hii guys please answer this question
if two -1 and 2 are two zeroes of the polynomial 2x3- x2 - 5x - 2, find its third zero
Answers
Answer:
-1/2
Step-by-step explanation:
Zeros of a polynomial function are its x-intercepts, the values of x that make the polynomial zero. Each zero x=p corresponds to a linear factor (x-p) of the polynomial.
Monic polynomialA monic polynomial is one that has a leading coefficient of 1. For a monic polynomial of degree n, the coefficient of the term of degree n-1 is the opposite of the sum of all of the zeros. The constant term of any odd-degree monic polynomial is the opposite of the product of the zeros.
The given polynomial can be made monic by dividing by its leading coefficient:
(2x^3 -x^2 -5x -2)/2 = x^3 -(1/2)x^2 -(5/2)x -1
Sum of zerosThe given polynomial has degree 3, so we're interested in the coefficient of the x^2 term. That coefficient is -1/2, so the sum of zeros will be ...
sum of zeros = -(-1/2) = 1/2
If z represents the third zero, then we have the sum ...
1/2 = -1 +2 +z
z = -1/2 . . . . . . subtract 1 from both sides
The third zero is -1/2.
Product of zerosThe given polynomial is of odd degree, so the product of the zeros is the opposite of the constant.
(-1)(2)(z) = -(-1)
z = 1/(-2) = -1/2 . . . . . divide by the coefficient of z
The third zero is -1/2.
GraphOf course, a graph will show all of the (real) zeros. The attached graph from a graphing calculator shows the third zero is -1/2.
Related Questions
The list price of a commodity is RM420 and the percentage profit is 40%. If the commodity is sold at a discount of 10%, the profit is____.
Answers
Answer:
56
Step-by-step explanation:
you first had to get the marked price so t you can get the profit.
just as illustrated in the picture above.
Karl’s math class is playing a number game. Each student is given a number card containing the numbers 1 to 6. The rules of the game are that each student must put a cross through two numbers on the card and hand it in to the teacher. The teacher has a bag containing six balls numbered 1 to 6. When all the number cards have been handed in the teacher draws out two balls from the bag. Every student who had chosen the same two numbers shown on the balls wins a prize. If there are 30 students in Karl’s class, how many students are likely to win a prize? Describe your reasoning
Answers
By finding the probability, we can expect that 2 out of the 30 students will win the prize.
How many of the 30 students will win the prize?
First, we should get the probability of winning this game.
Here the students select two numbers out of 6, just to make the calculations let's say that these numbers are 1 and 2.
Now, we need to get these two numbers in two balls. The probability of getting the ball with the number 1 out of the 6 balls is:
p = 1/6
The probability of getting the ball with the number 2 out of the remaining 5 balls (because we already got one) is:
q = 1/5
The joint probability is then:
P = 2*(1/6)*(1/5) = 1/15.
Where the factor 2 comes to take in account the permutations, for the case where we first draw the number 2 and then the number 1.
Then the expected number of students that will win is equal to the probability times the total number of students:
(1/15)*30 = 2
So out of the 30 students, we can expect that 2 will win.
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What is the volume of a cylinder, in cubic feet, with a height of 13 feet and a base
diameter of 4 feet? Round to the nearest tenths place.
Answers
Answer:
163.3
Step-by-step explanation:
3.14*r^2*h
h=13
4/2 = 2
r=2
2^2 = 4
3.14*4 = 12.56
12.56*13 = 163.28
Rounded = 163.3
I believe the answer is 163.3
Which function can be used to represent the graphed geometric sequence?
f(x) = 80(One-fourth) Superscript x minus 1
f(x) = 320(One-fourth) Superscript x minus 1
f(x) = 80(4)x – 1
f(x) = 320(4)x – 1
Answers
The function which is used to represent the graphed geometric sequence is
[tex]f(x) = 80{( \frac{1}{4}) }^{x - 1} [/tex]
Let a be first term and r common ratio of the Geometric progression.
The Geometric sequence is of the form a,ar,ar^2, ...
The common ratio will be ar/a.
From the graph, we can find out the sequence as 80,20,5, ...
Here we can see that the sequence is in Geometric Progression.
