For the function x³ - 6x² + 11x - 6, we have that:
a) The x-intercepts are: x = 1, x = 2, x = 3.
b) The y-intercept is of y = -6, while the end behavior is that it decreases to the left and increases to the right.
What are the x-intercepts of the function?The function is given as follows:
f(x) = x³ - 6x² + 11x - 6
x - 3 is a factor of the function, meaning that x = 3 is a x-intercept and the function can be written as follows:
x³ - 6x² + 11x - 6 = (x - 3)(ax² + bx + c)
Then we have to build a system of equations to find the coefficients as follows:
x³ - 6x² + 11x - 6 = ax³ + (b - 3a)x² + (c - 3b)x - 3c.
Then the coefficients are given as follows:
a = 1.b - 3a = -6 -> b = -3.-c = -6 -> c = 2.Then the factor is given by:
x² - 3x + 2.
Hence the other intercepts of the polynomial are found when:
x² - 3x + 2 = 0
(x - 2)(x - 1) = 0.
x - 2 = 0 -> x = 2.
x - 1 = 0 -> x = 1.
What is the y-intercept and the end behavior?The y-intercept is the value of f(x) when x = 0, that is, f(0), hence:
f(0) = 0³ - 6(0)² + 11(0) - 6 = -6.
For the end behavior, we need to find the limits as x goes to infinity, hence:
Positive infinity = (∞)³ = ∞. -> increases to right.Negative infinity = (-∞)³ = -∞. -> decreases to left.When the limit goes to infinity, we consider only the term with the highest exponent of the polynomial.
More can be learned about functions at https://brainly.com/question/24808124
#SPJ1
What’s x-5=1
Please please please help
Question 4 (10 points)
Answer:
1024
Step-by-step explanation:
4^5
= 4*4*4*4*4
= 16*4*4*4
= 64*4*4
= 256*4
= 1024
PRACTICE Describe the domain and range of each function using inequality or set-builder notation.
In the picture there are 4 graphs.
1st graph we get domain as (-∞,+∞) and range as (-∞,+∞).
2nd graph we get domain as [-4,4] and range as [3,-1].
3rd graph we get domain as [-4,1] and range as [1,-4].
4th graph we get domain as (-∞,4] and range as (-∞,-2].
Given that,
In the picture there are 4 graphs.
We have to find the domain and range of the each function using inequality or set-builder notation.
A function's domain is the set of values that we are allowed to enter into our function.
This set consists of the values of the x-axis for a function like f. (x).
The range of values that can be used as input for a function is called this. The values in this set hence, once we input an x value, the function returns. The y values are those.
1st graph we get domain as (-∞,+∞) and range as (-∞,+∞).
2nd graph we get domain as [-4,4] and range as [3,-1].
3rd graph we get domain as [-4,1] and range as [1,-4].
4th graph we get domain as (-∞,4] and range as (-∞,-2].
To learn more about domain visit: https://brainly.com/question/28135761
#SPJ1
Monster multiplacation Multiply using the standard algorithm. Show your stuff 92 43
The multiplication of 92 by 43 using standard algorithm is 3956.
What is standard algorithm?A standard algorithm or method in elementary mathematics is a certain computation technique that is typically taught for resolving particular mathematical issues.
To be more organized and effective, a typical algorithm uses the same steps each time we multiply, add, subtract, or divide.
Math problems are typically solved by aligning the places, starting with the ones on the right, moving on to the tens place, adding in any carryover numbers or regrouping if subtracting and so on.
