The HCF of the polynomials x^6 + 3x^4 + 3x^2 + 1 and x^3+3x^2 + 3x + 1 is 1
When we divide the polynomials f(x) / g(x) then we get f(x) = g(x) × q(x) + r(x). Assuming the degree of g(x) > degree of r(x).
If the remainder r(x) is zero, then q(x) is the highest common factor of polynomials.
Here, we have been given two polynomials x^6 + 3x^4 + 3x^2 + 1 and x^3+3x^2 + 3x + 1
Let f(x) = x^6 + 3x^4 + 3x^2 + 1 and g(x) = x^3 + 3x^2 + 3x + 1
We can write these polynomials as:
f(x) = x^6 + 3x^4 + 3x^2 + 1
f(x) = (x² + 1)^3
The factors of polynomial f(x) = x^6 + 3x^4 + 3x^2 + 1: 1 and (x² + 1)^3
And g(x) = x^3 + 3x^2 + 3x + 1
g(x) = (x + 1)^3
And the factors of g(x) = x^3 + 3x^2 + 3x + 1 : (x + 1)^3 and 1
Therefore, the HCF of the polynomials f(x) and g(x) = 1
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It took Xander 31 minutes to run a 5-kilometer race last weekend. If you know that 1 kilometer equals 0.621 mile, how many minutes did it take Xander to run 1 mile during the race
So it took Xander approximately 9.96 minutes to run 1 mile during the race.
To convert the distance of the race from kilometers to miles, you can use the conversion factor 1 kilometer = 0.621 miles.
To find the time it took Xander to run 1 mile, you can divide the total time it took him to run the entire race by the number of miles he ran.
First, convert the distance of the race from 5 kilometers to miles:
5 kilometers * 0.621 miles/kilometer = 3.105 miles
Then, divide the total time it took Xander to run the race by the number of miles he ran:
31 minutes / 3.105 miles = 9.96 minutes/mile
So it took Xander approximately 9.96 minutes to run 1 mile during the race.
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A scale model of a building is 16 inches long. The actual building is 62 feet long. In the model, the door is 2.4 inches tall. How tall is the actual door?
The scale model door of 2.4 inches is 9.3 ft tall in the actual building.
What is scaling?By scaling, we can create a drawing of an object that corresponds to the object's true size. In geometry, scaling refers to either growing or reducing figures in order to preserve their fundamental shape.
What is cross-multiplication?By multiplying the numerator of one fraction by the denominator of another and the first term's denominator by the numerator of another, we can do cross multiplication.
Given that:
16 inches = 62 ft
2.4 inches = x ft
To calculate the actual value cross multiply the values:
[tex]x= \frac{(62)(2.4)}{16} \\\\x= 9.3 ft[/tex]
Hence, the actual door is 9.3 ft tall.
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How to find the slope of a line that goes from (10,40) to (0,0)
If Mr. Brust can bambam 8 jamjams in 12 whamwhams, the how many jamjams can he bambamin 33 whamwhams? (Yes, I know this is weird)
Answer: 22 jamjams in 33 whamwhams
Step-by-step explanation:
33 ÷ 12 = 2.75 = 12 x 2.75 = 33
2.75 x 8 = 22
Answer:
Mr. Brust can bambam 22 jamjams in 33 whamwhams.
Step-by-step explanation:
Mr. Brust can bambam 8 jamjams in 12 whamwhams.
Mr. Brust can bambam x jamjams in 33 whamwhams.
Use a proportion.
8/x = 12/33
12x = 8 × 33
x = 8 × 33/12
x = 12
Answer:
Mr. Brust can bambam 22 jamjams in 33 whamwhams.
Find the length of the third side. If necessary, round to the nearest tenth
Answer:
25
Step-by-step explanation:
By the Pythagorean Theorem, the sum of the squares of the leg lengths is equal to the square of the hypotenuse:
[tex]a^2+b^2=c^2\\20^2+15^2=c^2\\400+225=c^2\\625=c^2\\25=c[/tex]
Hence, the hypotenuse has a length of 25
After learning how to fly, Wendy reduced her daily commute time by 75%. Previously, her commute took me minutes. Which of the following expressions could represent Wendy's commute time, in minutes, after she learned how to fly
The time taken by Wendy after she learned flying is m/4 minutes or 0.25m minutes.
