Answer:
[tex]p(x) = k(x -1)^{3} * (x -4)^{2} * (x +3)[/tex] --- General polynomial
The degree is 6
[tex]p(x) = -\frac{1}{3}(x -1)^{3} * (x -4)^{2} * (x +3)[/tex] --- The polynomial precisely
Step-by-step explanation:
Given
[tex](a,b,c)= (1,4,-3)[/tex] --- zeros
[tex](m_1,m_2,m_3) =(3,2,1)[/tex] --- multiplicities
Solving (a): The polynomial
The polynomial is represented as:
[tex]p(x) = (x -a)^{m_1} * (x -b)^{m_2} * (x -c)^{m_3}[/tex]
So, we have:
[tex]p(x) = (x -1)^{3} * (x -4)^{2} * (x +3)^{1}[/tex]
[tex]p(x) = (x -1)^{3} * (x -4)^{2} * (x +3)[/tex]
Include constant k; So, the polynomial becomes
[tex]p(x) = k(x -1)^{3} * (x -4)^{2} * (x +3)[/tex]
Solving (b): The degree (d)
To do this, add up the multiplicities
[tex]d = m_1 +m_2 +m_3[/tex]
[tex]d = 3+2+1[/tex]
[tex]d = 6[/tex]
The degree is 6
Solving (c): The actual polynomial
In (a), we have:
[tex]p(x) = k(x -1)^{3} * (x -4)^{2} * (x +3)[/tex]
[tex]p(0)=16[/tex] means:
[tex](x,p(x)) = (0,16)[/tex]
This gives:
[tex]16 = k(0 -1)^{3} * (0 -4)^{2} * (0 +3)[/tex]
[tex]16 = k(-1)^{3} * (-4)^{2} * (3)[/tex]
[tex]16 = k*-48[/tex]
Solve for k
[tex]k = \frac{16}{-48}[/tex]
[tex]k = -\frac{1}{3}[/tex]
So:
[tex]p(x) = k(x -1)^{3} * (x -4)^{2} * (x +3)[/tex]
[tex]p(x) = -\frac{1}{3}(x -1)^{3} * (x -4)^{2} * (x +3)[/tex]
Translate this phrase into an algebraic expression.
8 more than twice Matt's savings
Use the variable m to represent Matt's savings.
Answer:
2m+8
Step-by-step explanation:
Darcy harvests 8.3/4 acres of corn every 5/6 end fraction of an hour. Darcy harvests corn at a constant rate. How many acres does she harvest per hour?
Given:
Darcy harvests [tex]8\dfrac{3}{4}[/tex] acres of corn every [tex]\dfrac{5}{6}[/tex] of an hour.
Darcy harvests corn at a constant rate.
To find:
How many acres does she harvest per hour?
Solution:
We have,
Acres harvest in [tex]\dfrac{5}{6}[/tex] of an hours = [tex]8\dfrac{3}{4}[/tex]
Acres harvest in 1 hour = [tex]8\dfrac{3}{4}\times \dfrac{6}{5}[/tex]
= [tex]\dfrac{32+3}{4}\times \dfrac{6}{5}[/tex]
= [tex]\dfrac{35}{4}\times \dfrac{6}{5}[/tex]
Cancel out the common factors, we get
Acres harvest in 1 hour = [tex]\dfrac{7}{2}\times \dfrac{3}{1}[/tex]
= [tex]\dfrac{21}{2}[/tex]
= [tex]10\dfrac{1}{2}[/tex]
Therefore, she can harvest [tex]10\dfrac{1}{2}[/tex] acres of corn per hour.
The isosceles triangle has a perimeter of 7.5 m.
Which equation can be used to find the value of x if the
shortest side, y, measures 2.1 m?
y
O 2x-2.1 = 7.5
O 4.2 + y = 7.5
X
O y-4.2 = 7.5
0 2.1 + 2 x = 7.5
Mart this and return
Save and Exit
Next
Submit
Answer:
Option d) 2.1 + 2x = 7.5
Step-by-step explanation:
An isosceles triangle is a triangle with two equal sides.