Therefore, the multiplication is:
= 92 × 43
= 3956
Learn more about multiplication on:
https://brainly.com/question/10873737
#SPJ1
asap help please brainly okay
Answer:
2[tex]\sqrt{10}[/tex]
Step-by-step explanation:
using the rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] = [tex]\sqrt{ab}[/tex]
given
[tex]\sqrt{5}[/tex] × [tex]\sqrt{8}[/tex]
= [tex]\sqrt{5(8)}[/tex]
= [tex]\sqrt{40}[/tex]
= [tex]\sqrt{4(10)}[/tex]
= [tex]\sqrt{4}[/tex] × [tex]\sqrt{10}[/tex]
= 2[tex]\sqrt{10}[/tex]
PLEASE PLEASE PLEASE HELP DUE IN AN HOUR I WILL GIVE BRAINLIEST IF YOU ANSWER SHOW WORK HELPPPP ME THANK YOUU
The mean of the number of hours spent watching television is 15.75
The mean absolute deviation of the number of hours spent watching television is 6.625.
What is the mean and mean absolute deviation?Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number
Mean = sum of the numbers / total number
(10 + 11 + 22 + 7 + 17 + 17 + 20 + 31 + 0 + 12 + 19 + 23) / 12 = 189/12 = 15.75
Mean absolute deviation is the average of the sum of the absolute difference between the numbers and the mean.
MAD = 1/n ∑ l x - m(x) l
(|10 - 15.75) + |11 - 15.75| + |22 - 15.75| + |7 - 15.75| + |17 - 15.75|+ |17 - 15.75| + |20 - 15.75| + |31 - 15.75| + |0 - 15.75| + |12 - 15.75| + |19 - 15.75| + |23 - 15.75|
= (5.75 + 6.75 + 6.25 + 8.75 + 1.25 + 1.25 + 4.25 + 15.25 + 15.75 + 3.75 + 3.25 + 7.25) / 12 = 6.625
To learn more about mean, please check: https://brainly.com/question/25842202
#SPJ1
i need help with this, thanks
Answer:
151, 29, 151
Step-by-step explanation:
[tex]m\angle 2=29^{\circ}[/tex] (vertical angles)
[tex]m\angle 1=m\angle 3=151^{\circ}[/tex] (linear pair)
Answer:
[tex]m \angle 1= \boxed{159}\;^{\circ}\\\\m \angle 2= \boxed{21}\;^{\circ}\\\\m \angle 4= \boxed{21}\;^{\circ}[/tex]
Step-by-step explanation:
Angles on a straight line sum to 180°.
⇒ m∠3 + m∠4 = 180°
⇒ 159° + m∠4 = 180°
⇒ m∠4 = 21°
Vertical Angle Theorem
When two straight lines intersect, the opposite vertical angles are congruent.
Applying the Vertical Angle Theorem:
m∠1 = m∠3 = 159°m∠2 = m∠4 = 21°Vincent made a 2000 deposit into an account on august1 that yields 2% interest compounded annually. How much money will be in that account at the end of 5 years
The money in the account at the end of 5 years is 2208.16
Compound interestThe formula for calculating the compound interest is expressed according to the formula:
Compound interest = P(1+r)^t
Given the following parameters
Principal = 2000
rate = 2 % = 0.02
time = 5 years
Substitute
A = 2000(1+0.02)^5
A = 2000(1.02)^5
A = 2208.16
Hence the amount of money that will be in that account at the end of 5 years is 2208.16
Learn more on compound interest here: https://brainly.com/question/24924853
#SPJ1
What is the circumference of a circle with a radius of 14 feet using pie?
Answer:
Circumference 87.92 ft
Step-by-step explanation:
You have a radius of 14 so u multiply by 2 to get the diameter, then u mulptiply by pie (3.14) thats how u get the circumference.
14×2=28
28×3.14=87.92
Given that 2 x 108 = 20 × 107
Work out (2 x 108) + (4 × 107)
Give your answer in standard form.
The solution of the given expression will be ( 2.4 x 10⁸ ).
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that 2 x 10⁸ = 20 × 10⁷. The sum of the two exponential numbers will be calculated as:-
Sum = 2 x 10⁸ + ( 4 x 10⁷ )
Sum = 20 x 10⁷ + ( 4 x 10⁷ )
Sum = ( 20 + 4 ) x 10⁷
Sum = 24 x 10⁷
Sum = 2.4 x 10⁸
Therefore, the solution of the given expression will be ( 24 x 10⁷ ).
