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Explain how you know the following system of equations has at most 2 solutions.
Solve the system algebraically. Show your work.
Solve the system by graphing.
y= 2x-1
y= x^2-9
Answers
Answer:
Step-by-step explanation:
Answer:
The said explanation is the answer.
Step-by-step explanation:
1) Graphing the first function (y = 2x-1). When the exponents of the variables are all 1, that is there are no square, cubes, etc. the equation is a line. Then it is enough to find two points to draw it. We can calculate two points assigning a number to x and calculating the corresponding number for y. For example, when x= 0 y= 2 times 0 -1 = -1. Then the line will pass from the point (0,-1). We need a second point, we can take x=1, then y = 2 times 1 -1 = 1. The line will pass from (1,1). We can mark the two points on the plane and draw the line from these two points.
2) Graphing the second function (y = x^2-9). A quadratic equation is of the form: ax^2+bx+c= 0. We have: y= f(x) -9. Set y=0. We have the quadratic equation: x^2-9=0. Using the algebraic identity: a^2-b^2=(a+b)(a-b). We can rewrite x^2-9=0 as x^2-3^2=0: [(x+3)(x-3)=0] - [(x+3)=0,(x-3)=0] - [x= -3, x= 3]. Hence, there are two solutions for x. So we have two x-intercepts: (-3,0) and (3,0). To find the y-intercept, set x=0: [(y = (0)^2-9=0)] - [(y=-9)]. Hence the y-intercept: (0,-9)
In conclusion, this system of equations at most has two real solutions, since two points of both functions intersect each other.
Here's the graph:
Related Questions
Can you find the numbers as powers with the given bases as your clue? Example: the number is 64 and the base is 4. I test 4x4=16 Then 16x4=64 So my power must be 43 because 4x4x4=64. Now you try... 1. It has a value of 32; it has a base of 2 2. 81, base 9 3. 81, base 3 4. 100, base 10
Answers
Step-by-step explanation:
For 32:
The factors are as shown:
32 = 2*2*2*2*2
32 = 2²*2³
32 = 2²⁺³
32 = 2⁵ (Base of 2 and power of 5)
For 81:
factors
81 = 3*3*3*3
81 = 3²*3²
81 = 3²⁺²
81 = 3⁴ (Base of 3 and power of 4)
For 100:
factors
100 = 10*10
100 = 10² (Base of 10 and power of 2)
Which equation represents the line that is parallel to y = 4 and passes through (-3,1)?
Answers
Answer:
y=1
Step-by-step explanation:
slove for x in terms of p,m, and g
m=g-px
Answers
Answer:
- (m-g)/p =x
Step-by-step explanation:
subtract g
m-g=-p(x)
divide by -p
-(m-g)/p =x
Uh help i don`t get this (ez question) :D
Answers
Answer:
Dividend divided by Divisor = Quotient
5 divided by 8 = 0.625
Step-by-step explanation:
which expression is equivalent to −34÷(−812)?
Answers
Answer:
-34/-812 = 17/406
Step-by-step explanation: i think this is right...
Answer:
Your answer is: Look Below ↓
Step-by-step explanation:
Hope this helped : )
The wavelength of violet light is 4.0 x 10^−7 m. The wavelength of red light is 6.5 x 10^−7 m. How much longer is the wavelength of red than violet?
A 2.5 × 10^–7 m
B 1.05 × 10^–7 m
C 2.5 × 10^–6 m
D 1.05 × 10^–6 m
Answers
Answer:
A 2.5 × 10^–7 m
Step-by-step explanation:
Given
wavelength of violet light = 4.0 x 10^−7 m.
