The greatest common factor is 3x² and GCF form of polynomial is
3x²(3x-2).
The given polynomial is
9x³ - 6x²
We can write it as;
3x²(3x-2)
We know that
The greatest common factor (GCF) that divides two or more numbers is known as the greatest common divisor (GCD). The highest common factor (HCF) is another name for it.
Therefore 3x² is its GCD.
Divide each term of polynomial 3c,
6c³ ÷ 3c = 2c² and -9c ÷ 3c = -3
Thus,
3x²(3x-2) is the factored version of the polynomial with the highest common factor.
Also if GCD is 1 then after dividing each term by 1 we get same result
thus the polynomial be 3x²(3x-2).
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please help asap i’m stuck
Answer:
10%
Step-by-step explanation:
P(reading paper 'given' that they are <40)
= P(reading paper AND < 40) / P(< 40)
= (4/80) / (40/80)
= 4/40
=1/10
=0.1
=10%
Enter values to write the function that matches the graph shown.
Answer:
The roots of this function are at -4 and -1.
f(x) = (2x + 8)(-2x - 2)
= (2x + 8)(-2x + (-2))
The circle below has a radius of 8 inches, find it's approximate area and circumference. Use the fact that π ≈ 3.14.
.
The approximate area and circumference of the circle is given as 201 inch² and 20 inch respectively
What is the area of a circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the center. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is constant
The area and perimeter of a circle can be calculated using the formula
πr = πd, where r is the radius and d is the diameter of the circle
Area = πr² and
the perimeter is 2πr
r= 8 inch, π = 3.14
Area = 3.14 * 8 * 8
Area = 200.96 square inches
Area = 201 inch²
the perimeter is = 2*3.14*8
The perimeter is = 50.24 square inches
Perimeter = 50 inch
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The area and circumference of the circle with a radius of 8 inches are 200.96 square inches and 50.24 inches respectively.
What is the area and circumference of the circle?A circle is simply a closed 2-dimensional curved shape with no corners or edges.
The area of a circle is expressed mathematically as;
A = πr²
The circumference of a circle is expressed as:
C = 2πr
Where r is radius and π is constant pi ( π = 3.14 )
Given that the radius of the circle is 8 inches.
Substituting this value into the formula, we get:
A = πr²
A = 3.14 × ( 8 in )²
A = 3.14 × 64 in²
A = 200.96 in²
Next, we calculate the circumference:
C = 2πr
C = 2 × 3.14 × 8 in
C = 50.24 in
Therefore, the value of the circumference is 50.24 in.
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Which of the word problems exemplify a linear function?
A. Angie's swimming classes required $50 enrollment fee and $10 safeguard
insurance cost each month.
B. Ken's car value depreciates by about 20% in the first year and then at estimated
15% each year following the first year.
C. A candy manufacturing business began its venture with 1,200 packets of candy
varieties. Then, 3,600 and 10,800 packets on the 2nd and 3rd days respectively.
D. The area of a triangular yard that has a right angle.
The word problem that exemplifies a linear function is
- Angie's swimming classes required a $50 enrollment fee and a $10 safeguard insurance cost each month.
Option A is the correct answer.
We have,
A linear function is a mathematical model that represents a relationship between two variables that is a straight line.
In this problem,
The cost of Angie's swimming classes is a linear function of the number of months.
The enrollment fee of $50 is a fixed cost that does not depend on the number of months, and the safeguard insurance cost of $10 per month is a variable cost that increases linearly with the number of months.
Thus,
The word problem that exemplifies a linear function is
- Angie's swimming classes required a $50 enrollment fee and a $10 safeguard insurance cost each month.
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 write a quadratic function that is three units write four units down and five times narrower then y=x squared
Answer:
y = 5(x - 3)^2 - 4 + c
Step-by-step explanation:
The standard form of a quadratic function is y = ax^2 + bx + c, where a, b, and c are constants. To shift the graph three units to the right and four units down, we can modify the constant term c and the linear term bx:
y = a(x - 3)^2 - 4 + c
To make it five times narrower, we can modify the coefficient of the squared term a:
y = (1/5)a(x - 3)^2 - 4 + c
Since we want the shape to be the same as y = x^2, we can set a = 5:
y = 5(x - 3)^2 - 4 + c
The value of c will depend on the specific context of the problem or graph.
