The roots of the given equation are √5, - √5, 2i, and - 2i
Roots of a polynomial:The values of a variable for which the provided polynomial equals zero are referred to as a polynomial's roots. If n is the root of a polynomial p(x), then p(n) will be equal to zero.
Here we have
x⁴- x²- 20 = 0
To find the roots of the Equation factorize the given equation
=> x⁴- x²- 20 = 0
Let t = x²
=> t²- t - 20 = 0
Split the middle term
=> t²- 5t + 4t - 20 = 0
=> t(t - 5) + 4(t - 5) = 0
=> (t - 5) (t + 4) = 0
=> (t - 5) = 0 and (t + 4) = 0
Take t - 5 = 0
=> t = 5 => x² = 5
=> x = ±√5
Take (t + 4) = 0
=> t = - 4 => x² = -4
=> x = ± √- 4
=> x = ± 2i [ ∵ - 1 = i² ]
Therefore,
The roots of the given equation are √5, - √5, 2i, and - 2i
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pls help I don't want to fail
Answer:
y = 3x
Step-by-step explanation:
With each x value on the table, the y value is multiplied by 3
Answer:
y=3x
Step-by-step explanation:
Each y value is equal to the corresponding x value times three.
anna lisa bought two dozen apples for $\$$15.60. at that same rate, how much would three dozen of these apples cost?
Three dozen of these apples cost if Annalisa bought is equivalent to $23.40.
Given that:
Annalisa bought two dozen apples for $15.60.
Therefore, the value of one dozen apples will be calculated by dividing both values by 2.
i.e. We can say that,
Annalisa bought one dozen apples for $15.60/2 = $7.80.
So, we have to find out the value of three dozen of these apples.
Hence, we multiply both the 3 to get the cost of three dozen of apples.
Multiplying we get,
Annalisa if bought three dozen apple costs = $7.80 x 3 = $23.40.
We also know that, one dozen = 12 apples
So, three dozen = 36 apples
Therefore, we can say the cost of one apple = 23.40/36 = $0.65
Hence, it costs $23.40 for three dozen apples to Annalisa.
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4 Mackenzie drank 6.95 fluid ounces of water
after recess. Brianna drank 1.7 more fluid ounces
of water than Mackenzie. Combined, how much
water did the girls drink?
Answer:
15.6 ounces
Step-by-step explanation:
6.95 + (6.95 + 1.7) = 15.6 ounces
Jackie has 4 red blocks and 5 blue blocks that weigh 75 ounces. Sam has 4 red blocks and 4 blue blocks that
weigh 65 ounces. How much does the red block weigh? How much does the blue block weigh? Write a let
statement for each variable below, write a system of equations, then solve the system.
Answer:
(6.25, 10)
Step-by-step explanation:
red = x. blue = y
Jackie: 4x + 5y = 75
Sam: 4x + 4y = 65
Solving by elimination
4x + 5y = 75
4x + 4y = 65
--------------------
(4x + 5y = 75) × -1
-4x - 5y = -75
-4x - 5y = -75
4x + 4y = 65
------------------------
-y = -10
÷-1 ÷-1
--------------
y = 10
4x + 4y = 65
4x + 4(10) = 65
4x + 40 = 65
-40 -40
--------------------
4x = 25
÷4 ÷4
-------------
x = 6.25
(6.25, 10)
Each red block weighs 6.25 ounces.
Each blue block weighs 10 ounces.
I hope this helps!
(6 + 4 + 11 + 10 ÷ 2)
Answer:
[tex]\frac{31}{2} , 15.5[/tex]
Step-by-step explanation:
As you follow PEMDAS and go from left to right, you will begin with addition and end with division.
It may make it easier to visualize it as such:
( ( (6+4) +11+10) ÷ 2)
Furthermore, this will end up being
(31÷2)
This may be written as a fraction or decimal as either:
[tex]\frac{31}{2}[/tex] or [tex]15.5[/tex]
I really don't know where to start with this, but you have to solve for x.
(2x-90)+(2x-90)+x=180
Answer:
x = 72
Step-by-step explanation:
We first remove the parenthesis
2x-90+2x-90+x = 180
Group like terms
2x+2x+x-90-90 = 180
Add the like terms with each other
5x-180 = 180
Add 180 to both sides to cancel the -180 on the left side of the equation
5x = 180+180 = 360
We then divide 360 by 5 to get 72 as x
What is the meaning of closure property in mathematics?
The closure property states that any operation performed on the numbers of a set will be closed under that very state.
This means that in any mathematical operation like multiplication, addition, subtraction, or division when performed on two or more numbers of a particular set, the result will belong to that very set.
For example, addition is closed under whole numbers. This means tat the sum of any 2 whole numbers will always be a whole number.
For example, the sum of whole numbers 10 and 20 is 0, a whole number.
