For the form [tex]y = a(x-h)^2 + k[/tex], the vertex has coordinates (h, k). The vertex is found by (x, y).
What is the vertex form of a quadratic equation?If a quadratic equation is written in the form
[tex]y=a(x-h)^2 + k[/tex]
then it is called to be in vertex form.
It is called so because when you plot this equation's graph, you will see vertex point(peak point) is on (h,k)
First of all, we used this vertex formula thing since it is visible that there are quadratic functions.
Otherwise, you had to use calculus to get critical points, then a second derivative of functions to find the character of critical points as minima or maxima or saddle, etc to get the location of vertex point.
This point (h,k) is called the vertex of the parabola that the quadratic equation represents.
For the form
[tex]y = a(x-h)^2 + k[/tex], the vertex has coordinates (h, k)
Thus, for the obtained form, we get the coordinates of the vertex as:
[tex]h = -b/2a,, \\ k = c - a\times(b/2a)^2[/tex]
Thus, the coordinates of vertex of [tex]y = ax^2 + bx + c[/tex]is:
[tex](h,k) = (-b/2a, c - a \times (b/2a)^2 )[/tex]
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help! Solve each triangle (find all missing sides and angles) Round each answers to the nearest tenth
Answer:
D.
Step-by-step explanation:
sin 67 = b / 2.4
b = 2.4 sin 67
= 2.2
cos 67 = a / 2.4
a = 2.4 cos 67
= 0.9
M < A = 90-67 = 23 degrees.
in 130,426 the digit 2 is in the _____ place?
Please help me with this question. Thanks!
Assuming that all the grapes have the same probability of being randomly picked:
a) 0.11b) 0.24How to find the probabilities?
We know that there are 8 green grapes and 15 red grapes on the bowl, so there is a total of 23 grapes.
a) Here we need to find the probability that both grapes are green. Remember that the probability of getting a green grape is equal to the quotient between the number of green grapes and the total number of grapes, this is:
P = 8/23
But then he must take another, because he already took one, the number of green grapes is 7, and the total number of grapes is 22, so for the second grape the probability is:
P' = 7/22.
The joint probability is the product of the two individual probabilities:
prob = (8/23)*(7/22) = 0.11
b) For the first green grape we know that the probability is:
P = 8/23
Then he must get a red grape. There are 15 red grapes and 22 grapes in total, so the probability is:
P' = 15/22
Then the joint probability is:
prob = (8/23)*(15/22) = 0.24
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What is the value of the dot shown on the number line below? If the answer is not an integer, enter it as a fraction or mixed number.
There are 440 fish in a pond. If Dylan has caught 45% of them, how many has he caught?
Answer:
198
Step-by-step explanation:
45% of 440
= [tex]\frac{45}{100}[/tex] × 440
= 0.45 × 440
= 198
A password is 4 characters long and must consist of 3 letters and one number. if letters cannot be repeated and the password must end with a number, how many possibilities are there? a. 175,760 b. 158,184 c. 156,000 d. 140,400 please select the best answer from the choices provided a b c d
We will see that there are 156,000 different combinations, so the correct option is C.
How many possibilities are there?
First, we need to find the selections, here we have:
First letter.Second letter.Third letter.Number.Now we need to find the number of options for each of these selections.
First letter. (26 options)Second letter. (25 options, because we can't repeat letters)Third letter. (24 options)Number. (10 options).We assumed that the number can be any integer from 0 to 9.
The total number of possibilities is equal to the product between the numbers of options, we will have:
P = 26*25*24*10 = 156,000
So, the correct option is C.
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Casper collected 108 old baseball cards. He then bought new baseball cards to increase his collection by 25%. How many new baseball cards did he buy?
Answer:
27
Step-by-step explanation:
what I did is used a calculator and did 108 x 0.25 (25% as a decimal)
6 of 6
An equilateral triangle with side length 17 cm is shown in the
diagram, work out the area of the triangle.
Give your answer rounded to 1 DP.
The diagram is not drawn accurately.
cm²
Answer:
125.1 cm^2 to 1 D.P.
Step-by-step explanation:
We could use Heron's formula to do this
Area = √(s(s-a)(s-b)(s-c) ) where s is the semi-perimeter and a b and c are the lengths of the 3 sides
So we have:
s = (17+17+17) / 2 = 25.5
and Area = √(25.5)(25.5 - 17)^3)
= √15660.1875
= 125.14 cm^2
Simple probability maze
To solve a simple probability maze calculate the probability in each situation and move through the maze based on these answers.
What is simple probability?This refers to the chances an event happens out of the total outcomes or number of favorable events/ total events.
How to solve a simple probability maze?In this type of maze, you are requested to find the probability of different events and based on this, you can follow a specific pattern to get out of the maze. Due to this, to solve the maze:
Calculate the probability of the first event. For example, the changes of rolling a 6 on the dice. 1 /6 (the dice has 6 sides) = one sixth or 0.166.Now that you have the correct answer move through the direction of that answer, which will take you to another situation.Keep calculating the probabilites and moving based on the answers.Learn more about probability in: https://brainly.com/question/11234923
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sorry last question please awnser
Answer:
T': (9,8)
U': (0,8)
V': (8,4)
Step-by-step explanation:
explain how to correctly find the missing side
if correct, will mark brainlist :))
asap could really use someones help
Apply Pythagorean theorem
P²=H²-B²P²=13²-4²P²=169-16P²=153P=√153P=3√17PLEASE I NEED THIS RN!!!
Answer:
Increasing then decresing
Step-by-step explanation:
the graph is going up then down so therefore it is increasing then decresing.
Answer:
The left side of the parabola is increasing to the maximum, shown on the graph to be (3,6). Then, the right side is decreasing from the max point. The parabola opens down, which means it increases, then decreases.
Step-by-step explanation:
Always decreasing would mean it took a more linear shape, which this parabola is not doing. It is also not always increasing, because some x,y points are graphed on that curve which go from the center (0,0) to (3,6) back down to (6,0).
Ali is playing computer solitaire. He tallies the number of times he wins and loses.
A. Use Ali’s results to estimate the probability of him winning the next solitaire game.
B. How could Ali improve the accuracy of his estimate.
Answer:
use ali result to estimate the probability of him winning the next solitaire game
What is the area of adef with vertices d(-1,-5), e(4.-5),
and f(4,7)?
Answer:
Step-by-step explanation:
30 square unit is the area of the triangle DEF.
What are the properties of Triangle?The properties of the triangle are:
The sum of all the angles of a triangle (of all types) is equal to 180°. The sum of the length of the two sides of a triangle is greater than the length of the third side. In the same way, the difference between the two sides of a triangle is less than the length of the third side.We can use the coordinates of the three vertices of the triangle to find the length of its base and height, and then use the formula for the area of a triangle.
The base of the triangle is the line segment from point E to point F, which has a length:
|EF| = √[(4-4)^2 + (7-(-5))^2] = √(0^2 + 12^2) = 12
The height of the triangle is the perpendicular distance from point D to the line containing the base, which is the horizontal line y = -5.
Therefore, the height of the triangle is the vertical distance from point D to the line y = -5, which is 5 units.
The area of the triangle is then:
Area = (1/2) x (base) x (height)
= (1/2) x 12 x 5
= 30 square units.
Therefore, the area of triangle DEF is 30 square units.
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which function does NOT have a period of 2pi?
A. y= sec x
B. y= cos x
C. y= sin x
D. y=tan x
The periods of the functions such sine, cosine, secant and cosecant is 2π; while for tangent and cotangent, the period is π.
What is a function?A function is an expression that show the relationship between two or more numbers and variables.
Periodic functions are functions that repeat themselves over regular intervals. That is they have periods.
The periods of the functions such sine, cosine, secant and cosecant is 2π; while for tangent and cotangent, the period is π.
