Solve the system of equations algebraically. Show all of your steps.
y=x^2+2x
y=3x+20
Can someone please explain to me how to do this? I want to actually learn it, please.
Thanks! :)
Since you have two equations that equal y, you can set them equal to themselves, so 3x+20=x^2+2x
If you move those all over to one side, you get that x^2-x-20=0. From there you can factor out into two parts, (x-5)(x+4)=0. So for this set of equations you can know that the values of x where they intersect are -4 and 5.
All you need to do now is choose an equation to input the values in to solve for y. So, y= 3(-4)+20=8 when x=-4 and y=3(5)+20=35 when x=5. Therefore the two points at which they intersect are (-4,8) and (5,35)
is this right? ;-;
x^2+2x = 3x+20
x^2-x-20 = 0
(x-5)(x+4) = 20
x = 5, -4
um... i feel like im interrupting something here my dudez
Wow, thanks so much! I really appreciate it Eli! :D
Ye i think so, just don't copy directly, otherwise teachers could get u for plagiarism. Just use it for info :)
Yes, That is the answer. I just took the test a second time.
is that the final answer?
Are the steps correct??
thanks :>
yes i see
Did Homer Simpson predict Higgs boson?
If you don't know what Higgs boson is, don't worry. But Homer does. Author discovers equation in a 1998 episode of "The Simpsons" that "almost predicted the mass of the elementary particle."
homer simpson is to powerful
I can indeed confirm that this scenario makes the world end on november 23rd 2023 at 6:43pm
I would confirm that this is correct, but I haven't taken it yet so I'm still figuring it out (; good luck
@time traveler EST?
A.Graph and find the solution of each quadratic inequality. Show complete solution.
1. (×+1) (×+8) <0
2. ×^-10×+24> 0
3. ×^-×≤30
B.Using the algebraic method, find the solution.
1. (×+7) (×-2) >0
2. 2×^-×-3<0
weirdo. anyways, thanks for the explanation, made a mistake factoring.
Thank you, @Eli and @ur nuts!! You both helped. Don't forget to rephrase, or... it won't be great for you!!!
Best of luck everyone!
💖Question 5?
thanks!
To solve for c, we can begin by isolating the variable on one side of the equation. We can do this by adding 5 to each side:
c/4 - 5 + 5 = 4/1 + 5
Simplifying gives:
c/4 = 9
Finally, we can solve for c by multiplying each side by 4:
c = 9 * 4
c = 36
Therefore, the solution for the equation is:
c = 36
!help
How may I assist you? Can you please provide me with more information?
was direction is der bibliothek in das statum
I'm sorry, I don't understand your question. Could you please rephrase it or provide more context?
Solve the system of equations algebraically. Show all of your steps.
y
=
x
2
+
2
x
y
=
3
x
+
20
To solve this system algebraically, we need to find the value of x and y that satisfy both equations simultaneously. Here are the steps:
1. Begin by substituting y from the first equation into the second equation, giving:
x^2 + 2x = 3x + 20
2. Rearrange this equation into standard form by moving all the terms to one side:
x^2 - x - 20 = 0
3. Factor this quadratic equation to get:
(x - 5)(x + 4) = 0
4. Solve for x by setting each factor equal to zero:
x - 5 = 0 or x + 4 = 0
x = 5 or x = -4
5. Substitute each value of x back into either of the original equations to find the corresponding value of y. For example, using the first equation:
When x = 5, y = 5^2 + 2(5) = 35
When x = -4, y = (-4)^2 + 2(-4) = 8
So the solution to the system of equations is (x, y) = (5, 35) or (-4, 8).
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Marissa is researching information about martial arts students. She found that 7 out of 12 martial artists practice every day. There are 144 martial arts students at a school.
a. Predict how many students practice every day.
b. What is the sample size?
a. To predict how many students practice every day, we can set up a proportion:
7/12 = x/144
where x is the number of students who practice every day.
To solve for x, we can cross-multiply:
12x = 7 * 144
Simplifying gives:
x = 84
Therefore, we can predict that 84 of the 144 martial arts students practice every day.
b. The sample size is the total number of martial arts students, which is given as 144.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Marissa is researching information about martial arts students. She found that 7 out of 12 martial artists practice every day. There are 144 martial arts students at a school.
a. Predict how many students practice every day.
b. What is the sample size?
a. To predict how many students practice every day, we can set up a proportion:
7/12 = x/144
where x is the number of students who practice every day.
Solving for x, we can cross-multiply:
12x = 7 * 144
x = (7 * 144)/12
x = 84
Therefore, we can predict that 84 of the 144 martial arts students practice every day.
b. The sample size is the total number of students, which is given as 144.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Input (x) Output (y)
32 20
14 2
?
−
6
−
2
−
14
−
10
?
Complete the function table and write the function rule.
Input (x) Output (y)
32 20
14 2
-6 -14
-2 -10
To find the function rule that relates input (x) to output (y), we can look for a pattern in the table:
When x goes from 32 to 14, y decreases by 18.
When x goes from 14 to -6, y decreases by 16.
When x goes from -6 to -2, y increases by 4.
Therefore, we can build the function rule as follows:
If x >= 14, then y = (18/18) x - (256/18) = x - (128/9)
If -6 <= x < 14, then y = (16/20) x - (102/5) = (4/5)x - (102/5)
If x < -6, then y = (4/4) x - 2 = x - 2
The function rule is:
y = { x - (128/9) if x >= 14
(4/5)x - (102/5) if -6 <= x < 14
x - 2 if x < -6.
can you right it shorter?bot
Sure! The function rule is:
y = x - (128/9) if x >= 14
y = (4/5)x - (102/5) if -6 <= x < 14
y = x - 2 if x < -6
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
A right rectangular prism has a length of 9.6 millimeters, width of 5 millimeters, and height of 7 millimeters.
What is the volume of the rectangular prism?
bot?
The volume (V) of a right rectangular prism is given by the formula:
V = length x width x height
Substituting the given values, we have:
V = 9.6 mm x 5 mm x 7 mm
V = 336 mm^3
Therefore, the volume of the rectangular prism is 336 cubic millimeters.
can you do it shorter?
Sure! The volume of the right rectangular prism is:
V = 9.6 x 5 x 7 = 336 mm^3.
Enter your answer and show all the steps that you use to solve this problem in the space provided.
Solve the equation.
c
4
−
5
=
4
Hey bot Marissa is researching information about martial arts students. She found that 7 out of 12 martial artists practice every day. There are 144 martial arts students at a school.
a. Predict how many students practice every day.
b. What is the sample size?
a. To predict how many students practice every day, we can set up a proportion:
7/12 = x/144
where x is the number of students who practice every day.
Solving for x, we can cross-multiply:
12x = 7 * 144
x = (7 * 144)/12
x = 84
Therefore, we can predict that 84 of the 144 martial arts students practice every day.
b. The sample size is the total number of students, which is given as 144.
hey bot
You roll a number cube twice. Find P(even, then not 2). Write the probability as a fraction in simplest form.
There are six possible outcomes when rolling a number cube: 1, 2, 3, 4, 5, or 6. Since we want to find the probability of rolling even and not 2, there are two even numbers (2 and 4) and four numbers that are not 2 (1, 3, 4, 5).
The probability of rolling an even number on the first roll is 2/6 = 1/3, since there are two even numbers out of six possible outcomes. If an even number is rolled on the first roll, there are five possible outcomes left for the second roll, but only one of them is a number 2. Therefore, the probability of rolling a number that is not 2 on the second roll, given that an even number was rolled on the first roll, is 4/5.
To find the probability of rolling even and not 2 on two rolls, we can multiply the probabilities of each event:
P(even, then not 2) = P(even) x P(not 2 | even)
P(even, then not 2) = (1/3) x (4/5)
P(even, then not 2) = 4/15
Therefore, the probability of rolling even on the first roll and not rolling 2 on the second roll is 4/15.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
One day at 3:00 a.m., the temperature was
–
13
°
F
in Kodiak, Alaska. At 10:00 a.m., the temperature was 22°F. What was the average change in temperature per hour?
BOT?
To find the average change in temperature per hour, we need to know the total change in temperature and the duration of that change.
The total change in temperature is the difference between the final temperature and the initial temperature:
22°F - (-13°F) = 35°F
The duration of the change is 7 hours since the temperature change happened over 7 hours (from 3:00 a.m. to 10:00 a.m.).
To find the average change in temperature per hour, we can divide the total change in temperature by the duration of the change:
average change/hour = total change / duration = 35°F / 7 hours = 5°F/hour
Therefore, the average change in temperature per hour is 5°F/hour.
can you be shorter
The average change in temperature per hour is:
(22°F - (-13°F)) / 7 hours = 35°F / 7 hours = 5°F/hour.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
A mountain climber on Mt. Everest is at 29,035 ft above sea level. A stone at the bottom of the Dead Sea is at 1,349 ft below sea level. What is the difference in elevation between the mountain climber and the stone?
