Step-by-step explanation:
The graph of a quadratic equation in two variables (y = ax^2 + bx + c ) is called a parabola. The following graphs are two typical parabolas their x-intercepts are marked by red dots, their y-intercepts are marked by a pink dot, and the vertex of each parabola is marked by a green dot: (Given in attachment for diagram)
We say that the first parabola opens upwards (is a U shape) and the second parabola opens downwards (is an upside down U shape). In order to graph a parabola we need to find its intercepts, vertex, and which way it opens.
Given y = ax^2 + bx + c , we have to go through the following steps to find the points and shape of any parabola:
Label a, b, and c.
Decide the direction of the paraola:
If a > 0 (positive) then the parabola opens upward.
If a < 0 (negative) then the parabola opens downward.
Find the x-intercepts:
Notice that the x-intercepts of any graph are points on the x-axis and therefore have y-coordinate 0. We can find these points by plugging 0 in for y and solving the resulting quadratic equation (0 = ax^2 + bx + c). If the equation factors we can find the points easily, but we may have to use the quadratic formula in some cases. If the solutions are imaginary, that means that the parabola has no x-intercepts (is strictly above or below the x-axis and never crosses it). If the solutions are real, but irrational (radicals) then we need to approximate their values and plot them.
Find the y-intercept:
The y-intercept of any graph is a point on the y-axis and therefore has x-coordinate 0. We can use this fact to find the y-intercepts by simply plugging 0 for x in the original equation and simplifying. Notice that if we plug in 0 for x we get: y = a(0)2 + b(0) + c or y = c. So the y-intercept of any parabola is always at (0,c).
Find the vertex (h,k):
To find the x-coordinate for the vertex we use the following formula:
To find the y-coordinate for the vertex we plug in h in the original equation:
k = a(h)2 + b(h) + c
Plot the points and graph the parabola
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Last week, the daily low temperatures for a city, in degrees Celsius, were 5, 8, 6, 5, 10, 7, and 1. What was the average low temperature? Show your reasoning.
Help me on this question please
We need to split it into 2 + 3 + 5 = 10 'parts', meaning each 'part' is 18 KD.
Thus, Ahmed receives 18(2) = 36 KD, Qasim receives 18(3) = 54 KD, and Omer receives 18(5) = 90 KD
Define Hypotenus
I have forgotten what it is
In geometry, a hypotenuse is the longest side of a right-angled triangle, the side opposite the right angle. The length of the hypotenuse can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides.
It is useful in different situations involving the need to find distance or the measure of an angle.
Use the Pythagorean theorem to calculate the hypotenuse from right triangle sides. Take a square root of sum of squares: c = √(a² + b²)
sum difference place value of 2 in 4242
Answer:
[tex]\huge\colorbox{violet}{✏﹏ \: ᴀɴsᴡᴇʀ \: }[/tex]
4242
2 = 200 ( 2 is in hundred's place )
4242
2 = 2 ( one's place )
Difference = ?
[tex] = 200 - 2 \\ = 198[/tex]
Sum = ?
[tex] = 200 + 2 \\ = 2[/tex]
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
[tex] \huge\blue{ \mid{ \underline{ \overline{ \tt ꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐ }} \mid}}[/tex]
Simplify (x2y)3.
x2y3
x5y3
x6y3
Answer:
3x2^y
Step-by-step explanation:
brainleist plss
I nEd the answer pls
Answer:
C
Step-by-step explanation:
[tex]SA = 2(lw) + 2(lh) + 2(wh)[/tex]
Add and check 5,655+7,978
Answer: 13,633
Step-by-step explanation: 5,655+7,978=13633
Check: 13,633- 5,655=7,978
Plz help me well mark brainliest if you are correct!!.....
Step-by-step explanation:
the base is 5unit and the height is 9unit
Answer:
The base is 5 units the height is 9 units
Step-by-step explanation:
Just count the blocks in the diagram
base = 5
Height = 9
Consider the sequence of steps to solve the equation: 3(x - 4) + 5x 9x - 36
Given => 3(x-4)+ 5x 9x - 36
Step 1 = 3x - 12 + 5x-9x - 36
Step 2 -> 3x + 5x - 12-9x - 36
Step 3 8x - 12 - 9x - 36
Step 48x - 8x - 12 - 9x - 8x - 36
Step 5 => 0 - 12 - x - 36
Step 6-12 - 36
Step 7-12 + 36 x - 36 + 36
Step 8 = 24 x +0
Step 9 = 24 - x
Which property yields Step 1?
3)
A)
Distributive Property
B)
Multiplicative Identity
Multiplication Property of Equality
Answer:
Distributive Property
Step-by-step explanation:
You are distributing 3 to x and -4
PLEASE ANSWER ASAP FOR BRAINESLT!!!!!!!!
Mrs. Lee randomly surveyed 25 of her 125 students about their pets. Her survey indicate that 14 students have a dog, 7 students have a cat, 2 students have another kind of pet, and 8 students have no pet. (Note that some students have more than one pet). What is Mrs. Lee's best estimate of the total number of her students who have a dog?
A. 70
B. 35
C. 10
D. 40
Answer: Hello! When I tried solving the problem and I got the answer of 70.
Step-by-step explanation:
So, 14 out of the 25 kids have a dog. If you were to have 125 kids which if 5 times the first 25 kids it would be 14 x 5 which is 70.
