) = (4 - (-1))/(-3 -2)
(y - 4)/(x + 3) = 5/-5
(y - 4)/(x + 3) = -1
y - 4 = -1(x + 3
y - 4 = -x - 3
y = -x - 1
Which of the following tables represents a function?
X 6 6 7 7
y 2 -2 3-3
x 2-2 3-3
y 5 5 7 7
x 3 -3 3-3
y 6 7 8 9
X 4 4 5 5
y 1 2 3 4
Answers
Answer:
The second one:
x 2-2 3-3
y 5 5 7 7
Step-by-step explanation:
Each domain value or x can only have one range, y, so, with that said, the second one is the answer.
hellp meeeeeeeeeeeeeeee
Answers
Answer:
Step-by-step explanation:
yasss its C
PLZZ HELP ASAP
Order these numbers from least to greatest
Answers
Answer:
1.4722, 2.901, 2.9, 2.91
Step-by-step explanation:
Please help, Math- Sophie the stealth Sharp shooter challenges you to a game of chance. She charges you $25 to get a chance to shoot at a target. if you hit the bullseye, you get a $100 (win$75). If you miss the bullseye but are within two circles of it, you get your money back. Over the course of sophies career, she finds that 5% of people hit the bullseye and 30% of people miss but are within two circles. All other contestants miss by further and lose.
Make a distribution table of the situation.
What is the expected amount for you to win or lose?
How much money would you expect Sophie to win or lose if 100 people played the game?
What should she charge to make this game fair?
Show work, please
Answers
The expected result for each shot is a loss of $ 12.50, so if 100 people played, Sophie would win on average about $ 1250. Lastly, Sophie should charge $ 5.77 for this value to be fair.
Since Sophie charges you $ 25 to get a chance to shoot at a target, and if you hit the bullseye, you get a $ 100 (win $ 75), and if you miss the bullseye but are within two circles of it, you get your money back, and over the course of sophies career, she finds that 5% of people hit the bullseye and 30% of people miss but are within two circles, while all other contestants miss by further and lose; to determine what is the expected amount for you to win or lose; how much money would you expect Sophie to win or lose if 100 people played the game; and what should she charge to make this game fair, the following calculations must be performed:
(75 x 5 + -25 x 65) / 100 = X (375 - 1625) / 100 = X -1250 / 100 = X -12.5 = X
375 + 65X = 0 65X = 375 X = 375/65 X = 5.77
Therefore, the expected result for each shot is a loss of $ 12.50, so if 100 people played, Sophie would win on average about $ 1250. Lastly, Sophie should charge $ 5.77 for this value to be fair.
Learn more about maths in https://brainly.com/question/25885499
PLS HELP WILL MARK YOU BRAINLIEST!!
No fake answers pls
Answers
Answer:
The first one is true, also the second one. Third one as well and the forth also. They all are solutions of the equations. Weird but true.
Answer:
1) x= -6 isn't the correct solution.
2) x=15 is the correct solution.
3) x= -1 isn't the correct solution.
4) x= -4/5 is the correct solution.
Step-by-step explanation:
1) 2x=9+3
2x=12
x=6
2) x=17-2
x=15
3) (multiply both members per 12)
3x-4x=-1
-x=-1
x=1
4) -3x-15=2x-11
-3x-2x=15-11
-5x=4
x= -4/5
4 5/6 x 3/10
simplify the answer completely and change it to a mix number
Answers
Step-by-step explanation:
4+5/6*3/10
29/6*3/10
=87/60
=29/20
=1 9/20
We have : [tex]4\frac{5}{6}[/tex] × [tex]\frac{3}{10}[/tex] = [tex]\frac{29}{6}[/tex] × [tex]\frac{3}{10}[/tex] = [tex]\frac{29}{20}[/tex] = [tex]1\frac{9}{20}[/tex]
ANSWER: [tex]1\frac{9}{20}[/tex]
Ok done. Thank to me :>
Helpppp
Evan spent 20 hours doing homework last week. This week he spent 25 hours doing homework. He says that he spent 125% more time doing homework this week. Is he correct? Show your work to justify your decision.
Answers
Answer: Evan is incorrect
Step-by-step explanation:
20/20 - 25 x 100 =
5/20 x 100/1 =
500/20
500/20 = 20%
Evan would only be correct is he doubled the 20 hours to make it 40 hours
Hope this helps✌
simplify (89^6x91^3)^0
Answers
i dont know but i do know that OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO
Evaluate 4+(m-n)^4 when m =7 and n = 5
Answers
Answer:
20.
