all of the ways this system of equations can be solved.
6x - 3y = 9
4x - 5y = -18
Answers
Answer:
ok
Step-by-step explanation:
There are different methods to solve a system of equations, but two common ones are substitution and elimination:
Substitution method:
Solve one of the equations for one of the variables in terms of the other.
For example, from the first equation: 6x - 3y = 9 --> 2x - y = 3 --> y = 2x - 3.
Substitute the expression found for the variable into the other equation.
For example, in the second equation: 4x - 5y = -18 --> 4x - 5(2x - 3) = -18.
Solve for the remaining variable.
Simplifying the equation: 4x - 10x + 15 = -18 --> -6x = -33 --> x = 33/6 = 5.5.
Substitute the value found for the variable into one of the original equations to find the other variable.
For example, using the first equation: 6x - 3y = 9 --> 6(5.5) - 3y = 9 --> 33 - 3y = 9 --> y = (33-9)/3 = 8.
Therefore, the solution for the system of equations is x = 5.5 and y = 8, or (5.5, 8).
Elimination method:
Multiply one or both equations by constants that will make the coefficients of one of the variables equal in magnitude but opposite in sign.
For example, multiplying the first equation by 5 and the second equation by 2:
30x - 15y = 45
8x - 10y = -36.
Add or subtract the resulting equations to eliminate one of the variables.
Subtracting the second equation from the first: 30x - 8x - 15y + 10y = 45 - (-36) --> 22x - 5y = 81.
Solve for the remaining variable.
Solving for y: 22x - 5y = 81 --> 5y = 22x - 81 --> y = (22/5)x - 81/5.
Substitute the value found for the variable into one of the original equations to find the other variable.
Using the first equation: 6x - 3y = 9 --> 6x - 3[(22/5)x - 81/5] = 9 --> 6x - (66/5)x + 27 = 9 --> (24/5)x = -18 --> x = -15/2.
Substitute the values found for the variables into one of the original equations to check the solution.
Using the second equation: 4x - 5y = -18 --> 4(-15/2) - 5[(22/5)(-15/2) - 81/5] = -18, which simplifies to -18 = -18, confirming the solution.
Therefore, the solution for the system of equations is x = -15/2 and y = 33/5, or (-7.5, 6.6).
Answer:
x = 5.5 y = 8
Step-by-step explanation:
Related Questions
Numbers and Operations KA 8th grade- correct answers only ty, and have a great day folks (7 pts)
Answers
Answer:c
Step-by-step explanation:
Answer:
it's c
Step-by-step explanation:
khan academy
PLS ASAP OS FOR PRACTICE FSA PLS The diagram represents the shape and dimensions of kayla’s garden. What is the total area of the garden
Answers
Answer:
441 \(ft^{2}\)
Step-by-step explanation:
Area of a square and rectangle = bh
Square
Base = 15
Height = 15
15 x 15 = 225
Rectangle
Base = 24
Height = 9
24 x 9 = 216
Add them together
216 + 225 = 441
PLEASE HELP THE WORKSHEET IS: graphing speed.
I WILL GIVE 100 POINTS!!! ITS SCEINCE MIDDLE SCHOOL!!!
Analysis and Conclusion
1. Which task and distance resulted in the fastest speed?
2. Create a graph to show your fastest speed, using the times for 0, 5, and 10 meters.
3. Which task and distance resulted in the slowest speed?
4. Create a graph to show your slowest speed, using the times for 0, 5, and 10 meters.
Answers
Task 1: Walking 10 meters
Times:
0 meters: 0 seconds
5 meters: 7 seconds
10 meters: 15 seconds
Graph for fastest speed (walking 10 meters): As time increases from 0 to 15 seconds, distance increases linearly from 0 to 10 meters.
Distance (meters)
^
|
10 \\
| |\
5 / |
| / |
0 /
0 5 15
Time (seconds)
Task 2: Crawling 5 meters
Times:
0 meters: 0 seconds
5 meters: 25 seconds
10 meters: 50 seconds
Graph for slowest speed (crawling 5 meters):
Distance (meters)
^
|
10
/|
/ |
5/|
/ |
0
0 25 50
Time (seconds)
Q4H: The question is in the picture below (please show work) :
Answers
-3x-5(+5)=16+5
-3x=21
-3x/-3=21/-3
x=-7
-4(y-2)=12
-4y+8=12
-4y=4
y=-1
8.88=4.44(x-7)
8.88=4.44x-31.08
39.96=4.44x
9=x
5(y+2/5)=-13
5y+2=-13
5y=-15
y=-3
Under his cell phone plan, Alexander pays a flat cost of $69.50 per month and $5 per gigabyte. He wants to keep his bill under $85 per month. Write and solve an inequality which can be used to determine gg, the number of gigabytes Alexander can use while staying within his budget.
