Answer:
[tex]x = \frac{\sqrt 3}{ 3}[/tex]
Step-by-step explanation:
Given
See attachment for complete question
First, we calculate the water pipe length (AC):
[tex]AC^2 = AB^2 + BC^2[/tex]
[tex]AC^2 = 1^2 + x^2[/tex]
[tex]AC^2 = 1 + x^2[/tex]
[tex]AC = \sqrt{1 + x^2[/tex]
The cost of laying across water is twice (2 times) laying on land.
So, the total cost (C) is:
[tex]C = 2 * \sqrt{1 + x^2} + 1 * (4 - x)[/tex]
[tex]C = 2 \sqrt{1 + x^2} + (4 - x)[/tex]
Differentiate
[tex]C' = \frac{2x}{\sqrt{1 + x^2}} - 1[/tex]
To find the most economical cost, we simply minimize C' by equating C' to 0
[tex]C' = 0[/tex]
[tex]\frac{2x}{ \sqrt{1 + x^2}}-1 = 0\\[/tex]
[tex]\frac{2x}{ \sqrt{1 + x^2}}=1[/tex]
Cross multiply
[tex]2x= \sqrt{1 + x^2}[/tex]
Take square of both sides
[tex]4x^2 = 1+x^2[/tex]
Collect like terms
[tex]4x^2 -x^2= 1[/tex]
[tex]3x^2= 1[/tex]
Solve for [tex]x^2[/tex]
[tex]x^2 = \frac{1}{3}[/tex]
Solve for x
[tex]x = \sqrt{\frac{1}{3}}[/tex]
[tex]x = \frac{1}{\sqrt 3}[/tex]
Rationalize:
[tex]x = \frac{1}{\sqrt 3} * \frac{\sqrt 3}{\sqrt 3}[/tex]
[tex]x = \frac{\sqrt 3}{ 3}[/tex]
The Pythagorean Theorem is
c² = g²-6²
False
O True
O No answer text provided.
O No answer text provided.
Answer:
FalseStep-by-step explanation:
It depends on the triangle.
If a is the longest side then it's true, but usually when we talk about Pythagorean theorem we mean that c is the longest side of the right triangle. So:
c² = a² + b²Help plz helpppppppppppppp
Answer:
A = 45 cm²
Step-by-step explanation:
The area (A) of a trapezium is calculated as
A = [tex]\frac{1}{2}[/tex] h( b₁ + b₂)
where h is the height and b₁, b₂ the parallel bases
Here h = 5, b₁ = 10 and b₂ = 8 , then
A = 0.5 × 5 × (10 + 8) = 0.5 × 5 × 18 = 45 cm²
The points M( 10,3) and P(-4,"8) are graphed on the coordinate plane. To the nearest
tenth of a unit, what is the distance between points Mand P? Round to the nearest
tenth.
Answer: 12.5
Step-by-step explanation:
It is around 12.5 units
If cos (A+B) = cosAcos B – sinAsin B , find the value of cos 75
Answer:
Step-by-step explanation:
Cos 75 = Cos ( 30 + 45) {Use Cos (A + B) identity}
= Cos 30*cos 45 - Sin 30 Sin 45
[tex]= \frac{\sqrt{3}}{2}*\frac{1}{\sqrt{2}}-\frac{1}{2}*\frac{1}{\sqrt{2}}\\\\= \frac{\sqrt{3}}{2\sqrt{2}}-\frac{1}{2\sqrt{2}}\\\\=\frac{\sqrt{3}-1}{2\sqrt{2}}\\\\=\frac{(\sqrt{3}-1)*\sqrt{2}}{2\sqrt{2}*\sqrt{2}}\\\\=\frac{\sqrt{3}*\sqrt{2}-\sqrt{2}}{2*2}\\\\=\frac{\sqrt{6}-\sqrt{2}}{4}[/tex]
Hiiiooo! Can someone please help me❤️❤️❤️ :D
Answer:
wassup baby, whas the insta?
What is the value of 19-7-15+14
Answer: the answer is 11 :)
Step-by-step explanation: I hope this helped!
Answer:
11
Step-by-step explanation:
19 - 7 = 12 - 15 = -3 + 14 = 11
or, if your brain likes it better, add the positives, then add the negatives, then subtract:
19 + 14 = 33
-7 -15 = -22
33 - 22 = 11
Rafael and his sister bought snacks for movie night.
Rafael got 3 boxed candies and 1 bag of chips for $6.99.
His sister got 2 bags of chips and 1 boxed candy for $5.98.