The wavelength of red light = 6.5 x 10^−7 m
To find the how much longer is wavelength of red light than violet light we have to find difference of wavelength of red and violet light
Difference in wavelength of red light and violet light =
wavelength of red light -wavelength of violet light
= 6.5 x 10^−7 m - 4.0 x 10^−7 m
Difference in wavelength of red light and violet light = (6.5 - 4.0)*10^−7 m
Difference in wavelength of red light and violet light =2.5 x 10^−7 m
Thus,
wavelength of red light is 2.5 x 10^−7 m longer than wavelength of violet light
option A
If p varies directly as
the cube of q, and p =
26 when q = 2, find p
when q = 5
Answers
Answer:
The value of p at q = 5 is 406.25
Step-by-step explanation:
∵ p varies directly as the cube of q
→ That means p ∝ q³
∴ The equation of variation is p = kq³, where k is the constant of variation
∵ p = 26 when q = 2
→ Use them to find the value of k
∵ 26 = k(2)³
∴ 26 = k(8)
∴ 26 = 8k
→ Divide both sides by 8
∴ [tex]\frac{26}{8}=\frac{k}{8}[/tex]
∴ 3.25 = k
→ Substitute it in the equation of variation
∴ p = 3.25 q³ ⇒ equation of variation
∵ q = 5
→ Substitute it in the equation of variation to find p
∴ p = 3.25 (5)³
∴ p = 406.25
∴ The value of p at q = 5 is 406.25
expand and simplify (x +2)(x+ 1)
Answers
Answer:
x²+3x+3
Step-by-step explanation:
(x+2)(x+1)
x²+x+2x+3
=x²+3x+3
Answer:
x² + 3x + 2
Step-by-step explanation:
Given
(x + 2)(x + 1)
Each term in the second factor is multiplied by each term in the first factor, that is
x(x + 1) + 2(x + 1) ← distribute both parenthesis
= x² + x + 2x + 2 ← collect like terms
= x² + 3x + 2
-4(3+7m) please help i will give brainlest and do not answer just to get points this is DUE IN FIVE MINUTES
Answers
Answer:
-28m-12
Step-by-step explanation:hope that helps :)
=(−4)(3+7m)
=(−4)(3)+(−4)(7m)
=−12−28m
=−28m−12
Answer:
-4(3+7m) = -28m - 12
Step-by-step explanation:
-4 (3 + 7m)
= -4 (3) + -4(7)
= -12 + (-28)
= -12 -28m
What is the equation of the following graph
Answers
Answer:
Undefined
Step-by-step explanation:
what is half of 2^6?????
Need this asap so if you see this and are willing to help me please do
Answers
Answer:
32
Step-by-step explanation:
2 to the 6th power is also 2 x 2 x 2 x 2 x 2 x 2 which equals 64 so then you multiply it by .5 (half) to get 32 :)
Answer:
32
Step-by-step explanation:
2^6= 64
64/2= 32
Figure B is a scaled copy of Figure A.
Answers
Answer:
1/3
Step-by-step explanation:
On left side its 6:2 so 6/2 is 3
the scale factor is 1/3 because figure is a reduction
hope it helps ;)
Answer:
1/3
Step-by-step explanation:
The side that's highest is 9 units, the the image its 3. 3/9= 1/3
The perimeter of a kite can be found using the formula P = 2S + 2L. Which equation expresses S in terms of P and L?
Answers
Answer:
Step-by-step explanation:
P = 2S + 2L
2S + 2L = P
2S = P - 2L
S = [tex]\frac{P-2L}{2}[/tex]
Answer:
0.5P - L
Step-by-step explanation:
P = 2S + 2L
P - 2L = 2S +2L - 2L
P - 2L = 2S
0.5P - L = S
being a rectangle is a necessary condition for being a square
Answers
Answer:
false
Step-by-step explanation:
all rectangles are squares not all squares are rectangles
Explain how to write an equation from a graph in slope intercept form .
Answers
Step-by-step explanation:
To write an equation in slope-intercept form, given a graph of that equation, pick two points on the line and use them to find the slope. This is the value of m in the equation. Next, find the coordinates of the y-intercept--this should be of the form (0, b). The y- coordinate is the value of b in the equation.
pls give brainest i only have 2
The slope intercept form is given by y = mx + c
What is the Slope Intercept Form of a Line?The graph of the linear equation y = mx + c is a line with m as slope, m and c as the y-intercept. This form of the linear equation is called the slope-intercept form, and the values of m and c are real numbers.
Given here: Slope intercept form
We know that, the equation of a line in point slope form, where (x1, y1) is the point and slope m is:
(y – y₁) = m(x – x₁)
Here, (x, y₁) = (0, c)
Substituting these values, we get;
y – c = m(x – 0)
y – c = mx
y = mx + c
Therefore, the point (x, y) on the line with slope m and y-intercept c lies on the line if and only if y = mx + c
Hence, The slope intercept form is given by y = mx + c
Learn more about slope intercept form here:
https://brainly.com/question/29146348
#SPJ2
If -2z+3=9 what is the value of 2/3z?
