Consider this polynomial, where a is an unknown real number.
p(t) = x^4 +5x^3 + ax^2 - 3x + 11
The remainder of the quotient of P(x), and (x+ 1) is 17.
Braulio uses synthetic division to find the value of a, and Zahra uses the remainder theorem to find the value of a.
Answers
Answer:
Brauilo is wrong because he divided by (x+1) instead of (x-1)
Step-by-step explanation:
The remainder Theorem states that
if polynomial f(x) is divided by binomial x-a, the remainder will equal f(a). The factor is positive so the binomial is the same as
which is why we divide by -1, or subsitue -1 into the equation p(x).
The remainder of a polynomial division can be gotten using remainder theorem or synthetic division.
The true statement is: Brauilo did not find the value of a, because he divided by (x+1) instead of (x-1)
From the question, we have the following parameters:
[tex]\mathbf{p(x) = x^4 +5x^3 + ax^2 - 3x + 11}[/tex]
[tex]\mathbf{Divisor =x+ 1}[/tex]
[tex]\mathbf{Remainder = 17}[/tex]
First, we set the divisor to 0.
[tex]\mathbf{Divisor =x+ 1 = 0}[/tex]
So, we have:
[tex]\mathbf{x+ 1 = 0}[/tex]
Solve for x
[tex]\mathbf{x= -1}[/tex]
The above equation means that, the value of x that will be used to test the polynomial is -1
From the question,
Zahra used [tex]\mathbf{x= -1}[/tex]; this is represented as: P(-1)Braulio used [tex]\mathbf{x= 1}[/tex]; this is represented in the synthetic divisionHence, Braulio is incorrect, because he used the wrong value of x
Read more about polynomial division at:
https://brainly.com/question/12011809
Related Questions
10 less than k is 35 help please
Answers
Answer:
k = 45
Step-by-step explanation:
We can put this into an equation form:
k - 10 = 35
We can solve for k by adding 10 to both sides:
k = 45
Answer:
k-10=35
k=45
Step-by-step explanation:
Let's write this as an equation.
"10 less than k" means subtract 10 from k.
k-10
"is 35" means equals 35.
k-10=35
If we want to solve for k, we have to get k by itself on one side of the equation.
k-10=35
10 is being subtracted from k. The inverse of subtraction is addition. Add 10 to both sides of the equation.
k-10+10=35+10
k=35+10
k=45
Please answer this question now
Answers
Answer:
54
Step-by-step explanation:
To solve problems like this, always recall the "Two-Tangent theorem", which states that two tangents of a circle are congruent if they meet at an external point outside the circle.
The perimeter of the given triangle = IK + KM + MI
IK = IJ + JK = 13
KM = KL + LM = ?
MI = MN + NI ?
Let's find the length of each tangents.
NI = IJ = 5 (tangents from external point I)
JK = IK - IJ = 13 - 5 = 8
JK = KL = 8 (Tangents from external point K)
LM = MN = 14 (Tangents from external point M)
Thus,
IK = IJ + JK = 5 + 8 = 13
KM = KL + LM = 8 + 14 = 22
MI = MN + NI = 14 + 5 = 19
Perimeter = IK + KM + MI = 13 + 22 + 19 = 54
Please help please with geometry
Answers
Answer:
33
Step-by-step explanation:
HJ = HI + IJ
HJ = 3x - 9, HI = x and IJ = x + 5
So 3x - 9 = x + x + 5
Solve for x
Combine like terms
3x - 9 = 2x + 5
Add 9 to both sides
3x = 2x + 14
Subtract 2x from both sides
x = 14
Find HJ
HJ = 3x - 9
We have found that x = 14
HJ = 3(14) - 9
Multiply 3 and 14
HJ = 42 - 9
Subtract
HJ = 33
The ratio of the measures of the acute angles of a right triangle is $8:1$. In degrees, what is the measure of the largest angle of the triangle?
