Part of the graph of the function f(x) = (x + 4)(x - 6) is
shown below.
Which statements about the function are true? Select
two options.
py
The vertex of the function is at (1.-25).
6
4
The vertex of the function is at (1,-24).
The graph is increasing only on the interval -4< x < 6.
The graph is positive only on one interval, where x <-
4.
2-
-6
2
4
6
х
-2
-2
The graph is negative on the entire interval
4
4
6
Answers
Answer:
x-intercept(s):
( − 4 , 0 ) , ( 6 , 0 )
y-intercept(s):
( 0 , − 24 )
Step-by-step explanation:
The graph of the function f ( x ) = ( x + 4 ) ( x - 6 ) is plotted
What is a Parabola?A Parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone. A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line
The equation of the parabola is given by
( x - h )² = 4p ( y - k )
y = a ( x - h )² + k
where ( h , k ) is the vertex and ( h , k + p ) is the focus
y is the directrix and y = k – p
The equation of the parabola is also given by the equation
y = ax² + bx + c
where a , b , and c are the three coefficients and the parabola is uniquely identified
Given data ,
Let the parabolic equation be represented as A
Now , the value of A is
f ( x ) = ( x + 4 ) ( x - 6 ) be equation (1)
On simplifying , we get
The graph of the function is plotted and it is increasing only on the interval -4< x < 6
And , the vertex of the function is at P ( 1 , -25 )
Therefore , the function is f ( x ) = ( x + 4 ) ( x - 6 )
Hence , the function is f ( x ) = ( x + 4 ) ( x - 6 )
To learn more about parabola click :
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Related Questions
how do i round
$191.2392
Answers
Step-by-step explanation:
its round is 200.0000 .
hope it will help you Mark with brilliant
Answer:
$191
Step-by-step explanation:
What's a very complex equation that equals 3
Answers
Simplify to create an equivalent expression. -3(2+4k)+7(2k-)
Answers
Answer:
[tex]-3(2 + 4k) + 7(2k)[/tex] = [tex]2k - 6[/tex] or [tex]2(k - 3)[/tex]
Step-by-step explanation:
The question seem incomplete; however, the given parameter is assumed as
[tex]-3(2 + 4k) + 7(2k)[/tex]
Required
Simplify
[tex]-3(2 + 4k) + 7(2k)[/tex]
Start by opening the brackets
[tex]-3*2 -3* 4k + 7*2k[/tex]
[tex]-6 -12k +14k[/tex]
Collect Like Terms
[tex]-6 -12k +14k[/tex]
[tex]-6 + 2k[/tex]
Reorder the above expression
[tex]2k - 6[/tex]
The answer can be further simplified as
[tex]2(k - 3)[/tex]
Hence;
[tex]-3(2 + 4k) + 7(2k)[/tex] = [tex]2k - 6[/tex] or [tex]2(k - 3)[/tex]
Could someone clarrify this for me Factor completely 3x^2 + 2x − 1. (3x + 1)(x − 1) (3x + 1)(x + 1) (3x − 1)(x + 1) (3x − 1)(x − 1)
Answers
Answer:
(3x-1) (x+1)
Step-by-step explanation:
3x^2 + 2x − 1
3x^2 factors into 3x and x
-1 factors into -1 and 1
We want a postive 2x
(3x-1) (x+1)
Answer:
(3x-1)(x+1)
Step-by-step explanation:
3x² + 2x − 1
when factorizing , first look at the constant number( in this case it is 1 prime number), then find the GCF if found.
(3x )(x ) first step : 3x*x=3x^2
(3x- ) (x+ ) the sign for the constant is minus so the factoring has to be minus and plus on each side
(3x-1)(x+1) look at the 2x it has positive sign, means the sign is plus:
3x-1
x+1
regular standard multiplication
3x(x)-1(x)+1(3x)-1
3x²+2x-1
An architectural drawing lists the scale as 1/4" = 1'. If a bedroom measures 3 1/2" by 5 1/4" on the drawing, how large is the bedroom?
