Answer:
Hi! I'm pretty sure the question is: Two cities are 45 miles apart. Two trains, with speeds of 70 mph and 60 mph, leave the two towns at the same time so that one is catching up to the other. How long after the trains leave will they be 10 miles apart for the first time? How long after the trains leave will they be 10 miles apart for the second time?
I have had a similar question before, and I will answer yours. :)
Step-by-step explanation:
T1 - the time the trains are moving to each other.
For time T1, the first train will go the distance of 70*t.
The second train, for time t, will go the distance 60*t.
Both for time t1 - 70t+60(t1) = (70+60)*(t1).
45 - (70+60)*t is the distance between trains that left after t hours.
For the first time, they will be 10 miles apart when they are moving into each other
45 - (70+60)*t = 10
45-10 = (70+60)*t
35 = 130*t
t=35/130 h =7/26 h = 0.27 h
The train meets when distance = 0
45 - (70+60)*t = 0
45 = 130t
t =45/130 h = 9/26 h = 0.35 h when trains met.
Trains began to move apart from each other after 9/26 h moving,
After t2 time trains will be (70+60)*(t2) = 130*(t2) mi apart from each other.
130*(t2) = 10
t2 = 1/13h = 0.08h after they met, they are apart from each other 10 mi.
So after the beginning of the movement, it will be time when they met + time when they were moved 10 mi apart from each other
9/26 h+1/13h = 11/26 h = 0.42 h
what is the distance between point P (-5,7) and point Q (6,7) ?
Answer:
11
Step-by-step explanation:
Distance formula is square root of (x2-x1)^2+(y2-y1)^2
square root of (6-(-5))^2+(7-7)^2
square root of (11)^2+(0)^2
square root of 121+0
square root of 121
11
distance is 11
The perimeter of a rectangle can be found using the equation P = 2L + 2W, where P is the perimeter, L is the length, and W is the width of the rectangle.
Solve the equation for the variable w
When you have done that
state the value of 'w' if the perimeter of the rectangle is equal to 37 feet and the length is equal to 4 feet.
hurrryyyy pls
Answer:
14.5 feet
Step-by-step explanation:
To make subject as 'w' and solving:To make the subject as 'w', isolate w.
To isolate 'w', subtract 2L from both sides .2L + 2W =P
2W = P - 2L
Now, divide both sides by 2.[tex]\sf W = \dfrac{P-2L}{2}\\\\W =\dfrac{P}{2}-\dfrac{2L}{2}\\\\ \boxed{W = \dfrac{P}{2}-L}[/tex]
P = 37 feet
L = 4 feet
[tex]\sf W =\dfrac{37}{2}-4\\\\[/tex]
= 18.5 - 4
W = 14.5 feet
Solve the double-ended inequality:
2x-5<4x+2<2x-3
Answer: _ _ x _ _
Answer with a number in the first box, inequality in the second box, than after the x an inequality in the 3rd box and a number in the last box.
EG 5 > x > 18
The solution of the double-ended inequality is -7/2 < x < -5/2
Solving Linear InequalitiesFrom the question, we are to solve the doubled ended inequality.
The given inequality is
2x - 5 < 4x + 2 < 2x -3
From the inequality, we can write that
2x - 5 < 4x + 2 and 4x + 2 < 2x - 3
Now, we will solve each of the inequalities separately
Solving 2x - 5 < 4x + 2
Add 5 to both sides
2x - 5 + 5 < 4x + 2 + 5
2x < 4x + 7
Subtract 4x from both sides
2x - 4x < 4x - 4x + 7
-2x < 7
Divide both sides by -2 and reverse the sign
x > -7/2
-7/2 < x
Solving 4x + 2 < 2x - 3
Subtract 2x from both sides of the equation
4x - 2x + 2 < 2x - 2x -3
2x + 2 < -3
Subtract 2 from both sides
2x + 2 -2 < -3 - 2
2x < -5
Divide both sides by 2
x < -5/2
Putting the two solutions together, we get
-7/2 < x and x < -5/2
-7/2 < x < -5/2
Hence, the solution is -7/2 < x < -5/2
Learn more on Solving linear equations here: https://brainly.com/question/246993
#SPJ1
A line segment has endpoints at (–4, –6) and (–6, 4). Which reflection will produce an image with endpoints at (4, –6) and (6, 4)?