Perimeter of a triangle is some of all the 3 sides.
Let the equal sides be x
Let the third side be y
Therefore,
Perimeter = x + x + y
7.5 = 2x + y
7.5 = 2x + 2.1 [ given shortest side, y = 2.1m ]
How can you solve for X in the proportion of7/8 equals X/24
Answer and Step-by-step explanation:
The last answer choice is correct.
Set the product of 7 and 24 equal to the product of 8 and x, and then solve for x
The process being used in the last answer choice is called Cross multiplication, and is used to find the unknown value in fractions.
[tex]\frac{7}{8}[/tex] × [tex]\frac{x}{24}[/tex]
7 × 24 = 8x
168 = 8x
21 = x
#teamtrees #PAW (Plant And Water)
What is the following difference?
2ab2/192an? -5 V81a4 b5
Answer:
C
Step-by-step explanation:
2ab * sqrt[3](192ab^2) - 5 * sqrt[3](81 a^4b^5) =
= 2ab * sqrt[3](4^3 * 3 * a * b^2) - 5 * sqrt[3](3^3 * 3 * a^3 * a * b^3 * b^2)
= 2ab * 4 sqrt[3](3 * a * b^2) - 5 * 3 * a * b * sqrt[3](3 * a * b^2)
= 8ab * sqrt[3](3 * a * b^2) - 15ab * sqrt[3](3 * a * b^2)
= -7ab * sqrt[3](3ab^2)
Answer: C
in circle O, the measure of ABC is 68. what is the measure of AC?
Math help please help thanks
Answer:
62
Step-by-step explanation:
Draw a line from the bottom of the 4 foot line straight across (horizontally) until it hits the vertical line on your left.
The two lines (the one you drew and the left vertical line) meet at right angles.
The upper figure is a rectangle.
Area = L * W
L = 5
W = 4
Area = 5 * 4
Area = 20
Now the bottom rectangle can be found the same way.
Area = L * W
L = 14
W = 3
Area = 14 * 3
Area = 42
The total area = 42 + 20
Total area = 62.
The comment was correct.
What is first quartile, third quartile, and interquartile range of 21 32 17 24 15 30 28 and 26. I found this quite confusing to understand
Given:
The data values are:
21, 32, 17, 24, 15, 30, 28 and 26.
To find:
The first quartile, third quartile, and interquartile range.
Solution:
We have,
21, 32, 17, 24, 15, 30, 28, 26
Arrange the data values in ascending order.
15, 17, 21, 24, 26, 28, 30, 32
Divide the data set in two equal parts.
(15, 17, 21, 24), (26, 28, 30, 32)
Divide each parenthesis in two equal parts.
(15, 17), (21, 24), (26, 28), (30, 32)
Now, the first quartile is:
[tex]Q_1=\dfrac{17+21}{2}[/tex]
[tex]Q_1=\dfrac{38}{2}[/tex]
[tex]Q_1=19[/tex]
The third quartile is:
[tex]Q_3=\dfrac{28+30}{2}[/tex]
[tex]Q_3=\dfrac{58}{2}[/tex]
[tex]Q_3=29[/tex]
The interquartile range is:
[tex]IQR=Q_3-Q_1[/tex]
[tex]IQR=29-19[/tex]
[tex]IQR=10[/tex]
Therefore, the first quartile is 19, third quartile is 29 and the interquartile range is 10.
What is the inverse of the function f(x) = 169x2 when x > 0?
Answer:
y = (√x)/13 for x > 0
Step-by-step explanation:
Actually, this is f(x) = 169x^2; the " ^ " indicates exponentiation. The graph consists of the right-hand half of the parabola 169x^2. Before we attempt to find the inverse function, we determine whether or not this function passes the vertical line test. If x is restricted to (0, infinity), a horizontal line intersects this graph only once. Therefore, this function has an inverse.
1. Replace 'f(x)' with 'y:' y = 169x^2
2. Interchange x and y: x = 169y^2
3. Solve for y: y^2 = x/169, or y = (√x)/13 for x > 0
Simply x+1/x^2+6x+5 step by step
Pls
Answer:
1 / (x+5)
Step-by-step explanation:
Factor the denominator
(x+1)/ (x+5)(x+1)
Cancel both (x+1)
=1/(x+5)
Math question, please help
==========================================================
Explanation:
Let's say that a = 25, b = 37 and c = 32 are the side lengths.
The uppercase letters A,B,C are opposite their lowercase counterparts.
That means angle A is opposite side a = 25
Apply the law of cosines to find angle A
a^2 = b^2 + c^2 - 2*b*c*cos(A)
25^2 = 37^2 + 32^2 - 2*37*32*cos(A)
625 = 1369 + 1024 - 2368*cos(A)
625 = 2393 - 2368*cos(A)
625 - 2393 = -2368*cos(A)
-1768 = -2368*cos(A)
-2368*cos(A) = -1768
cos(A)= (-1768)/(-2368)
cos(A) = 0.746621621621622
A = arccos(0.746621621621622)
A = 41.7014263373247
A = 41.7
SUPER URGENT: Complete the general form of the equation of a sinusoidal function having an amplitude of 6, a period of 2pi/3, and a phase shift to the left 1 unit.
y =
Answer:
y = 6·sin(3·(x - 1)) + c
Step-by-step explanation:
The general form of an equation for a sinusoidal function is presented ad follows;
y = a·sin(b·(x - h) + c
Where;
a = The amplitude of the equation
T = The period = 2·π/b
h = The phase shift
c = The vertical shift
From the question, we have;
a = 6,
2·π/3 = 2·π/b
∴ b = 3
h = 1
We get;
y = 6·sin(3·(x - 1)) + c.
What is the simple interest on $7430 invested for 3 years at 5% per annum simple interest?
Step-by-step explanation:
Simple interest=principal× time× rate/100
=7430×3×5/100
=1114.5
Answer:
114.5
Step-by-step explanation:
The numbers of blue and green beads Emma uses to make five different pieces of jewelry are recorded below. Which of the following equations relate to the number of green beads, G, to the number of blue beads, b?
Answer:
a
Step-by-step explanation:
follow the proportions
Answer:
A
Step-by-step explanation:
Use a number line to find the difference. -2 - (-6)
Answer:
-2 + 6 = 4
Step-by-step explanation:
During a pancake making contest, Team A makes 8 more pancakes than team B. Team C made twice as many pancakes is team B. Together, the three teams made a total of 72 pancakes. How many pancakes did team A make?
Answer:
A = 24
Step-by-step explanation:
Use the problems provided info!
A = B+8
C = 2B
72 = B+8+2B+B
72-8 = 4B
6434 = 4B/4
16 = B
A = 24
B = 16
C = 32
Identify the lines that are perpendicular: Line 1: y=4 Line 2: y=1/5x-5 Line 3:y=8 Line 4:y+5=-5(x+1)
Help me with this!!!
Answer:
4th answer
Step-by-step explanation:
g(h(x)) means to put the formula for h(x) into the formula for g( ).
[tex]g(h(x))=g(2x-2)=-3(2x-2)^3-2(2x-2)^2\\=-3(8x^3-24x^2+24x-8)-2(4x^2-8x+4)\\=-24x^3+72x^2-72x+24-8x^2+16x-8\\=-24x^3+64x^2-56x+16[/tex]
Cubing the binomial 2x - 2 can take some time!
Que sucede al estudiar el comportamiento del coseno (en triangulos no rectangulos) de la misma forma que estudamos el seno?
Answer:
En contraste con el seno, el coseno permite diferenciar triángulos obtusángulos de triángulos acutángulos.
Step-by-step explanation:
Por Geometría Euclideana sabemos que la suma de todos los ángulos internos de un triángulo es igual a 180°, si el triángulo no es rectángulo, entonces acutángulo o obtusángulo.