Step-by-step explanation:
Plugging m = 7 and n = 5 into the given expression:
Answer = 4 + (7 - 5)^4
= 4 + 2^4
= 4 + 16
= 20.
What is the equation of this line in slope-intercept form?
(-1,5) (1,-1)
Answers
Answer:
y=-3x+2
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-1-5)/(1-(-1))
m=-6/(1+1)
m=-6/2
m=-3
y-y1=m(x-x1)
y-5=-3(x-(-1))
y-5=-3(x+1)
y=-3(x+1)+5
y=-3x-3+5
y=-3x+2
Put the trinomial x^2+8x+14 into (x+a)^2+b form where a and b can be positive or negative. Thanks!
Answers
(x + a)^2 + b form can be achieved by a method known as completing the square.
Step 1: Divide the b term by 2 and square it
8 / 2 = 4
4^2 = 16
Step 2: Add and subtract 16 from the expression
---Adding 16 creates a perfect square trinomial between x^2 + 8x + 16. But, if we add 16, we also need to subtract it. So, we will subtract 16 from our c term, 14.
x^2 + 8x + 16 + 14 - 16
x^2 + 8x + 16 - 2
Step 3: Factor the perfect square trinomial
(x^2 + 8x + 16) - 2
(x + 4)(x + 4) - 2
(x + 4)^2 - 2
Answer: (x + 4)^2 - 2
Hope this helps! :)
Solve the equation by finding the common multiple.
three fourths minus two sixths plus seven twenty fourths equals blank
seventeen twenty fourths
eighteen twenty fourths
nineteen twenty fourths
twenty twenty fourths
Answers
Answer:
1. 17/24
2. 1 1/8
3. 1 1/6
4. 1 5/24
5. 1. 1/4
Answer:
seventeen twenty fourths
Step-by-step explanation:
welcome
y=-2x2+12x-26
Rewrite the equation in vertex form and identify the vertex, the axis of symmetry, and the y-intercept.
Answers
Answer:
y = 12x - 22
Step-by-step explanation:
If we first write the equation in vertex form and we identify it (I think you meant to simplify y) we get y = 12x - 22 as your answer!
Someone help me please
Answers
Answer:
Step-by-step explanation:
any minus temperature is < 7oC
0 is < 7oC
1 ... 6 is < 7oC
add the expression(3x+2)+(2x+5)
Answers
What is the name of this?
Answers
Answer:
Circumference of a circle
how many days are in a year?
Answers
Answer:
365 days in a year
Step-by-step explanation:
Look at a calendar
Answer:
Three hundred and sixty-five
Step-by-step explanation:
We know this because it takes exactly 1 year (365 days) to make one rotation around the sun. But we see the sun every day because the earth is on a sort of axis that it rotates on so when one-half of the earth does not see the sun the other half does due to this axis.
PLEASE SOLVE THIS WITH FULL EXPLANATION ASAP I HAVE A MATH EXAM
Answers
Answer:
3/5y
Step-by-step explanation:
6y/35 ÷10y^2/7
to solve this you do reciprocal of 10y^2/7
then;
6y/35 x 7/10y^2
solving this
3/5y
The 1,600-meter race in the Olympics is very close to 1 mile long. How many kilometers is 1,600 meters?
Answers
What is the square root of -7
Answers
Answer:
negative numbers don't have square roots. a square is either positive or 0, so your questions answer doesn't exist. if you want positive 7 though, 5.291502... etc
Solve the inequality . Graph solution . 1/5 > d+ 4/5
Answers
Answer:
B
Step-by-step explanation:
Answer:
b. d>-3/5
Step-by-step explanation:
L.C.M=5
5×1/5>5×d+4/5×5
1>5d+4
1-4>5d
-3>5d
-3/5>5d/5
-3/5>d
branliest if correct.
Solve.
2.903=y+710
Enter your answer as a decimal in the box.
y =
Answers
( 2.903-0.7) = 2.203
The graph shows a proportional relationship between the number of books sold at a yard sale and the amount of money collected from book sales.
