Graph the systems of equations. 2x+y=8, -x+2y=6 use the line tool to graph the lines
Answers
The lines intersect at the point (2, 4). So, the solution to the system of equations is x = 2 and y = 4.
To graph the system of equations 2x+y=8 and -x+2y=6, we first need to rearrange each equation into slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. This allows us to easily graph each line by plotting the y-intercept and using the slope to find additional points on the line.
For the first equation, we can rearrange it as follows:
2x + y = 8
y = -2x + 8
So the slope of the first line is -2 and the y-intercept is 8.
For the second equation, we can rearrange it as follows:
-x + 2y = 6
2y = x + 6
y = (1/2)x + 3
So the slope of the second line is 1/2 and the y-intercept is 3.
To graph each line, we can use the line tool in a graphing software or manually plot points on a piece of graph paper. Starting with the first equation, we can plot the y-intercept at (0, 8) and use the slope of -2 to find additional points. For example, if we move one unit to the right (from x=0 to x=1), we can move two units down (since the slope is -2) to get to the point (1, 6). We can continue this process to plot more points and draw a straight line through them.
Next, we can graph the second equation by plotting the y-intercept at (0, 3) and using the slope of 1/2 to find additional points. For example, if we move two units to the right (from x=0 to x=2), we can move one unit up (since the slope is 1/2) to get to the point (2, 4). We can continue this process to plot more points and draw a straight line through them.
Once both lines are graphed, we can see where they intersect, which is the solution to the system of equations. In this case, the lines intersect at the point (2, 4). Therefore, the solution to the system of equations is x = 2 and y = 4.
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Related Questions
which portion of the ecg corresponds to repolarization of the atria?
Answers
The portion of the ECG that corresponds to repolarization of the atria is not usually visible on a standard ECG. In some cases, abnormalities in the repolarization of the atria may be visible on an ECG as changes in the shape or duration of the T wave.
The standard ECG only records electrical activity that is strong enough to cause depolarization of the ventricles, which creates the QRS complex. The repolarization of the atria occurs during the T wave, which represents ventricular repolarization. Therefore, the repolarization of the atria is usually hidden within the T wave and cannot be specifically identified on a standard ECG.
The electrical activity of the heart is recorded on an ECG as a series of waves and intervals that correspond to specific events in the cardiac cycle. The P wave represents the depolarization of the atria, which causes them to contract and pump blood into the ventricles. The QRS complex represents the depolarization of the ventricles, which causes them to contract and pump blood out of the heart. The T wave represents the repolarization of the ventricles, which allows them to relax and refill with blood. During the cardiac cycle, the repolarization of the atria occurs after their depolarization and contraction. This repolarization wave is very small and weak compared to the depolarization wave, and it is not usually visible on a standard ECG. Instead, the repolarization of the atria is hidden within the T wave, which represents the larger and more prominent repolarization wave of the ventricles.
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Suppose it was –5 degrees Celsius at 6:00 a.m. By noon, the temperature had Increased by 11 degrees. What was the temperature at noon?
Answers
Answer:
6
Step-by-step explanation:
11 - -5 = 6
The temperature at noon is 6 degrees Celsius.
GivenSuppose it was -5 degrees Celsius at 6:00 a.m.
By noon, the temperature had increased by 11 degrees.
What is temperature?Temperature declines as altitude increases.
The temperature at noon is calculated by adding the morning temperature and temperature in the afternoon.
The temperature in noon = temperature at 6;00 a.m. + increase in temperature in afternoon.
The temperature in noon = -5 + 11
The temperature in noon = 6 degrees.
Hence, the temperature at noon is 6 degrees Celsius.
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Two important ingredients for baking bread are yeast and flour. To make a loaf of bread of at most 30 servings, maintain a yeast to flour ratio of 1:200. If you're making a loaf of more than 30 servings, use a ratio of 1:180. If you're making 30 servings of bread and using 0.45 oz of yeast, how many ounces of flour do you need? If you're making 90 servings of bread and using 720 oz of flour, how many ounces of yeast do you need?
