Which graph represents the function f(x) = x2 + 3x + 2?
graph 1
graph 2
graph 3
graph 4
Answers
Answer:
Graph 1
Step-by-step explanation:
Here, the given equation is,
[tex]f(x)=x^2+3x+2-----(1)[/tex]
For x-intercept, f(x) = 0
[tex]x^2+3x+2=0[/tex]
[tex]x^2+2x+x+2=0[/tex]
[tex]x(x+2)+1(x+2)=0[/tex]
[tex](x+1)(x+2)=0[/tex]
[tex]\implies x=-1\text{ or } -2[/tex]
So, the x-intercept of the function are (-1,0) and (-2,0)
Since, the line must has at least one x-intercept.
⇒ Graph 2 and Graph 4 can not be the graph of the given function,
Also, for y-intercept,
Put x = 0 in equation (1),
We get, f(x) = 2,
Hence, the y-intercept of the given function is (0,2),
But in Graph 3 the y-intercept of the function = (0,1)
⇒ Graph 3 can not be the graph of the given function,
Therefore, Graph 1 is the correct graph of the given function.
Related Questions
The table below shows the surface area y, in square inches, of a shrinking puddle in x hours: Time (x) (hours) 1 4 7 10 Surface area (y) (square inches) 100 85 70 55 Part A: What is the most likely value of the correlation coefficient of the data in the table? Based on the correlation coefficient, describe the relationship between time and surface area of the puddle. [Choose the value of the correlation coefficient from −1, −0.99, −0.5, −0.02.] (4 points) Part B: What is the value of the slope of the graph of surface area versus time between 1 and 4 hours, and what does the slope represent? (3 points) Part C: Does the data in the table represent correlation or causation? Explain your answer. (3 points)
Answers
Part A. The correlation coefficient, R², is the quantitative evaluation of how the data points are well-fitted to a model. The closer it is to 1, the better. But a R²=1 is very ideal and rare. This can be only true if the points coincides exactly with the given model. Since we can see in the graph that the points are exaclty passed through by the linear model, the correlation coefficient is 1.
Part B. The slope of the graph is measured between two points as Δy/Δx. So, between 1 to 4 hours, the slope is: (85-100)/(4-1) = -5. The slope represents the instantaneous rate of change of surface area with time. It is called instantaneous because the change was only between than interval, not the whole set of data. Also, the negative sign signifies that the trend is decreasing.
Part C. The data represents causation if the time was the cause of the change of the pond's surface area. However, this is not technically true because there might be other factors to be considered like environmental conditions. But, definitely, these data are in correlation because together they show an observable trend.
How do you solve all of these ?
Answers
[tex]\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ 5}}\quad ,&{{ -3}})\quad % (c,d) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies -1 \\\\\\ % point-slope intercept y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-(-3)=-1(x-5) \\ \left. \qquad \right. \uparrow\\ \textit{point-slope form} \\\\\\ y+3=-x+5\implies y=-x+2[/tex]
6)
[tex]\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ 2}}\quad ,&{{ 1}})\quad % (c,d) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies 3 \\\\\\ % point-slope intercept y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-1=3(x-2) \\ \left. \qquad \right. \uparrow\\ \textit{point-slope form} \\\\\\ y-1=3x-6\implies y=3x-5[/tex]
7)
[tex]\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ 5}}\quad ,&{{ 2}})\quad % (c,d) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies 0 \\\\\\ % point-slope intercept y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-2=0(x-5) \\ \left. \qquad \right. \uparrow\\ \textit{point-slope form} \\\\\\ y-2=0\implies y=2[/tex]
8)
[tex]\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ -2}}\quad ,&{{ 0}})\quad % (c,d) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{5}{2} \\\\\\ % point-slope intercept y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-0=\cfrac{5}{2}(x-(-2)) \\ \left. \qquad \right. \uparrow\\ \textit{point-slope form} \\\\\\ y=\cfrac{5}{2}(x+2)\implies y=\cfrac{5}{2}x+5[/tex]
9)
[tex]\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ -2}}\quad ,&{{ 0}})\quad % (c,d) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{5}{2} \\\\\\ % point-slope intercept y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-0=\cfrac{5}{2}(x-(-2)) \\ \left. \qquad \right. \uparrow\\ \textit{point-slope form} \\\\\\ y=\cfrac{5}{2}(x+2)\implies y=\cfrac{5}{2}x+5[/tex]
10)
[tex]\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{-2}}\quad ,&{{ -2}})\quad % (c,d) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{3}{2} \\\\\\ % point-slope intercept y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-(-2)=\cfrac{3}{2}(x-(-2)) \\ \left. \qquad \right. \uparrow\\ \textit{point-slope form} \\\\\\ y+2=\cfrac{3}{2}(x+2)\implies y+2=\cfrac{3}{2}x+3\implies y=\cfrac{3}{2}x+1[/tex]
I need help with geometry.
Answers
In any trapezoid, the length of the midsegment is [tex] \frac{|base_1|+|base_2|}{2} [/tex]
substituting the known values:
[tex] \frac{24+|base_2|}{2}=19 [/tex]
[tex]24+|base_2|=38[/tex]
[tex]|base_2|=38-24=14[/tex]
2.
Notice that since D and have the same y-coordinate, then DE is horizontal, and since F and D have the same x-coordinate, FD is vertical.
Thus FD and DE are perpendicular, so the triangle FED is a right triangle.
The median drawn from the right angle, is equal to half the hypotenuse.
That is, |DO|=1/2 |FE|, thus |OE|=|OF|=|OD|, are all radii of the circle centered at O.
O is the midpoint of EF, and is found by the Midpoint formula:
[tex]O=( \frac{1+7}{2} , \frac{5+1}{2} )=(4, 3)[/tex]
Answer:
1. 14
2. (4, 3)
If 300 cm^2 of material is available to make a box with a square base and an open top, find the maximum volume of the box in cubic centimeters. Answer to the nearest cubic centimeter without commas. For example, if the answer is 2,000 write 2000.
Answers
Assume a the side of the base, b the height.
[tex]V=a^2*b\\ a^2+4ab=300==\ \textgreater \ b= \dfrac{300-a^2}{4a} \\ V=a^2*\dfrac{300-a^2}{4a}= \frac{1}{4} *(300a-a^3)\\ \dfrac{dV}{da} = \frac{1}{4} *(300-3*a^2)=0\\ ==\ \textgreater \ a=10 \ and\ b=5\\ V=10^2*5=500\\ [/tex]
The sum of 3 consecutive even numbers is 78
Answers
3x+6=78
3x=72
x=24
Final answer: 24, 26, 28
You have a total of 21 coins, all nickles and dimes. The total value is $1.70 Which of the following is the system of linear equations that represent this scenario? Let n= the number of nickles and let d= the number of dimes.
Answers
n+d=21
Secondly, you need one equation for the numerical value of those nickels and dimes. We know nickels are worth $0.05 and dime are worth $0.10:
.05n+.1d=1.70
In parallelogram ABCD, if angle C=110 and angle D=70, what is the sum of the measures of angle A and angle B?
Answers
To solve this problem, we must remember that the sum of interior angle of a polygon is:
Sum of interior angles = (n – 2) * 180˚
So, we can say that:
Sum of interior angles = angle A + angle B + angle C + angle D = (4 – 2) * 180˚
Where,
angle C + angle D = 110 + 70 = 180˚
Therefore substituting this value:
angle A + angle B + 180˚ = 2 * 108˚
angle A + angle B = 360˚ - 180˚
angle A + angle B = 180˚ (answer)
Hence we can also conclude that,
angle A + angle B = angle C + angle D
The answer is 180 degrees because...
angle A + angle B + 180˚ = 2 * 108˚
angle A + angle B = 3
angle A + angle B = 180˚ 60˚ - 180˚
Hope this helps, have a BLESSED and wonderful day! As well as as a safe one! :-)
-Cutiepatutie ☺❀❤
The formula used to calculate simple interest is modeled by I=prt, where I=simple interest, p=principle, r=interest rate, and t=time, measured in years. Which of the following options represent(s) an alternative equivalent version of the simple interest formula? select all that apply....TY
I = trp
I = p + rt
I - rt = p
t= l/rp
p= l/rt
Answers
I = trp
t= l/rp
p= l/rt
Step-by-step explanation:
The formula for simple interest is as follows.
I = prt
where, I = simple interest
p = principle
r = rate
t = time
This formula can be alternatively written by shifting I, r, t, and p either on the right or left side of equals sign.
Therefore, the formula can be rewritten as follows.
I = trp[tex]t = \frac{I}{rp}[/tex] [tex]p = \frac{I}{rt}[/tex]What is the 32nd term of the arithmetic sequence where a1 = 4 and a6 = 34 ?
Answers
the nth term of an arithmetic sequence is :
An =Ap+(n-p)d ....a common difference is : d
in thie exercice : p=1 and n=6
A6 = A1 + (6-1)d
34 = 4 +5d
5d= 30
d= 6
A32 = A1+(32-1)(6) =4 + 31(6) = 190
What is the probability of flipping a penny and a nickel and obtaining one head and one tail?
Answers
Final answer:
The probability of flipping a penny and a nickel and obtaining one head and one tail is 0.25, or 25%.
Explanation:
The probability of flipping a penny and a nickel and obtaining one head and one tail can be calculated by multiplying the probabilities of getting a head on one coin and a tail on the other coin. Since the chance of getting a head on a fair coin is 0.5 and the chance of getting a tail is also 0.5, the probability of getting one head and one tail is:
Probability = (Probability of getting a head on the penny) × (Probability of getting a tail on the nickel)
Probability = 0.5 × 0.5 = 0.25, or 25%.
A 125-inch pipe is cut into two pieces. one piece is four times the length of the other. find the lengths of the two pieces.
Answers
You can calculate the length of the two pieces of pipe by setting up and solving a simple equation: 'x' stands for the length of the shorter piece, '4x' stands for the length of the longer piece, which will add up to the total length, 125 inches. You will find that 'x' equals 25, meaning the shorter pipe is 25 inches long and the longer one is 100 inches long.
Explanation:This question revolves around a simple equation in algebra. If we say that the shorter piece of pipe's length is 'x', we know from the problem that the longer piece's length is four times this length, or '4x'. The total length of the pipe, 125 inches, is made up of these two pieces. Therefore, those two lengths must add up to 125 inches.
This gives us the equation 'x + 4x = 125'. Combining like terms gives us '5x = 125'. To find 'x', we then divide both sides of the equation by 5, giving us 'x = 25'. Therefore, the shorter piece of pipe is 25 inches long, and the longer piece, being four times this length, is 100 inches long.
Learn more about Equation Solving here:https://brainly.com/question/19297665
#SPJ2
Which of the following points is in the solution set of y>-x^2+5?
A. (0,5)
B. (1,3)
C. (2,4)
Answers
Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = -5 - 5 cos θ
Answers
-5-5cos(theta)=r
-r=5+5cos(theta)
no y-axis symmetry
x-axis symmetry=(r,theta)=(r,-theta)
cosine is an even function, so yes it is symmetric around x-axis
origin symmetry=(r,theta)=(-r,theta) or (r, theta+pi)
no, as there is no y-axis symmetry
Answer:
x-axis symmetry
Step-by-step explanation:
If a 72-candela light source is located at a distance of 3 meters from a surface, the illuminance on the surface is _______ lux.
Answers
The answer is 8 lux. Using the formula E= I/s^2, E stands for the illuminance on the surface that we are trying to solving, I stands for the intensity of the light from the sources it is candelas in the problem that we’re solving, and S stands for the distance from the light source to the surface it should be in meters.
E= I/s^2
E= 72/3^2
E=72/9
E= 8
Answer:
Penn Foster Students: 8
Step-by-step explanation:
A girl scout troop sold cookies. If the girls sold 5 more boxes the second week than they did the first, and if they doubled the sales of the second week for the third week to sell a total of 431 boxes of cookies, how many did they sell each week?
Answers
week1 = x
week2 = x+5
week3 = 2(x+5)
x + (x+5) + 2(x+5) = 431
x + x + 5 + 2x + 10 = 431
4x + 15 = 431
4x = 431 - 15
4x = 416
x = 104
week1 = x = 104 boxes
week2 = x+5 = 104+5 = 109 boxes
week3 = 2(x+5) = 2(104+5) = 2*109 = 218 boxes
What are the solutions of the equation 2x2=2 use a graph of the related function
Answers
2x² = 2
x² = 1
x = √1
x = 1
The solution is both -1 and 1 and the graph is shown below
Answer:
[tex]x=-1\text{ or }x=1[/tex]
Step-by-step explanation:
We have been given an equation [tex]2x^2=2[/tex]. We are asked to find the solutions of our given equation.
