On Monday, you run treadmill for 1/2 hour at x miles per hour. On Tuesday, you walk the same distance on the treadmill, at 2 mph slower, and it takes you 3/4 hour.
How many miles did you run on the treadmill on Monday?
Distance = rate * time
Let r = rate
Distance is the same for both runs, so:
.5r = D = 3/4(r - 2)
Distribute (and convert .5):
2/4r = 3/4r - 3/2
Subtract 3/4 r from both sides:
-1/4r = -3/2
Multiply both sides by -4 to get a solitary r:
r = -3 * -4 / 2
r = 3 * 2
r = 6 miles per hour
.5 hours * 6 mi/hr = 3 miles
check:
6 - 2 = 4
3/4 hours * 4 mi/hr = 3 miles
If a point P(x,y) is the equidistant from the points A(2,3) and B(6,1), find the equation of locus of moving point P.
please answer it and I will mark your answer as the brainliest..please..!!!
Answer:
[tex]y=2x-6[/tex]
Step-by-step explanation:
A locus can be defined as a curve or figure formed by all the points satisfying a particular equation of the relation between coordinates.
The condition stated in the question is such that a generic (x,y) point of the curve is equidistant from the points A(2,3) and B(6,1).
The distance d1 from (x,y) to (2,3) is:
[tex]d_1=\sqrt{(x-2)^2+(y-3)^2}[/tex]
The distance d2 from (x,y) to (6,1) is:
[tex]d_2=\sqrt{(x-6)^2+(y-1)^2}[/tex]
Since d1=d2:
[tex]\sqrt{(x-2)^2+(y-3)^2}=\sqrt{(x-6)^2+(y-1)^2}[/tex]
Squaring both sides:
[tex](x-2)^2+(y-3)^2=(x-6)^2+(y-1)^2[/tex]
Operating:
[tex]x^2-4x+4+y^2-6y+9=x^2-12x+36+y^2-2y+1[/tex]
Simplifying all the squares:
[tex]-4x+4x+4-6y+9=-12x+36-2y+1[/tex]
Moving the variables to the left side and the numbers to the right side:
[tex]-4x+12x-6y+2y=36+1-4-9[/tex]
Simplifying:
[tex]8x-4y=24[/tex]
Dividing by 4:
[tex]2x-y=6[/tex]
Or, equivalently:
[tex]\boxed{y=2x-6}[/tex]
the function f(x) is shown in this graph
the function g(x) = -6x -5
Answer:
C.
Step-by-step explanation:
someone please help me with this! please write out the steps as well, thank you!
Answer:
60°
140°
Step-by-step explanation:
From the given figures,
a. we use the concept of alternate angles.
Two parallel lines cut by a transversal will have equal alternate angles;
So;
6x + 12 = 7x + 4
collect like terms and solve for x;
6x - 7x = 4 - 12
-x = -8
x = 8
Now, 6x + 12 = 6(8) + 12
= 48 + 12
= 60°
b. Here we use alternate angles and angles on a line;
4x is an alternate angle to that angle to the left of 13x + 10
And sum of angles on a line = 180
4x + 13x + 10 = 180
17x = 170
x = 10
Now, 13x + 10 = 13(10) + 10 = 140°
In the diagram below
Answer:
m∠A = 39°
Step-by-step explanation:
From the figure attached,
BE ≅ BC
m∠C = 32°
m∠BFD = 103°
In ΔBCE,
m∠E = m∠C = 32° [Since, BE ≅ BC]
m∠E + ∠C + m∠EBC = 180°
32° + 32° + m∠EBC = 180°
m∠EBC = 116°
m∠EBC + m∠EBA = 180° [Linear pair of angles]
116° + m∠EBA = 180°
m∠EBA = 64°
Similarly, m∠AFB + m∠DFB = 180° [Linear pair of angles]
m∠AFB + 103° = 180°
m∠AFB = 77°
Now in ΔAFB,
m∠A + m∠AFB + m∠FBA = 180° [Sum of internal angles of a triangle = 180°]
m∠A + 77° + 64° = 180°
m∠A = 39°
PLEASE HELP THANK YOU
I think the answer is:
- 2(5x+3)/(x+1)(x-5)(x+3)
But another person said:
10x-6/(x+3)(x+1)(x-5)
Who is correct? *Btw for my answer the whole fraction is negative not just the top or bottom.*
Help me please I need to answer this
Answer:
three shirts an hour
Step-by-step explanation:
misty is driving on a scenic road trip, and the graph shows the number of hours traveled compared to the number of miles of the trip remaining. Use the graph below to the answer.