Find the cost for 1 of each of these items in dollars.
1 boxed candy costs $?
1 bag of chips costs $?
Answer:
1. $2.33
2. $2.99
Step-by-step explanation:
Answer:
bag of chips is 2.19
boxed candy is 1.60
Step-by-step explanation:
Desmos Calculator
Firas and Nabil are comparing their bank accounts. "I have four times more money than
you" , Firas says. "Anyway, I have only $240 less than you" , Nabil answers .
How much money does each one of them have in his account ?
should be solved as a system
Answer:
Firas = $320
Nabil = $80
Step-by-step explanation:
Firas = 4x
Nabil = x
x + 240 = 4x
3x = 240
x = $80
Firas = $240 + $80 OR $80 x 3 = $320
Nabil = $80
Hope that helps!
what is n if the equation is
n - 2 divided by -3 = -6
Please help me I am having a lot of trouble, thank you
OMG PLZZZZZZ HELP ME I REALLY NEED HELP :'( EVERYONE WHO HELPS ME GETS IT WRONG PLZZZ HELP ME IM BEGGING YOU
Answer:
1st Picture: d = -16
2nd Picture: g = -13.8
Step-by-step explanation:
1st Picture: Divide both sides by -11 to balance both sides and get the answer.
2nd Picture: Subtract 1.2 from both sides.
Answer:
Question 6:
We have -12.6 = g + 1.2, so we move the 1.2 to the left side to get -13.8 = g because when you move a number you are essentially minusing that number so 1.2 becomes -1.2 .
Question 7:
We have 176 = -11d so we divide by -11 to get -16 = d.
Hope this helped!
HELPPP PLEASE!! I NEED AN ANSWER. what expressions are equal to 18 x 13?
18×13 is equal to 234
Step-by-step explanation:
18×13=234
Find the equation of a line that passes through the point (-2, -1) and is
perpendicular to the line with equation y=-2x+8.
Answer:
2y-x=0
Step-by-step explanation:
Please mark as brainliest
Please, I need this done!
HELP PLS HELP PLS HELP PLS HELP PLS HELP PLS HELP PLS TY TY TY
Answer:-5+x<-1
Step-by-step explanation:
Answer:
H. -5 + x < -1
Step-by-step explanation:
Okay so let's first look at our little graph thing. What is it saying? It's telling us that what ever x is, it is NOT 4 (because the circle is not filled in) and it is less than 4 (because it's all shaded in before 4). Now that we know this, lets look at our possible answers.
F. x - 3 < 7
Now, for all of these possible answers, we can solve them exactly like normal equations (like x - 3 = 7).
x - 3 < 7
[add 3 to both sides to leave the x by itself]
x < 10
Whoa, that's not right! We don't even have 10 on our graph, so F is out of the running.
G. x + 6 [tex]\leq[/tex] 10
Okay, let's work smarter, not harder here. So we can see that there is a greater than or equal to sign there. So even if we solve it and we get 4 as the answer, our graph doesn't include 4. So we can throw this answer out right away.
H. -5 + x < -1
Solve like a normal equation in the first one.
-5 + x < -1
[add 5 to both sides to leave the x by itself]
x < 4
Hey! We got something! So let's read this with words. So whatever x is, it does not include 4, and is less than 4. So now looking back on our first brainstorm of the graph, this is in line with what we want.
So this is the answer! Yay!
Just for fun let's look at the last possible answer.
I. x - 8 > -4
Again, solve like a normal equation.
x - 8 > -4
[add 8 to both sides to leave x by itself]
x > 4
Oh! Another 4! But this time the sign is different. Let's read it again with words. So whatever x is, it does not include 4 (ok, good), and is greater than 4 (oh, not good). Our graph showed us that x is less than 4. So this answer is not the answer.
So again, we keep H. as our correct answer.
Please help!!
Choose whether the sampling is biased or unbiased
Questions are asked of randomly chosen workers at one of ten workplaces
1. Unbiased
2. Biased
The question asked is, “What do you think about the prison system in this state?”
1. Unbiased
2. Biased
The question asked is, “What do you think about the horrible prison system in this state?”
