What are the points of intersection between the graphs of the functions
f(x) = x²(x + 1) and g(x) = x + 1?
Answers
Answer:
(x1,y1) = (1, 2)
(x2,y2) = (-1,0)
Step-by-step explanation:
Given: f(x) = x²(x + 1) and g(x) = x + 1
To find the intersection, then set functions equal to each other to solve for x first.
x²(x + 1) = x + 1; divide by (x+1) from both sides
[tex]x^{2}[/tex] = 1; take the square root to both sides
x = ±1;
The graphs intersect at two points (x1,y1) and (x2,y2)
Use x=1
f(1) = x²(x + 1) = [tex]1^{2}[/tex](1+1) = 2
g(1) = x + 1 = 1 + 1 = 2
(x1,y1) = (1, 2)
Use x= -1
f(-1) = x²(x + 1) = [tex](-1)^{2}[/tex](-1+1) = 0
g(-1) = x + 1 = -1 + 1 = 0
(x2,y2) = (-1,0)
The points of intersection of two functions are required.
The points of intersection are [tex](-1,0)[/tex] and [tex](1,2)[/tex].
The given functions are
[tex]f(x)=x^2(x+1)[/tex]
[tex]g(x)=x+1[/tex]
Equating them with each other
[tex]x^2(x+1)=x+1\\\Rightarrow x^2=\dfrac{x+1}{x+1}\\\Rightarrow x^2=1\\\Rightarrow x=\pm 1[/tex]
Substitute the [tex]x[/tex] value in one of the functions.
[tex]x=1[/tex]
[tex]f(1)=1(1+1)=2[/tex]
[tex](1,2)[/tex]
[tex]x=-1[/tex]
[tex]f(-1)=(-1)^2(-1+1)=0[/tex]
[tex](-1,0)[/tex]
The points of intersection are [tex](-1,0)[/tex] and [tex](1,2)[/tex].
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Related Questions
B is the midpoint of AC, D is the midpoint of CE, and AE = 21.
Find BD. The diagram is not to scale.
Please help
Geometry
Answers
Answer:
Required Answer:-[tex]{:}\longrightarrow[/tex][tex]\sf BD={\dfrac {1}{2}}AE [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf BD={\dfrac {1}{2}}21[/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf BD={\dfrac {21}{2}}[/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf BD=10.5cm [/tex]
The line BD will be 10.5cm in the triangle ABC. Thus option D is correct.
What is a triangle?A closed shape with both inner and exterior angles, a triangular is created by three lines. the fundamental geometric shapes. a vertex-filled triangle. There is only one distinct triangle if the product of two fades on the sides is bigger than the longest side.
The value of AE is given as 21.
From the diagram that is given, it is indicated that according to the midpoint theorem
BD║AE
Also, BD= 1/2 ×AE
BD = 21/2
BD = 10.5 cm.
Therefore, option D is the correct option.
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The question is incomplete, the complete question will be :
A. 42
B. 21
C. 11.5
D. 10.5
Classify the following polynomials. Combine any like terms first
2-x² + 4x+x²
x – 5x²+3-2
x²-x²+x²-x²+3
7x-x² + x³+4x²
-6x-x² + 6x-4x
Answers
a. It is a binomial
b. It is a trinomial
c. It is a monomial
d. It is a trinomial
e. It is a binomial
To answer the question, we need to know what polynomials are
What are polynomials?Polynomials are algebraic expressions that contains variables and coefficients.
a.
2 - x² + 4x + x² = 2 - x² + x² + 4x
= 2 - 0 + 4x
= 2 + 4x
Since it has two terms, it is a binomial
b.
x - 5x² + 3 - 2 = x - 5x² + 1
= - 5x² + x + 1
Since it has three terms, it is a trinomial
c.
x² - x² + x² - x² + 3 = 0 + 0 + 3
= 3.
Since this contains a single term, it is a monomial
d.
7x - x² + x³ + 4x² = x³ + 4x² - x² + 7x
= x³ + 3x² + 7x
Since it has three terms, it is a trinomial
e.
-6x - x² + 6x - 4x = -6x - x² + 2x
= - x² + 2x - 6x
= - x² - 4x
Since it has two terms, it is a binomial
a. It is a binomial
b. It is a trinomial
c. It is a monomial
d. It is a trinomial
e. It is a binomial
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For every 1 litre of water used to make a medicine, 199 ml of sucrose and 47 ml of saline solution are used. Express the amount of water, sucrose and saline solution needed as a ratio in its simplest form.
Answers
Answer:
water : sucrose : saline = 1000 : 199 : 271
Step-by-step explanation:
Given Information:
water = 1 litreProcess:
convert everything to mL (same units)1 litre = 1000 mlwater = 1 litre = 1000 mlwater : sucrose : saline = 1000 : 199 : 271Find the value of f(-7).
