Answer:
system 2 and system 3 have the same solution.
Step-by-step explanation:
system 1:
[tex]4x-5y=2[/tex]
[tex]3x-y=4[/tex]
we'll solve the two equation by the method of elimintaion to get the value of x and y.
on solving we get [tex]x=\frac{18}{11} ,y=\frac{10}{11}[/tex].
system 2:
[tex]4x-5y=2\\10x-21y=10[/tex]
on solving the above two equation by the method of elimination we get the value of x and y.
on solving we get [tex]x=\frac{-4}{17},y=\frac{-10}{17}[/tex].
system 3:
[tex]4x-5y=2\\24x-47y=22[/tex]
on solving the above two equation by the method of elimination we get the value of x and y.
on solving we get [tex]x=\frac{-4}{17} ,y=\frac{-10}{17}[/tex].
system 4:
[tex]4x-5y=2\\10x+3y=15[/tex]
on solving the above two equation by the method of elimination we get the value of x and y.
on solving we get [tex]x=\frac{81}{62} ,y=\frac{20}{31}[/tex].
on looking for the solution of all the four system we see that system 2 and system 3 have the same value for x and y.
Hence, system 2 and system 3 have the same solution.
A ship is 2.8 degree off course .If the ship is traveling at 14.0 miles per hour,how far off course will it be after 2 hours?
In a recent year 36% of all college students were enrolled part time. If 6.2 million college students were enrolled part time that year what was the total number of college students. Round to the nearest million
To find the total number of college students, we solve a proportion equation using the given 36% for part-time students and 6.2 million part-time students to find a total of approximately 17 million students.
Explanation:This problem can be addressed with a simple proportion equation. We know that 36% (or 0.36 in decimal form) of all enrolled college students equals 6.2 million. So, if we let X be the total number of college students, the equation becomes 0.36X = 6.2 million.
To solve for X, we divide both sides of the equation by 0.36 and hence, X=6.2 million / 0.36. After doing the calculation, we get approximately 17.22 million. Since the question asks us to round to the nearest million, our final answer is approximately 17 million total college students.
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What is the slope of the line that passes through (3, -4) and (-2, 5). A)-5/9 B)-9/5 C)9/5 D)5/9
The side of a square is 12 feet. What is the area of the square?
a.12 sq. ft.
b.24 sq. ft.
c.48 sq. ft.
d.144 sq. ft.
Trig question how do I find m
How to solve this???
⭐️ Anyone know how to work this?...
What is 4.738rounded to the nearest thousandth? (Points : 1) 4.73 4.74 4.738 4.739
4.738 rounded to the nearest thousandth remains 4.738, as it is already at the required decimal precision.
To round to the nearest thousandth, you look at the digit in the thousandth place, which in this case is an 8. You do not need to alter the number since it is already at the thousandth decimal place. Therefore, 4.738 rounded to the nearest thousandth is simply 4.738.
Instead of focusing on the absence of mental illness as an indication of mental health, Abraham Maslow and CarlRogers would focus more on____________ (1 point),
When the sum of 7 and three times a positive number is subtracted from the square of the number, 0 results. find the number?
The required number is 10.
Given that,
When the sum of 7 and three times a positive number is subtracted from the square of the number, 0 results. That number is to be determined.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
Let the number be x,
The sum of 7 and three times a positive number is subtracted from the square of the number 0.
x²-x(3 + 7) = 0
x² = x(10)
x = 10
Thus, the required number is 10.
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M is the midpoint of PQ, N is the midpoint of MQ, and L is the midpoint of MN. If MN =14, find ML.
3. Which of the following is a solution to the equation 16= 4x-4?
a.-5
b.-4
c.5
d.16
please help. I'll give a medal + fan I wanna know how
The mass of Venus is
4.87 x 10^24 kilograms, and the mass of Jupiter is
1,898 x 10^24 kilograms.
The mass of Jupiter is about _____ times the mass of Venus.
Answer:
The mass of Jupiter is about 389.7331 times the mass of Venus.
Step-by-step explanation:
The question is asking for how much the two masses vary from one another. Since the mass of Jupiter is greater than that of Venus, what value is to be multiplied by the mass of Venus that would give the mass of Jupiter?
Thus, to determine this, we divide the mass of Jupiter by the mass of Venus;
= [tex]\frac{1898*10^{24} }{4.87*10^{24} }[/tex]
= [tex]\frac{1898}{4.87}[/tex]
= 389.7331
Therefore, the mass of Jupiter is about 389.7331 times the mass of Venus.
can someone help me? im not sure if my answers are right
In a pond, lotus flower multiply its self after every 4 days. One lotus multiplies into two after four days, into 4 after 8 days, into 8 after 16 days and so on. If you see one lotus flower in a pond today, how many flowers will be there in the pond after 32 days.
PLEASE HELP ME ON THIS
A cone with a radius of 12 cm and a height of 12 cm has the same volume as a cylinder with a radius of 8 cm. What is the height of the cylinder?
A) 3 cm
B) 6 cm
C) 9 cm
D) 12 cm
Answer:
The correct option is C. The height of the cylinder is 9 cm.
Step-by-step explanation:
The radius of cone is 12 cm and the height of cone is 12 cm.
The volume of cone is
[tex]V=\frac{1}{3}\pi r^2h[/tex]
[tex]V_1=\frac{1}{3}\pi (12)^2(12)[/tex]
[tex]V_1=576\pi[/tex]
The radius of cylinder is 8 cm. The volume of cylinder is
[tex]V=\pi r^2h[/tex]
[tex]V_2=\pi (8)^2h[/tex]
[tex]V_2=64\pi h[/tex]
It is given that the volume of cone and cylinder is same.
[tex]V_1=V_2[/tex]
[tex]576\pi=64\pi h[/tex]
[tex]\frac{576\pi}{64\pi}=h[/tex]
[tex]9=h[/tex]
Therefore the height of the cylinder is 9 cm and option C is correct.
To find the height of the cylinder that has the same volume as a cone, we can compare their volumes. By setting the volumes equal to each other and simplifying the equation, we find that the height of the cylinder is 9 cm.
Explanation:To find the height of the cylinder, we need to compare the volumes of the cone and the cylinder. The formula for the volume of a cone is V = (1/3)πr^2h, where r is the radius and h is the height. The volume of the cone with radius 12 cm and height 12 cm is (1/3)π(12^2)(12) = 576π cm³. Now, let's calculate the volume of the cylinder using the formula V = πr^2h, with radius 8 cm. We know that the volumes of the cone and the cylinder are equal, so 576π = π(8^2)h. Simplifying this equation, we get 576π = 64πh. Dividing both sides of the equation by 64π, we find h = 9 cm. Therefore, the height of the cylinder is 9 cm.
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Find the Value of X.
3
8
4
6
Divide by splitting up the numerator. 21x^3y^4-7x^2y^3+14x^2y^2-xy over 7x^2y^2
Take a look at the figure. What are the coordinates of the point labeled B in the graph shown?
A. (3, 2)
B. (–3, 2)
C. (–2, 3)
D. (–2, –3)
The area of a right triangle is 336 square centimeters. The base of the right triangle is 48 centimeters. What is the length of the hypotenuse of the right triangle? Enter your answer in the box.
Answer:
50
Step-by-step explanation:
First we have to find the height. Since we know the area we can use it to find the height. The area of a triangle is A=bh1/2 or half of the base times the height. So if we plug in what we know and solve, we can find the height. 336=48 x h x 1/2. The height is 14. Now we can solve for the hypotenuse using the Pythagorean Theorem. a^2 + b^2 = c^2 plug in what we know... 14^2 + 48^2 = c^2 simplify to get 196+2304= c^2 and further 2500= c^2 so find the square root of 2500. You will get 50.
6 grade course 1 countdown 8 and 7 weeks
use the formula a=h/n to find the batting average a of a batter who has h hits in n times at bat.Solve the formula for h. if a batter has a batting average of .290 and has at bat 300 times, how many hits does the batter have?,
Perform the indicated operation. (2x + y)(3x^2 + y)
Answer:
[tex](2x+y)(3x^2+y)=6x^3+3x^2y+2xy+y^2)[/tex]
Step-by-step explanation:
The given expression is [tex](2x+y)(3x^2+y)[/tex].
We expand the parenthesis using the distributive property to obtain;
[tex](2x+y)(3x^2+y)=2x(3x^2+y)+y(3x^2+y)[/tex]
We expand further to get;
[tex](2x+y)(3x^2+y)=6x^3+2xy+3x^2y+y^2)[/tex]
This gives us;
[tex](2x+y)(3x^2+y)=6x^3+3x^2y+2xy+y^2)[/tex]
What’s the correct answer
64,55,46,37,28,19 find the math patter what goes next
Kim had 160 cards in a box.She gave 4/10 of the cards to maddy.How many cards did Kim have left in the box
Tanya wants to find the height of the tree. She walks away from the base of the tree so the tip of her shadow coincides with the tip of the tree's shadow at point C. BE is two and a half times EC. Tanya is 5 feet, 3 inches tall. How tall is the tree in feet?
How many lines intersect at point O?
4
2
1
3
What happens to the maximum point of f(x) = -2x2 + 3x + 1, when the function is changed to f(x) = -2x2 + 9x + 1?
A) it shifts up and left
B) it shifts up and right
C) it shifts down and left
D) it shifts down and right
Answer: B
Step-by-step explanation: I did the usa test prep