Answers
Given:
The zeros of the polynomial are [tex]-2,\pm 5,4[/tex].
Degree = 4
Leading coefficient = 1
To find:
The polynomial.
Solution:
If c is a zero of a polynomial, then (x-c) must be a factor of the polynomial.
Here, -2,4,-5, 5, are zeros of the required polynomial, so (x+2), (x-4), (x+5), (x-5) are factors of required polynomial.
[tex]p(x)=(x+2)(x-4)(x+5)(x-5)[/tex]
[tex]p(x)=(x^2-4x+2x-8)(x^2-5^2)[/tex] [tex][\because a^2-b^2=(a-b)(a+b)][/tex]
[tex]p(x)=(x^2-2x-8)(x^2-25)[/tex]
Using distributive property, we get
[tex]p(x)=x^2(x^2-25)-2x(x^2-25)-8(x^2-25)[/tex]
[tex]p(x)=x^4-25x^2-2x^3+50x-8x^2+200[/tex]
On combining like terms, we get
[tex]p(x)=x^4-2x^3+(-25x^2-8x^2)+50x+200[/tex]
[tex]p(x)=x^4-2x^3-33x^2+50x+200[/tex]
Here, the leading coefficient is 1. So, it is the required polynomial.
Therefore, the correct option is E.
Related Questions
An algebraic expression that contains variables is called
Answers
Answer:
An algebraic expression that contains variables is called coefficients.
In the diagram M is the midpoint if the segment. Find the length of XZ
Answers
Answer:
XZ = 14
Step-by-step explanation:
x+2 = 2x-3
-1x from both sides
2 = x - 3
+3 to both sides
5 = x
(plug in x for XM and MZ equations)
(5 + 2) + ((2×5) - 3)
7 + 7 = 14
The numerical length of XZ = 14
We have a Line Segment XZ such that M is mid - point of XZ.
We have to determine the length of XZ.
What is Mid - point of Line Segment?The mid - point of a line segment is a point on a line that divides it into two equal parts.
According to question, we have -
XM = x + 2
MZ = 2x - 3
Since, M is the mid - point of XZ, therefore -
XM = MZ
x + 2 = 2x - 3
2 + 3 = 2x - x
x = 5
Now -
XZ = XM + MZ
XZ = x + 2 + 2x - 3
XZ = 5 + 2 + 10 - 3
XZ = 14
Hence, the numerical length of XZ = 14.
To solve more questions on Lines and Lengths, visit the link below -
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Amelia started a puzzle at 12:56 p.m. and solved it at 2:33 p.m.
How long did it take Amelia to solve the puzzle?
Answers
Step-by-step explanation:
12:56pm to 1:00pm = 4 min
1:00pm to 2:00pm = 1 hour
2:00pm to 2:33pm = 33 min
Total time = 4 min + 1 hour + 33 min = 1 hour 37 minutes.
The acceleration due to gravity is the constant of variation. What is the acceleration due to gravity of a falling object?
Answers
Answer:
9.8 because of the rate that is given
Step-by-step explanation:
a girl was asked about her age and she said she is half her mothers age and she was asked how old was her mother and she said i dont know but my mom is 5 years younger than my dad and we asked how old is your dad and she said i dont know but the sum of our ages is equal to 100years.how old is the dad ,the mom and the girl?
Answers
Answer: girl- 19yr old mom- 38yr old dad- 43 yr old
Step-by-step explanation:
5x+5=100
5x-5=100-5
5/5x=95/5
x=19
2(19)=38
38+5=43
What is the 20th term for the following sequence?
3,-9, 27,-81, ...
Answers
Answer: -3486784401
Step-by-step explanation:
This is a geometric progression and the formula to use to find the nth term will be: = ar^(n-1)
where,
a = 3
r = -9/3 = -3
n = 20
Therefore, ar^(n-1)
= 3 × -3^19
= 3 × -1162261467
= -3486784401
21, 31, 41, 51, ... Find S17
Answers
Answer:
181
Step-by-step explanation:
Answer:
21=
31=
41=
51=
S17=
Colton is making gift bags. He has 120 small prizes, and puts 3 in each gift bag. He also has 75 larger prizes,and puts 2 in each gift bag. Write the function f(x) that represents how many prizes Colton has left aftermaking x gift bags.