To know more about an expression follow
https://brainly.com/question/22390180
#SPJ1
i need help on this, thanks
Answer:
9
Step-by-step explanation:
Vertical angles are congruent, so:
[tex]16y=18y-18 \\ \\ -2y=-18 \\ \\ y=9[/tex]
Can someone explain how to do this to me!! Please thanks
Answer:
MP = 19
Step-by-step explanation:
MP = MN + NO + OP
we require to find OP and MN before we can evaluate MP
NO + OP = NP , that is
8 + OP = 15 ( subtract 8 from both sides )
OP = 7
and
MN + NO = M0 , that is
MN + 8 = 12 ( subtract 8 from both sides )
MN = 4
Then
MP = MN + NO + OP = 4 + 8 + 7 = 19
A(-3, 13), B(4, -15) Find the slope
what is 6 times 10 equal
Answer:
60
Step-by-step explanation:
10 + 10 + 10 + 10 + 10 + 10 = 60
Answer:
60
Step-by-step explanation:
Everytime you are multiplying by 10, you add a 0 to the number that you are multiplying by. In this case, the 6 turns into 60. This is a trick for the multiples of 10. Hope this helps!
round 38.4561 to 2 dp
Answer: 38.46
Step-by-step explanation:
↓
38.456 It means round by 0.05, so when you round you look at the place value after the specified digit.
in the usa, the cost of a phone is $1200. in the uk a phone is £920. using the exchange rate £1 = $1.36, work out the difference in cost of the phones in the usa and the uk
The difference between of the cost of the phones in the USA and the UK is $51. 2
What is exchange rate?Exchange rate can be defined as the price of the unit of foreign currency in terms of the home currency.
It is also known as the rate at which a currency is exchanged to another currency
From the information given, we have that;
The cost of a phone in the USA is $1200The cost of a phone in the UK is £920We also have that;
The exchange rate is expressed as;
£1 = $1.36
Now, let's convert the cost from dollars to euros, we have;
If £1 = $1.36
Then, £920 = $x
cross multiply, we have;
x = 920 × 1. 36
x = $1251. 36
Now, let's find the difference between the cost in the USA and UK, we have;
= $1251. 36 - $1200
= $51. 2
Hence, the difference is $51. 2
Learn more about exchange rate here:
https://brainly.com/question/2202418
#SPJ1
Bob purchased n notebooks. They were 4 dollars each. Write an equation to represent the total cost c that Bob paid.
Answer:
Cost Function is:
c = 4n
Or, using n as a function variable, we write:
c(n) = 4n
Step-by-step explanation:
c represents total cost
n represents notebook
4 represents cost per notebook
20 pointsssss
HELPPPPPPPPP
The coordinates of the point X are (1 + 2, 6 - 1.25) = (3,4.75).
The segments, PX and XQ, have lengths in a ratio of 1: 2.
What is meant by partition segment?A line segment is partitioned when it is divided into equal parts according to a specified ratio. The total number of partitions of the line segment must be equal to the sum of the two values in the ratio.
Suppose you have a line segment PQ on the coordinate plane, and you need to estimate the point on the segment 1/3 of the way from P to Q.
Where P exists at the origin and line segment is a horizontal one.
The length of the line exists 6 units and the point on the segment 1/3 of the way from P to Q would be 2 units away from P, 4 units away from Q and would be at (2, 0).
The segment exists not a horizontal or vertical line:
The components of the directed segment PQ exists (6, 3) and we require to estimate the point, say X on the segment 1/3 of the way from P to Q. Then, the components of the segment PX exists [tex]$\left\langle\left(\frac{1}{3}\right)(6),\left(\frac{1}{3}\right)(3)\right\rangle=\langle 2,1\rangle$[/tex].
