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.
What is the slope of the equation that passes through the points
(-5,4) and (5,2) ?
Answer:
[tex] - \frac{2}{10} [/tex]
or
-0.2
A circle is dilated by a scale factor of 1.5 to create a new circle. The area of the new circle is 1.5 times the area of the original circle.
True or false??
Given:
The given statement is "A circle is dilated by a scale factor of 1.5 to create a new circle. The area of the new circle is 1.5 times the area of the original circle."
To find:
Whether the given statement in true or false.
Solution:
Area of circle is
[tex]A=\pi r^2[/tex]
Where, r is the radius of the circle.
Let [tex]r_1[/tex] be the radius of the original circle. So, the area of the circle is
[tex]A_1=\pi (r_1)^2[/tex]
The circle is dilated by a scale factor of 1.5 to create a new circle. So, the radius of the new circle is:
[tex]r_2=1.5r_1[/tex]
The area of the new circle is
[tex]A_2=\pi (r_2)^2[/tex]
[tex]A_2=\pi (1.5r_1)^2[/tex]
[tex]A_2=2.25\pi (r_1)^2[/tex]
[tex]A_2=2.25A_1[/tex]
The area of the new circle is 2.25 times the area of the original circle.
Therefore, the given statement is false.
9. Select a set of corresponding angles.
A Angles M and D
B Angles B and L
C Angles C and J
D Angles K and A
Answer:
A. Angles M and D
The top of a ramp is 4 feet above the ground. The ramp makes a 21.3 degree angle with the ground. What is the length of the ramp
Answer:
Total ramp system length in feet: Includes the minimum number of 5′ x 5′ resting platforms and the 5′ x 5′ platform at the top of the ramp.
Step-by-step explanation:
hope this helps!
What does q equal?Please help me.
What is 48901x120412/12321 with a fraction of 6/9 + 29181041/21841x2912311203? It was one of my math questions couldn't find it online soooo??
4468886443222234578889953
What is the value of x?
Answer:
25
Step-by-step explanation:
Multiply the polynomials. (x-3)(x^2+2x+1)
Answer:
[tex]x^{3} -x^{2} -5x-3[/tex]
Step-by-step explanation:
you use distributive property for this, or you can do the box method
distributive:
[tex]x(x^{2} +2x+1)-3(x^{2} +2x+1)[/tex] (you multiply the second equation by x-3)
then distribute, or multiply everything
[tex]x^{3} +2x^{2} +x-3x^{2} -6x-3[/tex]
then collect like terms
[tex]x^{3} -x^{2} -5x-3[/tex]
Apply the distributive property to create an equivalent expression 4(x-2+y)
Answer:
4 * x
4 * -2
4 * y
4x-8+4y
Step-by-step explanation:
Answer:
4x+4y-8
Step-by-step explanation:
(✿◡‿◡) <-- she wants Brainliest
Will give brainliest! What is the range for the third size of the triangle 2,10?
Answer:
8 < x < 12
Step-by-step explanation:
Given 2 sides of a triangle then the third side x is in the range
difference of sides < x < sum of sides , that is
10 - 2 < x < 10 + 2
8 < x < 12
Sam paid £8 for two footballs.
One football cost £2 more than the other
What was the cost of the more expensive football?
[2 marks]
Answer
Answer:
£6 you do £8-£2= £6
Step-by-step explanation:
Answer:
£8-£2=£6
Step-by-step explanation:
what is equivalent to 10x + 80
A) 5(2x + 40) B) 10(x + 8) C) 5(2x + 80) D) 10(10x + 8)
Answer:B ithink
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
10(x + 8)
10x + 80
10× X and 10 × 8
Giving brainliest to whoever comments the right answer first
Answer:j
Step-by-step explanation:
Which expression is equivalent to 4a+2b
A.a+a+a+a+b+b
B. 4+2+a+b
C.6(a+b)
D.4+a x 2+b
Answer:
Answer is A
Step-by-step explanation:
a+a+a+a+b+b =4a+2b
Find the sides and angles please help me
Answer: if this uses the Pythagorean theorem then it’s the square root of 83.24
Step-by-step explanation: the formula is a^2+b^2=c^2 the hypotenuse is c^2
Multiple Choice
Look at the graph.
