The difference between the x's -2 and 1 = 3
The difference between the corresponding f(x) values is 3 -0 = 3
The average rate of change is f(x) / x = 3/3 = 1
Find the greatest common factor: 24y^8 + 6y^6
Find the Greatest Common Factor (GCF)
GCF = 6y^6
Factor out the GCF. (Write the GCF first. Then, in parenthesis divide each term by the GCF.)
6y^6(24y^8/6y^6 + 6y^6/6y^6)
Simplify each term in parenthesis
6y^6(4y^2 + 1)
Please answer this multiple choice question CORRECTLY for 30 points and brainliest!
Answer:
D
Step-by-step explanation:
because you need to times the indice 2 by the 3
You put $400 in a savings account. The account earns 2% simple interest per year. A. What is the interest earned after 6 years? The interest earned is $ after 6 years. B. What is the balance after 6 years? The balance is $ after 6 years.
Step-by-step explanation:
for the each year, the interest is increased by 2%,
so after 1 year, earned interest is 2% of $400
=2/100 × 400=$8
so the earned balance is $(400+8)=$408
so after 2 year, earned interest is 2% of $408
=2/100 × 408=$8.16
so the earned balance is $(408+8.16)=$416.16
after 3 year, earned interest is 2% of $416.16
=2/100 × 416.16=$8.32
so the earned balance is $(416.16+8.32)=$424.48
after 4 year, earned interest is 2% of $424.48
=2/100 × 424.48=$8.48
so the earned balance is $(424.48+8.48)=$480.48
after 5 year, earned interest is 2% of $480.48
=2/100 × 480.48=$9.6
so the earned balance is $(480.48+9.6)=$490.08
after 6 year, earned interest is 2% of $490.08
=2/100 × 490.08=$9.8
so the earned balance is $(490.08+9.8)=$499.88
therefore the interest earned after 6 years is
$(8+8.16+8.32+8.48+9.6+9.8)=$52.36
and the balance after 6 years is $499.88
Greatest to least
2 4/5 , 2 3/20 , 2 1/2 , 2 11/20 , 2 9/20
Answer:
2 (4/5) = 2.80
2 (11/20) = 2.55
2 (1/2) = 2.50
2 (9/20) = 2.45
2 (3/20) = 2.15
Step-by-step explanation:
Erin planted t tomato plants. Leo planted 5 fewer tomato plants than Erin. Filipe planted 10 fewer tomato plants than Erin. Drag and drop the expressions into the boxes to write an expression that represents the total number of tomato plants Erin, Leo, and Filipe planted in all.
Answer:
Total number of plants = 3t - 15 = 3(t-5) tomato plants
Explanation:
We are given that:
Erin planted t tomato plants
Leo planted 5 fewer tomato plants than Erin, this means that:
Leo planted = t - 5 tomato plants
Fillip planted 10 fewer tomato plants than Erin, this means that:
Fillip planted = t - 10 tomato plants
Now, we want to find the total number of tomato plants
This means that we will add the number of plants planted by Erin, Leo and Fillip
Therefore:
Total number of plants = t + t - 5 + t - 10
Total number of plants = 3t - 15 = 3(t-5) tomato plants
Hope this helps :)
Final answer:
The expression that represents the total number of tomato plants Erin, Leo, and Filipe planted is 3t - 15, where t is the number of plants Erin planted.
Explanation:
If Erin planted t tomato plants, then we can express the number of tomato plants Leo and Filipe planted using algebraic expressions that are based on this initial quantity. Leo planted 5 fewer tomato plants than Erin, so we can describe the number of plants Leo planted as t - 5. Similarly, Filipe planted 10 fewer tomato plants than Erin, and his number can be represented by t - 10.
