Step-by-step explanation:
To find - How can you determine the number of solutions of a system
of linear equations by inspecting its equations?
Proof -
There exists three types of solution for a system of linear equations.
1. No solution.
2. Unique solution.
3. Infinite many solutions.
Now,
Let the 2 linear equations are as follows :
y = ax + b
y = cx + d
1. For no solution -
a = c and b ≠d
For example-
y = -2x + 5
y = -2x - 1
Subtract first equation from second , we get
y - y = -2x - 1 - ( -2x + 5)
⇒0 = -2x - 1 + 2x - 5
⇒0 = -6
Not possible
So, There exist no solution.
2. For unique solution -
a ≠ c and b , d can be any value
For example -
If b and d are same ,
y = 2x - 4
y = -3x - 4
Subtract equation 1st from 2nd , we get
y - y = -3x - 4 - ( 2x - 4)
⇒0 = -3x - 4 - 2x + 4
⇒0 = -5x
⇒x = 0
⇒y = 2(0) - 4 = -4
∴ we get
x = 0, y = -4
If b and d are different
y = 2x - 4
y = -3x + 5
Subtract equation 1st from second
y - y = -3x + 5 - 2x + 4
⇒0 = -5x + 9
⇒-5x = -9
⇒x = [tex]\frac{9}{5}[/tex]
⇒y =2([tex]\frac{9}{5}[/tex]) - 4 = [tex]\frac{18}{5} - 4 = \frac{18 - 20}{5} = -\frac{2}{5}[/tex]
∴ we get
x = [tex]\frac{9}{5}[/tex] , y = [tex]-\frac{2}{5}[/tex]
3. Infinitely many solution -
a = c and b = d
For example -
y = -4x + 1
y = -4x + 1
Subtract equation first from equation second
y - y = -4x + 1 - ( -4x + 1)
⇒0 = -4x + 1 + 4x - 1
⇒0 = 0
Satisfied
So, Infinite many solution possible.
The equation shown has an unknown number.
Blank divided by 3/7 = 7/15
Enter a fraction that makes the equation true
Answer:
45/49
Step-by-step explanation:
brainliest for the fastest answer!!!!!!!!
its super easy
Answer:
The answer is B number os shoes ihope it help
Find the area of a circle with radius, r = 7.49m. Give your answer rounded to 2 DP.
Answer:
Area ≈ 176.24m²
Hope it helps
Please mark me as the brainliest
Thank you
Type the correct answer in each box. Use numerals instead of words. Bethany collected 200 survey responses regarding recycling behaviors in her city. Of those responses, 174 people responded that they participate in the city’s recycling program. Use this information to complete the statement. Round all answers to the nearest hundredth. The approximate sample proportion is , which means that % of the people surveyed do not participate in the city’s recycling program.
Answer:
13% did not participate in citys recycling program not sure about the first part
Step-by-step explanation:
Answer:
Step-by-step explanation:
Find the percent of increase from 36 inches to 43 inches. Round to the nearest tenth of a percent if necessary.
Answer:
27.78
Step-by-step explanation:
(46-36):36*100 =
(46:36-1)*100 =
127.77777777778-100 = 27.78
Now we have: What is the percentage increase/decrease from 36 to 46 = 27.78
PLEASE HELP ME!!! ILL MARK BRAINLIESY
Answer:
So, the answer is 7 y
Step-by-step explanation:
Both arrows are pointing toward the 7 and it is in y! I have been in 12 grade already so dont worry :)
If u can solve 6 word problems in 5 minutes how many could you solve per minute?
Answer:
You can solve 1.2 word problems per minutes
Step-by-step explanation:
If 6 word problems were solved in 5 minutes, you must put this into a fraction. We're looking for how many word problems could be solved per minute, so we divide 5 by itself to get 1 and whatever you do to the bottom, you must do to the top, so 6 divided by 5 is 1.2
Hope this helped ;)
YO SOMEBODY HELP PLS IM STUCK
Answer:
x > 1
Step-by-step explanation:
subtract 6 from both sides
Divide both sides by 2
Which expression is equivalent to 12x + 20y?
Please help me i need to pass math class
Simplify each expression.
1. (-6p - 8) - (2p - 6)
2. (-8r - 2) + (4r - 3)
3. (-z - 8) - (6z - 5)
4. (-s - 5) + (-2s + 2)
5. (-7s + 4) - (-8s + 4)
6. (-4f + 9) - (8f + 9)
7. (-8f) + (-f + 8)
8. (4p - 4) + (-7p - 7)
9. (7v - 9) - (6v + 9)
10. (-3g) + (5g - 5)
What is the solution to the inequality-6(p-8)<-12
Answer:
p < 10
Step-by-step explanation:
-6 (p - 8) < -12
-6p + 48 < -12
- 48 -48
-6p < -60
/-6 /-6
p < 10
Shrings dining room table is round and has a radius of 4.5 feet. What is the tabletops area? Plz
Answer:
The answer should be 63.63! you might need to round it to 63.6 or 64
Step-by-step explanation:
1. In triangle ABC, the measure of ∠ABC is 42°, and the measure of ∠BCA is 113º.
What is the measure of ∠CAB?