A. 20 ft by 30 ft
B. 7ft by 10.5 ft
C. 14 ft by 21 ft
D. 10 ft by 15 ft
Answers
Answer:
C. 14 ft by 21 ft
Step-by-step explanation:
First you want to set up an equation:
3 1/2" over x' = 1/4" over 1'
7/2 = 1/4x
14' = x
Next, do the same thing for the other side of the drawing (5 1/4")
5 1/4" over y' = 1/4" over 1'
21/4 = 1/4y
21' = y
So the answer is 14 ft by 21 ft (C)
The circle shown below is a unit circle, where ∠a=π/3 and the radius of the circle is 1.
Answers
Answer:
Step-by-step explanation:
A square and a triangle have equal perimeters. The lengths of the three sides of the triangle are 6.1 cm, 8.2 cm and 9.7 cm. What is the area of the square in square centimeters?
Answers
Answer:
Area of the square: 36
Step-by-step explanation:
6.1+8.2+9.7=24. Squares have 4 sides so 24/4=6. Area= base times highet, Base=6 Highet=6. 6 times 6=36!
Answer:
A=36 cm²
Step-by-step explanation:
the perimeter of triangle=a+b+c
P=6.1+8.2+9.7
P= 24 cm
P of triangle = P of square ( square has 4 equal sides):
24=4a
a=24/4=6
Area of square : a²
A=6² = 36 cm²
What is the underlined sentence mean can someone explain
Answers
Step-by-step explanation:
1235
Now when we talk about place values we have ones tens hundreds thousands ten thousands and so on. So when you look at no.1 its place value is ones because 1 is the first value.
So 2 is in tens.
Now the difference of tens and hundreds is tens follows the 2 place value and hundreds the next.
HOPE ITS HELPFUL
Answer:
4544
Step-by-step explanation:
The underlined sentence means that the 2nd and third values must be different, for example
4554 has 5 in the 2nd and 3rd place so cannot be this
4545 and 4544 have 4 and 5 in 2nd/3rd place so this is fine
Since the number is even then it is 4544
on the unit circle, which of the following angles has the terminal point coordinates of (\sqrt(2))/(2),-(\sqrt(2))/(2)
a)5pi/4
b)pi/4
c)3pi/4
d)7pi/4
Answers
Answer:
c)3pi/4
Step-by-step explanation:
I REALLY NEED HELP ASAP WITH THESE 3 QUESTIONS!!!!!!!!!
Answers
None
Some
None
None
6. Y= -x-14.50
7. x<11, in words x is less than eleven.it has infinite solutions.
8.
Give another name plane L
Answers
Answer:
Any one of these three works:
plane MOU
plane MNU
plane NOU
Step-by-step explanation:
A plane can be named by a single letter, such as L in this problem, or by any three non-collinear points that lie on the plane. Non-collinear points are points that do not all lie in a single line.
Points M, N, O, and U lie on plane L, so you can choose any 3 of the 4 points to name the plane with, but make sure all 3 points are non-collinear.
To name plane L with points, you cannot use points MNO together since they are collinear, but you can name it using point U plus any two of the points M, N, and O.
plane L can be named
plane MOU
plane MNU
plane NOU
Do not name it plane MNO
Which system of equations represents the matrix shown below?
Answers
Answer:
D
Step-by-step explanation:
just compare the augmented matrix to the possible answers and you will see it the option D
Which number line represents the solution set for the inequality –negative StartFraction one-half EndFraction x is greater than or equal to 4.x ≥ 4?
A number line from negative 10 to 10 in increments of 2. A point is at negative 2 and a bold line starts at negative 2 and is pointing to the left.
A number line from negative 10 to 10 in increments of 2. A point is at negative 8 and a bold line starts at negative 8 and is pointing to the left.
A number line from negative 10 to 10 in increments of 2. A point is at negative 2 and a bold line starts at negative 2 and is pointing to the right.
A number line from negative 10 to 10 in increments of 2. A point is at negative 8 and a bold line starts at negative 8 and is pointing to the right.
Answers
Answer:
it's b :)
Step-by-step explanation:
A number line which represents the solution set for the given inequality is: option B.
What is a number line?A number line refers to a type of graph with a graduated straight line which contains numerical values (both positive and negative numbers) that are placed at equal intervals along its length.