To find the total number of tomato plants all three of them planted together, you would add these expressions:
Total number of plants = Erin's plants + Leo's plants + Filipe's plants
Total = t + (t - 5) + (t - 10)
Simplify the expression by combining like terms:
Total = t + t - 5 + t - 10
Total = 3t - 15
So the expression that represents the total number of tomato plants Erin, Leo, and Filipe planted in all is 3t - 15.
find the radius of a cylinder with a volume of 108ft and height of 12 ft
Answer:
1.69 ft (approx.)
Step-by-step explanation:
Formula for Volume of cylinder: pi x radius squared x height
Plug in 108 for volume, 3.14 for pi and 12 for height:
108 = 3.14 x r squared x 12
Multiply 3.14 and 12
108 = 37.68 x r squared
Divide both sides by 37.68
2.87 = r squared
"Unsquare" both sides (square root)
1.69 ft. = radius (approximate answer, rounded to nearest hundredth)
Answer:
1.69 ft
Step-by-step explanation:
V = πr²h formula of a cylinder.
Volume = 108 ft
Height = 12 ft
Radius = r
V = πr²h
108 ft = 22/7 × r² × 12 ft
π = 22/7 or 3.14
108 ft = 264/7r²
108 ft = 37.71r²
divide both sides by 37.71
108 ft/37.71 =r²
2.86 ft = r²
square root both side
√2.86 ft = √r²
the square cancels the square root
1.69 ft.
To check
V = πr²h
108 = 22/7 × (1.69)² 12
108 = 22/7 × 2.8561 × 12
108 = 107.61≈108
108 ft = 108 ft.
Pls help!!!
The tip of a probe has the shape of an inverted rectangular prism, as shown in the diagram.
How many cubic centimeters of titanium are needed to manufacture one tip?
Answer:
The area of the base B is equal to [tex]770\ cm^{2}[/tex]
The volume is equal to [tex]10,087\ cm^{3}[/tex]
Step-by-step explanation:
I will proceed to resolve the problem indicated in the attached figure.
The figure shown a inverted rectangular pyramid
The base is a rectangle
The area of the base B is equal to
[tex]B=(35)(22)=770\ cm^{2}[/tex]
To find how many cubic centimeters of titanium are needed to manufacture one tip, calculate the volume of the figure
Find the volume of the inverted rectangular pyramid
The volume of the pyramid is equal to
[tex]V=\frac{1}{3}BH[/tex]
we have
[tex]B=770\ cm^{2}[/tex]
[tex]H=39.3\ cm[/tex]
substitute
[tex]V=\frac{1}{3}(770)(39.3)=10,087\ cm^{3}[/tex]
Please help me find the slope of the line graphed below!
Answer:
slope = - 3
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (0, - 3) ← 2 points on the line
m = [tex]\frac{-3-0}{0+1}[/tex] = [tex]\frac{-3}{1}[/tex] = - 3
Here it is described. Its really easy.
Gustave measured his pace and determined that for him, sss steps make up one mile. One day Gustave walked 630063006300 steps, which was 333 miles. Write an equation to describe this situation. How many steps are in one mile for Gustave?
Answer: Equation to describe this situation.
[tex]3s=6300[/tex]
Number of steps in one mile for Gustave =2100
Step-by-step explanation:
Given : Gustave measured his pace and determined that for him, s steps make up one mile.
1 mile = s steps (1)
One day Gustave walked 6300 steps, which was 3 miles.
i.e. 3 miles = 6300 steps (2)
Using (2), the number f steps in 3 steps will be :_
3 miles = 3s steps (3)
From (2) and (3), we have
[tex]3s=6300[/tex]
Dividing both sides by 3 , we get
[tex]s=\dfrac{6300}{3}=2100[/tex]
Hence, the number of steps in one mile for Gustave =2100
Gustave takes 189 steps to walk one mile. We derived this by dividing the total steps, 63,000, by the distance in miles, 333. The equation used was 63000 = s * 333.