Answers
Answer: f(x) = 195 - x*5
Step-by-step explanation:
Colton has 120 small prizes and 75 larger prizes.
Then at the start, he has 120 + 75 = 195 prizes.
In each bag, he puts 3 small prizes and 2 larger prizes, then in each bag there are 3 + 2 = 5 prizes.
Then if he fills x bags, he will have: x*5 fewer prizes, then we can write the equation f(x) as:
f(x) = 195 - x*5
Where when x = 0, this means that he filled zero bags, then he has the initial amount of prizes, 195.
In the first quadrant, you start at (1,3) and move 2 units right What point will you end up on?
Answers
Answer:3,3
Step-by-step explanation:
The point on which we will end up on is (3,3).
We are given that;
The starting point (1,3)
Number of units= 2
Now,
Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
To find the point where you end up after moving 2 units right from (1,3), you need to add 2 to the x-coordinate of (1,3) and keep the y-coordinate the same.
This is because moving right along a horizontal line does not change the y-value, but increases the x-value by the amount of units moved.
(1 + 2, 3) = (3, 3)
Therefore, by algebra the answer will be (3,3).
More about the Algebra link is given below.
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-75x/4>14/2 I don't get this can someone help me with this?
Answers
Is this the equation ur supposed to solve because the question was a little bit messy
[tex] \frac{ - 75x}{4} > \frac{14}{2} [/tex]
Answer
solve for x
29=4x-11
Answers
Answer:
The Right Answer is X=10
Solve for x 2x-10=4x
Answers
Answer:-5
Step-by-step explanation:
2x-10=4x
-10=2x (subtract 2x from both sides)
-10/2=x (divide both sides by 2)
-5=x
20 POINTS and BRAINLIEST
Solve the simultaneous equation!
Answers
Answer:
x=3 y=-1
Step-by-step explanation:
Answer:
X=3 and
Y=-1
and good luck for your test
Which scatterplot demonstrates a non-linear relationship between x and y?
Answers
Answer:
D, or the bottom right.
Step-by-step explanation:
The right lower (U shape) scatter plot : demonstrates a non linear relationship between x & y.
The straight scatter plots denote linear relationships.
The upward sloping curve shows direct or positive linear relationship. The downward sloping curve shows inverse, indirect or negative positive relationship.
The scatter plot parallel to x axis, denotes constant values of y at various levels of x.
The parabolic U shaped curve demonstrates a non linear, ie quadratic relationship between dependent variable y & independent variable x.
To learn more, refer https://brainly.com/question/21839842?referrer=searchResults
I need help with this asap, i will mark you brainliest!!
Solve for the value of x
Answers
15=30/2 so 10/2=x
use a proportion to find the length of side x for the pair of similar figures
Answers
Answer:
30.8
Step-by-step explanation:
1. Write the ratio for the smaller triangle as 14/10 and the ratio for the larger triangle as x/22.
2. Set the ratios equal to each other.
14/10 = x/22
3. Cross multiply and solve for x.
14 x 22 = 308
10 x x = 10x
4. Divide by 10
x = 30.8
Answer:
30.8cm they are correct
Step-by-step explanation:
i am from connexus 8th grd pre algrabra
unit 5 lesson 3
1. 1:2
2. C. yes they are similar they have porportional side lengths and = ange measures
3. x = 4.5m
4. x = 30.8cm
5. x = 6 m
у = 3х – 2
y = — 2х +8
How do I solve it by graphing?
Answers
5
If you scale up the ratio on the left, what will you get for the unknown quantity on the right?
$155
20hours
$465
?
A) 10 hours
B 40 hours
c) 60 hours
D) 100 hours
Answers
Answer:60hours
Step-by-step explanation:
465/155×4
=60 hours
Which function is quadratic?
