200 + 10x = 120 + 15x now solve the equation to find x, the number of hours that both companies will charge the same ammount
Answers
Answer:
16
Step-by-step explanation:
Given the equation, [tex] 200 + 10x = 120 + 15x [/tex], let's solve for x as follows,
Subtract 200 from both sides
[tex] 200 + 10x - 200 = 120 + 15x - 200 [/tex]
[tex] 10x = - 80 + 15x [/tex]
Subtract 15x from both sides
[tex] 10x - 15x = - 80 + 15x - 15x [/tex]
[tex] -5x = - 80 [/tex]
Divide both sides by -5
[tex] \frac{-5x}{-5} = \frac{-80}{5} [/tex]
[tex] x = 16 [/tex]
Related Questions
What is the degree of
the polynomial below?
I
x2 + 2x - 3x4 +5 + 3x?
Answers
Determine algebraically whether f(x)=3x-2 and g(x)=(x+2)/3 are inverse functions. Show all work.
Answers
Answer:
Yes
Step-by-step explanation:
f(x)=3 x-2
y= 3 x-2
x= 3y - 2
3 y -2 = x
3 y -2 + 2 = x + 2
3 y = x + 2
3 3 3
3 y = x + 2
3 3 3
y = x + 2 replace y with f ^ -1(x)
3 3
f ^-1 (x) = x + 2
3 3
I NEED HELP...finding the slope-intercept form equation
of the line passing through this points
(-12, 6) and (-36, 32)
Answers
Answer: y=-13/12x-7
Step-by-step explanation:
To find the slope-intercept form, we first need to find the slope. To find the slope, you use the formula [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]. We use the two given points to find the slope.
[tex]m=\frac{32-6}{-36-(-12)} =\frac{26}{-24} =-\frac{13}{12}[/tex]
Now that we have our slope, we can start filling out the slope-intercept form equation.
y=mx+b
y=-13/12x+b
Since we don't know the y-intercept, we can use one of the given points and solve for b.
6=(-13/12)(-12)+b [multiply (-13/12) and -12]
6=13+b [subtract both sides by 13]
b=-7
With the y-intercept, we can complete our equation.
y=-13/12x-7
9. An air conditioning system can circulate 350 cubic feet of air
per minute. How many cubic yards of air can it circulate per
minute?
Answers
An air conditioning system can circulate 350 cubic feet of air
per minute. How many cubic yards of air can it circulate per
minute?
About 13.0 cubic yards
The amount of air in cubic yards per minute will be 12.96 cubic yards per minute.
What is conversion?Conversion means to convert the same thing into different units.
Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.
An air conditioning system can circulate 350 cubic feet of air per minute.
We know that 1 foot = (1/3) yards, then the 1 cubic foot = (1/27) cubic yards.
350 cubic feet / minute = (1/27) x 350 cubic yards / minute
350 cubic feet / minute = 12.96 cubic yards / minute
The amount of air in cubic yards per minute will be 12.96 cubic yards per minute.
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Three-fifths of the students on a school trip are boys. There are 33 boys on the trip. How many students are on the trip?
Answers
Answer:
55 students
Step-by-step explanation:
Write an equation.
3/5 = 33
Divide by 3 to get a unit fraction.
3/5 / 3 = 1/5
33 / 3 = 11
1/5 = 11
Multiply by 5
1/5 x 5 = 1
11 x 5 = 55
1 = 55
So, there are 55 students on the school trip.
Which sum or difference identity would you use to verify that cos (180° - q) = -cos q?
a.
sin (a -b) = sin a cos b – cos a sin b
b.
cos (a -b) = cos a cos b – sin a sin b
c.
cos (a -b) = cos a cosb + sin a sin b
d.
sin (a + b) = sin a cos b + cos a sin b
Answers
cos(a - b) = cos(a)cos(b) + sin(a)sin(b)
In this case, we'd have a = 180 and b = q, so,
cos(a-b) = cos(a)cos(b) + sin(a)sin(b)
cos(180 - q) = cos(180)cos(q) + sin(180)sin(q)
cos(180 - q) = -1*cos(q) + 0*sin(q)
cos(180 - q) = -cos(q) + 0
cos(180 - q) = -cos(q)
Find three positive integers x, y, and z that satisfy the given conditions. The product is 125, and the sum is a minimum.
Answers
Answer:
Step-by-step explanation:
Given 3 positive integers x, y and z, if their product is 125, then;
xyz = 125 .......... 1
Sum of the integers S(x, y, z) = x+y+z ........... 2
From equation 1; x = 125/yz ........3
Substitute equation 3 into 2
S(x, y, z) = 125/yz+y+z
Sy = -125/y²z + 1
Sz = -125/z²y + 1
For the sum to be minimum, Sy = Sz = 0
-125/y²z + 1 = 0
-125/y²z = -1
-125 = -y²z
125 = y²z
Also; is Sz = 0
-125/z²y + 1 = 0
-125/z²y = -1
-125 = -z²y
125 = z²y
Hence y²z = z²y = 125
From y²z = 125, z = 125/y²
Substitute z = 125/y² into the equation 125 = z²y
125 = (125/y²)²× y
125 = 125²/y⁴ × y
125 = 125²/y³
1 = 125/y³
y³ = 125.
y = 5
Since 125 = y²z
5²z = 125
25z = 125
z = 5
From the product xyz = 125
x(5)(5) = 125
25x = 125.
x = 5
Hence x = y = z = 5
Which of the following are solutions to the equation below?
Check all that apply.
9x^2- 6x + 1 = 7
Answers
The answer is C and D
First we must make one side of the equation zero, so we subtract 7 on both sides of the equation, making the equation 9x^2 - 6x - 6 = 0
Then we will use the quadratic formula to find the answers.
using the Quadratic Formula where:
a = 9, b = -6, and c = -6
and the formula is 6 +- [tex]\sqrt{6^{2} } -4 (9)(6) /2 (9)[/tex]
Fifty part-time students were asked how many courses they were taking this term. The incomplete) results are shown below.
Part (b)
What percent of students take exactly two courses?
Part (c)
What percent of students take one or two courses?
%
Answers
Answer:
There are 50 part-time students:
15 of them, take only one course.
10 of them, take only two courses.
then the rest, this is:
50 - 10 - 15 = 25
25 students take 3 courses.
b) What percent of students take exactly two courses?
15 out of 50 take exactly two courses, the percentage is:
p = (10/50)*100% = 20%.
c) What percent of students take one or two courses?
This will be the percentage of students that take only one course plus the percentage of students that take two courses:
The percentage of students that take two courses is already known: 20%.
Now, for 1 course we have 15 students out of 50, the percentage is:
p = (15/50)*100% = 30%.
Then the percentage that take 1 or 2 courses is:
P = 30% + 20% = 50%
20% of students take exactly two courses, and 50% of students take one or two courses.
Given that fifty part-time students were asked how many courses they were taking this term, of which 15 take only 1 course, while 10 take 2 courses, to determine what percent of students take exactly two courses, and what percent of students take one or two courses, the following calculation must be performed:
(10/50) x 100 = X 0.2 x 100 = X 20 = X
(25/50) x 100 = X 0.5 x 100 = X 50 =X
Therefore, 20% of students take exactly two courses, and 50% of students take one or two courses.
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When you multiply numbers, the answer is the product of those numbers. Name two different pairs of whole numbers whose product is 12.
Answers
Answer: 4 x 3 = 12
6 x 2 = 12
Step-by-step explanation:
12 x 1 = 12
3 x 4 = 12
Considere as mesas com 4 cadeiras, com 6 cadeiras e com 8 cadeiras. ©Shutterstock/jenjira Com base nessa sequência de imagens, qual expressão indica a quantidade de cadeiras utilizadas ao colocarmos n mesas lado a lado?
Answers
Responder:
C. Tₙ = 2n + 2Explicación paso a paso:
De la pregunta, la secuencia de imágenes, cuya expresión indica es 4 cadeiras, 6 cadeiras, 8 cadeiras ...
Se puede ver la secuencia una progresión aritmética de la forma 4, 6, 8 ... Para obtener la expresión que indica la cantidad de cadenas utilizadas o colocaremos n tablas una al lado de la otra, tendremos que encontrar el enésimo término de la secuencia que usa la fórmula para encontrar el enésimo término de una secuencia aritmética.
El enésimo término de un AP se expresa como Tₙ = a + (n-1) d donde;
a es el primer término
n es el número de términos es la diferencia común
De la secuencia generada, a = 4, d = 6-4 = 8-6 = 2
Tₙ = 4+ (n-1) 2
abre el paréntesis
Tₙ = 4 + 2n-2
Tₙ = 2n + 4-2
Tₙ = 2n + 2
Por lo tanto, la expresión que indica la cantidad de cadenas utilizadas o colocaremos n tablas una al lado de la otra es 2n + 2
How many ounces of a 30% alcohol solution must be mixed with 18ounces if a 35% alcohol solution to make a 33% alcohol solution
Answers
Answer:
12 ounces
Step-by-step explanation:
0.30 x + 0.35 (18) = 0.33 (x + 18)
0.30 x + 6.3 = 0.33 x + 5.94
0.36 = 0.03 x
x = 12
Bodie Raptor's Iphone 11 has 4/5 of the battery still remaining. His phone battery drains at a rate of 1/3 every hour. If he uses his phone continuously, how many more hours will his phone last. Please give your answer as a mixed number in simplest form in the form of A . b/c
Answers
Answer:
[tex]2\frac{2}{5}[/tex] hours, or 1 hours and 24 minutes
Step-by-step explanation:
4/5 battery remaining
drains at rate of 1/3 per hour
[tex]\frac{1}{3}h=\frac{4}{5}\\\frac{3}{1}(\frac{1}{3}h)=\frac{3}{1}*\frac{4}{5}\\h=\frac{3*4}{1*5}=\frac{12}{5}=2\frac{2}{5}[/tex]
He has 2 2/5 hours or 2 hours and 24 minutes left until his phone dies. (A fifth of an hour is 12 minutes and we have 2/5 to deal with, so 12 times 2 is 24 mins.)
the domain for f(x) is all real numbers. (Blank) than or equal to 3
Answers
Answer:
greater
Step-by-step explanation:
The domain is the number that x can be
sqrt(x-3) must be greater than or equal to zero
x-3 must be greater than or equal to zero
x must be greater than or equal to three
The other restriction is x+2 cannot equal zero
x cannot equal -2
The first restriction is more restrictive so that is the one we go with
What is the equation of the slant asymptote of the rational function? f(x)=6x3−15x2+x−43x2−1 y=x−5 y=2x−5 y=x−17/3 y=2x−17/3
Answers
Answer:
2x − 5
Step-by-step explanation:
To solve, divide the numerator by the denominator. The result (not including the remainder) will be the equation of the slant asymptote.
We can tell the first term of the quotient will be 2x, so the answer will be either 2x − 5 or 2x − 17/3.
The easiest method here is to simply multiply these by denominator.
(3x² − 1) (2x − 5) = 6x³ − 15x² − 2x + 5
(3x² − 1) (2x − 17/3) = 6x³ − 17x² − 2x + 17/3
So the answer must be 2x − 5.
Alternatively, you can use long division.
Answer:
2x-5
Step-by-step explanation:
f(x)=(6x^3−15x^2+x−4 )/(3x^2−1)
To find the slant asymptote,divide the numerator by the denominator
2x +(-15x^2+3x-4)/ (3x^2-1)
-5 + (3x-9)/(3x^2-1)
The divisor is (2x-5) and the remainder is ( 3x-9)
Find A∩B, given A={−6,−2,0,2,6} and B={−4,0,1,2,5,6}.
Answers
Answer:
Step-by-step explanation:
A ∩ B = {0, 2, 6}
x+z-w/r=1 solve for z
Answers
Answer: z=1−x+w/r
Step-by-step explanation:
Subtract x from both sides.
z-w/r=1-x
Add w/r to both sides.
z=1−x+w/r
hope i helped
-lvr
Question 1 (1 point) How many terms are in the polynomial? 3x3 + 4x2 - 8x - 5 3 4 7
Answers
Answer:
4
Step-by-step explanation:
The polynomial 3x^3 +4x^2 -8x -5 has 4 terms. A term is a product or single variable or constant separated from other terms by a plus or minus sign.
The four terms are ...
3x^34x^2-8x-5Brand on has 25 buttons.Mason has 6 times as many buttons.How many buttons does Mason have?
