Which of the following is the quadratic parent function?
A. F(x) = x + 1
B. F(x) = Ixl
C. F(x)=x²
D. F(x) = 2x
Answers
Answer:
C
Step-by-step explanation:
A quadratic has to have an exponent of 2 somewhere. The only one of these functions that does is C
The quadratic parent function is f ( x ) = x²
What is Quadratic Equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
where ( b² - 4ac ) is the discriminant
when ( b² - 4ac ) is positive, we get two real solutions
when discriminant is zero we get just one real solution (both answers are the same)
when discriminant is negative we get a pair of complex solutions
Given data ,
Let the quadratic equation be represented as A
Now , the value of A is
f ( x ) = x²
The graph of the function f(x) = x² is a parabola that opens upward, symmetric with respect to the y-axis, and its vertex is at the origin (0, 0)
Now , the value of y is the square of x
Hence , the parent function is f ( x ) = x² and graph is plotted
To learn more about quadratic equations click :
https://brainly.com/question/25652857
#SPJ7
Related Questions
There is a lighthouse that is 25 meters tall and a boat is sinking 204 meters away from the lighthouse. To the nearest whole degree, what is the angle of depression from the top of the lighthouse to the sinking boat?
Answers
The angle of depression from the top of the lighthouse to the sinking boat is 6.9°.
What is trigonometry?Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.
From ΔABC it is obtained that;
Height of lighthouse, AC = 25 meters
Distance of boat from the lighthouse, BC = 204 meters
The angle of depression from the top of the lighthouse to the sinking boat is;
[tex]\rm tan \theta = \frac{P}{B} \\\\ \rm tan \theta = \frac{AC}{BC} \\\\ tan \theta = \frac{25}{204} \\\\ \theta = tan^{-1}(0.12)\\\\ \theta = 6.9 ^0[/tex]
Hence, the angle of depression from the top of the lighthouse to the sinking boat is 6.9°
To learn more about trigonometry, refer to the link https://brainly.com/question/26719838.
#SPJ1
2/6+5/6 as a whole number
Answers
Answer: 2/6+5/6 + 1.167
Answer:
1.16
Step-by-step explanation:
Help please asap points an brainlist
Answers
M —> given point on the line
(X1,y1)—> any point on line
4. Minnie bought 6 postcards during 3 days of vacation. After 8 days of vacation, how many total postcards will Minnie have bought?
A. 4
B. 5
C. 16
D. 12
Answers
If you look at 6/3 you get 2.
Minnie is buying 2 postcards a day.
2 times 8 is 16.
whats the polynomial of (7x+7)(x+2)
Answers
Answer:
okkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk
will you be my friend
Step-by-step explanation:
.......... okkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk
= 7x^2 + 14x + 7x + 14
= 7x^2 + 21x + 14
Question 3 of 21
Which of the following are the domain and range that represent the inverse of
the function f(x), given the mapping diagram of f(x) below?
Answers
Answer: C
Step-by-step explanation:
The inverse of a function maps the domain onto the range.
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
x < 5
–6x – 5 < 10 – x
–6x + 15 < 10 – 5x
A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
Answers
A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
Which is the correct representation of the inequality?
Here we have.
-3(2x - 5) < 5*(2 - x)
First, we need to isolate x in one side, let's expand both sides:
-6x + 15 < 10 - 5x
15 - 10 < 6x - 5x
5 < x
This will be represented with a number line where we have an open circle at 5, and an arrow that goes to the right. So the correct option is:
"A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right."
If you want to learn more about inequalities:
https://brainly.com/question/18881247
#SPJ1
Car A is traveling east at a steady speed of 50 miles per hour. After 2 hours, it is 140 miles east of Johnstown.
Car B is traveling east on the same road. its distance east of Johnstown is represented by the graph.
Where were the two cars in relation to each other when they began traveling?
Answers
The two cars in relation to each other when they began travelling will be car B was 20 miles east of car A. Then the correct option is A.
What is speed?The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.
We know that the speed formula
Speed = Distance/Time
Car A is travelling east at a steady speed of 50 miles per hour.
Then the equation of car A is given as
y = 50x + C
where x be the number of miles and x be the number of hours.
Then we have
After 2 hours, it is 140 miles east of Johns town.
Then we have
y = 50x ..1
Car B is travelling east on the same road. its distance east of Johns town is represented by the graph.
Then the equation of car B will be
y = [(120 - 20) / (2 - 0)]x + 20
y = 50x + 20 ...2
Then the two cars in relation to each other when they began travelling will be car B was 20 miles east of car A.
Then the correct option is A.
More about the speed link is given below.
https://brainly.com/question/7359669
#SPJ1
Answer:
Car A was 20 miles east of car B.
Step-by-step explanation:
Find the derivative of y = 4x^3.
Find the derivative of y = 2/x^4.
Find the derivative of y = 3√x.
Find the derivative of y = 3/√x.
Find the derivative of y = x^3/4.
Find the derivative of y = 3 x^5.
Answers
Answer:
[tex]\fbox {See below} \downarrow[/tex]
Step-by-step explanation:
Question 1 :
[tex]\mathsf {\frac{dy}{dx} = \frac{d}{dx}(4x^{3})}[/tex]
[tex]\mathsf {\frac{dy}{dx} = 4(3)x^{3-1}}[/tex]
[tex]\mathsf {\frac{dy}{dx} = 12x^{2}}[/tex]
Question 2 :
[tex]\mathsf {\frac{dy}{dx} = \frac{d}{dx}(\frac{2}{x^{4}})}[/tex]
[tex]\mathsf {\frac{dy}{dx} = \frac{d}{dx}(2x^{-4})}[/tex]
[tex]\mathsf {\frac{dy}{dx} = 2(-4)x^{-4-1}}[/tex]
[tex]\mathsf {\frac{dy}{dx} = -8x^{-5}}[/tex]
[tex]\mathsf {\frac{dy}{dx} = -\frac{8}{x^{5}}}[/tex]
Question 3 :
[tex]\mathsf {\frac{dy}{dx} = \frac{d}{dx}(3\sqrt{x})}[/tex]
[tex]\mathsf {\frac{dy}{dx} = \frac{d}{dx}(3(x)^{\frac{1}{2}})}[/tex]
[tex]\mathsf {\frac{dy}{dx} = 3(\frac{1}{2})x^{\frac{1}{2}-1}}[/tex]
[tex]\mathsf {\frac{dy}{dx} = \frac{3}{2}x^{-\frac{1}{2}}}[/tex]
[tex]\mathsf {\frac{dy}{dx} = \frac{3}{2\sqrt{x}}}[/tex]
Question 4 :
[tex]\mathsf {\frac{dy}{dx} = \frac{d}{dx}(\frac{3}{\sqrt{x}})}[/tex]
[tex]\mathsf {\frac{dy}{dx} = \frac{d}{dx}(3x^{-\frac{1}{2}})}[/tex]
[tex]\mathsf {\frac{dy}{dx} = 3(-\frac{1}{2})x^{-\frac{1}{2}-1}}[/tex]
[tex]\mathsf {\frac{dy}{dx} = -\frac{3}{2}x^{-\frac{3}{2}}}[/tex]
[tex]\mathsf {\frac{dy}{dx} = -\frac{3}{2x\sqrt{x}}}[/tex]
Question 5 :
[tex]\mathsf {\frac{dy}{dx} = \frac{d}{dx}(\frac{x^{3}}{4})}[/tex]
[tex]\mathsf {\frac{dy}{dx} = \frac{1}{4}(3)x^{3-1}}[/tex]
[tex]\mathsf {\frac{dy}{dx} = \frac{3}{4}x^{2}}[/tex]
Question 6 :
[tex]\mathsf {\frac{dy}{dx} = \frac{d}{dx}(3x^{5})}[/tex]
[tex]\mathsf {\frac{dy}{dx} = 3(5)x^{5-1}}[/tex]
[tex]\mathsf {\frac{dy}{dx} = 15x^{4}}[/tex]
What is the exact value of sin (165 degrees)
Answers
Answer:
Step-by-step explanation:
(√6 - √2)/4
Can someone help me with fill the blanks of this pls? It’s about geometry
Answers
Answer:
see below
Step-by-step explanation:
2: letter at the vertex, placing a letter or number inside .... , or by using 3 letters
3:
WXY
WXZ
YXZ
4: X
Work out the area of this triangle
Answers
Step-by-step explanation:
the area of a triangle is
baseline × height / 2
baseline and height must be at a right angle with each other.
so, in our case
6 × 11 / 2 = 3 × 11 = 33 cm²
Answer:
Area = 33 cm²
Step-by-step explanation:
[tex]\textsf{Area of a triangle}=\sf \dfrac{1}{2}bh[/tex]
where:
b is the baseh is the height (perpendicular to the base)If we turn the triangle counterclockwise, so that the side that measures 6 cm is the base, we will see that the length that measures 11 cm is the height of the triangle (see attached).
Therefore:
b = 6 cmh = 11 cmSubstitute the found values into the formula and solve for A:
[tex]\implies \sf A=\dfrac{1}{2}(6)(11)[/tex]
[tex]\implies \sf A=\dfrac{1}{2}(66)[/tex]
[tex]\implies \sf A=33[/tex]
Therefore, the area of the triangle is 33 cm²
The enrollment for a new program is 1,500 students. the program is expected to grow at a rate of 0.03. what is the expected enrollment in 7 years? round to the nearest whole number.
Answers
The expected enrolment in 7 years is 1845.
What is the expected enrolment?The formula for calculating future value of the number of students is an exponential equation with this form:
FV = P (1 + r) ^n
FV = Future populationP = Present populationR = rate of growth of the populationN = number of years1500 x (1.03)^7 = 1845
To learn more about future value, please check: https://brainly.com/question/18760477
#SPJ1
Scientists are using a computer simulation to test ideas about climate on Earth. Looking at one period of time in the simulation, they notice that more energy entered the Earth system than exited. How might the amount of carbon dioxide have changed to cause this, and how would this have changed the energy in the Earth system? In the simulation,
A. Carbon dioxide decreased, leading to less energy in the Earth system and less energy absorbed by Earth’s surface.
B. Carbon dioxide decreased, leading to more energy in the Earth system and more energy absorbed by Earth’s surface.
Carbon dioxide increased, leading to less energy in the Earth system and less energy absorbed by Earth’s surface.
D. Carbon dioxide increased, leading to more energy in the Earth system and more energy absorbed by Earth’s surface.
Answers
Answer:
Step-by-step explanation:
ore energy entered the Earth system than exited due to the greenhouse effect, solar energy trapping systems like solar panel, etc.
How CO₂ changed the energy in the Earth system due to many reasons:-
Carbon dioxide forces the Earth's energy budget out of balance by absorbing thermal infrared energy radiated by the surface. It absorbs thermal infrared energy with wavelengths in a part of the energy spectrum that other gases, such as water vapor, co₂, etc.
The greenhouse effect also increases energy in the earth's system.
An increase in the amount of carbon dioxide creates an overabundance of greenhouse gases that trap additional heat.
These greenhouse gas emissions have increased the greenhouse effect and caused the earth's surface temperature to rise.
Learn more about the greenhouse effect here: brainly.com/question/19521661
BC and DE are tangents to this circle. Work out the size of angle 0. Give reasons for your answer. A 52° B O D 27° E 0 C Not drawn accurately BC and DE are tangents to this circle . Work out the size of angle 0 . Give reasons for your answer . A 52 ° B O D 27 ° E 0 C Not drawn accurately
Answers
Answer:
Θ = 39°
Step-by-step explanation:
OA = OB ( radii of the circle ) , then
Δ AOB is isosceles with base angles congruent , that is
∠ ABO = ∠ BAO = 52°
the exterior angle of a triangle is equal to the 2 opposite interior angles.
∠ DOB is an exterior angle of the triangle , so
∠ DOB = ∠ ABO + ∠ BAO = 52° + 52° = 114°
the angle between a tangent and the radius at the point of contact is 90°, then
∠ OBC = ∠ ODE = 90°
the sum of the 4 interior angles of quadrilateral OBCD = 360°
∠ OBC + ∠ DOB + ∠ ODC + ∠ BCD = 360°
90° + 114° + (90 + 27)° + Θ = 360°
90° + 114° + 117° + Θ = 360°
321° + Θ = 360° ( subtract 321° from both sides )
Θ = 39°
The Volume of a cube depends on the length of its sides.This can be written in function notation as v(s).What is the best interpretation of V(3)=27
Answers
Answer and Step-by-step explanation:
There is a cube with side length 3. The volume of this cube is 27.
Which ordered pairs make both inequalities true? Check all that apply
Answers
Answer:.
Step-by-step explanation:
What is the quadratic equation for 0=-2x+3x^2
Answers
x = 2/3 , 0 .
Question :
[tex] {3x}^{2} - 2x = 0[/tex]
use quadratic formula :
[tex]x = \frac{( - b)± \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]
Solution :
[tex]a {x}^{2} + bx + c = 0 \\ a = 3 \\ b = - 2 \\ c = 0[/tex]
[tex]x = \frac{ - ( - 2)± \sqrt{ { (- 2)}^{2} - 4 \times 3 \times 0} }{2 \times 3} \\ \\ x = \frac{2± \sqrt{4 - 0} }{6} \\ \\ x = \frac{2± \sqrt{4} }{6} \\ \\ x = \frac{2± 2}{6} [/tex]
separate into two equations :
[tex]x = \frac{2 + 2}{6} = \frac{4}{6} = \frac{2}{3} .[/tex]
[tex]x = \frac{2 - 2}{6} = \frac{0}{6} = 0.[/tex]
the values of x are 2/3 and 0 .
A hiking club is planning a hike in the mountains. They estimates that it will take 3.5 hours to walk 6km. How long will it takes the group to walk 24km?
Answers
Answer:
14
Step-by-step explanation:
First divide 24 and 6 to find how much 6's there are in 24.
24/6=4
Now, we take that number and multiply it by 3.5 to find how long it will take the group to walk 24km.
3.5*4=14.
It will take the group 14 hours to walk 24 km.
Hope this helps!
If not, I am sorry.
Which foundation drawing matches this orthographic drawing?
Answers
The figure second represents the foundation drawing of a provided front, right, and top view option second is correct.
What is orthographic drawing?Three-dimensional objects can be represented in two dimensions via an orthographic projection.
As we have given orthographic drawings.
The front, right, and the top view is shown in the picture of the cuboid if merge all the view we will find the three-dimensional figure is a cuboid.
We can represent the cuboid by 2×3 grids as shown in the picture second.
Thus, the figure second represents the foundation drawing of a provided front, right, and top view option second is correct.
Learn more about the orthographic drawing here:
https://brainly.com/question/2508352
#SPJ1
5x + 13y=232
12x + 7y= 218
Answers
Answer:
x=10, y=14
Step-by-step explanation:
added in the picture
The set of life spans of an appliance is normally distributed with a mean mu = 48 months and a standard deviation sigma = 8 months. what is the z-score of an appliance that stopped working at 64 months?
Answers
The z-score of an appliance that stopped working at 64 months is 2.
What is mean?The mean of observations is equal to the ratio of sum of all the observations and the number of observations.
Given, the set of life spans of an appliance is normally distributed with a mean mu = 48 months and a standard deviation sigma = 8 months
The z-score is then calculated as
z = x - μ /σ
For an appliance that stopped working at 64 months, we have
x = 64
On substituting the values, we get
z = 64-48/8
z = 2
Hence, the z-score of an appliance that stopped working at 64 months is 2
Learn more about mean.
https://brainly.com/question/11822836
#SPJ1
Answer:
D on edge
Step-by-step explanation:
2
Find the distance between the point (3, 5) and a line with the equation 5 x - 3 y + 10 = 0
Answers
The distance between the point (3, 5) and a line with the equation 5x – 3y + 10 = 0 will be 10 / √(34) units.
What is the distance between a point and a line?Let (x₁, y₁) be the point and ax + by + c = 0 be the line.
Then the distance between a point and a line will be
[tex]\rm d = \dfrac{|ax_1 + by_1 + c|}{\sqrt{a^2 + b^2}}[/tex]
The point (3, 5) and a line with the equation 5x – 3y + 10 = 0.
Then the distance between them will be
[tex]\rm d = \dfrac{|5 *3 - 3 *5 + 10|}{\sqrt{5^2 + (-3)^2}}\\d = \dfrac{10 }{\sqrt{34}} \ units[/tex]
Learn more about the distance between a point and a line here;
https://brainly.com/question/11558698
#SPJ1
If the point (7, 3) is on the graph of an equation, which statement must be true?
Answers
Answer:
The values x = 7 and y = 3 make the equation true.
Step-by-step explanation:
hope this helps
y = 2x² - 9x + 10
solve the following quadratic function by factoring
Answers
y = (x - 2)(2x - 5)
please give it a like :)
A culture started with 2,000 bacteria. After 2
hours, it grew to 2,400 bacteria. Predict how
many bacteria will be present after 10 hours.
Round your answer to the nearest whole
number.
P
Aekt
Answers
how many time did it in rose within the 2 hours?
Solve for h in A = ½ ah - ½ bh. Solve for h in A = ½ ah - ½ bh .
Answers
Answer:
h = A / ( 1/2 a - 1/2 b)
Step-by-step explanation:
A = ½ ah - ½ bh
Factor out an h
A = h( 1/2 a - 1/2 b)
Divide each side by ( 1/2 a - 1/2 b)
A / ( 1/2 a - 1/2 b) = h ( 1/2 a - 1/2 b)/ ( 1/2 a - 1/2 b)
A / ( 1/2 a - 1/2 b) = h
h = A / ( 1/2 a - 1/2 b)
Weekly wages at a certain factory are
normally distributed with a mean of
$400 and a standard deviation of $50.
Find the probability that a worker
selected at random makes between
$350 and $400.
[ ? ]%
Answers
√2/√2+√3-√5 rationalise the denominator
Answers
answer is
(2√6+√15+6)/12
whats is 452 divided by2
Answers
Answer:
452/2 = 226
Step-by-step explanation:
45 divided by 2 is 22 and the remainder would be 12, which could be divided by 2 again to get 6. Add this to the total and you get 226.
Hope this helps! :D
