Given :
A 13ft ladder is leaning against a wall when its base starts ti slide away from the wall.
By the time its base is 12 feet from the wall, the base is moving at the rate of 5ft/sec.
To Find :
How fast is the top of the ladder sliding down the wall.
Solution :
By, Pythagoras theorem, distance of ladder from horizontal to wall is 5 feet.
Now, [tex]x^2 + y^2 = 13^2[/tex]
Differentiating both sides, we get :
[tex]2x\dfrac{dx}{dt}+2y\dfrac{dy}{dt}=0\\\\(2\times 12\times 5) + (2\times 5 \times \dfrac{dy}{dt})=0\\\\\dfrac{dy}{dt}= -12 \ feet/sec[/tex]
You want to learn karate at a fitness center. You have two options; option A is to pay a $300 registration fee plus $10 per additional lesson. Option B is pay $35 for each lesson you attend. Make equations to represent the total cost of Option A and B.
Answer:
Option A: 300 + 10x
Option B: 35x
Step-by-step explanation:
option A:
$300 + $10 per lesson
Total cost = 300 + 10x
Option B:
$35 per lesson
Total = 35x
Where,
x = number of lessons
The equations to represent the total cost of Option A and B are 300 + 10x and 35x respectively
Use your trendline to find the temperature of your Spaghettios after 40 minutes. Is this an example of interpolation or extrapolation?
NEED HELP ASAP WITH SHOWN WORK!!!!!!!!!!!!
Answer:
in 40 minutes, 15 degrees Farenheit will be e
Step-by-step explanation:
QUESTIONS AT BOTTOM!’
HELP PLEASE 10 POINTS
Answer:
Positive slope
y intercept is 0,-4
i dont know the equation
Step-by-step explanation:
The Bootle Corporation paid Leslie a quarterly dividend check for $828. Leslie owns 450 shares of Bootle. What was the quarterly dividend for one share of Bootle?
Type the correct answer in each box. Use numerals Instead of words. If necessary, use / for the fraction bar(s).
Complete the inverse function for the function glven below.
Answer:
0.5x + 2
Step-by-step explanation:
You switch x and y and then solve for x to find the inverse.
#2 Rewrite this expression in standard from. (y-2) = 3(x + 1) O 3x - y = -5 0 4x + y = 2 O x + y = 5 0-3x + y = 5 Next >
Answer:
Step-by-step explanation:
B
Answer:
It is -3x + y = 5
Step-by-step explanation:
So the answer is D
please help me with this question
Answer:
top right and bottom left
Step-by-step explanation:
im in precal and if i get this wrong i am so sorry
but im pretty sure those r what increasing graphs look like as the increase in a positive direction
hope this is correct and helps :)
Mr. Lebsock is 1 year younger than 10 times Addy’s age. If Mr. Lebsock is 29, write and solve equation to solve for Addy’s age.
Answer:
3
Step-by-step explanation:
29 = 10x - 1
+4
30 = 10x
30 divided by 10 = 3
3 = x
So Addy is 3.
determine the measure of each segment then indicate whether the statements are true or false
Answer:
[tex]d_{AB}\ne d_{JK}[/tex]
[tex]d_{AB}\ne \:d_{GH}[/tex]
[tex]d_{GH}\ne \:d_{JK}[/tex]
Therefore,
Option (A) is false
Option (B) is false
Option (C) is false
Step-by-step explanation:
Considering the graph
Given the vertices of the segment AB
A(-4, 4)B(2, 5)Finding the length of AB using the formula
[tex]d_{AB}\:=\:\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]
[tex]=\sqrt{\left(2-\left(-4\right)\right)^2+\left(5-4\right)^2}[/tex]
[tex]=\sqrt{\left(2+4\right)^2+\left(5-4\right)^2}[/tex]
[tex]=\sqrt{6^2+1}[/tex]
[tex]=\sqrt{36+1}[/tex]
[tex]=\sqrt{37}[/tex]
[tex]d_{AB}\:=\sqrt{37}[/tex]
[tex]d_{AB}=6.08[/tex] units
Given the vertices of the segment JK
J(2, 2)K(7, 2)From the graph, it is clear that the length of JK = 5 units
so
[tex]d_{JK}=5[/tex] units
Given the vertices of the segment GH
G(-5, -2)H(-2, -2)Finding the length of GH using the formula
[tex]d_{GH}\:=\:\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]
[tex]=\sqrt{\left(-2-\left(-5\right)\right)^2+\left(-2-\left(-2\right)\right)^2}[/tex]
[tex]=\sqrt{\left(5-2\right)^2+\left(2-2\right)^2}[/tex]
[tex]=\sqrt{3^2+0}[/tex]
[tex]=\sqrt{3^2}[/tex]
[tex]\mathrm{Apply\:radical\:rule\:}\sqrt[n]{a^n}=a,\:\quad \mathrm{\:assuming\:}a\ge 0[/tex]
[tex]d_{GH}\:=\:3[/tex] units
Thus, from the calculations, it is clear that:
[tex]d_{AB}=6.08[/tex]
[tex]d_{JK}=5[/tex]
[tex]d_{GH}\:=\:3[/tex]
Thus,
[tex]d_{AB}\ne d_{JK}[/tex]
[tex]d_{AB}\ne \:d_{GH}[/tex]
[tex]d_{GH}\ne \:d_{JK}[/tex]
Therefore,
Option (A) is false
Option (B) is false
Option (C) is false
What is the solution set for
−4x + 10 ≥ 5x + 55?
Answer:
x[tex]\leq[/tex]-5
Step-by-step explanation:
What is the y-intercept and slope of the following equation y=8-2x
Answer:
Sloper = -2
y-intercept = (0,8)
Step-by-step explanation:
y=8-2x
y=-2x+8
m=-2
b=8
Answer:
slope(m)=-2
y-intercept (c)=8
Step-by-step explanation:
here,y=-2x+8
reducing it into slope intercept form we get,
y=(-2)x+8
comparing it with y=mx+c we get,
slope(m)=-2
y-intercept(c)=8
It takes 2.5 ounces of flour to make one pancake. How many whole pancakes can Jenifer make with 16 ounces of flour?
(You can either Multiply or Divide and the answer has to be 5/6 or 6)
Answer:
6
Step-by-step explanation:
I made 2.4 a fraction got 5/2 then did 16 divided by 5/2 and got 6.4 so for the amount of whole pancakes it would be 6 with .4 ounces of flour left over
You are at a festival and notice a lady is making winter wear by knitting. She sells five hats and three scarves for a total cost of $99 while three hats and five scarves cost $85. What is the cost of one hat and one scarf
Answer:
Cost of Hats = $15
Cost of Scarves = $8
Step-by-step explanation:
Let
Cost of Hats = x
Cost of Scarves = y
5x + 3y = 99 (1)
3x + 5y = 85 (2)
Multiply (1) by 5 and (2) by 3
25x + 15y = 495
9x + 15y = 255
Subtract
25x - 9x = 495 - 255
16x = 240
Divide both sides by 16
x = 240 / 16
= 15
x = $15
Substitute x = 15 into
5x + 3y = 99
5(15) + 3y = 99
75 + 3y = 99
3y = 99 - 75
3y = 24
y = 24/3
= 8
y = 8
Cost of Hats = $15
Cost of Scarves = $8
PLS THIS IS TIMED! I WILL GIVE BRAINLIEST!!!!
Answer:
the answer is y= 5(0.25)^x or C
Step-by-step explanation:
A triangle has a perimeter of 165 cm. The first side is 65 cm less than twice the second side. The third side is 10 cm less than the second side. Find the length of each side of the triangle.
What equation represents the length of the third side if the second side is length s?
2s - 10
2s + 10
s - 10
s + 10
Answer:
side - equation - measurement
1st side - 2s - 65 - 55cm
2nd side - s - 60cm
3rd side - s - 10 - 50cm
Step-by-step explanation:
total = 165
side - s
1st side = 2s - 65
2nd side = s
3rd side = s - 10
1st side + second side + 3rd side = 165
2s - 65 + s + s - 10 = 165
2s + s + s - 65 - 10 = 165
4s - 75 = 165
4s = 165+ 75
4s = 240
s = 60
1st side = 2s - 65
= 2(60) - 65
= 120 - 65
= 55cm
2nd side = s
= 60cm
3rd side = s - 10
= 60 - 10
= 50cm
3rd side is represented by s - 10 as it is less than the second side by 10cm hence taking away the 10 from the side forming the equation s - 10
Answer:
s-10
I took the quiz
please help!! im confused
Answer:
6x+3
yep hellooo he looo hey it's sksksn she's. d e s f e. s
Answer:
im confused as if the question but,
you know what to do and if you want you can post more of the question if there is more but ye,
your welcome
Step-by-step explanation:
x=2(for the example)
so,
2+3+5x2=
PEMDAS
5x2=10
2+3=5
soo,
10+5=15
I need help for my finals review.
Find the area of triangle FGH with coordinates F(-6,1) G(-5,-4) and H(2,1).
A. 21.7 units
B. 10 units
C. 20 units
D. 40 units
Find the value of x so that the function has the given value:
f(x)=6*x
f(x)=-24
I'm struggling SOS
Answer: x=-4
Step-by-step explanation:
f(x)=6*x
f(x)=-24
-24= 6x
X=-4
Which inequality represents the situation ten less than a number is a minimum of 30?
Answer:
x - 10 ≥ 30
Step-by-step explanation:
I'm 99.8% sure
It says 10 less than a number so that means subtract 10 from a number
Then it says minimum of 30 so that means the number has to be 30 or more so that's why I use the more than of equal to sign.
Hope this helps!
You buy five books that are equal in
price and a DVD for $8. Your tal
comes to $26.50. Write an equation
that would help you determine the cost
of one book.
Answer:
26.50 - 8 = 18.50 then divide by 5
Step-by-step explanation:
this equation will help u find the exact amount of one book
what's the answer?
Answer:
80 degrees
Step-by-step explanation:
ALL TRIANGLES MUST EQUAL 180 DEGREES!
180-70-30 = 80
Say it with me.
ALL TRIANGLES MUST EQUAL 180 DEGREES!
ALL TRIANGLES MUST EQUAL 180 DEGREES!
ALL TRIANGLES MUST EQUAL 180 DEGREES!
Also, triangle CED reflects over the invisible y-axis. Angle C is shared = 70. Angle E is Angle A, and Angle B is Angle D (which is 80 degrees).
nelson middle school raised $19950 on ticket sales for its carnival fundraiser last year at $15 per ticket. if the school sells the same number of tickets this year but charges $20 per ticket how much money will the school make? can you explain i dont want tue anwer
Which statement is not always true for a parallelogram?
Answer:
b
Step-by-step explanation:
Answer:
Diagonals are congruent drop a like if you got it right
Step-by-step explanation:
This question I don’t know how to do can someone tell me the Mc answer
Answer:
x = 2
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Algebra I
Function NotationStep-by-step explanation:
Step 1: Define
m(x) = 4x - 10
m(x) = -2
Step 2: Solve for x
Substitute: -2 = 4x - 10Isolate x term: 8 = 4xIsolate x: 2 = xRewrite: x = 2Each blank on the coordinate plane has an address called the blank,blank
Answer:
adress, Like ( make up an adress)
Step-by-step expanation:
Answer:
Each point on the coordinate plane has an address called the ordered pair.
Step-by-step explanation:
What is the area for a circle with a diameter of 4*
Answer: A = 12.57
Step-by-step explanation: Hope this helps
Answer:
12.56637
Step-by-step explanation:
A=πr²
d=2r
A=1/4πd²=1/4·π·4²=12.56637
Jacob stated that he solved the equation 2x+3=5 using addition and multiplication property of equality. Which statement is true?
A. Jacob added -3 to both sides and multiplied both sides by 1/2
B. Jacob added -3 to both sides and multiplied both sides by 2
C. Jacob added 3 to both sides and multiplied both sides by 1/2
D. Jacob added 3 to both sides and multiplied both sides by 2
Answer:
It is A.
Step-by-step explanation:
It shows the steps that distribute everything properly
What is the image of (-4, 7) after a dilation by a scale factor of 3
centered at the origin?
Answer:
(-12, 21)
Step-by-step explanation:
You would multiply the coordinates by 3
pleaseeee helpppppp !!!!!!! Will mark Brianliest !!!!!!!!!!!!!!
Answer:
6.85565
Step-by-step explanation:
For a group trip, a travel agency charges $300 per person. Write an expression to show the cost of a group trip for p people.
Answer:
c = 300p
Step-by-step explanation:
What we know:
For a group trip, a travel agency charges $300 per person.
How equations work are:
dv = k(iv)
The cost of the trip is the dependent variable, so that's on the left side of the equation. (I've represented that with c)
c = k(iv)
The independent variable is people, so that's on the right side. (represent with p)
c = kp
Our constant (k) is 300.
c = 300p is the full equation.
Answer:
Nice c
Step-by-step explanation: