Ralph and Liza are both driving from Los Angeles to Santa Fe. Ralph leaves at 7:00 and averages 60 mph (miles per hour) on the way. Liza leaves at 7:25 and averages 65 mph on the way. The situation is modeled by this system, where x is the number of hours after Liza leaves and y is the distance each will travel: y= 60x + 25 y = 65x How long after Liza leaves will she pass Ralph, and how far will they each have traveled?
Answers
The given equations are
\(y=60x+25\)\(y=65x\)Where x is the number of hours, and y is the distance each will travel.
We can graph these functions to find the answers.
As you can observe in the graph above, the common point is (5,325). This means after 5 hours and 325 miles, they will find each other.
Related Questions
PLS HELP 50 POINTS!!
Answers
The line segment FG represent the volume of water decreases in Katherine's water bottle.
From the given graph, x-axis represents the distance from home (km) and the y-axis represents the volume (L).
The line segment FG represent the volume of water decreases in Katherine's water bottle, the line segment HI represent the volume of water increases in Katherine's water bottle and the line segment KL represents there is no change in water level.
Therefore, the line segment FG represent the volume of water decreases in Katherine's water bottle.
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PLEASE HELP!!! An ID at the zoo consists of 3 letters followed by 2 number (0-9). How many unique IDs are possible?(SHOW YOUR WORK)(WILL MARK BRAINLIEST)
Answers
Answer:
1,757,600.
Step-by-step explanation:
I am assuming you are allowing duplicates.
Number of possible letters = 26^3
Possible numbers = 10^2
Number of unique Ids = 10^2 * 26*3
= 1,757,600.
If a wheelchair access ramp has to have an angle of elevation no more than 4.8 degrees and it has to rise 18 inches above the ground, how long must the ramp be?
Answers
The wheelchair access ramp must be 216.09 inches long.
To find the length of the wheelchair access ramp, we can use trigonometry.
The tangent function relates the angle of elevation to the ratio of the opposite side (height) to the adjacent side (length of the ramp).
Let's denote the length of the ramp as "x".
The height of the ramp is given as 18 inches.
Using the tangent function:
tan(angle of elevation) = height/length of the ramp
tan(4.8 degrees) = 18/x
To solve for x, we can rearrange the equation:
x = 18 / tan(4.8 degrees)
Using a calculator to evaluate the tangent of 4.8 degrees:
x = 18 / 0.08331
x= 216.09
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Write the equation for the horizontal line passing through (3, 4).
Answers
Answer:
equation for a straight horizontal line passing through the coordinates (3,4):
y=4
Step-by-step explanation:
Triangle DEF and triangle CBD are similar right triangles. What statement about the slopes DF and CD is true?
Answers
Similar triangles may or may not have equal side lengths
The true statement is (a) the slope of DF is equal to the slope of CD
How to determine the slopes of DF and CDThe similar triangles are given as:
Triangle DEF and triangle CBD
The above means that the corresponding lines DF and CD have equal slope
The slope of segment DF is calculated as:
\(m =\frac{7 - (-2)}{1 - (-2)}\)
While the slope of segment CD is:
\(m =\frac{-2 - 4}{-2 - 0}\)
Hence, the true statement is (a)
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If each of the numbers in the following data set were multiplied by 18, what
would be the new median of the data set?
14, 20, 18, 58, 71, 36, 28
what would be the new median of the data set ?
Answers
The answer is 28 or 504. My explanation....
ALRIGHT! So, it took me a little while to do it all.... since I wasn't really sure if it was already multiplied by 18 or not.
So the normal numbers in order from least to greatest,(because that's easier)
14, 18, 20, 28, 36, 58, 71.
The new numbers I multiplied by 18 are...
252, 324, 360, 504, 648, 1044, 1268.
When I put it like that you can clearly see the new median. 28 and 504!
A college student completed some courses worth 6 credits and some courses worth 4 credits. The student earned a total of 104 credits after completing 21 courses.How many courses worth 4 credits did the student complete?A. 11B. 26C. 13 D. 10
Answers
Let x be the number of four credit courses and let y be the number of six credit courses.
We know that the student have completed 21 courses, this means that:
\(x+y=21\)We also know that he has 104 credits in total. This means that:
\(4x+6y=104\)Then we have the system of equations:
\(\begin{gathered} x+y=21 \\ 4x+6y=104 \end{gathered}\)To solve the system we solve the first equation for y and plug the value in the second one. That is:
\(y=21-x\)\(\begin{gathered} 4x+6(21-x)=104 \\ 4x+126-6x=104 \\ -2x=104-126 \\ -2x=-22 \\ x=\frac{-22}{-2} \\ x=11 \end{gathered}\)Therefore, the student has taken 11 four credit courses.
A salesperson earns a commission of $308 for selling $ 2200 in merchandise. Find the commission rate.
Answers
Answer:$247
Step-by-step explanation
Liam bought a car for 12,478 the car depreciates at a rate of 7% per year how long until the car is worth less than 3,000
Answers
Answer: after 6 years, the car's value will be less than $3,000.
Step by step explanation:
To solve this problem we need to determine how many years it will take for the car's value to drop below $3,000.
First, we can calculate how much the car will depreciate in one year by multiplying its value by the depreciation rate:
12,478 x 0.07 = 873.46
So after one year, the car will be worth:
12,478 - 873.46 = 11,604.54
We can continue this process to determine the value of the car after each subsequent year.
After two years:
11,604.54 x 0.07 = 812.32
11,604.54 - 812.32 = 10,792.22
After three years:
10,792.22 x 0.07 = 755.45
10,792.22 - 755.45 = 10,036.77
After four years:
10,036.77 x 0.07 = 702.57
10,036.77 - 702.57 = 9,334.20
After five years:
9,334.20 x 0.07 = 653.39
9,334.20 - 653.39 = 8,680.81
After six years:
8,680.81 x 0.07 = 607.66
8,680.81 - 607.66 = 8,073.15
I need the area can someone help meeee pls?
Answers
Answer:
54ft
Step-by-step explanation:
9ft x 6ft
Use synthetic division to find the quotient if polynomial P(x) = x³ - 7 x + 6 is divided by x - 2
A) x²+2 x+3
B) x²-2 x-3
C) x²-2 x+3
D) x²+2 x-3
Answers
The polynomial function p(x) = x³ - 7x + 6 divided by x - 2 = x² + 2x - 3
Synthetic Division of PolynomialsSynthetic division is a method used to perform the division operation on polynomials when the divisor is a linear factor. One of the advantages of using this method over the traditional long method is that the synthetic division allows one to calculate without writing variables while performing the polynomial division, which also makes it an easier method in comparison to the long division.
We can represent the division of two polynomials in the form:
p(x)/q(x) = Q(x) + R/(q(x))
where,
p(x) is the dividendq(x) is the linear divisorQ(x) is quotientR is remainderThe polynomial function p(x) = x³ - 7x + 6 is divided by x - 2
x³ - 7x + 6 ÷ x - 2 = (x - 1)(x + 3)
x² + 3x - x - 3 = x² + 2x - 3
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What is 4/7 x 4
Helppppp
Answers
16/7
2 and 2/7
Answer: 2 2/7
Step-by-step explanation:Make 4 to a fraction which is 4/1.And now you multiply 4/7 by 4/1 .ANd when you mutliply them together you get 16/7.Lastly,you change 16/7 to a mixed number which is 2 2/7.
i don't understand how to do this.. can someone help, please
Answers
The possible values for angles 1, 2, and 3 given that lines a and b are parallel lines include the following:
m∠1 = 60°.m∠2 = 120°.m∠3 = 60°.What are parallel lines?In Mathematics and Geometry, parallel lines are two (2) lines that are always the same (equal) distance apart and never meet or intersect.
Note: Assuming angle 1 is equal to 60 degrees.
In Mathematics and Geometry, the vertical angles theorem states that two (2) opposite vertical angles that are formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other:
m∠1 ≅ m∠3 = 60°.
Based on the linear pair postulate, the measure of angle 2 can be determined as follows;
m∠1 + m∠2 = 180°
60° + m∠2 = 180°
m∠2 = 180° - 60°
m∠2 = 120°
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Minimize
z = 20x1 + 32x2 + 40x3,
subject to
3x1 + x2 + 6x3 ≥ 9
x1 + x2 ≥ 9
4x2 + x3 ≥ 12
x1 ≥ 0, x2 ≥ 0, x3 ≥ 0.
solve for x1, x2, x3 and z
Answers
Answer:
Step-by-step explanation:
1. constraints with "\(\geq\)" we should subtract surplus variable S1, S2, S3 and add artificial variable A1, A2, A3
Hence Z = 20 x1 + 32x2 + 40x3 + 0S1 + 0S2 + 0S3 + MA1 + MA2 + MA3
subject to
\(3x_1 +x_2+6x_3-S_1+A_1=9\)
\(x_1+x_2-S_2+A_2=9\)
\(4x_2+x_3-S_3+A_3=12\)
and \(x_1,x_2,x_3,S_1,S_2,S_3,A_1,A_2,A_3\geq 0\)
f(x)=-x^2-9x-7
f(x)=−x
2
−9x−7
f = 3
Answers
Answer:
Assuming the question posed is to find the values of x thtat satisfy the equation f(x) = x^2 - 9x - 7, this is a quadratic equation of the form Ax^2 + Bx + C which has the closed-form solution x = (-b +/- Sqrt[b^2 - 4 ac])/(2a) - widely known as the "quadratic equation."
Step-by-step explanation:
By applying the quadratic equation, we find that the solutions to this equation are
x = 1/2 * (9-Sqrt[109])
x = 1/2 * (9+Sqrt[109])
You have just made your first $2,000 contribution to your retirement account. Assume you earn a return of10 percent and make no additional contributions.
a. What will your account be worth when you retire in 30 years?
b. What will your account be worth if you wait 5 years before contributing?
Answers
Answer:
BELOW
Step-by-step explanation:
Assuming no compounding
then interest = prt = 2000 * .1 * 30 = 6000
add original deposit to get 8000 total at end of 30 years
Assuming annual compounding
amount = 2000 ( 1+ .1)^30 = 34 898.80 dollars
Which definitely shows the POWER of COMPOUNDING !
if you are in a 200 meter race and finish 19 meters ahead of your opponent, if you were to run the race again, where woild you have to start to end the race in a tie?
Answers
Answer:
i haven't done this in years but i'm pretty sure -19 meters
Step-by-step explanation:
The sum of three numbers is 2100 the first number (x) is equal to each other what are the three numbers (x,y,z)
Answers
The sum of three numbers is 2100
And the three numbers are equal to each other.
So we have :
\(\begin{gathered} x+x+x=2100 \\ 3x=2100 \\ x=\frac{2100}{3} \\ x=700 \end{gathered}\)The answer is (700, 700, 700)
NZ is the angle bisector of ∠LNM. What is LZ? Enter the numerical value only.
Answers
Answer:
LZ = 3
Step-by-step explanation:
given NZ is the angle bisector of ∠ LNM , then it divides the opposite side into segments that are proportional to the other 2 sides, that is
\(\frac{LZ}{MZ}\) = \(\frac{NL}{NM}\) ( substitute values )
\(\frac{LZ}{5-LZ}\) = \(\frac{3}{2}\) ( cross- multiply )
2 LZ = 3(5 - LZ) ← distribute parenthesis
2 LZ = 15 - 3 LZ ( add 3 LZ to both sides )
5 LZ = 15 ( divide both sides by 5 )
LZ = 3
A fashion designer wants to know how many new dresses women buy each year. Assume a previous study found the standard deviation to be 1.3. He thinks the mean is 5.5 dresses per year. What is the minimum sample size required to ensure that the estimate has an error of at most 0.1 at the 95% level of confidence? Round your answer up to the next integer.
