8.
Fit a quadratic function to these three points:
(−2, 8), (0, −4), and (4, 68)
A. y = −2x2 − 2x − 4
B. y = −2x2 + 2x − 4
C. y = 4x2 + 2x − 4
D. y = −4x2 − 2x − 4
Answers
Answer: y= 4x² +2x -4
C. y = 4x2 + 2x − 4
Step-by-step explanation: f(x)=4x^2+2x-4
Given three points
P1(-2,8)
P2(0,-4)
P3(4,68)
We need the quadratic equation that passes through all three points.
Solution:
We first assume the final equation to be
f(x)=ax^2+bx+c .............................(0)
Observations:
1. Points are not symmetric, so cannot find vertex visually.
2. Using the point (0,-4) we substitute x=0 into f(x) to get
f(0)=0+0+c=-4, hence c=-4.
3. We will use the two other points (P1 & P3) to set up a system of two equations to find a and b.
f(-2)=a(-2)^2+b(-2)-4=8 => 4a-2b-4=8.................(1)
f(4)=a(4^2)+b(4)-4=68 => 16a+4b-4=68.............(2)
4. Solve system
2(1)+(2) => 24a+0b-12=84 => 24a=96 => a=96/24 => a=4 ......(3)
substitute (3) in (2) => 16(4)+4b-4=68 => b=8/4 => b=2 ..........(4)
5. Put values c=-4, a=4, b=2 into equation (0) to get
f(x)=4x^2+2x-4
Check:
f(-2)=4((-2)^2)+2(-2)-4=16-4-4=8
f(0)=0+0-4 = -4
f(4)=4(4^2)+2(4)-4=64+8-4=68
So all consistent, => solution ok.
...............................................................................................................................................
Answer:
y = 4x² + 2x − 4
Step-by-step explanation:
The y-values go down and up again, so the parabola opens upward. That means the x² coefficient must be positive. All answer choices are eliminated except one.
y = 4x² +2x -4
There are other ways to get the answer. One of them is to use the quadratic regression function of a spreadsheet or graphing calculator. The one attached shows the points are matched by the equation ...
y = 4x² +2x -4 . . . . . as above
...............................................................................................................................................
Related Questions
Second Graph problem! Can anybody please help me out with this? (Almost done for today) (Algebra graph problem)
Answers
Answer:
x = -2
Step-by-step explanation:
The expression f(x) = 1 corresponds to the point on the graph that is 1 unit above the x-axis. You can locate that horizontal line and see where it intersects the graph. That point of intersection is 2 grid squares to the left of the y-axis, where x = -2.
f(-2) = 1
x = -2
In a math class, the teacher asked the students to find the approximate value of one of the x-coordinates of a point of intersection of two functions: f(x) = 2x2 − 3x + 4 g(x) = 5x − 1 Her students gave her different answers. Which answer is the most accurate?
A.
0.8
B.
0.9
C.
1.9
D.
1.1
Answers
Answer:
A. 0.8Step-by-step explanation:
An easy way is to substitute values into both equations and compare:
A. x = 0.8
f(x) = 2(0.8)² - 3(0.8) + 4 = 2.88g(x) = 5(0.8) - 1 = 3B. x = 0.9
f(x) = 2(0.9)² - 3(0.9) + 4 = 2.92g(x) = 5(0.9) - 1 = 3.5C. x = 1.9
f(x) = 2(1.9)² - 3(1.9) + 4 = 5.52g(x) = 5(1.9) - 1 = 8.5D. x = 1.1
f(x) = 2(1.1)² - 3(1.1) + 4 = 3.12g(x) = 5(1.1) - 1 = 4.5As we see the most accurate one is A
Let's graph both function(Attached)
Let's round 0.775
[tex]\\ \sf\longmapsto 0.775[/tex]
[tex]\\ \sf\longmapsto 0.77[/tex]
[tex]\\ \sf\longmapsto 0.8[/tex]
Option A is correct
❗❗CORRECT ANSWER+EXPLANATION=BRAINLIEST❗❗
Simplify: (question in the pic)
Answers
The simplified form of the function is [tex]f(x) = \frac{x+3}{x}[/tex]
Functions and equationGiven the following function as shown:
[tex]f(x)=\frac{x^2-9}{x^2-3x}[/tex]
This can be factorized as:
[tex]f(x)=\frac{x^2-3^2}{x(x-3)}\\f(x)= \frac{(x+3)(x-3)}{x(x-3)} \\[/tex]
Cancel out the common terms:
[tex]f(x) = \frac{x+3}{x}[/tex]
Hence the simplified form of the function is [tex]f(x) = \frac{x+3}{x}[/tex]\
Learn more on functions here: https://brainly.com/question/10439235
Hi Phoenix! :)
I'm much late lol.