Function f is defined by f(x) = 1.5^x. Function g is defined by g(x) = 500x^2 + 345x
1. Function f
2. Function g
Answers
Answer:
g(x) is a quadratic function ⇒ 2
Step-by-step explanation:
The quadratic function is the function that has 2 as the greatest power of the variable The form of the quadratic function is f(x) = ax² + bx + c, where a, b, and c are constantLet us use the information above to solve the question
∵ f(x) = [tex]1.5^{x}[/tex]
∵ x is the exponent of the base 1.5
→ That means f(x) is not in the form of the quadratic function
∴ f(x) is not in the form of the quadratic function above
∴ f(x) does not represent a quadratic function
∴ f(x) is not a quadratic function
∵ g(x) = 500x² + 345x
∴ The greatest power of x is 2
→ That means g(x) is in the form of the quadratic function above
∵ g(x) is in the form of the quadratic function above, where a = 500,
b = 345, and c = 0 (constant values)
∴ g(x) represents a quadratic function
∴ g(x) is a quadratic function
Don has four different chicken coops on his farm. He gathers eggs from each coop every day to sell at the local farmer's market each week. During one week in the summer, the production levels from the coops were compared. • The number of eggs from coop B can be found by subtracting 10 from coop A's production, and then multiplying this result by two-fifths. • The number of eggs from coop C can be found by adding 3 to coop A's production, multiplying this amount by 3, subtracting 4 from this total, and then dividing the whole result by 4. • The number of eggs from coop D can be found by adding 7 to coop A's production, doubling this amount and then dividing the result by 3. A. Define a variable for the number of eggs produced by coop A. Then write expressions for the number of eggs produced by the other coops. B. If coop A produced 125 eggs, how many did each of the other coops produce? C. If the sum of the number of eggs from coop B and coop C was 24 more than the number
Answers
Answer:
The answer is below
Step-by-step explanation:
Don has four different chicken coops on his farm. He gathers eggs from each coop every day to sell at the local farmer's market each week. During one week in the summer, the production levels from the coops were compared. • The number of eggs from coop B can be found by subtracting 10 from coop A's production, and then multiplying this result by two-fifths. • The number of eggs from coop C can be found by adding 3 to coop A's production, multiplying this amount by 3, subtracting 4 from this total, and then dividing the whole result by 4. • The number of eggs from coop D can be found by adding 7 to coop A's production, doubling this amount and then dividing the result by 3. A. Define a variable for the number of eggs produced by coop A. Then write expressions for the number of eggs produced by the other coops. B. If coop A produced 125 eggs, how many did each of the other coops produce? C. If the sum of the number of eggs from coop B and coop C was 24 more than the number from coop D. How many eggs did each coop produce
Solution:
a) Let the number of eggs from coop A be w, number of eggs from coop B be x, number of eggs from coop C be y and number of eggs from coop D be z.
x = 2/5(w - 10) (1)
y = (3(w + 3) - 4)/4
y = (3w + 5) / 4 (2)
z = 2(w + 7)/3 (3)
b) Given that w = 125 eggs:
x = 2/5(125 - 10) = 46 eggs
y = (3(125) + 5) / 4 = 95 eggs
z = 2(125 + 7)/3 = 88 eggs
c) x + y = z + 24.
i.e. 2/5(w - 10) + (3w + 5)/ 4 = 2(w + 7)/3 + 24
multiply through by 60:
24w - 240 + 45w + 75 = 40w + 280 + 1440
69w - 165 = 40w + 1580
29w = 1885
w = 65 eggs
x = 2/5(65 - 10) = 22 eggs
y = (3(65) + 5) / 4 = 50 eggs
z = 2(65 + 7)/3 = 48 eggs
1/2 x 3/10 in simplest form
Answers
Answer: 3/10
Step-by-step explanation: 1/2 x 3/10 = 3/20 and we can’t simplify that.
Answer:
The simplest form of 1/2 x 3/10 would be 3/20
If you need it in decimal form it's: 0.15
Use the picture below to answer questions 14a and 14b
14a) What is the value of x?
14b) What is the measure, in degrees, of angle BDE?
Answers
Answer:
x = 35, ∠ BDE = 130°
Step-by-step explanation:
(4x - 10) and (x + 95) are corresponding angles and are congruent, then
4x - 10 = x + 95 ( subtract x from both sides )
3x - 10 = 95 ( add 10 to both sides )
3x = 105 ( divide both sides by 3 )
x = 35
Thus
∠ BDE = 4x - 10 = 4(35) - 10 = 140 - 10 = 130°
A unicycle wheel has a diameter of 16 inches. How many inches will the unicycle travel in 7 revolutions?
Use π = 3.14 and round your answer to the nearest hundredth of an inch.
Answers
Answer:
The unicycle will travel 351.68 inches in 7 revolutions
Step-by-step explanation:
The circular shape moves a distance equal to its circumference in each revolution, then the rule of the distance of the circular shape travels n turns is D = π d n, where
d is the diameter of the circular shapen the number of revolution∵ A unicycle wheel has a diameter of 16 inches
∴ d = 16 inches
∵ The unicycle will travel 7 revolutions
∴ n = 7
→ Substitute them in the rule of the distance above
∵ D = π(16)(7)
∵ π = 3.14
∴ D = 3.14(16)(7)
∴ D = 351.68 inches
→ No need to round it, it is in the hundredth of an inch
∴ The unicycle will travel 351.68 inches in 7 revolutions
6 of 10
As an estimation we are told £3 is €4.
Convert €32 to pounds.
Answers
help me please and thank you
Answers
Given:
A line passes through (-2,-6) and has a slope of [tex]\dfrac{1}{3}[/tex].
To find:
The point slope form of the given line.
Solution:
If a line passes through a point [tex](x_1,y_1)[/tex] with slope m, then the slope intercept form of the line is
[tex]y-y_1=m(x-x_1)[/tex]
The line passes through (-2,-6) and has a slope of [tex]\dfrac{1}{3}[/tex]. So, the point slope form of the line is
[tex]y-(-6)=\dfrac{1}{3}(x-(-2))[/tex]
[tex]y+6=\dfrac{1}{3}(x+2)[/tex]
Therefore, the correct option is A.
What is true about the rise of all horizontal lines ?the rise is
Answers
Answer:
left to right
Step-by-step explanation:
Answer:
the slope is 0
Step-by-step explanation:
i know this because i asked a math teacher
find the percent of the number
105% of 400
Answers
Answer:
105% of 400 is 420, the percent is 42000%
Step-by-step explanation:
A technician makes $34,400 a year and
a computer programmer makes $46,500 a
year. How much more does a computer
programmer make a year compared to a
technician.
Answers
a computer programer is making 12,100 more dollars than the technichan.
Evaluate the expression 2ac is a = 1/2 and c = 9.
Answers
Answer:
9
Step-by-step explanation:
the expression is 2ac, so multiply everything together
2 * 1/2 = 1
1 * 9 = 9
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Use the given information to find the measures of all angles formed by parallel lines a and b, and transversal m. b One angle is 25° greater than another.
Correct answer gets brainliest!
Answers
Answer:∠1 = ∠3 = ∠5 = ∠7 = 77.5°
∠2 = ∠4 = ∠6 = ∠8 = 102.5°
Step-by-step explanation:
In the picture attached, the parallel lines and the transversal are shown.
8 angles are formed, where:
∠1 ≅ ∠3 ≅ ∠5 ≅ ∠7
∠2 ≅ ∠4 ≅ ∠6 ≅ ∠8
On the other hand, ∠1 + ∠2 = 180°, and ∠2 is 25° greater than ∠1, that is ∠1 + 25° = ∠2, therefore:
∠1 + ∠1 + 25° = 180°
2∠1 = 180° - 25°
∠1 = 155°/2
∠1 = 77.5°
and
∠2 = 77.5° + 25° = 102.5°
Answer:
<1=<5
<4=<8
<2=<6
<3=<7[these all are corresponding angle]
<1=<3
<4=<2
<8=<6
<5=<7 [these all are vertically opposite angle]
a.If one angle is 77°let<1=70°
than
<1=<5=<7=<3=77°
again
<1+<2=180°[linear pair]
<2=180°-72=98°
Than
<2=<6=<4=<8=98°
b One angle is 25° greater than another.
let <1=x than <2=<x+25°
<1+<2=180°[linear pair]
x+x+25=180°
2x=180-25
x=155.2
x=77.5°
x+25=77.5°+25°=102.5°
either
<1=<5=<7=<3=77°
<2=<6=<4=<8=102.5°
Or
<1=<5=<7=<3=102.5°
<1=<5=<7=<3=102.5°<2=<6=<4=<8=77°