Answers
Answer:
The equations 3·x - 6·y = 9 and x - 2·y = 3 are the same
The possible solution are the points (infinite) on the line of the graph representing the equation 3·x - 6·y = 9 or x - 2·y = 3 which is the same line
Step-by-step explanation:
The given linear equations are;
3·x - 6·y = 9...(1)
x - 2·y = 3...(2)
The solution of a system of two linear equations with two unknowns can be found graphically by plotting the two equations and finding the coordinates of the point of intersection of the line graphs
Making 'y' the subject of both equations gives;
For equation (1);
3·x - 6·y = 9
3·x - 9 = 6·y
y = x/2 - 3/2
For equation (2);
x - 2·y = 3
x - 3 = 2·y
y = x/2 - 3/2
We observe that the two equations are the same and will have an infinite number of solutions
Related Questions
PLEASE HELP!!!!
Quadrilateral ABCD is similar to quadrilateral EFGH. What is the value for x, the length
of side CD?
A-10
B-16
C-14
D-18
Answers
-》D
Answer:
D 18
Step-by-step explanation:
Write the exact value of the side length of a square whose are in square units are given. For example, use sqrt(9) to represent the square root of 9. Areas: 36 37 100/9 2/5 0.0001 0.11
Answers
Answer:
a.) Side length of the square is 6 units.
b.) Side length of the square is sqrt(37) units.
c.) Side length of the square is 10/3 units.
d.) Side length of the square is sqrt(2/5) units.
e.) Side length of the square is 0.01 units.
f.) Side length of the square is sqrt(11)/10 units.
Step-by-step explanation:
To find - Write the exact value of the side length of a square whose are in square units are given
a) 36
b) 37
c) 100/9
d) 2/5
e) 0.0001
f) 0.11
Proof -
We know that ,
If a is the side length of the square then,
Area of square = a²
Now,
a) 36
⇒a² = 36
⇒a² = (6)²
⇒a = 6
∴ we get
Side length of the square is 6 units.
b.) 37
⇒a² = 37
⇒a² = [sqrt(37)]²
⇒a = sqrt(37)
∴ we get
Side length of the square is sqrt(37) units.
c.)100/9
⇒a² = 100/9
⇒a² = [10/3]²
⇒a = 10/3
∴ we get
Side length of the square is 10/3 units.
d.)2/5
⇒a² = 2/5
⇒a² = [sqrt(2/5)]²
⇒a = sqrt(2/5)
∴ we get
Side length of the square is sqrt(2/5) units.
e.)0.0001
⇒a² = 0.0001
⇒a² = [0.01]²
⇒a = 0.01
∴ we get
Side length of the square is 0.01 units.
f.)0.11
⇒a² = 0.11
⇒a² = [sqrt(11)/10]²
⇒a = sqrt(11)/10
∴ we get
Side length of the square is sqrt(11)/10 units.
We get the value of the,
a.) Side length of the square is 6 units.
b.) Side length of the square is sqrt(37) units.
c.) Side length of the square is 10/3 units.
d.) Side length of the square is sqrt(2/5) units.
e.) Side length of the square is 0.01 units.
f.) Side length of the square is sqrt(11)/10 units.
We have to find the exact value of the side length of a square whose are in square units are given
a) 36
b) 37
c) 100/9
d) 2/5
e) 0.0001
f) 0.11
We have given that,sqrt(9) to represent the square root of 9.
We know that ,
If a is the side length of the square then,
what area of the square?Area of square = a²
For option a) 36
⇒a² = 36
⇒a² = (6)²
⇒a = 6
∴ we get side length of the square is 6 units.
For the option b is 37.
⇒a² = 37
⇒[tex]a^2 = \sqrt{37} ^2[/tex]
⇒[tex]a = sqrt(37)[/tex]
∴ we get side length of the square is [tex]\sqrt(37)[/tex] units.
c.)100/9
⇒[tex]a^2 = 100/9[/tex]
⇒[tex]a^2= [10/3]^2[/tex]
⇒[tex]a = 10/3[/tex]
∴ we get side length of the square is 10/3 units.
for the option d.)2/5
[tex]a^2= 2/5[/tex]
[tex]a^2 = [\sqrt(2/5)]^2[/tex]
⇒[tex]a = \sqrt(2/5)[/tex]
∴ we get side length of the square is [tex]\sqrt(2/5)[/tex]units.
for the option e.)0.0001
[tex]a^2 = 0.0001[/tex]
[tex]a^2 = [0.01]^2[/tex]
[tex]a = 0.01[/tex]
∴ we get side length of the square is 0.01 units.