We will solve this problem with the help of Percentages.
In the concept of percentages, we know that:
100% = 100/100 = 1
75% = 75/100 = 3/4
50% = 50/100 = 1/2
25% = 25/100 = 1/4
In our question, it is given that previously wendy took ‘m’ minutes to commute.
Now she reduced her daily commute by 75% after learning how to fly.
So, our new time = (100-75)% of previous time
= 25% of m minutes
= 25/100 of m minutes = ¼ of m minutes = m/4
So our final answer will be m/4 minutes or 0.25m minutes taken by wendy to commute now.
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Warren is tiling his bathroom. He wants to cut three different sizes of square tiles. Tile A must be square inches, tile B must be square inches, and tile C must be square inches. He needs to know the side length of each tile. Part A In the table, note your guesses and checks to find the length of tile A, which has an area of square inches. Estimate the value to five decimal places
The length of tile A is 2.36068 inches.
The quantity of square units required to completely fill a square is known as the area of a square.
The region that lies inside the confines of a flat item or a two-dimensional figure is generally referred to as the area.
The measurement is made using square units, with square meters serving as the standard unit (m^2).
The square unit serves as the unit of area.
Let us recall that the area of a square is given by;
A = side^2
This is because, all the sides of a square are equal hence
When A = 5 square inches
5 = side^2
side = √5
side = 2.36068 inches
Therefore, The length of tile A is 2.36068 inches.
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Solve the system of inequalities by graphing.
y≤10x–3
y>
–
1
2
x+1
In the story "How Tacos Conquered America" and "The Story of Spaghetti and
Meatballs" have a lot of similarities and differences. Read more to find out what they
have in different and what they have in common. Although the stories had a lot of
similarities it also had a lot of differences for reference Where do these beloved foods
have their roots Tacos were Originated in mexico where a owner of taco bell
"There was just one problem. The cooks at the restaurant hated making them! Each cornmeal tortilla shell had to be
individually fried in scalding oil. The cooks had to turn each tortilla by hand until it was perfectly crispy. The process
was dangerous and painful. The cooks had the burns to prove it ".Juvencio Maldonado was going to
change that. He got to work and made his Mechanical fryer which made up to 7 tacos at a time
and no more burns.
Dose this sound good
GIVING BRAINLIEST AND MANY POINTS FOR ANSWER I BEG PLEASE PLEASE
1. Use the Distributive Property to simplify the expression.
6(5 - q)
Group of answer choices
11 - 6q
11 - q
30 - 6q
1 - q
Answer:
C) 30 - 6q--------------------------
Distributive Property is:
a(b + c) = ab + acApply it to the given expression:
6(5 - q) = 6*5 - 6*q = 30 - 6qThe matching choice is C.
Answer:
[tex] \sf \: c) \: 30 - 6q[/tex]
Step-by-step explanation:
Given expression,
→ 6(5 - q)
Let's simplify the expression,
→ 6(5 - q)
→ 6(5) - 6(q)
→ (6 × 5) - (6 × q)
→ (30) - (6q)
→ 30 - 6q
Hence, option (c) is correct.
6. It took Mrs. Whitaker's class 4 hours to build a snowman.
They decided to build a second snowman, but this time it took
only half the time it took to build the first one. What was the
total amount of time to build both?
The two snowmen took a combined six hours to construct, compared to the four hours it took to construct the first.
what is equation ?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to express the connection between two phrases on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
given
1st snowman took time t = 4 hours
2nd snowman take half of the first t / 2 = 2 hours
so total time
= t + t/2
= 4 + 2
= 6 hours
The two snowmen took a combined six hours to construct, compared to the four hours it took to construct the first.
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Geometry
If BE = 2x + 2, BD = 5x - 3, and
AE = 4x - 6, what are the values
of x and AC?
In parallelogram, x=7 and AC = 44 units are the values of x and AC .
What do math parallelograms mean?
A unique kind of quadrilateral known as a parallelogram is defined by having both pairs of its opposite sides parallel and equal.
A parallelogram ABCD with the coordinates AB II CD and AD II BC can be seen in the provided illustration. Moreover, AB = CD and AD = BC. Non-Example: A parallelogram is not represented by a trapezium.
Here in parallelogram ABCD , AC and Bd are diagonals intersecting at E.
BE = 2x + 2, BD = 5x – 3, and AE = 4x – 6
Using (i)
BE = BD/2
2x + 2 = (5x- 3)/2
2(2x + 2) = 5x - 3
4x + 4 = 5x - 3
x = 7
Now , AE = 4(7)-6 = 28-6 = 22
AC =2 AE = 2 (22) =44 units.
Hence, x=7 and AC = 44 units.
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Dennis made an extra 245. 00 do for selling furniture was 7% of the total value of the furniture he sold. What was the total value of the furniture Dennise sold?
The total value of the furniture that was sold by Dennis is 3,500 dollars.
What is the percentage?
The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.
Dennis made an extra $245.00 for selling furniture.
Let the cost of the furniture be x.
Let the total value of the furniture be x + 245.
The extra $245.00 was 7% of the total value of the furniture he sold.
0.07(x + 245) = 245
x+ 245 = 3500
x = 3255
Then the total value of the furniture is (3,255 + 245 =) $3,500.
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4) It was recommended that the trees be planted 10 feet apart. The school chose to plant the first tree 15 feet away from the property line fence and then to space the trees 10 feet apart accordingly. Write a linear equation with y representing the total distance (in ft.) away from the property line fence and x representing the number of trees used.
a) Write another linear equation for this situation but use a different form.
b) Graph the situation described in question #4.
The linear function that model this problem is y = 10x + 15 and in standard form is 10x - y = -15
What is a Linear EquationA linear equation is an algebraic equation in which each term is either a constant or a product of a constant and a single variable. It is of the form ax + b = 0, where a and b are constants and x is a variable.Sometimes, a linear function can also be said to be a linear equation which is an equation that can be written in the form Ax + By = C, where A, B, and C are constants and x and y are variables. Linear equations are used to describe relationships between two variables, and they can be used to solve a wide range of problems.
In this problem, we can write an equation in slope-intercept form.
This can be modelled in y = mx + c
To model the problem,
y = 10x + 15
a) To rewrite the problem in another form of linear equation, we can write this in the standard form.
Ax + By = C
10x - y = -15
b) The graph of the problem is attached below
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Determine the missing angle measure.
Answer:
38°
Step-by-step explanation:
We have supplementary angles, which mean they add up to 180°, so we can simply solve for x° by doing 180°-142°=38°
Answer:
X=38 degrees
Step-by-step explanation:
A straight line is 180 degrees so to find the missing part you can do 180-142.
That way you get the missing angle measurement.
Ben Nevis has a height of approximately 1300 metres above sea level.
Assuming that temperature decreases by 1°C for every 100 metres above
sea level, work out the temperature at the summit of Ben Nevis when the
sea level temperature is 5°C.
The temperature at the summit of Ben Nevis, when the sea level temperature is 5°C is -15°C.
To work out the temperature at the summit of Ben Nevis, we can use the formula:
Temperature at summit = Sea level temperature - (Altitude above sea level / 100) ×Temperature change per 100 metres
We are given that the sea level temperature is 5°C and the height of Ben Nevis is 1300 metres above sea level, and the temperature decreases by 1°C for every 100 metres above sea level.
So, after putting the values into the formula:
Temperature at summit = 5 - (1300/100) × 1 = -15°C
Therefore, the temperature at the summit of Ben Nevis, when the sea level temperature is 5°C is -15°C
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**Please help ASAP
A sum of $2000 needs to be split among three people so that the first person receives $120 more than the second person and the third person receives twice as much as the second person. Set up and solve an equation or equations to determine how much each person will receive.
