One month, a homeowner used 150 units of gas and 520 units of electric for a total of 54.20. The next month he used 210 units of gas and 405 units of electric for a total of 82.35.
I understand the 2 equations are
150g + 520e = 84.20
210g + 405g = 82.35
I dont understand how to get the value of g and e though, like someone said to use 7 to multiply against the first equation and -5 the second, but like where are we getting 7 and -5 from.
The solution to the system of equations is:
e = 0.109
g = 0.183
How to solve the system of equations?Defining the variables:
g = cost of the unit of gas.
e = cost of the unit of electricity.
Then the system of equations is:
150*g + 520*e = 84.20
210*g + 405*e = 82.35
Now we want to solve this.
To do so, we need to isolate one of the variables in one of the equations. Let's isolate g in the first one:
g = (84.20 - 520*e)/150
Now we replace that in the other equation so we get:
210*(84.20 - 520*e)/150 + 405*e = 82.35
Now we can solve this for e:
210*(84.20 - 520*e)/150 + 405*e = 82.35
(210/150)*(84.20 - 520*e) + 405*e = 82.35
117.6 - 728*e + 405*e = 82.35
117.6 - 323*e = 82.35
e = (117.6 - 82.35)/323 = 0.109
Then:
g = (84.20 - 520*0.109)/150 = 0.183
Then we can conclude that:
e = 0.109
g = 0.183
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Four times a number, subtracted from 8, is twice the number. Find the number.
Answer:
3/4 or 0.75
Step-by-step explanation:
8-4x=2x
-4x-2x=-8
-6x=-8
x=-6/-8
=3/4 or 0.75
Five more than the quotient of eight and two
Answer:
9
Step-by-step explanation:
a quotient is the result of dividing one number by the other, so we know 8 is being divided by 2
8÷2 is 4
five more just means adding 5
so we are left with 4+5 which =9
EASY POINTS WILL GIVE BRAINLIST TO BEST ANSWER
What is the result of solving this equation for t ?
Mt – 5ab = nRT
explain!!
The required equation would be t = (nRT + 5ab)/M which is the result of the equation for t.
What is an equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
The equation is given as
Mt - 5ab = nRT
We have to determine the result of solving this equation for t
⇒ Mt - 5ab = nRT
⇒ Mt = nRT + 5ab
⇒ t = (nRT + 5ab)/M
Therefore, the required equation would be t = (nRT + 5ab)/M which is the result of the equation for t.
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The value of the surface area (in square centimeters) of the cone is equal to the value of the volume (in cubic centimeters) of the cone. The formula for the surface area S of a right cone is S=πr2+πrl, where r is the radius of the base and l is the slant height. Find the height of the cone.
The height of this cone is 3( 1 + [tex]\frac{l}{r}[/tex] ). Which have the same volume and surface area.
Given that
The value of the surface area (in square centimeters) of the cone is equal to the value of the volume (in cubic centimeters) of the cone.
The formula for the surface area S of a right cone is S=πr2+πrl, where r is the radius of the base and l is the slant height.
To find
The height of the cone.?
So, according to the question
We have,
The surface area of the cone = The volume of the cone.
We know that
The surface area of the cone,
S = πr²+πrl
And,
The volume of the cone,
V = [tex]\frac{1}{3} \pi r^2h[/tex]
So, from question
The surface area of the cone = The volume of the cone
S = V
Now, put the all values,
πr²+πrl = [tex]\frac{1}{3} \pi r^2h[/tex]
πr(r+ l) = [tex]\frac{1}{3} \pi r^2h[/tex]
(r+l) = [tex]\frac{1}{3}[/tex] × [tex]\frac{\pi r^2h}{\pi r}[/tex]
(r+l) = [tex]\frac{1}{3}[/tex] × rh
[tex]\frac{3(r+l)}{r}[/tex] = h
h = 3( [tex]\frac{r}{r} + \frac{l}{r}[/tex] )
h = 3( 1 + [tex]\frac{l}{r}[/tex] )
So the height of this cone is 3( 1 + [tex]\frac{l}{r}[/tex] ).
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If AD=5x+8 and BD=3x-10, what is the length of AB?
A)28
B)148
C)74
D)222
I need to find the values of X
Answer:
[tex](f + g)( \times ) = { \times }^{4} [/tex]
Add. −5/6 + (−2 5/8) Enter your answer as a simplified fraction by filling in the boxes.