Answers
Answer:
The angles in the triangle and 10, 80 and 90
Step-by-step explanation:
The two angles that are left in a right triangle add to 90 degrees
8:1 means that there total is 9
8x+1x = 9x
9x = 90
Divide by 9
9x/9 = 90/9
x = 10
8*10 = 80
1*10 = 10
The angles are 80 and 10
The angles in the triangle and 10, 80 and 90
In an experiment you are to flip a two sided coin 100 times and record 55 heads up and 45 tails up. Determine the theoretical and experimental probability of getting a heads up in the experiment.
theorical = 11/20, experimental = 11/20
theorical = 1/2, experimental = 1/2
theorical = 1/2, experimental = 11/20
theorical = 11/20, experimental = 1/2
Answers
Answer: The answer is C.
Step-by-step explanation:
Because in the theory of the outcome is a 50/50 chance landing heads or tails. So, the theorectical probability is 1/2. Now the experimental must be 11/20.
Answer:
theory=1/2, experimental=11/20
Step-by-step explanation:
so when talking about theoretical probability you only consider the only possible outcomes which are either head or tail and since you haven't carried out any sort of experiment yet (many flips) you consider the number of outcomes of tossed once since it's theory which are two therefore the probability of each will be 1/2
but in experimental probability you now consider the number of times tossed and the outcomes of each side which is this case of heads will be 55/100 but in the answers they have simplified so it will be 11/20
What’s 4%x56? 2 A.2.24 B.1.12 or C.0.448
Answers
Answer:
A. 2.24
Step-by-step explanation:
Multiply 56 by 0.04
56(0.04)
= 2.24
Answer:
Option A
Step-by-step explanation:
4% * 56 =
0.04 * 56 = (Convert the percent into a decimal.)
2.24 (Multiply)
Hope this helps.
Write an equation to model the distance between the point (2,4) and any point along the curve
y=4x3 + 1.
Answers
Answer:
Distance D = √ [(2 - x)^2 + (3 - 4x^3)^2].
Step-by-step explanation:
Use the distance formula:
D = √[(x2 - x1)^2 + (y2 - y1)^2].
So here it is
D = √[(2 - x)^2 + (4 - y)^2] where x,y is any point on the curve.
D = √[2 - x)^2 + (4 - (4x^3 + 1))^2]
D = √ [(2 - x)^2 + (3 - 4x^3)^2]
68) Volume of a Bucket: Determine the volume of a cylindrical bucket in cubic inches if the bucket's radius is 5 in.
and the height is 12 in. The formula for the volume of a cylinder is V = yrah. Use the Te key on your calculator.
Answers
Answer:
V = 300[tex]\pi[/tex] in³ or 942.48 in³
Step-by-step explanation:
Use the cylinder volume formula, V = [tex]\pi[/tex]r²h, where r is the radius and h is the height.
Plug in the values and solve:
V = [tex]\pi[/tex](5²)(12)
V = 300[tex]\pi[/tex] in³ or 942.48 in³
Use graphing technology to find the range of the function f(x)=|x-3|
Answers
Answer:
[0,infinity)
Step-by-step explanation:
Since it's a modulus function, f(x) will have a range of [0,infinity). Use desmos for graphing it
A gardener has 1300 saplings. He wants to plant these in such a way that the number of columns and the number of rows remain same. Find the least number of more saplings he needs for this.
Answers
Answer:
69
Step-by-step explanation:
Square root of 1300= 36
(37)²>1300>(36)²
Therefore , the requirement no. to be added to get a perfect square
=(37)²=1369
= 1369- 1300=69
The least no. Of sapling he needs for this = 69
Shelly and Terrence earned points in a game by completing various tasks. Shelly completed x tasks and scored 90 points on each one. The expression below shows Terrence's total points in the game: 90x − 20 What does the constant term of the expression represent? (2 points)
Answers
Answer:
the constant term of the expression represents the difference between Shelly and Terrence points.
Trevor spent $27 and now has no money left. He had $___ before his purchase. He had $__before his purchase
Answers
Answer:
27
Step-by-step explanation:
Which expression is equivalent to the product of p+7/3 and6/p , where p0? PLZZZZ HELPPPPPPP
Answers
Answer: [tex]6+\dfrac{14}{p}[/tex] .
Step-by-step explanation:
To find : The expression is equivalent to the product of [tex]p+\dfrac73\text{ and }\dfrac6p[/tex], where p ≠0.
