Answer:
[tex]\sqrt{13}[/tex]
The rate of change of distance between two cars at the given time is required.
The required rate of change is [tex]\sqrt{13}[/tex] feet/s
Rate of changea = Distance covered in 5 s by bike A = [tex]2\times 5=10\ \text{feet}[/tex]
b = Distance covered in 5 s by bike B = [tex]3\times 5=15\ \text{feet}[/tex]
c = Distance between A and B in 5 s = [tex]\sqrt{10^2+15^2}=5\sqrt{13}\ \text{feet}[/tex]
Applying Pythagoras theorem
[tex]a^2+b^2=c^2[/tex]
Differentiating with respect to time
[tex]2a\dfrac{da}{dt}+2b\dfrac{db}{dt}=2c\dfrac{dc}{dt}\\\Rightarrow \dfrac{dc}{dt}=\dfrac{a\dfrac{da}{dt}+b\dfrac{db}{dt}}{c}\\\Rightarrow \dfrac{dc}{dt}=\dfrac{10\times 2+15\times 3}{5\sqrt{13}}\\\Rightarrow \dfrac{dc}{dt}=\sqrt{13}\ \text{feet/s}[/tex]
Learn more about rate of change:
https://brainly.com/question/8728504
2x²+30y-3y²+4xy-14-x
Option 1,2,3 or 4?
Here are the ingredients needed to make 8 pancakes.
250 ml milk
1 egg
140 g flour
5g butter
a
Simon makes 32 pancakes.
Work out how much milk he needs.
b)
Craig makes 20 pancakes.
Work out how much flour he needs.
GO
Answer:
A. 1,000 ml milk B. 3,500 g flour
Step-by-step explanation:
Divide: 250 divided by 8. You get 31.25.
Multiply: 31.25 times 32. You get 1,000
Divide: 140 divide by 8. You get 17.5
Multiply: 17.5 times 20. You get 3,500
Hope I helped!! :) Sorry if it's wrong! :(
A rectangular field is 10m longer than wide. The area of the field is 2000m². Find the perimeter of the field.
Answer:
180m
Step-by-step explanation:
Let L = length of field,
W = width of field,
A = field area = 2000 m^2
Lenght = Width + 10m
Let Lenght= x
Width=y
A = X ×Y = (Y + 10)Y= 2000
Y^2 + 10Y- 2000 = 0
Solving using Quadratic eqn with plot
Y= 40 or -50 but we go for the positive root
Width=40m
Length= 40m +10m
= 50m
Perimeter= 2(l+w)
=2(50+40)
180m
Hence, the perimeter is 180 m
CHECK THE ATTACHMENT FOR THE QUADRATIC PLOT
Mr.Klein's class is selling candy for a fundraiser. The class has a goal of raising $450 for selling (c) boxes of candy. Each box of candy costs $3.75.
Answer:
so since their goal is to get $450 and each candy box is $3.75, what you do is divide $3.75 by $450 you will get $120, soooooooooooooooooooooooooooo you times $3.75 by $120 you will get $450.
Step- by-step explanation:
Using the Triangle Sum Theorem, please solve for the value of x.
Please type out ALL OF YOUR WORK along with your answer for x. Work is worth 5 points, answer for x is 2 points.
3x
1
12x
55°
Answer:
x = 25
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Sum the 3 angles and equate to 180
2x + 3x + 55 = 180, that is
5x + 55 = 180 ( subtract 55 from both sides )
5x = 125 ( divide both sides by 5 )
x = 25
6 boy students make up 24% of the total class how many total students are in class
Answer:
There are 25 students in the class.
Step-by-step explanation:
1. Set up an equation. The equation would be 6 = 24/100x.
2. Solve the equation. You can solve this by multiplying both sides by 100/24, and 100/24 * 6 = 25. You would then get that x = 25, which means that the number is 25.
Answer:
25 students
Step-by-step explanation:
25 x 0.24 = 6
I need help with Geometry
9514 1404 393
Answer:
(5, 1)
Step-by-step explanation:
Reflection across the x-axis negates the y-coordinate:
(x, y) ⇒ (x, -y) . . . . reflection across the x-axis
Rotation 90° CCW is the transformation ...
(x, y) ⇒ (-y, x) . . . . rotation 90° CCW
The two transformations together give ...
(x, y) ⇒ (y, x) . . . . reflection across the x-axis, then rotation 90° CCW
For point B, this gives ...
B(1, 5) ⇒ B'(5, 1)
A train 180m long travels through a station at 60 km/h. Find how many seconds it takes for the train to pass a person who is standing on the station platform
Answer:
180sec
Step-by-step explanation:
180÷60
3
1min =60seconds
60×3
=180secinds
Andre says that 1/4 is less than -3/4 because, of the two numbers, 1/4 is closer to 0. Do you agree? Explain your reasoning.