Property of 10+5=5+10
Answer:
Commutative Property of Addition
Answer:
Commutative property
Step-by-step explanation:
The commutative property is when the order of the addends is changed, the sum stays the same.
Ex. 3+7 = 7+3
Both 3+7 and 7+3 = 10
A circle has a diameter of 12cm. Find the arc length if the central angle is 37°.
Round to the nearest tenth.
Answer:
40
Step-by-step explanation:
37 is greater than five and the next number with a zero would be 40
Plz help me well mark brainliest if correct!!
Plz help me well mark brainliest if correct!.,....
Answer:
6cm
Step-by-step explanation:
I did 24 divided by 4 since a square has 4 sides
Jonah wants to make a one-sample
z
zz interval using
99
%
99%99, percent confidence to estimate what proportion of silicon wafers at his factory are defective. He wants the margin of error to be no more than
3
%
3%3, percent. A previous study suggests that about
6
%
6%6, percent of these wafers are defective.
If we assume
p
^
=
0.06
p
^
=0.06p, with, hat, on top, equals, 0, point, 06, what is the smallest sample size required to obtain the desired margin of error?
Answer:
416
Step-by-step explanation:
Kahn Academy
find the midpoint of (-1,2) (-4,-9)
Answer:
use this info to help answer it
Measure the distance between the two end points, and divide the result by 2. This distance from either end is the midpoint of that line. Alternatively, add the two x coordinates of the endpoints and divide by 2. Do the same for the y coordinates.
In the triangle below,
y = [? ] cm. Round to the
nearest tenth.
15 cm
X
35°
909
Answer:
12.3
Step-by-step explanation:
You will use cosine to solve for y because you are given the hypontenuse and need to find the adjacent side.
cos 35 degrees = adjacent/hypontenuse
cos 35 = y/ 15
15( cos35 ) = y
y=12.287
=12.3
What is the midline equation of y = -4sin (2x - 7) + 3?
Step-by-step explanation:
Thank you this is your answerPlease Help! Lateena solved an equation. Explain why or why not her solution is correct.
Answer:
Actually her answer is wrong because it's a quodratic equation.
Determine the equation of the quadratic function shown below.
Select the correct answer. Consider functions fandg f(3) = 5.2.1, for 3 + 2 and = + -6 4:2 – 16: + 16 96) = 4+ 48, for : * -12 Which expression is equal to 10) (+? OA . OB. 1 Ос. OD. 5+2 6
Answer:
A
Step-by-step explanation:
Hyo spent $48.84 for a gold-plated trophy that costs $37 per pound. How much did the trophy weigh?
3. Calculate the value of x in the figure to the right: (2 Points)
Answer:
x = 12
Step-by-step explanation:
When two chords intersect each other inside a circle, the products of their segments are equal.
------------------
2x = 6 * 4
2x = 24
Divide both sides by 2
x = 12
1. A guitar is on sale with a 55% discount.
If it regularly sells for $270, what is the
amount of discount?
Answer:
it should be 148.5
Step-by-step explanation:
Answer:
$121.50 is the new amount! The discount is $148.50
Step-by-step explanation:
Minutes No. of Homework
Problems
2 or Less
3-4
5-6
7-8
9 or more 8
4
2
0
3
What is the number of homework problems that took less than 5 minutes in the given table?
A.
4
B.
14
C.
12
D.
8
The Sine Function
Your sine regression model for a given problem is
y = 0.500 sin (0.222x - 1.509) + 0.521.
Use your model to predict y(95). Round your answer to the nearest hundredth.
a. y(95) = 0.27
b. y(95) = 0.47
c. y(95) = 0.17
d. y(95) = 0.85
Please select the best answer from the choices provided
Answer:
D. y(95) = 0.85
Step-by-step explanation:
I calculated it logically
Which describes how the figure below was transformed?
Answer: Rotation
Step-by-step explanation: This is a rotation because the figure is rotated 90°. This is not a translation because it isn't moved to a different position. This is not a reflection because it isn't mirrored. This is not a dilation because the size didn't change. Therefor, it is a Rotation, because this figure was rotated 90°
Examples are below if you still don't quite understand.
PLZ HELP I WILL GIVE BRAINLIEST
Answer:
33 m^2
Step-by-step explanation:
Since the area of a kite can be found by h1*b1 + h2*b2, the area is
3 * 1 + 3 * 10 = 33 m^2
Can you construct a triangle with side lengths of 1 meter, 7 meters, and 8 meters?
Yes or no and explain
Answer:
No.
Step-by-step explanation:
No.
Each side of a triangle must have a length between the difference and the sum of the lengths of the other two sides.
Let's look at the sum and difference of lengths of 2 sides.
Side with length 1 and side with length 7; third side with length 8
sum of lengths of first two sides = 1 + 7 = 8
difference = 7 - 1 = 6
The third side would have to have a length between 6 and 8. The third side has a length of 8. For a triangle, the third side must be between the sum and difference. Here, the third side is equal to the sum, so there is no triangle.
As soon as one side does not work, there is no triangle, and you don't need to check the sums and differences of the other two sets of two sides.
you have the following coins in your pocket five quarters six dimes two nickels and 12 pennies what is the probability as a decimal you would draw a dime.
Answer: The probability of you drawing a dime is 0.24
Step-by-step explanation:
5 quarters, 6 dimes, 2 nickels, 12 pennies
5+6+2+12= 25
6/25= 0.24 or 24%
Answer:
0.24
Step-by-step explanation:
P(dime) = 6/25 which is 0.24