Another case is that of subtraction, which is closed under integers.
For example- the difference between integers 30 and 40 is -10, which is an integer.
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does anyone know what the sum of y and 4 is but as an expresion
I NEED HELP FASTT PLS HURRY 20 POINTS
Answer:
D
Step-by-step explanation:
the line isn’t dotted so we take also the points that lies on the line
the shaded part is right the line so we take the points >
The value of square root x to the 2nd power is a real and irrational number when x is equal to
Explain how you got you answer
Answer:
x
Step-by-step explanation:
square root x to the 2nd power is x
square root and 2nd power eliminate each other so it leaves you with x
hopes this helps
Raquel is playing a game where she throws balled-up paper called a "trashball" into her trash
can. The diameter of the top of the trash can is 20 in. Raquel wants the "trashball" to have a
diameter that is the diameter of the top of the trash can.
What should the diameter of Raquel's
"trashball" be?
d= 5 in.
What should the circumference of
the "trashball" be? Use 3.14 for T.
C= ?
in.
20 in.
The diameter of Raquel's "trashball" should be equal to 5 inches.
The circumference of the "trashball" should be equal to 15.7 inches.
How to calculate the diameter of a circle?In order to calculate the circumference of Raquel's trashball, we would use the formula for the circumference of a circle. Mathematically, the circumference of a circle can be calculated by using this formula:
C = 2πr
C = πD
Where:
D represents the diameter of a circle.C represents the circumference of a circle.r represents the radius of a circle.Since Raquel wants the "trashball" to have a diameter that is 1/4 the diameter of the top of the trash can, we have;
Raquel's trashball diameter = 1/4 × diameter of the top of the trash can.
Raquel's trashball diameter = 1/4 × 20
Raquel's trashball diameter = 5 inches.
Next, we would determine the circumference of the "trashball" as follows;
C = 3.14 × 5
C = 15.7 inches.
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Answer:
Part 1 is 5 inches
Part 2 is 15.7 inches
-12 + = 8
I need help with this one
Answer:20
Step-by-step explanation:
Answer:
Step-by-step explanation:
-12+8=
-4
you would subtract 12 and 8 and then you'd get 4 but you'd put a negative sign with it because 12 is negative.
Which graph represents the function f(x) = -|x + 3|?
Answer: i think
Step-by-step explanation:
Answer:
Graph B!!!!
On Edge 2023 Quiz
Step-by-step explanation:
A circle has a diameter of 4 inches. Which statement about the area and circumference of the circle is true?
A comparison of the area and circumference of the circle is not possible because there is not enough information to find both.
The numerical values of the circumference and area are equal.
The numerical value of the circumference is greater than the numerical value of the area.
The numerical value of the circumference is less than the numerical value of the area.
Answer:
Option B is correct
The numerical values of the circumference and area are equal.
Step-by-step explanation:
Circumference(C) and Area (A)of the circle is given by:
....[1]
......[2]
where, r is the radius of the circle.
As per the statement:
A circle has a diameter of 4 inches.
We know:
Diameter = 2 (radius(r))
then;
4 = 2r
Divide both sides by 2 we have;
r = 2 inches
Substitute these in [1] and [2] we have;
Therefore, the numerical values of the circumference and area are equal i.e 12.56
Find the dimensions of a rectangle (in m) with perimeter 60 m whose area is as large as possible. (enter the dimensions as a comma-separated list. ).
The dimension of a rectangle is 15m and 15m.
Here we have to find the area of a rectangle as large as possible.
Data given:
Perimeter = 60m
The formula for the perimeter of the rectangle:
perimeter = 2(length + breadth)
60 = 2( l + b)
l + b = 30
We have to find the largest area, so when we will take the length and
breadth same then we get the largest area.
So length = breadth
2 length = 30
length = 15m
length = breadth = 15m
Therefore the dimensions are 15m and 15m.
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Proofs For Geometry need at least 7 proofs
The given result ∠Q = ∠S is proved by the criteria of two congruent triangles.
What are the criteria for congruent triangles?Two triangles are said to be congruent when all of their corresponding sides and angles are equal. For this relation between two triangles, there are many criteria such as SSS, SAS, ASA and RHS.
The given triangle shows the following information,
R is the midpoint of QS. It implies that QR = QS.
And, PQ = PS
Now, the relation between ΔPQR and ΔPRS is shown as follows,
In ΔPQR and ΔPRS
PQ = PS (Given information)
PR = PR (Common sides)
QR = RS (R is the midpoint)
Thus, ΔPQR ≅ ΔPRS by SSS criteria.
Since for two congruent triangles, the corresponding sides and angles are equal. For the given triangles ∠Q = ∠S.
Hence, it is proved that ∠Q = ∠S as triangles ΔPQR ≅ ΔPRS.
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How do you make a area?
The area is measurement of the surface of a shape. To find the area of a rectangle or a square you need to multiply the length and the width of a rectangle or a square. Area, A, is x times y.
(Adding and Subtracting with Scientific Notation MC) help asap
Simplify (2.5 x 10−9) − (5.8 x 10−8). Write the final answer in scientific notation.
A)−5.55 x 10−8
B) −5.55 x 10−9
C) −3.3 x 101
D)−3.3 x 10−1
explain pls
The expression (2.5 x 10⁻⁹) − (5.8 x 10⁻⁸) simplies to -5.55 × 10⁻⁸. Option A. is the answer
How to add and subtract with Scientific Notation?
Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form
Given: (2.5 x 10⁻⁹) − (5.8 x 10⁻⁸)
In order to simplify (2.5 x 10⁻⁹) − (5.8 x 10⁻⁸) rewrite one of the expressions so that the expressions will have the same power. Then, subtract. That is:
(2.5 x 10⁻⁹) − (5.8 x 10⁻⁸) = (0.25 x 10⁻⁸) − (5.8 x 10⁻⁸)
= (0.25 − 5.8) × 10⁻⁸
= -5.55 × 10⁻⁸
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A regular polygon is shown. 10 sided regular polygon Determine the measure of one of its angles.
The measure of one of 10 sides regular polygon angles is 144 degrees.
What is regular polygon?
A regular polygon is one that is direct equiangular and equilateral in Euclidean geometry. Regular polygons can be skew, convex, or star-shaped.
If a polygon's sides and angles are equal, it is said to be regular. As a result, an equilateral triangle is a regular triangle, and a regular quadrilateral is a square.
Let the given regular polygon is 10 sides.
Since, sum of all angels of a 'n' sided polygon = (n - 2)180 degrees.
Value of each angle, in a 'n' sided regular polygon = [(n - 2)180]/n.
So, a 10 sided polygon, sum of all the angles
= (10 - 2) × 180
= 1440 degrees.
Value of each angle, in case it is a regular polygon = 1440/10 = 144 degrees.
Hence, the measure of one of 10 sides regular polygon angles is 144 degrees.
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Help me please !!!!
Answer:
Step-by-step explanation:
2.) 143 7/23
3.) 291 46/48
4.) 220
5.) 56
6.) 1292 63/4
Freshman and sophomores were surveyed during lunch about their favorite professional football team.
A bar graph with the first bar labeled Jaguars, divided into freshmen from 0 to 40 percent and sophomores from 40 to 100 percent. The second bar is labeled Dolphins, with freshman from 0 to 45 percent and sophomores from 45 to 100 percent, and the third bar is labeled Buccaneers, with freshmen from 0 to 45 percent and sophomores from 45 to 100 percent.
If 140 students selected Jaguars, how many of those students are freshman?
56 students
63 students
77 students
84 students
With the use of proportions, it was discovered that (D) 96 of the 160 students who chose the Jaguars as their favorite team were sophomores.
What are proportions?A percentage is a component of the total amount, and the three-step rule is used to relate the measurements.
This makes it possible to construct direct or inverse proportional relationships between variables to find the necessary measures in the issue.
When determining if two ratios or fractions are equivalent, the proportion formula is utilized.
By dividing the supplied values, we may determine the missing value.
So, we know that 160 students chose the Jaguars as their favorite team for this issue.
Given that 100 - 40 = 60% of the students in the bar graph were sophomores, the number of sophomores who support the Jaguars is as follows:
96 students are 0.6 times 160.
Therefore, with the use of proportions, it was discovered that (D) 96 of the 160 students who chose the Jaguars as their favorite team was sophomores.
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Complete question:
Freshmen and sophomores were surveyed during lunch about their favorite professional football team.
A bar graph with the first bar labeled Jaguars, divided into freshmen from 0 to 40 percent and sophomores from 40 to 100 percent. The second bar is labeled Dolphins, with freshmen from 0 to 45 percent and sophomores from 45 to 100 percent, and the third bar is labeled Buccaneers, with freshmen from 0 to 45 percent and sophomores from 45 to 100 percent.
If 160 students selected Jaguars, how many of those students are sophomores?
a. 64 students
b. 72 students
c. 88 students
d. 96 students
can anyone help please !
Answer:
See pictures below
Step-by-step explanation:
Desmos is a free graphing calculator. Draw the line of the equation and then < will be everything below the line and > will be everything above the line. The portion that is shaded by both colors is the answer.
y = mx + b
The "b" part of the equation tells you the point that the graph crosses the y axis.
The "m" part is the slope. The rise over the run.
Nora invests $800 that pays simple interest at a rate of 6% per annum and $1200 that pays simple interest at a rate of 7% per annum. What is her total annual interest on these two investments?
Answer:
To find the total annual interest on Nora's two investments, we need to calculate the interest earned on each investment and then add the two amounts together. To find the interest earned on the first investment, we need to multiply the amount invested by the interest rate and the length of time the investment is held. The investment of $800 is held for one year, so the interest earned on this investment is $800 x 6% x 1 = $48. To find the interest earned on the second investment, we need to use the same formula. The investment of $1200 is also held for one year, so the interest earned on this investment is $1200 x 7% x 1 = $84. The total interest earned on both investments is $48 + $84 = $132. Therefore, Nora's total annual interest on these two investments is $132.
Step-by-step explanation:
What is 2/3 of a figure?
Multiply your number by 2/3. If you have a whole number, divide it by a denominator of 1 to get a fraction.
Calculate numerator times numerator, then denominator times denominator when multiplying fractions. For instance, multiply 2/3 x 18/1 to get 36/3 in order to discover two thirds of 18.
Divide the resulting fraction by the common denominator to reduce it as necessary. For instance, 36 and 3 both have 3 as their common denominator. You get a fraction of 12/1 when you divide 36 and 3 by 3, which is equal to 12. Therefore, 12 is equal to 2/3 of 18.
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What is the range of this graph?
Answer: -5
Step-by-step explanation:
Let's start with what we know:
Range is the lowest point on the graph subtracted from the highest point on the graph. Therefore, in this equation, we do:
-9 - (-4) = -5
So the range is -5.
Line k has an equation of y= 10 3 x+9. Line includes the point ( – 3, – 2) and is parallel to line k. What is the equation of line ?
y = (10/3)x + 8 will be the equation for the parallel line that passes through the point (-3, -2).
What is the equation of a parallel line?Make the line's equation y = MX + c.
The parallel line that is parallel to the line y = MX + c is therefore given the equation as, y = MX + d.
The equation for line k is y=(10/3)x+9.
Line l is parallel to line k and comprises the coordinates (-3, -2).
y = (10/3)x + d
The line's equation is passing across (–3, –2). The parallel line's equation is therefore given as:
–2 = (10/3)(–3) + d
–2 = –10 + d
d = 10 – 2
d = 8
Therefore, y = (10/3)x + 8 will be the equation for the parallel line that passes through the point (-3, -2).
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Complete question:
Line k has an equation of y= 10/3x+9. Line l includes the point ( – 3, – 2) and is parallel to line k. What is the equation of line l?
The diagram shows two different forces acting on a cyclist riding a bicycle. The total mass of the cyclist and the bicycle is 120.0 kg. Based on this information, what is the acceleration of the cyclist?
Answer:
0.55 m/s²
Step-by-step explanation:
Fnet = 150 N - 84 N = 66 N
a = Fnet/m = (66 N) / (120 kg) = 0.55 m/s²
Which expression is equivalent to (1 + cos(x))2Tangent (StartFraction x Over 2 EndFraction) )?
sin(x)
1 – cos(x)
1 – cos2(x)
(1 + cos(x))(sin(x))
(1 + cos(x)) sin(x) is equivalent to the expression (1 + cos(x))² tan(x/2)
How to find which expression is equivalent to (1 + cos(x))² tan(x/2)?
Trigonometric Identities are the equalities that involve trigonometry functions and holds true for all the values of variables given in the equation
Given: the expression (1 + cos(x))² tan(x/2)
(1 + cos(x))² tan(x/2)
In trigonometric Identity:
Since tan(x/2) = sinx / (1+cosx). We have:
(1 + cos(x))² tan(x/2) = (1 + cos(x))² [sin(x) / (1+cos(x))]
(1 + cos(x))² tan(x/2) = (1 + cos(x)) sin(x)
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the salaries of physicians in a certain speciality are approximately normally distributed. if 25 percent of these physicians earn less than $180,000 and 25 percent earn more than $320,000, approximately what fraction earn
Answer:
We know P(x<$180,000)=.25 and P(x>$320,000)=.25
Using the formula for normal distributions, we can find the mean and standard deviation (z = (x-mean)/SD) using the given info. Then you'll have two equations with two unknowns.
Finally when finding part a, make sure to do a continuity correction [P(x<$200,000) = P(x≤$200,000.5) = ?]
Step-by-step explanation:
I don't understand this tbh and I have been stuck on it foreverr
The height of the balloon before it started its' descent is; 2660 ft
How to solve function tables?We are given a function table with;
time after descent on x-axis in minutes
Height of descent on the y-axis in feet
Let us calculate the slope with the formula;
Slope = (y₂ - y₁)/(x₂ - x₁)
Picking two coordinates;
Slope = (1960 - 2380)/(5 - 2)
Slope = -420/3
Slope = -140 feet/minutes
Now, the equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
when x = 11, y = 1120
Thus;
1120 = -140(11) + c
c = 1120 + (140 * 11)
c = 1120 + 1540
c = 2660 feet
We conclude that it is the height of the balloon before descent
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