Please Explain the steps.
Answers
Answer:
-2
Step-by-step explanation:
1.Subtract 3 from both sides and the equation is -2z=6
2.Divide both sides by -2 and the equation is z=-3
3.Multiply -3 by 2/3 and you get -2
Answer:
2/3z = -2
Step-by-step explanation:
1. First you want to find out what z is, so you have to solve for z.
2. To solve for z, first subtract 3 from the 3 and the 9. 3 minus 3 is equal to 0, so it cancels out. 9 minus 3 is equal to 6.
3. The new equation is -2z = 6, so now you have to divide -2z by -2 and 6 by -2. -2z divided by -2 is equal to 1z or z, and 6 divided by -2 is equal to -3.
4. The simplified equation is z = -3.
5. Now that we solved for 1z, we have to solve for 1/3 by dividing 1 by 3 and -3 by 3. 1 divided by 3 is 1/3, and -3 divided by 3 is -1.
6. We have solved for 1/3z (1/3z = -1), but now we want to solve for 2/3z so we have to multiply 1/3z by 2, and -1 by 2. 1/3z times 2 is 2/3z, and -1 times 2 is equal to -2.
7. The simplified equation for the value of 2/3z in the equation -2z + 3 = 9 is 2/3z = -2
A 3-yard roll of butcher paper costs $8.55. What is the price per foot?
Answers
Answer:
$2.85
Step-by-step explanation:
8.55/3
Answer:
$2.85 per foot
Step-by-step explanation:
all u gotta do is 8.55/3
Find the value of f(-5).
y=f(x)
Answers
Answer:
???
Step-by-step explanation:
???
I NEED HELP NOWWWWW AHHHHHHHHH IM SO DUMB AND THANK YOU FOR HELPING ME
Answers
Answer:
9
Step-by-step explanation:
someone help me on my homework before i lose my sanity pls its my most recent question im done <3
DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA
Answers
Answer:
da de da da da de do re mi fa so la mi AAAAAAAAAAA
Step-by-step explanation:
I can speak the language of the gods xD
you earn $25 for washing 5 cars how much do you earn for washing 4 cars
Answers
what is the slope of a line perpendicular to the line whose equation is 2x-y=-6
Answers
Answer:
m⊥ = –½
Step-by-step explanation:
First, put the given equation in slope-intercept form:
2x – y = –6
–y = –2x – 6
y = 2x + 6
The slope of the line perpendicular to the line given will be the negative reciprocal of the given line's slope, so:
If m = 2, then m⊥ = its negative reciprocal:
m · –1
2 · –1
–2 → –½
So, the negative reciprocal of 2 is –½.
please i need help asap. if u can help that’d be great
Answers
Answer:
The answer is B. (2x-3)
Jessica prepared 36 kilograms of dough after working 6 hours. How much dough did Jessica prepare if she worked for 8 hours? Assume the relationship is directly proportional.
Answers
Answer:
48
Step-by-step explanation:
because 36 divided by 6 is 6 and that is how much dough she produces in an hour so if you added two more 6s to 6 to make it 8 meaning you are adding 12 because that is how much dough she makes in an hour
Use the distributive property to simplify the expression, then combine like terms -12 - 5p +2(6p+p)
Answers
Answer:
-12 + 9p
Step-by-step explanation:
Original Equation:
-12 - 5p + 2(6p + p)
Distributive property.
2 x 6p = 12p
2 x p = 2p
Equation:
-12 - 5p + 12p + 2p
Subtract 5p from 12p
-12 + 7p + 2p
Add.
-12 + 9p
Hope this helped :)
Please consider Brainliest :)
Express 48 1/4 in simplest radical form.
Answers
To take a root of a fraction, take the root of the numerator and denominator separately
Final answer should be around 6.94622
For the expression 34- 34a to have a negative value, what must be true about the value of a ?
Answers
Answer:
a>0
Step-by-step explanation:
if a is negative then the subtraction sign would switch. therefore, for the expression to have a negartive value a must be greater than 0
what is 200 times 1238
Answers
Step-by-step explanation:
the answer is 247,600
hope this helps
Answer: the answer is 247,600
Step-by-step explanation:
Help and brainliest? :(
Answers
I think
Solve for X
-9x - 8+5x=28
Answers
Answer:
X=-9
Step-by-step explanation:
plug it in and see what works -9 is the only one you can plug in to get 28