To determine how many steps are in one mile for Gustave, we start with the information provided:
Gustave took 63,000 steps, which equals 333 miles.Step 1: Write the Equation
We can write the equation as:
63000 = s * 333
Step 2: Solve for s
To find out how many steps make up one mile, we solve for s by dividing both sides of the equation by 333:
s = 63000 / 333
Step 3: Calculate the Value
When we divide 63,000 by 333, we get:
s = 189
This means that Gustave takes 189 steps to walk one mile.
Example Calculation
Since 63,000 steps equal 333 miles, and dividing both 63,000 steps by 333 miles gives us the number of steps per mile:
189 steps per mile.
In conclusion, Gustave takes 189 steps to walk one mile. This equation and process help us determine the number of steps per mile based on the given total steps and distance covered.
Solve the equation 2x^2+8x-1=0 by completing the square. Give you answers correct to 2 decimal places.
The given quadratic equation 2x² + 8x - 1 = 0 can be rearranged as (x + 2)² = 4.5 through the method of completing the square. Taking the square root of both sides gives two solutions for x: x = -2 + √4.5 and x = -2 - √4.5, when rounded to two decimal places.
Explanation:To solve the equation 2x² + 8x - 1 = 0 by "completing the square", we first divide everything by the coefficient of x², in this case 2, to make the equation look like x² + 4x - 0.5 = 0. The coefficient of x now becomes 4.
We then take half of this coefficient, square it and add it to both sides of the equation. Half of 4 is 2, and squaring it gives us 4. So the equation now reads as x² + 4x + 4 = 4 + 0.5 which simplifies to x² + 4x + 4 = 4.5.
This equation can be further simplified by realizing that (x + 2)² = x² + 4x + 4, thus we have (x + 2)² = 4.5. Taking the square root of both sides finally gives us x = -2 ± √4.5, giving us two solutions for x to two decimal places, that are x = -2 + √4.5, and x = -2 - √4.5.
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To solve the equation by completing the square, divide by the leading coefficient, move the constant term to the other side, complete the square, take the square root of both sides, and then solve for x, yielding two solutions: approximately -0.12 and -3.88.
Explanation:To solve the equation 2x²+8x-1=0 by completing the square, follow these steps:
Divide the entire equation by 2 to simplify the coefficient in front of x^2, resulting in x²+4x-0.5=0.Move the constant term to the other side: x²+4x=0.5.To complete the square, add the square of half the coefficient of x to both sides. This number is (4/2)² = 4, so add 4 to both sides giving x²+4x+4=4.5.The left-hand side is now a perfect square: (x+2)²=4.5.Take the square root of both sides: x+2=±√4.5.Subtract 2 from both sides to solve for x: x= -2 ± √4.5.Computing the square root of 4.5 and subtracting 2 gives two solutions, accurate to two decimal places: x≈-0.12 and x≈-3.88.Learn more about Completing the Square here:
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Warren measured a rectangular window to find out how much plastic he would need to cover it. The window measured 5 ft 6 inches by 2 ft 9 inches. About how many square inches of plastic does Warren need to cover the window?
5 feet 6 inches is equal to ((5*12)+6) inches, which is equal to 66 inches since 5*12=60 and 60+6=66
2 feet 9 inches is equal to ((2*12)+9) inches, which is equal to 33 inches since 2*12=24 and 24+9=33
Since 66 and 33 are the length and width (there isn't any specific order as to which measurement is the length or width) and the question is asking for square inches,(which is the area) so what needs to be done next is 66*33, which equals 2178, the square inches of plastic needed is 2718 square inches.
I couldn't keep the answer in the format of _ft _in because they are asking for the area in inches, and I don't think it would be smart to convert inches to decimal values of feet for reasons I won't talk about.
So yeah, your answer is 2178 square inches of plastic.