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Answer: D
Step-by-step explanation:
A function is an expression that show the relationship between two or more numbers and variables.
Periodic functions are functions that repeat themselves over regular intervals. That is they have periods.
The periods of the functions such sine, cosine, secant and cosecant is 2π; while for tangent and cotangent, the period is π.
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Please help me thanks!!!!!!!
Answer:
See below ~
Step-by-step explanation:
Subpart (a) :
⇒ Surface area = 2(3 × 4 + 4 × 5 + 3 × 5)
⇒ Surface area = 2(12 + 20 + 15)
⇒ Surface area = 2(47)
⇒ Surface area = 94 in²
===============================================================
Subpart (b) :
⇒ Volume = 3 × 4 × 5
⇒ Volume = 12 × 5
⇒ Volume = 60 in³
=============================================================
Subpart (c) :
⇒ New surface area = 2 x 94
⇒ New surface area = 188 in²
=============================================================
Subpart (d) :
⇒ New : Original
⇒ 188 : 94
⇒ 2 : 1
At a cricket match, 37 of the spectators were in the covered arena while 15000 were in open. Find the total number of spectators.
Answer:
15037
Step-by-step explanation:
37 are in the covered, while 15000 were in the open area. So, to find the total, all we have to do is add these two figures together:
15000 + 37 = 15037
Hope this helps. Feel free to ask any more questions and I will try my best to help you.
- profparis
Answer:
15,037 spectators
Step-by-step explanation:
Total number of spectators :
⇒ Spectators in covered area + Spectators in the open
⇒ 15000 + 37
⇒ 15,037 spectators
why is 64006 not a perfect square
Answer:
This might not be the best answer but here goes:
A perfect square has to be a number that is expressed by 2 of the same integer multiplied by each other.
To check if a number is a perfect square, you find the square root of it. 64006 does not have a whole square root, meaning it is not a perfect square number. Its square root is:
252.9940711... (very close but not quite whole)
1. A perfect square number always has its square root to be a whole number. But, the square root of 64006 is is 252.99407... (not whole), so it is not a perfect square.
2. A perfect square number can only be written as the product of 2 odd numbers or 2 even numbers. But, 64006 can be written as 32003 x 2 -> NOT a perfect square.
Find the x-intercept and the y-intercept.
3x-2y=6
Show work to get Brainliest
Answer:
There are several different ways to get the x-intercept and y-intercept of an equation. The way that I usually do it is setting one of the variables to zero and finding what the other variable is equal to. For example, if we set x to 0 that means that we are finding the y-intercept as the value of x is 0 which is the y-axis. This is also how it works when setting y to 0. First lets find the x intercept by setting y to 0.
[tex]3x - 2y = 6[/tex]
[tex]3x - 2(0) = 6[/tex]
[tex]\frac{3x}{3} = \frac{6}{3}[/tex]
[tex]x = 2[/tex]
We now know that the x-intercept is 2 and now we need to determine what the y-intercept is. Now we can just set the x to 0 and find the y-intercept.
[tex]3x - 2y = 6[/tex]
[tex]3(0) - 2y = 6[/tex]
[tex]\frac{-2y}{-2} = \frac{6}{-2}[/tex]
[tex]y =- 3[/tex]
Therefore, we know that our x-intercept is (2, 0) and our y-intercept is (0, -3) because the first spot in the coordinate pair is the x-value and the second one is the y-value.
Hope this helps
7. Refer to the bar chart in question 6. Which age group recorded the highest number of children
Answer:
The age group that recorded the highest number of children is 7.
Step-by-step explanation:
We can clearly can see from the graph, that the 7 year old age group has 5 children, which is more than the rest of the age groups.
Hope this helps:) Goodluck!
Select the correct answer from each drop-down menu. determine the number of real solutions for each of the given equations. equation number of solutions y = -3x2 x 12 y = 2x2 - 6x 5 y = x2 7x - 11 y = -x2 - 8x - 16
It should be noted that in the equation y = -3x² + x + 12, there are two real solutions.