Answers
Answer:
f(-7) = -4
Step-by-step explanation:
We want to find the value of the function when x = -7
The y value of the function when x= -7 is -4
f(-7) = -4
Answer:
f(-7)=-4
Step-by-step explanation:
If you look at the x, in this case -7, and follow it down to where it stops on the parabola, you will see that it's y value is -4.
PLEASE PLEASE HELP WILL GIVE A LOT OF POINTS!
Answers
Answer:
X-intercept- ( 3/7,0)
Y-intercept- (0,-3)
Step-by-step explanation:
To find the y-intercept(s), substitute in 0 for x and slove for y
y=7(0)-3
simplify y=-3
to find the x-intercept(s), substitute in 0 for y and slove for X
0=7x-3
rewrite equation- 7x-3=0 and slove
which would equal 3/7
please help me this question
Answers
Answer:
(b) or (d)
Step-by-step explanation:
stidents who play basketball = 4y^2 + y - 8 - (2y + 16) = 4y^2 - y - 24
This is a question on forming and solving equations and expressions. If you wish to venture further into it/understand this topic better, you may want to follow my Instagram account (learntionary), where I post some of my own notes on certain topics and also some tips that may be useful to you :)
Answer: Choice (b) 4y^2 - y - 24; top right corner
===========================================================
Work Shown:
T = total number of students in the class
T = 4y^2 + y - 8
F = number of students who play football
F = 2y+16
B = number of students who play basketball
B = unknown for now
Since a student either plays football or basketball, but not both, this means
T = F+B
which rearranges to
B = T-F
Plug in the given expressions and simplify
B = T-F
B = (4y^2+y-8) - (2y+16)
B = 4y^2+y-8 - 2y - 16
B = 4y^2 + (y-2y) + (-8-16)
B = 4y^2 - y - 24
Do I add all the cost up then divide by four?
Answers
Answer:
Yeh that's what you have to do.....
Divide the total amount by four
Answer:
yes
Step-by-step explanation:
137 x 45
Pleze hurry i mite fale
Answers
Answer:
6165
Step-by-step explanation:
Answer:
6165
Step-by-step explanation:
137 × 45 = 6165I hope this helps!
almost due. would appreciate help please :)!!
Answers
the distance between two towns is 300 km two cars start simultaneously from this towns and move towards each other the speed of one car is more than the other by 7 km per hour if the distance between the cars after 2 hours is 34 kilometre find the speed of the cars
Answers
Answer: I think its 131.19, but not too sure.
Step-by-step explanation:
To find the speed, you would do distance/time, so I added 300 and 7. I got 307, then I divided 307 (distance) from 2.34 (time). I got 131.19
Do you want the speed of both cars? then the answer would be:
(300)- first car= 128.20
(307)- second car= 131.19 (if you need to round this answer, it would be 131.2)
solve what is 1 4/5 x 5/6
Answers
Answer:
Step-by-step explanation:
1 4/5*5/6
3/2 or 1 1/2
Write an algebraic rule to describe the relationship in the table.
Answers
Answer:
um idrk lol but I LIKE UR CUT G!!!!
ABC is a central angke in a cirvle with center B. The length of the radius is 13 km and m
Answers
Answer:
[tex]\frac{1170pi}{360m}[/tex]km
Step-by-step explanation:
To find the length of the minor arc, you find the circumference of the circle multiplied by the arc angle, which is [tex]\frac{45}{m}[/tex] over 360 degrees.
Circumference of the circle with center B = 13×2×pi
= 26pi
Length of minor arc = 26pi × [tex]\frac{45}{m}[/tex] ×[tex]\frac{1}{360}[/tex]
= [tex]\frac{1170pi}{360m}[/tex]km
How do I Find x, y and z
Answers
Answer: to solve the 3 unknown variables X, Y and Z in a set of 3 equations. Each equation has containing the unknown variables X, Y and Z. This 3 equations 3 unknown variables solver computes the output value of the variables X and Y with respect to the input values of X, Y and Z coefficients. In mathematic calculations, there are many situation arises where the usage of equation containing 3 unknown variables need to be solved prior to go further with the calculations. Therefore when it comes to online calculation, this Find the value of X, Y and Z calculator is an essential tool to assist you to find out the variable values given in the equation.
Step-by-step explanation: X = 2
Y = -1
Z = 1
1.) We can write a equation of a line when we know only the slope and the _____________ of any point of the line.
2.) Given only two points, it is easy to find the equation of the line when you find first the _______________.
Answers
Answer:
1) coordinates
2) slope
Step-by-step explanation:
The equation of a line is given by the two equations:
[tex]y=mx+b[/tex], where m is the slope and b is the y-intercept, or
[tex]y-y_1=m(x-x_1)[/tex], where x₁ and y₁ is the location of any point on the line, and m is the slope.
