Complete the square to transform the expression x2 - 2x - 2 into the form a(x - h)2 + k
Answer:
A
Step-by-step explanation:
Find the vertex form of the quadratic function below.
y = x^2 - 4x + 3
This quadratic equation is in the form y = a{x^2} + bx + cy=ax
2
+bx+c. However, I need to rewrite it using some algebraic steps in order to make it look like this…
y = a(x - h)^2 + k
This is the vertex form of the quadratic function where \left( {h,k} \right)(h,k) is the vertex or the “center” of the quadratic function or the parabola.
Before I start, I realize that a = 1a=1. Therefore, I can immediately apply the “completing the square” steps.
STEP 1: Identify the coefficient of the linear term of the quadratic function. That is the number attached to the xx-term.
STEP 2: I will take that number, divide it by 22 and square it (or raise to the power 22).
STEP 3: The output in step #2 will be added and subtracted on the same side of the equation to keep it balanced.
Think About It: If I add 44 on the right side of the equation, then I am technically changing the original meaning of the equation. So to keep it unchanged, I must subtract the same value that I added on the same side of the equation.
STEP 4: Now, express the trinomial inside the parenthesis as a square of a binomial, and simplify the outside constants.
After simplifying, it is now in the vertex form y = a{\left( {x - h} \right)^2} + ky=a(x−h)
2
+k where the vertex \left( {h,k} \right)(h,k) is \left( {2, - 1} \right)(2,−1).
Visually, the graph of this quadratic function is a parabola with a minimum at the point \left( {2, - 1} \right)(2,−1). Since the value of “aa” is positive, a = 1a=1, then the parabola opens in upward direction.
Example 2: Find the vertex form of the quadratic function below.
The approach to this problem is slightly different because the value of “aa” does not equal to 11, a \ne 1a
=1. The first step is to factor out the coefficient 22 between the terms with xx-variables only.
STEP 1: Factor out 22 only to the terms with variable xx.
STEP 2: Identify the coefficient of the xx-term or linear term.
STEP 3: Take that number, divide it by 22, and square.
STEP 4: Now, I will take the output {9 \over 4}
4
9
and add it inside the parenthesis.
By adding {9 \over 4}
4
9
inside the parenthesis, I am actually adding 2\left( {{9 \over 4}} \right) = {9 \over 2}2(
4
9
)=
2
9
to the entire equation.
Why multiply by 22 to get the “true” value added to the entire equation? Remember, I factored out 22 in the beginning. So for us to find the real value added to the entire equation, we need to multiply the number added inside the parenthesis by the number that was factored out.
STEP 5: Since I added {9 \over 2}
2
9
to the equation, then I should subtract the entire equation by {9 \over 2}
2
9
also to compensate for it.
STEP 6: Finally, express the trinomial inside the parenthesis as the square of binomial and then simplify the outside constants. Be careful combining the fractions.
It is now in the vertex form y = a{\left( {x - h} \right)^2} + ky=a(x−h)
2
+k where the vertex \left( {h,k} \right)(h,k) is \left( {{{ - \,3} \over 2},{{ - 11} \over 2}} \right)(
2
−3
,
2
−11
).
Example 3: Find the vertex form of the quadratic function below.
Solution:
Factor out - \,3−3 among the xx-terms.
The coefficient of the linear term inside the parenthesis is - \,1−1. Divide it by 22 and square it. Add that value inside the parenthesis. Now, figure out how to make the original equation the same. Since we added {1 \over 4}
4
1
inside the parenthesis and we factored out - \,3−3 in the beginning, that means - \,3\left( {{1 \over 4}} \right) = {{ - \,3} \over 4}−3(
4
1
)=
4
−3
is the value that we subtracted from the entire equation. To compensate, we must add {3 \over 4}
4
3
outside the parenthesis.
Therefore, the vertex \left( {h,k} \right)(h,k) is \left( {{1 \over 2},{{11} \over 4}} \right)(
2
1
,
4
11
).