Since the initial point of the segment exists at origin, the coordinates of the point X exists given by (0+2, 0+1) = (2, 1).
where neither P nor Q exists at the origin.
Use the end points of the segment PQ to estimate the components of the directed segment.
[tex]$\left\langle\left(x_2-x_1\right),\left(y_2-y_1\right)\right\rangle=\langle(7-1),(2-6)\rangle[/tex]
= (6,-4)
The components of the segment PX where X exists a point on the segment 1 / 3 of the way from P to Q are
[tex]$\left\langle\left(\frac{1}{3}\right)(6),\left(\frac{1}{3}\right)(-4)\right\rangle=(2,-1.25)$$[/tex]
To estimate the coordinates of the point X add the components of the segment PX to the coordinates of the initial point P.
Therefore, the coordinates of the point X exists (1+2,6-1.25) = (3, 4.75).
The segments, PX and XQ, have lengths in a ratio of 1: 2.
To learn more about partition segment refer to:
brainly.com/question/12913610
#SPJ13
Please help, I honestly have no clue what I’m doing.
Given the table below, determine the following
Y = -4x+15
(Picture below)
Answer:
y=-1
y=43
x=14
Step-by-step explanation:
So, you have the equation: [tex]y=-4x+15[/tex], and if we know one value we can easily solve for the other using some algebraic manipulation.
Find y when x=4.
For this we know one value, "x", and the other "y" value is unknown. This is actually not to hard if you notice that the equation we're given expresses the value of "y" in terms of "x".
So let's plug in the x-value: [tex]y=-4(4)+15\implies y=-16+15=-1[/tex]
So we get: y=-1, which turns out to be the solution!
Find y when x=-7
This is a similar process, so let's just get straight into it and plug x as -7
[tex]y=-4(-7)+15\\y=28+15\\y=43[/tex]
This is our solution, y=43
Find x when y = -41
So this case is a bit different since we're given the y-value and not the x-value, and as I mentioned the equation represents the value of y in terms of x.
We still do a similar process, except we'll use some more algebraic manipulation, but let's start by plugging in the known value:
[tex]-41=-4x+15[/tex]
Let's move the constant, 15, to the other side by subtracting by 15 to cancel both sides.
[tex]-56 = -4x[/tex]
Now we want to get the x alone, and the only "operation" being done on the x, is that it's being multiplied by the coefficient of -4. To cancel this out we want to divide both sides by -4 to maintain equality & cancel out the coefficient of -4 to one, which is just 1 * x which can be expressed as x as it's implied the coefficient is 1
[tex]14=x[/tex]
Now we have our solution!
CO2 How many atoms of each element are in the formula shown?
The number of atoms of each element in CO2 are; Number of O atoms = 2 and Number of C atoms = 1
What is the number of atoms present in the element?The number of atoms present in the molecule of an element is known as its Atomicity. For Example: In the H2O molecule, its atomicity is 3 as it has 2 molecules of hydrogen and 1 molecule of oxygen
Similarly, for the antiperspirant Al₂Cl(OH)₅. the number of atoms in each element can be found as follows;
Number of Al atoms = 2
Number of Cl atoms = 1
Number of H atoms = 1 x 5 = 5
Number of O atoms = 1 x 5 = 5
Applying the above to our question gives;
Number of C atoms = 1 atom
Number of O atoms = 2 Atoms
Read more about Number of Atoms in Element at; https://brainly.com/question/9049646
#SPJ1
In triangle OPQ, m/O = (2x - 5)°, m/P = (3x − 8)°, and m/Q = (10x - 17)°. What is the value of x?
The value of x is 14 °
What is angle sum property of triangle?The sum of the interior angles in a triangle is supplementary. In other words, the sum of the measure of the interior angles of a triangle equals 180°. So, the formula of the triangle sum theorem can be written as, for a triangle ABC, we have ∠A + ∠B + ∠C = 180°.