Divide the following polynomial and then place the answer in the proper location on the grid. Write your answer in order of descending powers of y. (y^3 - y^2 + y + 3) ÷ (y + 1)
PLEASE HELPPPPPPPPP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
PRETTY PLEASE WITH ICING AND CHERRIES ON TOP
given,
[tex] \frac{ {y}^{3} - {y}^{2} + y + 3}{y + 1} \\ = \frac{ {y}^{3} + {y}^{2} - 2 {y}^{2} - 2y + 3y + 3}{x + 1} \\ = \frac{{y}^{2} (y + 1) - 2y(y + 1) + 3(y + 1)}{(y + 1)} \\ = \frac{(y + 1)( {y}^{2} - 2y + 3) }{(y + 1)} \\ = {y}^{2} - 2y + 3[/tex]
Final answer:
The polynomial y^3 - y^2 + y + 3 divided by y + 1 results in a quotient of y^2 - y + 2, with a remainder of 1. The complete division statement is (y^3 - y^2 + y + 3) / (y + 1) = y^2 - y + 2 + 1/(y + 1).
Explanation:
To divide the polynomial y^3 - y^2 + y + 3 by y + 1, we use polynomial long division. First, divide y^3 by y to get y^2, subtract the result from the polynomial, and bring down the next term. Repeating this process gives us the following steps:
Divide y^3 by y to get y^2. Multiply y + 1 by y^2 and subtract from the original polynomial.
Bring down the next term, which is y, and divide -1 by y to get -1. Multiply y + 1 by -1 and subtract from the result of the first step.
Bring down the last term, which is 3, and divide 2 by y to get 2. Multiply y + 1 by 2 and subtract to get the remainder.
The final quotient of this division is y^2 - y + 2, and the remainder is 1.
The result of the division is y^2 - y + 2 with a remainder of 1. To express this as a complete division statement, we write:
(y^3 - y^2 + y + 3) ÷ (y + 1) = y^2 - y + 2 + 1/(y + 1)
Please please help me out
Answer:
A trinomial of degree 5
Step-by-step explanation:
A monomial has only 1 term
A binomial has 2 terms
A trinomial has 3 terms
4[tex]x^{5}[/tex] + 3x³ - 7x ← has 3 terms and is therefore a trinomial
The degree of a polynomial is determined by the largest exponent of the variable in the expression
4[tex]x^{5}[/tex] is the term with the largest exponent in the expression
Hence a polynomial of degree 5
Describe the relationship between the two acute angels in a right triangle
Answer:
they are complementary
Step-by-step explanation:
The sum of angles in a triangle is 180°. When one of those angles is a right angle (90°), the sum of the other two must be 90°. When the sum of two angles is 90°, they are said to be complementary angles.
Which function rule matches the graph below?
In the map below, the path from the zebras to the monkeys is parallel to the path from the tigers to the elephants.
What is the distance between the lions and the monkeys?
a.40 feet
b.88 feet
c.92 feet
d.198 feet
Answer:
Step-by-step explanation:
88
The distance between the lions and the monkeys is 88 feet
To determine the distance between the lions and the monkeys, we make use of the following equivalent ratio
x : 132 = 80 : 120
Express as fraction
[tex]\frac{x}{132} = \frac{80}{120}[/tex]
Solve for x
[tex]x = \frac{80}{120} * 132[/tex]
Multiply
[tex]x = 88[/tex]
Hence, the distance between the lions and the monkeys is 88 feet
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What is the exact value of sin 30 degrees?
Answer:
1/2
Step-by-step explanation:
Final answer:
The exact value of sin 30 degrees is 0.5, and this is derived from the special 30-60-90 triangle.
Explanation:
The value of sin 30 degrees is 0.5.
This can be determined using the unit circle or by using the trigonometric function of 30 degrees.
When we evaluate sin 30 degrees, we can look at the special right triangle with angles 30-60-90 where the ratio of the opposite to the hypotenuse in a 30-degree angle is 1/2. In this triangle, the side opposite to the 30-degree angle is half the length of the hypotenuse. Therefore, sin 30 degrees is equal to 1/2 or 0.5.
A Web music store offers two versions of a popular song. The size of the standard version is 2.5 megabytes (MB). The size of the high-quality version is 4.4 MB. Yesterday, the high-quality version was downloaded four times as often as the standard version. The total size downloaded for the two versions was 5427 MB. How many downloads of the standard version were there?
Answer:
270 downloads
Step-by-step explanation:
Call x the number of times the standard quality version was downloaded and call y the number of times the high quality version was downloaded.
So, we know that
[tex]2.5x + 4.4y = 5427[/tex] MB (1)
We also know that the high-quality version was downloaded four times as often as the standard version.
So
[tex]y = 4x[/tex] (2)
We substitute equation (2) in equation (1) and solve for x.
[tex]2.5x + 4.4 (4x) = 5427\\\\2.5x +17.6x = 5427\\\\20.1x=5427\\[/tex]
[tex]x = 270\ downloads[/tex]
Suppose that a restaurant chain claims that its bottles of ketchup contain 24 ounces of ketchup on average, with a standard deviation of 0.4 ounces. If you took a sample of 49 bottles of ketchup, what would be the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample?
A. 24+-0.029
B. 24+-0.057
C. 24+-0.229
D. 24+-0.114
Answer:
D. 24+-0.114
Step-by-step explanation:
The question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle given the following statistics;
Sample mean = 24
standard deviation, σ = 0.4
Sample size , n = 49
The confidence interval for a population mean is calculated using the formula;
Sample mean ± z-score*(σ/sqrt(n))
The z-score associated with a 95% confidence interval, from the standard normal tables, is;
1.96
Substituting these values into the formula;
24 ± 1.96*[tex]\frac{0.4}{\sqrt{49} }[/tex]
= 24 ± 0.112
From the choices given, choice D is closest to the above expression;
Please please help me out
Area = base * height
Area = 15 * 8 = 120 square centimeters
4. A discus is thrown from a height of 4 feet with an initial velocity of 65 ft/s at an angle of 44° with the horizontal. How long will it take for the discus to reach the ground?
I believe the time would be about 4 seconds
Answer:
9.29 seconds
Step-by-step explanation:
Attached is my work because it's difficult to type
Attached is an image of where I got my equations from
the answer may be wrong
What is the volume of the prism given below? The height is 3 and the bases are 8 and 12.
Answer:
Your answer would be 288
Step-by-step explanation:
You start off with the equation ( V= Bh )
Where "B" represents the area of the base ( which case you multiply 8 and 12 and thus getting 96 as your answer for finding "B")
and Lastly you multiply your "B" with the "h" ( which represents the height) and therefore you multiply 96 and 3
which equals to 288
( hope this helps )
Answer: 144
Step-by-step explanation:
which of the following can be determined from the table above?
A. events D and A are independent
B. events D and B are independent
C. events A and B are independent
D. events E and B are independent
Answer:
D. Events E and B are independent.
Step-by-step explanation:
It can be determined that Events E and B are independent. The correct answer is: D.
To determine independence between events, we can use the formula:
[tex]\[ P(A \cap B) = P(A) \times P(B) \][/tex]
Let's check for events D and A:
[tex]\[ P(D \cap A) = 0.2 \][/tex]
[tex]\[ P(D) \times P(A) = 0.5 \times 0.2 = 0.1 \][/tex]
Since [tex]\(0.2 \neq 0.1\),[/tex] events D and A are not independent.
Checking for events D and B:
[tex]\[ P(D \cap B) = 0.3 \][/tex]
[tex]\[ P(D) \times P(B) = 0.5 \times 0.3 = 0.15 \][/tex]
Since [tex]\(0.3 = 0.15\)[/tex], events D and B are independent.
Similarly, events A and B:
[tex]\[ P(A \cap B) = 0.15 \][/tex]
[tex]\[ P(A) \times P(B) = 0.2 \times 0.5 = 0.1 \][/tex]
Since [tex]\(0.15 \neq 0.1\)[/tex],events A and B are not independent.