Answer:
1st person will receive = $590
2nd person will receive = $470
3rd person will receive = $940
Step-by-step explanation:
Total divisible amount = $2000
according to the question:
let 2nd person's received amount = x
1st person's received amount = x + 120
3rd person's received amount = 2x
x + x + 120 + 2x = 2000
4x + 120 = 2000
4x = 2000 - 120
4x = 1880
x = 1880 / 4
thus,
x = 470
1st person will get = x + 120 = 470+120 = $590
2nd person will get = x = $470
3rd person will get = 2x = 2 * 470 = $940
Net of a square pyramid showing 4 triangles and the square base. The square base has side lengths of 3 inches. The height of each triangle attached to the square is 6 inches. The base of the triangle is the side of the square. What is the surface area of the solid? (1 point) a 18 square inches b 27 square inches c 36 square inches d 45 square inches
The correct option regarding the surface area of the solid is given as follows:
d. 45 square inches.
How to calculate the surface area?The surface area of a solid is composed by the sum of the areas of all the pars of the figure.
The composition of the figure in this problem is given as follows:
4 triangles of base 3 and height 6.One square of side length 3.Thea area of a triangle is given by half the multiplication of the base by the height, hence the area of the four triangles in this problem is given as follows:
At = 4 x 1/2 x 3 x 6
At = 36 square inches.
The area of a square is given by the square of the side length, hence:
As = 3³
As = 9 square inches.
Thus the surface area of the solid in this problem is given as follows:
S = At + As
S = 36 + 9
S = 45 square inches.
Meaning that option d is correct.
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In the figure below, N is between M and O, and O is between N and P. If NO=6, NP=8, and MP=16, find MO.
P
A line segment is merely a portion of a line, one with definite ends and a finite length.
What is a line?A line segment is merely a portion of a line, one with definite ends and a finite length. An object with only one dimension, a line has length but no width. A line is made up of several points that are endlessly stretched in the opposing directions. In a two-dimensional plane, it is specified by two points. Collinear points are described as two points that are on the same line.
An endlessly long, two-directional line is referred to as a line. It just has one, and that is length. Collinear points are those that are situated along the same path. Two points make up a line, which is written as follows with an arrowhead: AB.
O is between M and P, and N is the midpoint of MO. IF NO=3 and MP = 10, find OP.
Given the following details as:
N is between M and O.
O is between N and P .
NO=6 and NP = 8.
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What is the AAA theorem?
According to the Angle-Angle-Angle (AAA) criterion, "if in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion), and hence the two triangles are identical."
Proof:
Consider two triangles ABC and DEF, such that ∠A = ∠D, ∠B = ∠E, and ∠C = ∠F
Now, cut DP= AB and DQ= AC and join PQ. Hence, we can say that a triangle ABC is congruent to the triangle DPQ.
(i.e) ∆ ABC ≅ ∆ DPQ, which gives ∠B = ∠P = ∠E, and also, the line PQ is parallel to EF.
Therefore, by using the basic proportionality theorem, we can write
DP/PE = DQ/QF.
(i.e) AB/DE = AC/DF. …(1)
Similarly,
AB/DE = BC/EF …(2)
From (1) and (2), we can write:
AB/DE = BC/EF = AC/DF.
Therefore, the two triangles ABC and DEF are similar.
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What is an equation of the line that passes through the points (4,-3) and (2,0)
y = 3/2x - 9/2
The equation of the line that passes through the points (4,-3) and (2,0) can be found using the point-slope form of a linear equation. The point-slope form of a linear equation is y-y1=m(x-x1), where m is the slope of the line and (x1,y1) is a point on the line.
To calculate the slope, we will use the formula m = (y2-y1)/(x2-x1). In this equation, (x1,y1) = (4,-3) and (x2,y2) = (2,0). Substituting these values into the slope formula, we get m = (0-(-3))/(2-4) = 3/(-2) = -1.5.