→ As such, we know that given the slope and the coordinates of any point on a line, we can write the line's equation.
We can also find the slope of a straight line between two points with the following equation:
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex], where m is the slope, x1 and y1 is the location of the first point, and x2 and y2 is the location of the second point. Remember: rise (y) over run (x).
→ So, given only two points, it is easy to find the equation of the line when you first find the slope.
Find a solution to the system. Make sure to write as a coordinate.
Answers
Answer:
x=2, y=3
Step-by-step explanation:
This is a system of equations.
To solve a system of equations, we use the substitution method.
We can plug in the first equation, [tex]x=2y-4[/tex], into the value for x in the second equation. Now, the second equation looks like this:
[tex]2*(2y-4)+y=7[/tex]
We simplify and solve for y:
→ [tex]4y-8+y=7[/tex]
→ [tex]5y=15[/tex]
→ [tex]y=3[/tex]
Now, we plug in the value for y, which is 3, into either equation. I will just use the first equation:
→ [tex]x=2*3-4[/tex]
→ [tex]x = 2[/tex]
Let me know if my explanation is unclear.
Taylor plans to borrow $4,500 from the bank to purchase a used vehicle. If he borrows the money at a rate of 4% interest for 2 years, what is the total amount he will have to pay back to the bank?
Answers
Answer:
$4867.2
Step-by-step explanation:
How do I solve this equation?
Answers
Answer:
X = 4 X = -6
Step-by-step explanation:
X + 1 = 5 X + 1 = -5
X = 5 - 1 X = -5 -1
X = 4 X = -6
Answer:
Step-by-step explanation:
What absolute values of x will fit.
l4+1l=5
l -6+1l=5
Hi, anyone able to help with qn 7? Thanks :)!
Answers
Answer:
Step-by-step explanation:
I used the quadratic formula to find the roots of [tex]x^{2} + x -1[/tex]
[tex]a=\frac{-1-\sqrt{5}}{2} b=\frac{-1+\sqrt{5} }{2}[/tex]
[tex]\frac{1 }{\sqrt{3} } *(\frac{-1-\sqrt{5}}{2} )^{2} * \frac{-1+\sqrt{5}}{2}[/tex]
[tex]\frac{1 }{\sqrt{3} } *(\frac{-1-\sqrt{5}}{2} ) * \frac{-1+\sqrt{5}}{2}*(\frac{-1-\sqrt{5}}{2} )[/tex]
[tex]\frac{1 }{\sqrt{3} } *(\frac{-1-\sqrt{5}}{2} ) * \frac{-1+\sqrt{5}-\sqrt{5} -4}{4}[/tex]
[tex]\frac{1 }{\sqrt{3} } *(\frac{-1-\sqrt{5}}{2} ) * \frac{ -4}{4}[/tex]
[tex]\frac{1 }{\sqrt{3} } *(\frac{-1-\sqrt{5}}{2} ) * -1[/tex]
[tex]\frac{-1-1\sqrt{5} }{2\sqrt{3} }*-1[/tex]
[tex]\frac{-1-1\sqrt{5} }{2\sqrt{3} } = \frac{\sqrt{5}+1 }{2\sqrt{3} }[/tex]
HELP ASAP!!!!!!!!!!!!!!!!
Answers
Answer:
160
Step-by-step explanation:
20% of 800 = 0.20 * 800 = 160
Hey can someone please help quickly thanks!
Answers
Answer:
360,000
Step-by-step explanation:
just multiply by 3
Answer:
3,120 second year 3,244.80 the third year.
Step-by-step explanation:
4% of 3,000 is 120
so 3,120 then 3,244.80 the third year after the 4% is compounded
ASAP PLS!! BRAINLIEST GIVIN!!
Answers
Step-by-step explanation:
( 0,4 ) is the point in the graph
At the beginning of the season, Jamie pays full price for a ticket to see the Panthers, her favorite baseball team. the panthers currently have 33 wins and 31 losses. A. Represent the total change in the cost of a ticket given their losses B.What is the cost of a ticket for the nest game they play. (A or B question)
Answers
Answer: a. -$12.71
b. $36.93
Step-by-step explanation:
Given data:
No of loss = 31
No of wins = 33
•Had to complete the question first,
Given that the price of the ticket at the beginning of the season = $49.64
the ticket price decrease = $0.41 for every loss
Solution:
a) The cost of the ticket decreases by $0.41 for every game loss.
Change in cost = -$0.41 × number of losses
= -$0.41 × 31
= -$12.71
b) The cost of a ticket for the next game given they have 31 losses is:
Cost of ticket = Initial cost of ticket + change in cost
= $49.64 - $12.71
= $36.93
Davaughn has 24 coins that are all dimes and quarters. The value of the coins is $3.75. How many dimes and how many quarters does Davaughn have?