Suppose a jar contains 15 red marbles and 32 blue marbles. If you reach in the jar and pull out 2 marbles at random at the same time, find the probability that both are red.
The probability of drawing 2 red marbles is 0.081 or 8.1%.
There are 15 red marbles and 32 blue marbles, so there are 15+32=47 marbles total.
The probability of pulling a red marble on the first draw is 15/47.
If the first marble drawn is red, then there are 14 red marbles and 32 blue marbles remaining.
So, the probability of pulling a second red marble is 14/46.
To find the probability of both events happening, we multiply the probabilities:
P(both red) = P(first red) × P(second red | first red)
P(both red) = (15/47) × (14/46)
P(both red) = 0.081 (rounded to 3 decimal places)
Therefore, the probability of drawing 2 red marbles is approximately 0.081 or 8.1%.
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A recent random survey of 100 individuals in Michigan found that 78 drove to work alone. A similar survey of 120 commuters in New York found that 58 drivers drove alone to work. Find the 95% confidence interval for the difference in proportions
The 95% confidence interval for the difference in proportions is approximately 0.0957 to 0.4977.
To find the 95% confidence interval for the difference in proportions between Michigan and New York commuters who drove alone to work, we can use the formula:
CI = (p1 - p2) ± Z * sqrt((p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2))
Where:
p1 and p2 are the proportions of Michigan and New York commuters who drove alone to work, respectively.
n1 and n2 are the sample sizes of Michigan and New York commuters, respectively.
Z is the critical value corresponding to the desired confidence level (95% confidence level has Z ≈ 1.96).
Given:
Michigan: p1 = 78/100 = 0.78, n1 = 100
New York: p2 = 58/120 = 0.4833, n2 = 120
Plugging in the values:
CI = (0.78 - 0.4833) ± 1.96 * sqrt((0.78 * (1 - 0.78) / 100) + (0.4833 * (1 - 0.4833) / 120))
CI = 0.2967 ± 1.96 * sqrt(0.006456 + 0.004074)
CI = 0.2967 ± 1.96 * sqrt(0.01053)
CI ≈ 0.2967 ± 1.96 * 0.1026
CI ≈ 0.2967 ± 0.201
The 95% confidence interval for the difference in proportions is approximately 0.0957 to 0.4977.
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(Worth 100 Brainly points)After a dreary day of rain, the sun peeks through the clouds and a rainbow forms. You notice the
rainbow is the shape of a parabola.
The equation for this parabola is y=-x² + 36
1.Create a table of atleast 4 values of the function that includes two points of intersection between the airplane and the rainbow
2.What is the domain and range of the rainbow? Explain what the domain and range represent.Do all of the values make sense in the situation. Why or why not.
3.what are the x and y intercepts of the rainbow. Explain what each intercept represents.
1) Equation for the parabola y = - x² + 36.
2) A drone is in the distance, flying upward in a straight line. It intersects the rainbow at two points. Choose the points where your drone intersects the parabola and create a table of at least four values for the function.
The points of intersection will be: (0,36) and (4, 20)
Table of values for a linear function and the parabola
x linear function parabola y = - x² + 36
0 36 (0)² + 36 = 36
1 32 - (1)² + 36 = 35
2 28 - (2)² + 36 = 32
3 24 -3² + 36 = 27
4 20 -4² + 36 = 20
It is a linear function because the rate of change is constant: for each increase of 1 unit in x, there is a decrease of 4 units in y: ⇒ slope = - 4
Remember to include the two points of intersection in your table. Analyze the two functions; they are there (0,36) and (4, 20)
Answer the following reflection questions in complete sentences. What is the domain and range of the rainbow?
Explain what the domain and range represent. Do all of the values make sense in this situation? Why or why not? What are the x- and y-intercepts of the rainbow? Explain what each intercept represents.
The domain is all the real values of x between - 6 and 6: - 6 ≤ x ≤ 6
The range is all the values between 0 and 36: 0 ≤ y ≤ 36
The domain represents the horizontal distance between the extremes of the rainbow at the ground.
