Answer:
A = 50 + 0.02x
Step-by-step explanation:
Let the fixed amount be m
Let the charge for each cubic ft used be c
Let the amount of cubic ft of water used be x.
Let the total cost per month be A
Now, for the first household, they used 1500 cubic feet in a month and were billed $80.
This means, x = 1500 ft³ and A = $80
Since, we are told they are charged a fixed amount plus a fee per cubic ft consumed. We can say that;
m + cx = A
Thus,
m + 1500c = 80 - - - - (eq1)
For 2nd household:
They used 2100 cubic feet was billed $92.
Thus;
m + 2100c = 92 - - - - (eq 2)
Let's subtract eq1 from eq 2 to get;
2100c - 1500c = 92 - 80
600c = 12
c = 12/600
c = 0.02
Putting 0.02 for C in eq1 gives;
m + 1500(0.02) = 80
m + 30 = 80
m = 80 - 30
m = 50
From m + cx = A, we can say that;
50 + 0.02x = A
On the njmber line below, the numbers x and y are the same distance from 0. What is x + y? Explain how you found your answer
Answer:
Step-by-step explanation:
either x+y=0
∵ if they are on number line and at same distance. then x=-y
or x+y=0
find the difference of 5.95 and 4.7
Answer:
1.25 is your answer.
Rachel, Hong, and Manuel have a total of 95 in their wallets. Hong has 3 times what Manuel has. Rachel has $10 more than Manuel. How much does each have?
Answer:
Rachel has 27
Hong has 51
Manuel has 17
Step-by-step explanation:
Let R represent Rachel, H represent Hong, and M represent Manuel.
They combined have a total of 95. Thus:
[tex]R+H+M=95[/tex]
Hong has 3 times what Manuel has. Therefore:
[tex]H=3M[/tex]
Rachel has 10 more than Manuel. Therefore:
[tex]R=10+M[/tex]
Substitute:
[tex]R+H+M=95\\(10+M)+(3M)+M=95[/tex]
Combine like terms:
[tex]5M+10=95[/tex]
Subtract 10 from both sides:
[tex]5M=85[/tex]
Divide by 5:
[tex]M=17[/tex]
Therefore, Manuel has 17.
Now, find Rachel and Hong's money.
[tex]H=3M\\H=3(17)=51[/tex]
So, Hong has 51.
And for Rachel:
[tex]R=10+M\\R=10+17=27[/tex]
Rachel has 27.
Translate to an algebraic expression. m plus the product of 6 and n
x(2x + 3) + (x - 3)(x - 4)
Answer:
3x²-4x+12
Step-by-step explanation:
Answer:
[tex]=3x^2-4x+12[/tex]
Step-by-step explanation:
So we have the expression:
[tex]x(2x+3)+(x-3)(x-4)[/tex]
To simplify, distribute the left side and the right:
[tex]=x(2x)+x(3)+(x-3)(x)+(x-3)(-4)[/tex]
Distribute:
[tex]=(2x^2+3x)+(x^2-3x)+(-4x+12)[/tex]
Combine like terms:
[tex]=(2x^2+x^2)+(3x-3x-4x)+(12)[/tex]
Simplify:
[tex]=3x^2-4x+12[/tex]
a cylinder container can hold 2.45l of water. it radius is 4.00cm. what is the the volume of it in cm3
Answer:
Step-by-step explanation:
Ion know
Evaluate the expression for x = 5 and y = 3.
3x – 4y2
A. 9
B. 27
C. 39
D. 81
ILL GIVE YOU BRAINLIST ! Marlene is given 7 feet of fabric to design a dress. She uses 6 1/9 feet of fabric. How much fabric is left?
Answer:
This question is a lot easier than it seems. What you have to do here is subtract 6 1/9 from 7.