For option f.)0.11
⇒[tex]a^2 = 0.11[/tex]
⇒[tex]a^2= [\sqrt(11)/10]^2[/tex]
[tex]a = \sqrt(11)/10[/tex]
∴ we get side length of the square is[tex]\sqrt(11)/10[/tex] units.
Therefore we get,we get the value of the,
a.) Side length of the square is 6 units.
b.) Side length of the square is sqrt(37) units.
c.) Side length of the square is 10/3 units.
d.) Side length of the square is sqrt(2/5) units.
e.) Side length of the square is 0.01 units.
f.) Side length of the square is sqrt(11)/10 units.
To learn more about the area visit:
https://brainly.com/question/25292087
Find the distance between the points (1,3) and (3,4)
Answers
Answer:
[tex]\sqrt{} 5[/tex]
Step-by-step explanation:
Answer:
Square root of five
Step-by-step explanation:
Find m angle ADB !!!!!
Answers
Answer:
[tex]<ADB=9[/tex]×[tex]5+4[/tex][tex]=49[/tex]
Step-by-step explanation:
[tex]<(13x-16)=<(9n+4)\\\\13x-9x=4+16\\\\4x=20\\\\x=\frac{20}{4} \\\\x=5\\\\<ADB=9*5+4=49[/tex]
hope it helps....
Find the volume of a pyramid with a square base, where the side length of the base is 4.7\text{ in}4.7 in and the height of the pyramid is 4.5\text{ in}4.5 in. Round your answer to the nearest tenth of a cubic inch.
Answers
Answer:
33.1in³
Step-by-step explanation:
Volume of the square based pyramid = BH/3
B is the base area
H is the height
Base area = L²
Base area = 4.7²
Base area = 22.09 square inches
Height = 4.5in
Get the volume
Volume of the pyramid = 22.09*4.5/3
Volume of the pyramid = 22.09 * 1.5
Volume of the pyramid = 33.135in³
Hence the volume of the square based pyramid to the nearest tenth of a cubic inch is 33.1in³
A bank teller had 125 Bills in $10 and $20 bills to start the day. If the total in her register was $1650, how many of each bill did the teller start off with ?
Answers
Answer:
40 twenties and 85 tens
Step-by-step explanation:
10x+20y=1650
10x+10y=1250
10y=400
y=40
Use substitution to determine if O is a solution of 5x = 5.
HELP!
Answers
Answer:
x=1
Step-by-step explanation:
5x1=5
It takes Diego 1/24of an hour to complete a lap on a circular bike track. The track is 1/3 of a mile long. What is Diego's bike speed in miles per hour?
Answers
Answer:
Step-by-step explanatio
1mile = 5280 feet
607,200 / 5280 = 115
607,200 feet per hour = 115 miles per hourn
The equation of the line A is 3x+2y=10.line B is parallel to line A and passes through the points (4,6).find the equation of the line B.
Answers
Answer: [tex]y=-\frac{3}{2}x+12[/tex]
Step-by-step explanation:
To find the equation of line B, we need to find the slope first, then the y-intercept. We first want to convert line A into slope-intercept form, so we can find the slope.
[tex]3x+2y=10[/tex] [subtract both sides by 3x]
[tex]2y=10-3x[/tex] [divide both sides by 2]
[tex]y=5-\frac{3}{2}x[/tex]
With the slope-intercept form of line A, we can see that the slope is [tex]-\frac{3}{2}[/tex]. We take the slope and the given point (4,6) to find the y-intercept of line B.
[tex]y=-\frac{3}{2}x+b[/tex] [plug in (4,6)]
[tex]6=-\frac{3}{2}(4)+b[/tex] [multiply]
[tex]6=-6+b[/tex] [add both sides by 6]
[tex]b=12[/tex]
With the y-intercept, we know the equation for line B is [tex]y=-\frac{3}{2}x+12[/tex].
Manuel borrowed $1,500 from his bank and signed a
contract to make monthly payments for two years at 4%
interest compounded annually. How much total interest
will Manuel pay on this loan?
Answers
Answer:
The total interest to pay back on the loan is $122.40
Step-by-step explanation:
Here. we want to get the amount of interest on the loan
We are going to use the compound interest formula here
A = P(1 + r/n)^nt
where A is the amount to be paid back
P is the amount borrowed called the principal which is $1,500
r is the interest rate which is 4% annually
This is same as 4/100 = 0.04
n is the number of times the interest will be compounded per year ; annually means yearly and so for this case, n = 1
t is the number of years = 2
So we have;
A = 1500(1 + 0.04/1)^(2)(1)
A = 1500(1.04)^(2)
A =$ 1,622.40
So the amount of interest is the difference between the amount borrowed and the value to pay back
That will be;
$1,622.40 - $1,500
= $122.40
PLEASE HELP ME !!
If you put $375 into a savings account that pays 6% interest compounded monthly, how much money would you have in your account after 3 years?
How much did you earn in interest?
Answers
Answer:
$448.76
$73.76
Step-by-step explanation:
We are to calculate the future value with monthly compounding
The formula for calculating future value:
FV = P (1 + r/m)^mn
FV = Future value
P = Present value
R = interest rate
m = number of compounding
N = number of years
$375 x ( 1 + 0.06/12)^12 x 3
$375 x (1.005)^36 = $448.76
Interest earned = future value - amount saved
$448.76 - $375 = $73.76
What is the intersection (x, y) of the two lines generated by the 2 equations:
y= x+3
y=-x +7
Answers
Answer:
x=2
y=5
Step-by-step explanation:
y= x+3...(1)
y= -x+7...(2)
(1) + (2):
y+y= (x+3) + (-x+7)
2y= (x-x) + (3+7)
2y= 10
y= 5
By substituting y=5 into (1),
we have
5= x+3
x+3=5
x= 5-3
x= 2
(5 x 10^2)^−2
i dont get it
Answers
Answer:-250,000
Step-by-step explanation:
The two triangles are similar. Find the unknown variables.
Answers
Answer:
Y= 57°
Q at both of them 33° each.
57 +90=147
180-147=33
What y’all think helps guysss!!!:((((
Answers
Answer:
pretty sure it's a yes
Step-by-step explanation:
Did it on khan a few months ago
sorry if I made it wrong, my memory isn't too well right now
Answer:
Yes.
Step-by-step explanation: Figure B is just a larger scale of figure A.
Write an equation of the line below.
Answers
Answer:
y = 4x-2
Step-by-step explanation:
y = mx+b
y = 4x+b
y = 4x-2
Simplify the following expression:
x(x+2) - x(x+3)
Answers
Answer:
-x
Step-by-step explanation:
How far is the Earth away from the Sun? Question 4 options: 1 AU (astronomical unit) 1 light year 10 AU 10 light years
Answers
Answer: The answer to your question is 1.
Answer:
1 AU
Step-by-step explanation:
I searched on the web.
It takes 8 light-years, so options 2 & 4 are out.
The internet says 1 AU so that is the answer.
Good Luck!
Please help with this :)
Answers
Answer:
15 -2
Step-by-step explanation:
Which equation is equivalent to 2 1/4+2/4=2 3/4?
Answers
Answer:
11/4
Step-by-step explanation:
Sandra has a 1/3 chance of making the team. What is the probability that Sandra will not make the team?
please help!
Answers
Answer:
2/3 is the probability that Sandra will not make the team.
Hope it helps!!!
Answer:
2/3
Step-by-step explanation:
If something will happen with 100% certainty, then the probability is 1 or 100%.
If she has a 1/3 chance of making the team, the the chance of not making the team is 1 - 1/3 which equals 2/3.
Answer: 2/3
PLEASE HELP!!! I REALLY NEED IT!!!
So, this is kind of random, but can someone give, like, a step-by-step explanation of how to do this equation?
(22+(-6/20)) * (214-10(-6/20)) - (284.75)=4424.15
Thank you so much, I just... I cannot will myself to figure out this problem today. Love youuu!
Answers
Step-by-step explanation:
(22 + (-6/20) × (214 - 10 ( -6/20)) - (284.75)
(22 - 6/20) × (214 + 60/20) - (284.75)
(22 - 0.3) × (214 + 3) - (284.75)
(21.7 × 217) - 284.75
4708.9 - 284.75
= 4424.15
Edwin buys a painting of the beach online for $23. If shipping and handling are an additional 30% of the price, how much shipping and handling will Edwin pay?
Answers
Answer:
$6.90
Step-by-step explanation:
23/100 X 30 = $6.90
certain plant grows 1 3 4 inches every week. How long will it take the plant to grow 6 1 4 inches? How long will it take the plant to grow 6 1 4 inches?
Answers
Answer:
it will take around 4.5 weeks
Step-by-step explanation:
614 divided by 134 will give you 4.582
Answer:
4.6 weeks
Step-by-step explanation:
In the question, it stated that the plant grows at the rate of 134 inches per week. And we can get the proportion:
[tex]\frac{1 week}{134 inches}[/tex]
Now, if you want to get the number of weeks it takes to grow 614 inches, set up the proportion
[tex]\frac{x }{614 inches}[/tex]
with x representing the number of weeks we are trying to find.
Since the two fractions are proprtional - we assume that the plant will always grow at the same rate, then we can state:
[tex]\frac{x }{614 inches}[/tex] = [tex]\frac{1 week}{134 inches}[/tex]
Now, cross multiply and simplify:
134x = 614
x = 614/134
x = 4.6 (Weeks)
Write the equation of the line that passes through the points (-1, -2) and (5, -4).
Answers
Answer:
y = -1/3x - 7/3
Step-by-step explanation:
To find the slope, you have to plug the values into the slope formula.
y2 - y1/ x2 - x1
-4 - (-2) / 5 - (-1)
-1/3
Now to find the y-intercept, plug in one of the coordinates into the equation.
y = -1/3x + b
-2 = -1/3(-1) +b
-2 = 1/3 + b
-7/3 = b
The equation is y = -1/3x - 7/3.
The Solution is Y = - ( 1 / 3 )X - 7 / 3 where points are ( 5 , - 4) and ( - 1 , - 2) that passes through a straight line. Y = MX + C is the Formula for Straight line equation.
As per given problem, M is Slope
M = (Y2 - Y1) / (X2 - X1)
M = (- 4 - (- 2)) / ( 5 - (- 1))
M = - (1 / 3)
Now, Line becomes
- 2 = - ( 1 / 3) x (- 1)+ C
- 2 = 1 / 3 + C
C = - (7 / 3)
So, Solution: Y = - (1 / 3)X - (7 / 3)
To know more about Straight Line Problems, refer to the below link
brainly.com/question/1617520
pythagorean theorem
Answers
Pythagorean Theorem
Step-by-step explanation:
a squared time b squared plus c squared I think
Answer:
3ft
Step-by-step explanation:
c^2 = a^2 + b^2 so, we have c = 5ft, and lets call this one a = 4ft
so: x^2 = 5^2 - 4^2 => x = sqrt(25 - 16) => x = 3ft
Sarah needs a PVC pipe with a diameter of 10 inches and a heigh of 2 inches, how much
material is needed to make 5 pipes?
Answers
Answer:
314.2in^2
Step-by-step explanation:
GIven data
diameter= 10in
radius= 5in
Height= 2in
The expression for the curved surface area (CSA) of a cylinder is given as
CSA=2πrh
CSA=2*3.142*5*2
CSA=62.84 in^2
The material needed to make one pipe is 62.84in^2
Hence the material need for 5 pipes is
=62.84*5
=314.2in^2
Write the absolute value equations in the form |x−b|=c (where b is a number and c can be either number or (an expression) that have the following solution sets:
Two Solutions: x=2, x=14
Answers
Answer:
|x − 8| = 6Step-by-step explanation:
|x − b| = c1. x - b = c ⇒ x = b + c2. x - b = -c ⇒ x = b - cWe have solution:
b + c = 14b - c = 2Add up these two equations:
2b = 16b = 8Find c:
c = 8 - 2 = 6The original equation is:
|x − 8| = 6which are the complementary angles?
Answers
Answer:
Two angles are called complementary when their measures add to 90 degrees. Two angles are called supplementary when their measures add up to 180 degrees.
Step-by-step explanation:
please amrk this answer as brainliest
QUESTION IN JPG CAN YOU ANSWER A B AND C
Answers
Answer: 8:10, 7:54, 26 minutes
Step-by-step explanation:
a) Go to the row labeled Church Street, start in the column with time 7:59, read down until you get to the row labeled Bus Station.
b) Go to the High Street row. The latest arrival time that is still before 8:30 is 8:10. Starting in the column with 8:10, read UP to the Hope Street row. The bus leaves there at 7:54
c) Pick any column in the row for School Road. In that column, read down to the Bus Station row. The difference between the two times is 26 minutes no matter which column is selected.