Answers
Answer:
649
Step-by-step explanation:
Given that
Mean number of dresses is 5.5
Standard deviation of the sample, S.D is 1.3
Margin of error, M.E is 0.1
Level of confidence is 95% or 0.95
The formula for margin of error, M.E is
Z * (S.D/√n) , where
Z = Value for level of confidence which is 1.96
Proceeding further, we have
0.1 = 1.96 * (1.3/√n)
0.1 = 2.548 / √n, making √n subject of formula, we have
√n = 2.548 / 0.1
√n = 25.48, squaring both sides
n = 25.48²
n = 649.23
Therefore the number of sample size we're looking for is n = 649.23, when rounded to the nearest integer, we have it to be 649
Determine the number k so that there is a solution to the differential equation ky'- y = x that satisfies the conditions y(1) = 0 and y'(1) = 1
Answers
To solve for k, we first take the derivative of the differential equation to obtain:
ky'' - y' = 1
Then we substitute y = 0 and y' = 1 when x = 1, giving us:
k(1) - (1) = 1
k = 2
Therefore, the value of k that satisfies the given conditions is k = 2.
Math Homework: Unit 3 Assignment
Answers
Apply the limit laws to evaluate the ff. limits
Answers
Limit's characteristics include its laws. The limit of a function is determined using them. A constant's limit is that very same constant.
How do limitations get assessed?By assessing the function at values close to x=0, we can determine the value of a limit, if one exists. We are unable to immediately determine the value of a function for x=0 since the outcome would be undefined as its denominator would be 0.Limit's characteristics include its laws. The limit of a function is determined using them. A constant's limit is that very same constant.By assessing the function at values close to x=0, we can determine the value of a limit, if one exists. We are unable to immediately determine the value of a function for x=0 since the outcome would be undefined as its denominator would be 0.The complete question is,
Which limitations rules apply?
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Write the number in decimal form.
3.39 x 1012
Answers
Answer:
3,390,000,000,000
Which is equivalent to (negative 2 m + 5 n) squared, and what type of special product is it?
4 m squared + 25 n squared; a perfect square trinomial
4 m squared + 25 n squared; the difference of squares
4 m squared minus 20 m n + 25 n squared; a perfect square trinomial
4 m squared minus 20 m n + 25 n squared; the difference of squares
Answers
Answer:
4 m squared minus 20 m n + 25 n squared; a perfect square trinomial
Step-by-step explanation:
(-2m+5n)(-2m+5n)
4\(m^{2}\)-20mn+25\(n^{2}\)
By expanding the given expression, we conclude that the equivalent expression will be the perfect square trinomial:
4m^2 + 20m*n + 25n^2
How to get an equivalent expression to the given binomial?We have a polynomial given by the expression:
(2m + 5n)^2
If we expand the binomial (binomial means that it hastwo terms), we will get:
(2m)^2 + 2*(2m)*(5n) + (5n)^2
= 4m^2 + 20m*n + 25n^2
This is a perfect square trinomial (trinomial because has 3 terms and perfect square because is the square of a binomial).
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which is the right andwer?????????? please help me
Answers
Answer:
The first one
The figure has line(s) of symmetry. What type(s) of symmetry does the figure have?
Answers
Answer:
i domisa
Step-by-step explanation:
20. in this problem we assume that fish are caught at a constant rate h independent of the size of the fish population. then y satisfies dy dt
Answers
the solution of the given derivative will be y = k/2(1±√(1-4h/rk))
What is derivative?
A function's varied rate of change with respect to an independent variable is referred to as a derivative. When there is a variable quantity and the rate of change is irregular, the derivative is most frequently utilised. The derivative is used to assess how sensitive a dependent variable is to an independent variable (independent variable). In mathematics, a quantity's instantaneous rate of change with respect to another is referred to as its derivative. Investigating the fluctuating nature of an amount is beneficial.
dy/dt = 0
-r/k y²+ry-h=0
y = k/2(1±√(1-4h/rk))
Hence the solution of the given derivative will be y = k/2(1±√(1-4h/rk))
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12a – 10b + 6
coefficients:
help plsss
Answers
Answer:
12 and -10
Step-by-step explanation:
a coefficient is a number multiplied by a variable
A student writes the equation for a line that has a slope of -6 and passes through the point (2, –8).
y -(-8) = -6(x - 2)
y -(-8) = -6x + 12
y -(-8) + 8 = -6x + 12 + 8
y = -6x + 20
Explain why the work is not correct.
Answers
Answer:
y = -6x + 20
Step-by-step explanation:
Answer:
This is not correct because it shows y+10 minus y but thats not correct!
Step-by-step explanation: