2x + 4y = 123x - 5y = 10
A. Write the equations in slope-intercept form. (Show your work.)
B. Graph the pair of linear equations.
C. Use the graph to estimate the solution to the system of equations.
Help??
Answers
A. The first equation in slope-intercept form is y = -0.5x + 3. The second equation in slope-intercept form is y = 0.6x - 2.
B. The graph of the two equations is attached below.
C. The solution of the system of equation is (4.545,0.727)
A. To write the equations in slope-intercept form (y = mx + b), where "m" represents the slope and "b" represents the y-intercept, we need to isolate "y" on one side of each equation.
1. 2x + 4y = 12
First, isolate "y" by subtracting 2x from both sides:
4y = -2x + 12
Next, divide both sides by 4 to get "y" by itself:
y = (-2x + 12) / 4
Simplify the equation:
y = -0.5x + 3
So, the first equation in slope-intercept form is y = -0.5x + 3.
2. 3x - 5y = 10
First, isolate "y" by subtracting 3x from both sides:
-5y = -3x + 10
Next, divide both sides by -5 to get "y" by itself:
y = (-3x + 10) / -5
Simplify the equation:
y = 0.6x - 2
So, the second equation in slope-intercept form is y = 0.6x - 2.
B. To graph the pair of linear equations, plot the y-intercept (where x = 0) and use the slope to find other points.
1. Graph the equation y = -0.5x + 3:
Plot the y-intercept at (0, 3).
Use the slope -0.5 to find another point; for example, if x = 2, then y = -0.5(2) + 3 = 2.
2. Graph the equation y = 0.6x - 2:
Plot the y-intercept at (0, -2).
Use the slope 0.6 to find another point; for example, if x = 3, then y = 0.6(3) - 2 = 0.
C. To estimate the solution to the system of equations, look for the point where the two lines intersect. This point represents the x and y values that satisfy both equations simultaneously. From the graph, we can interpret that the solution of the system of equation is (4.545,0.727)
To know more about equation:
#SPJ6
2x+4y=12
-2x -2x
4y=-2x+12
/4 /4
y=-1/2x+3
3x-5y=10
-3x -3x
-5y=-3x+10
/-5 /-5
y=3/5x-2
2) To graph SIF, you need to know what each aspect of the equation is. The formula is y=mx+b.
m stands for slope. A great way to remember it is rise/run (rise over run). Basically, the numerator in "m" is how far up you go to graph each point, and the denominator is how far left or right you go (remember, left is negative, right is positive). Let me give you an example. y=3/5x. In this formula, to graph each point, on the line, you'd go up 3, and to the right 5, then plot a point, then up 3, right 5, plot another one... you get it. What if the equation was y=3x though? The slope would be 3/1, or up 3, right one.
You know how to plot the points, but what coordinate do you startat? That's where the Y-Intercept comes into play. The Y-Intercept is basically where the line crosses the Y-axis. The b in the SIF formula is the y-intercept, and where you plot your very first coordinate on the line. If the SIF equation was y=1x+3, your first coordinate would be on the y axis, at an elevation of 3. Since the y-axis is at x=0, the coordinate would be (0,3).
3) Look at the graph now. Where do the lines cross? The x should be somewhere between 4 and 5, and the y is somewhere between 1.5 and 2. Therefor, your "estimation" should be something like (4.5,1.75)
I really hoped this helped you! It took a while to write so I'd appreciate if you'd choose the Brainliest answer -- thanks!
Related Questions
If you can only use 3 of these numbers once to find a sum of 30 without subtracting or adding additional numbers, what three numbers would you use out of 1, 3, 5, 7, 9, 11, 13, and 15? ()+()+()=30
What is 15%off of $3.00
A culture started with 2000 bacteria. After 2 hours it few to 2200 bacteria. Predict how many bacteria will be present after 19 hours.
Find the value of 83 - [59 - (22 - 18)].162864
Answers
The shadow of a 265m long building would be b. 151 m
What are ratio and proportion?
A ratio is a comparison between two similar quantities in simplest form.
Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.
In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.
Given, Ms. Kraus is 1.75 m tall. When her shadow is 1 m.
Let the shadow of a 265 m tall building be 'x' m.
Therefore by the ratio proportion method.
1.75 : 1 : : 265 : x.
1.75/1 = 265/x.
1.75x = 265.
x = 265/1.75.
x = 151.42 Or 151 m.
learn more about proportion here :
#SPJ2
Answer:
b. 151m
Step-by-step explanation:
Step-by-step explanation:
That's the right answer on edge
Answers
Answer:
1 1/4
Step-by-step explanation:
All this is, is division. You do 61/4 dived by 5. To divide fractions you flip the numerator and denominator of the second number and multiply them.
25/4 *1/5
Therefore the answer is 25/20 which is 1 and 5/20
That can be simplified to 1 and 1/4.
Answers
Answer:
a)7x - 10
b) 70 g
Step-by-step explanation:
a)
Mass of 1st chemical which was mixed = 10g
Mass of 2nd chemical which was mixed = 2x
Mass of 3rd chemical which was mixed = 5x-20
So total mass of the the mixture which was formed after mixing all the 3 chemicals are =
10 + 2x + 5x - 20
=> 7x - 10
b)
Mass of the mixture = 235 g
From (a) , we know that
7x - 10 = 235
=> 7x = 235 + 10 = 245
=> x = 245 / 7 = 35
Hence x = 35
We also know that mass of the 2nd chemical was = 2x.
So putting the value of x gives :-
2 × 35 = 70 g
Answers
Bon apetit ! What more can I say ?
Was there a question ?
If your objective is to feed 6 students with 5 pizzas, then do it like this:
(5 pizza) / (6 student) = 5/6 pizza per student.
Cut each pie in 6 equal pieces, and give each student 5 of the pieces.
Answers
I
I
I_
I_I______
Here is a (very crude) sketch of two perpendicular lines. The box between the place where the lines intersect indicates a right angle.
Hope this helps!
Answers
Answer:
There are 27,720 ways to select the committee
Step-by-step explanation:
First, it is necessary to know how many ways are there to select 3 members, if there are 9 members of the mathematics department. This can be found using the following equation:
Where nCk gives as the number of ways in which we can select k elements from a group of n elements. So, replacing n by 9 and k by 3 members, we get:
So, there are 84 ways to select 3 members from 9 members of the mathematics department.
At the same way, we can calculate that there are 330 ways to select 4 members from the 11 that belong to the Computer science department as:
Finally the total number of ways in which we can form a committee with 3 faculty members from mathematics and 4 from the computer science department is calculated as:
9C3 * 11C4 = 84 * 330 = 27,720