Answer:
[tex]\boxed{ \cfrac{x + 3}{x}} [/tex]
Step-by-step explanation:
Given:
[tex] \cfrac{x {}^{2} - 9}{x {}^{2} - 3x } [/tex]
Solution:
[Here the best option is to factorise the expression.]
Rewrite the numerator of the expression as
[tex] \cfrac{x {}^{2} - 3 {}^{2} }{x {}^{2} - 3x} [/tex]
It can be seen that the numerator is like an algebraic identity:
> a² - b² = (a+b)(a-b)
ATP, numerator : a = x² and b = 3²
[tex] \cfrac{(x + 3)(x - 3)}{ {x}^{2} - 3x} [/tex]Now in the denominator take x common:
[tex] \cfrac{(x + 3)(x - 3)}{x(x - 3)} [/tex](x-3) in the denominator and (x-3) in the numerator gets canceled.
[tex] \cfrac{(x + 3) \cancel{(x - 3)}}{x \cancel{(x - 3)}} [/tex][tex] \boxed{\cfrac{x + 3}{x} }[/tex]Welp,Done, that's it! :D
At football practice on Monday, Brandon threw a football into the target 5 times. The next Monday, he tripled the number of targets he hit. On the following Monday, his hits double that of the week before. Write and evaluate a numerical expression to find how many times he hit the target during those three weeks.
Enter the correct answers in the boxes.
Expression:
Answers
Answer:
try using a different app, it helps with all types of mathematical equations
helpppp pleaseeeee✋
Answers
Answer:
5 x 3 = 15 / 4 x 8 = 32 / 6 x 1.5 = 9
Step-by-step explanation:
Answer:3,8,3/2
Step-by-step explanation:
1) 5*x=15
X=15/5=3
2) 4*x=32
X=32/4=8
3)
6*x=9
X=9/6=3/2
Last year, Dante had $10,000 to invest. He invested some of it in an account that paid 7% simple interest per year, and he invested the rest in an account
that paid 8% simple interest per year. After one year, he received a total of $730 in interest. How much did he invest in each account?
Answers
a = amount invested at 7%
b = amount invested at 8%
we know that total that he invested was 10000, therefore a + b = 10000.
hmmm how muich is 7% of "a"? well (7/100) * a => 0.07a.
how much is 8% of "b"? well (8/100) * b => 0.08b.
After a year he received in interest $730, so we know that at simple interest rate, 0.07a + 0.08b = 730.
[tex]\begin{cases} a+b=10000\\ 0.07a+0.08b=730\\[-0.5em] \hrulefill\\ b = 10000 - a \end{cases}\qquad \stackrel{\textit{substituting on the 2nd equation}}{0.07a+0.08(10000-a) = 730} \\\\\\ 0.07a+800-0.08a=730\implies 0.07a-0.08a=-70\implies -0.01a=-70 \\\\\\ a=\cfrac{-70}{-0.01}\implies \boxed{a = 7000} ~\hfill \stackrel{\textit{we know that}}{b = 10000 -a}\implies \boxed{b = 3000}[/tex]
what is 3/4 divided by 11/20
Answers
Answer:
11/15
Step-by-step explanation:
11/20 / 3/4
11/20*4/3
44/60
22/30
11/15
Answer:
15/11
Step-by-step explanation:
3/4 divided by 11/20?
Reduce the expression, if possible, by canceling the common factors.
Exact Form: 15/11
decimal form: 1.36
mixed number form: 1 4/11
The sum of two numbers is 65. The larger number is 5 more than the smaller number. What are the numbers?
Answers
Answer:
30 and 35
Step-by-step explanation:
Put this question into equation form:
Let x be the smaller number, if the larger number is 5 more and the total is 65:
x + 5 + x = 65
2x + 5 = 65
Subtract 5 from both sides
2x + 5 - 5 = 65 - 5
2x = 60
Divide both sides by 2:
2x ÷ 2 = 60 ÷ 2
x = 30
As the larger number is 5 bigger:
30 + 5 = 35
So the two numbers are 30 and 35.
Hope this helps!
Answer:
Small number 30
Large Number 35
Step-by-step explanation:
The sum of x and y is 65. In other words, x plus y equals 65 and can be written as equation A:
x + y = 65
The difference between x and y is 5. In other words, x minus y equals 5 and can be written as equation B:
x - y = 5
Now solve equation B for x to get the revised equation B:
x - y = 5
x = 5 + y
Then substitute x in equation A from the revised equation B and then solve for y:
x + y = 65
5 + y + y = 65
5 + 2y = 65
2y = 60
y = 30
Now we know y is 30. Which means that we can substitute y for 30 in equation A and solve for x:
x + y = 65
x + 30 = 65
X = 35
Therefore the large and small number us 35 and 30 respectively.
A scale model of a bicycle has a scale of 1 : 25. The real bicycle has a length of 1.75 m. What is the length of the model in cm?
Answers
Answer:
It's 7 I just did this question today and got it right
If you own a car with an assessed value of 23,300 in the state of West Virginia, which has a 1.66% tax rate, what would your property taxes be for your vehicle
Answers
Answer:
Average County Tax Rate
0.520%
(Mercer County)
Property Taxes
$121
(Annual)
Step-by-step explanation: I'm assuming this is the answer, if you can please can you mark me Brainliest.
If an item that originally cost $12 is increased to $16, what is the percentage of increase in the item?
Answers
Answer:
33.33%
Step-by-step explanation:
if 6sinx=3cosx the value of tanx is
Answers
Step-by-step explanation:
tanx=sinx/cosx=3/6=1/2
Which mixed number is represented by the shaded
area?
0 1 1/4
0 1 3/4
0 2 1/4
0 2 3/4
Hurry up plz I’m being timed
Answers
Explanation: count all the orange boxes, the one is completely full which is all orange which is 1 and then there’s only 1 box filled on the second one
Hope this helps!
the answer to the question is 11/4
Circle the multiplication problem that does not belong with the other three. explain 12×8=,22×4=,42×2=,33×3=
Answers
Answer: 12 x 8
Step-by-step explanation: The other three are not the basic multiplication facts from 0 - 12.
Rewrite 2/3 and 1/15 as a unit rate
Answers
Answer:
10:1
Step-by-step explanation:
Answer:
Step-by-step explanation:
The unit rate is found by dividing.
2/3 = 0.(6)
1/15 = 0.(6)
f(x) = 3x + 1 and f-1 = f-1 = x-1 / 3
then f -'(7) =
Answers
Answer:
2
Step-by-step explanation:
f^-1 (7) = [tex]\frac{x-1}{3}[/tex] = [tex]\frac{7-1}{3}[/tex] = [tex]\frac{6}{3}[/tex] = 2
A rectangular field is 350 meters long and 200 meters wide. What is the area of the field in square kilometers? Do not round your answer. Be sure to include
the correct unit in your answer.
0
km
km2
km
Answers
The area of the rectangular field is 0.07 square kilometers (km²).To find the area of the rectangular field in square kilometers, we need to convert the given dimensions from meters to kilometers.
To find the area of the rectangular field in square kilometers, we need to convert the given dimensions from meters to kilometers and then calculate the area.
Given:
Length of the field = 350 meters
Width of the field = 200 meters
To convert from meters to kilometers, we divide the measurements by 1000, since there are 1000 meters in a kilometer.
Length in kilometers = 350 meters / 1000 = 0.35 kilometers
Width in kilometers = 200 meters / 1000 = 0.2 kilometers
Now that we have the dimensions of the field in kilometers, we can calculate the area.
Area of the field = Length in kilometers * Width in kilometers
Area of the field = 0.35 kilometers * 0.2 kilometers
Multiplying the values, we get:
Area of the field = 0.07 square kilometers
Therefore, the area of the rectangular field is 0.07 square kilometers.
It's important to include the correct unit in the answer, which is "square kilometers" (km²). This represents the unit for measuring the two-dimensional area. In this case, the area of the field is 0.07 km².
For more such questions on area
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The student government snack shop sold 64 snacks this week. 8 of the snacks sold were fruit cups. What percentage of all snacks sold were fruit cups?
Rewrite the equation as a division equation.
Answers
Answer:
8/64 = 0.125 = 12.5%
Step-by-step explanation:
8/64 = 0.125 = 12.5%
show work plz!!!!!!!!!!!!!
Answers
Here, we have been asked to find the order of rotational symmetry of a symmetry of a regular pentagon. First let us learn about rotational symmetry and some basic terms related to it.
1. Rotational Symmetry: -
It is the property a shape has when it looks the same after some rotation by a partial turn. For example: - an equilateral triangle will look the same after a partial rotation of 120∘
2. Centre of rotation: -
The fixed point around which the rotation occurs is called the centre of rotation. For example: - the centre of rotation of a fan is the centre of the fan from which its blade originates.
3. Angle of Rotational Symmetry: -
The angle of rotational symmetry is the smallest angle for which the figure can be rotated to coincide with itself. For example: - the angle of rotation of an equilateral triangle is 120∘
4. Order of Rotational Symmetry: -
The order of rotational symmetry of a shape is the number of times it can be rotated around a full circle and still look the same. For example: - an equilateral triangle can be rotated 3 times around a full circle, each time at the angle of 120∘
, so its order of rotation will be 3.
In general, a regular polygon having n – sides have ‘n’ lines of symmetry and their order of rotational symmetry is ‘n’.
Now, let us come to the question. We have to find the order of rotational symmetry of a regular pentagon.
We know that a regular pentagon has 5 sides.
Hence, it will have 5 lines of symmetry and its order of rotational symmetry will be 5.Solve the following equation for x: 5x-3 1/2 = 9x+4 Enter answers as a decimal with no variable, no spaces, and no equal sign. DO NOT ROUND.
Answers
Answer:
− 1.875
Step-by-step explanation:
Do you want an explanation?
Hey everybody! Can anybody help me out with this algebra problem? I would really appreciate it if you can!
The following relation is a variation. Which description best represents the relation?
Answers
Answer:
x and y are directly related because y = -3x
Step-by-step explanation:
ASAP
which of the following values of 'x' is the equation 4(x-2)-3x
= x +2 true?
A. -1
B. All Real Numbers
C. The equation has no solution
D. 3
E. 2
Answers
Answer: A
Step-by-step explanation:
Please take a look at the picture
Answers
Step-by-step explanation:
option c is correct answer
Answer:
A) -11/-4
Step-by-step explanation:
-11/-2=11/4
Rewrite the fraction.
-(-11/4)
=11/4
Hope this helps :)
Emily took an airplane trip. Her plane flew an equal number of miles each hour. Write an equation to represent one way you can find how many miles Emily's plane flew each hour.
Use this to help you:
Air travel time: 12 hours
Destination: 2,184 miles
Answers
182.00 miles per hour
y = 182x will be the equation to represent one way you can find how many miles Emily's plane flew each hour.
What is the equation?A formula that expresses the connection between two words on each side of an indication. A calculation with an integer multiple is referred to as an equation. Algebra is widely used in equations. In performing calculations but unsure of the precise amount, algebra is utilized.
The information that is provided is
the air travel time is 12 hours
The destination miles will include 2,184 miles
Assuming the values of x and y
x = number of hours n
y = distance covered
The equation that will be made will be:
y = (2184 / 12)x
y = 182x
Therefore, the equation will be y = 182x.
Learn more about equation, Here:
https://brainly.com/question/14686792
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WHAT is the next sequence
Answers
Answer: its 21
Step-by-step explanation:
the sequence goes up by 1 each time
Answer:
21
Step-by-step explanation:
a1=1
a2=a1+2
a3=a2+3
a4=a3+4
...
a(n)=a(n-1)+n
A drug company is considering marketing a new local anesthetic. The effective time of the anesthetic the drug company is currently producing has a normal distribution with a mean of 7.4 minutes with a standard deviation of 1.2 minutes. The chemistry of the new anesthetic is such that the effective time should be normally distributed with the same standard deviation, but the mean effective time may be lower. If it is lower, the drug company will market the new anesthetic; otherwise, they will continue to produce the older one. A sample size of 36 results in a sample mean of 7.1. A hypothesis test will be done to help make the decision. True or False: If the level of significance had been chosen as 0.05, the company would market the new anesthetic.
Answers
Testing the hypothesis using the z-distribution, it is found that the statement is False.
At the null hypothesis, we test if the mean is still of 7.4 minutes, that is:
[tex]H_0: \mu = 7.4[/tex]
At the alternative hypothesis, we test if the mean is of less than 7.4 minutes, that is:
[tex]H_1: \mu < 7.4[/tex]
We have the standard deviation for the population, thus, the z-distribution is used. The test statistic is given by:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean. [tex]\mu[/tex] is the value tested at the null hypothesis. [tex]\sigma[/tex] is the standard deviation of the sample. n is the sample size.For this problem, the values of the parameters are as follows: [tex]\overline{x} = 7.1, \mu = 7.4, \sigma = 1.2, n = 36[/tex].
Hence, the value of the test statistic is:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{7.1 - 7.4}{\frac{1.2}{\sqrt{36}}}[/tex]
[tex]z = -1.5[/tex]
The p-value of the test is the probability of finding a sample mean of 7.1 or lower, which is the p-value of z = -1.5.
Looking at the z-table, z = -1.5 has a p-value of 0.0668.
Since the p-value of the test is 0.0668 > 0.05, there is not enough evidence to conclude that the time is lower, hence the statement is False.
A similar problem is given at https://brainly.com/question/16695704
range of the function f(x) = -x^2 - 5
Answers
Answer:
Step-by-step explanation:
help me out guys I don't get this ?!
Answers
Answer:
B: (-2,-3)
Step-by-step explanation:
The problem basically wants you to find the vertex because that is the turning point of an absolute value graph where the slope goes from negative to positive immediately. B is the best choice because the vertex is translated 2 to the left and 3 down.
Task 1:
Taxi Cab Company A: $8 per ride and $0.35 per mile
• Write an equation in slope intercept form to represent the cost of a
taxi ride using company A.
Hint: use y=mx+b
OY =
• What does the y-intercept mean in the context of this problem?
Hint: What do you pay to step into the cab?
Answers
Using the slope - intercept form to represent the scenario described, the equation obtained would be y = 0.35x + 8
The cost per ride represents the intercept = $8
The cost per mile represents the slope = $0.35
The slope - intercept form of a linear equation is expressed as :
y = bx + c b = slope ; c = interceptTherefore, the slope intercept form for the cost of taxi ride is y = 0.35x + 8
Learn more : https://brainly.com/question/18796573
3x + 5.5 < 20.5
please help
Answers
Answer:
x < 5
Step-by-step explanation:
[Given] 3x + 5.5 < 20.5
[Subtract 5.5 from both sides] 3x < 15
[Divide both sides by 3] x < 5
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather