Polynomials form a system like to that of integers hence they are closed under the operations of addition and subtraction.
Exponents of polynomials are whole numbers.
Hence the resultant exponents will be whole numbers , addition is closed for whole numbers. As a result, polynomials are closed under addition.
If an operation results in the production of another polynomial, the resulting polynomials will be closed.
The outcome of subtracting two polynomials is a polynomial. They are also closed under subtraction as a result.
The word polynomial is a Greek word. We can refer to a polynomial as having many terms because poly means many and nominal means terms. This article will teach us about polynomial expressions, polynomial types, polynomial degrees, and polynomial properties.
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a number is 6.14 what way represent the value of the 4 in 6.14
Answer:
Step-by-step explanation:
the value of the 4 in 6.14 is 0.04.
this is because the 4, or in this case 0.04
is in the hundredths place. So it is
suppose to have 0, where the 6 goes (also
the ones or units) The decimal point, another 0
where the 1 goes, ( the tenths) and finally back
to the 4. (Like I said, it’s the hundredths place)
so there you have it. Your answer will be 0.04
help me please i really need this im failing pls try to understand and help me
Answer:
Blaaaaaaaa Blaaaaaaaa Blaaaaaaaa I do not know
•18 POINTS• don’t explain
a.) neither
b.)SAS
c.)HL
SAS congruence theorem should be used.
Option (B) is correct.
What is the SAS congruence theorem?
In Euclidean geometry, the SAS congruence theorem states that if two triangles have two sides of one triangle congruent (equal in length) to two sides of the other triangle, and the included angle is congruent, then the triangles are congruent. This theorem is often abbreviated as SAS, and is used in combination with other congruence theorems, such as ASA and SSS, to prove that triangles are congruent.
In the given picture, we can say both triangles has the same side of length 7 and along with it, one more side is of equal length.
and both triangles are having the right-angle,
so we can say that we can prove these triangles congruent by using SAS congruence theorem.
Hence, SAS congruence theorem should be used.
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Translate: (x - 2)/3 + x^2. Select the one answer.
Answer:
its the first answer choice
Step-by-step explanation:
C) Will Qamar have enough lacquer to cover the floor below? (pictured)
D) Justify your answer.
E) If your answer is “No,” how much more lacquer does she need? If your answer is
“Yes,” how much lacquer will she have left over? Show your work to justify your
answer.
Based on the information provided, Qamar will have enough lacquer to cover the floor and 24 square feet will be left over.
How much lacquer does Qamar have?Based on the information given, Qamar has 600 square feet.
How much lacquer does Qamar need?To calculate the total lacquer Qamar needs, it is necessary to calculate the area of the floor that has to be covered. In the case of a parallelogram, the area can be calculated using the following formula:
Area = Base x heigh (in a parallelogram, the height is the distance between the two horizontal lines using a straight line)Area = 48 feet x 12 feetArea = 576 square feetNow, if the total of material available is 600 feet, it can be concluded there is enough material to cover this floor. Let's calculate the lacquer left over:
600 - 576 = 24 feetNote: This question is incomplete; here is the missing information:
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ANSWER ASAP! WILL
MARK BRAINLIEST
8. Find x and y.
A) x = 56, y = 68
B) X = 68, y = 56
C) x = 57, y = 66
D) X = 66, y = 57
Answer:
i depends on what the equation is.
Luke and Seth each need to buy the same amount of fencing for their gardens. While Seth's garden is square in shape, Luke's garden is rectangular with the length 3 feet longer than Seth's. Luke's width is half of the length of his own garden.
How much fencing did each buy? Need this asap please and thank you.
option
40. 5 feet
81 feet
72 feet
36 feet
Fencing that Luke and Seth did each buy is 72 feet
Using the information given, you can set up and solve the system of equations. Let x be the length of Seth's garden.
Seth's garden is square, so it has four times the perimeter.
The perimeter of Luke's garden is a rectangle of length x + 3 feet and width x/2 feet, so 2(x + 3) + 2(x/2).
We also know that Luke and Seth should buy the same amount of fences. So:
4x = 2(x + 3) + 2(x/2)
Solving this equation for x gives x = 6 feet.
So Seth's yardage is 6 feet and Luke's yardage is 9 feet.
So the fence required for Seth's garden is 46 = 24 feet
and the fence required for Luke's garden is 2(9) + 2(9/2) = 29 + 2*4.5 = 36 + 9 = 45 It's feet.
So the total fencing required is 24 + 45 = 72 feet.
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A rental car company charges $80 per day to rent a car and $0.10 for every mile driven. Alyssa wants to rent a car, knowing that: She plans to drive 150 miles. She has at most $300 to spend. Which inequality can be used to determine xx, the maximum number of days Alyssa can afford to rent for while staying within her budget?
Answer:
400
Step-by-step explanation:
Car A costs 80d + 0.25m, where d is days and m is miles. Car B costs 100d + 0.10m. If you plug in 3 for d and make the equations equal, you get 240 + 0.25m = 300 + 0.10m. Combining like terms gives you 0.15m = 60, and dividing gives you m = 400.
Using the inequality concept, the expression which models the maximum number of days in which she can rent the car is 80x + 15 ≤ 300
Maximum amount to spend = 300Fixed charge per day $80Charge per mile = $0.10The inequality which represents the number of days Can be expressed thus :
(Charge per day × number of days) + (charge per mile × number of miles) ≤ 300
80x + 0.10 × 150 ≤ 30080x + 15 ≤ 300Hence, the required inequality expression is 80x + 15 ≤ 300
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Octagon ABCDEFGH with side lengthsABCDEFGII 10 and BC=DE FG = HA= 11 isformed by removing 6-8-10 triangles from the corners of a 23 x 27 rectanglewith side AH on a short side of the rectangle, as shown. Let J be the midpointof AH, and partition the octagon into 7 triangles by drawing segments JB,JC, JD, JE, JF, and JG. Find the area of the convex polygon whosevertices are the centroids of these 7 triangles.
Area of the convex polygon whose vertices are the centroids of these 7 triangles is 184.
What is a convex polygon?
A polygon that forms the edge of a convex set is said to be convex polygon. This indicates that the union of the interior and the boundary of the polygon has the line segment connecting two points of the polygon.
Given,
AB = CD = EF = GH = 10
BC = DE = FG = HA = 11
Triangles of side length 6,8,10 is cut from corners 23×27 rectangle.
Using the above information, we marked the position of A,B,C,D,E,F,G,H and J, taking the upper left corner of rectangle as origin.
The centroid of a triangle can be found using the formula,
Centroid = [tex](\frac{x_{1} + x_{2}+x_{3}}{3} , \frac{y_{1} +y_{2}+y_{3}}{3})[/tex]
For ΔJAB,
[tex]C_{1}[/tex] = (8/3 , -35/6)
For ΔJBC,
[tex]C_{2}[/tex] = ( 9 , -23/6)
For ΔJCD,
[tex]C_{3}[/tex] = ( 46/3, -35/6)
For ΔJDE,
[tex]C_{4}[/tex] = ( 18 , -23/2)
Area of convex polygon = [tex]\frac{1}{2} [x_{1} y_{2} + x_{2}y_{3}+.........+x_{n}y_{1}] - [y_{1}x_{2}+y_{2}x_{3}+......+y_{n}x_{1}][/tex]
From figure we find the area of C₁C₂C₃C₄C₈, where C₈ = (8/3 , -23/2)
Area =
[tex]\frac{1}{2} [8/3 (-23/6 )+ 9(-35/6)+46/3(-23/2)+18(-23/2)+8/3(-35/6)] - [(-35/9)9+(-23/6)46/3+(-35/6)18+(-23/2)8/3+(-23/2)8/3][/tex]
= 184 / 2
Therefore total area of convex polygon = 2 × 184/2 = 184 sq. units
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Why are Trig ratios only for right triangles?
For Trigonometric functions to work we need a hypotenuse, which we can only get in right triangles.
What are Trigonometric functions?
The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.
Here,
We have to find out why trigonometric ratios are used only for right triangles.
We concluded that when we are dealing with triangles other than right triangles, the solution is to draw a perpendicular line to create right triangles. For Trigonometric functions to work we need a hypotenuse, which we can only get in right triangles.