I don't know how to write inequality
69.50 dollars + 5 dollars is 74.50 dollars add 5 dollars 79.50 add 5 dollars again and 84.50
Answers
Answer- 5g+ 69.50= 85 ; 3.1 (3)
An inequality is an equation with letters and number that sum to ONE whole.
In this case we have a flat cost, which is standalone and 5 dollars per gigabyte which is not standalone. Let G stand for each gigabyte.
This means our equation is 5g(five dollars times each gigabyte used) +69.50 that is gives. He has to keep his entire month under 85 dollars, which means our equation must equal 85. Now our equation will look like this.
Inequality- 5g+ 69.50= 85.
In order to solve how many gigabytes will be used we solve our equation backwards. We subtract 69.50 from 85,because we know that must has already been spent. This gives us 15.50. This means we will have to divided 15.50 into five dollars to see how many gigabytes are spent. 15.50 divided into five is 3.1 gigabytes.
This means Alexander will have to use 3.1 (or 3 if you have to round) gigabytes in order to spend 85 dollars or less per month.
69.50+5(3)>_85
84.50>_85
ANSWER QUICKLY!!!
Which graph shows all real numbers closer to 0 than they are to 4?
Answers
Answer:
Graph A
Step-by-step explanation:
It’s the real numbers closer 0 then they are at 4.
I hope this helps
the ratio of the number of oranges to apples to bananas is 8:5:2. if there are 120 fruits in total, how many bananas are there
Answers
Answer:
Step-by-step explanation:
To find the number of bananas, we need to determine the proportion of bananas in the total number of fruits based on the given ratio.
Let's assume that the ratio of oranges, apples, and bananas can be represented by 8x, 5x, and 2x, respectively, where x is a common multiplier.
The sum of the parts in the ratio is 8x + 5x + 2x = 15x.
We know that the total number of fruits is 120. Therefore, we can set up the following equation:
15x = 120
To solve for x, we divide both sides of the equation by 15:
x = 120 / 15
x = 8
Now that we know the value of x, we can find the number of bananas by multiplying it by the corresponding part of the ratio:
Number of bananas = 2x = 2 * 8 = 16
So, there are 16 bananas in total.
We can add all the parts to the ratio and get 15. Out of 15 parts, 2 are bananas. Now we can calculate how many fruits are in one part. One fifteenth of 120 is 8, so there are 8 fruits in one part. 2 parts are bananas, so multiplying 8 with 2 gives us our answer, 16.
What historical reality is represented in this excerpt?
Navajo children were taken from their parents to be educated far away.
Many Navajo children did not come back to the reservation.
The parents of Navajo children created their own educational system.
Many Navajo parents wanted their children to be educated but not taken away.
Answers
Answer:
Navajo children were taken from their parents to be educated far away.
Step-by-step explanation:
Answer:
I got the same answer as the other person its A.) Navajo children were taken from their parents to be educated far away.
Step-by-step explanation:
Multiply the pairs of numbers and match them with their products. Tiles (-5)(4.2) (-7)(-3) (4) (5) (2.5)(-9) Pairs 22.5 21 -22.5 -21 111
Answers
Here are the pairs matched with their products:
- (-5)(4.2) matches with -21
- (-7)(-3) matches with 21
- (2.5)(-9) matches with -22.5
Pairs (4) and (5) do not have corresponding products in the given options.
(-5)(4.2) = -21
(-7)(-3) = 21
(4)(5) = 20
(2.5)(-9) = -22.5
So, the pairs of numbers and their products are as follows:
(-5)(4.2) = -21 matches with -21.
(-7)(-3) = 21 matches with 21.
(4)(5) = 20 matches with 20.
(2.5)(-9) = -22.5 matches with -22.5.
I hope this helps!
In February of 2006, there was a
record snowfall of 26.9 inches in one
day in New York City. The normal
snowfall for the month of February in
New York City is 8.5 inches and March
is 5.1 inches. How much more snow
fell in the one day storm in 2006 than
normally falls in February and March
combined
Answers
Answer:
40.5 inches
Step-by-step explanation:
I’m not sure if this is correct or not but my thinking is that you just add 26.9, 8.5, and 5.1 together since it says “How much more snow fell in the one day storm in 2006 than normal falls in February and March combined?” And combined basically means all together.
Answer: 13.3 more inches of snow fell in one day storm than normally falls in February and March combined.