WILL GIVE BRAINLIEST!!
Answer: [tex]-1 \frac{19}{24}[/tex]
Step-by-step explanation:
5/6 + (−2 5/8)=
5/6 + (−2 - 5/8)=
5/6 −2 - 5/8=
(5/6 −2 - 5/8)*24/24= ==> 24 is the LCM of 6 and 8
[tex]\frac{(5*24/6 -2*24-5*24/8)}{24}[/tex]=
[tex]\frac{(120/6 -48-120/8)}{24}[/tex]=
[tex]\frac{(20-48-15)}{24}[/tex]=
(-28-15)/24=
-43/24 =
(-24-19)/24=
-24/24 -19/24=
-(24/24 +19/24)=[tex]-1 \frac{19}{24}[/tex]
What sets of elements does the square root of square root of -10 apply to?
Integer
Real number
Rational
Irrational
Natural
Whole
The square root of - 10 is not a real number but a complex number, an irrational number.
What number set does an element belong to?
Numbers can be classified in real numbers and complex numbers. Real numbers are classified in natural numbers (i.e. 1, 4, 5), whole numbers (i.e. 0, 1, 4, 5), integers (i.e. - 4, -1, 0, 5, 6) and rational numbers (i.e. 5 / 7, 0, - 13 / 3) and part of the irrational numbers (i.e. √3, π) and the rest of irrational numbers are complex numbers (i.e. i 4, - 4 + i 5).
In consequence, the square root of - 10 is not a real number but a complex number, an irrational number.
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Mo is sorting number cards with ratios. All of these ratios are equivalent to 3:5. Circle the ratios that are not equivalent.
13:15
30:50
7:9
3x:5x
5:3
Ratios which are not equivalent to 3: 5 are 13: 15, 7:9, 5:3.
As given in the question,
Mo is sorting number cards with ratios
Ratio = 3 : 5
Equivalent ratio to 3 : 5
13 : 15 cannot be reduced.
13 : 15 not equivalent to 3:5
30:50 = (3 ×10) : (5×10)
= 3:5
7:9 cannot be reduced . It is not equivalent to 3:5
3x:5x = 3:5
5:3 reciprocal of 3:5 .It is not equivalent to 3:5.
Therefore, ratios which are not equivalent to 3: 5 are 13: 15, 7:9, 5:3.
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Please help asap
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Solve five sixths times c minus 1 equals 1 plus five sixths times c.
Infinite solutions
No solution
c equals five sixths
c equals twelve tenths
Answer:
No solution!
Step-by-step explanation:
I just took the quiz and got 100%
help pleaseeeeeee :(((
Answer: are there any options?
Step-by-step explanation:
It’s probs easy but help pls
Answer:
frequency =12 and mass x (kg)=20<=x<30The cost to rent a boat is $25 per hour plus a non-refundable $30 deposit
A. write an expression to rent a boat for h hours
B. Evaluate the expression for h=2
Answer:
A. 25h+30=80
B.25(2)+30=80
Total number of possible equal parts in a fraction (a) denominator (b) numerator (c) mixed number (d) divisor?
Denominator: The value in a fraction that appears below the fractional bar and indicates the total number of equal parts.
In a fraction, the value that appears above the horizontal line is referred to as the numerator. It represents the number of pieces removed from the whole. The denominator of a fraction is the numerical value that comes before the vinculum.
A mixed number is a representation of both a whole number and a legal fraction. In most cases, it denotes a number that falls between any two whole numbers.
An integer that totally or partially divides another integer is known as a divisor.
In a division equation, a divisor is represented by the formula
Dividend ÷ Divisor = Quotient.
The correct option is (a).
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Please help due in 20mins
Using the common factors, the expression can be rewritten as follows:
1 / 4 xy (x² + 3y)How to rewrite an expression using common factors?The expression can be represented as follow using common factor.
1 / 4 x³y + 3 / 4 xy²
Using the common factors,
The common factors of 1 / 4 x³y and 3 / 4 xy² is 1 / 4 xy.
Therefore,
1 / 4 x³y + 3 / 4 xy² = 1 / 4 xy (x² + 3y)
Therefore, rewriting 1 / 4 x³y + 3 / 4 xy² using the common factors is 1 / 4 xy (x² + 3y).
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Determine which integer in the solution set will make the equation true.
2s − 10 = −12
S: {−1, 0, 1, 2}
−1
0
1
2
Answer:
- 1 makes the equation true
Step-by-step explanation:
2s - 10 = - 12 ( isolate the term in s by adding 10 to both sides )
2s = - 2 ( divide both sides by 2 )
s = - 1
The integer ion in the solution set will make the equation true is -1. The correct option is a.
What are integers?Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers.
An integer, pronounced "IN-tuh-jer," is a whole number that can be positive, negative, or zero and is not a fraction. Any positive or negative number without fractions or decimal places is known as an integer, often known as a "round number" or "whole number."
Given equation is
2s - 10 = - 12 ( isolate the term in s by adding 10 to both sides )
2s = - 2 ( divide both sides by 2 )
s = - 1
Therefore, the correct option is a, −1.
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ridden a bike course that is 40 miles long. so far he has ridden 28 miles of the course. what percentage of the course has he ridden so far
So far, he has ridden 70% of the bike course.
Percentage, which was adapted from the Latin word "per centum", which means "by the hundred", is a fraction or a ratio in which the value of whole is always 100. It is represented by the symbol "%".
The formula to get the percentage is:
Percentage = (Value / Total Value) × 100
If the total value of the bike course is 40 miles and the value which the percentage we are looking for is 28 miles, evaluating the equation:
Percentage = (Value / Total Value) × 100
Percentage = (28 / 40) × 100
Percentage = (0.7) × 100
Percentage = 70
Therefore, he has ridden 70% of the bike course so far.
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nth term of the sequence 9 6 3 0 -3 -6
Answer:
-3n+12
Step-by-step explanation:
Term to term rule:
9-6=3
6-3=3
3-0=3
term to term rule is -3
-3 x n + 9 - (-3)
-3n + 12
HELP ASAP
True or false:
What is the value of the expression below when x=7
The value of the expression when x = 7 is 70
What are algebraic expressions?Algebraic expressions are expressions made up of variables, terms, coefficients, factors and constants.
They are also made up of mathematical operations such as addition, multiplication, division, subtraction, etc.
Given the expression;
2x^2- 5x - 3
To determine the the value, we substitute the value of x a 7 into the expression, we have;
2(7)² - 5(7) - 3
expand the bracket
2(49) - 25 - 3
98 - 25 - 3
Find the difference
70
Thus, the value of the expression when x = 7 is 70
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Help me please I will mark the person as a brainliest.
Answer:
200 km/hr
Step-by-step explanation:
We can find the speed by dividing the distance by the time taken for the trip.
[tex]\sf \boxed{Speed = \dfrac{distance }{time}}[/tex]
[tex]\sf r = \dfrac{300}{t}[/tex]
In the above equation, substitute t = 1.5 hours and find the train's rate.
[tex]\sf r = \dfrac{300}{1.5}\\\\= \dfrac{300*10}{1.5*10}\\\\= \dfrac{3000}{15}\\\\r = 200 \ kilometers \ per \ hour[/tex]
-11 to the power of 0
the following is a list of steps for solving a quadratic equation by completing the square. write the correct step number in the blanks. if the leading coefficient is not 1, divide both sides by the coefficient so that the resulting equation has a leading coefficient of 1 . write the equation in the form a x 2 b x
1- if the main coefficient isn't always 1, divide each facets by way of the coefficient so that the resulting equation has a leading coefficient of 1.
2- write the equation within the form ax²+ bx = c
3- write the left aspect of the equation because the rectangular of a binomial and simplify the proper side if possible.
4- add the rectangular of half of the coefficient of the linear time period to both aspects of the equation.
5- practice the rectangular root property for equation and solve as usual.
What do you mean by quadratic?
Quadratics can be defined as a polynomial equation of a second degree, which means that it incorporates a minimum of one time period that is squared. it's also referred to as quadratic equations. the general shape of the quadratic equation is: ax² + bx + c = 0.
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HELP MEEEEEEEE I WILL GIVE BRAINLIST 2 AND EXTRA POINTS
why do 3 wholes 1/2- 4 wholes 7/8 = 3/8
PLEASE HELPPPPPPPPPP
3 1/2 subtracted from 4 7/8 is equal to 3/8.
What is the value of the subtraction?A fraction is a quantity that is not a non-integer. A fraction usually has a numerator and a denominator. The numerator is the number above. While the denominator is the number below. An example of a fraction is 1/2.
A mixed number is a number that has a whole number and a proper fraction. A proper fraction is a fraction is which the numerator is less than the denominator. An example of a mixed number is 3 1/2.
Subtraction is the mathematical operation that is used to determine the difference of two or more numbers. The sign used to represent subtraction is -.
[tex]3\frac{1}{2} - 4\frac{7}{8}[/tex]
[tex]-1\frac{4 - 7}{8}[/tex]
[tex]-1\frac{-3}{8}[/tex] = 3/8.
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in the dominican republic in august, the distribution of daily high temperature is approximately normal with mean 86 degrees fahrenheit (°f). approximately 95% of all daily high temperatures are between 83°f and 89°f. what is the standard deviation of the distribution? 1°f 1 degree fahrenheit 1.5°f 1.5 degrees fahrenheit 2°f 2 degrees fahrenheit 3°f 3 degrees fahrenheit 6°f
The standard deviation of the distribution = 1.5°F
Given that the distribution of daily high temperature is approximately normal.
Population mean, [tex]\mu[/tex] = 86°F
Also approximately 95% of all daily high temperatures are between 83°F and 89°F.
So here [tex]X_1[/tex] = 83°F and [tex]X_2[/tex] = 89°F
We have the z - statistic ,
[tex]z=\frac{x-\mu}{\sigma}[/tex]
where [tex]\sigma[/tex] is the Standard deviation.
For 95% probability, the z-value for normal distribution is 1.96.
As we consider the positive z-value, take X = [tex]X_2[/tex] = 89°F
So, [tex]z=\frac{x-\mu}{\sigma}[/tex]
⇒ [tex]\sigma = \frac{x-\mu}{z} = \frac{89-86}{1.96} =1.53[/tex] ≈ 1.5°F
So the standard deviation of the distribution = 1.5°F
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Solve the inequality.
x+1>3
0 −4 < x < 2
Ox<-4 orx > 2
O-2
O x < -2 or x > 4
Answer:
answer of the first one
x+1>3 equal to x>2 by subtracting 1 from each side
so x>2 equal ]2,infinity[
answer of the second
-4<x<2 so the quantity of x is all the numbers from -4 to 2 but when it be greater than or smaller than without saying or equal we put the brackets opened so the result is ]-4,2[
but i can,t understand 3 and 4
5x-5=9x+3 Solve for x
Answer:
x = -2
Step-by-step explanation:
5x - 5 = 9x + 3
- 5 = 4x + 3
- 8 = 4x
- 8/4 = 4x/4
x = -2
After a 7.5% pay rise Mr Jones salary was £29455. What was his salary before the pay rise?
Answer:
£27400
Step-by-step explanation:
The original salary of x.
The raise was 7.5% = 7.5/100 = 0.075 of the salary.
The original salary plus the raise is x + 0.075x = 1.075x.
The new salary is £29455.
Therefore,
1.075x = £29455
Divide both sides by 1.075.
x = £27400
Answer: £27400
Triangle UML has coordinates U (-3, -4), M(-1, -1) , and L(-2, -5). If the triangle is translated 5 units up and 1 unit left to form triangle U’M’L’, what will be the coordinates of L’?
After the translation the coordinates of L' are (-3, 0) for the new triangle of U’M’L’.
What is defined as the translation?In geometry, translation refers to a function which moves an object a specified distance. The object is not elsewhere altered. It is not rotated, mirrored, or resized.Every location of the object should be moved within the same direction for the same distance during a translation.When performing a translation, this same initial object is referred to as the pre-image, and also the object just after translation is referred to as the image.The coordinates of triangle are-
U (-3, -4), M(-1, -1) , and L(-2, -5).
The triangle is translated 5 units up and 1 unit left to its original place.
Thus, for the 5 units up translation 5 units will get added to the y-coordinates.
New y-coordinate of L' is -5 + 5 = 0.
For 1 unit left , 1 units will get reduced from the original x-coordinate.
New x-coordinate = -2 - 1 = -3
Thus, the new coordinates L' becomes (-3, 0).
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