Hence, for Trigonometric functions to work we need a hypotenuse, which we can only get in right triangles.
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The perimeter of a square is given as 24x + 20. Write two diffrerent expressions to represent the perimeter. Use factoring to write one of the expressions
The perimeter of a square is given as 24x + 20 and can be written as 4 ×(5x+6) and 2 × (10x+12).
The perimeter of a square is the sum of all of the 4 sides of the square. Here, the perimeter of the square is given as the function of x, for finding the length of each side of the square.
Here, in the given problem, we can factorize the expression 20x+24 as, 4 ×(5x+6) so this is the 1st different way of writing the given expression. For another expression, we can take 2 commons from 20 x+24 that will be 2 × (10x+12).
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The water works commission needs to know the mean household usage of water by the residents of a small town in gallons per day. They would like the estimate to have a maximum error of 0.1 gallons. A previous study found that for an average family the variance is 5.76 gallons and the mean is 19.5 gallons per day. If they are using a 90% level of confidence, how large of a sample is required to estimate the mean usage of water? Round your answer up to the next integer.
Answer:
The right solution is "1559".
Step-by-step explanation:
The given values are:
Variance,
[tex]\sigma=\sqrt{5.76}[/tex]
[tex]=2.40[/tex]
Maximum error,
[tex]M.E=0.1[/tex]
At 90% confidence level,
[tex]\alpha=0.1[/tex]
According to the z-table, the critical value will be:
[tex]Zc=1.645[/tex]
Now,
The sample size will be:
⇒ [tex]n=(Zc\times \frac{\sigma}{E} )^2[/tex]
On substituting the values, we get
⇒ [tex]=(1.645\times \frac{2.4}{0.1} )^2[/tex]
⇒ [tex]=(1.645\times 24)^2[/tex]
⇒ [tex]=(39.48)^2[/tex]
⇒ [tex]=1558.67[/tex]
or,
⇒ [tex]=1559[/tex]
Answer the statistical measures and create a box and whiskers plot for the following
set of data.
7, 10, 11, 12, 12, 13, 13, 14, 14, 16, 17
Min: .Med: 03 Max:
Answer:
Min:7
Q1:11
Med:13
Q3:14
Max:17
Step-by-step explanation:
Hope the picture helps. :)
In a triple batch of spice mix, there are 6 teaspoons of garlic powder and 15 teaspoons of salt. Answer the following questions about the mix. If you get stuck, create a double number line.
In a double number line diagram, equal ratios are represented by two parallel number lines. On both number lines, the tick marks are in the same places. Though the other numbers are frequently varied, the tick marks labeled with 0 always line up.
How to create a double number line?According to question:-
How much more garlic powder than salt is in the triple batch?
Answer: 6 teaspoons of garlic powder - 15 teaspoons of salt = -9 teaspoons. So there is 9 teaspoons less garlic powder than salt in the triple batch.
How much spice mix is in the triple batch?
Answer: 6 teaspoons of garlic powder + 15 teaspoons of salt = 21 teaspoons of spice mix.
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PLEAS EHLPE BESTIES
Look at the venn diagram. How many people like vanilla only?
1 point
vanilla
8
4
chocolate
Your answer
answer:
8 people like vanilla only
hope this helped!
Answer:
8
Step-by-step explanation:
Brainliest??
(PLEASE HELP AS SOON AS POSSIBLE)
Answer:
you answer would be F: Point W
Write and solve an inequality to find the values of x for which the perimeter of the rectangle is less than 112.
x+4
The inequality to discover the values of x for which the rectangle's perimeter is under 112 is x< 26.
what is inequality ?An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal symbol (). Different inequalities are used to contrast values, no matter how small or large. Many simple inequalities can be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.
given
perimeter of a rectangle = length + length + width + width
length + length + width + width = perimeter of a rectangle
(x +4) + (x+4) + x + x < 112
x + 4 + x + 4 + x + x < 112
4x + 8 < 112
4x < 104
x < 26
So ,The inequality to discover the values of x for which the rectangle's perimeter is under 112 is x< 26.