Answers
If you're making 30 servings of bread and using 0.45 oz of yeast, how many ounces of flour do you need? ANSWER=90
If you're making 90 servings of bread and using 720 oz of flour, how many ounces of yeast do you need? ANSWER=4
The flour that will be used for 30 servings is 0.90 oz, while the yeast that will be used for 90 servings is 90 oz.
Given to us
To make a loaf of bread of at most 30 servings, maintain a yeast to flour ratio of 1:200.
To make a loaf of bread of more than 30 servings, maintain a yeast to flour ratio of 1:180.
Ratio for 30 ServingsA.) If We are making 30 servings of bread and using 0.45 oz of yeast,
As it is given that for 30 servings we must maintain a yeast to flour ratio of 1:200, therefore,
\(\rm \dfrac{Yeast}{Flour} = \dfrac{1}{200}\)
Using the ratio for 0.45 oz of yeast,
\(\rm \dfrac{0.45\ oz}{Flour} = \dfrac{1}{200}\)
\(\rm {Flour} = 200 \times 0.45\ oz\)
\(\rm {Flour} = 90\ oz\)
Thus, we will use 90 oz of the flour for 0.45 oz of yeast to serve 30 people.
Ratio for 90 ServingsB.) If We are making 90 servings of bread and using 720 oz of flour,
As it is given that for more than 30 servings we must maintain a yeast to flour ratio of 1:180, therefore,
\(\rm \dfrac{Yeast}{Flour} = \dfrac{1}{180}\)
Using the ratio for 720 oz of flour,
\(\rm \dfrac{Yeast}{720\ oz} = \dfrac{1}{180}\)
\(\rm {Yeast} = \dfrac{720\ oz}{180}\)
\(\rm {Flour} = 90\ oz\)
Thus, we will use 90 oz of the flour for 0.45 oz of yeast to serve 30 people.
Hence, the flour that will be used for 30 servings is 0.90 oz, while the yeast that will be used for 90 servings is 90 oz.
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A woman works out by running and swimming. When she runs, she burns 7 calories per minute. When she swims, she
burns 9 calories per minute. She wants to burn at least 441 calories in her workout. Write an inequality that describes
her options for the number of minutes of running, x, and the number of minutes of swimming, y, in a workout.
A. 7x+9y≤441
B. 9x+7y2441
C. 7x+9y2441
D. 7x+9y+441 ≤0
Answers
The inequality that describes the calories burned is 7x + 9y ≥ 441
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depends on other variable while a dependent variable is a variable that depends on other variable.
let x represent the number of minutes of running and y represent the number of minutes of swimming, hence:
7x + 9y ≥ 441
The inequality that describes the calories burned is 7x + 9y ≥ 441
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Substitution Property
If x=-2 and y+3x=10, then
Answers
Answer:
y=16
Step-by-step explanation:
If x=-2, then we can substitute for x in the y+3(-2)=10. y-6=10, we add 6 to both sides to isolate y giving y=16
Pls help
Melissa crochets baby blankets. Her current project is a baby blanket with alterna of soft yellow and pastel green. All stripes have the same length and width. If the yellow stripes totals 57% of the blanket and the area of the green stripes totals 1,134 , what is the total area of the blanket rounded to the nearest ?
Answers
Answer:
C. 2,637 square inches
Step-by-step explanation:
A particular computer takes 10 minutes to download a 40-minute TV show. How long will it take the computer to download a 1.5-hour movie
Answers
Answer:
A particular computer takes 15 min to download a 45-min TV show. How long will it take the computer to download a 2-h movie? - Slader. ... (Then buy a faster computer.) RESULT. x = 40 min. Your solution is not live yet. ... How many hours would it take the insect to crawl 1 mi if the insect crawls at the same rate?
Plz help due tomorrow
Answers
Answer:
1. 2.19g + 0.59b + 1.49p
2. 6.57 + 1.77 + 2.98 = 11.32
Answer:
Part A.) 2.19g + 0.59b + 1.49p
Part B.) 11.32
Step-by-step explanation:
Part A.)
basically they give you the price for each item in the upper description. Just use g,b,p in terms that they gave you
Part B.)
plug in the amount of fruit per pound for each matching variable
2.19(3) + 0.59(3) + 1.49(2) = 11.32
Solve for K:
0.4k + 0.4k - 0.02 = 4.02
Answers
0.8k -0.02 = 4.02
0.8k = 4.04
k = 5.05
How do you solve this?
Geometric Mean Middle, Left, Right
Determine the value of x, y, w and z.. Round to the nearest tenths place if necessary.
X =
y =
W =
Z=
Answers
Answer:
w=5 x=2.1 y=5.4 z= 14.1
Step-by-step explanation:
w² = 13² - 12² = 25
w = 5
cos ∠1 = 12/13 = 13/(12+x)
12 (12+x) = 13 x 13 = 169
144 + 12x = 169
12x = 25
x = 25/12 = 2.08 = 2.1
∠1 + ∠2 = 90°
∠2 + ∠4= 90° ∠4 = ∠1
sin ∠4 = x/y = sin ∠1 = 5/13
5y = 13x
y = 13/5 x = 13/5 * 25/12 = 65/12 = 5.4
z = 12 + x = 12 + 2.08 = 14.08 = 14.1
Can someone help me with this three part question please? I need help ASAP
Answers
It is not a triangle.
Does given feet is a triangle or not?
The Triangle Inequality theorem states that in a triangle, , where and are shorter side lengths and is the longest side length.
Given that 5+9<15, the given side lengths do not compose a valid triangle.
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If p=180−0.2D, calculate the optimal profit if the total cost is $30,500.
Answers
To calculate the optimal profit, we need to find the value of D when the total cost is \($30,500\) and then substitute it into the given equation.
To find D, we can rearrange the equation to solve for D: Given:\(p = 180 - 0.2D\) and total cost =\($30,500\) Now, substitute the total cost ($30,500) into the equation to find D:
Since D cannot be negative in this context, it means that the given equation is not applicable for a total cost of \($30,500\). it is not possible to calculate the optimal profit using the given equation and the total cost of \($30,500\).
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Find the slope and the y-intercept of the line.
- 8x+4y=-4
Write your answers in simplest form.
slope:
.
08
Undefined
X
$
?
y-intercept: 1
Answers
Answer:
slope - (2x)
y-intercept - (-1)
Step-by-step explanation:
-8x + 4y = - 4
4y = 8x - 4
y = 2x - 1
If four people equally share a 1/2 page to 3/4page.what fraction of the page in the photograph
Answers
Step-by-step explanation:
fraction of page of photograph is 3/32
(1/2÷4)*3/4
1/2*1/4*3/4
1/8*3/4
=3/32
Evaluate the following expression.
18+ [8x (17-14)-15]
Answers
Answer:
27
Step-by-step explanation:
Let's start by simplifying the expression inside the brackets using the order of operations (PEMDAS):
8 x (17-14) = 8 x 3 = 24
Now, we can substitute 24 into the original expression:
18 + [24 - 15]
= 18 + 9
= 27
Therefore, the final answer is 27.
Four students found the mean of the data set 26, 31, 39, 30, 16, 16, 18, 38. which student found the correct mean? ashrita’s work: startfraction 26 31 39 30 16 16 18 38 over 8 endfraction = startfraction 214 over 8 endfraction = 26.75 collette’s work: startfraction 26 38 over 2 endfraction = startfraction 64 over 2 endfraction = 32 daniel’s work: startfraction 26 31 39 30 18 38 over 7 endfraction = startfraction 198 over 7 endfraction = 28.29 lora’s work: startfraction 30 16 over 2 endfraction = startfraction 46 over 2 endfraction = 23
Answers
In calculating the mean of this data set Ashrita did the best job.
The Mean of the data set is the most commonly used measures of central tendency.
It means the average value of the data set.
one doesn't have to arrange the data in order for finding it.
What is the meaning of mean?The data set value takes is to add them all together and divide that by the number of the data.
It can be written as
\(,(x_1 + x_2 + x_3 + ..... + x_n) / n\)
Where \(x_1 , x_2 , x_3 , ..... ,x_n\)are the values in the data set
Therefore we can conclude that Ashrita did the best job in calculating the mean of this data set.
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Matsuki is very very bored...
34 + 35 x (60/2) - (40/2) = ?
Answers
I believe the answer is 1064.
P.s. your cute matsuki <3
Marguerite draws a net of a solid figure. The net has 1 square face and 4 triangular faces. For which polyhedron did Marguerite draw a net? Choose the correct answer below. A triangular prism A triangular pyramid A square pyramid A rectangular prism
Answers
Marguerite drew a net of a polyhedron that has one square face and four triangular faces. We can conclude that Marguerite drew a net for a square pyramid.
From the information given in the problem, we know that Marguerite's net has one square face and four triangular faces. This means that the polyhedron that the net represents must have five faces in total. We can use the number of faces, along with the fact that the faces are either triangles or squares, to determine which polyhedron it is.
A triangular prism has two triangular faces and three rectangular faces. Therefore, it is not possible that Marguerite drew a net for a triangular prism.
A triangular pyramid has one triangular face and three triangular faces. Therefore, it is not possible that Marguerite drew a net for a triangular pyramid.
A square pyramid has one square face and four triangular faces. Since this is the only option with one square face and four triangular faces, it must be the polyhedron that Marguerite drew a net for.
A rectangular prism has six faces, and none of them are triangles. Therefore, it is not possible that Marguerite drew a net for a rectangular prism.
Therefore, we can conclude that Marguerite drew a net for a square pyramid.
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A triangle has angles 110, 30, and 20. What kind of triangle is this?
A. Acute and scalene
B. Acute but not scalene
C. Right but no isosceles
D. Obtuse but not scalene
E. Brussels and scalene
Answers
Answer:
Step-by-step explanation:
This is not a triangle at all. You must have typed the angles incorrectly. A triangle's angles have to add up to 180 and yours only add up to 160...
x - 3 < 4
graph the inequality
Answers
Answer: See the image below.
4(x + 2) = 4x + 2
Are these two Equivalent
Answers
Answer:
no they're not
Step-by-step explanation:
4(x+2) = 4x +8
4x+2= 4x+2
Answer:
No they are not equivalent
First we would have to solve 4(x+2)
In order to solve this we need to multiply. So 4×X is equal to 4x. 4×2=8 Therefore when solving Its 4x+8..and 4x+8 is not equivalent to 4x+2
Pls help! find the area of each figure. use 3.14 for π
Answers
8x4=32
(3x3)/2=4.5
(3x2)/2=3
32+4.5+3= 39.5
Answer:
39.5
Step-by-step explanation:
1 Triangle; 3
other Triangle; 4.5
Rectangles; 32
Hope This Helps! :)
What type of graph is best to use for making comparisons among data?
A: Bar graph
B: Venn Diagram
C: Histogram
D: Circle Graph
Answers
Reserved tickets for the football game cost $20 each and general admission tickets cost $12 each. The total ticket sales brought in $900. The equation below can be used to find out how many of each type of ticket were sold, where x is the number of general admission tickets.
20x+12y =900
Which of the following graphs shows the graph of this equation?
Answers
Answer:
so what you would do is 20 x 12 and see what you get and the subtract it from 900
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Solve the equation.
x/3 + 5 = 9
X=
Answers
Answer:
X=12
Step-by-step explanation:
Subttract 5 on both sides
x/3=4
Multiply by 3 on both sides to isolate the X
x=12
Answer:
x = 12
Step-by-step explanation:
Step 1: Write equation
x/3 + 5 = 9
Step 2: Solve for x
Subtract 5 on both sides: x/3 = 4Multiply both sides by 3: x = 12Step 3: Check
Plug in x to verify it's a solution.
12/3 + 5 = 9
4 + 5 = 9
9 = 9
How to convert 9hours 36 minutes to a fraction
Answers
Answer:
Step-by-step explanation:
9*60+36= 540+ 36= 576 minutes
so it is = 576/ 60 hours
PLEASE PLEASE PLEASE PLEASE PLEASE PLEASE PLEASE PLEASE PLEASE PLEASE PLEASE PLEASE PLEASE PLEASE HELP ME OUT WITH THIS ISSUE PLEASE
Answers
Answer:
3 7/8
7 3/4
11 5/8
15 1/2
Step-by-step explanation:
3 7/8 is equal to 31/8.
31 x 2 is 62. 62/8 simplified is 7 6/8 or 7 3/4
31 x 3 is 93. 93/8 simplified is 11 5/8
31 x 4 is 124. 124/8 simplified is 15 4/8 or 15 1/2
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Are the shapes congruent figures? A. Yes, the shapes are congruent because they are both hexagons. B. Yes, the shapes are congruent because they both have the same measurements. C. No, they are not congruent because one of the shapes is rotated. D. No, they are not congruent because one of the shapes only has 5 sides.
Answers
Answer:
Yes, and its B
Step-by-step explanation:
if you flip and turn the one to the right, it matches up to the one on the left
hope that helps :)
Answer:
B
Step-by-step explanation:
suppose the 99% confidence interval for the mean sat scores of applicants at a business college is given by [1,692, 1,842]. this confidence interval uses the sample mean and the sample standard deviation based on 25 observations. what are the sample mean and the sample standard deviation used when computing the interval?
Answers
The upper bound is 1842 and lower bound is 1692. By using these boundaries and t-table, the sample mean is 1767 and sample standard deviation = 133.98.
Here, the two boundaries are 1692 and 1842.
Mean = (1692+1842) /2 = 1767
Here the degree of freedom, df = (n-1) = 25-1 =24
Margin of error = (1842-1692)/2 = 75
Confidence level = 99%
From the t table, value of T with confidence level 99% and df= 24 is 2.80
The equation for margin of error is M = Ts/√n
M= 75 , T= 2.80, n =25
75 = (2.80 × s) / √25
75 = 2.80s/ 5
s = (75×5)/2.80 = 133.928 = 133.93
So the sample mean is 1767 and the standard deviation is 133.93.
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A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus the diameter of the semicircle is equal to the width of the rectangle. See the figure below If the perimeter of the window is 24 ft, find the value of x so that the greatest possible amount of light is admitted
Answers
The perimeter equation is:
2x + x + (1/2)πx = 24 ft.
Simplifying the equation, we have:
(5/2)πx + 3x = 24 ft.
To find the value of x, we solve the equation:
(5/2)πx + 3x = 24 ft.
This equation can be solved numerically or algebraically to find the value of x.
The perimeter of a Norman window can be calculated by adding the lengths of all its sides. In this case, the perimeter is given as 24 ft.
Let's break down the components of the Norman window:
- The rectangular part has two equal sides and two equal widths. Let's call the width of the rectangle "x" ft.
- The semicircle on top has a diameter equal to the width of the rectangle, which is also "x" ft.
To find the perimeter, we need to consider the lengths of all sides of the rectangle and the semicircle.
The perimeter consists of:
- Two equal sides of the rectangle, each with a length of "x" ft. So, the total length for both sides of the rectangle is 2x ft.
- The width of the rectangle, which is also "x" ft.
- The curved part of the semicircle, which is half the circumference of a circle with a diameter of "x" ft. The formula for the circumference of a circle is C = πd, where C is the circumference and d is the diameter. So, the circumference of the semicircle is (1/2)πx ft.
To summarize, the perimeter equation is:
2x + x + (1/2)πx = 24 ft.
Simplifying the equation, we have:
(5/2)πx + 3x = 24 ft.
To find the value of x, we solve the equation:
(5/2)πx + 3x = 24 ft.
This equation can be solved numerically or algebraically to find the value of x.
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