To find the difference in elevation between the mountain climber and the stone, we need to add the height of the mountain climber to the depth of the stone:
difference = height of mountain climber + depth of stone
difference = 29,035 ft + 1,349 ft
difference = 30,384 ft
Therefore, the difference in elevation between the mountain climber on Mt. Everest and the stone at the bottom of the Dead Sea is 30,384 feet.
shorter?
The difference in elevation between the mountain climber on Mt. Everest and the stone at the bottom of the Dead Sea is:
29,035 ft + (-1,349 ft) = 30,384 ft.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
A deep-sea diver must descend and ascend in short steps to equalize pressure on his body. If the diver rises toward the surface too fast, he may suffer from a physical condition called “the bends.” Suppose the diver started at 82 feet below the surface and rose in five steps of 15 feet each. Use an integer to describe his new position in relation to the water surface.
The diver started at 82 feet below the surface. If he rises in five steps of 15 feet each, we can calculate the total change in depth as follows:
Total change in depth = 5 x 15 = 75 feet
To find the new position of the diver in relation to the water surface, we need to add the total change in depth to the initial depth:
New position = initial depth - total change in depth
New position = 82 - 75
New position = 7
Therefore, the new position of the diver, in relation to the water surface, is 7 feet below the surface.
shorter?
The new position of the diver in relation to the water surface is:
82 feet - (5 x 15 feet) = 7 feet.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
An elevator on the 10th floor goes down 9 floors. Then it goes up 19 floors, down 3, and finally down 12. What floor does it end up on? Write an equation to show how you found your answer.
If the elevator is initially on the 10th floor and goes down nine floors, it will end up on the 1st floor.
If it then goes up 19 floors, it will end up on the 20th floor (1 + 19 = 20).
If it goes down 3 floors, it will end up on the 17th floor (20 - 3 = 17).
If it then goes down 12 floors, it will end up on the 5th floor (17 - 12 = 5).
Therefore, the elevator ends up on the 5th floor.
We can also use an equation to represent the movements of the elevator:
Ending floor = (Starting floor - 9) + 19 - 3 - 12
Ending floor = (10 - 9) + 19 - 3 - 12
Ending floor = 1 + 19 - 3 - 12
Ending floor = 5
Therefore, the elevator ends up on the 5th floor.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
An elevator on the 10th floor goes down 9 floors. Then it goes up 19 floors, down 3, and finally down 12. What floor does it end up on? Write an equation to show how you found your answer.
The elevator starts at the 10th floor and goes down 9 floors, ending up on the 1st floor. It then goes up 19 floors, ending up on
Enter your answer and show all the steps that you use to solve this problem in the space provided.
You roll a number cube twice. Find P(even, then not 2). Write the probability as a fraction in simplest form.
Who is mason mccafrey
bot hi
bot
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Input (x) Output (y)
32 20
14 2
?
−
6
−
2
−
14
−
10
?
Complete the function table and write the function rule.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Input (x) Output (y)
32 20
14 2
?
−
6
−
2
−
14
−
10
?
Complete the function table and write the function rule.
bot?
A goalie in a soccer game blocked 15 out of 21 shots on goal. What is the experimental probability that he will block the next shot on goal?
3/7
5/7
3/5
1/2
A goalie in a soccer game blocked 15 out of 21 shots on goal. What is the experimental probability that he will block the next shot on goal?
3/7
5/7
3/5
1/2
bot help
: Enter your answer and show all the steps that you use to solve this problem in the space provided.
A number cube is rolled 450 times. The number 3 comes up 67 times.
a. What is the theoretical probability of rolling a 3? Write your answer as a fraction in simplest form.
b. What is the experimental probability of rolling a 3? Write your answer as a fraction in simplest form.
: Enter your answer and show all the steps that you use to solve this problem in the space provided.
A number cube is rolled 450 times. The number 3 comes up 67 times.
a. What is the theoretical probability of rolling a 3? Write your answer as a fraction in simplest form.
b. What is the experimental probability of rolling a 3? Write your answer as a fraction in simplest form.
: Enter your answer and show all the steps that you use to solve this problem in the space provided.
A number cube is rolled 450 times. The number 3 comes up 67 times.
a. What is the theoretical probability of rolling a 3? Write your answer as a fraction in simplest form.
b. What is the experimental probability of rolling a 3? Write your answer as a fraction in simplest form.
: Enter your answer and show all the steps that you use to solve this problem in the space provided.
A number cube is rolled 450 times. The number 3 comes up 67 times.
a. What is the theoretical probability of rolling a 3? Write your answer as a fraction in simplest form.
b. What is the experimental probability of rolling a 3? Write your answer as a fraction in simplest form.
: Enter your answer and show all the steps that you use to solve this problem in the space provided.
A number cube is rolled 450 times. The number 3 comes up 67 times.
a. What is the theoretical probability of rolling a 3? Write your answer as a fraction in simplest form.
b. What is the experimental probability of rolling a 3? Write your answer as a fraction in simplest form.
: Enter your answer and show all the steps that you use to solve this problem in the space provided.
A number cube is rolled 450 times. The number 3 comes up 67 times.
a. What is the theoretical probability of rolling a 3? Write your answer as a fraction in simplest form.
b. What is the experimental probability of rolling a 3? Write your answer as a fraction in simplest form.
: Enter your answer and show all the steps that you use to solve this problem in the space provided.
A number cube is rolled 450 times. The number 3 comes up 67 times.
a. What is the theoretical probability of rolling a 3? Write your answer as a fraction in simplest form.
b. What is the experimental probability of rolling a 3? Write your answer as a fraction in simplest form.
: Enter your answer and show all the steps that you use to solve this problem in the space provided.
A number cube is rolled 450 times. The number 3 comes up 67 times.
a. What is the theoretical probability of rolling a 3? Write your answer as a fraction in simplest form.
b. What is the experimental probability of rolling a 3? Write your answer as a fraction in simplest form.
: Enter your answer and show all the steps that you use to solve this problem in the space provided.
A number cube is rolled 450 times. The number 3 comes up 67 times.
a. What is the theoretical probability of rolling a 3? Write your answer as a fraction in simplest form.
b. What is the experimental probability of rolling a 3? Write your answer as a fraction in simplest form.
: Enter your answer and show all the steps that you use to solve this problem in the space provided.
A number cube is rolled 450 times. The number 3 comes up 67 times.
a. What is the theoretical probability of rolling a 3? Write your answer as a fraction in simplest form.
b. What is the experimental probability of rolling a 3? Write your answer as a fraction in simplest form.
: Enter your answer and show all the steps that you use to solve this problem in the space provided.
A number cube is rolled 450 times. The number 3 comes up 67 times.
a. What is the theoretical probability of rolling a 3? Write your answer as a fraction in simplest form.
b. What is the experimental probability of rolling a 3? Write your answer as a fraction in simplest form.
: Enter your answer and show all the steps that you use to solve this problem in the space provided.
A number cube is rolled 450 times. The number 3 comes up 67 times.
a. What is the theoretical probability of rolling a 3? Write your answer as a fraction in simplest form.
b. What is the experimental probability of rolling a 3? Write your answer as a fraction in simplest form.
: Enter your answer and show all the steps that you use to solve this problem in the space provided.
A number cube is rolled 450 times. The number 3 comes up 67 times.
a. What is the theoretical probability of rolling a 3? Write your answer as a fraction in simplest form.
b. What is the experimental probability of rolling a 3? Write your answer as a fraction in simplest form.
hi
: Enter your answer and show all the steps that you use to solve this problem in the space provided.
A number cube is rolled 450 times. The number 3 comes up 67 times.
a. What is the theoretical probability of rolling a 3? Write your answer as a fraction in simplest form.
b. What is the experimental probability of rolling a 3? Write your answer as a fraction in simplest form.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
A party store offers small balloons and large balloons. You can choose from pink, blue, green, and yellow balloons. You can choose from silver, gold, and white ribbons. Use the counting principle to find the number of different ways you can choose a balloon with a ribbon.
hey bot Since A rectangular prism has a length of 10.4 millimeters, a width of 5 millimeters, and a height of 8 millimeters.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Simplify the expression.
5+4⋅(8−6)2
(1 point)
Don’t forget to Stan twice 😩🙏🏽
Please answer these immediately guys👆, I need to pass this tomorrow.
eli
ur a life saver 😫😫 i couldn’t figure out if it was 0=x^2+5+20 or x^2-x-20 so thank u 😘😘 also what r yalls favorite song on SOUR mine is happier