First term a=80
Common ratio r= ar/a
= 20/80
=1/4
General term of Geometric sequence is
[tex]f(x) = a {r}^{x - 1} [/tex]
Substituting the value a = 80 and r = 1/4,
we get,
[tex]f(x) =80 { (\frac{1}{4} )}^{x - 1} [/tex]
Hence, the correct answer is
[tex]f(x) =80 { (\frac{1}{4} )}^{x - 1} [/tex]
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what is the principle value of sin^-1(1)
Answers
The Sine or Sinθ in a right-angle triangle is the ratio of its perpendicular to its Hypotenuse. The principal value of sin⁻¹(1) is 90°.
What is Sine (Sinθ)?The Sine or Sinθ in a right-angle triangle is the ratio of its perpendicular to its Hypotenuse. it is given as,
Sin(θ) = Perpendicular/Hypotenuse
where,
θ is the angle,
Perpendicular is the side of the triangle opposite to the angle θ,
The hypotenuse is the longest side of the triangle.
The principal value of sin⁻¹(1) is,
θ = Sin⁻¹(1)
θ = 90°
Hence, the principal value of sin⁻¹(1) is 90°.
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Matt is trying to measure the height of a tree using
trigonometry. He is having trouble because of the
terrain around the tree. The horizontal distance
from the tree to Matt's eyes is 120 feet. The angle
of depression from the horizontal is 30°. Matt's
angle of sight to the top of the tree is 23°. What is
the height of the tree? (Round to the nearest foot.)
Answers
The height of the tree will be 18.35 feet.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
Matt is trying to measure the height of a tree using trigonometry.
He is having trouble because of the terrain around the tree.
The horizontal distance from the tree to Matt's eyes is 120 feet.
The angle of depression from the horizontal is 30°.
Matt's angle of sight to the top of the tree is 23°.
The diagram is given below.
Let x be the height of tree and AM be h.
The value of (h + x) will be
tan 30° = (x + h) / 120
x + h = 69.288
Then the value of h will be
tan 23° = h / 120
h = 50.94 feet
Then the height of the tree will be
⇒ h + x – h
⇒ 69.29 - 50.94.
⇒ 18.35 feet
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C
2
1
3
A. 21
B. 23
C.24
D. 25
b7
#
5
4
In the figure, which angle has the same measure as /2?
Answers
Answer:
the angle that has the same measure as /2 is A
Points
Find f(−2)
given f(x)=−x3−3x2+8
Answers
Answer:
12 :D
Step-by-step explanation:
First we substitute all x's for -2 :)
f(-2)=−-2^3−3(-2)^2+8
Now we solve :)
f(-2)=−-2^3−3(-2)^2+8
f(-2)=− -8 −3(-2)^2 + 8
f(-2) = -8 - 3(-4) + 8
f(-2) = - 8 + 12 + 8
f(-2) = 4 + 8
f(-2) = 12 :)
f will equal 12 :)
Have an amazing day!!
Please rate and mark brainliest!!
what is the equation of x2 + 6x + 8 + 0 algebraically
Answers
Answer:
x = - 4 , x = - 2
Step-by-step explanation:
x² + 6x + 8 = 0
consider the factors of the constant term (+ 8) which sum to give the coefficient of the x- term (+ 6)
the factors are + 4 and + 2 , since
4 × 2 = 8 and 4 + 2 = 6 , then
(x + 4)(x + 2) = 0 ← in factored form
equate each factor to zero and solve for x
x + 4 = 0 ⇒ x = - 4
x + 2 = 0 ⇒ x = - 2
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Consider the equation.
Answers
2.x=-3
1. Working
px+1=16
xp=16-1
xp=15
p=15/x
2. 4(-5x+1)=64
-5x+1=16
-5x=16-1
-5x=15 ,
x=-3
I hope this helps^^
same side interior angles are _____ congruent
A.always
B.never
C.sometimes
Answers
Answer:
B. Never
Step-by-step explanation:
that's just what my math teacher told us...
umm.. i fr don’t know how to do this … help pls
Answers
Answer:
2 solutions: ( -4,0 )
( -6,0 )
2 Non solution: ( 2,0 )
( 4,0 )
Answers:
Refer to the graph below
Two solution points are (-5,-4) and (-4,-3)
Non solution points are (0,3) and (1,4)
=========================================================
Explanation:
The boundary line for [tex]y \ge 3x+3[/tex] is [tex]y = 3x+3[/tex]
This linear equation has a y intercept of (0,3) and another point on the line is (1,6). Plot these two points and draw a straight line through them. This line is a solid boundary line because of the "or equal to" as part of the inequality sign. This means points on the boundary adjacent to the shaded region area part of the solution set.