Now that we have the slope, we can plug the point (4,-3) and the slope (-1.5) into the point-slope form of a linear equation to get y-(-3)=-1.5(x-4). Simplifying this equation, we get y+3=-1.5x+6, which is the equation of the line that passes through the points (4,-3) and (2,0).
The casino game of chuck-a-luck seems quite simple and that it would be a pretty good bet. In this game, three dice are rolled (usually inside a wire cage). You can bet a set amount, let's say $5, on a specific number 1-6. You win the amount of your bet for each appearance of your number on the dice. If the number does not appear, you lose your bet. For example, let's say you bet $5 on the number 3. If it appears on exactly one die, you win $5 (and keep your bet) with probability 75/216. If it appears on exactly two dice, you win $10 (and keep your bet) with probability 15/216. If it appears on all three dice, you win $15 (and keep your bet) with probability 1/216. If it appears on none of the dice, you lose your original $5 bet. Construct the probability distribution for chuck-a-luck and determine your expected winnings on a $5 bet.
The expected winnings on a $5 bet are -0.1157 dollars. This means that on average, you will lose about 11.57 cents for each $5 bet you make.
Therefore, the game is not a good bet, as you are expected to lose money in the long run.
What is the probability distribution?
A probability distribution is a mathematical function that describes the probability of different possible values of a variable.
The probability of winning on a $5 bet on a specific number in chuck-a-luck is determined by the number of ways that the number can appear on the three dice and the total number of possible outcomes.
If the number appears on exactly one die, there are 3 ways that this can happen out of a total of 6^3 = 216 possible outcomes, giving a probability of 3/216 or 1/72.
If the number appears on exactly two dice, there are 3 ways to choose the two dice on which it appears, and 3 ways to choose the third die, giving a total of 33 = 9 ways out of 216 possible outcomes, giving a probability of 9/216 or 1/24.
If the number appears on all three dice, there is only 1 way this can happen out of 216 possible outcomes, giving a probability of 1/216.
If it appears on none of the dice, there are (543) ways this can happen, giving a probability of (54*3)/216 = 20/216.
We can use this information to construct the probability distribution for chuck-a-luck:
x P(x)
-5 (losing the bet) 20/216
5 (winning the bet for one appearance) 1/72
10 (winning the bet for two appearances) 1/24
15 (winning the bet for three appearances) 1/216
To find the expected winnings on a $5 bet, we can multiply the value of each outcome by its corresponding probability, and sum the results:
E(X) = (-5)(20/216) + (5)(1/72) + (10)(1/24) + (15)(1/216)
E(X) = -5/43.2 + 5/72 + 5/12 + 15/216
E(X) = -0.1157
Hence, the expected winnings on a $5 bet are -0.1157 dollars. This means that on average, you will lose about 11.57 cents for each $5 bet you make.
Therefore, the game is not a good bet, as you are expected to lose money in the long run.
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Find the centre focus,vertex,directrix and axis of each parabola and sketch the graph? (x-1)² = y+2
The answers to each part of the question are mentioned above.
What is parabola?In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped.The general equation of a parabola is given by -y = a(x – h)² + k or x = a(y – k)² +h.
where - (h, k) denotes the vertex.
Given is the equation of a parabola as -
(x - 1)² = y + 2
We can write the equation as -
y = (x - 1)² - 2
The coordinates of the vertex are : (h, k). So, we can write the coordinates of the vertex as V(1, - 2).The equation of a parabola is -[tex]$y=\frac{1}{4 \left(f - k\right)} \left(x - h\right)^{2} + k[/tex]
We can rewrite the equation of the parabola given as -[tex]$y=\frac{1}{4 \left(\frac{-7}{4} - (-2)\right)} \left(x - h\right)^{2} + k[/tex]
The coordinates of the focus are : (h, f). The coordinates of the focus will be - F(h, f) or F(1, -7/4)The distance from the focus to the vertex is the same as the distance from the vertex to the directrix so -- 2 - (- 7/4) = d - (- 2)
d = - 9/4
The equation of directrix will be :y = d
y = -9/4
The axis of symmetry is the line perpendicular to the directrix that passes through the vertex and the focus: x = 1
Therefore, the answers to each part of the question are mentioned above.