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can anyone help with this one?! will mark brainliest!
Answer:
D =44°
Step-by-step explanation:
Angle ACB = 2 angle ADB
So, ADB = ACB/2
= 88°/2
= 44°
what can 7 and 5 both be divided by
i need help asap!!! thx u
The distance of the ball thrown is 67 ft. approx.
What are trigonometric functions?In mathematics, trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. The six trigonometric functions are Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent.
Given here θ=63 and length of the field as 60 and let d be the distance
∴ Cos (180-63-90)=60/d
d = 60/cos(27)
d = 67 (approx)
Hence, The distance of the ball thrown is 67 ft. approx.
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The table shows the shoe sizes of women of different ages. A 2-column table with 4 rows. The first column is labeled age with entries 18, 30, 52, 64. The second column is labeled shoe size with entries 7, 10, 6, 9. Which best describes the strength of the model? a weak positive correlation a strong positive correlation a weak negative correlation a strong negative correlation
Answer:
A.) weak positive correlation
The person above just wanted to steal points.
Step-by-step explanation:
Answer:
The correct answer is a weak positive correlation
or
A
Step-by-step explanation:
In a 45°-45°-90° triangle, the length of the hypotenuse is 11. Find the length of one of the legs.
The length of the leg of the right-angled triangle is (11√2) / 2. The correct option is C.
What is trigonometry?The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry. The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.
Given that the right angles triangle has 45-45-90 angles. The hypotenuse is 11.
The length of the leg will be,
Cos45 = Base / Hypotenuse
1 / √2 = Base / 11
Base = 11 / √2
Rationalize the numbers,
Base = 11√2 / 2
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F the altitude of a triangle meet at one of the triangles vertices then the triangle is
When the given altitude of the triangle meet at one of the vertices of the given triangle then it represents the option 1. right angled triangle.
As given in the question,
Given is the altitude of the triangle.
Given Condition is :
Altitude of the triangle meet at one of the vertices of the triangle.
⇒ This means altitude is representing the height of the triangle.
Height is always represented by perpendicular line.
⇒One of the side having altitude forms a angle of measure 90°.
⇒Given triangle is right angled triangle.
Therefore, when the altitude of the triangle meet at one of the vertices of the given triangles it represents the option 1. right angle triangle.
The above question is incomplete, the complete question is :
If the altitudes of a triangle meet at one of the triangle’s vertices, then the triangle is
1) a right triangle
2) an acute triangle
3) an obtuse triangle
4) an equilateral triangle
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I have x N50 note and y N100 note. There are eight note altogether and their total value i N550. How many of each note do I have?
So I have 5 and 3 notes each
You need to use simultaneous equations to solve this problem since there are 2 variables.
50x + 100y = 550 (value of the notes x the number of each note)
x + y = 8 (the number of each note added).
Multiply the second equation by 50 so that it the x variables are the same in both equations. Thus, 50x + 50y = 400.
Subtract 50x + 50y = 400 from 50x + 100y = 550.
The subtraction results in 50y = 150.
Divide by 50. y = 3, so x must equal 5.
So I have 5 and 3 notes each
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What is a midpoint for zero?
The midpoint for zero is (0,0).
The midpoint can be zero. This is dependent on the value of the two points. For two points on a number line on points with values -4, and 4, the midpoint is 0. And for two points such as (-2, 5), and (2, -5), the midpoint is equal to (0, 0).
The midpoint of a line segment is known as the midpoint in geometry. It is the centroid of the segment and of the ends, and it is equally distant from both of them. It cuts the section in half.
A compass and straightedge setup can be used to locate the midpoint of the line segment they determine given two points of interest. By initially building a lens out of circular arcs with equal radii centered at the two endpoints and joining the cusps of the lens, one can determine the midpoint of a line segment immersed in a plane. The midpoint of the segment is then the place where the line joining the cusps intersects the segment.
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The temperature changed from 3 degrees below zero at midnight to 7 degrees below
zero at 2 a.m. How much did the temperature decrease?
The temperature has decreased by 4 degrees Celsius.
We have a temperature change from 3 degrees below zero at midnight to 7 degrees below zero at 2 a.m.