Example 4: Find the vertex form of the quadratic function below.
y = 5x^2 + 15x - 5
Solution:
Factor out 55 among the xx-terms. Identify the coefficient of the linear term inside the parenthesis which is 33. Divide it by 22 and square to get {9 \over 4}
4
9
.
Add {9 \over 4}
4
9
inside the parenthesis. Since we factored out 55 in the first step, that means 5\left( {{9 \over 4}} \right) = {{45} \over 4}5(
4
9
)=
4
45
is the number that we need to subtract to keep the equation unchanged.
Express the trinomial as a square of binomial, and combine the constants to get the final answer.
Therefore, the vertex \left( {h,k} \right)(h,k) is {{ - \,3} \over 2},{{ - \,65} \over 4}
2
−3
,
4
−65
.
Answer:
(x - 1 )^2 - 3
Step-by-step explanation:
( x - 1 )^2 + ( -3)
x^2 - 2x + 1 - 3
x^2 - 2x - 2
NEED HELP!
Create a table of points from the equation f (x)= 3x^2 -8x + 2
Answer:
The second table
Step-by-step explanation:
To create table of points using the function, [tex] f(x) = 3x^2 - 8x + 2 [/tex], substitute the value of x in each case.
Thus,
For x = -1,
[tex] f(-1) = 3(-1)^2 - 8(-1) + 2 = 3(1) + 8 + 2 = 3 + 8 + 2 [/tex]
[tex] f(-1) = 13 [/tex]
For x = 0
[tex] f(0) = 3(0)^2 - 8(0) + 2 = 3(0) - 0 + 2 = 0 - 0 + 2 [/tex]
[tex] f(0) = 2 [/tex]
For x = 1,
[tex] f(1) = 3(1)^2 - 8(1) + 2 = 3(1) - 8 + 2 = 3 - 8 + 2 [/tex]
[tex] f(1) = -3 [/tex]
For x = 2,
[tex] f(2) = 3(2)^2 - 8(2) + 2 = 3(4) - 16 + 2 = 12 - 16 + 2 [/tex]
[tex] f(2) = -2 [/tex]
For x = 3,
[tex] f(3) = 3(3)^2 - 8(3) + 2 = 3(9) - 24 + 2 = 27 - 24 + 2 [/tex]
[tex] f(3) = 5 [/tex]
The second table is the correct answer.
Ten people were chosen at random and surveyed. The survey asked participants for the number of hours they sleep per night and the amount of their annual income. Letting X represent the number of hours the participant sleeps per night and Y represent the participant's annual income, the surveyor calculated the correlation coefficient between X and Y to be 0.29. Interpret the correlation coefficient calculated by choosing the statement below which correctly describes the correlation between X and Y. A. weak negative correlation B. strong negative correlation C. strong positive correlation D. weak positive correlation
Answer:
A. R=0.86; strong correlation
Step-by-step explanation:
The correlation coefficient of 0.29 indicates that the correlation is a weak positive correlation. Thus option (D) is the correct answer.
What is correlation?"Correlation is a statistical tool that studies the relationship between two variables. Data sets have a positive correlation when they increase together, and a negative correlation when one set increases as the other decreases".
For the given situation,
Correlation coefficient = 0.29
Positive correlation: the two variables change in the same direction.
Negative correlation: the two variables change in opposite directions.
No correlation: there is no association or relevant relationship between the two variables.
The correlation coefficient lies between 0 to 0.3 indicating that the correlation is a weak positive correlation.
Hence we can conclude that option (D) weak positive correlation is the correct answer.
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The number of boxes of cookies you buy or the amount the cookies will cost in dollars which one is independent vairable
Answer:
Step-by-step explanation:
When you go shopping for anything, you know that the more of that something you buy, the more money you are going to spend. In other words, the amount of money you spend depends directly upon the amount of stuff you buy. So the number of boxes of cookies you buy is the independent variable and the amount of money you spend on the cookies is the dependent variable.
Find the standarddeviation of 125, 136, 150, 119, 150, and 143.
Answer:
S.D=46.04
Step-by-step explanation:
steps are in the picture.
If you have question about it you can ask.Thanks
I suck at math so please help :)
Answer:
the answer to this question is
B. 1/2
hope this helps u
The graph below shows the survey results for a group of students who were asked how many honors classes they have taken and how many elective classes: How many elective classes would a student likely have taken if he or she has taken 12 honors classes? 15, because y = one halfx + 9 12, because y = y = negative one halfx + 9 6, because y = one halfx + 9 3, because y = negative one halfx + 9
Answer:
3, because [tex]y=-\frac{1}{2}x+9[/tex].
Step-by-step explanation:
Looking at this graph, we can start to determine the equation for it.
The y-intercept of this graph is 9, therefore there will be a constant of 9.
We can find the slope by looking at rise over run. It vertically travels -1 for every 2 horizontally. So the slope is [tex]-\frac{1}{2}[/tex].
Making this into an equation gets us [tex]y=-\frac{1}{2}x+9[/tex].
Now we can substitute 12 into this equation as x.
[tex]y=-\frac{1}{2}(12)+9\\ y=-6+9\\y=3[/tex]
Hope this helped!
Answer:
the other person is correct! C:
Step-by-step explanation:
what is the volume of the circular cone below?
Answer:
200.96
Step-by-step explanation:
Volume of cone=(1/3)*pi*r^2*h
Volume=(1/3)*pi*16*12=64*3.14=200.96
How many positive even factors of 48 are greater than 24 and less than 48
Answer: 0
Work Shown:
Factors of 48 = {1, 2, 3, 4, 6, 8, 12, 16, 24, 48}
Erase the odd numbers of that list to get {2, 4, 6, 8, 12, 16, 24, 48}
Then highlight stuff that is greater than 24, and less than 48 at the same time.
No factors fit this description since 24 cannot be larger than itself, and 48 cannot be smaller than itself.
Answer: 0
Step-by-step explanation:
There is no number greater than 24 and less than 48.
b) The area of 4-walls and ceiling of a room is 118 m². If the room is 6 m long and 4 m high, find the breadth of the room.
Step-by-step explanation:
you can check the answer by putting 5 on the place of B... you will get the lateral surface area
118 m²...
hope it helps
photo of freedom fighter quotes on white sheet.
pls send me fast
Answer:
Freedom is any case,
is only possible
by constantly
struggling for it.
Albert Einstein
PLS SIMPLIFY b3·b^−5·b^11
A) b^9
B) b^15
C) b^19
D) b^-165
Answer:
a) b⁹
Step-by-step explanation:
b³ • b⁻⁵ • b¹¹
add the exponents
b³ ⁺ ⁽⁻⁵⁾ ⁺ ¹¹
b⁹
Answer:
b^9
Step-by-step explanation:
b^3·b^−5·b^11
Since the bases are the same, and we are multiplying, we can add the exponents
b^(3+-5+11)
b^9
Legolas shoots 3 arrows at once from his bow. He has 177 arrows. How many times can Legolas shoot his bow before he needs more arrows?
Answer:
59
Step-by-step explanation:
3x=177
3x represents the # of arrow he can shoot at once every time
177 represents the total # of arrow he has
Answer:
59
Step-by-step explanation:
177/3=59
Correct answer gets brainliest and 5 stars
Answer:
16 ft
Step-by-step explanation:
Slant Height=sqrt(Radius^2+Height^2)
Height=sqrt(20^2-12^2)=sqrt(256)=16 ft
Correct answer gets brainliest and 5 stars
Answer:
Does the answer help you?
please help me with that
Answer:
[tex]\frac{16}{81}[/tex]
Step-by-step explanation:
[tex](\frac{27}{8} )^{-\frac{4}{3} }[/tex]
[tex]=((\frac{3}{2} )^3)^{-4/3}[/tex]
[tex]=(\frac{3}{2} )^{-4}[/tex]
[tex]=(\frac{2}{3} )^{4}[/tex]
[tex]=\frac{16}{81}[/tex]
Answer:
16/81
Step-by-step explanation:
a negative exponent means 1/...
the number in the numerator means "to the power of".
the number in the denominator means take the root of that power.
so, we have to take the third root of the expression, or this then to the power of 4, and finally build 1/... if the whole result.
and the sequence is not making a difference.
the third root of of 27/8 = 3/2
this to the power of 4 = 81/16
this 1/... = 16/81
what are the prime numbers
Answer:
numbers that cannot be reduced when squared, ex: 1,3,5,
Step-by-step explanation:
These numbers factors are themselves and 1, to find if it is a prime number you can try to find the factors and if it is just itself and 1, then it is a prime number
can someone please help me
Answer:
y=3
Step-by-step explanation:
7y-(5y+4)=10
7y-5y+4=10
-4 -4
7y-5y=6
2y=6
÷2 ÷2
y=3
Multi-Step Literal Equations
Solve the following equation for a. Be sure to take into account whether a letter is capitalized or not.
g= b(a+[tex]D^{2}[/tex])
[tex]\\ \sf\longmapsto g=b(a+D^2)[/tex]
[tex]\\ \sf\longmapsto g=ba+bD^2[/tex]
[tex]\\ \sf\longmapsto g-bD^2=ba[/tex]
[tex]\\ \sf\longmapsto a=\dfrac{g-bD^2}{b}[/tex]
or
[tex]\\ \sf\longmapsto a=\dfrac{g}{b}-D^2[/tex]
[tex]x^{2} +5x+3[/tex]+2x^{2}+10x-15=0
please mark this answer as brainlist
Which of the following options have the same value as 75\%75%75, percent of 969696?
Answer:
90
Step-by-step explanation:
A Food Marketing Institute found that 35% of households spend more than $125 a week on groceries. Assume the population proportion is 0.35 and a simple random sample of 75 households is selected from the population. What is the probability that the sample proportion of households spending more than $125 a week is between 0.36 and 0.42
Answer:
The probability that the sample proportion of households spending more than $125 a week is between 0.36 and 0.42 is 0.3115
Step-by-step explanation:
From the question, we can deduce the following;
n = 75
p = 0.35
where q = 1-p = 1-0.35 = 0.65
To compute the probability that the sample proportion of households spending more than $125 a week is between 0.36 and 0.42, we start by calculating the standard deviation of sample proportion.
Mathematically;
Standard deviation of sample proportion = √pq/n
SD = √(0.35)(0.65)/75 = 0.055 which is approximately 0.06
Let’s now compute the z-scores
For 0.36, we have ; (0.36-0.35)/0.06 = 0.01/0.06 = 0.17
For 0.42, we have; (0.42-0.35)/0.06 = 0.07/0.06 = 1.17
So the probability we want to calculate is :
P(0.17<z<1.17) = P(z<1.17) - P(z < 0.17) = 0.8790 - 0.5675 = 0.3115
A city has a property tax rate of 70 mills and an assessment level of 40%.
What is the effective property tax rate? Round your answer to the nearest
tenth of a percent.
Mill rate is a tax rate—the amount of tax payable per dollar of the assessed value of a property. Mill is derived from the Latin word millesimum, meaning thousandth. As used in property tax, 1 mill is equal to $1 in property tax levied per $1,000 of a property's assessed value.
Item 4
Ellie has 20 books on her shelf. Four of these books are nonfiction, and the rest are fiction.
What is the ratio of fiction books to nonfiction books on the shelf?
5:4
5:1
4:1
I don't know.
Answer:4:1 just taking to test as soon as you
Step-by-step explanation:
The ratio of fiction books to nonfiction books on the shelf is, 4
What is the ratio?A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, while the divisor or number that is dividing is referred to as the consequent.
Given that,
Ellie has 20 books on her shelf
Four of these books are nonfiction
The rest are fiction
The ratio of fiction books to nonfiction books on the shelf = ?
The number of fiction books = ?
The number of fiction books = 20 - 4
= 16
Ratio = fiction/nonfiction
= 16/4
= 4
Hence, the ratio is 4
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PLEASE HELP ME I WILL MARK BRAINLIEST!
compute the range of the figures into the table
Create a triangle of your choice on the grid. Measure the lengths of all the sides on the triangle and record them in the table.
Step-by-step explanation:
The program I used tells me the lengths, though I could use the law of cosines or Pythagoras's Therom for this.
AB: 2
BC: 3
AC: About 3.61
Also, point A is (-2, 4), point B is (-2, 2), and point C is (1, 2)
Hope this helps!
37/50 of a number is what percentage of that number?
Answer:
74% percentage of 37/50
Answer:
74%
Step-by-step explanation:
37/50 * 100 = 74%
When you want to obtain percentages, in most of the cases you multiply by 100.
Which statement about the transformation is true?
Consider the transformation.
It is isometric because the side lengths remained the
same.
It is isometric because all angle measures remained the
same.
It is not isometric because the side lengths did not remain
the same.
It is not isometric because the angle measures did not
remain the same.
The image of the transformation is missing so i have attached it;
Answer:
Option C - The transformation is not isometric because the lengths did not remain the same.
Step-by-step explanation:
Transformation means that it preserves the length of the original figure which means that it is a distance preserving transformation.
Now, from the image of the question attached, the two figures can be said to be isometric if they are congruent.
Now, for the figure displaying the transformation we can see that the size of the original figure has changed.
We can see that the figure is dilated by a scale factor of 2 as each of the sides of the polygon which is a trapezoid is increased by a factor of 2.
Due to the fact that the lengths of sides of the original figure and transformed figure are are not same, we can say that the lengths are not preserved.
Thus, the transformation is not isometric because the lengths did not remain the same.
Answer:
C : It is not isometric because the side lengths did not remain the same.
Credits go to the person above me.
;)
Step-by-step explanation:
EDGE 2021
1) Complete the table
2) find the mean of the random variable x. Use the formula in the photo
Answer:
a. Please check the explanation for filling of the empty column on the table
b. The mean of the random variable x is 7/11
Step-by-step explanation:
a. Firstly, we are concerned with completing the table.
To do this, we simply need to multiply the values in the column of x by the values in the column of p(x)
Thus, we have the following;
2. 3 * 2/36 = 6/36
3. 4 * 3/36 = 12/36
4. 5 * 4/36 = 20/36
5. 6 * 5/36 = 30/36
6. 7 * 6/36 = 42/36
7. 8 * 5/36 = 40/36
8. 9 * 4/36 = 36/36
9. 10 * 3/36 = 30/36
10. 11 * 2/36 = 22/36
11. 12 * 1/36 = 12/36
b. We want to find the mean of the random variable x.
All what we need to do here is add all the values of x•P(x) together, then divide by 11.
Thus, we have
(2/36 + 6/36 + 12/36 + 20/36 + 30/36 + 42/36 + 40/36 + 36/36 + 30/36 + 22/36 + 12/36)/11
Since the denominator is same for all, we simply add all the numerators together;
(252/36) * 11 = 252/396 = 63/99 = 7/11
i give you 5 stars please help
Answer:
C....................
Answer:
(C) [tex]x=4[/tex]
Step-by-step explanation:
A line will be parallel to the y-axis if It’s x never changes.
In A, x is always being -y, so that’s going to change all the time.
In B, x is always becoming y, so that is changing too.
In C, x is always being 4, so this never changes.
In D, x is always 4 times y, so this changes.
Hope this helped!