Un triángulo es acutángulo cuando todos sus ángulos son agudos, es decir, cuyas medidas sean mayores que 0° y menores que 90°, mientras que un triángulo es obtusángulo cuando uno de sus ángulos es mayor que 90° y menor que 180° y los dos ángulos restantes son agudos.
El seno es una función periódica y acotada entre -1 y 1, que es positiva entre 0° y 180°, significando que esta función trigonométrica es demasiado "débil" para diferenciar a un triángulo obtusángulo de uno acutángulo. En cambio, el coseno es una función periódica y acotada entre -1 y 1, que es positiva entre 0° y 90°, y negativa entre 90° y 180°, convirtiéndola en un criterio "fuerte" para diferenciar triángulos obtusángulos de triángulos acutángulos.
Subtract the
rational
7 - 12
Answer:
-5
Step-by-step explanation:
12-7=5
7-12=-5
If this helps please mark as brainliest
Arithmetic
7-12
Meaning, 12 less than 7.
7-12=-5
Finding the volume of the sphere
Answer:
16
Step-by-step explanation:
correct me if im wrong
if iam right follow me heart this answer
carry on learning
yourhelpinghandishereforyou
Answer:
V≈2144.66058
Step-by-step explanation:
V=(4/3)(π)r^3
V=(4/3)(π)(8)^3
V≈2144.66058
Find the missing angle
Answer:
∅ ≈ 34º
Step-by-step explanation:
sin = opp/hyp
∅ = arcsin opp/hyp
∅ = arcsin 14/25
Use calculator
∅ = 34.055797742567906
∅ ≈ 34º
Answer:
is 55
Step-by-step explanation:
×[tex]\frac{x}{1}*\frac{14}{25}[/tex]⇒0.56
cos0.56
55
Name the labelled points between A and C B and D B and E E and A
Help, need index form
Refer to the attachment for complete calculation.
3²× 11^-9
The volume of the following figure is
240 in² which of the following is the missing side length?
A. 7 in
B. 6 in
C. 8 in
D. 5 in
Answer:
B cause it same
Step-by-step explanation:
If am wrong correct me thanks
Which statement is true?
Question 13 options:
A)
–|3| = 3 and |4| = 4
B)
|–3| = 3 and –|–4| = –4
C)
|–3| = 3 and –|4| = 4
D)
|–3| = 3 and |–4| = –4
what is the value of x?
Answer:
6 sqrt(3) = x
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp/ hyp
sin 60 = x/12
12 sin 60 =x
12 ( sqrt(3)/2) =x
6 sqrt(3) = x
Answer:
x=6[tex]\sqrt{3}[/tex]
Step-by-step explanation:
take 60 degree as reference angle
using sin rule
sin 60=opposite/hypotenuse
[tex]\sqrt{3[/tex]/2=x/12
do cross multiplication
2*x=12*[tex]\sqrt{3}[/tex]
x=12[tex]\sqrt{3}[/tex] /2
x=6[tex]\sqrt{3}[/tex]
need some help...............
Answer:
I dont see the whole question
Step-by-step explanation:
Answer:
Remember the relation:
Distance = Speed*Time.
Then if we define:
y = distance
x = time
Speed = 50km/hr
Then we can write the relation between distance and time is:
y = (50km/hr)*x
This is the equation we need to graph.
To graph it, we can just find two points of that equation, and then draw a line that connects them:
For example if we have x = 0hr then:
y = (50km/hr)*0hr = 0km
then we have the point (0hr, 0km)
If now we use the point x = 1hr, then:
y = (50km/hr)*1hr = 50km
Then we also have the point (1hr, 50km)
Now we can draw these two points and connect them by a line, that line is the graph of the equation.
The graph of the equation can be seen below:
please help me with this equation
What is -33 + m = -29
Answer:
m = 4
Step-by-step explanation:
m = -29 + 33
Answer:
the answer is m=4
hope this helps
have a good day :)
Step-by-step explanation:
33+-29=4