Answers
Answer: 9 quarters and 5 dimes
Step-by-step explanation:
What effect can be observed because of the gravitational pull between Earth and the moon.
HURRY THIS IS DUE IN 11 MINUTES! I NEED ANSWERS ASAP!!!!!
Answers
Answer:
The moon's gravitational pull on the Earth is the main cause of the rise and fall of ocean tides.
Step-by-step explanation:
The moon's gravitational pull causes two bulges of water on the Earth's oceans—one where ocean waters face the moon and the pull is strongest and one where ocean waters face away from the moon and the pull is weakest.
Hope it helped!!
Which of the following can be used to find the measure of angles
Answers
How would I unrationalize this fraction?
I am trying to find the cotangent in simplest form
Answers
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[tex] \cot(teetha) = - 1[/tex]
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The cotangent in simplest form is -1.
What is trigonometry?Trigonometry is mainly concerned with specific functions of angles and their application to calculations. Trigonometry deals with the study of the relationship between the sides of a triangle (right-angled triangle) and its angles.
For the given situation,
cos θ = √2 / 2
We know that from trigonometric ratio,
[tex]cos \theta = \frac{Adjacent}{Hypotenuse}[/tex] , [tex]cot \theta = \frac{Adjacent }{ Opposite }[/tex]
So, the adjacent side = √2 and the hypotenuse side = 2.
The other side of the right triangle can be found by Pythagoras theorem,
[tex]hypotenuse^{2}=adjacent^{2}+opposite^{2}[/tex]
⇒ [tex]2^{2}=(\sqrt{2} )^{2} +opposite^{2}[/tex]
⇒ [tex]opposite^{2} = 4-2[/tex]
⇒ [tex]opposite = \sqrt{2}[/tex]
Thus, [tex]cot \theta = \frac{\sqrt{2} }{\sqrt{2} }[/tex]
⇒ [tex]cot \theta = 1[/tex]
Since cot θ < 0, [tex]cot \theta = - 1[/tex]
Hence we can conclude that the cotangent in simplest form is -1.
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How many times smaller is a group of 4 coins than a group of 16 coins?
Answers
Answer:
4 times.
Step-by-step explanation:
16/4 = 4.
Hope this helped!
simplify 5/4+4(3/4−1/2)^2
Answers
Step-by-step explanation:
5/4+(12/4_1/2)^2
5/4+((12_8)/4)^2
5/4+1
9/4
Answer:
[tex]\frac{3}{2}[/tex]
Step-by-step explanation:
Given
[tex]\frac{5}{4}[/tex] + 4 ([tex]\frac{3}{4}[/tex] - [tex]\frac{1}{2}[/tex] )²
= [tex]\frac{5}{4}[/tex] + 4 ([tex]\frac{1}{4}[/tex] )²
= [tex]\frac{5}{4}[/tex] + 4 × [tex]\frac{1}{16}[/tex]
= [tex]\frac{5}{4}[/tex] + [tex]\frac{1}{4}[/tex]
= [tex]\frac{6}{4}[/tex]
= [tex]\frac{3}{2}[/tex]
Explain what is happening at this step in the solving equation process.
1. 10 − 6 x = 4 + 5 x
2. 7-6x=1+5x
Answers
Answer:
1. After solving we get value of x: [tex]\mathbf{x=\frac{6}{11} }[/tex]
2. After solving we get value of x: [tex]\mathbf{x=\frac{6}{11} }[/tex]
Step-by-step explanation:
We need to Solve the equations.
1. [tex]10 - 6 x = 4 + 5 x[/tex]
Step 1: Subtract 5x on both sides
[tex]10 - 6 x-5x = 4 + 5 x-5x\\10-11x=4[/tex]
Step 2: Subtract 10 on both sides
[tex]10-11x-10=4-10\\-11x=-6[/tex]
Step 3: Divide both sides by -11
[tex]\frac{-11x}{-11}=\frac{-6}{-11}\\x=\frac{6}{11}[/tex]
So, after solving we get value of x: [tex]\mathbf{x=\frac{6}{11} }[/tex]
2. [tex]7-6x=1+5x[/tex]
Step 1: Subtract 5x on both sides
[tex]7 - 6 x-5x = 1 + 5 x-5x\\7-11x=1[/tex]
Step 2: Subtract 7 on both sides
[tex]7-11x-7=1-7\\-11x=-6[/tex]
Step 3: Divide both sides by -11
[tex]\frac{-11x}{-11}=\frac{-6}{-11}\\x=\frac{6}{11}[/tex]
So, after solving we get value of x: [tex]\mathbf{x=\frac{6}{11} }[/tex]