Answer:
Andre is wrong
Step-by-step explanation:
Andre is wrong because 1/4 is a positive number and -3/4 is a negative number so that makes Andre wrong for that, but if it is who is closer to 0 then Andre is right because when you look at it on a table you can see that 1/4 is closer.
HELP ASAP
simplify the expression-3÷(-2/5)
Answer:
7.5
Step-by-step explanation:
the two triangles shows the congruent ABC LMN. based on this information which of the following is a true statement
Answer:
It's D I think.... Line up B and C with M,N
What is the value of X what is the measure of 2 PLEASE HELPPP
Answer:
x = 11 , m∠2 = 31
Step-by-step explanation:
We know that m∠1 is equal to both 6x+8 and 74
Therefore, 6x+8 = 74
And 6x = 66
x = 11
To find m∠2, we just plug in the value of x that we got earlier
(7x-2) + m∠2 = 106
(77-2) + m∠2 = 106
m∠2 = 31
if g(x) =x -7, what if the value of x when g(x) =6
Answer:
x=13
Step-by-step explanation:
1. Place 6 in
6=x-7
2. Evaluate
x=6+7
x=13
jacorey works at an animal shelter. He is responsible for 96 dogs and cats today. The number of dogs is six more than twice the number of cats. how many dogs are at the shelter today?
PLEASE HELP
...........
PLEASE ANSWER I NEED HELP
Kayla gets paid $15 to rake the lawn. Kayla gets paid 3 times as
much to rake the lawn as she does to mow the lawn. How much
does Kayla get paid to mow the lawn?
Answer:
$5
Step-by-step explanation:
The opposite of multiplication is division.
$15/Raking = 3 times more pay than mowing the lawn.
Divide $15/Raking by 3 and you'll get the pay for mowing the lawn.
15/3 = 5
Answer:
5
Step-by-step explanation:
A market research survey has 15 questions and will be sent to 500 people. What is the total cost to conduct the survey if it has a $1,000 base fee plus $5 per question and $2 per person surveyed?
Answer:
Total cost to conduct survey = $2075
Step-by-step explanation:
Given that:
Number of questions on survey = 15
Number of people = 500
Base fee = $1000
Per question charge = $5
Per person surveyed = $2
Let,
q be the number of questions
p be the number of people
Total cost = Base fee + 5q + 2p
Total cost = 1000 + 5(15) + 2(500)
Total cost = 1000 + 75 + 1000
Total cost = $2075
Hence,
Total cost to conduct survey = $2075
A bag contains 3 red marbles and 5 blue marbles.
Find the probability of drawing a blue marble,
keeping it, and drawing another blue marble. Write
the probability as a fraction in simplest form.
A worm squiggles 10 cm in 5 minutes. What was it average speed
Joe is making lunch for his crew. Joe took 3 hours to prepare the vegetables. The vegetables were made up of 9 kilograms. How long do you think it will take Joe to prepare 30 kilograms of vegetables?
Answer:
10 hours to make 30 kilograms
please help fast will mark brainliest
Answer:
(2,6)
Step-by-step explanation:
Hope this helps!
Answer:
x = 2; y = 6
Step-by-step explanation:
y=3x
x+y=8 [substitute y for 3x]
x+3x=8; 4x=8; x=2
if x=2, y=3x or y=3(2) = 6
Can you anser the question number 7
Answer:
Length of rectangle = 64 inches
Width of rectangle = 32 inches
Step-by-step explanation:
Perimeter of rectangle = 192 in
Length = x
Width = [tex]\frac{1}{2}x[/tex]
We need to find the length and width.
The formula used is: [tex]Perimeter\:of\:rectangle=2(Length+Width)[/tex]
Putting values and finding value of x
[tex]Perimeter\:of\:rectangle=2(Length+Width)\\192=2(x+\frac{x}{2} )\\192=2(\frac{2x+x}{2} )\\192=2(\frac{3x}{2} )\\192=3x\\x=\frac{192}{3}\\x=64[/tex]
So, we get x = 64
The length of rectangle x = 64
The width of rectangle = [tex]\frac{1}{2}x[/tex] = [tex]\frac{64}{2} = 32[/tex]
So, Length of rectangle = 64 inches
Width of rectangle = 32 inches
Answer:
Length of rectangle = 64 inches
Width of rectangle = 32 inches
Step-by-step explanation:
I need help, I’ve been trying to figure out answers and I’m not getting anywhere is there anyone who could help me with (work shown)
find the value of x.
Answer:
X= 20 degrees
Step-by-step explanation:
Because all the sides are the same length, we know this triangle is an equilateral triangle. In an equilateral triangle, all the angle measures are the same as well, and the sum of all the angles in a triangle is 180 degrees. So we have the equation:
(3x)3= 180
9x= 180
X =20
What is this answer?
