Suppose that y varies directly with x and inversely with z, and y = 6 when x = 8 and z = 4. Write the equation that models the relationship. Then find y when x = 2 and z = 3
Answer:
y=18
Step-by-step explanation:
explanation is in the attachment above
A soda costs $1.25 in a vending machine. A 12-pack of the same soda costs $3.49 at a grocery store. How much do you save by buying a dozen cans at the grocery store?
Answer:
you would save 11.51 dollars
Step-by-step explanation:
12 cans times the vending machine price of 1.25$= $15
15-3.49=11.51
In the equation 5b = 45, b = 10
True or False
Answer:
False b=9
Step-by-step explanation:
In the equation 5b+45, b is equal to 9
The way we get this answer is by dividing each term by 5 and then simplifying
45/5
45/5=9
Hope this helps :)
help with 4 please thank you
Answer:
=3x^2+4
Step-by-step explanation:
Subtract 8 from 12.
3x^2+4
PLEASE HELP 100 POINTS!!! PLEASE DON'T ANSWER IF YOU DON'T KNOW!!
Alana and Kelsa are training for a marathon. To prepare for this marathon they have been training and tracking their progress periodically.
In the first week of training Alana ran an average of 20 minutes per mile. Later, in week seven of training she ran an average of 14 minutes per mile.
In the first week of training Kelsa ran an average of 15 minutes per mile. Later, in week five of training she ran an average of 13 minutes per mile.
Assuming that Alana and Kelsa continue to train and improve their times at the same rate your task is to determine which week they will have the same average minutes per mile. We will assume that the relationship is linear as they will be training for a maximum of 43 weeks. To complete this task follow the steps below.
1. Determine the equation of a line in standard form that represents Alana’s training progress. Her progress corresponds to the points (1, 20) and (7,14).
2. Determine the equation of a line in standard form that represents Kelsa’s training progress. Her progress corresponds to the points (1, 15) and (5,13)
3. Solve the system of equations (you must show all your work to receive full credit).
4. In which week will Alana and Kelsa have the same average minutes per mile?
5. If Alana and Kelsa continue to train until week 30, what will their times be?
6. Do you believe a linear model best represents the relationship of the time of the runners and the weeks that passed?(Hint: look at question 5). What do you think this says about problems in the real world? Justify your thoughts in 3-4 sentences.
Answer: Alana's training experience in (weeks, minutes per mile) is (1, 12) and (5, 6).
Kelsa's training experience is (1, 10), (11, 5).
Find:
A linear equation in standard form that describes Alana's experience
A linear equation in standard form that describes Kelsa's experience
A solution to the pair of linear equations
The week in which the number of minutes per mile is the same
Minutes per mile for Alana and Kelsa at week 25
Comment on the use of a linear model in this context
Solution:
Please note that in parts 1 and 2 a "standard form" linear equation has a positive leading coefficient and the numbers have no common factor.
1. A linear equation can be written from two points (x1, y1) and (x2, y2) as ...
... (y2 -y1)(x -x1) -(x2 -x1)(y -y1) = 0
Using the given points in order, this becomes
... (6-12)(x -1) -(5 -1)(y -12) = 0 . . . . above equation with values filled in
... -6x +6 -4y +48 = 0 . . . . . . . . . . eliminate parentheses
... 3x +2y -27 = 0 . . . . . . . . . . . . . divide by -2 to make x-coefficient positive
... 3x +2y = 27 . . . . . . . . . . . . . . . . Alana's training experience
2. In similar fashion, we can write the equation for Kelsa's experience.
... (5 -10)(x -1) -(11 -1)(y -10) = 0
... -5x +5 -10y +100 = 0 . . . . . . eliminate parentheses
... x +2y -21 = 0 . . . . . . . . . . . . . divide by -5
... x +2y = 21 . . . . . . . . . . . . . . . . Kelsa's training experience
3. We note that both equations have the term 2y, so we can subtract the second equation from the first to eliminate that term:
... (3x +2y) -(x +2y) = (27) -(21)
... 2x = 6 . . . . . . . simplify
... x = 3 . . . . . . . . divide by 2
... 3·3 +2y = 27 . . . substitute x=3 into Alana's equation
... 2y = 18 . . . . . . . . subtract 9
... y = 9 . . . . . . . . . . divide by 2
The solution is (weeks, minutes) = (x, y) = (3, 9).
4. The solution of part 3 tells us both have an average time of 9 minutes per mile in week 3 of training.
5. Substituting x=25 into the equations of parts 1 and 2, we get ...
... 3·25 +2y = 27
... y = (27 -75)/2 = -24 . . . . Alana's time per mile at week 25
... 25 + 2y = 21
... y = (21 -25)/2 = -2 . . . . . Kelsa's time per mile at week 25
6. A linear model makes no sense in this context. At some point a linear equation for minutes per mile will always have a value of 0. We know that marathon runners will never have a time of zero minutes per mile. Under the best of conditions, we expect training to improve time toward some asymptotic limit determined by body mechanics. A linear model is completely inappropriate for describing such training effects. Not every real-world problem is appropriately represented by a linear equation.
Step-by-step explanation:
_______divisible by both 2 and 5
Step-by-step explanation:
____2__divisible by both 2 and 5
A bag is filled with green and blue marbles. There are 43 marbles in the bag. If there are 7 more green
marbles than blue marbles, find the number of green marbles and the number of blue marbles in the bag.
Equation (use x as your variable):
The number of blue marbles is:____
The number of green marbles is:____
Answer:
Blue marbles: 18
Green marbles: 25
Step-by-step explanation:
First off, we have to define our variables.
g = # of green marbles
b = # of blue marbles
We know two equations:
g + b = 43 and g = b + 7
If you're wondering how I got the first equation, it was because the number of green and blue marbles is 43. For the second equation, we know that there are 7 more green marbles than blue marbles.
Now, we have an equation for the number of green marbles. We can plug that equation into the equation g + b = 43.
So, (b + 7) + b = 43.
When we simplify it, we get 2b + 7 = 43.
We subtract 7 from both sides, which gets us 2b = 36.
Now, b = 36/2.
b = 18.
So, we found out the number of blue marbles that we have. We know that g + b = 43. Now, all we have to do is plug in the number of blue marbles into that equation to find out the number of green marbles.
g + 18 = 43.
g = 43 - 18.
g = 25.
Thus, the number of green marbles we have is 25 and the number of blue marbles is 18.
If you know this please answer all fake answers will be reported thanks
Answer:
50.24 inches
Step-by-step explanation:
[tex]3.14 * 4^{2}[/tex]
3.14 * 16
= 50.24
Ethan uses the function f(x) = 2x2 + 2x + 4 to track the temperature of a substance over 8 hours. You know that f(3) = 28 meaning that the temperature of the substance is 28°C when you plug in a 3 for x. What is the domain of Ethan’s function?
The domain of the function f(x) = 2x² + 2x + 4 is (-∞, ∞).
What is Quadratic equation?The polynomial equation whose highest degree is two is called a quadratic equation or sometimes just quadratics. It is expressed in the form of:
ax² + bx + c = 0
where x is the unknown variable and a, b and c are the constant terms.
You have the quadratic function
f(x) = 2x² + 2x + 4 ,
and remember that all quadratic functions are parabolas opening at point called the vertex.
Since you can plug any real number in our parabola here, its domain is all the real numbers, and this is true for all the quadratic functions of the form ax² + bx + c = 0.
Thus, in interval notation the domain of the function is (-∞, ∞).
Learn more about Quadratic Equation from;
https://brainly.com/question/2263981
#SPJ1
f(x) = 2^x
what is the domain ?
range ? asymptote ? and transformation
y=2x
Step-by-step explanation:
I dont know what else there is sry
Please help!! 10-15 much appreciated! :)
Answer:
Step-by-step explanation: sin β = [tex]\frac{oposite }{hypotenuse}[/tex] ; cos β = [tex]\frac{Adjacent}{Hypotenuse}[/tex]
10) sin [tex]32^{0}[/tex] = [tex]\frac{x}{18}[/tex]
18 sin [tex]32^{0}[/tex] = x
18 (0.53) = x
x= 9.5 units
cos [tex]32^{0}[/tex] = [tex]\frac{y}{18}[/tex]
18 cos [tex]32^{0}[/tex] = y
y = 18 (0.85)
y = 15.3 units
You use the same strategy for the rest of the questions. Feel free to reach out if you have more questions.
Which would be an equivalent way to write y= 2 - 3x ?
a) y= -3x - 2
b) y= -3x + 2
c) y= 3x - 2
d) y= 3x + 2
10 + 20 = 2(5 + __)
a
11
b
30
c
10
d
7
Answer:
C=10. They did distributive property. Hope this helped!
Step-by-step explanation:
Are the graphs of the given equations identical lines parallel lines are lines intersecting on a single point
12 1/2 − 9 1/4
This problem comes from subtract mixed numbers
5 3/4 - 2 5/12
7 1/5 - 3 7/10
11 2/3 - 8 1/2
At the Football game they expect that for every 4 people that attend 3 hot dogs will be sold. What is the equation
Answer:
If [tex]p[/tex] is people and [tex]h[/tex] is hot dogs, the equation is [tex]3h=4p[/tex].
The relation among people who attend and hot dog sold is 4x = 3y.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
At the Football game they expect that for every 4 people that attend 3 hot dogs will be sold.
let the are total x people and y number of hot dogs will be sold.
So, the relation among people who attend and hot dog sold is
4x = 3y
Learn more about equation here:
https://brainly.com/question/29538993
#SPJ2
please help will give brainliest
Answer:
I think it is C.
Step-by-step explanation:
Answer:
volume is length x width x height, the answer is 160 cubed feet.
Step-by-step explanation:
Length x width x height and bam, there is your answer
Are heart rate and age proportional or non proportional for each method
Answer:
Yes
Step-by-step explanation:
For example
Doctors have two methods of calculating maximum heart rate. With the first method, maximum heart rate, y, in beats per minute is y=220−x, where x is the person’s age.
Tony made $208 for 13 hours of work. At the same rate, how many hours would he have ro work to make $144
Answer:
9 hours
Step-by-step explanation:
208 / 13 = $16 per hour
144 / 16 = 9 hours
Answer:
9 hours
Step-by-step explanation:
208 divided by 13 is 16. So then u take 16 and divide it by 144, and if you do long division you would get 9. Hopefully this helps
What is the sum of all exterior angles in a polygon?
Please help me, i am honestly confused, its about 1am, and i rlly, rlly need help
y=2
There is no slope because the y value stays constant. When the table is graphed, it is a horizontal line at 2. I hope this helps!
11k = -143 I need help with this question
Answer:
k = -13
Step-by-step explanation:
-143/11 = -13
Answer:
11k = -143
k=-143/11=-13 is a required answer
Courtney is flying a kite and 125 ft of the string is let out. The angle of elevation between the kite and the ground is 48°. Find the approximate height of the kite.
Answer:
rrrrrrreeeeeeeeeee
Step-by-step explanation:
jjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjj
If you chose to use substitution to solve this system what should your equation look
like?
y=5x-5
y= -4x+22
Step-by-step explanation:
y=5x-5
y= -4x+22
1- use y=5x-5 solve for y (here you don't really have to do anything)
This stays the same, Therefore y = 5x-5
2- you will substitute y=5x-5 for y in y= -4x+22. The problem should now look like this:
5x-5= -4x+22
Solving for xnow, with the equation above you will solve for x-
5x-5= -4x+22 (add 4x to both sides)
9x-5= 22 (add 5 to both sides)
9x=27 (divide by 9)
x=3
Solving for yNow that you Know that x=3 you can substitute x=3 for x in y=5x-5. The problem should look like this:
y= 5(3)-5
Now with the equation above you can solve for y
y= 5(3)-5 (multiply 5 by 3)
y= 15-5 (subtract)
y=10
Now you have your answers X=3 Y=10
i hope this helps!
Question: The table shows pairs of random digits. The pairs in each group simulate the 5 shots taken by the opponent.
The paired digits 00 to 99 represent 100 shots.
Let 00 to 72 = a shot that is saved. Which digits represent a goal scored? Explain.
Answer:
ANSWER
Step-by-step explanation:
28, 30, 24, 96, 33
Mean
Range =
Median =
IQR =
Mode =
Variance
Midrange=
Standard Deviation=
Answer:
I know some .
median : 24
Step-by-step explanation:
Mean : you add all of them up then divide by how many numbers there are .
range : the biggest number minus the smallest number .
median : the middle number . the middle number is 24 .
I know what is mode but the answer is not in there
Simplify the expression ((x^3 * y^-3))^4/ 2x^1 * y^4
In a family of 6 children what is the probability there are exactly 4 girls?
Answer:
sonn 12 laalkznjsnl nalslaonhfj. alallkzhdbb nLaojahdnldl
Kimberly's family has a dinner bill of $56.95 and wants to leave a 15% tip for their server. How much will this family spend for the meal plus the tip? 50 points!
Answer:
This family spend for the meal plus the tip : $56.95 + $8.54 = $65.49
The tip = $56.95 x 15% =$8.54
Step-by-step explanation:
Teri earned $18.25 an hour at the semiconductor plant. The payroll deductions reduced her paycheck by $182.50. If her first weekly paycheck was at least $547.50 after the deductions, how many hours did she work that week?
Answer:
40 hours
Step-by-step explanation:
did 18.25*40 then subtracted 182.50 and it equaled 547.50