The range represents: the altitude of the rainbow from the ground (y = 0). The height is at x = 0, y = 36.
The x-intercepts are - 6 and 6, that is the opening of the rainbow at the ground level.
The y-intercept is when x = 0, it is y = 36, and is the height of the rainbow.
Is the linear function you created positive or negative? Explain. What are the solutions or solution to the system of equations created? Explain what it or they represent.
The linear function is positive and decreasing. It is positive because it goes above the x-axis, this is y ≥ 0.
The solutions were already signaled: (0,6) and (4, 20). They are the points at which the drone intercepts the rainbow.
Use the information above to answer the questions that follow. Show that the total floor area to be tiled is 32 m². You may use this formula: Area of a rectangle = length x width Determine how many boxes of tiles Tshego will need if an extra 10% of the number of tiles must be added for cutting and breakages. S 2.1 2 Show by means of calculations if Ishego's budget is enough to finish the tiling project. (9)
Tshego's budget is more than R7200, then it would be enough to finish the tiling project. If his Budget is less than R7200, then it would not be enough.
We are not provided with any information in the question, so we cannot answer it as is. However, we can use the formula provided to calculate the total floor area to be tiled:
Area of a rectangle = length x width
Let's say the length is L and the width is W. Then, the total floor area to be tiled is:
Total floor area = L x W
We are not given the values of L and W, so we cannot calculate the exact total floor area. However, we can assume that Tshego has already calculated the total floor area to be 32 m².
To determine how many boxes of tiles Tshego will need, we need to know the size of each box of tiles and the total area that one box can cover. Let's assume that each box of tiles covers an area of 1 m².
If the total floor area to be tiled is 32 m², and an extra 10% of the number of tiles must be added for cutting and breakages, then the total area to be covered with tiles would be:
Total area to be covered = 32 m² x 1.1 = 35.2 m²
Therefore, Tshego would need 36 boxes of tiles to cover the entire floor area.
To determine if Tshego's budget is enough to finish the tiling project, we need to know the cost of each box of tiles and the total cost of the project. Let's assume that each box of tiles costs R200.
The total cost of the project would be:
Total cost = Number of boxes x Cost per box
Total cost = 36 x R200 = R7200
If Tshego's budget is more than R7200, then it would be enough to finish the tiling project. If his budget is less than R7200, then it would not be enough.
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compare a and 0 if -12a<-2a
The variable a can take infinite many values (including 0)
Comparing the variable a and the number 0From the question, we have the following parameters that can be used in our computation:
-12a < -2a
This expression can be expressed as
-2a > -12a
Divide both sides by -2a
So, we have
1 < 6
The above expression is true
This means that the variable a can take infinite many values (including 0) i.e. 0 is a subset of a
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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
Two friends visited a taffy shop. Jon bought 4 kilograms of strawberry taffy and 1 kilogram of banana taffy for $23. Next, Charlotte bought 5 kilograms of strawberry taffy and 2 kilograms of banana taffy for $34. How much does the candy cost?
A kilogram of strawberry taffy costs $____, and a kilogram of banana taffy costs $____.
A kilogram of strawberry taffy costs $4, and a kilogram of banana taffy costs $7.
Let us assume
the price of 1 kg strawberry taffy = $x
And the price of 1kg banana taffy = $y
Then according to given information
the expression for Jon be,
4x + y = 23 ....(i)
the expression for Charlotte be,
5x + 2y = 34 ...(ii)
Now use elimination method
2x(i) - (ii) we get,
3x = 12
x = 4
Plug it into (i) we get
y = 7
Hence, costs are:
1 kg strawberry taffy = $4
1kg banana taffy = $7
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Find the length of the hypotenuse of the right triangle.
Answer:
The length of the hypotenuse is 100.
Step-by-step explanation:
To find the length of the hypotenuse, we use the following formula:
c=[tex]\sqrt{a^2+b^2}[/tex]
c=[tex]\sqrt{28^2+96^2}[/tex]
c=[tex]\sqrt{10,000}[/tex]
c=100
Therefore, the length of the hypotenuse is 100.
What conclusion can be determined from the dot plot below?
The number of observations is 10.
The median of the data set is 10.
The mean of the data set is 15.
The range of the data set is 12.
The conclusion can be determined from the dot plot is
The median of the data set is 10.
1. The number of observations is 10:
There are total 15 observations.
2. The median of the data set is 10.
From the dot plot the data is
9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 12
Thus, the median is 10.
3. Mean = Sum of observation / Total Number of observation
Mean = (9+9+9+9+9+10+10+10+10+10+10+11+11+11+12) /15
Mean= 150/15=10
Thus, the Mean is 10.
4. Range = 12 - 9
Range = 3.
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The first rule is add 10, then divide by 2 starting from 2. The second rule is multiply by 3, then subtract 2 starting from 2. What are the first four ordered pairs using the two sequences? (4 points)
(2, 0), (6, 4), (8, 12), (9, 32)
(2, 2), (6, 4), (8, 10), (9, 28)
(6, 4), (8, 10), (9, 28)
(2, 2), (10, 8), (16, 20), (18, 56)
The ordered pair of the two sequences are (6, 4), (8, 10), (9, 28)
Given data ,
The first sequence is add 10, then divide by 2 starting from 2
The second sequence is multiply by 3, then subtract 2 starting from 2
On simplifying , we get
Let the first number be 2
So , ( 2 + 10 )/2 = 6
Now , ( 2 x 3 ) - 2 = 4
And , the first ordered pair is ( 6 , 4 )
Now , ( 6 + 10 ) / 2 = 8
And , ( 4 x 3 ) - 2 = 10
So , the second ordered pair is ( 8 , 10 )
Now , ( 8 + 10 ) / 2 = 9
And , ( 10 x 3 ) - 2 = 28
So , the third ordered pair is ( 9 , 28 )
Hence , the sequence is solved and (6, 4), (8, 10), (9, 28)
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Intelligence Iq scores are often reported to be normally distributed with u=100.0 and o=15.0. A random sample of 47 people is taken. What is the probability of a random person on the street having an IQ score of less than 96?
2 questions please answer both parts
A)Find the perimeter of the plot land
B) Find the area of the plot land without the building and parking lot.
The perimeter of the plot land is 78.49 units and the area of the plot land without the building and parking lot is 210 square units
Finding the perimeter of the plot landFrom the graph, the vertices of the land are
A = (0, 20), B = (25, 19), C = (20, 2) and D = (5, 0)
Calculate the distance between adjacent vertices
So, we have
AB = √[(0 - 25)² + (20 - 19)²] = 25.02
BC = √[(20 - 25)² + (2 - 19)²] = 17.72
DC = √[(20 - 5)² + (2 - 0)²] = 15.13
AD = √[(0 - 5)² + (20 - 0)²] = 20.62
The perimeter of the plot land is
P = 25.02 + 17.72 + 15.13 + 20.62
P = 78.49 units
Finding the area of the plot landThis is calculated as
Area = Plot land - Building - Parking lot
Using the vertices, we have
Area = 1/2 * |0 * 19 + 25 * 2 + 20 * 0 + 5 * 20 - (20 * 25 + 19 * 20 + 2 * 5 + 0 * 0)| - [1/2 *(15 - 7 + 17 - 7) * (15 - 10)] - [(18 - 10) * (10 - 5)]
This gives
Area = 295 - 45 - 40
So, we have
Area = 210
Hence, the area is 210 square units
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X<= -5 or x >= 3 which answer represents the inequality in interval notation
The inequality x ≤ -5 or x ≥ 3 in interval notations is (-∞, -5] ∪ [3, ∞)
Inequality is the relationship between two expressions or values that are not equal to each other
The inequality x ≤ -5 or x ≥ 3 represents the solution set of all real numbers less than or equal to -5 or greater than or equal to 3.
The interval notation of the given inequality is (-∞, -5] ∪ [3, ∞)
The closed brace means the number is included and open bracket doesnot includes a number
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PLEASE ANSWER QUICKLY
What is the correct definition for sec 0? A. sec 0 = cos-1 0 B. sec 0 = sin-1 0 C. sec 0 = 1/sin 0 D. sec 0 = 1/cos 0 E. sec 0 = 1/tan 0
sec(theta) = 1/cos(theta)
I believe that is your option D
The volume of a triangular pyramid is 120 units cubed. If the base and height of the triangle that forms its base are 10 units and 6 units respectively, find the height of the pyramid.
The height of the pyramid is 12 units
To find the height of the pyramid, we need to use the formula for the volume of a pyramid,
V = (1/3) * B * h,
where V is the volume, B is the area of the base, and h is the height of the pyramid.
In this case, we know that the volume of the pyramid is 120 units cubed, and the base of the pyramid is a triangle with a base of 10 units and a height of 6 units.
Therefore, the area of the base is,
(1/2) * 10 * 6 = 30 square units.
Plugging these values into the formula for the volume of a pyramid, we get:
120 = (1/3) * 30 * h
Multiplying both sides by 3, we get:
360 = 30 * h
Dividing both sides by 30, we get:
h = 12
Therefore, the height of the pyramid is 12 units.
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g(n)=−50−15ng, left parenthesis, n, right parenthesis, equals, minus, 50, minus, 15, n
Complete the recursive formula of
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g(n)g, left parenthesis, n, right parenthesis.
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=
g(1)=g, left parenthesis, 1, right parenthesis, equals
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g(n)=g(n−1)+g, left parenthesis, n, right parenthesis, equals, g, left parenthesis, n, minus, 1, right parenthesis, plus
The recursive formula of g(n) g(1) = -50 and g(n) = g(n-1) - 15
g(n) = g(n-1) - 15
Start with the given formula: G(n) = -50 - 15n
To find the recursive formula, we need to find the value of g(n) in terms of g(n-1).
To do this, we can subtract 15 from both sides of the equation:
G(n) - 15 = -50 - 15n - 15
Simplifying the equation, we get:
G(n) - 15 = -65 - 15n
Rearranging the equation, we get:
G(n) = -65 - 15n + 15
Now, we can substitute g(n-1) for -65 - 15n:
G(n) = g(n-1) - 15
Finally, we can find the value of g(1) by substituting n = 1 into the original equation:
G(1) = -50 - 15(1)
G(1) = -50 - 15
G(1) = -65
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Complete question is also attached below:/
G(n)=−50−15n complete the recursive formula of g(n)
g(1)=
g(n)=g(n−1) +=
Monique and two friends want to zip line through the mountains in the national park. Each person must rent zip gear which includes a harness, gloves and a helmet. They must also pay one experienced trainer to zip with them. If the total bill is for $70.25, how many hours did they zip line for? About how much did each person pay?
To find out how many hours they zip lined for, we need to subtract the cost of the gear and trainer from the total bill and then divide the remaining amount by the hourly rate.
Cost of gear per person:
Shoes: $10
Helmet: $3
Gloves: $2.50
Harness: $5.00
Total gear cost per person: $10 + $3 + $2.50 + $5.00 = $20.50
Total cost of gear for 3 people: $20.50 x 3 = $61.50
Cost of trainer: $15.00
Total bill (including gear and trainer): $70.25
Remaining amount for zip lining:
= $70.25 - $61.50 - $15.00
= $-6.25
Since the remaining amount is negative, it seems there might be an error in the calculation or information provided. The total bill should not be lower than the cost of gear and trainer.
However, if we assume the total bill is correct and there was an error in the calculation, we can proceed with finding out how many hours they zip lined for and how much each person paid.
Approximate number of hours:
Number of hours = Remaining amount / Hourly rate = $6.25 / $4.75 ≈ 1.32 hours
Approximate amount each person paid:
Amount each person paid
= Total bill / 3
= $70.25 / 3
≈ $23.42
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Find the volume of the sphere show ur work it’s
Answer:
904.78 [tex]in^{3}[/tex]
Step-by-step explanation:
The volume formula for a sphere is the following:
[tex]v=\frac{4}{3} \pi r^{3}[/tex]
[tex]d = 2r[/tex]
Replace with values and the answer is 904.78
twice the sum of a number and 2 is equal to three times the difference of the number and 2
Answer:
10---------------
Let the number be n.
Set up an equation per the problem:
2(n + 2) = 3(n - 2)Distribute and solve for n:
2n + 4 = 3n - 63n - 2n = 4 + 6n = 10The number is 10.
Divide: 5m³n-25m²n²
5m²n
Om³n² - 5m²n³
Om-25m²n²
Om-20n
Om-5n
Answer:m-5n
Step-by-step explanation:
25° с Solve for c. 14 60° Length of c c = [?] C Round your final answer to the nearest tenth. Enter D O O
The measure of length c using the law of cosines is 11.79 units
Calculating the measure of length C using the law of cosinesfrom the question, we have the following parameters that can be used in our computation:
The triangle (see attachment)
The measure of length c is calculated using the following law of cosines
c² = a² + b² - 2ab * cos(C)
So, we have
c² = 10² + 3² - 2 * 10 * 3 * cos(120)
Evaluate
c² = 139
Take the square root of both sides
This gives
c = 11.79
Hence, the value of c is 11.79
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what is the mean of this data set 3,5,15
Answer:
7.6
Step-by-step explanation:
when trying to find the mean of a data set
you begin by finding the sum of all the numbers.
3+5+15=23. Then because there are only three
numbers in the data set you'll need to divide
23 by 3. 23 / 3 = 7.6.
you are given f(x) = x + 3 and g(x) = 2x + 1
find g[g(-3)
find f[g(x)]
find g[f(x)]
Answer:
Step-by-step explanation:
f(x) = x + 3
g(x) = 2x + 1
g(g(-3)) = g(-5) = -9
f(g(x) = f(2x + 1) = 2x + 1 + 3 = 2x + 4
g(f(x) = g(x + 3) = 2(x + 3) + 1 = 2x + 7
5.2 Given that cos 20° = p Without using a calculator, write EACH of the following in terms p: 5.2.1 5.2.2 5.2.3 cos 200° sin(-70°) sin 10°
The trigonometric ratio in terms p are
cos 200 = -p
- sin 70 = -p.
To express each of the given trigonometric values in terms of p:
Since the cosine of 0° is equal to 1, we can say that cos 0° = p.
cos 200°: Using the identity
cos(180° + θ) = -cos(θ), we can rewrite
cos 200° = -cos(180° + 20°).
Since cos 20° = p, we can express cos 200° as -p.
sin(-70°): Using the identity
sin(-θ) = -sin(θ), we can rewrite
sin(-70°) as -sin(70°)
=- sin (90- 20)
= - cos 20
= -p
sin 10°: Since sin 10° is not related to p, we cannot express sin 10° in terms of p.
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Help as soon as possible please!!
The coordinates of the triangle A'B'C' after rotating triangle ABC 90 degrees clockwise are A'(3, 6), B'(3, 2), and C'(7, 4).
To rotate the points of a triangle 90 degrees clockwise, we can use the following formula for a 2D rotation:
x' = x cos(θ) + y sin(θ)
y' = -x sin(θ) + y cos(θ)
Let's apply this formula to each point of the triangle ABC:
For point A(-6, 3):
x' = -6 cos(90°) + 3 sin(90°) = -6 (0) + 3(1) = 3
y' = -(-6) sin(90°) + 3 cos(90°) = 6 (1) + 3 (0) = 6
So, point A' is (3, 6).
For point B(-2, 3):
x' = -2 cos(90°) + 3 sin(90°) = -2 .0 + 3. 1 = 3
y' = -(-2) sin(90°) + 3 cos(90°) = 2 .1 + 3 .0 = 2
So, point B' is (3, 2).
For point C(-4, 7):
x' = -4 cos(90°) + 7 sin(90°) = -4 .0 + 7 . 1 = 7
y' = -(-4) sin(90°) + 7 cos(90°) = 4.1 + 7 .0 = 4
So, point C' is (7, 4).
Therefore, the coordinates of the triangle A'B'C' after rotating triangle ABC 90 degrees clockwise are A'(3, 6), B'(3, 2), and C'(7, 4).
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I WILL GIVE THE BRAINLIEST 69 POINTS
Step-by-step explanation:
the answer is 3
the answer is 3
Answer:
3
Step-by-step explanation:
explanation
f(x) =2x + 1 and g(x) = [tex]x^{2}[/tex]- 7
Thus, we have:
(g/f ) (x) = g(x) / f(x) = [tex]x^{2}[/tex]-7 ÷ 2x ÷ [tex]x^{2}[/tex] + 1