February and March combined: 8.5+5.1 = 13.6
Since the question asked how much more, that means you subtract:
26.9 - 13.6 = 13.3
hope this helped =)
-YinAhara
60. Calculate the mean absolute deviation of the values below, by answering each question.1, 4, 21, 4, 35, 20, 3 and 8
Complete the table of values, finding the distance of each value from the mean.
Answers
Determine the length of AB¯¯¯¯¯¯¯¯. Write your answer in simplest form.
pls help i need the answer soon
Answers
Answer:
\(x = 2.4\)
Step-by-step explanation:
Step 1: Find the length of AB
\(\frac{ED}{EA} = \frac{EC}{EB}\)
\(\frac{15}{12} = \frac{18}{12+x}\)
Cross Multiply
\(15(12+x) = 12(18)\)
Distribute
\((15*12)+(15*x) = 216\)
\(180 + 15x = 216\)
Divide
\(15x / 15 = 36 / 15\)
\(x = 2.4\)
Answer: \(x = 2.4\)
−1/5÷20 as a fraction
Answers
Answer:
1/100
Step-by-step explanation:
I used a calculator…
Answer:
- 1/100 or you could use -0.01 instead
Petra is making a batch of extra large donuts by stamping circles in dough using a pastry stamp with a diameter of 5 inches. For the donut hole, she stamps out a circle using a pastry stamp that has a diameter of 2 inches.
How many square inches of dough are left in the donut after the hole has been removed?
Step 1 - Find the radius of each circle
Step 2 - Find the area of the large circle
Step 3 - Find the area of the small circle
Step 4 - Area of large circle minus area of small circle
Area = \(\pi\)²
Describe how you solved this problem using complete sentences and include all relevant formulas and calculations. Use 3.14 for \(\pi\)
Answers
Answer:
16.49
Step-by-step explanation:
First we are going to find the area of the larger circle. You don't need to find the radius, you can just use the diameter(the radius is 2.5). 3.14 times 2.5 squared=19.63. Next, the radius of the smaller circle is 1. So, 3.14 ^1 squared=3.14 19.63 - 3.14= 16.49
month money help PLs
Answers
Answer:
second answer: y = 5x + 120; $180
Step-by-step explanation:
he starts with $120.
so, whatever else he does per month, there will always be the $120 starting amount to be added.
so, the third and the fourth answers are out.
then think : $5 every month.
that is how much after 2 months ? 2×5 = $10.
how much after 3 months ? 3×5 = $15.
so it has to be an equation that contains 5x (5 times the number of months).
combining both thoughts :
y = 5x + 120
now let's use x = 12 (for 12 months = 1 year).
5×12 + 120 = 60 + 120 = $180.
yes, it is that simple. no hidden "hocus pocus" is needed. just common sense.
A movie theater sold 6,030 tickets in 30 days. They sold the same number of movie tickets every night.
Part A
How many tickets did the movie theater sell each night? Show the equation you used to find the answer.
Part B
Jamie says that the movie theater sold 21 tickets each night. Explain Jamie’s reasoning.
Part C
How can understanding the relationship between multiplication and division help Jamie determine that her answer is incorrect?
Answers
Answer:
Part A : 201
Step-by-step explanation:
6030/30
because they sold the same number of movie every night ..... I'm not sure
B: Jamie did 63/3 and not 6,030/30
C: understanding that 0’s don’t just add nothing and do add value and are important for proper multiplication/division would help Jamie
Can someone please help me with this problem..and explain it. Don't mind the numbers and dots i'm pretty sure they're wrong
Answers
Answer:
59°
Step-by-step explanation:
The maximum temperature is just the y-coordinate of the uppermost point on the graph, which is (6 hr, 59°). Hence, it is 59°.
Pablo has 20 balloons for his party. He will either take 2 for a stack or 3 for a stack. How many more stacks will Pablo need if he takes 3 on each stack?
Answers
Geometry
Answer with a proper explanation
Answers
Answer:
15 sides
Step-by-step explanation:
As we know the full angles of a polygon is 360°
And
Each side has angle 24°
So,
n = 360/24
n = 15 sides
I hope my answer helps you.
The polygon has 5 sides.
Step-by-step explanation:
Given in the diagram, the angle between the ends of each side is given i.e. 24degrees between ends of a side from the centre. Or it can also be said that each side of the polygon subtends an angle at the centre 'O' i.e. each 24*.
=> We know that sum of angles around a point = 360*, so sum of angles around centre = 360*
And 24* in the centre subtends a side of the polygon;
Using the logic - no. of sides = 360*/24* = 15 = 15 sides
At a recent football game of 8,450 in attendance, 150 people were asked what they prefer on a hot dog. The results are shown.