Write an equation of the graph in slope-intercept form.
A. y=-100/3x+450
B. y=100/3x-450
C. y=450x+100/3
Answer:
omg im finding the answer too i go to bcms i see the travid isd thing on ur tabs
Step-by-step explanation:
Answer:
Option A. y=-100/3x+450 is correct.
Step-by-step explanation:
Lea wrote a number riddle. Her clues were: 9 is 10 times the value of the 9 in 329,513 2 is 110 the value of the 2 in 7,562 6 is 110 the value of the 6 in 4.68 Which number is an answer to Lea's riddle? 19,426 95,826 341,950.26 498,173.26 I need help solving this question can someone plz help me
Answer: 498,173.26.
Step-by-step explanation:
Place value of the 9 in 329,513 = 9,000
9 is 10 times the value of the 9 in 329,513.
Then, place value of 9 in required number = 10x 9,000 = 90,000
from options only 95,826 and 498,173.26 has 9 at ten thousands place. (cancel all other options)
Also, 2 is [tex]\dfrac1{10}[/tex] the value of the 2 in 7,562.
place value of 2 in required number =[tex]\dfrac1{10}\times2=0.2[/tex]
i.e. place value of 2 in required number 2 tenths
which is in 498,173.26 [place value of 6 is [tex]\dfrac1{10}[/tex] the value of the 6 in 4.68]
Hence, th required number is 498,173.26.
The 12th term of the sequence is 16 the term to term rule is subtract 3.
Work out the 5th term of the sequence. *
Answer:
a₅ = 37
Step-by-step explanation:
The term to term rule ' subtract 3 ' is the common difference d of an arithmetic sequence with n th term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₁₂ = 16, then
a₁ + 11d = 16 ← substitute d = - 3
a₁ + 11(- 3) = 16
a₁ - 33 = 16 ( add 33 to both sides )
a₁ = 49 , then
a₅ = 49 + (4 × - 3) = 49 - 12 = 37
Give the place of the digit 1 in 296,518.4
296,518,417
Answer:
296,518.4 the one is in the tenths place sunce it's after the decimal
296,518,417 the first 1 in 518 is in the tenths place but the 2nd .. 1 is in the tens place bc no decimal
two in 1 more points
Answer:
Your photo wont show up
Step-by-step explanation:
Answer:
Hello
1. B. 2.35 * 10^11
2. A. 3 * 10^-2
PLS ANSWER THIS CORRECTLY AND GET 30 PTS AND BRAINLY
Answer:
(-0,1)
Really sorry if it's wrong! Have a good day!!
What is the area of a circle with a diameter of 8 cm?
256 cm^2
64 cm^2
8 cm^2
16 cm^2
I really need the answers or im dead
Answer:
graph it and all of the #s will be negitive
Step-by-step explanation:
Answer:
W: (1, 4)
X: (4, 4)
Y: (6, 2)
Z: (5, 1)
Step-by-step explanation:
Rule for rotaion 270° counterclockwise (90° clockwise): (x, y) ⇒ (y, -x)
J: (-4, 1) ⇒ W: (1, 4)
K: (-4, 4) ⇒X: (4, 4)
L: (-2, 6) ⇒ Y: (6, 2)
M: (-1, 5) ⇒ Z: (5, 1)
tia has 53 balloons equally among 4 kids how many balloons will be left over
Answer:
There will be 1 balloon left over.
Step-by-step explanation:
Each kid will be able to get 13 balloons, and 4 times 13 is 52, so 1 balloon will be left.
Answer:
1Step-by-step explanation:
Because 4 times 13 = 52
4 times 13.25 = 53
Each kid will get 13, but
in return, you will get 1 of your balloon's left.
Hope this helps! <3
How do you solve 26 = 18v Equation
Answer:
v = 1.444
Step-by-step explanation:
v = 26/18
v = 1.444
Answer:
26 = 18v
=> 26 / 18 = v (By the law of transposition)
=> 13/9 = v
=> 1.44444 repeating = v (After solving)
If my answer helped, kindly mark me as the brainliest!!
Thank You!!
HELP PLS (picture below)
C
Because it will equal 5,260 but all the other are bigger
Can someone help me create a slope story???
Answer:
I was walking home which I had to go up a hill I wanted to stop by the gas station which was a small hill upwords went back down that hill and the big hill to reach home.
Step-by-step explanation:
y axs = elavation
x axs = time
Hope that helped a little I need to do my hw but seen you needed help sorry if I did not help :(
A blouse that is size x in country A is size s(x) in country B, where s(x)x. A blouse that is size x in the country B is size t(x) in country C, where t(x)x. Find a function f(x) that will convert blouse sizes in country A to blouse sizes in country C.
Answer:
f(x) = [k(x): x = s(x) = t(x)]
Step-by-step explanation:
To make the question clearer, rewrite;
A blouse that is size x in country A is size s(x) in country B.
s(x) = x
A blouse that is size x in country B is size t(x) in country C.
t(x) = x
Find a function f(x) that will convert blouse sizes in country A to blouse sizes in country C.
f(x) = [k(x): x = s(x) = t(x)]
Interpretation:
f of x is equal to k of x such that x is equal to s of x which is also equal to t of x.
Where the other blouse sizes are represented by k(x) or as a function of the given size x.
Write the domain and range of the function as an inequality
Domain = [tex]-\infty < x < +\infty[/tex]
Range = [tex]y \le -4[/tex]
======================================
Explanation:
The arrows on the graph indicate it goes on forever in both left and right directions. So the domain is the set of all real numbers and as an inequality, we write [tex]-\infty < x < +\infty[/tex] which is the same as saying [tex]-\infty < x < \infty[/tex]
This says x is between negative infinity and positive infinity.
In set builder notation, we would say [tex]\{x | x \in \mathbb{R}\}[/tex] and in interval notation, we would write [tex](-\infty, \infty)[/tex]
As you can probably see, the domain is the set of all possible x inputs of a function.
--------------------------
The range is the set of all possible y outputs of a function.
The largest output is y = -4 which is where the vertex is located.
There is no smallest y value as the arrows point down, and the graph goes forever in that direction.
So we say the range is [tex]-\infty < y \le -4[/tex] which shortens to [tex]y \le -4[/tex]
The range in set builder notation is [tex]\{y | y \in \mathbb{R}, \ y \le -4\}[/tex]
The range in interval notation is [tex](-\infty, -4][/tex] The square bracket says to include the endpoint, while the parenthesis excludes the endpoint.
Is this a function or no
Answer: Yes it is a function
Step-by-step explanation:
Answer:
YES
Step-by-step explanation:
In the expression 3x2y + 4x – 5x2y, are the terms 3x2y and –5x2y like terms? Explain by providing support for your answer.
Answer:
yes
Step-by-step explanation:
These are like terms because they have the same variables and powers. The coefficients do not need to match for it to be considered a like term.
Answer:
Sample Response: Yes, they are like terms because like terms have the same variables raised to the same powers. Both terms contain an x and y variable with the x variable squared.
Step-by-step explanation:
2. Lauren is thinking about spending all of her allowance money to buy a new bike. If she has $224
and she can only afford of the price of the bike, how much does the bike cost?
Answer:
$224
Step-by-step explanation:
The bike costs $224
From the expression of the problem, we know that she used all her money to buy the bike.
That means;
Allowance money = bike cost
Therefore, the cost of the bike is $224
· Yolanda deposited $3,547 into an account that earns 4.5%
simple annual interest. Calculate the interest Yolanda will earn
after 6 years. How much will Yolanda have in her account after 6
years?
Answer:
$4,504.69
Step-by-step explanation:
Carlos has saved $19.80. Shaq saved 5/6 of the amount that Carlos saved. Deontae saved 4 times as much as shaq. What is the total saved amount of all threw
Which number is rational, an integer, and a real number?
A. 1.5
B.
C. There is no such nurnber.
D. -5
PLS HELP ILL MARK YOU BRAINEST DUE SOON
Answer:
A, B, C, D or simplify all of them
Step-by-step explanation:
Answer:
all 4 of them
Step-by-step explanation:
a. 29x + 92 = 29x - 11
0x + 92 = -11
0x ≠ -103
b. 29x + 11 = 29x - 11
0x + 11 = -11
0x = -22
0 ≠ -22
c. 29x - 29 = 29x - 11
0x = 18
0 ≠ 18
d. 29x + 29 = 29x - 11
0x + 29 = -11
0x = -40
0 ≠ 40
1.) 9x + 2x - 5x + 7 - 6
Answer:
6x+1
Step-by-step explanation:
9x+2x-5x+7-6
11x-5x+7-6
6x+1
Awnser: 6x+1 :D
What you do is you split it in half so 9x plus 2x is 11x minus 5x is 6x. 7-6 is 1. Put them together and you get 6x+1