The required expression of the reflection of the point is (-x, y).
Given that,
A line segment has endpoints at (–4, –6) and (–6, 4). Which reflection will produce an image with endpoints at (4, –6) and (6, 4) is to be determined.
The expression is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
Here,
A line segment has endpoints at (–4, –6) and (–6, 4) and an image with endpoints at (4, –6) and (6, 4) is produced the equation of the reflection is given as,
(x, y) ----> (-x, y)
Thus, the required expression of the reflection of the point is (-x, y).
Learn more about expression here:
brainly.com/question/10413253
#SPJ1
two equal rectangular lots are enclosed by fencing the perimeter of a rectangular lot and then putting a fence across its middle. if each lot is to contain 300 square feet, what is the minimum amount of fence (in ft) needed to enclose the lots (include the fence across the middle)?
The minimum amount of fence needed to enclose the lots is 120ft.
Adding areas of both fields, the combined area comes about to be 600sq ft.
The dimensions of the new plot are x length and y breadth. According to the question, there is a fence in the middle with y breadth.
g(x, y, z) = xy - 600
g(x, y, z) = 2x + 3y
∇g = ∇ (xy - 600) = (y, x)
∇f = ∇(2x + 3y) = (2, 3)
Now from the Lagrange method,
∇f = λ∇g
2 = λy
3 = λx
Now to get the value of lambda,
(2/y) = (3/x) = λ
x = 1.5y
Solving now we get,
1.5y² = 600
y = 20
x = 1.5 × 20 = 30
Thus after getting (x,y) we can put the value in the function to get the answer as 120ft.
To learn more about Lagrange multipliers,
https://brainly.com/question/4609414
#SPJ4
[tex]x^{2} x^{2} x^{2} x^{2} x^{2} x^{2} x^{2} x^{2} x^{2} x^{2} x^{2} x^{2} x^{2} \\[/tex]
Answer: [tex]x^{26}[/tex]
Step-by-step explanation:
The [tex]x^2[/tex] appears 13 times. Using the exponent rule [tex]x^a x^b=x^{a+b}[/tex], we get that:
[tex]x^2x^2x^2x^2x^2x^2x^2x^2x^2x^2x^2x^2x^2=x^{2(13)}=x^{26}[/tex]
Round 45.4673
off each number
to two (2) Decimal Place
Answer:
45.47
Step-by-step explanation:
Which algebraic expression represents “the apples were divided equally into seven boxes”?
Answer:
Step-by-step explanation:
a=apples
a/7
The demand function for a certain make of replacement cartridges for a water purifier is given by the equation p=−0. 01x2−0. 1x+21 where p is the unit price in dollars and xis the quantity demanded each week, measured in units of a thousand. Determine the consumers' surplus if the market price is set at $9/cartridge. (Round your answer to two decimal places. )
The demand function for a certain is given by the equation p=−0. 01x2−0. 1x+21 then the determined values will be −50.905557, −0.427737,41.333295.
From the given values,
R=px
9 = (−0. 01x2−0. 1x+21) x
0.01x3+0.1x2−21x−9=0
By reducing the equation,
X = −50.905557, −0.427737,41.333295.
Therefore, the determined values will be −50.905557, −0.427737,41.333295.
Learn more about Equation here
https://brainly.com/question/15707224
#SPJ4
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The function has a maximum value of 30 at x = 3.
Given Function:
f(x) = -3[tex]x^{2}[/tex]+18x+3
here a = -3 , b = 18 , c = 3
a is negative so it has maximum value
x = -b/2a
= -18/2*(-3)
= -18/-6
= 18/6
= 3
f(x) = -3*[tex]3^2[/tex] + 18*3 + 3
= -3*9+54+3
= -27+54+3
= 27+3
= 30
Therefore the function has a maximum value of 30 at x = 3.
Learn more about the function here:
https://brainly.com/question/5975436
#SPJ1
Find the product. (a2)(2a3)(a2 â€"" 8a 9) 2a7 â€"" 16a6 18a5 2a7 â€"" 16a6 â€"" 18a5 2a8 â€"" 16a7 18a6 2a12 â€"" 16a7 18a6
What is the solution set for ly-9| ≤122
O y23 ory≤21
O
-35y≤21
O y2-3 ory$21
0 35ys21
The solution set for the inequality is.
-113 ≤ y ≤ 131
What is the solution set for the inequality?Here we have the following inequality:
|y - 9| ≤ 122
Any absolute value inequality can just be decomposed as follows:
|y - 9| ≤ 122
to:
-122 ≤ y - 9 ≤ 122
Now we can solve this for y by adding 9 in all places:
-122 + 9 ≤ y - 9 + 9 ≤ 122 + 9
-113 ≤ y ≤ 131
That is the solution set.
Learn more about inequalities:
https://brainly.com/question/24372553
#SPJ1
In the image below, the measure of angle 3 is equal to the sum of the measures of angle 6 and what other angle?
For the given figure, angle 3 will be equal to angle 2.
According to the question,
We have the following information:
We have a figure where some angles are marked in form of numbers and the measure of angle 3 is equal to the sum of the measures of angle 6.
Now, we know that vertically opposite angles are equal and angle 1 and angle 4 are vertically opposite angles like angle 2 and angle 3.
(More to know: the sum of three angles of a triangle is equal to 180°.)
Hence, for the given figure, angle 3 will be equal to angle 2.
To know more about angle here
https://brainly.com/question/68367
#SPJ1
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The number of bicycles that must be manufactured to minimize the cost of 250 and the minimum cost is $11,500.
In the given question,
The cost C in dollars of manufacturing x bicyles at a production plant is given by the function shown below;
C(x) = 3x^2-1500x+199,000
(a) In the given question we have to find the number of bicyles that must be manufactured to minimize the cost.
The given function is
C(x) = 3x^2-1500x+199,000
To find the maximum or minimum value we firstly find the value of f'(x).
C'(x) = 6x-1500
Now put f'(x)=0
6x-1500=0
Add 1500 on both side, we get
6x=1500
Divide by 6 on both side we get
x=250
Hence, the number of bicycles that must be manufactured to minimize the cost of 250.
(b) Now finding the value of function at x=250
C(250) = 3(250)^2-1500*250+199,000
C(250) = 3*62,500-375,000+199,000
C(250) = 187,500-375,000+199,000
C(250) = 11,500
The minimum cost is $11,500.
To learn more about maximim and minimum value of quadratic equation link is here
brainly.com/question/28769828
#SPJ1
a fair coin is tossed 28 times. what is the probability that at most 25 tails occur? a) 0.99998628 b) 0.00000152 c) 0.99999848 d) 0.00001220 e) 0.01001372 f) none of the above.
The probability that at most 25 tails occur is 0.99999848.
We know that,
P(x = x) = ⁿCₓ × pˣ × [tex]q^{n-x}[/tex]
p = probability of success = 0.5
n = number of trials = 28
q = 1 - p = 0.5
The probability of the tail occurring at most 25 times can be written as
P(X ≤ 25) = P (X = 0) + P(X = 1) + ..... + P(X = 25)
Using a binomial probability calculator,
P(X ≤ 25) = 0.99999848
Therefore the probability that at most 25 tails occur is 0.99999848
To learn more about binomial probability,
https://brainly.com/question/13384135
#SPJ4
prove that cos A - sin A +1 / cos A + sin A-1 = cosec A+ cot A
(Pls help, urgently needed)
We have to prove (cosA−sinA+1)/(cosA-sinA-) = cotA+cosecA using Trigonometric Functions
What is Trigonometric Functions?
Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.
L.H.S=(cosA−sinA+1)/(cosA-sinA-)
dividing by sinA
=cotA+1−cosecA/cotA−1+cosecA
=(cotA−1+cosecA)(cotA+1+cosecA)/(cotA+1)²-cosec²A
=(cotA+cosec)²-1/2cotA
=cotA+cosecA(R.H.S)
Hence the above trigonometric function is proved.
Learn more about Trigonometric Functions, by the following link.
https://brainly.com/question/24349828
#SPJ1
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
everyone can someone help me here please (complete solution and graph)
Answer:
1: x^2+y^2-6x-4y-3=0
2: x^2+y^2-10x+4y=0
3: x^2+y^2-10x+2y+1=0
Could someone help quick
The constant of proportionality is known to be the ratio of two proportional values that is said to be in a constant value.
What is the constant of proportionality?The constant of proportionality is a term that is defined as the rate or the ratio of two proportional values which are known to be at the same value.
constant of proportionality = 2.5
Given : y = 2.5x.
To find : What is constant of Proportionality in the equation.
Solution : We have given
y = 2.5x.
On comparing with equation of proportionality : y = kx,
Where, k is the constant of proportionality.
On comparing y = 2.5 x by y = kx .
We get k = 2.5
So, constant of proportionality = 2.5
Therefore, constant of proportionality = 2.5
To learn more about constant of proportionality refer
https://brainly.com/question/28413384
#SPJ1
The value of constant proportionality is 2.5. The constant of proportionality is known to be the ratio of two proportional values that is said to be in a constant value.
What is the constant of proportionality?The constant of proportionality is a term that is defined as the rate or the ratio of two proportional values which are known to be at the same value.
constant of proportionality = 2.5
Given : y = 2.5x.
To find : What is constant of Proportionality in the equation.
Solution : We have given
y = 2.5x.
On comparing with equation of proportionality : y = kx,
Where, k is the constant of proportionality.
On comparing y = 2.5 x by y = kx .
We get k = 2.5
So, constant of proportionality = 2.5
Therefore, constant of proportionality = 2.5
To learn more about constant of proportionality refer
brainly.com/question/28413384
#SPJ1
how do i solve 8x-8=4x
The solution to the algebraic equation 8x - 8 = 4x is x = 2
How to solve algebraic equation?Algebra: This is the system for computation using letters or other symbols to represent numbers, with rules for manipulating these symbols.
8x - 8 = 4x
Collect like terms8x - 4x = 8
4x = 8
divide both sides by 4x = 8/4
x = 2
Check:
8x - 8 = 4x
substitute x = 2 into the equation
8(2) - 8 = 4(2)
16 - 8 = 8
8 = 8
Other examples of algebraic equation
3x + 5 = 11
substract 5 from both sides
3x = 11 - 5
3x = 6
divide both sides by 3
x = 6/3
x = 2
Therefore, the value of x from the equation is given by 2
Read more on algebraic equation:
https://brainly.com/question/4344214
#SPJ1
examples of linear equation
A sample survey of 54 discount brokers showed that the mean price charged for a trade of 100shares at 50 per share was $33. 77 (AAII Journal, February 2006). The survey is conducted annually. With the historical data available, assume a known population standard deviation of $15.
a. Using the sample data, what is the margin of error associated with a 95% confidence interval?
b. Develop a 95% confidence interval for the mean price charged by discount brokers for a trade of 100 shares at $50 per share
a) The margin of error associated with a 95% confidence interval is 4.
b) The 95% confidence interval for the mean price charged by discount brokers for a trade of 100 shares at $50 per share is ($29.77,$37.77)
a) We are given with the information that the mean for 54 discount brokers is $50 for 100 shares is $33.77 Also the population standard deviation is $15.