For events E and B:
[tex]\[ P(E \cap B) = 0.15 \][/tex]
[tex]\[ P(E) \times P(B) = 0.3 \times 0.5 = 0.15 \][/tex]
Since [tex]\(0.15 = 0.15\)[/tex], events E and B are independent.
Therefore, the correct answer is: D. Events E and B are independent.
The histogram below shows the number of properties in a town that sold within certain time periods.
Why might the graph be considered misleading?
The scales on the x- and y-axes are unequal.
The interval on the x-axis is too large for the data set.
The scale on the y-axis misrepresents the difference in the heights of the bars.
The interval on the y-axis is too large for the data set.
Answer:
Option c) The scale on the y-axis misrepresents the difference in the heights of the bars.
Step-by-step explanation:
Given is a histogram that shows the number of properties in a town that are sold within certain periods.
On x axis is given number of days to sell and on y axis the number of properties
X axis is given in interval form with interval width 30 and on y axis scales are marked as 0,1,2....12,13 etc
The mistake is on y axis after 0, 10 is marked with unit distance from 0 but from 10 to 11 also distance is shown as 1 unit.
Hence correct option is
Option c) The scale on the y-axis misrepresents the difference in the heights of the bars.
Answer:
C
Step-by-step explanation:
E2020
What is the cosine ratio for angle F?
Answer:
option D
Step-by-step explanation:
Given in the question, a right angle triangle FGH.
Base of triangle = 12
Height of triangle = 5
Hypotenuse of triangle = 13
To solve the question we will use trigonometry identity.
cos(F) = adj / hypocos(F) = height / hypo
cos(F) = 5 / 13
So the cosine ration for angle F is 5 / 13
4−(−5∗9−1)÷2+(5)2−7
Answer:
Your answer will be 30
Step-by-step explanation:
An object is launched into the air. The projectile motion of the object can be modeled using the function h(t) = –16t2 + 72t + 5, where t is the time in seconds since the launch and h(t) represents the height in feet of the object after t seconds. What is true about the projectile motion of this object?
Answer:
Step-by-step explanation:
Height is 5 feet
A bag has 3 red marbles, 2 blue and 4 yellow. What is the theoretical probability of pulling a red?
Answer:1/3
Step-by-step explanation:
3 (amount of reds)
------------------------
3+2+4 (sum of all marbles red+Blue+Yellow)
simplfy
3 /3
---- =1/3
9 /3
To find out the theoretical probability of drawing a red marble, divide the total number of red marbles (3) by the total number of marbles (9). Therefore, the theoretical probability is 1/3.
Explanation:
The subject of your question falls under the branch of Mathematics and it's about a concept known as theoretical probability. In this case, the total number of marbles in the bag is 3 red + 2 blue + 4 yellow = 9 marbles. The probability of drawing a red marble from the bag is calculated by dividing the number of red marbles by the total number of marbles. Therefore, the theoretical probability of pulling a red marble is 3/9 which simplifies to 1/3, meaning there is a one in three chance of drawing a red marble.
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Which three-dimensional figure is formed by the rotation given?
PLeaseee help 12p!!
Shown below
Step-by-step explanation:What if you rotate a plane figure around a straight line called the axis? Well, in doing so, you will get what in mathematics is called a solid of revolution, which is a solid figure. In this case, we have a triangle with a side matching the axis and this side. The solid that result when rotating that triangle is a cone. The side that matches the axis is the height of the cone while the side perpendicular to the axis is the radius of the base of the cone. The rotation is performed by the hypotenuse of the triangle (a straight line) through the origin and by an angle of 360 degrees.
Please help me out please
Answer:
31
Step-by-step explanation:
For rectangle ABCD, AC and BD are the lengths of the diagonals. The diagonals of a rectangle are congruent.
AC = BD
3x + 7 = 131 - x
Add x to both sides.
4x + 7 = 131
Subtract 7 from both sides.
4x = 124
Divide both sides by 4.
x = 31