Next, we would solve the given inequality:
-½x ≥ 4
-x ≥ 4 × 2
x ≤ -8.
Therefore, a number line which represents the solution set for the given inequality is a number line from -10 to 10 in increments of 2 with a point at -8 and a bold line starts at -8 while pointing to the left.
Read more on number line here: brainly.com/question/24644930
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Is 2.73234(34 repeating) rational or irrational?
Answers
It's rational because of the repeating digits.
We have
x = 2.732343434…
Then
1,000x = 2,732.343434…
and
100,000x = 273,234.343434…
Subtracting these makes the fractional part go away, leaving you with
100,000x - 1,000x = 273,234.343434… - 2,732.343434…
100,000x - 1,000x = 273,234 - 2,732
99,000x = 270,502
x = 270,502/99,000 = 135,251/49,500
which is clearly a rational number.
Joey went for 15 auditions. Out of those 15 auditions, he got called back for 30% of them. Approximately how many did he get called back for?
Answers
Answer:
2
Step-by-step explanation:
Basically,
You just have to find 30% of 15...
So
The formula is...
BASE x PERCENT= AMOUNT
x times 0.3= 15
0.3/15=0.02
0.02 x 100= 2
So
Joey got called back for approximately 2 auditions.
Find the point-slope equation for
the line that passes through the
points (7,-21) and (-4,23). Use
the first point in your equation.
y +[? ] = [ ](x + [ ])
Answers
Answer:
y+(21)=-4(x-7)
Step-by-step explanation:
the point slope equation , two point
m=y2-y1/x2-x1
m=23+21/-4-7=44/-11= -4
y+(21)=-4(x-7)
45.55 to 1 decimal place
Answers
Answer:
45.6
Step-by-step explanation:
45.55
We want to round to the tenths place
we look at the hundredths place
.x5 Since the number in the hundredths place is 5 or greater, we round up 1
45.55 becomes 45.6
Answer:
the answer is 45.6
Step-by-step explanation:
[tex]\sf{}[/tex]
♛┈⛧┈┈•༶♛┈⛧┈┈•༶
3x+1/x^(2)-1=2/x-2+x/x-1
Answers
Answer:
x = 0 and 3 other real roots. See below.
Step-by-step explanation:
This is what you wrote:
[tex] 3x + \dfrac{1}{x^2} - 1 = \dfrac{2}{x} - 2 + \dfrac{x}{x} - 1 [/tex]
I don't think that is what you meant to write.
I think you meant to write this:
[tex] 3x + \dfrac{1}{x^2 - 1} = \dfrac{2}{x - 2} + \dfrac{x}{x - 1} [/tex]
I'm going to answer the second equation because that is what I think you meant.
[tex] 3x + \dfrac{1}{(x - 1)(x + 1)} = \dfrac{2}{x - 2} + \dfrac{x}{x - 1} [/tex]
[tex] 3x(x - 1)(x + 1)(x - 2) + (x - 2) = 2(x - 1)(x + 1) + x(x + 1)(x - 2) [/tex]
[tex] (3x^2 - 6x)(x^2 - 1) + x - 2 = 2x^2 - 2 + x(x^2 - x - 2) [/tex]
[tex] 3x^4 - 3x^2 - 6x^3 + 6x + x - 2 = 2x^2 - 2 + x^3 - x^2 - 2x [/tex]
[tex] 3x^4 - 7x^3 - 4x^2 + 9x = 0 [/tex]
[tex] x(3x^3 - 7x^2 - 4x + 9) = 0 [/tex]
[tex] f(x) = 3x^3 - 7x^2 - 4x + 9 [/tex]
[tex] f(-3) = -123 [/tex]
[tex] f(-2) = -35 [/tex]
[tex] f(-1) = 3 [/tex]
[tex] f(0) = 9 [/tex]
[tex] f(1) = 1 [/tex]
[tex] f(2) = -3 [/tex]
[tex] f(3) = 15 [/tex]
One root is x = 0.
There is a root between x = -2 and x = -1.
There is a root between x = 1 and x = 2.
There is a root between x = 2 and x = 3.
Plot the graph of f(x) = 3x^3 - 7x^2 - 4x + 9 and try to read the other three roots.
PLEASE ANSWER ASAP!!!!!!!!!!!!!!!!!!!!! The price of coffee has dropped to $2.30. Yesterday's price was $2.55. Find the percentage decrease. Round your answer to the nearest tenth of a percent
Answers
9.8 percent. All you have to do is subtract 2.30 from 2.55 and then divide that answer by 2.55 and then multiply that by 100
Answer:
9.8%
Step-by-step explanation:
Step 1: Find the change in price
2.55 - 2.30 = $0.25
Step 2: Divide change with original price
0.25 / 2.55 = 0.098....%
Step 3: Multiple by 100 to get percent
0.098 x 100 = 9.8%
Please Help Me With This I Will Mark Brainliest If You Are Correct!!!!!!!!!!! Determine the intervals on which the function is increasing, decreasing, and constant. A coordinate axis is drawn with a parabola pointing up that has vertex of 0,3. A). Increasing x 0 B). Increasing x > 0; Decreasing x 3 D). Increasing x > 3; Decreasing x < 3
Answers
Answer:
Increasing x> 3
Decreasing x< 3
Step-by-step explanation:
If you imagine drawing a tangent line (a line which touches a curve or shape at one point) at some point on the graph, you can see if a curve is increasing or decreasing at that point; and on the whole interval.
Doing this I find that the curve is decreasing on x< 3 and increases on x> 3
Jason wants to cut a rope that is 60 feet long into several equal pieces with nothing left over. How many pieces will he have if the length of each piece is the greatest integer possible? A)2 B)4 C)6 D)10
Answers
Answer:
A
Step-by-step explanation:
In order for the length of the pieces to be as great as possible, the number of pieces must be as small as possible. Jason can't keep the rope in one piece, that doesn't count as cutting the rope into pieces because he hasn't cut the rope. If there were 2 equal pieces, each piece would be 60 / 2 = 30 feet, and since 30 is an integer, the answer is 2.
what are the possible polynomial expression for dimensions of the cuboid whose volume is 12y2 + 8y -20
!
!
!
!
!
plz answer fast
Answers
Answer:
The answer is below
Step-by-step explanation:
The volume of a cuboid is the product of its length, height and breadth. It is given by:
Volume = length × breadth × height
Since the volume is given by the expression 12y² + 8y - 20. That is:
Volume = 12y² + 8y - 20 = 4(3y² + 2y - 5) = 4(3y² + 5y - 3y -5) = 4[y(3y + 5) -1(3y + 5)]
Volume = 4(y-1)(3y+5)
Or
Volume = 12y² + 8y - 20 = 2(6y² +4y - 10) = 2(6y² + 10y - 6y -10) = 2[y(6y + 10) -1(6y + 10)]
Volume = 2(y-1)(6y+10)
Therefore the dimensions of the cuboid are either 4, y-1 and 3y+5 or 2, y-1 and 6y+10
Answer:
plz mark me as brainiest
Help me please I need it
Answers
Answer:
Equation B.
Step-by-step explanation:
Subtract 4 from both sides in the equation 11r+4=55. You will see that it is equivalent to equation B.
Questions attached below ( *︾▽︾) Thanks for the help :)
Answers
Answer:
See below
Step-by-step explanation:
Attachment 1 : (a) Remember that it mentions x is the years since 1900. That would mean that the table is a bit different. To create this " new table " simply subtract 1900 from the years provided, and substitute.
To create this equation we will need a regression calculator. The equation will be as follows.
y = 0.125873x - 7.11916 ( note that you can double check this equation be substituting points from the table in the attachment )
(b) 2025 - 1900 = 126 years,
y = 0.125873(125) - 7.11916 = $ 8.614965
Minimum Wage : $ 8.614965
Attachment 2 : The rest of the problems can be solved similarly...
(a) Quadratic Regression Equation : - 0.49311x² + 23.2798x + 996.029
(b) - 0.49311(20)² + 23.2798(20) + 996.029 = 1264.381 mg/cm³
Attachment 3 : (a) Exponential Regression : 9.08292(1.09965)ˣ
(b) 9.08292(1.09965)⁶⁰ = [tex]2713.27743\dots[/tex] ( About 2713 recommendations )
If ∠A and ∠B are vertical angles, what is true about their measures?
Answers
Answer:
they are equal due to the vertical angles theorem
vertical angles theorem states that vertical angles, angles that are opposite each other and formed by two intersecting straight lines, are congruent
Answer:
They are equal
Step-by-step explanation:
I just had it on a exam and can I have brainliest Im trying to level up
Mr. Evans is considering offering a second after-school tutoring session for his math students each week. He records the number of students who attend his current sessions each week. The results from the last twelve weeks are shown in the dot plot below.
Answers
Answer:
The correct options are:
Four families said they ate out twice the previous week.
One family said they ate out 5 times the previous week.
The median best represents the data set.
Step-by-step explanation:
We are given a data set as:
4, 2, 2, 0, 1, 6, 3, 2, 5, 1, 2, 4, 0, 1
On arranging this data set in the frequency table we get:
Number of times they went for dinner Number of families
0 2
1 3
2 4
3 1
4 2
5 1
6 1
Hence, the range of the number line is between 0 to 6.
Also there are 4 dots above 2.
Hence, Four families said they ate out twice the previous week.
Also there is one dot above 5.
Hence, One family said they ate out 5 times the previous week.
The data set is not symmetrical since the median is 2 and the data points to the left and to the right do not have symmetry.
Hence, the data set is not symmetrical.
Also we know that the median of the data is the central tendency of the data and always best represents the data.
Hence, The median best represents the data set.
Hope it helped u!.... Btw can u plz mark me BRAINLIEST.. If it helped u?
Tysm!
Answer: The data is skewed left option c
Step-by-step explanation: A set of data is skewed when the entries of the data set are either distributed more to the left or more to the right on the number line. In this case, most of the data lies to the right. Therefore, the data is skewed left.
What are the approximate solutions of 4x2 + 3 = −12x to the nearest hundredth
Answers
Answer:
-0.28 and -2.73
Step-by-step explanation:
4x² + 12x + 3 = 0
(-12 +/- √144-48)/8
(-12 + 9.8)/8 and (-12 - 9.8)/8
-0.28 and -2.73
Find the following measure for this figure.
3
The volume for this figure??
Answers
Answer:
24
Step-by-step explanation:
Volume of a cuboid = length*base*height or 4*2*3=24. The volume of this cuboid is 24.
Which of the following are good ideas to use when gathering your resources?
Check all that apply.
O A. Form an equation:
B. Draw a diagram.
C. List potential formulas.
D. Guess at the solution and see if you are close.
E. Organize into a table.
F. Write down the facts.
Answers
Answer:
Organize into a table for good gatherings.
help me with this im giving out a lot of points like seriously -_-
Answers
Answer:
17.25 miles
1 hour, 56 minutes, and 20 seconds.
4 hours, 47 minutes, and 38 seconds.
Step-by-step explanation:
Part I:
For his three cycling sessions, he had traveled for 25.8 miles, 17.25 miles, and 27.42 miles.
The shortest distance he cycled is 17.25 miles.
Part II:
For his three cycling sessions, he spent: 1) 1 hour, 56 minutes, and 20 seconds, 2) 1 hour, 1 minute, and 13 seconds, and 3) 1 hour 50 minutes and 5 seconds.
The longest time he cycled for was 1 hour, 56 minutes, and 20 seconds.
Part III:
Lance's total cycling time is all the times added together. Therefore:
[tex]1\text{ hr} +1\text{ hr} +1\text{ hr} +56\text{ min} +1\text{ min}+50\text{ min} +20\text{ sec}+13\text{ sec} +5\text{ sec} \\\\=3\text{ hr} +107\text{ min}+38\text{ sec} \\\\=4\text{ hours, }47\text{ minutes}\text{ and 38 seconds}[/tex]
Answer:
i) 17.25 miles.
ii) 1 hrs :56 mins :20 secs
iii) 4 hrs :47 mins: 38 secs total.