The formula for margin of error is Z = zα/2 σ √ n
Now we know from our z-table that value of zα/2 for 95% confidence interval is 1.96
So, the value of error margin is zα/2 σ √ n =1.96 (15/√54) = 1.96 x 2.04
= 4
b) We know from part a that margin of error is 4.
Also, the mean price charged for a trade of 100shares at 50 per share was $33. 77
The value of confidence interval for population mean is,
x ± zα/2 σ √ n = 33.77 ± 4 = (29.77,37.77)
Thus, the 95% confidence interval for the mean price charged by discount brokers for a trade of 100 shares at $50 per share is ($29.77,$37.77)
Get to know more about Confidence Intervals and Error of Margins from here:
https://brainly.com/question/24131141
#SPJ4
What is the quotient (x2 − 9x + 20) ÷ (x − 4)? (1 point) x − 5 x − 4 x + 4 x + 5
Answer:
The guy under me is correct
Step-by-step explanation:
Answer:
x - 5
Step-by-step explanation:
Factor the expressions that are not already factored
(x^2 - 9x + 20) / (x - 4)
Cancel out x - 4 in both numerator and denominator
[tex]\frac{(x-5)(x-4)}{x-4}[/tex]
x - 5
Kaela wants to purchase a pair of shoes at Macy’s that cost $80. If Macy’s charges a
6% sales tax, how much will Kaela pay for the shoes, including tax?
Answer: $84.80
Step-by-step explanation:
The actual sales tax was 4.80 because 6% of 80 is 4.80
Then add the 4.80 to the 80 to get your total
Hope this helped :)
Mrs. Shelly paid $3 for 6 muffins and Mrs. Kloske paid $9 for 18 muffins. How much did
Mrs. Smith pay for 30 muffins?
Explain your answer
a) $3
b) $10
c) $15
d) $30
13) Mr. Harrington wants to buy a new TV for $500. He has a 10% off coupon and knows the tax
be 13.5%. How much money will he need to save to buy the TV?
a) $510.75
c) $450
b) $432.50
d) $567.50
Mr. Harrington will need $510.75 to buy the TV
The correct answer is an option (a)
In this question, Mr. Harrington wants to buy a new TV for $500
He has a 10% off coupon.
After applying this coupon, the cost of TV would be,
500 - (10 percent of $500)
= 500 -[ (10/100) * 500]
= 500 - 50
= 450
He knows the tax be 13.5%.
13.5 percent of 450 would be,
(13.5/100) * 450
= 60.75
So, the amount he will need to save to buy the TV,
$450 + $60.75 = $510.75
Therefore, Mr. Harrington will need $510.75 to buy the TV
The correct answer is an option (a)
Learn more about the percentage here:
https://brainly.com/question/16797504
#SPJ9
lin rode he skateboard 3 miles in 9 minutes. she rode at a constant speed. how far did she go if she only went for 1 minute?
First, break down the problem.
Someone can skate 3 miles in 9 minutes.
What is their speed? How far would they go if they did that speed for 1 minute?
To find speed given time and distance, divide distance by time.
3/9 = 1/3
Speed is 1/3 mile per minute
if they travel one minute, they will travel 1/3 of a mile
hope this helps :)
Help pls I'll give you brainliest and 15 points asap.
How does the graph of g(x)=4⌊x⌋ differ from the graph of f(x)=⌊x⌋?
1. Multiplying by 4 shifts the graph of g(x)=4⌊x⌋ up 4 units.
2.Multiplying by 4 shifts the graph of g(x)=4⌊x⌋ down 4 units.
3.Multiplying by 4 stretches the graph of g(x)=4⌊x⌋ vertically by a factor of 4.
4.Multiplying by 4 shifts the graph of g(x)=4⌊x⌋ right 4 units.
Question 2
How does the graph of g(x)=⌊x⌋−3 differ from the graph of f(x)=⌊x⌋?
1.The graph of g(x)=⌊x⌋−3 is the graph of f(x)=⌊x⌋ shifted right 3 units.
2.The graph of g(x)=⌊x⌋−3 is the graph of f(x)=⌊x⌋ shifted left 3 units.
3.The graph of g(x)=⌊x⌋−3 is the graph of f(x)=⌊x⌋ shifted up 3 units.
4.The graph of g(x)=⌊x⌋−3 is the graph of f(x)=⌊x⌋ shifted down 3 units.
Answer:
Question 1: #3 is correct.
Question 2: #4 is correct.
(Help!)
#8 The tables represent some points on the graphs of lines m and n. Which system of equations is represented by lines m and n?
(A) −6x − y = 8 −3x + 2y = 9
(B)6x + y = −8 3x − 2y = 9
(C) 6x − y = −8 −3x − 2y = 9
(D) 6x − y = 8 3x + 2y = 9
#9 A produce company sells crates filled with a mixture of apples and oranges during the holiday season to grocery stores. Each crate contains a total of 72 pieces of fruit. Suppose that a crate has 8 more apples than oranges.
Which system of linear equations can be used to determine the number of pieces of each kind of fruit in the crate?
(A) a + o = 72 o = a + 8
(B) 8a + o = 72 a + o = 8
(C) a + o = 72 a = o + 8
(D) a + 8o = 72 a + o = 8
#10 The tables represent some points on the graphs of lines r and s. Which system of equations is represented by lines r and s?
(A) −4x + 3y = 12 2x − 5y = −10
(B) −4x − 3y = −12 −2x + 5y = 10
(C) 4x + 3y = −12 2x − 5y = 10
(D) 4x − 3y = −12 −2x − 5y = 10
The linear functions representing the systems of equations in each case are given as follows:
8. (D) 6x − y = 8 3x + 2y = 9
9. (C) a + o = 72 a = o + 8.
10. (C) 4x + 3y = −12 2x − 5y = 10.
What is a linear function?The slope-intercept representation of a linear function is presented by the rule as follows:
y = mx + b
The coefficients of the function and their meaning are listed as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x increases by one.b is the y-intercept of the function, being the numeric value of the function when the input variable x assumes a value of 0.For the line m, we have that when x increases by 6, y increases by 36, hence the slope is:
m = 36/6 = 6.
Considering the positive slope of 6, at x = 0, the numeric value is 12 less than the numeric value at x = 2, hence the intercept is:
b = 4 - 2 x 6 = -8.
Hence the equation is:
y = 6x - 8.
6x - y - 8.
Thus option d is correct.
For item 9, we use the variables a and o. The total is of 72, hence:
a + o = 72.
Suppose that a crate has 8 more apples than oranges, hence:
a = o + 8.
Thus option c is correct.
For line r in item 10, when x increases by 3, y decays by 4, hence the slope is:
m = -4/3.
When x = 0, y = -4, hence the intercept is:
b = -4.
Thus the equation is:
y = -4x/3 - 4
3y = -4x - 4.
4x + 3y = -12.
Meaning that option c is correct.
More can be learned about linear functions at https://brainly.com/question/24808124
#SPJ1
3.472 divided by ____=0.112 free 25 points!!
When the divisor is missing, you divide the dividend (3.472) by the quotient (0.112)
So, we will do 3.472 divided by 0.112
3.472/0.112 = 31
Another method is multiplication. Multiplication is the opposite of division. We'd multiply 0.112 by 31.
0.112 x 31 = 3.472
In conclusion,
3.472/31 = 0.122
If you need extra help, use this video as a reference
https://youtu.be/9ui8Yh0bwCI?t=83
Answer: 3.472/31 = 0.122
Step-by-step explanation: I hope this helps:)