Note: There must be -4 instead of 4 otherwise all options are incorrect.
Given:
A polynomial function has a leading coefficient of 3 and roots -4, 1, and 2, all with multiplicity 1.
To find:
The polynomial function.
Solution:
The general polynomial function is defined as:
[tex]P(x)=a(x-c_1)^{m_1}(x-c_2)^{m_2}...(x-c_n)^{m_n}[/tex]
Where, a is the leading coefficient, [tex]c_1,c_2,...,c_n[/tex] are the zeros with multiplicity [tex]m_1,m_2,...,m_n[/tex] respectively.
It is given that a polynomial function has a leading coefficient of 3 and roots 4, 1, and 2, all with multiplicity 1. So, the polynomial function is defined as:
[tex]P(x)=3(x-(-4))^1(x-1)^1(x-2)^1[/tex]
[tex]P(x)=3(x+4)(x-1)(x-2)[/tex]
Therefore, the correct option is A.
Question 1 of 10
Which function results after applying the sequence of transformations to
f(x) = x5?
• shift left 1 unit
• vertically compress by
3
• reflect over the y-axis
Answer: B) [tex]f\left(x\right)=\frac{1}{3}\left(-x-1\right)^{5}[/tex]
Step-by-step explanation:
When graphing x5 the parent function and plugging in the equation for B the only equation that fits the criteria of
*shifting left 1 unit
*vertically compressed by 1/3
*reflect over the y-axis
So the answer is B
The function after the transformation is f ( x ) = ( 1/3 ) ( -x + 1 )⁵
How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units: y=f(x+c) (same output, but c units earlier)
Right shift by c units: y=f(x-c)(same output, but c units late)
Vertical shift:
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
Stretching:
Vertical stretch by a factor k: y = k × f(x)
Horizontal stretch by a factor k: y = f(x/k)
Given data ,
Let the function be represented as f ( x )
Now , the value of f ( x ) is
f ( x ) = x⁵
On reflecting over the y axis , we get
f ( x ) = ( -x )⁵
On vertically compressing by a factor of ( 1/3 ) , we get
f ( x ) = ( 1/3 ) ( -x )⁵
And , shifting 1 unit to the left , we get
f ( x ) = ( 1/3 ) ( -x + 1 )⁵
Hence , the transformed function is f ( x ) = ( 1/3 ) ( -x + 1 )⁵
To learn more about transformation of functions click :
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what is the answer of this questoin 2c-3b+6+7b-2b+11?
Answer:
[tex]2c+2b+17[/tex]
Step-by-step explanation:
-----------------------
Given:
[tex]2c-3b+6+7b-2b+11[/tex]
---------->>>>
Collect like terms.
[tex]2c+(-3b+7b-2b)+(6+11)[/tex]
---------->>>>
Simplify
[tex]2c+2b+17[/tex]
------------------------
Hope this is helpful.
Answer:
2c-2b+17 if using algebra
Step-by-step explanation:
firstly group like terms 2c+(-3b)+7b-2b+6+11
2c-2b+17
exterior angle equation is 3p-15 interior angles are p and p+15
9514 1404 393
Answer:
p = 30
angles 30°, 45°; exterior: 75°
Step-by-step explanation:
The exterior angle is equal to the sum of the remote interior angle:
3p -15 = p + (p +15)
p = 30 . . . . . . . . . . . . . add 15-2p
The interior angles are 30°, 45°; the exterior angle is 75°.
Which equation does the graph above represent?
A. y = 2x
B. y = 1/2x
C. y = 1/2
D. y = 2 + x
Answer:
y=2x
Step-by-step explanation:
Hi there!
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when x is 0).
1) Determine the slope (m)
The slope is the rate of change, or the number of units the line moves up divided by the number of units the line moves to the right.
Looking at the graph, we can see that for every 1 space the line travels to the right, the line travels 2 spaces up. This makes the slope of the line 2. Plug this into [tex]y=mx+b[/tex]:
[tex]y=2x+b[/tex]
2) Determine the y-intercept (b)
When x=0 on the graph, y=0. Therefore, the y-intercept is 0. Plug this into [tex]y=2x+b[/tex]:
[tex]y=2x+0\\y=2x[/tex]
I hope this helps!
30g of cornflakes contain 2.5 grams of fat how many grams of fat are there in 320g of cornflakes
Hello :)
Use proportionality
We know that :
30g of cornflakes ⇒ 2.5g of fat
320g of cornflakes ⇒ xg of fat
x = 320 * 2.5 ÷ 30 ≈ 26.7 g of flat
Have a nice day!