Because of the "greater than" portion, we'll shade above the solid boundary line. This only works because y is isolated.
Keep in mind that we're also told that [tex]y < -2[/tex] which means we'll also shade the region below the boundary line [tex]y = -2[/tex]. This is a dashed line through -2 on the y axis. A dashed line does not include points on the boundary as part of the solution.
---------------
To summarize: We shade above y = 3x+3 (solid) but below y = -2 (dashed).
Refer to the diagram below to see what's going on.
The entire southwest region is shaded.
That blue shaded region represents all (x,y) points that make the system true.
For example, the point (-5,-4) is in the blue region.
Notice how plugging the coordinates into the first inequality gets us...
[tex]y \ge 3x+3\\\\-4 \ge 3(-5)+3\\\\-4 \ge -15+3\\\\-4 \ge -12\\\\[/tex]
which is a true statement. If you plugged y = -4 into [tex]y < -2[/tex], you would also get another true statement.
Both inequalities are true for (x,y) = (-5,-4) which confirms it to be a solution point.
You should also find that a point like (-4,-3) is another solution in the blue region following similar steps. There are infinitely many solution points to pick from. Feel free to choose others.
Non-solution points are such that they aren't in the shaded region. We could also pick points on the dashed boundary line as non-solutions.
Side note: you can pick points on the solid boundary as solution points, but those points must be adjacent to the shaded region. The point (0,3) is NOT a solution even though it's on the solid boundary line.
What is the slope of the linear relationship shown in this table of values?
Answers
The difference of y/ the difference of x
If you want further help ask
Answer:
B
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (2, - 1) and (x₂, y₂ ) = (- 4, 11) ← 2 ordered pairs from the table
m = [tex]\frac{11-(-1)}{-4-2}[/tex] = [tex]\frac{11+1}{-6}[/tex] = [tex]\frac{12}{-6}[/tex] = - 2
Which is a rational function?
A. Y=5
B. Y=√x-3
C. Y=x²-3x+5
D.Y = x-5/x
Answers
PLEASE HELP ME WITH THIS ASAP
Answers
Answer:
x=46
Step-by-step explanation:
4(x+1)-3x=50
first you gotta take care of the () so multiple by 4
(4x+4) -3x=50
combine like terms, subtract 4-3 to get 1 so you have 1x left
4 + x = 50
and then solve for x
x=46
( i checked it to make sure it was right so dw)
What are the first 10 digits after the decimal point (technically the hexadecimal point...) when the fraction frac17 is written in base 16?
Answers
We happen to have
[tex]\dfrac17 = \dfrac18 + \dfrac1{8^2} + \dfrac1{8^3} + \cdots[/tex]
which is to say, the base-8 representation of 1/7 is
[tex]\dfrac17 \equiv 0.111\ldots_8[/tex]
This follows from the well-known result on geometric series,
[tex]\displaystyle \sum_{n=1}^\infty ar^{n-1} = \frac a{1-r}[/tex]
if [tex]|r|<1[/tex]. With [tex]a=1[/tex] and [tex]r=\frac18[/tex], we have
[tex]\displaystyle \sum_{n=1}^\infty \frac1{8^{n-1}} = 1 + \frac18 + \frac1{8^2} + \frac1{8^3} + \cdots \\\\ \implies \frac1{1-\frac18} = 1 + \frac18 + \frac1{8^2} + \frac1{8^3} + \cdots \\\\ \implies \frac87 = 1 + \frac18 + \frac1{8^2} + \frac1{8^3} + \cdots \\\\ \implies \frac17 = \frac18 + \frac1{8^2} + \frac1{8^3} + \cdots[/tex]
Uniformly multiplying each term on the right by an appropriate power of 2, we have
[tex]\dfrac17 = \dfrac2{16} + \dfrac{2^2}{16^2} + \dfrac{2^3}{16^3} + \dfrac{2^4}{16^4} + \dfrac{2^5}{16^5} + \dfrac{2^6}{16^6} + \cdots[/tex]
Now observe that for [tex]n\ge4[/tex], each numerator on the right side side will contain a factor of 16 that can be eliminated.
[tex]\dfrac{2^n}{16^n} = \dfrac{2^4\times2^{n-4}}{16^n} = \dfrac{2^{n-4}}{16^{n-1}}[/tex]
That is,
[tex]\dfrac{2^4}{16^4} = \dfrac1{16^3}[/tex]
[tex]\dfrac{2^5}{16^5} = \dfrac2{16^4}[/tex]
[tex]\dfrac{2^6}{16^6} = \dfrac4{16^5}[/tex]
etc. so that
[tex]\dfrac17 = \dfrac2{16} + \dfrac4{16^2} + \dfrac9{16^3} + \dfrac2{16^4} + \dfrac4{16^5} + \dfrac9{16^6} + \cdots[/tex]
and thus the base-16 representation of 1/7 is
[tex]\dfrac17 \equiv 0.249249249\ldots_{16}[/tex]
and the first 10 digits after the (hexa)decimal point are {2, 4, 9, 2, 4, 9, 2, 4, 9, 2}.
Select the correct answer.
Which calculation correctly uses prime factorization to write √48 In simplest form?
OA √48 = √2-2-2-2-3-2√12
OB. √48√4 - 12 = 2√12
OC. √48 = √2-2-2-2-3= 4√3
OD. √48 =√16-3 = 4√3
Answers
D. √48 =√16*3 = 4√3
Simplify the radical by breaking the radicand up into a product of known factors.
16*3 = 48
this means that √48 = √16*3, but this can be simplified.
√16 = 4, √3 = √3 because it cannot be simplified farther
making the most simplified answer 4√3
Use properties of exponents to simplify the expression. First, express the
answer in exponential form. Then, evaluate the expression.
(1^3) ^4
Answers
Step-by-step explanation:
[tex] = { ({1}^{3} )}^{4} [/tex]
[tex] = {1}^{3 \times 4} [/tex]
[tex] = {1}^{12} [/tex]
[tex] = 1[/tex]
Round 2
5. A Cadillac Escalade gasoline tank has a capacity of 24
gallons. The car uses approximately 1 gallon for every 25
miles it drives. If the tank starts full, write an equation that
describes the amount of gas, g, left in the tank after it has
been driven for m miles.
Answers
Answer:
g = 24 - 1/25m
Step-by-step explanation:
Since the Cadillac Escalade can travel 25 miles per gallon, each mile the Escalade travels is 1/25th of a gallon of gas.
This means that every mile the Escalade travels, 1/25th of a gallon is subtracted from the gas tank. Since the gas tank has a capacity of 24 gallons, the value of the gas tank is 24.
This leads us to the equation:
g = 24 - 1/25m
where g is the amount of gas left, and m is the number of miles driven.
On a number line, 2.5 would be located ______. Choose all answers that make a true statement.
2.5
《----|----|----|----|----|----|----|----|----|----|----》
A. to the right of 2.52
B. between 2.45 and 2.55
C. to the left of 2.3
D. between of 2.4 and 2.6
Answers
Answer:
It is both answers B and D
Find the following, giving your answers
to 1 decimal place.
10 cm/
6 cm
8 cm
a) The volume of the cone.
b) The curved surface area of the cone.
Answers
Answer:
a) 301.6 cm³
b) 188.5 cm²
Step-by-step explanation:
The volume and lateral surface area of the cone can be found using the given dimensions with the given formulas. All that is needed is to substitute the appropriate values and do the arithmetic.
__
a) volumeThe volume is given by the formula ...
V = 1/3πr²h
The dimensions are given on the diagram: r = 6 cm, h = 8 cm. Using these values in the formula, we find the volume to be ...
V = 1/3π(6 cm)²(8 cm) = 96π cm³ ≈ 301.6 cm³
The volume of the cone is about 301.6 cm³.
__
b) areaThe lateral area of the cone is given by the formula ...
A = πrl
The dimensions are given on the diagram: r = 6 cm, l = 10 cm (the slant height). Using these values in the formula, we find the area to be ...
A = π(6 cm)(10 cm) = 60π cm² ≈ 188.5 cm²
The area of the curved surface is about 188.5 cm².
What is the independent variable in the equation y=-5x+2?
Answers
Answer: x
Step-by-step explanation:
For this equation, the variable y is dependent on the value of x. The value of y changes depending on the value of x. This means that x is the independent variable for this equation.
Look at pictures attached for question and answer choices
Answers
The answers are a rhombus, bisect a pair of opposite angles, and SAS congruency postulate respectively.
What is a rhombus?A rhombus is a two-dimensional shape having four parallel opposite pairs of straight, equal sides. This shape resembles a diamond and is what you'd find on a deck of cards to represent the diamond suit. Rhombuses can be encountered in a variety of common situations.
We have a rhombus shown in the picture.
The intersection point is P
From the definition of the rhombus: JK ≅ KM
According to the SAS congruency postulate, two triangles are congruent if a triangle has two sides and an included angle that are congruent to the two sides and an included angle of another triangle.
Thus, the answers are a rhombus, bisect a pair of opposite angles, and SAS congruency postulate respectively.
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how to say i like chees burgers without saying that like how to say im not gonna date you while i still will im just dum what is 1+1
Answers
Answer:
2
I believe that the answer my friend
In a school, the number of girls is 70 more than boys. the total number of students is 1280. find the number of girls and boys
Answers
Answer:
Step-by-step explanation:
Conditions
Let the girls = g
Let the boys = b
Equations
g + b = 1280
g = b + 70
Solution
Put the value for the girls (second equation) into the first equation.
b + 70 + b = 1280 Subtract 70 from both sides
b + 70 - 70 + b = 1280 -70 Combine
2b = 1210 Divide both sides by 2
2b/2 = 1210/2
b = 605 Substitute this value into the top equation
g + 605 = 1280 Subtract 605 from both sides
g + 605 - 605 = 1280 - 605
g = 675
Answer
# boys = 605
# girls = 675
Find the value of x.
5
X
11
y
Answers
The value of the variable is 4√5. Then the correct option is C.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
The similar triangles are shown in the diagram.
16 / x = x / 5
x² = 16 × 5
x = 4 √5
Then the value of the variable is 4√5.
Then the correct option is C.
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What are the missing parts that correctly complete the proof?
Drag the answers into the boxes to correctly complete the proof.
(Please refer to the images provided for the answer options and equation image.)
Answers
It has been proved that point A is equidistant from the sides of angle PQR.
What is a Bisector ?Any line or point that divides an angle or a side in equal parts is called a Bisector.
It is given that
Point A is the bisector of Angle PQR
Referring to the image
1. QA is the bisector of angle PQR : Given
2.Angle PQA = Angle RQA : Definition of Bisector
3.Angle QXA = Angle QYA : Definitions of Perpendicular
4. Angle QXA = Angle QYA : All right angles are congruent.
5. QA ≅QA : Reflexive Property of Congruence
6. ΔPQA ≅ΔRQA : AAS Congruence Postulate
7. AX ≅AY Corresponding parts of Congruent Triangles
8. Point A is equidistant from the sides of Angle PQR : Definition of equidistant.
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I’m having trouble understanding how to solve this someone please help ASAP thank you!
Use the Law of Cosines to solve the problem. You must solve for BC first. Solve this problem in order.
A ship travels due west for 94 miles. It then travels in a northwest direction for 119 miles and ends up 173 miles from its original position. To the nearest tenth of a degree, how many degrees north of west (x) did it
turn when it changed direction? Show your work.
Answers
Which of the following is equal to m
Answers
Answer: tan^-1 (c/a)
Step-by-step explanation: An angle C ∈ ℝ such that angle C > 0 can be defined by the trigonometric ratio Arctangent (or rather tan^-1) where side "c" divided by side "a" ≠ 0.
what is the inverse of f(x)=(-2x+2)/(x+7)?
Answers
By applying the concept of the inverse of a function and algebraic handling, we conclude that the inverse of f(x) = (- 2 · x + 2)/(x + 7) is g(x) = (- 7 · x + 2)/(x + 2).
How to find the inverse of a function
In this question we have a rational function f(x) and finding its inverse consists in clearing x in terms of f(x). Prior any algebraic handling, we need to apply the following substitutions:
[tex]x \to y[/tex]
[tex]f(x) \to x[/tex]
[tex]x = \frac{-2\cdot y + 2}{y+7}[/tex]
x · (y + 7) = - 2 · y + 2
x · y + 7 · x = - 2 · y + 2
2 · y + x · y = - 7 · x + 2
y · (2 + x) = - 7 · x + 2
[tex]g(x) = \frac{- 7\cdot x + 2}{x + 2}[/tex]
By applying the concept of the inverse of a function and algebraic handling, we conclude that the inverse of f(x) = (- 2 · x + 2)/(x + 7) is g(x) = (- 7 · x + 2)/(x + 2).
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