Answer:
The answer is (-1,-10)
hope this helps
Step-by-step explanation:
Solve for the first variable in one of the equations, then substitute the result into the other equation.
Answer:
D. (-1, -10)
Step-by-step explanation: I put your question into a math calculator and got this as your answer. Good luck!
The lines AB and CB intersect at B
(a) Find the co-ordinates of the midpoint of AB
(b) Find the equation of the line CB
Step-by-step explanation:
Soln
given,
from the figure
coordinate of B is (5,3),
A(7,0) and C(0,4)
A. solution
let, M(x,y) be the mid point of AB
A(7,0) = (x1,y1)
B(5,3) = (x2,y2)
we know
x = (x2+x1)/2
or, x = (5+7)/2
or, x = 12/2
or, x = 6
and for y
y = (y2+y1)/2
or, y = (3+0)/2
or, y = 3/2
therefore M(x,y) = (6,3/2)
B. solution
let,
C(0,4) = (x1,y1)
B(5,3) = (x2,y2)
equation of line is ;
(y - y1)/(x - x1) = (y2 - y1)/(x2 - x1)
or, (y - 4)/(x -0) = (3 - 4)/(5 - 0)
or, (y - 4)/(x - 0) = -1 / 5
by cross multiply
or, 5×(y - 4) = -1×(x)
or, 5y - 20 = -x
or, x + 5y = 20 is the required equation.
find an equation in standard form of a parabola passing through the points below
(1,-1),(5,31),(6,44).
Answer:
Basic parabola: y = ax2 + bx + c
We have 3 points we can plug in for (x, y) to create 3 simultaneous equations
(-2, 24): 24 = 4a - 2b + c {equation 1}
(3, -1): -1 = 9a + 3b + c {equation 2}
(-1, 15): 15 = a - b + c {equation 3}
Solve this system to find the values of a, b, c
Let's first eliminate variable c:
4a - 2b + c = 24 {equation 1}
a - b + c = 15 {equation 3}
--------------------- subtract
3a - b = 9
9a + 3b + c = -1 {equation 2}
a - b + c = 15 {equation 3}
-------------------- subtract
8a + 4b = -16
We now have two equations with 2 unknowns we can use to find a, b
3a - b = 9 {equation 4}
8a + 4b = -16 {equation 5}
Multiply equation 4 through by 4 and add equations
12a - 4b = 36
8a + 4b = -6
----------------- add
20a = 30
a = 30/20
a = 3/2
8a + 4b = -6
8(3/2) + 4b = -6
12 + 4b = -6
4b = -6- 12
4b = -18
b = -18/4
b = -9/2
Plug these 2 values into one of the original equations and solve for c
15 = a - b + c {equation 3}
15 = 3/2 + 9/2 + c
15 = 12/2 + c
15 = 6 + c
c = 15-6
c = 9
y = (3/2)x2 - (9/2)x+ 9
Upvote
•
0
Downvote
Add comment
Still looking for help?
Step-by-step explanation:
On Monday, Vanessa and Ishaan decided to see how fast they could sprint 200 meters. They asked their friend, Luis, to time them with a stopwatch.
Vanessa sprinted first and ran 200 meters in 54.91 seconds. When it was Ishaan's turn, he sped off and completed the run in 46.07 seconds.
How much faster was Ishaan than Vanessa?
Answer: seconds faster
Answer:
22
Step-by-step explanation:
Please help.
Mary is currently 14 years older than her friend Courtney. In 5 years she will be 2 times as old as Courtney. Let x be Courtney’s age and solve for both of their ages.
How old is Courtney?
Answer:
x = 19
Step-by-step explanation:
x = Courtney's current age
14+x = Mary's current age
Mary's current age: 14 + 19 = 33
14 + x + 5 = 2x
19 = x
help me with this pls
Answer:
9, -8, 15
Step-by-step explanation:
Equation 1
[tex]5(x+7)-3(x-4)=7x+2 \\ \\ 5x+35-3x+12=7x+2 \\ \\ 2x+47=7x+2 \\ \\ 47=5x+2 \\ \\ 45=5x \\ \\ x=9[/tex]
Equation 2
[tex]4(3x+5)-3=9x-7 \\ \\ 12x+20-3=9x-7 \\ \\ 12x+17=9x-7 \\ \\ 3x+17=-7 \\ \\ 3x=-24 \\ \\ x=-8[/tex]
Equation 3
[tex]\frac{1}{3}(5x-9)=2\left(\frac{1}{3}x+6 \right) \\ \\ 5x-9=2(x+18) \\ \\ 5x-9=2x+36 \\ \\ 3x-9=36 \\ \\ 3x=45 \\ \\ x=15[/tex]