Answers
Answer: Mason has 150 buttons.
Step-by-step explanation: Brandon has 25 buttons. If Mason has 6 times as many, all you have to do is multiply 25 times 6. You end up with 150 buttons.
6. Isabella decides to sell handmade stationery. She decides to sell 2 cards for $9. Which table below show the possible values of c, the number of cards Isabella sells, and d, the number of dollars she charges? F. H. G. J. CARDS, c 2 9 11 15 DOLLARS, d 9 40.5 50.5 67.5 CARDS, c 9 18 27 36 DOLLARS, d 2 4 6 8 CARDS, c 2 4 7 10 DOLLARS, d 9 18 31.5 45 CARDS, c 2 3 4 5 DOLLARS, d 9 10 11 12
Answers
Answer:
G.
Step-by-step explanation:
cards = 2
dollars = 9
to check that the number of cards with the correct amount d;
use the ratio and proportion.
(3 x 18)/9 = 4
(4 x 31.5)/18 = 7
(7 x 45)/31.5 = 10
therefore, option G. table G. is the correct answer
try doing the ratio and proportion on the other table and the number of cards DO NOT match with the amount. (see attached)
Round 72.46387 to the nearest whole number
Answers
Answer:
72Step-by-step explanation:
[tex]72.46387 = 72[/tex]
4 is not up to 5
PLEASE HELP!! ALGEBRA! For a movie theater 4,000 tickets were sold, and the proceeds were $37,000. Tickets for children 16 and younger, were $10, adults were $12, and seniors 60 and older were $8. There were 4 times more seniors than adults at the movie theater. What system of equations represents the number of children, c, adults, a, and seniors, s, that attended the movie theater?
Answers
Answer: Fourth answer choice
c+a+s = 4000
10c+12a+8s = 37000
4a = s
==========================================
Explanation:
The first equation
c+a+s = 4000
is fairly straightforward. We add the individual counts of children (c), adults (a) and seniors (s) to get the total number of people (4000) who attended
-------------
If 1 child ticket costs $10, then 2 of them cost 20, and so on. If we don't know how many children there are, then we say 10c is the total cost for just the children alone. The c is a placeholder for some number.
Similarly, 12a represents the total cost for just the adults since 1 adult pays $12
8s is the total cost for all the seniors only
10c+12a+8s is the total cost of everyone and this total cost is 37000 dollars
The second equation is therefore
10c+12a+8s = 37000
----------------
We're told that "There were 4 times more seniors than adults at the movie theater" meaning
number of seniors = 4*(number of adults)
s = 4a
which is the same as 4a = s since we can flip both sides. So this is the third equation of our system.
------------------
We found these three equations
c+a+s = 4000
10c+12a+8s = 37000
4a = s
Find the pattern and use inductive reasoning to predict the next number in the sequence 100,50,80,40,70,35,…
Answers
Answer:
65
Step-by-step explanation:
100, 50, 80, 40, 70, 35, 65.
|____|__|___|___|__|__|
÷2. +30. ÷2. +30 ÷2. +30
A pattern is a recurring arrangement of numbers, forms, colors, and so on. The next number in the given pattern will be 65.
What is a pattern?In mathematics, a pattern is a recurring arrangement of numbers, forms, colors, and so on. The Pattern may be applied to any form of event or object. A pattern is defined as a group of integers that are connected to each other in a specified way.
If the given pattern is observed closely then it can be observed that the second number is decreased by half the previous one, while the next number is formed by adding 30, therefore,
The First Number = 100The second number, half of the previous = 50For the third number, add 30 = 80The fourth number, half of the previous = 40For the fifth number, add 30 = 70The sixth number, half of the previous = 35For the seventh number, add 30 = 65Hence, the next number in the given pattern will be 65.
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The map shows the route for a race.You are at X, 6000 ft from the first checkpoint C.The second checkpoint D is located at the midpoint between C and the end of the race Y.The total race is 3 miles how far apart are the 2 checkpoints? I know the answer is 4920 but i don’t know how to work it out
Answers
Answer:
Distance between the two check point (C and D) is 4920 ft.
Step-by-step explanation:
From the question given above, we obtained the following information:
X is 6000 ft from C (1st check point)
D (2nd check point) is the midpoint point between C and Y ( the end of the race)
Total race = 3 miles
1 mile = 5280 ft
Next, we shall express the total race in feet (ft).
This is illustrated below:
1 mile = 5280 ft
Therefore,
3 miles = 3 × 5280 = 15840 ft
Next, we shall determine the distance between the 1st check point (C) and the end of the race (Y)
This can be obtained as follow:
Total distance = 15840 ft
Distance between X and C = 6000 ft
Distance between C and Y =?
Distance between C and Y = (Total distance) – (Distance between X and C)
Distance between C and Y = 15840 – 6000
Distance between C and Y = 9840 ft
Finally, we shall determine the distance between the two check point (C and D) as follow:
Since D is midpoint between C and Y, therefore, we shall we shall divide the distance between C and Y by 2 in order to obtain the distance between the two check point (C and D).
This is illustrated below:
Distance between C and Y = 9840 ft
Distance between the two check point (C and D) = 9840/2 = 4920 ft
Therefore, the distance between the two check point (C and D) is 4920 ft
How many quarts of pure antifreeze must be added to 5 quarts of a 10 % antifreeze solution to obtain a 20 % antifreeze solution?
Answers
Solve the given initial-value problem by finding, as an appropriate integrating factor.
(x2 + y2 − 3) dx = (y + xy) dy, y(0) = 1
Answers
Answer:
hello attached below is the detailed solution
answer : In |x+1| + [2/(x+1)] + [1/(1+x)^2] - [y^2/2(1+x)^2] = 5/2
Step-by-step explanation:
Given
(x^2 + y^2 - 3) dx = ( y + xy ) dy, y(0) = 1
solving the given initial-value problem
What is the value of the underline digit?
14.097
Answers
Answer:14.097
Step-by-step explanation:
In a poll, 22% of 714 surveyed adults said that . What is the actual number of adults who said that
Answers
Answer:
157 surveyed adultStep-by-step explanation:
IF 22% of 714 surveyed adult made a statement, the actual number of those that made the statement can be gotten by simply evaluating 22% of 714 as shown below;
= 22% of 714
= 22/100 * 714
= (22*714)/100
= 15708/100
= 157.08
≈ 157 surveyed adult
This means that about 157 surveyed adults made the statement.
The width of a rectangle is 4 inches (in) and the area of the rectangle is 32 in2? Which of the following represents the length of the rectange?
a. 8 in
b. 128 in
c. 28 in
d. 36 in
Answers
Answer:
A. 8
Step-by-step explanation:
32 divided by 4 = 8
The answer is a. 8 in.
Since the width of the rectangle is 4 inches (in) and the area of the rectangle is 32 in², we need to find the length of the rectangle.
We know that the area of a rectangle with length, L and width, W is A = LW.
Since we need to find the length of the rectangle, we make the length, L subject of the formula.
Since A = LW,
L = A/W
Given that A = 32 in² and W = 4 in
Substituting the values of the variables into the equation, we have
L = 32 in²/4 in
L = 8 in
So, the length of the rectangle is 8 in
So, the answer is a. 8 in.
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Find the equation for the set of points whose distance from the y-axis equals the distance from the xz-plane.
Answers
Answer:
[tex]$ x_1^2 + z_1^2 = y_1^2$[/tex]
Step-by-step explanation:
Let [tex]$ p(x_1, y_1, z_1)$[/tex] be the point.
Any point on y-axis is (0, y, 0)
So, distance is
= [tex]$ \sqrt{x_1^2+0 + z_1^2} $[/tex]
= [tex]$ \sqrt{x_1^2 + z_1^2} $[/tex] ......(1)
Now any point on x-z plane is [tex]$ ( x_1, 0, z_1 ) $[/tex]
Distance from p to this point is
= [tex]$ \sqrt{0+y_1^2 + 0} $[/tex]
= [tex]$\sqrt{y_1^2}$[/tex] .........(2)
Equating (1) and (2), we get
[tex]$ \sqrt{x_1^2 + z_1^2} = \sqrt{y_1^2}$[/tex]
[tex]$ x_1^2 + z_1^2 = y_1^2$[/tex]
This is the required equation.