Find the length of AC. Round to the nearest hundredth if necessary.
Answer:
13.86
Step-by-step explanation:
In ∆ ABC ,
cos 30° = AC/BC√3/2 = AC/ 16 AC = 16 * √3/2 AC = 8√3 AC = 8 * 1.732AC = 13.86A single equation representing both lines x+y=0 and x+2y = 0 is ?
Answer:
The single equation is [tex]y = 0[/tex]
Step-by-step explanation:
We are given the following system of equations:
[tex]x + y = 0[/tex]
[tex]x + 2y = 0[/tex]
From the first equation:
[tex]x = -y[/tex]
Replacing in the second equation:
[tex]-y + 2y = 0[/tex]
[tex]y = 0[/tex]
The single equation is [tex]y = 0[/tex]
Help mee A scout troop are hiking in a forest. Starting from their base, they walk 4.2km south followed by 7.1km west. They want to walk the shortest distance back to their base. On what bearing should the scouts walk?
Answer:
They should walk on a bearing of 59.4 degrees
Step-by-step explanation:
Given
[tex]South = 4.2km[/tex]
[tex]West = 7.1km[/tex]
Required
The bearing back to the base
The given question is illustrated with the attached image.
To do this, we simply calculate the measure of angle a using:
[tex]\tan(a) = \frac{Opposite}{Adjacent}[/tex]
[tex]\tan(a) = \frac{7.1}{4,2}[/tex]
[tex]\tan(a) = 1.6905[/tex]
Take arctan of both sides
[tex]a = \tan^{-1}(1.6905)[/tex]
[tex]a = 59.4^o[/tex]
The bearing that the scout should work is N59.4W for the shortest distance
Trigonometric ratioTrigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.
Let A represent the angle that the scouts walk
tan∠A = 4.2/7.1
A = 30.6°
The bearing that the scout should work is N59.4W (90 - 30.6) for the shortest distance
Find out more on Trigonometric ratio at: https://brainly.com/question/4326804
Type the correct answer in each box. Use numerals instead of words.
Consider this expression.
- 4x2 + 2x - 5(1 + x)
What expression is equivalent to the given expression?
Answer:
4x² + 3x + 5
Step-by-step explanation:
Given:
- 4x² + 2x - 5(1 + x)
Open parenthesis
= - 4x² + 2x - 5 - 5x
= - 4x² + 2x - 5x - 5
= - 4x² - 3x - 5
Multiply through by -1
= - 1( - 4x² - 3x - 5)
= 4x² + 3x + 5
Write
4 in the first box
3 in the second box
5 in the third box
P and Q are points on the line 3y - 4x = 12
a Complete the coordinates of P and Q.
P(0, 1) Q(,0)
Answer:
Step-by-step explanation:
Since the coordinates of P are (0, 1), this makes P the y-intercept of that line. The y-intercept exists where x = 0. And in the coordinate (0, 1), x does in fact equal 0.
Since the one coordinate given in Q is (?, 0), this means that Q is the x-intercept of the line. The x-intercept exists where y = 0. And in the coordinate (?, 0), y does in fact equal 0. So in order to solve for the x coordinate of Q, we plug in a 0 for y and solve for x:
3(0) - 4x = 12 and
-4x = 12 so
x = -3
Find the area of this parallelogram.
13 cm
15cm
h
20cm
Answer:
260 square centimeters
Step-by-step explanation:
The formula for the area of a parallelogram is:
b x h
Where the base (b) is multiplied by the height (h) perpendicular to it.
The base here is 20 cm
The height perpendicular to the base is 13 cm
20 x 13 = 260
Or you can decompose and rearrange it into a rectangle. You will get 20 cm as the length and 13 cm as the width. The answer will be just the same!
Hope this helps!
Answer: 260 cm²
Step-by-step explanation: A parallelogram is a
quadrilateral with two pairs of parallel sides.
The formula for the area of a parallelogram is A = bh.
Since the base of the parallelogram is 20 cm and the height
of the parallelogram is 13 cm, we can plug this information into the formula
to get (20 cm)(13 cm) which gives us 260 cm².
So the area of the parallelogram shown is 260 cm².
Find the scale factor of the dilation. Then tell whether the
dilation is a reduction or an enlargement
Answer:
Enlargement
k =[tex]\frac{18}{4}[/tex] = [tex]\frac{9}{2}[/tex]
Step-by-step explanation:
k = [tex]\frac{new}{old}[/tex]
If k > 1 then its an enlargement.