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Of the 6,960 balloons thrown in a water-ballon fight, 870 were red. At this rate, how many balloons out of 48 would be red? WRITE JUST THE ANSWER WITHOUT UNITS
The number of balloons out of 48 that will be red would be = 3/435
How to calculate the number of red balloons?The number of balloons thrown in a water-ballon fight = 6,960 balloons.
The number of red balloons =870 balloons.
The number of balloons out of 48 that would be red; divide through by two.
= 48/6,960
= 24/3,480
= 12/1740
= 6/870
= 3/435
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What should be added to the product of X and 2 to get x * 1 point?
To get x * 1 point, the product of X and 2 should have x added to it.
let us assume unknown value = y
2x+y=x
y=x-2x
y=-x
so if we add "-x" in the product of x and 2 we get x
Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.
These expressions are represented with the help of unknown variables, constants and coefficients. The combination of these three (as terms) is said to be an expression. It is to be noted that, unlike the algebraic equation, an algebraic expression has no sides or equal to sign.
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During a football game the hawks lost 5 yards due to a penalty and lost 6 yards from a quarterback sack. Write and solve an expression that represents the situation.
An expression that describes the given situation is; Total yards = -6 - 5 and the solution is -11
How to solve basic number problems?
In mathematics, a positive number means we have a plus sign before the number which means if we have +2, it means that there has been a gain of 2 units. In a similar manner, a negative number represents a loss which means that if we have -3, it simply means there is a loss or reduction of 3.
Now, we are told that during a football game, the hawks lost 5 yards due to a penalty and lost 6 yards from a quarterback sack. Thus, using the concept of positive and negative numbers above, we can develop the total number of yards as;
Total yards = -6 - 5
Total yards = - 11 yards
This represents a loss.
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Julie wants to check out a book from her local library, but it is not available. Julie decides to visit the library in Lanberry, 15 kilometers away, to see if that location has a copy of the book. On a map, the two libraries are 25 centimeters apart. What is the scale of the map?
The easiest way to find this is to use the library's catalog. Depending on the integrated library system (or ILS) the library subscribes to, the process might be slightly different. Generally, you can use a catalog system on a computer to search by title, author, subject, and more.
For positive acute angles A and B, it is known that tan A = 12/35 and sin B = 9/41. Find the value of cos(A - B) in the simplest form
The simplest form of the value of the trigonometric identity cos(A-B) is
1508/1517.
What is are the trigonometric identities?
Trigonometric Identities are equality conditions that apply to all values of the equation's variables and which require trigonometry functions.
There are numerous unique trigonometric identities that involve both the side length and angle of a triangle. Only the right-angle triangle is valid for the trigonometric identities to work.
cos(A-B) = cosA cosB + sinA sinB
Given,
tan A = 12 / 35
So sin A = 12 / [tex]\sqrt{12^2 + 35^2}[/tex] = 12 / 37
cos A = 35 / 37
Now,
sin B = 9/41
cos B = [tex]\sqrt{1 - sin^{2} B }[/tex] = [tex]\sqrt{1 - (\frac{9}{41} )^{2} }[/tex] = 40/41
Now substituting the above values in the cosine formula
cos(A-B) = cosA cosB + sinA sinB
= (35/37) (40/41) + (12/37) (9/41)
= 1508/1517 = 0.994
Therefore the simplest form of cos(A-B) is 1508/1517.
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What is the median? Help please
Answer:
-65
Step-by-step explanation:
Median = middle number
-76, -74, -67, -65, -63, -58, -48
out of the numbers I am shown, from the photo, I would say "-65" is the answer, but if there is another number I'm missing, add it to the row of numbers above and add the two numbers together and divide by 2
I hope this helps!
6. Subtract and simplify. 1/6m- (-5/8m + 1/3)
Answer:
19/24m-1/3
Step-by-step explanation: