Quadratic equations are polynomial equations of degree 2. They can be written in the form ax² + bx + c = 0, where a, b, and c are constants. The graph of a quadratic equation is a parabola.
Transformations involve shifting or reflecting the graph of a quadratic equation. The most common transformations are shifting the graph left or right (by adding or subtracting a constant from x), shifting the graph up or down (by adding or subtracting a constant from y), and reflecting the graph across the x-axis or y-axis.
How to explain the mathematical termsThe axis of symmetry is a vertical line that divides the parabola into two symmetrical halves. The equation of the axis of symmetry for a quadratic equation of the form y = ax² + bx + c is x = -b/2a.
The vertex is the point on the parabola where it reaches its maximum or minimum value. The vertex of a quadratic equation of the form y = ax^2 + bx + c is (-b/2a, c - b²/4a).
The domain of a quadratic equation is the set of all real numbers for which the equation is defined. The range is the set of all possible y-values that the equation can take. You can find the domain and range of a quadratic equation by looking at its graph.
In recognizing quadratic equations, you can tell if an equation is quadratic by looking at the powers of the variables. A quadratic equation will always have a variable raised to the power of 2.
When substituting negative numbers into a quadratic equation, it can be helpful to use parentheses to avoid confusion. For example, to evaluate y = x² - 4x - 6 at x = -2, you would write y = (-2)² - 4(-2) - 6 = 16 + 8 - 6 = 18.
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Which property is illustrated in the example: -5 + 2 = 2 + (-5)
A. Associative Property
C. Distributive Property
B. Commutative Property
D. Identity Property
Answer: Commutative.
Step-by-step explanation: The Commutative Property of addition states that changing the order of the addends does not change the sum. Here that is proven as -5 and 2 are switched and the equal sign remains, meaning the sun will not change like the property says.
One kilogram is 2.2 pounds. Complete the tables. What is the interpretation of the constant of proportionality in each case?
pounds
2.2 11 5.5 1
kilograms
1
pounds
2.2
______ kilogram per pound
kilograms
1
7 30 0.5
______ pounds per kilogram
Answer:
Step-by-step explanation:
3 and 5
Which inequality is represented by this graph?
Answer:
x ≥ -53
Step-by-step explanation:
The solid dot means that -53 is included in the solution.
The arrow pointing right means all numbers greater than -53 are also included.
The graph means -53 and all numbers greater than -53.
Answer: x ≥ -53
Answer choices
(6,-4)
(-3,2)
(4,5)
Answer:
(6,4)
(-3,2)
(4,5)
Evaluate.
4 to the power of 3
Answer:64
Step-by-step explanation:
it means you should mutliply 4 with itself 3 times:
4*4*4=64
Answer:
64
Step-by-step explanation:
4^3 = 4*4*4=64
For the following, use the information given by the inequality to describe the relative position of the numbers on a horizontal number line.
Answer:
duh
Step-by-step explanation:
-0.1 is greater than -0.2
Answer:-0.2 > -0.1
Step-by-step explanation:-0.2 > -0.1
can someone pls help
Step-by-step explanation:
A triangle has its interior angle sum as 180°
[tex]{ \tt{ \angle R + \angle S + \angle T = 180 \degree}}[/tex]
[tex]{ \colorbox{silver}{input \: angles}} \\ \\ { \tt{31 \degree + (x + 4) \degree + (3x + 9) \degree = 180 \degree}} \\ \\ { \tt{44 + 4x = 180 \degree}} \\ \\ { \tt{4x = 136}} \\ \\ { \tt{x = 34}} \\ \\ { \colorbox{silver}{for \:R }} \\ \\ { \tt{ m\angle S =x + 4 = 34 + 4}} \\ \\ { \boxed{ \tt{m \angle S = 38 \degree}}} \\ \\ { \colorbox{silver}{for \:T }} \\ \\ { \tt{m \angle T = 3x + 9 = (3 \times 34) + 9}} \\ \\ { \tt{m \angle T = 111 \degree}}[/tex]
Which value is included in the solution set for the inequality graphed on the numberline?
Answer: -2
Step-by-step explanation:
Because it is in the negative and has an open hole. sorry if it wrong
A circular sinkhole has a circumference of 75.36 meters. A week later, it has a circumference of 150.42 meters.
a. Estimate the diameter of the sinkhole each week.
At first, the sinkhole has an approximate diameter of
meters. A week later, the diameter is about ____
meters.
b. How many times greater is the diameter of the sinkhole a week later?
The diameter of the sinkhole now is about ___
times greater compared to a week later.
Answer:
diamater is two times the radius
Step-by-step explanation:
please help me
again
Answer:
Your answer is d) x - 2 < 10
Step-by-step explanation:
The statement is if x = -16 which state is true.
Plug in x = - 16 into each of the multiple choice to see if its true.
a)
[tex]-x-2 < 10\\-(-16)-2 < 10\\16-2 < 10\\14 < 10[/tex]False
b)
[tex]-x-2 < -10\\-(-16)-2 < -10\\16-2 < -10\\14 < -10[/tex]False
c)
[tex]x-2 > 10\\(-16)-2 > 10\\-16-2 > 10\\-18 > 10[/tex]False
d)
[tex]x-2 < 10\\(-16)-2 < 10\\-16-2 < 10\\-18 < 10[/tex]True
The figure below is dilated with the center of dilation at the origin and a scale factor of
1/2 . What are the coordinates of the image of point E after this transformation?
Answer:
-6 ; 3
Step-by-step explanation:
Which angles are complementary to each other? Select all that apply.
I think it's angles 5 and 2, angle 3 and 6, angles 4 and 1.
Step-by-step explanation:
i guess
The measures of the legs of a right triangle both measure 7 yards. What is the length of the hypotenuse? Round your answer to the nearest tenth.
A. 7 yards
B. 9.8 yards
C. 9.9 yards
D. 10 yards
Answer: 9.9 yards
Step-by-step explanation: Since we know that the legs of the right triangle both measure 7 yards, we can use the Pythagorean theorem to find the length of the hypotenuse, which is the longest side of the right triangle.
According to the Pythagorean theorem, the square of the hypotenuse equals the sum of the squares of the legs. In this case, we have:
c^2 = 7^2 + 7^2 c^2 = 49 + 49 c^2 = 98
To find the length of the hypotenuse, we need to take the square root of both sides of the equation:
c = √98
Using a calculator, we can find that √98 is approximately 9.9. Therefore, the length of the hypotenuse is approximately 9.9 yards.
The answer is C. 9.9 yards.
PLEASE HELP THIS IS URGENT
What is the volume of the composite figure.
A. 104ft
B. 120ft
C. 150ft
D. 160ft
Answer:
D
Step-by-step explanation:
Answer:
I'm getting 140, though
Step-by-step explanation:
120 i think
An $800 deposit for 24 months earned $200 in interest.
SIMPLE INTEREST
NEED RATE & TOTAL VALUE
Answer:
x=12.5% (hope this right if not I am so sorry)
Answer Explanation:
let x%= annual interest rate
deposit = $800
interest earning period = 24 months = 24/12 years
interest earned = $200
so $200 = $800 * x /100* 24/12
200 = 800 * x/100 * 2
solve for x,
x = 12.5% per annum
Answer: X = 12.5%
Step-by-step explanation:
Could someone help me? Please.
Answer:
Slope : -1/3
Y- intercept : (0,3)
Make sure you graph on the coordinates (0,3) and (3,2)
(Look at my picture to make sure yours look like mine)
Step-by-step explanation:
Answer this for me!!
Answer:A=2b square root 2
Step-by-step explanation: the base is b and the exponent is 2 the factor b repeats2 time so the base is b and exponent is 2
PLS HELPPPPPPPPPPPPP
Nadia is a stockbroker. She earns 12% commission each week. Last week, she sold $6,400 worth of stocks. How much did she make last week in commission? If she averages that same amount each week, how much did she make in commission in 2011?
Answer:
Nadia made a commission of 768 last week
The amount she made in 2011 is 40,045.824
Step-by-step explanation:
What is a commission?
A commission is the fee got for the services, given by the percentage of the total worth.
If Nadia gets a 12% commission for $6400,
Commission = percentage × worth of stock
= 12% × 6400
= 768
There are 52.143 weeks per year.
The amount of commissions she made in 2011 is,
768 × 52.143 = 40,045.824
Hence, Nadia made a commission of $852 for $6400 worth of stocks. If she averages the same amount each week, Nadia made a commission of $40,045.824
help me pls. i dont get it
Answer:
-4d=16
d=-4
Step-by-step explanation:
Last question on the hw and I need quick help.
Please help
What is angle 2?
Answer: 145
Step-by-step explanation: 180 is a staight line so 180-35=145 would make sense
pleaseee help me out w this question
Find the Surface area of the cylinder
Answer:
1187.522 square inches
Step-by-step explanation:
I used a calculator (below, using desmos's graphing calculator) and input the equations with the variables. r is used for circle radius (7 in) and h for height (20 in).
Let me know if this helped by rating, hitting thanks/brainliest! If not, please comment and I'll get back to you ASAP.
The Pyramid Arena In Memphis, Tennessee, is a square pyramid that is 321 feet tall. The base has 600-foot sides. Find the volume of the pyramid.
Answer:
38,400,000 cubic feet.
Step-by-step explanation:
To find the volume of a pyramid, you can use the formula:
V = (1/3) * base area * height
In this case, the base is a square with sides of 600 feet, so its area is:
base area = 600 * 600 = 360,000 square feet
The height of the pyramid is given as 321 feet.
Now we can plug in the values into the formula:
V = (1/3) * 360,000 * 321
V = 38,400,000 cubic feet
Therefore, the volume of the Pyramid Arena in Memphis, Tennessee, is approximately 38,400,000 cubic feet.
X < -200
Select EACH correct answer
X = -210
X = -120
X = -200
X= -102
X= -201
Answer: A, and E
Step-by-step explanation:
x is anything less than -200. Because youre in the negatives you have to think about it backwards. -120 is closer to 0 same with 102 and because x isnt less than or equal to -200, its not an answer either
Answer:{x|x<-200}
Step-by-step explanation:
write the inequality in set builder notation as the set of the all real numbers x such that x is less than -200
I NEED HELP!!!!!!!!!!!!!!!
1 Because 100% of something is 1 - at least reduced
Answer: 1
Step-by-step explanation:
Which inequality is represented by the graph?
Answer:
-34.5 > x
Step-by-step explanation:
solve for a,b,c,and d.
Help ASAP!
Which number line shows the graph of x>11
Answer: the second one.
Step-by-step explanation:
it means any number greater than or equal to 11. so it would be a closed circle going towards any number greater than 11 :)
Answer: 2
Step-by-step explanation:
Create a number line that represents the solution set of the inequality w divided by 7 > 38. Show all your work
Answer:
Step-by-step explanation:
To represent the solution set of the inequality w divided by 7 > 38 on a number line, we first need to isolate the variable w:
w/7 > 38
w > 7 x 38
w > 266
This means that any value of w greater than 266 satisfies the inequality.
We can represent this on a number line by marking a closed circle at 266 (since the inequality is not inclusive of this value), and drawing an arrow to the right to indicate all values greater than 266:
<--o======(266)---------------->
This represents the solution set of w/7 > 38.