In ΔOPQ,
∠O = (2x- 5)°
∠P = (3x-8)°
∠Q= (10x- 17)°
Thus by angle sum property of triangle we know:
∠O+ ∠P + ∠Q = 180
thus 2x - 5 + 3x - 8 + 10x - 17 = 180
15x - 30 = 180
= 15 x = 180 + 30
= 15 x = 210
= x= 210 / 15
= x = 14 .
Thus ∠O = (2x- 5)° = 2X 14 - 5 = 23 °
∠P = (3x-8)° = 3× 14 - 8 = 44°
∠Q= (10x- 17)° = 10 × 14 - 17 = 123°
To know more about triangles visit:
https://brainly.com/question/8492819
#SPJ9
Given that △ABC ~△PQR, AC/PR=2.5 and the area of △PQR is equal to 8 cm, find the area of △ABC
The triangle ABC has an area of 50 square cm
How to determine the area of the triangle ABC?From the question, the given parameters are:
△ABC ~△PQRAC/PR =2.5 Area of △PQR is equal to 8 cm squareThe given parameters above mean that:
The triangles ABC and PQR are similar triangles
So, the area of the triangle ABC is then calculated as
Area of △PQR = Area of △ABC x (AC/PR)²
Substitute the known values in the above equation
So, we have the following equation
Area of △PQR = 8 x (2.5)²
Evaluate the product
Area of △PQR = 50
Hence, the area of the triangle ABC is 50 square cm
Read more about areas at
https://brainly.com/question/11920446
#SPJ1
**Please Help Im Trying To Make My Parent Proud Of Me i'll try to brainlistt!!** Angelina added 0.45 to 0.333 and made the conclusion that the sum of two rational numbers is rational. Is Angelina correct? Explain.
a
No, she is incorrect because 0.45 and 0.333 are irrational numbers.
b
Yes, she is correct because 0.45 and 0.333 are integers.
c
Yes, she is correct because 0.45 and 0.333 are rational numbers.
d
No, she is incorrect because the decimal numbers must be the same.
Answer:
c. Yes, she is correct because 0.45 and 0.333 are rational numbers. The sum of two rational numbers is a rational number.
Line AB is a straight
line.
9
1. m∠AOB = ____
Statement
1. ________
Reason
2. m∠AOE+m∠EOF+m∠FOB=m∠____ 2. ________
3. x + ____ +20° = ____ 3. Substitution
4. x = ____ 4. Algebra
The two column proof of the given angles are;
Statement 1; m∠AOB = 180°
Reason 1; Sum of angles on a straight line sums up to 180°
Statement 2; m∠AOE + m∠EOF + m∠FOB = m∠AOB
Reason 2; Opposite angles
Statement 3; x + 3x + x + 12 = 152
Statement 3; Substitution
Statement 4; x = 28°
Reason 4; Algebra
How to solve two column proof?From the attached image, we can complete the two column proof as follows;
Statement 1; m∠AOB = 180°
Reason 1; Sum of angles on a straight line sums up to 180°
Statement 2; m∠AOE + m∠EOF + m∠FOB = m∠AOB
Reason 2; Opposite angles
Statement 3; x + 3x + x + 12 = 152
Statement 3; Substitution
From statement 3, we can use algebra to find x as;
x + 3x + x + 12 = 152
5x + 12 = 152
5x = 152 - 12
5x = 140
x = 28°
Thus;
Statement 4; x = 28°
Reason 4; Algebra
Read more about two column proof at; https://brainly.com/question/18286984
#SPJ1
lenge You buy 3.16 pounds of oranges, 1.15 pounds of peaches, and 2.24 pounds of apples.
Using the addition, if you buy 3.16 pounds or oranges, 1.15 pounds of peaches and 2.24 pounds of apples , then the total bill is 6.55 pounds
The cost of the oranges = 3.16 pounds
The cost of the peaches = 1.15 pounds
The cost of the apples = 2.24 pounds
Then the total bill = The cost of the oranges + The cost of the peaches + The cost of the apples
Here we have to use the addition
Substitute the values in the equation
Then the total bill = 3.16 + 1.15 + 2.24
= 6.55 pounds
Hence, using the addition, if you buy 3.16 pounds or oranges, 1.15 pounds of peaches and 2.24 pounds of apples , then the total bill is 6.55 pounds
Learn more about addition here
brainly.com/question/658182
#SPJ1
How many miles does the car travel in 1.5 hours
Answer:
97 miles
Step-by-step explanation:
pls mark brainlest
Answer:
97 miles
Step-by-step explanation:
65 mph * 1.5 hours = 97 miles
the object on the scale drawing is 4 inches long. How many feet long is it in real life?
Answer:
half of a foot
Step-by-step explanation:
Conditional Statement: If the object has a remote, then it is a television.
Part A: Write the converse to the conditional statement.
Part B: Write a biconditional statement from the conditional statement.
Part C: Validate the biconditional statement from Part B. Use details to support your answer.
For given conditional statement 'If the object has a remote, then it is a television.'
Part A: converse to the conditional statement
'If it is a television, then the object has a remote.'
Part B: a biconditional statement
'The object has a remote if and only if it is a television.'
Part C: validation of biconditional statement
The biconditional statement is true because the conditional statement and the converse are true.
In this question, we have been given a conditional statement: 'If the object has a remote, then it is a television.'
Part A:
We need to write the converse to the conditional statement.
The converse of given conditional statement would be:
'If it is a television, then the object has a remote.'
Part B:
We need to write a biconditional statement from the conditional statement.
A biconditional statement of the given conditional statement would be:
'The object has a remote if and only if it is a television.'
Part C:
We need to validate the above biconditional statement.
The biconditional statement is true because the conditional statement and the converse are true.
Therefore, for given conditional statement 'If the object has a remote, then it is a television.'
Part A: converse to the conditional statement
'If it is a television, then the object has a remote.'
Part B: a biconditional statement
'The object has a remote if and only if it is a television.'
Part C: validation of biconditional statement
The biconditional statement is true because the conditional statement and the converse are true.
Learn more about conditional statement here:
https://brainly.com/question/28804708
#SPJ1
Keiko's penny bank is 1/6
full. After she adds 320 pennies, 1/2 it is full. How many pennies can Keiko's bank hold?
Answer: 960
Step-by-step explanation:
Let the number of pennies Keiko's bank hold be x
Now, According to the question,
[tex]\frac{1}{6} \times x+320=\frac{1}{2} \times x[/tex]
⇒ [tex]\frac{1}{6} \times x+320=\frac{x}{2}[/tex]
⇒ [tex]\frac{(x+1960)}{6}=\frac{x}{2}[/tex]
⇒ 2(x + 1920) = 6x
⇒ 2x + 3840 = 6x
⇒ 6x - 2x = 3840
⇒ 4x = 3840
⇒ [tex]x = \frac{3840}{4}[/tex]
⇒ x = 960
Hence, the total number of pennies Keiko's bank hold = 960.
The area of the Mojave desert is 25000 square miles.
A scale drawing of the Mojave desert has an area of 10 square inches.
What is the scale of the map
The scale of the map given the area of the desert and the area of the scale drawing is 1 square inch represents 2,500 square miles.
What is the scale?A scale drawing is either a larger or smaller image of another image or object. A scale drawing is enlarged or reduced using a scale. A map is a smaller scale drawing of an area. The scale is used to keep the proportion of the dimensions between the scale drawing and the original place similar.
In order to determine the scale of the drawing, divide the original square area by the square area of the scale drawing.
Scale of the drawing = original dimensions / dimensions of the scale drawing
25,000 square miles / 10 square inches = 2,500 square miles
The scale is 1 square inch represents 2,500 square miles. or 1 : 2,500.
To learn more about scale drawings, please check: https://brainly.com/question/26388230
#SPJ1