How do you know that is the answer?
Answer:
if I am correct it would be 25 degrees. hope this helps!
Step-by-step explanation:
Write 4/5 as a decimal
Answer:
4.5 : i think thats the answer i don't know
For every 2 apples in kail's orchard,there are 4 pears. In sam's orchard , there are 10 pears for every 5 apple. If the number of pears in proportional to the number of apples, What is constant proportionality
Answer:
2/5
Step-by-step explanation:
cause u divied
1. Find the value of the variable x.
A) 7 √2/2
B) 7 √3/2
C) 14 √3
D) 14/3
Answer:
[tex] \frac{ \sqrt{7} }{2} [/tex]
Step-by-step explanation:
The triangle is an isosceles triangle. Because the triangle is an isosceles triangle, the height and base of the triangle are equal to eachother.
a² + b² = c²
right now we have c² which is 7
a² + b² = 7
[tex] \frac{ \sqrt{7} }{2} [/tex]
because a² and b² are = to eachother
now im lost dony listen to me lol.
Use synthetic division to solve
Ben takes a 45 minute test. After answering 10 questions, the timer indicates that one-fifth of the total time is up. How much time did Ben take to answer the 10 questions *
it took Ben 9 minutes to answer 10 questions
HELP ME PLS NOW I NEED YOU PPLS BRAINS
Answer:
C and D
Step-by-step explanation:
I went to a website (https://mathbitsnotebook.com/JuniorMath/Equations/IQBasicInequalities.htm) and double-checked what the correct answers were. I apologize for the hassle I may have caused you.
Need this done in 5 minutes
Step-by-step explanation:
40, 58, 58, 72, 74, 74, 76, 81, 83, 84, 92
1 2 3 4 5 6 5 4 3 2 1
1) A. 74
2) B. 40
3) A. 92
4) A. 58
Brainlist pls!
Percy has $50 in a savings account. The interest rate is 10% per year and is not compounded. How much will he have in 1 year?
Answer:
Step-by-step explanation:
Take the 50 and multiply by 1.1 (this is 10% if you dont want to go .1 and add that to 50)
50*1.1=x
50*1.1=55
There will be a total of 55 Dollars in the savings account. He has earned 5 dollars in interest.
Hope This helps :)
Answer:
70
Step-by-step explanation:
just doubled
https://wfs.fireflycloud.net/resource.aspx?id=677205
Answer:
huh????????????????.??????
due tomorrow i need help
A(b) is a function.
. A(b)
A. True
B. False
Answer:
B
Step-by-step explanation:
NOTE:
it might be wrong since im in geometry, not algebra, i used to know this
Question
2
1 pts
José invested $3000 in a 5 yr GIC that paid 3.95%/yr, compounded annually.
Answer:
this doesn't make any sense
Step-by-step explanation:
9. A 16-ft ladder is leaning against the side of a house. The ladder touches the ground 9 ft away from the house. What angle does the ladder make with the ground?
Round to the nearest WHOLE number.
Note: this is a trigonometry question
Answer:
Check pdf
Step-by-step explanation:
55.77°
EXPLANATION:In ◣ ABC, (consider the diagram)
cosΦ = b/h = 9/16
cosΦ = 9/16
Φ = 9/16 × cos-¹
Φ = 55.77
Hence, the angle between the ladder and ground is approximately 56°.
can anyone plz help me with my trigonometry homework
Answer:
I really dont know
Step-by-step explanation:
the explination is i
Can someone help and give me a step by step explanation please?!
9514 1404 393
Answer:
∠QSR = 78°∠SQR = 51°Step-by-step explanation:
The measure of an inscribed angle (QTR) is half the measure of the arc it intercepts. The measure of an arc is the same as the measure of the central angle it intercepts. So, we have ...
∠QSR = 2×∠QTR
∠QSR = 2×39°
∠QSR = 78°
__
Sides SQ and SR are radii of circle S, so are the same length. That means triangle QRS is an isosceles triangle and the base angles SQR and SRQ are congruent. The sum of angles in a triangle is 180°, so we have ...
∠QSR + 2(∠SQR) = 180°
78° + 2(∠SQR) = 180° . . . . fill in the value we know
2(∠SQR) = 102° . . . . . . . . . subtract 78°
∠SQR = 51° . . . . . . . . . . . . .divide by 2
PLEASE HELP ASAP I WILL GIVE BRAINLIEST TO FIRST CORRECT ANSWER
Find the values of x, y and z.
Answer:
X = 53 degrees
Y = 74 degrees
Z = 53 degrees
Step-by-step explanation:
So if you knew that all angles in triangles add up to 180 degrees. You first want to find Y. 180 - 36 - 70 is equal to 74. So, Angle Y is 74 degrees. Line XYZ is a line that has a 180 degree on there. So 180 - 74 and divide that by 2 to find X and Z. 180 - 74 is 106. 106/2 = 53. Therefore, X and Z are 53 degrees, Y is 74 degrees.
Y =74
Step-by-step explanation:
Add the number till u get 180
What is the length of the unknown side?
Answer:
use Pythagoras theorem
✓12x12+16x16
✓400
20
Answer:
20
Step-by-step explanation:
Hope this helped!