The graph shows a line through the points left parenthesis negative 1 comma negative 2 right parentheses and left parenthesis 2 commas 1 right parenthesis.
The slope of the line is _______.
A. positive
B. negative
C. zero
D. undefined
Answer:
the slope is POSITIVE (answer A)
Step-by-step explanation:
The line goes through: (-1, -2) and ( 2, 1)
Then the slope can be calculated as:
slope = (y2 - y1) / (x2 - x1)
in our case:
slope = (1 - -2) / (2 - -1) = (1 + 2) / (2 + 1) = 3 / 3 = 1
Therefore, the slope is POSITIVE (answer A)
math pls help and thanks
Answer:
Is red 3.33 triangle
If ƒ(x ) = x 2 + 1 and g(x ) = 3x + 1, find 2 · ƒ(4).
A. 34
B. 18
C. 65
Answer: The answer would be (B) 18
Step-by-step explanation: Have a brilliant day of learning!
pls help will give brainliest when i can
Solve −3(7n+3)<6n. Write the solution using set-builder notation.
The set builder notation of the inequality - 3(7n + 3) < 6n is,
{n : n ∈ R, n > - 3 }.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given, An inequality - 3(7n + 3) < 6n.
Now, distributing the terms we get,
- 21n - 9 < 6n.
- 21n - 6n < 9.
- 27n < 9.
27n > - 9. (Think of moving the variable to the other side to make it
positive).
n > - 27/9.
n > - 3.
learn more about inequalities here :
https://brainly.com/question/28823603
#SPJ2
Solve for X. Please solve all four. First person to do so will get brainliest.
Answer:
x=-12
x=10
x=-8
x=-5
Step-by-step explanation:
Answer:
1.x=-12
2.x=10
3.x=-8
4.x=-5
Step-by-step explanation:
El 10% de que numero es 32
Can someone identify this
Answer:
no entindendol ingels
Step-by-step explanation:
Answer:
8
Step-by-step explanation:
square 6, which is 36. then square 10, which is 100. then do:
100-36=64
take the square root of 64, which is 8.
need help ASAP.
what is the best estimate for the value of the expression?
Answer:
11
Step-by-step explanation:
u do 4x5 which is 20
Can somebody help me with this math question, all you have to do is answer the equation, then it's described, and then it draw it out I'll give you 100 points and a Brainliest
Answer:
X= - 2
Step-by-step explanation:
-3 (5x+6) - 3x = 6-6x
Remove the parentheses
-15x-18-3x=6-6x
Collect the like terms
-18x-18=6-6x
Move the variable to the left-hand side and change its sign
18x+6x=6+18
Collect the like terms
-12x=24
Divide both sides
X=-2
Which figure will this net make
Answer:
C
Step-by-step explanation:
Rectangle base, tiny triangle sides, but rectangle top
What is m ∠ ZUB?
23.7°
32.8°
33.5
57.2°
Answer:
23 .7 ruim
57.2 sol
32 .8 mais ou menos
tchau bj
What are the next three terms in the sequence? -112, -129, -146, ___________
Explain your answer.
Answer:
-163, -180, -197
Step-by-step explanation:
-146--129=-17
the difference of them is 17 so keep adding it
What is the following product?
Answer:
the image is not opening
Answer:
The answer is the third one :)
Step-by-step explanation:
I don't know how to explain it sorry
Joe is 6 feet tall and cast a 3 foot shadow. He is standing next to a building that cast a shadow that is 20 feet long. How tall is the building.
Answer:
40 feet
Step-by-step explanation:
Answer:
40 feet tall
Step-by-step explanation:
6/2 =3
?/2 =20
*2 *2
? = 40
you do inverse operations because 6 divided by 2 is 3... the ? is the variable for how tall the building is... ? divided by 2 = 20 so you multiply 2 and 20 to get the total height