How to calculate the real solutions?It should be noted that the number of real solutions of a quadratic equation is represented by y = ax² + bx - c.
In the equation, equation y = -3x² + x + 12, the coefficients are a = -3, b = 1 and c = 12. The discriminant will be:
= 1² - 4(-4)(12)
= 145
It is positive, therefore, it has two solutions.
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Which of the following equations is not a linear equation?
x + y = 4
B. 2x – y = 1
C. x 3=2
D. y = 4
Answer:
C
Step-by-step explanation:
A linear equation consists of Ax+By=C
That is the only one without that kinda format
Answer:
The Answer Is C
Step-by-step explanation:
3. Carmen received the following
scores on her last six homework
pages: 23, 24, 20, 19, 19, and 21.
What is Carmen's average
homework score?
A 19
8 20
C 21
D 22
Сот
"A
1
What is the perimeter of the triangle?
An equations that has zero POI with 2x -6y = 12
(must have different values)
Answer: Y= 1/3x - 2
Step-by-step explanation:
How would you write this expression as a sum or difference?
The provided log can be written as sum of (1/5)log₃(x) + log₃(y) after using the log property.
What is a logarithm?It is another way to represent the power of numbers, and we say that 'b' is the logarithm of 'c' with base 'a' if and only if 'a' to the power 'b' equals 'c'.
[tex]\rm a^b = c\\log_ac =b[/tex]
We have:
[tex]= \rm log_3(\sqrt[5]{x} . y)[/tex]
As we know:
log(mn) = logm + logn
logmⁿ = nlogm
[tex]= \rm log_3({x^{\dfrac{1}{5}}} . y)\\\\= \rm log_3({x^{\dfrac{1}{5}}} )+log_3 (y)\\\\= \rm \dfrac{1}{5}log_3({x^{}} )+log_3 (y)\\\\[/tex]
Thus, the provided log can be written as sum of (1/5)log₃(x) + log₃(y) after using the log property.
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HELPPPP this is 7TH grade math and I don’t understand
Answer:
B.3x+8=66
Step-by-step explanation:
i think ito po Ang answer hehehe
Part A
x = some unknown number
x+8 = add on 8 to the number
3(x+8) = triple the previous result
Therefore, one equation to set up is 3(x+8) = 66
This is the same as 3x+24 = 66 because 3(x+8) = 3x+3*8 = 3x+24. Use the distributive property to multiply that outer 3 to each term inside.
Answers:C) 3x+24 = 66
D) 3(x+8) = 66
============================================================
Part B
Let's solve for x. I'll show the steps for each equation mentioned. When you write out the steps, you probably only need to pick one equation to solve.
3(x+8) = 66
x+8 = 66/3
x+8 = 22
x = 22-8
x = 14
Or
3x+24 = 66
3x = 66-24
3x = 42
x = 42/3
x = 14
Either way, we get the same x value. To confirm this answer, replace x with 14 in either equation and simplify fully. You should get 66 on both sides.
Answer: x = 14If a positive is subtracted from a negative, will the answer be true or false. ans:true
Answer:
It depends. If the negative number is greater than the positive, the answer is true. Otherwise, false.
Please help me.. First person who answers, gets brainliest :)
Answer:
i believe the answer is 41312432
Joseph built a sandbox in his backyard that is 2 meters wide, 4 meters long, and 2 meters tall. What volume of sand does he need to completely fill the sandbox?
A) 20 cubic meters
B) 16 cubic meters
C) 8 cubic meters
D) 12 cubic meters
Answer: B) 16 cubic meters
Step-by-step explanation:
To find the volume of a rectangular prism like this sandbox, multiply the length, height, and width together. 2*2*4 = 16.
Answer:
the answer would be 16 cubic meter because l*w*t which is because l*w*t which is 4*2*2