Answer:
2x + 3y = 6
Step-by-step explanation:
The equation of a line in slope- intercept fprm is
y = mx + c ( m is the slope and c the y- intercept )
Given
2x + 3y = 5 ( subtract 2x from both sides )
3y = - 2x + 5 ( divide terms by 3 )
y = - [tex]\frac{2}{3}[/tex] x + [tex]\frac{5}{3}[/tex] ← in slope- intercept form
with slope m = - [tex]\frac{2}{3}[/tex]
Parallel lines have equal slopes, then
y = - [tex]\frac{2}{3}[/tex] x + c ← is the partial equation
To find c substitute (3, 1 ) into the partial equation
1 = - 2 + c ⇒ c = 1 + 2 = 3
y = - [tex]\frac{2}{3}[/tex] x + 3 ( multiply through by 3 to clear the fraction )
3y = - 2x + 6 ( add 2x to both sides )
2x + 3y = 6 ← equation of parallel line
45 is what percent of 60 as an equation
Answer:
75% of 60 = 45
Step-by-step explanation:
In order to find the answer to this question you need to divide the percentage of the number by one-hundred and then divide that number by the number the number you are trying to find the percentage of.
60/x=100/75
(60/x)*x=(100/75)*x
60=1.33333333333*x
(1.33333333333) to get x
60/1.33333333333=x
45=x
x=45
75% of 60 = 45
Hope this helps.
My backyard has a square garden and the area of the garden is 57 square feet. Are the lengths of each side of the garden rational? Why/Why Not?
PLEASE HELP WILL MARK BRAINLIEST!
state the gradient and the y-axis intercept of
y=3x+7
Step-by-step explanation:
the slope (or gradient) of a line is the factor of x.
in our case here : 3
it is expressed as ratio y/x and represents the amount of units y changes (and via the sign in what direction), when x changes a certain amount of units (again, via the sign in what direction). like when going from a point 1 to a point 2.
so, here we have 3 = 3/1, and that means, when x changes by 1 unit to the right (positive), y changes 3 units up (positive).
the y-axis intercept is simply the point, where x = 0. clearly, any point with the x coordinate being unequal to 0 cannot be on the y axis.
so, here
y = 3×0 + 7 = 7
=>
the y-axis intercept point is (0, 7).
triangle abc is dilated with a scale factor of 1/3 label the angle measurements in triangle abc
Answer:
B=1 and the rest Im unsure of sorry hope this helps
Step-by-step explanation:
Which equation represents a line parallel to the line x-4y=-2
a: y=-4x - 2
b: y=-1/4 + 5
c: y= 1/4x - 3
d: y=4x - 8
Answer:
c
Step-by-step explanation:
the slope of x-4y=-2 is 1/4
two speedboats leave the dock at the same time and travel in opposite directions. one travels 9 mi/hr faster than the other. After 2 hr the boats are 170 mi apart. How fast is each boat travelling ?
Answer: [tex]\frac{170}{X}[/tex]+[tex]\frac{170}{X-9}[/tex]=2
(=)17 0x +170x+1530=2x²+18x
(=)-2 x² +322x+1530=0
Δ=b²-4ac
Δ=115924
[tex]\sqrt{}[/tex]Δ=340,476>0
because Δ>0 so that 2 X
=>x₁=2 (true), x₂=-161(false)
X+9= 2+9=11
first travel 2 mi/hr
second travel 11 mi/hr
Step-by-step explanation:
please help!! i will give a thanks and brainliest !
Answer:
19. is 18
31. is 10y-x
Step-by-step explanation:
thats only what i know sorry
PLEASE HELP ME!! I DON'T KNOW WHAT TO DO????
Answer:
Step-by-step explanation:
x-10=4
bring the 10 over and add it to the 4 and that equals 14 so
x=14 hope this helps have a great day
I forget how to do this lol
Answer:
-0.83
Step-by-step explanation:
Mario has 3750 paper clips. Chi has 2993 paper clips. How many more paper clips does
Mario have than Chi?
Answer: Mario has 757 more paper clips than Chi.
Step-by-step explanation:
Subtract 2,993 from 3,750. The answer is 757.
Solve for x -29+11=3x - 6x ???
Answer:
the right answer is x = 9/2
Selena has been hired as a sales associate at Better Rooms furniture store. She has two salary options. She can choose to receive either a fixed salary of $850 per week or a salary of $400 per week plus a 6% commission of her weekly sales. Which solution set below represents the dollar amount of sales that she must generate each week in order for the option with commission to be the better choice? Let s represent the sales for the week
Answer:
Sales have to be more than $7,500.
Step-by-step explanation:
850 > 400 + 0.06s
850 - 400 < 0.06s
450/0.06 < s
7500 < s
Select the choice that translates the following verbal phrase correctly to algebra:
the product of k and m
km
k + m
k − m
k ÷ m
Answer:
km that is k×m means k is multiplied by m
graph the line that passes through the point (0, -3) and is perpendicular to another line whose slope is 2
Answer:
y = -1/2x -3
Step-by-step explanation:
The line perpendicular to one with a slope of 2 will have a slope that is the negative reciprocal of 2, that is, -1/2. The given point is the y-intercept of the required line, so we can write its equation directly in slope-intercept form:
y = mx + b
where m is the slope (-1/2), and b is the y-intercept (-3). Your line is ...
y = -1/2x -3
1. What is the solution to the equation 3(x - 2)= 15?
Answer:
X=7
Step-by-step explanation:
Answer:
x=7
Step-by-step explanation:
3x-6=15
3x-6+6=15+6
3x=15+6
3x = 21
---- ----
3 3
x=7
Please help
Consider the matrices.
_ _
| - 17 |
PQ = | - 3 |
| - 37 |
|_ 49 _|
y=4x-36
find the zero of each function by graphing
Answer: X = 9
Step-by-step explanation:
First insert the function into a graphing calculator.
We are trying to find the x intercepts, we substitute y=0.
With a graphing calculator look at where the line intercepts the x axis, (9,0) , and we find that x=9.
Solve for X
A) -6
C) 12
E) 9
B) 8
D) 3
Answer:
In my thinking the answer is 9.
A car rental agency charges $70 per day, which includes 100 miles. For each mile over 100 miles, there is an additional cost of $0.40 per
Write an equation relating m, the number of miles driven, if the total cost for a one-day rental was $212.
Answer:
212=70+(m X 0.40)
If $212 is the total cost for a one-day rental, the number of miles driven is 455 miles.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
Cost of car rent per day for 100 miles = $70
Additional cost per mile = $0.40
Let m = number of miles driven
Total cost for one day rental = $212
The equation that represents the additional m = miles driven for a day that cost $212 is:
212 - 70 = 0.40m
142 = 0.40m
m = 142 / 0.40
m = 355
This means 355 additional miles were driven.
The number of miles driven for the day is:
= 100 + 355
= 455 miles
Thus if $212 is the total cost for a one-day rental, the number of miles driven is 455 miles.
Learn more about equations here:
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15^6*8^8(9)^8 what is it
Answer:
8.2263565e+21
Step-by-step explanation:
im smart
is the equation 2x+y=4 and 2x^2+y=6 linear.. if so, how do i graph them?
Answer:
No, but you can graph them by converting to mx+b form
Step-by-step explanation:
The procedure for solving simultaneous linear equations now called Gaussian elimination appears in the ancient Chinese mathematical text Chapter Eight: Rectangular Arrays of The Nine Chapters on the Mathematical Art. Its use is illustrated in eighteen problems, with two to five equations.[4]
Systems of linear equations arose in Europe with the introduction in 1637 by René Descartes of coordinates in geometry. In fact, in this new geometry, now called Cartesian geometry, lines and planes are represented by linear equations, and computing their intersections amounts to solving systems of linear equations.
The first systematic methods for solving linear systems used determinants, first considered by Leibniz in 1693. In 1750, Gabriel Cramer used them for giving explicit solutions of linear systems, now called Cramer's rule. Later, Gauss further described the method of elimination, which was initially listed as an advancement in geodesy.[5]
In 1844 Hermann Grassmann published his "Theory of Extension" which included foundational new topics of what is today called linear algebra. In 1848, James Joseph Sylvester introduced the term matrix, which is Latin for womb.
Linear algebra grew with ideas noted in the complex plane. For instance, two numbers w and z in {\displaystyle \mathbb {C} }\mathbb {C} have a difference w – z, and the line segments {\displaystyle {\overline {wz}}}{\displaystyle {\overline {wz}}} and {\displaystyle {\overline {0(w-z)}}}{\displaystyle {\overline {0(w-z)}}} are of the same length and direction. The segments are equipollent. The four-dimensional system {\displaystyle \mathbb {H} }\mathbb {H} of quaternions was started in 1843. The term vector was introduced as v = x i + y j + z k representing a point in space. The quaternion difference p – q also produces a segment equipollent to {\displaystyle {\overline {pq}}.}{\displaystyle {\overline {pq}}.} Other hypercomplex number systems also used the idea of a linear space with a basis.
Arthur Cayley introduced matrix multiplication and the inverse matrix in 1856, making possible the general linear group. The mechanism of group representation became available for describing complex and hypercomplex numbers. Crucially, Cayley used a single letter to denote a matrix, thus treating a matrix as an aggregate object. He also realized the connection between matrices and determinants, and wrote "There would be many things to say about this theory of matrices which should, it seems to me, precede the theory of determinants".[5]
Benjamin Peirce published his Linear Associative Algebra (1872), and his son Charles Sanders Peirce extended the work later.[6]
The telegraph required an explanatory system, and the 1873 publication of A Treatise on Electricity and Magnetism instituted a field theory of forces and required differential geometry for expression. Linear algebra is flat differential geometry and serves in tangent spaces to manifolds. Electromagnetic symmetries of spacetime are expressed by the Lorentz transformations, and much of the history of linear algebra is the history of Lorentz transformations.
The first modern and more precise definition of a vector space was introduced by Peano in 1888;[5] by 1900, a theory of linear transformations of finite-dimensional vector spaces had emerged. Linear algebra took its modern form in the first half of the twentieth century, when many ideas and methods of previous centuries were generalized as abstract algebra. The development of computers led to increased research in efficient algorithms for Gaussian elimination and matrix decompositions, and linear algebra became an essential tool for modelling and simulations.[5]
Vector spaces
Main article: Vector space
Until the 19th century, linear algebra was introduced through systems of linear equations and matrices. In modern mathematics, the presentation through vector spaces is generally preferred, since it is more synthetic, more general (not limited to the finite-dimensional case), and conceptually simpler, although more abstract.
A vector space over a field F (often the field of the real numbers) is a set V equipped with two binary operations satisfying the following axioms. Elements of V are called vectors, and elements of F are called scalars. The first operation, vector addition, takes any two vectors v and w and outputs a third vector v + w. The second operation, scalar multiplication, takes any scalar a and any vector v and outputs a new vector av. The axioms that addition and scalar multiplication must satisfy are the following. (In the list below, u, v and w are arbitrary elements of V, and a and b are arbitrary scalars in the field F.)[7]
s = bc -5, for b whats the answer?
-2.4 - 4.9=
It’s not 2.5
Answer:
-7.3
Step-by-step explanation:
You can't subtract a negative number. Enjoy and brainliest would make my day :D
Answer:
-7.3
Step by step explanation:
−2.4−4.9
=−2.4−4.9
=−2.4+−4.9
=−7.3
The table below shows Amelia's earnings on the job.
Time (hours) Earnings (dollars)
4
$108.80
9
$244.80
17
$462.40
How long does it take her to make $414.80?
Answer:
15.25 hours
Step-by-step explanation:
her pay per hour is $27.2
414.80÷27.2=15.25
7 (-2) - 15 =
Find the value of the expression.
Answer:
-29?
Step-by-step explanation:
Marsha has $400 in a savings account. The interest rate is 5% per year and is not compounded. How much will she have in total in 1 year?
The total amount in the account after 1 year will be $420
Based on the information given, the following can be deduced:
Principal = $400
Interest rate = 5%
Time = 1 year
Therefore, the simple Interest will be:
= PRT/100
= ($400 × 5 × 1)/100
= $2000/100
= $20
Therefore, the amount will then be:
= Principal + Interest
= $400 + $20
= $420
Therefore, the total amount is $420
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what is the domain and range of y=4x+4
Answer:
all real numbers
Step-by-step explanation:
domain is all the possible numbers for x
here x can be any real number
range is all the possible numbers for y
here y can also be any real number based on y
so for both domain and range the answer is all real numbers
(secA - cosecA)^3+ 3secA.cosecA (secA - cosecA )
bru
Answer: what?
??????..???
The length of a rectangle is 5 in longer than its width.
If the perimeter of the rectangle is 74 in, find its length and width.
Answer:
Length = 21
Width = 16
Step-by-step explanation:
We know that the formula for perimeter is:
P=2W+2L
And we also know that:
L=W+5
So then we put all that we know in the formula:
74=2W+2(W+5)
Now we expand the brackets and do some algebra:
74=4W+10 (-10)
64=4W (÷4)
16=W
Now that we know the width we can pop that into the length equation:
L=16+5
L=21