Ketchup Relish Chili
54 36 60
Based on the data in this sample, how many of the people in attendance would prefer ketchup on a hot dog?
4,225
3,380
3,127
3,042
Answers
By proportion that is:(54/150) * 8450= 54 * 56 1/3= 3042
Answer:
By proportion that is:(54/150) * 8450= 54 * 56 1/3= 3042
Step-by-step explanation:
Wat is the product of 8/9 and 2/7
Answers
Answer:
16/63
Step-by-step explanation:
Given problem,
→ (8/9) × (2/7)
Let's solve the problem,
→ (8/9) × (2/7)
→ (8 × 2)/(9 × 7)
→ 16/63
Hence, answer is 16/63.
In the diagram of a fan below, CA = 9.5 in. this is the distance from the center to a point on the fans blade. what is the distance point A travels in one rotation of the fans blade
Answers
Answer:
About 59.66 inch
Step-by-step explanation:
To find the circumference you first have to find the diameter which is the double the radius. Since 9.5 is the radius of this circle, the diameter is, 9.5x2=19.
With the diameter of 19, you multiply the 19 with pie which is approximately 3.14. The answer is 19x3.14=59.66
C = 2 * pi * r
C = 2 * pi * 9.5
C = 59.69 in.
So point A travels a distance of approximately 59.69 inches in one rotation of the fan's blade.
ivan and jeff buy a package of 8 pen for 4.00. ivan want 5 of the pen. how many should ivan pay?
Answers
Answer:
$2.50
Step-by-step explanation:
Let's set up a proportion using the following setup.
price / pens = price / pens
We know that it costs $4.00 for 8 pens.
$4.00 / 8 pens = price / pens
We don't know how much it costs for 5 pens. Therefore, we can say it costs $x for 5 pens.
$4.00 / 8 pens = $x / 5 pens
4/8=x/5
We want to solve for x (the cost for 5 pens). Therefore, we must get x by itself on one side of the equation. x is being divided by 5. The inverse of division is multiplication, so multiply both sides of the equation by 5.
5*(4/8)=(x/5)*5
5*(4/8)=x
5*0.5=x
2.5=x
x= $2.50
Ivan should pay $2.50 for 5 pens.
Answer:
4.00
Step-by-step explanation:
Will give brainliest!!! It's is an application problem for exponential functions. I am getting a bit confused with the year. I think the year is supposed to be 42 but I don't know so please help me and thank you
Answers
Answer:
Step-by-step explanation:
The growth factor is 1.06.
The year is 2020 - 1978 = 42.
This is exponential growth as the growth factor is > 1.
The equation is V = 40000(1.06)^42
V works out to $462,281
The figure below shows three quadrilaterals on a coordinate grid:
A coordinate grid is shown from positive 8 to negative 8 on the x-axis and from positive 8 to negative 8 on the y-axis. An image of a rectangle labeled P is shown on ordered pair negative 1, negative 1 and negative 3, negative 1 and negative 3, negative 2 and negative 1, negative 2. Another image of a rectangle labeled Q is shown on ordered pair negative 2, negative 2 and negative 6, negative 2 and negative 6, negative 4 and negative 2, negative 4. Another image of a rectangle labeled R is shown on ordered pair 1, 1 and 1, 2, and 3 , 2 and 3, 1.
Which of the following statements is true about the three quadrilaterals?
Q and R are similar and congruent.
Q and P are similar and congruent.
P and R are similar but not congruent.
P and Q are similar but not congruent.
Answers
Answer: con
Step-by-step explanation:
Evaluate the expression when b=9 and c=4 . bc+12.3 =
Answers
9*4 = bc, equals 36
36+12.3, equals 48.3
Can someone pls help?!
Find the product of........ The rest of the question is down below.
Answers
Answer: The answer is −2x+14 just take away the parentheses.
Ana is graphing function F on a coordinate plane. What is the maximum number of different output
values of F for an input value of 2?
Answers
Solve for X
X^2 + 43 = 572
Answers
Answer:
23
Step-by-step explanation:
x^2 + 43 = 572
x^2 = 572 - 43
x^2 = 529
( 529 = 23 x 23 = 23^2 )
x^2 = 529
x^2 = 23^2
x = 23
X^2=572-43
X^2=529
X=+23
Write the solutions, one with a sign and one with a sign
X=-23
X=23
Simplify the expression: (16-9)^9/[(4+3)^2]^3
Answers
![Simplify the expression: (16-9)^9/[(4+3)^2]^3](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/nhhscTJkld1dQacppFHTvArlQGRZZeV7.png)