We can convert a parabola equation from standard form to vertex form. This is in the vertex form and has the formula y = a (x - h)2 + k. The vertex, in this case, is (h, k)=(-1,-6)
Standard Form
A parabola's standard form is: y = ax2 + bx + c
Here, a, b, and c are real numbers (constants), with a = 0. x and y are variables, with (x, y) representing a parabola point.
Vertex Form
A parabola's vertex form is: y = a (x - h)2 + k
Here, a, h, and k are real numbers, with a = 0. x and y are variables, with (x, y) representing a parabola point.
There is a "whole square" in the vertex form, y = a (x - h)2 + k. To convert from standard to vertex form, we simply need to complete the square. Aside from that, we have a formula method for doing this. Let us investigate both methods.
By Finishing the Square
Consider the following standard-form parabola: y = -3x2 - 6x - 9 and complete the square to get the vertex form. First, we must ensure that the x2 coefficient is 1. If the coefficient of x2 is NOT 1, the number will be placed outside as a common factor. We'll get: y = 3x2 6x 9 = 3 (x2 + 2x + 3).
Now, the coefficient of x2 is 1. Here are the steps to convert the above expression into the vertex form.
Determine the x coefficient. 3 (x2 + 2x + 3)
Divide it in half and square the result.
(2/2)^2 = 1^2 = 1
Y= -3(x2+2x+1-1 +3)
Using the appropriate identity, factor the perfect square trinomial formed by the first three terms.
We can use x2 + 2xy + y2 = (x + y) in this case.
x2 + 2x + 1 = (x + 1) in this case.
The preceding expression becomes:
Y= -3 (x2 + 2x + 1-1 +3)
Y= -3(x+1)^2 – 1 +3
The last two numbers should be simplified, and the outside number should be distributed.
Here, -1 + 3 = 2. As a result, the preceding expression becomes:
Y= -3(x+1)^2 + 2
Y = -3(x+1)^2 - 6
This is in the vertex form and has the formula y = a (x - h)2 + k. The vertex, in this case, is (h, k)=(-1,-6)
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For the question, let x be a rational number not equal to zero and let z be an irrational number. Determine whether the operation results in a value that is always rational, never rational, or sometimes rational.
x+z
x + z can't be result in a value that's rational.
x + z is never rational.
Given,
In the question:
Let x be a rational number not equal to zero and let z be an irrational number.
To determine whether the operation results in a value that is always rational, never rational, or sometimes rational.
Now, According to the question;
Assume, x + z results in a value that is rational
m = x + z
z = m - x (m, x is rational)
∴ m - x is a rational.
but z is an irrational number.
So, x + z can't be result in a value that's rational.
x + z is never rational.
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Help mee someoneeeeee
When collecting data, what is a sample?
Thank you for helping.
According to the given graph, the type of sample is continuous.
Sampling:
Basically, sampling refers the a statistical methodology that uses a portion of a total population to represent the full population.
Given,
Here we have the graph and that represents the data collection.
Now, we need to find the type sample used.
In order to find the type of sample used in the given data, we have to carefully looking into the point representation of the graph.
While we looking into the graph, we have identified that the point one the graph continuous and it will gradually moving upwards.
Therefore, the type of sample use here is continuous.
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ANSWER THIS FOR BRAINLISTEST
HELP ASAP !!!!
Write and graph linear equations
Answer:
first graph the y-intercept start at 0 and go up 2 plot that. Then, go up 7 from 2 and to the right 1
Step-by-step explanation:
Find the product of 4√6 and √10 in simplest form. Also, determine whether the
result is rational or irrational and explain your answer.
Answer:
8√15
Step-by-step explanation:
4√6 × √10 = 4√(6 × 10) = 4√60 = 8√15
Why is it 4 and 1/2? Where did you get the 1/2 and shouldn’t it be 5/10?
The reason for 1/2 and not 5/10 is it is a norm in math to reduce fractions to the least terms
What is equivalent form of fractions?This is a term used to refer to fractions that are equal even though they have different values in both he numerator and the denominator
Fractions are class of numbers that are of two parts the upper part is the numerator while the lower part is called the denominator.
In the given problem, 1/2
1 is the numerator2 is the denominator5/10 is an equivalent form of 1/2, this means that they are equal.
5/10 is shown to be equal to 1/2 by dividing by 5, this reduces the fraction to the least term which is 1/2. Using calculator can still show it that both numbers equal 0.5
In mathematics, it is preferred to reduce fractions to it's least form except it was stated.