This will give you 0.8 of the fabric left, or 8/9.
what is. - 3 7/8 × - 4 3/5 help please
Answer: 1/ 40 x (-155x-184)
Answer:
[tex]:\quad \frac{713}{40}=17\frac{33}{40}[/tex]
Step-by-step explanation:
[tex]-3\frac{7}{8}\times \:-4\frac{3}{5}\\\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\quad 3\frac{7}{8}=\frac{31}{8}\\-\frac{31}{8}\times \:-4\frac{3}{5}\\\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\quad 4\frac{3}{5}=\frac{23}{5}\\-\frac{31}{8}\times \:-\frac{23}{5}\\\mathrm{Apply\:rule}\:-\left(-a\right)=a\\=\frac{31}{8}\times \frac{23}{5}\\\mathrm{Multiply\:fractions}:\quad \frac{a}{b}\times \frac{c}{d}=\frac{a\:\times \:c}{b\:\times \:d}\\[/tex]
[tex]=\frac{31\times \:23}{8\times \:5}\\\\=\frac{713}{40}\\\\\mathrm{Convert\:improper\:fractions\:to\:mixed\:numbers}:\\\quad \frac{713}{40}=17\frac{33}{40}[/tex]
If f(x) = х2 – 2х + 3, thеn find
f(-3).
Answer:
[tex]\huge\boxed{\sf f(-3) = 18}[/tex]
Step-by-step explanation:
[tex]\sf f(x) = x^2 - 2x + 3[/tex]
Put x = -3
[tex]\sf f(-3) = (-3)^2 -2(-3) + 3\\f(-3) = 9 + 6 + 3\\f(-3) = 18[/tex]
A triangle has a base of 16 inches and a height of 18 inches. What is its area?
Answer:
The answer is
144 square inchesStep-by-step explanation:
Area of a triangle is given by
[tex]A = \frac{1}{2} bh[/tex]where
b is the base
h is the height
From the question
b = 16 inches
h = 18 inches
Substitute the values into the above formula and solve for the area
That's
[tex]A = \frac{1}{2} \times 16 \times 18 \\ = 8 \times 18 \: \: \: \: \: \: [/tex]We have the final answer as
144 square inchesHope this helps you
Find the distance between the two points in simplest radical form.
(3,7) and (9,9)
Answer:
The answer is
[tex]2 \sqrt{10} \: \: units[/tex]Step-by-step explanation:
The distance between two points can be found by using the formula
[tex]d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\ [/tex]where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
(3,7) and (9,9)
The distance between them is
[tex]d = \sqrt{ ({3 - 9})^{2} + ({7 - 9})^{2} } \\ = \sqrt{ ({ - 6})^{2} + ({ - 2})^{2} } \\ = \sqrt{36 + 4} \\ = \sqrt{40} [/tex]We have the final answer as
[tex]2 \sqrt{10} \: \: units[/tex]Hope this helps you
The length of a rectangle is one more than four times its width. If the perimeter of the rectangle is 62 meters, find the dimensions of the rectangle.
Answer:
Length = 25 meters
Width = 6 meters
Step-by-step explanation:
62 = 2(a+b)
a = 4b + 1
a = length
b = width
then:
62 = 2((4b+1)+b)
62/2 = 4b+b+1
31 = 5b + 1
31 - 1 = 5b
30 = 5b
b = 30/5
b = 6m
a = 4b + 1
a = 4*6 + 1
a = 24 + 1
a = 25m
Check:
62 = 2(6+25)
62 = 2*31
Gasoline at a particular gas station costs $2.78 per gallon. If Cory buys $18 of gas, how many gallons did he buy?
Answer:
Cory bought 6.474 gallons of gasolline.
Step-by-step explanation:
The total cost of gasoline ([tex]C[/tex]), measured in dollars, is given by the following expression:
[tex]C = n\cdot c[/tex]
Where:
[tex]n[/tex] - Amount of gasoline, measured in gallons.
[tex]c[/tex] - Unit cost, measured in dollars per gallon.
Given that [tex]C = \$\,18[/tex] and [tex]c = \$\,2.78\,\frac{1}{gal}[/tex], the amount of gasoline is cleared and calculated:
[tex]n = \frac{C}{c}[/tex]
[tex]n = \frac{\$\,18}{\$\,2.78\,\frac{1}{gal} }[/tex]
[tex]n = 6.474\,gal[/tex]
Cory bought 6.474 gallons of gasolline.
one number is 7 more than twice the other number. if the sum of the two numbers is 19, find the two numbers
Answer:
4 and 15
Step-by-step explanation:
Let the two numbers be a and b.
The sum of the two is 19. Therefore:
[tex]a+b=19[/tex]
One number (let's use a) is 7 more than twice the other. Thus:
[tex]a=7+2b[/tex]
Solve for the system of equations. Substitute the second equation into the first:
[tex]a+b=19\\(7+2b)+b=19[/tex]
Subtract 7 from both sides:
[tex]2b+b=12[/tex]
Combine like terms:
[tex]3b=12[/tex]
Divide by 3:
[tex]b=4[/tex]
So, b is 4.
And since they add up to 19, this means that a is:
[tex]a+b=19\\a+4=19\\a=15[/tex]
So our numbers are 4 and 15
And we are done :)
Answer:
the equation is: 2x+7+x=43
the 2 numbers are: 12 and 31.
2/9 * 5/6
Multiply. Write the answer as a fraction in simplest form.
Answer:
5 / 27
Step-by-step explanation:
If you get this you are a critical thinker.
I enter the garden.
There are 34 people.
You kill 30.
How many people are in the garden.
Step-by-step explanation:
I'm not sure, but I think just 0
Because no one will even stand there and watch you kill 30 people
The police will come for you and the 1 dead person will be sent away lol
Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease. y=570(0.98)^x
Answer:
decay2% decreaseStep-by-step explanation:
The growth factor is the base of the exponent: 0.98. Its relation to the rate of change is ...
growth factor = 1 + rate of change
0.98 = 1 + (-0.02)
So, the rate of change is -0.02 = -2%. Since the rate of change is a 2% decrease, it represents decay.
in 2016 the average Raleigh driver spent 18 hours in traffic jams, which accounted for 6% of their total driving time. How many hours did the average Raleigh driver spend behind the wheel in 2016
Answer: 300 hrs
The time spent behind the wheel by the average Raleigh driver in 2016 is 300 hrs
Step-by-step explanation:
Given that;
Raleigh driver spent 18 hours in traffic jams
And it accounts for 6% of their total driving time
Now
let total driving time be = x hrs
so
6% of total driving time = 18 hrs
6/100 × x = 18hrs
6x = 1800 hrs
x = 1800/6
x = 300 hrs
∴ The time spent behind the wheel by the average Raleigh driver in 2016 is 300 hrs
43,761 rounded to the nearest thousands
Answer:
44,000
Step-by-step explanation:
The number 43,761 rounded to its nearest thousands is 4400.
What is place value?The place value of a number is given as:
Example:
1234.567
1 = thousand place value
2 = hundred place value
3 = tens place value
4 = ones place value
5 = tenths place value
6 = hundredths place value
7 = thousandths place value
We have,
43,761
3 is in the thousand place.
So,
We will round 3761 to its nearest thousand value.
There are two options:
3000 or 4000
If It is greater than 3499 it will round to 4000.
If it is less than 3500 it will round to 3000.
Now,
3761 > 3499.
So,
The number is rounded to 4000.
Thus,
43,761 is rounded to 4400.
Learn more about place value here:
https://brainly.com/question/27734142
#SPJ2
Given m parallel to I, and m2 7 = 94, find the measure of angle 5
O 10
045
O 97
O 120
Answer:
97
Step-by-step explanation:
Given a standard day, at what altitude is the true airspeed of an aircraft approximately twice of what the airspeed indicator reads
Answer:
40000ftMSL
Step-by-step explanation:
We know that airspeed is measured using a pilot tube
And the air pressure is a function of density given as
Pressure= 1/2 xdensityx V²
So at 40,000ftMSL
Is this is replaced for V in the equation then the density of air will be 1/4 that of sea level
So since we are deriving velocity from pressure and pressure is 1/4 so the velocity Will be half of its pressure since velocity is squared from The equation above
The school paper charges $1.50 for an ad, plus 25 cents per word. Carl wants to spend only $12.00 on the ad.
What is the maximum number of words that can be in his ad?
Answer:
42 words
Step-by-step explanation:
To solve just solve 0.25x +1.50 = 12.00 for x
f(x) = (10/x)^3 what is the value of f(2)?
Which expression is equivalent to : (-4x-3y-5)2
Chiang is filling a 50ft container with water at a rate of 0.5 ft/ min. interpret the key features for this situation
Answer:
The key features are
50ft³ = the volume
0.5ft³/min = rate
Time= 100 minutes
Step-by-step explanation:
Chiang is filling a 50ft container with water at a rate of 0.5 ft/ min.
50ft³ = the volume
0.5ft³/min = rate
There is a key future missing which is the time it will take to fill the 50 ft³ container
Time = volume/rate
Time= 50 ft³/0.5ft³/min
Time= 50/0.5 min
Time = 100 min
The key features are
50ft³ = the volume
0.5ft³/min = rate
Time= 100 minutes
Goran is sitting in a movie theater, 5 meters from the screen. The angle of elevation from his line of sight to the top of the screen is 18, and the angle of depression from his line of sight to the bottom of the screen is 48. Find the height of the entire screen.
Answer:
Approximately
Height of screen= 7.1 meters
Step-by-step explanation:
Angle of elevation= 18°
Angle of depression= 58°
Distance of Goran from screen= 5 m
Height of screen from the attachment below
X+y
First let's determine angle a and b
a= 180-90-18
a= 72°
b= 180-90-48
b= 43°
Using sine formula
5/sin a= x/sin 18
5/sin 72= x/sin18
(5*sin 18)/sin 72= x
1.6246 = x
X= 1.6246 m
Y/sin 48= 5/sin b
Y= (5*sin 48)/sin 43
Y= (5*1.08965779)
Y= 5.4483 m
Height of screen= x+y
Height of screen= 1.6246+5.4483
Height of screen= 7.0729
Approximately
Height of screen= 7.1 meters
How many solutions exist for 2 |x - 1| = 8?
A. 0
B. 1
C. 2
D. 3
Answer:
I believe the correct answer is C.
Step-by-step explanation:
So to get 0 solutions the absolute value would have to equal a negative number. To get 1 solution the absolute value would have to equal 0. To get 2 solutions the absolute value would have to equal a positive number.
2 |x - 1| = 8
divide by 2
|x - 1| = 4
The absolute value equals a positive so it has 2 solutions.
PLSSS HELP MARKING BRAINLIST PLSSSS GUYS NO ONE IS GOING TO HELP ME?
Answer:
top
question 1 is 25
question 2 is 0.2
------------------------------
bottom
question 3 is the second graph
the last question is the first graph
Step-by-step explanation:
Suppose that on each play of a game, a gambler either wins 1 with probability p or loses 1 with probability 1–p (or q). The gambler keeps betting until she or he is either up a total of n or down a total of m. What is the probability the gambler will quit an overall winner? You must consider both cases when p = 0.5 and when p ≠ 0.5
Answer:
Step-by-step explanation:
From the given information,
Considering both cases when p = 0.5 and when p ≠ 0.5
the probability that the gambler will quit an overall winner is:
[tex]P = \dfrac{1 - (\dfrac{1-p}{p} )^K}{1- (\dfrac{1-p}{p})^N } \ \ \ is \ p \neq 0.5 \ and\ K/N = \dfrac{1}{2}[/tex]
where ;
N.k = n and k = m
Hence, the probability changes to:
[tex]P = \dfrac{1 -(\dfrac{1-p}{p})^m}{1 -(\dfrac{1-p}{p})^{m+n}}[/tex] is p ≠ 0.5 and k/N = [tex]\dfrac{m}{m+n}[/tex] is P = 0.5