First of all, let us divide both sides of our equation by 2.
[tex]\frac{2x^2}{2}=\frac{2}{2}[/tex]
[tex]x^2=1[/tex]
Upon taking square root of both sides of our equation we will get,
[tex]x=\sqrt{1}[/tex]
[tex]x=\pm 1[/tex]
[tex]x=-1\text{ or }x=1[/tex]
Therefore, [tex]x=-1\text{ or }x=1[/tex] are two solutions for our given function.
The base of a triangle measures (3x − 6) units and the height measures (2x + 4) units. Part A: What is the expression that represents the area of the triangle? Show your work to receive full credit. (4 points) Hint: Area = 0.5bh Part B: What are the degree and classification of the expression obtained in Part A? (3 points) Part C: How does Part A demonstrate the closure property for polynomials? (3 points)
Answers
To answer this item, we use the equation given for the calculation of the area of the triangle.
A = 0.5bh
Substituting the known expressions,
A = (0.5)(3x – 6)(2x + 4)
Part A: Use distribution method to simplify the expression for the calculation of area.
A = 0.5(6x^2 + 12x – 12x – 24)
A = 0.5(6x^2 – 24)
A = 3x^2 – 12
Part B: The equation for area of has a degree of two because the highest exponent is 2.
Part C: The closure property of polynomials is always closed for multiplication.Answer With Step-by-step explanation:
Part A:
.5[ (3x – 6) (2x + 4) ]
.5(6x^2 - 24)
3x^2 - 12
Part B:
Second Degree Binomial
Part C:
For Part A, a polynomial was multiplied by another polynomial. The resulting product was a polynomial. This is a demonstration of the closure property for multiplying polynomials.
Harmony can spend up to $100 on a shopping trip. She needs to buy socks and shoes. Each pair of socks costs $5.00 and each pair of shoes costs $20.00. Which graph shows all of the ways she can purchase shoes and socks, spending up to $100?
Answers
4y+x≤20 subtract x from both sides
4y≤-x+20 divide both side by 4
y≤-0.25x+5
So just in simplest terms, the slope is slightly negative and it should be shaded under the line since y is less than the line...so it is the second graph.
A hair-styling salon charges $11.00 for a haircut, and an average of 75 people stop in for haircuts each day. The owner is thinking of increasing the price, and he estimates that every time he raises the price of a haircut by $1.00, the number of people coming in for haircuts will decrease by 3 per day. Which of these functions represents the estimated revenue per day from haircuts as a function of the number of dollars the price of a haircut is raised?
Answers
The estimated daily revenue function, given the described price increase and corresponding customer decrease, can be represented as R(x) = (11 + x)(75 - 3x), where x is the number of dollars by which the price is raised.
Explanation:The question asks us to find a function that represents the estimated revenue per day from haircuts as a function of the number of dollars the price of a haircut is raised. Initially, the salon charges $11.00 for a haircut with an average of 75 people per day. When the price increases by $1, the number of customers decreases by 3.
Let x represent the number of dollars by which the haircut price is raised. The new price will be $11.00 + x. The number of customers is initially 75, and for each $1 increase, we lose 3 customers, so the new number of customers will be 75 - 3x. The daily revenue, R(x), can be found by multiplying the new price by the new number of customers:
R(x) = (11 + x)(75 - 3x)
This function will give us the estimated daily revenue after increasing the haircut price by x dollars.
You decide to put $150 in a savings account to save for a $3,000 down payment on a new car. If the account has an interest rate of 2.5% per year and is compounded monthly, how long does it take you to earn $3,000 without depositing any additional funds?
10.1101 years
119.954 years
121.321 years
134.34 years
Answers
A=p (1+r/k)^kt
3000=150 (1+0.025/12)^12t
Solve for t
3000/150=(1+0.025/12)^12t
Take the log
Log (3000/150)=12t×log (1+0.025/12)
12t=Log (3000/150)÷log (1+0.025/12)
T=[Log (3000/150)÷log (1+0.025/12)]÷12
T=(log(3,000÷150)÷log(1+0.025÷12))÷12
T=119.954 years
What are the solutions of 2x^2+3x=-8
Answers
2x² + 3x + 8 = 0
The quadratic formula used for the determination of the roots is,
x = (-b +/- sqrt (b² - 4ac)) / 2a
In the quadratic equation above, we have the numerical coefficients.
a = 2
b = 3
c = 8
Substituting the known values,
x = (-3 +/- sqrt (3² - 4(2)(8))/ (2)(2)
x = -0.75 + 1.854i and x = -0.75 - 1.854i
By the calculated roots above, it is known that the roots are imaginary.
The surface areas of two similar solids are 289 ft2 and 900 ft2. The volume of the larger solid is 1,755 ft3. What is the volume of the smaller solid?
Answers
There were n balloons at the beginning of the party. By the end of the party, 5 of them had popped. Using n, write an expression for the number of balloons that were left
Answers
Answer:
The expression for the number of balloons that were left is [tex]n-5[/tex].
Step-by-step explanation:
There were n balloons at the beginning of the party.
By the end of the party, 5 of them had popped.
Let the remaining balloons be represented by x
So, x = total balloons minus 5
This gives: [tex]x=n-5[/tex]
Therefore, the expression for the number of balloons that were left is [tex]n-5[/tex].
Given the function f(x), you can get a picture of the graph of it inverse F^-1(x) by flipping the original graph f F(x) over the _____.
A. y=-1
B x= -1
C y=x
Answers
y=x
Answer:
y=x
Step-by-step explanation:
apex
The size of a television is usually indicated by the length of the screens diagonal if a person buys a 20 inch television set that is 12 inches tall how wide is the television
Answers
diagonal = sqrt(a^2 +b^2)
20 = sqrt(12^2 +b^2)
20= sqrt(144+b^2)
20^2 = 144 + b^2
400 = 144 + b^2
256 = b^2
b = sqrt(256) = 16
it is 16 inches wide
A scientist begins an experiment with a petri dish containing a culture of bacteria cells and records the cell growth every hour. At 1 hour, the bacteria had grown to 880 cells, and at 2 hours, had grown to 3,520 cells. Which function can be used to represent the relationship between the number of bacteria cells, y, and the time in hours, x?
y = 4 x
y = 220(4) x
y = 880(4) x
y = 880(0.25) x
Answers
3520 = 220(4)2
B is correct choice.
Answer:
B
Step-by-step explanation:
OQ is a diagonal of quadrilateral NOPQ. If NO=PQ, NQO=7y-37, and POQ=2y+93, find POQ such that NOPQ is a parallelogram. A.26° B.63° C.97° D.145°
Answers
its not 26.
Just saying
its D. 145
Answer: D! 145!
Step-by-step explanation:
your almost done!!! Ah good luck xoxo
To raise money for charity,Polly climbs the 1,776 steps in the CN Tower in Toronto,Canada.If it takes her 40 minutes to complete the climb,what is Polly's average rate per minute?
Answers
*WILL GIVE BRAINLIEST*(08.03)Consider the following set of equations:
Equation A: y = 2x + 4
Equation B: y = 3x + 1
Which of the following is a step that can be used to find the solution to the set of equations?
2x + 4 = 3x + 1
2x = 3x + 4
2x + 4 = 3x
2x + 1 = 3x + 4
Answers
Finding the solution step by step:
Given- Equation A: y=2x+4; Equation B: y=3x+1
y=y, so 2x+4=3x+1
Get variables on one side and numbers on the other..
4-1=3x-2x
3=x
Substitute x into one of the equations (doesn't matter which): y= 2(3)+4
y=6+4
y=10
Solution- (3,10)
Hope the explanation helped!
Find cos θ if sin θ = negative twelve divided by thirteen and tan θ > 0. negative five divided by twelve negative five divided by thirteen twelve divided by five negative thirteen divided by twelve
Answers
Sin∅=opposite side / hypotenuse, in a right triangle, as shown in the figure.
In this triangle, the length of the hypotenuse is 13, the length of one side 12, and the other side can be found by the Pythagorean theorem to be:
[tex] \sqrt{13^{2} - 12^{2} }= \sqrt{169-144}= \sqrt{25}=5 [/tex]
2.
The value of the cosine is (adjacent side)/(hypotenuse)=5/13.
3.
The tangent is positive in the first and third quadrants.
Since Tan=Sine/Cosine, and Sine is negative, then cosine must be negative as well
Answer: -5/13