Answers
Answer:
1.5
Step-by-step explanation:
6/4
solve this to pretty pretty pls
Answers
Answer:
3) 161
Step-by-step explanation:
Indeed this is pretty easy :D
What we need to find is the surface area of the rectangular prism excluding the area of the hole. First, let's find out the width of the box, we can do this by using the area, the length, and the height, and we can write:
[tex]V=lhw[/tex]
(Formula to find the volume of a rectangular prism)
[tex]140=(4)(7)w\\ 140=28w\\ 5=w[/tex]
Now that we have the width, can find the area of the top part of the prism:
[tex](5)(4)=20[/tex]
The area of the top part of the prism is 20, and the circle has 1/4 of the area of that:
[tex]A_{circle} = \frac{A_{top part} }{4}\\ A_{circle} = \frac{20}{4} \\ A_{circle} = 5[/tex]
So the area of the circle is 5. Now we just need to find the surface area of the rectangular prism and subtract that result with the area of the circle:
[tex]A_{circle}=5\\ SA_{rec.pri.}=2(lh+lw+wh)\\ SA_{rec.pri.}=2((4)(7)+(4)(5)+(5)(7))\\ SA_{rec.pri.}=2(28+20+35)\\ SA_{rec.pri.}=2(83)\\ SA_{rec.pri.}=166[/tex]
Subtract these two results...:
[tex]166-5=161[/tex]
And we are done!
x over 2 +2= 15 two step equations
Answers
Answer:
[tex]\boxed{\boxed{\sf x=84}}[/tex]
Step-by-step explanation:
[tex]\sf \cfrac{x}{6} +2=16[/tex]
Multiply both sides of the equation by 6:
[tex]\sf x+12=96[/tex]
Subtract 12 from both sides:
[tex]\sf x=96-12[/tex]
Subtract 12 from 96:
[tex]\sf x=84[/tex]
_________________________________
Answer:
[tex] \sf \: \longmapsto\frac{x}{6} + 2 = 16[/tex]
[tex]\sf \: \longmapsto\frac{x}{6} = 16 - 2[/tex]
[tex]\sf \: \longmapsto \frac{x}{6} = 14[/tex]
[tex]\sf \: \longmapsto \: x = 14 \times 6[/tex]
[tex]\sf \: \longmapsto \: x = 84[/tex]
Step-by-step explanation:
[tex]\fbox {\fbox {\fbox {\fbox{ \pink{HeavenMistress}}}}}[/tex]
What is the value of the digit in the ten thousands place?
16,985,717
A. 90,000
B. 8,000
C. 10,000,000
D. 80,000
Answers
Answer:
D. 80,000
Step-by-step explanation:
A tip might be to read the number outloud and then the answers to see the similarities.
Hope this is helpful :)
simplify and factor if necessary
Answers
Hello there today we will solve your problem, we will need to factorize btw...
[tex]{\huge{\boxed{\mathfrak{Equation}}}[/tex]
[tex]{\big{\boxed{\frac{x^2-5x+4}{x^2-4x}}}}[/tex]
First we will factor [tex]x^2-5x+4[/tex], which gives us [tex]\left(x-1\right)\left(x-4\right)[/tex]
[tex]\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\left(x-1\right)\left(x-4\right)}{x^2-4x}\\[/tex]
factorize [tex]x^2-4x[/tex] giving us [tex]x\left(x-4\right)[/tex]
[tex]\frac{\left(x-1\right)\left(x-4\right)}{x\left(x-4\right)}[/tex]
cancel the common factor [tex]x-4[/tex]
and we get [tex]\frac{x-1}{x}[/tex]
Andrew is painting a wall on the side of his house. He has a 20 foot ladder wich makes a 79 degree angle with the ground. Standing on the second to past rung of the ladder, Andrew can reach 5 feet above the point where the ladder rests against the wall. How high up the wall can Andrew paint
Answers
Andrew can reach a maximum of [tex]24.6ft[/tex] high up the wall.
The right-angled triangle formed can be solved using the [tex]sine[/tex] ratio. that is
[tex]sin(72^\circ})=\dfrac{h}{20}[/tex]
where [tex]h[/tex] is the distance from the foot of the wall to the tip of the ladder where it rests on the wall. Substituting, and solving for [tex]h[/tex], we get
[tex]0.9816=\dfrac{h}{20}\\\\h=20\times0.9816\\\\h=19.632ft[/tex]
Since Andrew can reach an extra [tex]5ft[/tex] above the point where the ladder rests against the wall, the maximum height Andrew can paint is
[tex](19.632+5)ft=24.632ft\\\\\approx24.6ft[/tex]
Another solved word problem on trigonometry can be found here: https://brainly.com/question/12146092
HELP!! joels apartment building is 42 ft tall and casts a shadow of 20ft. If Joel is 6 ft tall, how long is his shadow
Answers
Step-by-step explanation:
an object and its shadow create a right-angled triangle.
2 objects and their shadows create 2 similar right-angled triangles.
that means the angles are the same, and the side lengths of one triangle all correlate with the corresponding side lengths of the other triangle via the same factor.
so,
42 × f = 6
f = 6/42 = 1/7
the length of Joel's shadow is then
20 × f = 20 × 1/7 = 2.857142857... ft