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Orlando and Tanya are experimenting
with different mix ratios. Determine
whether each mix below will result in a
more concentrated (more
"grapefruity") or a less concentrated
(less "grapefruity") mix than the
original mix instructions. (The original
mix is the "Mix one can of concentrate
with 4 cans of cold water.")
Answer:
Whichever ratio has more water will be less concentrated (less "grapefruity"), and whichever ratio has more of the concentrate will be more concentrated (more"grapefruity").
assume that the heights of women are normally distributed with a mean of 63.5 inches and a standard deviation of 2.5 inches. a) what percentage of women have heights between 64 and 66 inches? b) find the third quartile q3; that is, find the 75th percentile.
The percentage of women that have heights between 64 and 66 inches is 42.06%
The third quartile is 65.1875 inches
Part a
Given: mean=63.5 inches
std. deviation=2.5 inches
To find percentage: we calculate probability and convert to percentage
P(64<X<66) would mean
Z statistic=64-63.5/2.5=0.2
=66-63.5/2.5=1
From Z table, we find corresponding probability values.
Therefore, P(64<X<66)=P(0.2<Z<1)=0.84134-0.42074
=0.4206
Thus percentage=0.4206*100
=42.06%
Part b
Finding the third quartile, Q3
Q3=mean+(0.675)*std. dev
Q3=63.5+(0.675*2.5)
=65.1875 inches
Hence, the third quartile is 65.1875 inches
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A line passes through the points (–14, 1) and (–4, 11). What is its equation in slope-intercept form?
Answer:
slope: (11-1)/(-4+14)
m: 10/10
M: 1
11 = -4 + b
b = 15
y = x + 15
3 1 0 -2
7 7 7 7
linear or not linear
I will give a star for the right one
The relationship given in the table is linear, as the rate of change of the output relative to the input is of zero.
How to identify linear relationships?Linear relationships are relationships in which the rate of change of the output relative to the input is constant, and called slope.
The points from the table in this problem are listed as follows:
Input of 3 with an output of 7.Input of 1 with an output of 7.Input of 0 with an output of 7.Input of -2 with an output of 7.The rate of change is given by the change in the output divided by the change in the input. Since the output remains constant, the rate of change remains constant at zero, and thus, this is a linear relationship.
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Find the value of x
6x-10
8x -20°
what is the major difference between the two sample t-test and paired t-test? when should we use one versus the other? g
Two sample t-test is used when the two samples of the data are statistically independent and the paired t-test is used, when data is in the form of matched pairs
The two-sample t-test defined as the method used to test whether the unknown population means of two groups are equal. The two sample t-test is also called independent samples t-test. Because the two samples of the data are statistically independent.
A paired t-test is used to find the difference between two variables usually separated by time for the same subject. By using the paired t-test we can find the mean difference between pairs of measurements is zero or not. So paired t-test is used, when data is in the form of matched pairs
Hence, two sample t-test is used when the two samples of the data are statistically independent and the paired t-test is used, when data is in the form of matched pairs
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Shay is painting a fence. The fence has 7 sections that are each 4 feet long and one 18 foot long section. What is the total length of the fence shay is painting?
Answer:
You would have to add all of them up, which is (7*4) + 18 = 46.
Therefore the answer is 46 feet for the length of the fence.
Kimberly's school is having a spring carnival. When Kimberly carries a bin of water balloons outside for the balloon toss, she trips and breaks 11 balloons. She counts the remaining water balloons, and there are 13 left.
Which equation can you use to find the number of water balloons w in the bin before Kimberly trips?
Equation can use to find the number of water balloons w in the bin before Kimberly trips is w-11=13.
Given that, Kimberly carries a bin of water balloons outside for the balloon toss, she trips and breaks 11 balloons.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The number of water balloons w in the bin before Kimberly trips.
She counts the remaining water balloons, and there are 13 left.
According to the question, the equation is
w-11=13
⇒ w=13+11
⇒ w=24
Hence, equation can use to find the number of water balloons w in the bin before Kimberly trips is w-11=13.
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Andrea mixes 2 cups of water with 2/3 of lemonade concentrate. Nicholas mixes 1.5 cups of water with 1/3 cup of lemonade concentrate. whose lemonade mixture tastes stronger. (bonus points to the first person to show there work!)
Complete an equation in slope-intercept form for the line that passes through (6, 5) and is parallel to the line x + 3y = 9.
The slope-intercept form is y = -1/3x +7 .
What is an explanation of the slope-intercept form?
A line's equation can be written in the slope-intercept form so that the slope (steepness) and y-intercept (where the line crosses the vertical y-axis) are immediately visible. This form is frequently known as the y = mx + b form.The standard form equation can be found by using the given point values in the given equation to find the new constant.
x +3y = (6) +3(5) = 21
Solving for y puts this equation into slope-intercept form.
3y = -x +21 . . . . . . . subtract x
y = -1/3x +7 . . . . . . divide by 3.
This is slope-intercept form.
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If f (x) = -3x - 2, find f (3).
Answer:
f(-3) = |(-3)-2| = |-5| = 5
cans of corn on sale at 10 for AED 32 find the cost of 15 cans
The cost of 15 cans will be AED 48.
According to the question,
We have the following information:
Cost of 10 cans = AED 32
Now, in order to find the cost of 15 cans, first we will find the cost of 1 can by dividing the total cost of 10 cans by the number of cans.
So, we have the following expression:
Cost of 1 can = 32/10
Cost of 1 can = AED 3.2
Now, we will find the cost of 15 cans using multiplication:
Cost of 15 cans = 15*3.2
Cost of 15 cans = AED 48
Hence, the cost of 15 cans will be AED 48.
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Complete the description of a real-world situation that could be modeled by the equation 30 +1.25x = 15
+25X.
A pet sitter charges a flat fee of $
sitter charges a flat fee of $15 plus $
two pet sitters the same?
plus $1.25 per hour to keep a dog during the day. A second pet
per hour. After (select)
Is the charge for the
Answer:
The question is possibly mistyped. The response below explains why, but also answers the questions based on a imagined relationship, instead of the one given.
Step-by-step explanation:
The equation 30 + 1.25x = 15 + 25X cannot be interpreted in the manner the questions are written. It is really only an expression, since there is no y in the equation, only x. We can, however, solve for x:
30+1.25x = 15 + 25x
30 - 15 = 25x - 1.25x
15 = 13.75x
x = (15/13.75)
x = 1.0909
There is no other information to discern what x represents. It could be light years to a particular comet, grams of a reagent, hours until the meat is cooked, or anything the imagination allows.
If, however, the equation were something like:
y = 1.25x + 15
we could answer the questions, as follows;
A pet sitter charges a flat fee of $15
sitter charges a flat fee of $15 plus $1.25/hr
The rest of the questions are not coherent.
==========
"two pet sitters the same?
plus $1.25 per hour to keep a dog during the day. A second pet
per hour. After (select)
Is the charge for the"
Identify the horizontal asymptote of f(x) = 3 over 5 x. y = 3 over 5 y = 0 y = 5 over 3 no horizontal asymptote
y = 0 is the horizontal asymptote for the given equation f(x)
To find : Horizontal Asymptote of function f(x)
Horizontal Asymptote
A horizontal line that a function's graph appears to coincide with but does not actually do so is said to be its horizontal asymptote. The end behavior of the function is determined using the horizontal asymptote.
Given that,
A function is provided as
f(x) = 3/5x
x serving as the denominator
By setting the denominator equal to 0, we can easily determine the vertical asymptote i.e,
Make x=0,
Specifically, the vertical asymptote is at y=0 or x=0
Identifying the horizontal asymptote
Write x in terms of y, then look for any instances where y differs.
We are able to write the given function
x=3/5
Here, y=0 renders x undefinable.
Thus y=0 is the horizontal asymptote.
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Answer:
B
Step-by-step explanation:
Got it right.
solve for x
2(x - 3 1/2)=10 3/4
exact form
x=71/8
Decimal Form:
x=8.875
Mixed Number Form:
x= 8 7/8
Answer:
Step-by-step explanation:
8 7/8
Sally rode 39 miles in 3 hours. To compute Sally's unit rate, divide both the numerator
and denominator by ___
The correct statement is 'Sally rode 39 miles in 3 hours. To compute Sally's unit rate, divide both the numerator and denominator by 3'
In this question, we have been given a statement 'Sally rode 39 miles in 3 hours. To compute Sally's unit rate, divide both the numerator and denominator by ____'
We need to complete given statement.
We know that, the denominator in unit rate is always 1.
So, to find unit rate we need to divide the denominator with the numerator in such way that the denominator becomes 1.
Sally's unit rate is 39/3 miles per hour
numerator = 39 and denominator = 3
We need to make denominator 1 so divide numerator as well as denominator by 3.
So, the unit rate would be, 13/1 = 13 miles per hour
Therefore, the correct statement is 'Sally rode 39 miles in 3 hours. To compute Sally's unit rate, divide both the numerator and denominator by 3'
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Please help, I'm having trouble
Answer:
Step-by-step explanation:
Okay, I can help. Please specify your question further so I can actually help you.
Select each relation that has a range of {-5, 0, 4, 7}?
Responses
A{(4, 2), (0, 6), (-5, 12), (7, 6), (4, -3)}
B{(18, 4), (-1, 0), (-3, -5), (6, 7), (2, 4)}
C{(6, -5), (-11, 0), (6, 4), (-3, 7), (2, 9)}
D{(0, 6), (-5, 12), (7, 6), (4, -3)}
E{(6, -5), (-2, 4), (4, 7), (1, 0)}
F{(-5, 4), (-2, 4), (4, 7), (1, 0)}
Answer: E and B
I did the quiz
A relation that has a range of {-5, 0, 4, 7} is:{(6, -5), (-2, 4), (4, 7), (1, 0)}
The correct answer is an option (E)
In this question, we have been given some relations.
We need to find a relation that has a range of {-5, 0, 4, 7}
We know that in a relation is a set of ordered pairs (x, y)
where x is input and y is output.
We know that range is collection of all output values.
Therefore, a relation that has a range of {-5, 0, 4, 7} is:
E {(6, -5), (-2, 4), (4, 7), (1, 0)}
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Determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in simplest form. 4 , 20 , 100
THe given series is GP series
common ratio n =5
The series is given 4,20,100...
then common ratio is 20/4=5
and another is 100/20=5
so common ratio is same
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slove the simultaneous equation 9x+4y=51
x intercept is 9/4 and y intercept is -51/4 for equation 9x+4y=51.
What is slope intercept form of line?The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
Given equation is nine times of x plus four y equal to fifty one
9x+4y=51
We have to convert this equation to slope intercept form
4y=51-9x
4y=9x-51
Divide both sides by 4
y=9/4x-51/4
x intercept is 9/4 and y intercept is -51/4
Hence x intercept is 9/4 and y intercept is -51/4 for equation 9x+4y=51.
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A recipe calls for 3 ounces of flour for every 2 ounces of sugar.Find the constant of proportionality
Answer:the answer is 3:2
Step-by-step explanation:
it is ratio of flour to sugar so the answer is 3:2
Answer:
1.5
Step-by-step explanation:
A recipe calls for 3 ounces of flour for every 2 ounces of sugar.Find the constant of proportionality
we have a ratio of 3 : 2
the constant of proportionality is:
3 : 2 = 1.5
please help with part (b) of this question!! thank you!!!
Answer:
p = 0, q = - 0.5-------------------------------
Part (b)Simplify first:
2p = q√76 + √192p = q(√4×√19) + √192p = 2q√19 + √192p = √19(2q + 1)We need both p and q be rational numbers and we know √19 is irrational.
It is only possible if both side are equal to zero:
2p = 0 ⇒ p = 0,2q + 1 = 0 ⇒ 2q = - 1 ⇒ q = - 0.5Answer:
[tex]\textsf{(a)} \quad h=3, \quad k=-2[/tex]
[tex]\textsf{(b)} \quad p=0, \quad q=-\dfrac{1}{2}[/tex]
Step-by-step explanation:
Part (a)Rearrange the given equation so that both sides are in the same form:
[tex]\begin{aligned}2-h\sqrt{11}&=-3\sqrt{11}-k\\2-h\sqrt{11}+k&=-3\sqrt{11}-k+k\\k+2-h\sqrt{11}&=-3\sqrt{11}\\k+2-h\sqrt{11}-2&=-3\sqrt{11}-2\\k-h\sqrt{11}&=-2-3\sqrt{11}\\\\\implies h&=3\\\implies k&=-2\end{aligned}[/tex]
Part (b)Rewrite and factor the right side of the equation.
As p and q are rationals, both sides of the equation have to equal zero.
[tex]\begin{aligned}2p&=q\sqrt{76}+\sqrt{19}\\2p&=q\sqrt{4 \cdot 19}+\sqrt{19}\\2p&=q\sqrt{4} \sqrt{19}+\sqrt{19}\\2p&=2q\sqrt{19}+\sqrt{19}\\2p&=\sqrt{19}(2q+1)\\\\\implies 2p&=0 \implies p=0\\\implies 2q+1&=0 \implies q=-\dfrac{1}{2}\end{aligned}[/tex]
hii help pls n thanks
Answer:
(1,8.5)
Step-by-step explanation:
find the midpoint of x and yx=(-1+3)÷2
=1
y=(9+8)÷2
=8.6
(1 , 8.5)