Product of [tex]p+\dfrac73\text{ and }\dfrac6p[/tex] = [tex](p+\dfrac73)\times\dfrac6p[/tex]
Using distributive property: [tex](b+c)a= ba+ca[/tex]
[tex](p+\dfrac73)\times\dfrac6p=p\times\dfrac6p+\dfrac73\times\dfrac6p\\\\= 6+\dfrac{7}{1}\times\dfrac2p\\\\=6+\dfrac{14}{p}[/tex]
Hence, the required expression is [tex]6+\dfrac{14}{p}[/tex] .
Answer:
B!!!
Step-by-step explanation:
Multiply then divide every number by 2 to simplify.
Please help me solve this, urs really important for me. Thank you
Answers
Answer:
24 pieces
Step-by-step explanation:
Adam
1/2's means 2 pieces each so 8 *2 = 16 pieces
Briana
1/4 means 4 pieces each 8*4 = 32 pieces
Carlos
1/9 so 9 pieces each 8*9 = 72 pieces
Carlos - ( adam+ briana)
72 - ( 16+32)
72 -(48)24
Find the surface area and volume of cone. A = rs + r2 V = 1/3r2 h A cone's slant height (s) is 15 cm and its radius is 8 cm. Surface area (to the nearest tenth) = cm2 Volume (to the nearest tenth) = cm3
Answers
Answer:
a) 483.6cm²b) 850.1 cm³Step-by-step explanation:
Given the slant height 's' and its radius 'r' to be 15cm and 8cm respectively.
the total surface of the cone A = πrs+πr² and the volume is expressed as
V = 1/3πr²h
For the surface area of the cone;
Given parameters
radius = 8 cm and slant height s = 15 cm
Total surface area A = π(8)(15) + π(8)²
A = 90π+64π
A = 154π
If π = 3.14
A = 154(3.14)
A = 483.56cm²
A = 483.6cm²
Hence the total surface area of the cone to the nearest tenth is 483.6cm²
For the volume of the cone;
V = 1/3πr²h
Using pythagoras theorem to get the height of the cone;
l² = h²+r²
h² = l²-r²
h² = 15²-8²
h² = 225-64
h² = 161
h = √161
h = 12.69cm
V = 1/3π* (8)² * 12.69
V = 1/3π* 64 * 12.69
V = 1/3*3.14* 64 * 12.69
V = 2550.1824/3
V = 850.06 cm³
V = 850.1 cm³
Hence, the volume of the cone is 850.1 cm³ to the nearest tenth.
3/8-(-51/4) simplest form
Answers
Answer:
13 1/8
Step-by-step explanation:
3/8-(-51/4)
Subtracting a negative is like adding
3/8 + 51/4
get a common denominator
3/8+ 51/4 *2/2
3/8 + 102/8
105/8
8 goes into 105 13 times with 1 left over
13 1/8
Write the mixed numbers as fractions.
1/2/3
Answers
Answer:
5/3
Step-by-step explanation:
1) The denominator will be multiply to the whole number to find the improper fraction. 3 (denominator) x 1 (whole number)
2) 1 plus 2 (numerator) equal 5
3) Always keep the denominator (3) for you improper fraction.
4) 5 will be the numerator and 3 will be the denominator.
5/3
Find the value of x.
Answers
Answer:
70°
Step-by-step explanation:
an inscribed angle is half of the intercepted arc
arc = 2(15) = 30
1/2(x - 30 ) = 20
x - 30 = 40
x = 70
Algebra 1 need help ASAP
Answers
Answer:
see explanation
Step-by-step explanation:
Given
10 - 3x < x + 30 ( subtract x from both sides )
10 - 4x < 30 ( subtract 10 from both sides )
- 4x < 20 ( divide both sides by - 4 and flip the sign )
x > - 5
I'm new to algebra and I'm having trouble solving this equation can someone answer with steps
Answers
Answer:
[tex]u(u + 1)[/tex]
Step-by-step explanation:
first and foremost you have positive and minus 1 which will cancel out to zero
then we're left with
[tex] {u}^{2} + u \\ factorize \: \: u \: out \: to \: get \\ u(u + 1)[/tex]
m∠QPSm, is a straight angle m∠RPS=6x+11 m∠QPR=7x+143 ;Find RPS
Answers
Answer:
23
Step-by-step explanation:
6x + 11 + 7x + 143 = 180
13x + 154 = 180
13x = 26
x = 2
m<RPS = 6(2) + 11 = 23
Can someone please help!
Answers
Plot point F where angle alpha is located.
Triangle ABF has two interior angles x and 80. They add to the exterior angle alpha due to the remote interior angle theorem.
alpha = x+80
Answer: Choice Dcomplete the square to solve
f(x)=x^2-6x+5
Answers
Explanation:
x^2 - 6x + 5 = 0
(x^2 - 6x + 9) + 5 - 9 = 0
(x - 3)(x - 3) - 4 = 0
(x - 3)^2 = 4
x - 3 = +-2 (sqrt both sides)
x - 3 = 2
x = 5
x - 3 = -2
x = 1
Solve for v: w = v/r
Answers
Answer:
v = wr
Step-by-step explanation:
[tex](r)w=\frac{v}{r}(r)\\wr=v[/tex]
Answer:
v = w/r
Step-by-step explanation:
w = v/r
v = w/r
The total cost of a watch and a radio is Rs 500. If the watch is cheaper than the Equations radio by Rs 150, find their cost.
Answers
Answer:
the watch is Rs 175
the radio is Rs 325
Step-by-step explanation:
x = price of the watch
y = price of the radio
x+y = 500
x + 150 = y
=>
x + (x+150) = 500
2x + 150 = 500
2x = 350
x = 175
=>
y = 175 + 150 = 325
what is a coterminal angles
Answers
Answer: Coterminal Angles are angles who share the same initial side and terminal sides. Finding coterminal angles is as simple as adding or subtracting 360° or 2π to each angle, depending on whether the given angle is in degrees or radians.
Ссппер
What is the image of (7, -2) after a reflection over the line y = -x?
Answers
Answer:
(2, -7)
Step-by-step explanation:
When three is added to four times a number, the result is 15
(a) Write an equation to represent the above information.
Answer
(b) Solve your equation in (a)
Answers
Answer:
A. 4y + 3 = 15
B. y = 3
Step-by-step explanation:
Three is added to four times a number, the result is 15
A. Equation to represent the above information:
Let the unknown number= y
4 * y + 3 = 15
4y + 3 = 15
B. Solve your equation in (a)
4y + 3 = 15
Collect like terms
4y = 15 - 3
4y = 12
Divide both sides by 4
4y / 4 = 12 /4
y = 3
Therefore, the unknown number is 3
Two interior angles of a convex pentagon are right angles and the other three interior angles are congruent. in degrees, what is the measure of one of the three congruent interior angles?
Answers
Answer:
[tex]120^{0}[/tex]
Step-by-step explanation:
Given: pentagon (5 sided polygon), two interior angles = [tex]90^{0}[/tex] each, other three interior angles are congruent.
Sum of angles in a polygon = (n - 2) × [tex]180^{0}[/tex]
where n is the number of sides of the polygon.
For a pentagon, n = 5, so that;
Sum of angles in a pentagon = (5 - 2) × [tex]180^{0}[/tex]
= 3 × [tex]180^{0}[/tex]
= [tex]540^{0}[/tex]
Sum of angles in a pentagon is [tex]540^{0}[/tex].
Since two interior angles are right angle, the measure of one of its three congruent interior angles can be determined by;
[tex]540^{0}[/tex] - (2 × [tex]90^{0}[/tex]) = [tex]540^{0}[/tex] - [tex]180^{0}[/tex]
= [tex]360^{0}[/tex]
So that;
the measure of the interior angle = [tex]\frac{360^{0} }{3}[/tex]
= [tex]120^{0}[/tex]
The measure of one of its three congruent interior angles is [tex]120^{0}[/tex].
Write the equation of the line that passes through the point (-1, -2) and is parallel to the
graph of y-3x - 2.
XY
Answers
Answer:
y = -3x - 5
Step-by-step explanation:
In order to form a parallel line, the two lines must have the same slope. Substitute the values into the point-slope formula to make the equation.
[tex]y-y_1=m(x-x_1)\\y-(-2)=-3(x-(-1))\\y+2=-3(x+1)\\y+2=-3x-3\\y=-3x-5[/tex]
Therefore, the equation is y = -3x - 5.