1. Unbiased
2. Biased
1. biased
2.unbiased
2. biased prisoners should be treated equally and the system is messed up
help? please and thank you
Answer:
first one
relationship between base and perpendicular is
given by tan angle
tan x=P/h
remember perpendicular is opposite side of taken angle
tan x=13/8
<x=tàn-¹(13/8)=58.39°
for second one
relationship between base and hypotenuse is given by cos angle
cos G=b/h
cos G=24/32
<G=cos-¹(24/32)=41.4 is your answer
Plz plz help I’m failing math and need help
Answer:
5 sweat shirts- $100
8 sweat shirts- $160
9 sweat shirts- $180
12 sweat shirts- $240
Step-by-step explanation:
Each sweat shirt costs $20
Colin buys a tv for £800. It depreciates at a rate of 4% per year. How much will it be worth in 3 years? Give your answer to the nearest penny where appropriate
Answer:
£707.8
Step-by-step explanation:
Given data
Price= £800
Rate= 4%
Time= 3 years
Let us apply the compounding formula
A=P(1-r)^r-------------Note the negative sign is because of depreciation
substitute
A= 800(1-0.04)^3
A= 800(0.96)^3
A=800*0.884736
A= £707.8
Hence the value will be £707.8
how to calculate the Triangle Proportionality Theorem
Step-by-step explanation:
If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.
Simplify (y+1)+4
Help
Answer:
y+5
Step-by-step explanation:
Answer: y+5
Step-by-step explanation:hope this help
Miguel has a garden that has an area of 300 square feet. If the corn in his garden covers 160 square feet, what percent of the garden is corn?
Im not sure of my answer but I got 5.33 and the 3 repeats
Answer:
Im sorry if I'm wrong but I think it's 300+160=460
Answer:
yes your correct but wrong
Step-by-step explanation:
To find the area that's covered in corn you need to first write your fraction.
160/300
After you do that you have to turn it into a decimal.
.53333...
After that you need to turn it into a percent so your final answer will be....
53.333...%
BTW try looking to see if you need to round, normally it tells you to do that
What has an absolute value of 9?
Answer:
the first one 9 or -9
Step-by-step explanation:
they both have absolute values of 9
hope this helps :)
Answer:
Your answer would be 9 or -9.
Step-by-step explanation:
The absolute value of a number means the distance from 0. -9 is 9 units away from 0, as well as 9 itself. Hope this helps; have a great day!
Walmart sells shirts for $8.00 and hats for $12.
Tony is shopping and can spend no more than $50.
Which inequality represents the number of shirts, s and number of hats, h
that Tony can buy without going over budget.
help :/
Answer:
Step-by-step explanation:
8s+12h≤50
The width of a rectangle measures (8.1g-6.5)(8.1g−6.5) centimeters, and its length measures (4.7g-9.2)(4.7g−9.2) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
Answer:
P = (25.6g - 31.4)
Step-by-step explanation:
Given that,
The width of a rectangle = (8.1g−6.5) cm
The length of a rectangle, = (4.7g−9.2)
We know that,
The perimeter of a rectangle is given by :
P = 2(l+b)
Substitute all the values,
P = 2(8.1g−6.5+4.7g−9.2)
= 2(12.8g-15.7)
= 25.6g - 31.4
So, the perimeter of the rectangle is equal to (25.6g - 31.4).
Jeremy buys 1,045 ceramic tiles. He can take 25 tiles to his truck at a time in his shopping cart. What is the minimum number of trips Jeremy must make to get all the tiles to his truck?
Answer:
42
Step-by-step explanation:
its 41.8, but you cant take 41.8 trips, so you have to round it
Answer:
1020
P.S: I think this answer is right may be not
we want to find the zeros for this polynomial: p(x) = 5x^3 - 5x^2 - 10x
Answer:
x= 0, 2, -1
Step-by-step explanation:
solve the system of equations y=5x y=x^2+4
answer:(1,5) and (4, 20)
What is the length of the hypotenuse of the triangle when x = 11?
The length of the hypotenuse is about
(Round to the nearest tenth as needed.)
Helppppp
Answer:
6(11)+4=70
5(11)=55
70²+55²
=7259
square root if 7259=85.20
and that's your answer
Goodnight
Kayla goes for a long walk. This graph shows her time and distance traveled throughout the walk.
somebody please answer only 11. and 13. ANSWER QUICKLY
Answer:
Step-by-step explanation:
y=mx+b where m is the slope and b is the y intercept, value of y when x=0
11.
Since we are given the point (0,4) we already know that b=4
slope is m=(y2-y1)/(x2-x1), using our two points (0,4)(-1,3) we have
m=(3-4)/(-1-0)
m=-1/-1=1 so the line is
y=x+4
12.
Again they gave us point (0,1) so we know b=1, from points (0,1)(4,2) we find
m=(2-1)/(4-0)
m=1/4 so our line is
y=x/4+1 (or more neatly)
y=(x+4)/4