We have to determine how much did the temperature decrease.
' The temperature of an area is x degrees below zero '. What does this statement mean ?A temperature of x degrees below zero means that the temperature of an area is equal to = - x degrees i.e., T = 0 - x = - x.
According to question -
Initial Temperature T(i) = 0 - 3 = - 3 degrees
Final temperature T(f) = 0 - 7 = - 7 degrees
Change in temperature ΔT = T(f) - T(i) = -7 - (-3) = -7 + 3 = - 4
Hence, the temperature has decreased by 4 degrees Celsius.
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Question:
1. Find the minimum or maximum value of this function by completing the square.
f(x) = x2 + 8x + 6
The geometric sequence an = 2an – 1 with an initial value of a1 = LaTeX: \frac{1}{8}1 8 represents the amount of money a person has saved after n years of investing. What is the sum of the first 11 terms?
The sum of the first 11 terms of the geometric sequence aₙ = 2aⁿ - 1 with an initial value of a₁ = 1/8 is -10.71.
Therefore the answer is -10.71.
The geometric sequence aₙ = 2aⁿ - 1 with an initial value of a₁ = 1/8 represents the amount of money saved after n years of investing.
So sum of n terms
Sn = 2a - 1 + 2a² - 1 + ... + 2aⁿ - 1
Sn = 2( a + a² + ... + aⁿ) - n
The sum of the first n terms of a geometric sequence aₙ = arⁿ⁻¹ with first term a₁ and common ratio r is given by the formula:
Sn = a₁(1 - rⁿ)/ (1 - r), that is
[tex]S_{n} = a_{1}\frac{ (1 - r^n)}{1 - r}[/tex]
So a + a² + ... + aⁿ = a(1 - aⁿ)/ (1 - a)
Thus Sn = 2( a + a² + ... + aⁿ) - n
Sn = 2a(1 - aⁿ)/ (1 - a) - n
In this case, a₁ = a = 1/8 and n = 11
So the sum of the first 11 terms of the geometric sequence is:
Sn = 2×1/8×( 1 - (1/8)¹¹)/ (1 - 1/8) - 11
Sn = -10.71
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Can someone help me!!!!!!
The y - intercept of the graph, given the formula of 2 y - 5x = 16, is y - intercept : ( 0, 8)
How to find the y - intercept ?To find the y - intercept, use the slope - intercept form of the equation of a line which is:
y = mx + b
m = slope
b = y - intercept
So first rewrite the formula given to look like the slope - intercept :
2 y - 5x = 16
2 y = 5x + 16
( 2 y = 5x + 16 ) / 2
y = 5/ 2 x + 8
The y- intercept is therefore 8. As a point on the graph, this is ( 0, 8 )
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A boat is traveling due east for 130 miles. The boat travels another 72 miles at a bearing N38E. Determine the distance, direction angle, and bearing of the boat from its original location.
The distance of the boat is 191.2 miles, 12.8° and N12.8E from the original location.
Using Trignometry to find the boat's distance:To calculate the distance, direction angle, and bearing of the boat from its original location, we will need to use trigonometry to determine the final position of the boat.
a) The distance traveled in the eastward direction is 130 miles. Then, using the bearing of N38E, we can calculate the northward and eastward distances traveled in the second leg of the journey. The bearing of N38E can be thought of as an angle of 38 degrees measured clockwise from due east.
Using trigonometry to calculate the northward distance traveled, we have,
(72 miles) * (sin 38°)
= 36 miles
And the eastward distance traveled is (72 miles) * (cos 38°)
= 59.04 miles.
The final position of the boat is at a distance can be calculated by:
130 miles east + 59.04 miles east
= 189.04 miles east and 36 miles north from the original location.
b) To find the distance from the original location, we use the Pythagorean theorem,
d = [tex]\sqrt{189.04^{2} +36^{2} }[/tex]
d = 191.2 miles
To find the direction angle, we use arctan(north/east) = arctan(36/189.04) = 12.8°
Bearing is the direction angle measured clockwise from north. So, bearing = 12.8°
Hence, the final position of the boat is 191.2 miles, 12.8°, and N12.8E from the original location.
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