Using the concept of linear equation we can conclude that the number of marbles sold by Mark is 23 and the number of marbles sold by Don is 72.
What is a linear equation?An equation is said to be linear if the highest power of the variable is 1. It is also called as one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variable is x and A is the coefficient of x, while B is a constant.
Let the number of marbles Mark sells be ‘x’
then, the number of marbles Don sells can be given by ‘3x+3’
Total number of marbles sold=95
We can for equation by adding the number of marbles Mark sells and the number of marbles Don sells to the total number of marbles sold. The equation formed is
x+3x+3=95
4x+3=95
4x=95-3
4x=92
x=23
The number of marbles Mark sells =23
Number of marbles Don sells=3x+3
Substituting value of ‘x’
Number of marbles Don sells=(3×23)+3
Number of marbles Don sells=69+3
Number of marbles Don sells=72
Thus, the number of marbles sold by Mark is 23.
While, the number of marbles sold by Don is 72.
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Two towns are 52 km apart. Buses travelling
between the two towns leave at the same
time but travel in opposite directions. The
bus from town A is travelling 80 km/h and
the bus from town B is travelling 70 km/h.
How long after they leave will they pass each
other? (Reminder: there are 60 minutes in an
hour!)
Step-by-step explanation:
x = number of km bus from A drives until they meet.
y = number of km bus from B drives until they meet.
x/80 is the time for the bus from A to reach the meeting point.
x/70 is the time for the bus from B to reach the meeting point.
both times must be equal, as they start at the same time.
so,
x/80 = y/70
but then we also know that together they have traveled the full 52 km to meet.
so,
x + y = 52
x = 52 - y
with that we go into the first equation :
(52 - y)/80 = y/70
(52 - y)/8 = y/7
7×(52 - y)/8 = y
7×(52 - y) = 8y
364 - 7y = 8y
364 = 15y
y = 364/15 km = 24.26666666... km
x = 52 - y = (780-364)/15 = 416/15 = 27.73333333... km
they will meet after (using bus from B)
364/15 / 70/1 = 364/1050 hours
= 182/525 hours =
= 60×182/525 = 10920/525 minutes =
= 728/35 = 104/5 = 20.8 minutes =
= 20 minutes 60×8/10 seconds =
= 20 minutes 48 seconds
control (using bus from A) :
416/15 / 80/1 = 416/1200 hours =
= 26/75 hours =
= 60×26/75 = 1560/75 minutes =
= 104/5 = 20.8 minutes
correct.
Write an equation for line L in point-slope form and
slope-intercept form.
L is perpendicular to y = 2x.
6
-2
6
15
y = 2x
(12)
2
50
Write an equation for line L in point-slope form.
(Simplify your answer. Use integers or fractions
for any numbers in the equation.)
Step-by-step explanation:
the line is perpendicular to
y = 2x.
and it goes through the point (1, 2).
the point-slope form looks like
y - y1 = a(x - x1)
"a"being the slope, and (x1, y1) being a point on the line.
the slope-intercept form is
y = ax + b
"a" is again the slope, "b" is the y-intercept (the y value when x = 0).
as you can see, we need the slope of the new line in both cases.
then we will start with the point-slope form, and transform it into the slope-intercept form.
the slope of a line is generally the ratio (y coordinate change / x coordinate change) when going from one point on the line to another.
it is always the factor of x.
we can see it is 2 for the original line. that means 2/1.
a perpendicular slope is turning the x and y values upside down, and is flipping the sign.
so, in our case it is
-1/2
so, starting with the new slope and the point to create the point-slope form :
y - 2 = -1/2 × (x - 1)
and from there we transform into the slope-intercept form :
2y - 4 = -x + 1
2y = -x + 5
y = (-x + 5)/2 = -1/2 x + 5/2 = -1/2 × (x - 5)
all of the expressions in the last line are valid forms to write it.
Find the value of c in the equation c3 = -64
Answer:
c = -4
Step-by-step explanation:
c³ = -64
∛c³ = ∛-64
c = -4
Check:
-4 *-4 * -4 = -64
Please please help me out with this !
Answer:
1. 11,207.23
2. 11,285.58
3. 11,303.49
4. 11312.52
I don't know if the last one is correct
can anybody help me with this question
Answer:
45.83/100
Step-by-step explanation:
assuming all participate in a language
German=1/6
French=3/8
Italian=remaining percentage=a
1/6+3/8+a=1
8/48+18/48+a=1
a=48/48-26/48
a=45.83/100
Write the slope-intercept form equation of the line that passes through the points (1,−6) and (9,−5).
Complete the equation in the space below (do not enter "y = ").
Answer:
Step-by-step explanation:
Point slope form y-y₁ = m(x-x₁)
-5 - (-6) = m(9 - 1)
1 = m(8)
1/8 = m
y= 1/8x + b
-6 = 1/8(1) + b
b = -6.125
y = 1/8x -6.125
You are driving across America from Knoxville, Tennessee to Nashville, Tennessee. It takes 2 hours and 20 minutes. Nashville is an hour behind Knoxville. If you leave Knoxville 11:13, What time will you arrive in Nashville?
The time that you will arrive in Nashville is 1:33.
How to compute the time?From the information given, the person leaves Knoxville at 11:13, and the journey takes 2 hours and 20 minutes.
Therefore the time when the person will arrive will be the addition of the time given.
This will be:
= 11:13 + 2:20
= 1:33
Therefore, the person will arrive by 1:33.
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An open-top water tank is in the shape of a cuboid. The tank has a square base of side length s m, and has a volume of 216 m^3. Find expressions, in terms of s, for:
a) the height of the tank.
b) the surface area of the tank
Given that the surface area of the open-top water tank is minimised:
c) find the value of s.
(looking for clear workouts and reasoning / explanation behind every step taken no matter how basic it may be)
Answers:
a) h = 216/s^2
b) A = s^2 + 864
c) s = cube root of 432
The height of the tank is h = 216/s^2, the surface area is s^2 + 864/s and the value of s is ∛432
How to determine the height of the tank?The given parameters are
Volume = 216
Base length = s
Height = h
The base shape is a square.
So, we have
Volume = s^2h
This gives
216 = s^2h
Divide through by s^2
h = 216/s^2
Hence, the height of the tank is h = 216/s^2
The surface area of the tankThis is calculated as
A = s^2 + 4sh
So, we have
A = s^2 + 4 * s * 216/s^2
Evaluate
A = s^2 + 4 * s * 216/s^2
This gives
A = s^2 + 864/s
How to determine the value of s?Here, we have
A = s^2 + 864/s
Differentiate
A' = 2s - 864/s^2
Set to 0
2s - 864/s^2 = 0
Divide through by s
2 - 864/s^3 = 0
So, we have
864/s^3 = 2
This gives
2s^3 = 864
Divide by 2
s^3 = 432
Take the cube root
s = ∛432
Hence, the value of s is ∛432
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Jayme buys a painting for $179.99 for his apartment. The tax rate is 6.5%. How much did Jayme spend after tax?
Answer:
$191.69
Step-by-step explanation:
To prepare for his mountain biking trip, Rhyan bought four tire patches. Rhyan paid using a gift card that had $22.20 on it. After the sale, Rhyan’s gift card had $1.90 remaining. Which equations could you use to find the price of one tire patch? Select all that apply. 4x – 1.9 = 22.2 4x – 22.2 = 1.9 4x + 1.9 = 22.2 4x + 22.2 = –1.9 22.2 – 4x = 1.9
Answer:
437 33473333336575848
Answer:
4x + 1.9 = 22.2
22.2 - 4x = 1.9
Answer choice: C & E.
Step-by-step explanation:
Glad to help.
put the unknown price of the four tire patches as x,
and for all, it should add up to $22.20 and you're to subtract $1.90.
(30 POINTS) A construction worker is pouring concrete stairs. The first step requires 1.7 cubic feet of concrete, and the first 4 steps require a total of 17 cubic feet. If the steps follow an arithmetic series, how much concrete is required for the first 12 steps?
51 cubic feet
93.5 cubic feet
132.6 cubic feet
244.8 cubic feet
The volume of concrete required for the first 12 steps is 132.6 cubic feet
Given data
the first step requires 1.7 cubic feet of concrete
the first 4 steps require a total of 17 cubic feet
How to solve for the first 12 stepsthe first term = a = 1.7
4th step = n/2 ( 2a + ( n - 1 ) d )
d is common difference
n = number of terms
17 = 4/2 ( 2*1.7 + ( 4 - 1 ) d )
17 = 2( 3.4 + 3d )
8.5 = 3.4 + 3d
5.1 = 3d
3d = 5.1
d = 1.7
sum of AP at 12th step
12th = n/2 ( 2a + ( n - 1 ) d )
12th = 6( 2 * 1.7 + ( 12 - 1 ) * 1.7)
12th = 6 (3.4 + 11 * 1.7)
12th = 6 * 22.1
12th = 132.6 cubic feet
The volume of concrete required for the first 12 steps is 132.6 cubic feet
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Una empresa tiene costos fijos de $300 y vende cada artículo en $15. Si se sabe que el punto de equilibrio es q=100. Plantear la función de Costos Totales
CT=__________________________
Based on the fixed costs and the equilibrium point, the function for total costs would be TC = 300 + 100VC
What s the function for total cost?The total cost that a company incurs for making a good or service is a combination of both the fixed cost and the variable cost.
The total variable cost is found as:
= Number of units produced x variable cost per unit
= 100 units x vc
= 100vc
The total cost would therefore be:
= Fixed cost + Total variable cost
= 300 + 100vc
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$2500.00 invested in stock market. Four months later the value dropped to $22.48. Find average monthly change in the value
Professor Dale records the following final grades in one of her classes: A, A, A, A, B, B, B, B, B, B, B, C, C, C, C, C, C, C, C, D, D, D, F, F Which value would complete the frequency table for these grades? Grade Frequency Relative Frequency Cumulative Frequency A 4 16.70% 4 B 7 29.20% 11 C ???? 33.30% 19 D 3 12.50% 22 F 2 8.30% 24 Total 24 100% 24
The value of the frequency for grade C from given table of final grade is 8.
As given,
Given frequency table is:
Grade: A B C D F
Frequency: 4 7 ? 3 2
Relative Frequency: 16.70% 29.20% 33.30% 12.50% 8.30%
Cumulative Frequency: 4 11 19 22 24
Given records: A, A, A, A, B, B, B, B, B, B, B, C, C, C,C, C, C, C, C,D,D,D, F,F
Here : frequency of grade C is 8 times
or Cumulative frequency (19-11=8).
Therefore, the value of the frequency for grade C from the given table of final grade is 8.
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1.) Ab+ac
2.) 6m+8
3.) 27d²+8d³-15d4t
4.) 27 m²n³p5-20m5n²p
Answer:
1.) ab × ac
a × (b + c)
2.) 6m + 8
2 (3m + 4)
3.) 27d²+8d³-15d4t
27d²+8d³- (15 × 4)dt
27d²+8d³- 60dt
4.) 27m²n³p5-20m5n²p
135m²n³p - 20m × 5n²p
135m²n³p - 100mn²p
A car rental company's standard charge includes an initial fee plus an additional fee for each mile driven. The standard charge S (in dollars) is given by the function =S+16.950.60M, where M is the number of miles driven.
The company also offers an option to insure the car against damage. The insurance charge I (in dollars) is given by the function =I+4.900.15M.
Let C be the total charge (in dollars) for a rental that includes insurance. Write an equation relating C to M. Simplify your answer as much as possible.
Step-by-step explanation:
A car rental company's standard charge includes an initial fee plus an additional fee for each mile driven. The standard charge S (in dollars) is given by the function =S+16.950.60M, where M is the number of miles driven.
The company also offers an option to insure the car against damage. The insurance charge I (in dollars) is given by the function =I+4.900.15M.
Let C be the total charge (in dollars) for a rental that includes insurance. Write an equation relating C to M. Simplify your answer as much as possible.
Cheryl's softball batting average is 0.340 and Karen's is 0.304. Karen says they have the same average. What error did she make
The mistake is that in both numbers 0.304 and 0.340, 4 is in the tenth position following the point.
What is place value system?The combination of numerical variables and operations expressed by the addition, subtraction, multiplication, and division signs is known as a mathematical expression. A place-value system gives a number's specific location within a series a value.
Karin's softball batting average is 0.304, whereas Cheryl's is 0.340. They have the same average, according to Karin.
Because the numbers 0.340 and 4 are in the tenth position, as opposed to 0.304 and 4, the values are different from one another.
He made a mistake in his estimation because both averages are equal.
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Justify -7k=-42 , then k=6
Answer: K=6 is correct
Step-by-step explanation:
If you substitute 6 for k and then multiply -7 the answer equals correctly!
500 g of a radioactive element is decaying exponentially. After 8 days 358 g of the element is left.
a. Write a function in the form y = yo ekt giving the number of grams of the element after t days.
358 f(t)
b. Write the function from part a in the form y=Yo
500
c. Use the answer from part a to find the half-life of the element.
a. The exponential equation in the form y=yoekt is
(Round to three decimal places as needed.)
The answers are given below:-
a) The exponential function is: [tex]y(t) = 500e^{-0.0117593}[/tex]
b) The rule is: [tex]y(t) = y(0)(\dfrac{358}{500})^{\frac{t}{8}[/tex]
c) The half-life of the element is of 16.599 days.
What is the exponential function?The mathematical expression [tex]f(x) = e^x[/tex] denotes the exponential function. The phrase typically refers to the positive-valued function of a real variable, unless otherwise specified.
Following t days, the substance's amount's exponential function is given by:
[tex]y(t) = y(0)e^{-kt}[/tex]
For this problem, we have that:
y(0) = 500, y(8) = 358.
Hence we can solve for k as follows:
[tex]y(t) = y(0)e^{-kt}[/tex]
[tex]358=500e^{-8k}[/tex]
[tex]e^{-8k}=\dfrac{358}{500}[/tex]
[tex]lne^-8k}=ln0.716[/tex]
-8k = ln(0.716)
k = -ln(0.716)/8
k = 0.041759389.
Hence:
[tex]y(t) = 500e^{-0.0117593}[/tex]
For item b, 358/500 of the material is what is left over after each 8-day period, therefore f(t) = t/8, and the rule is as follows:
[tex]y(t) = y(0)(\dfrac{358}{500})^{\frac{t}{8}[/tex]
For item c, using the rule from item a, we have to find t for which y(t) = 0.5y(0), hence:
[tex]y(t) = y(0)e^{-0.0117593}[/tex]
[tex]0.5y(0)=y(0)e^{-0.0117593[/tex]
[tex]e^{-0.0117593}=0.5[/tex]
[tex]lne^{-0.0117593}=ln0.5[/tex]
-0.041759389t = ln(0.5)
t = -ln(0.5)/0.041759389
t = 16.599.
The half-life of the element is of 16.599 days.
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find it quick please
Answer:
i. 13/40
Step-by-step explanation:
i. [tex]5 \div 8 + 3 \div - 10[/tex]
Taking LCM of 8 & 10, we get 40
[tex]25 - 12 \div 40[/tex]
So, we get 13/40
[tex] \frac{6}{7} + \frac{1}{2} =[/tex]
Add. Write the answer in simplest form?
m = x+y/3 solve for y
Answer:
y=3m-3x
Step-by-step explanation:
[tex]m=x+\frac{y}{3} \\ \\ m-x=\frac{y}{3} \\ \\ y=3m-3x[/tex]
Please answer quickly but only if you are sure
Answer:
C - 8.2*10^-2
Step-by-step explanation:
Answer:
C.
Step-by-step explanation:
10^-2 = 0.01
0.01 × 8.2 = 0.082
Solve the equation.
2+|2x−4|=10
Enter your answers by filling in the boxes.
x =
or x =
Answer:
Step-by-step explanation:
|2x+4|=8
2x+4=8 and 2x+4=-8
x=2 and x=-6
I’m confused can someone help?
Answer: Maybe you have to divide $525 over 5 friends so you will get how much each one gets.
Red can clean a room in 20 hours alone, while Blue can clean the same room in 10 hours. If they started cleaning a room together at 8:00am, then at what time will they finish cleaning the room together?
Answer:
No.
Step-by-step explanation:
Blue will be done cleaning the room at 6:00PM, while Red will be done by 4:00AM.
Point J is on line segment I K ‾ IK . Given J K = 10 JK=10 and I K = 19 , IK=19, determine the length I J ‾ . IJ
The length of the line segment IJ is 9.
What is the length of a line segment?
In this question we find that the line segments IJ and JK are collinear, that is, part of one same line. By Euclidean geometry and algebra, we construct the following formula:
IK = IJ + JK
IJ = IK - JK
If we know that IK = 19 and JK = 10, then the length of the missing line segment is:
IJ = 19 - 10
IJ = 9
The length of the line segment IJ is 9.
RemarkThe statement is poorly formatted, correct form is shown:
The point J is on line segment IK. Given that JK = 10 and IK = 19, determine the length IJ.
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If f(x)=3x-2 , find f^-1(x)
Answer:
See below
Step-by-step explanation:
y = 3x-2 switch x's and y's then solve for y
x = 3y-2
x+2 = 3y
y = (x+2) / 3 <===== this is f^-1 (x)
Now you can try the one posted in the picture.....
Graph this function.
f (x) = ¾x -2
The points of the graph are (0,-2), (4,1) and they are drawn on the graph below. The graph of the equation y= (3/4)x – 2 is a straight line.
What do you mean by a function's graph?The totality of the points in the plane with the form (x, f(x)) that make up the graph of a function f. The graph of y = f is another name for the graph of f. (x). Thus, the graph of an equation serves as a particular illustration of the graph of a function.
The given equation is
f(x)= ¾ x-2
Put x=0 in the equation
y = (¾)(0)-2
y = -2
Put x=4 in the equation
y = (3/4) (4)-2
y = 3-2
y = 1
Graph the points of the function on a graph as given below
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A Ferris wheel has 15 cars that are equally spaced around the circumference of the wheel.
The wheel rotates so that the car at the bottom of the ride is replaced by the next car. By
how many degrees does the wheel rotate?
The Ferris wheel rotates____
between successive cars being at the bottom.
The Ferris wheel in discuss which has 15 cars that are equally spaced around the circumference as described rotates 24° between successive cars being at the bottom.
What is the angle measure over which the Ferris wheel rotates between successive cars?It follows from the task content that the Ferris wheel in discuss has 15 cars spaced around it.
Since the Ferris wheel in discuss is circular and has a total angle measure of 360.
Hence, the total angle rotated between successive cars can therefore be evaluated as;
Angle rotated = 360°/15
= 24°.
Ultimately, The Ferris wheel in discuss which has 15 cars that are equally spaced around the circumference as described rotates 24° between successive cars being at the bottom.
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