If k < 1 then its a reduction
Use the coordinates of the labeled point to find the point- slope equation of the line
Answer:
[tex]A(0,3)(x_1,y_2)[/tex]
[tex]B(2,-5)(x_2,y_2)[/tex]
[tex]slope(m)=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\longrightarrow[/tex] [tex]\frac{-5-3}{2-0}[/tex]
[tex]\longrightarrow \frac{8}{2}[/tex]
[tex]\longrightarrow -4[/tex]
[tex]y-y_2=m(x-x_2)[/tex]
[tex]\longrightarrow y-(-5)=-4(x-2)[/tex]
[tex]\longrightarrow y+5=-4(x-2)[/tex]
[tex]ANSWER:B[/tex]
--------------------------
hope it helps...
have a great day!!
Hi, may someone help me with this question? Thank you!:)
“If f(x) = x^2 + 7, find f(x+2)”
Answer:
=x^2 +4x+11
Step-by-step explanation:
f(x) = x^2 + 7,
Replace x with x+2
f(x+2) = (x+2)^2 + 7
= (x+2)(x+2) +7
FOIL
= x^2 +2x+2x+4 +7
Combine like terms
=x^2 +4x+11
Answer:
[tex]f(x+2)=x^2+4x+11[/tex]
Step-by-step explanation:
In [tex]f(x)=x^2+7[/tex], for all values of [tex]x[/tex], we substitute [tex]x[/tex] (what is in the parentheses) into [tex]x^2+7[/tex] to output a [tex]y[/tex] value.
In [tex]f(x+2)[/tex], the term [tex](x+2)[/tex] is in the parentheses. Therefore, substitute [tex](x+2)[/tex] for [tex]x[/tex] in [tex]x^2+7[/tex] to find [tex]f(x+2)[/tex]:
[tex]f(x+2)=(x+2)^2+7[/tex]
Expand using [tex](a+b)^2=a^2+2ab+b^2[/tex],
[tex]f(x+2)=x^2+4x+4+7[/tex]
Combine like terms:
[tex]\boxed{f(x+2)=x^2+4x+11}[/tex]
options: (50)^1/2, (65)^1/2, (105)^1/2, (145)^1/2
last sentence options: 55.21, 85.16, 105.26, 114.11
Answer:
Step-by-step explanation:
Vertices of ΔABC are,
A(-3, 6), B(2, 1) and C(9, 5)
Use the formula to get the distance between two points [tex](x_1,y_1)[/tex] and[tex](x_2,y_2)[/tex],
Distance = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
By using the formula,
AB = [tex]\sqrt{(1-6)^2+(2+3)^2}[/tex]
= [tex]\sqrt{50}[/tex] units
BC = [tex]\sqrt{(5-1)^2+(9-2)^2}[/tex]
= [tex]\sqrt{65}[/tex] units
AC = [tex]\sqrt{(6-5)^2+(-3-9)^2}[/tex]
= [tex]\sqrt{145}[/tex]
Use cosine rule to find the measure of ∠ABC.
AC² = AB² + BC²- 2(AB)(BC)cos(B)
[tex](\sqrt{145})^2=(\sqrt{50})^2+(\sqrt{65})^2-2(\sqrt{50})(\sqrt{65})\text{cosB}[/tex]
145 = 50 + 65 - 2(√3250)cosB
cos(B) = [tex]-(\frac{145-115}{2\sqrt{3250}})[/tex]
= -0.26312
B = [tex]\text{cos}^{-1}(-0.26312)[/tex]
B = 105.26°
Find the area of the shape below.
11 cm
14 cm
9 cm
20 cm
Answer:
length divided by breadth divided by height
pls add me as brainliest
Solution:
20 - 1 1 = 9 cm
We can divide figure in 2 parts
rectangle = 14 cmx 11 cm
square = 9 cm x 9 cm
Area of rectangle = 14 * 11 = 154 cm²
Area of square = 9 * 9 = 81 cm²
Total area = 154 + 81
= 235 cm²
By how much does the price of a ticket for the gold section exceed the price for a ticket for the silver section?
Answer:
$8
Step-by-step explanation:
This system of equations relates the ticket price, in dollars, for seats in the silver (x) and gold (y) sections at a rock concert. x + 2y = 82 3x + y = 96 By how much does the price of a ticket for the gold section exceed the price for a ticket for the silver section?
Two equations are presented in this question
x + 2y = 82 equation 1
3x + y = 96 equation 2
Multiply equation 1 by 3
3x + 6y = 246 equation 3
subtract equation 2 from 3
5y = 150
y = 30
Substitute for y in equation 1
x + 2(30) = 82
x = 82 - 60
x = 22
difference in price = 30 - 22 = $8
x =
Plane X contains point C. Plane Y contains points A and
B.
How many planes exist that pass through points A, B,
and C?
f(x) = 3x + 2
What is (5)?
O A. 21
B. 17
C. 15
O D. 10
Is it possible to relate cyclones to mathematics? If yes, explain your thinking with the help of drawings (no need to use downloaded images) What are the mathematical concepts, theorems and shapes related to cyclones.
Answer:
hi shaurya
Step-by-step explanation:
Find the Value of x a.86 b.79 c.65 .72
Answer: D
Step-by-step explanation:
360° - 90° - 90° - 108° = 72°
(Sum of angles in a quadrilateral = 360°)
please help me please help me
Answer:
the answer is 1
Step-by-step explanation:
(√4 / √6) + (√6 / √4)
(2 / 2√3) + (2√3 / 2)
√3 / √3
= 1
use abc to find the value of sin b
Answer:
12/37
Step-by-step explanation:
We know ,
=> sin B = p/h
=> sin B = 12/ 37
Answer:
Step-by-step explanation:
[tex]Sin \ B = \frac{opposite \ side }{hypotenuse}\\\\Sin \ B = \frac{35}{37}\\\\[/tex]
For every quarter in his pocket, John also has 5 pennies in his pocket. If the total of the coins in John’s pocket is $ 5.40, how many quarters does John have in his pocket.
If a student receives a score of 80, how many questions did this student answer ... (5). Let x = the first number, and y = the second number ... If John only has 25 coins in his pocket, how many of the coins are quarters?
ages of Raju and Ravi are in the ratio 3:4 .Four years from now the ratio of their ages will be 4:5 . Find their present ages
Answer:
Their present ages are 12 years and 16 years.
Step-by-step explanation:
Given that,
Ages of Raju and Ravi are in the ratio 3:4 .Four years from now the ratio of their ages will be 4:5.
Let their present age is 3x and 4x.
Ages after four years from now will be:
[tex]\dfrac{3x+4}{4x+4}=\dfrac{4}{5}\\\\5(3x+4)=4(4x+4)\\\\15x+20=16x+16\\\\20-16=16x-15x\\\\x=4[/tex]
So,
Raju's present age is 3(4) = 12 years
Ravi's present age is 4(4) = 16 years
What is the value of p?
A)180
B)90
C) 116
D)58
Can someone help I don’t understand
Answer:
58
Step-by-step explanation:
If xy = 6 and x = 2, then x + y =
Answer:
5
Step-by-step explanation:
xy= 6
x= 2
x + y = ?
Plug in x=2 in the first equation:
2y=6
y=3
then plug x=2 and y=3 into the one you're solving for:
2+3=5
Hope that helps!
Glass bottles are worth 10 cents and aluminum cans are worth 5 cents. If Joe returns 12 glass bottles and 48 aluminum cans, how much money will he receive?
$1.20
$3.60
$2.40
$4.80
Answer: The answer is 3.60 dollars.
Step-by-step explanation:
1 bottle = 10 cents
12 bottles = 120 cents
100 cents = 1 dollar
1 cent = 1/100
120 = 1/100 * 120 = 1.2 dollars
now
1 aluminium can = 5 cents
48 cans = 5*48 = 240 cents
240 cents = 1/100 * 240 = 2.4 dollars
so total = (1.2+2.4) dollars
= 3.6 dollars
Which is the largest three-digit number of the form 9k + 1, where k is any positive integer?
Answer:
991
Step-by-step explanation:
We are looking for a number that is one more than a multiple of 9(denoted by the 9k) and is a three digit number. We can start by looking for 3-digit number divisible by 9 which are close to 1,000, since that is the next number larger than the largest three-digit number. We can tell that 999 is divisible by 9 because when divided it does not leave a remainder(you can also figure this out with divisibility tricks). We add one to get 1,000. This is not a three-digit number, so we need to look for a smaller multiple of 9. Subtracting 9 from 999, we get the next largest multiple of 9. We can add 1, and this time, the number, 991, is a three digit number, and the largest that can be in the form 9k + 1.
In a right triangle ABC angle B is the right angle and m angle C = 30 degrees if AC = 10 what is AB
Answer:
AB = 5Step-by-step explanation:
This is a 30°-60°-90° right triangle.
AC is hypotenuse, AB is opposite side to 30° angle.
We know that in such a triangle the side opposite to 30° angle is half the hypotenuse.
So we have:
AB = 1/2AC = 1/2(10) = 5