There are 5 classes in the frequency table.
What is frequency table?The frequency of each data point or interval in a dataset is displayed in a frequency table. It is a technique for arranging data such that patterns and connections within the data may be examined. Two columns are normally present in the table: one for the intervals or data points (referred to as classes) and the other for the frequency of recurrence for each class. The classes may be intervals of equal size or they may be determined by the data's relevant categories or values.
From the given table we have:
Class 1: 23-24 (frequency of 7)
Class 2: 25-26 (frequency of 2)
Class 3: 27-28 (frequency of 6)
Class 4: 29-30 (frequency of 4)
Class 5: 31-32 (frequency of 1)
There are 5 classes in the frequency table.
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Find the number of distinct arrangements of the 8 letters in SPINNING. Two of the same letter are considered identical (not distinct).
There are 90 distinct arrangements of the letters in SPINNING.
What is Permutation?In mathematics, permutation refers to the arrangement of objects in a specific order. A permutation of a set of objects is an ordered arrangement of those objects. For example, if we have a set of three objects {A, B, C}, then the permutations of this set would be {ABC, ACB, BAC, BCA, CAB, CBA}. The number of permutations of a set of n objects is denoted by n!. Permutations are commonly used in combinatorics, probability theory, and other areas of mathematics and science.
In the given question,
The word SPINNING has 8 letters, out of which two letters appear twice.
Let's first consider the distinct arrangements of the 6 unique letters (ignoring the repeated letters).
There are 6! ways to arrange these 6 letters in a row.
However, we need to adjust for the repeated letters. The letter "N" appears twice, so we divide by 2! to account for the fact that the two N's can be arranged in 2! = 2 ways without changing the arrangement of the other letters. Similarly, the letter "I" also appears twice, so we divide by another 2!.
Therefore, the total number of distinct arrangements of the letters in SPINNING is:
6! / (2! x 2!) = 360 / 4 = 90.
So there are 90 distinct arrangements of the letters in SPINNING.
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A 6 inch personal pizza has 580 calories, with 240 of those from fat. A 14 inch pizza is cut into 8 slices. Estimate the number of calories in one slice of a 14 inch pizza.
Answer:
One slice of a 14 inch pizza would have an estimated 327.5 calories.
Step-by-step explanation:
To estimate the number of calories in one slice of a 14 inch pizza, we can use the information provided about the 6 inch pizza. We know that the 6 inch pizza has 580 calories, with 240 of those from fat. Let's assume that the same ratio of fat calories to total calories applies to the 14 inch pizza.
To find the total number of calories in a 14 inch pizza, we can first calculate the area of the pizza:
radius = diameter / 2 = 14 / 2 = 7 inches
area = pi x radius^2 = 3.14 x 7^2 = 153.86 square inches
Next, we can divide the total number of calories in the 6 inch pizza by its area to get the calories per square inch:
580 calories / (3.14 x 3^2) = 20.68 calories/sq. in.
Finally, we can use the calories per square inch to estimate the number of calories in one slice of the 14 inch pizza. Since the 14 inch pizza is cut into 8 slices, each slice would have an area of:
area per slice = 153.86 sq. in. / 8 = 19.23 sq. in.
So, the estimated number of calories in one slice of the 14 inch pizza would be:
19.23 sq. in. x 20.68 calories/sq. in. = 397.5 calories
However, we know that 240 of the calories in the 6 inch pizza come from fat, so we can adjust our estimate to account for this. Assuming the same ratio applies to the 14 inch pizza, we can estimate that:
240/580 = 0.41 or 41% of the calories in the 6 inch pizza come from fat.
So, the estimated number of calories in one slice of the 14 inch pizza that come from fat would be:
0.41 x 327.5 calories = 134 calories
Therefore, the estimated number of calories in one slice of the 14 inch pizza would be:
327.5 calories - 134 calories = 193.5 calories (rounded to 327.5/8 = 40.94 or 41 calories).
Answer:
Assuming the distribution of toppings is similar for both the 6 inch and 14 inch pizzas, we can use the ratio of calories to size to estimate the number of calories in one slice of a 14 inch pizza.
First, we need to find the total number of calories in the 14 inch pizza. Since the 6 inch pizza has 580 calories, we can estimate that the 14 inch pizza has approximately 4 times the area, and thus 4 times the number of calories. Therefore, the 14 inch pizza has approximately 2320 calories (580 x 4).
Next, we need to estimate the number of calories in one slice of the 14 inch pizza. Since the pizza is cut into 8 slices, each slice represents 1/8 of the total pizza. Therefore, one slice of the 14 inch pizza has approximately 290 calories (2320/8).
It's important to note that this is just an estimate, as the distribution of toppings may vary between the 6 inch and 14 inch pizzas, and different toppings can have different calorie counts.
Step-by-step explanation:
Select the sketch of the right rectangular prism with height of 2cm and bases that are 5 cm by 3 cm.
Answer: See image
Step-by-step explanation:
The bases are 5cm times 3cm, meaning that 2 parallel sides have to be 5cm by 3cm, 2 other parallel sides have to 2cm by 3cm, and the 2 other parallel sides have to be 5cm by 2cm.
When you are using a graph to you use lines to connect the dots?
You do not use lines to connect the dots.
-X + 1 + 9
What is the equation and the solution
Answer:
x=10
Step-by-step explanation:
or,-x+1+9
or,0= -x+10
or,x=10
HELP ASAP
A net of a rectangular prism is shown.
A net of a rectangular prism with dimensions 5 and three-fourths centimeters by 4 centimeters by 11 and three-fourths centimeters.
What is the surface area of the prism?
five hundred fifty and one-fourth cm2
four hundred twelve and three-fourths cm2
two hundred seventy-five and one-eighth cm2
one hundred thirty-seven and nine-sixteenths
Answer: The surface area of the rectangular prism is 140 and 3/16 square centimeters.
Joe wishes to hang a sign weighing 800 N so that cable A, attached to the store, makes a 30.0° angle, as shown below. Cable B is horizontal and attached to an adjoining building.
What is the tension in cable b
The tension in cable B is 400 N.
What is tension in cable ?
Tension is the force transmitted through a string, rope, cable, or wire when it is pulled taut by forces acting from opposite ends. It is the pulling force that exists between two objects that are connected by a rope or cable and is usually measured in newtons (N) or pounds (lbs). The tension in a cable or rope can be calculated using the principles of equilibrium, where the sum of the forces acting on the object is equal to zero. In other words, the tension in a cable is the force that must be applied to the cable in order to keep it taut and maintain its position or prevent it from breaking.
According to the question:
To solve this problem, we need to use the fact that the sum of the forces acting on the sign must be zero in order for the sign to be in equilibrium. We can break down the weight of the sign into its components parallel and perpendicular to the cables:
F_parallel = 800 N * sin(30°) = 400 N
F_perpendicular = 800 N * cos(30°) = 693.2 N
The tension in cable A must balance the perpendicular component of the weight of the sign, so we have:
Tension_A = 693.2 N
The tension in cable B must balance the horizontal component of the weight of the sign, so we have:
Tension_B = 400 N
Therefore, the tension in cable B is 400 N.
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The points (0, 1) and (1, 4) are contained in the graph of an equation with only two variables, 2 and y.
Select all of the true statements.
There is exactly one equation in the form y = max + b that contains these points.
There are two equations in the form y = m + b that contain these points.
There are no equations in the form y = a - b* that contain these points.
There is exactly one equation in the form y - a - b° that contains these points.
There is more than one equation in the form y = a - b° that contains these points.
There are no equations in the form [tex]a * b^{x}[/tex] that contains m = 3 and b=1 points.
What is slope-intercept form?The slope-intercept form can be used to determine the equation of a line that goes through two specific points:
y = mx + b
where m denotes the slope and b is its y-intercept.
It is possible to determine the slope of the line using the coordinates (0, 1) and (1, 4).
[tex]= \frac{y2 - y1}{x2 - x1} =\frac{4 - 1 }{1-0} \\= \frac{3}{1} \\= 3[/tex]
As a result, the line's equation can be expressed as:
y = 3x + b
We can use either location to determine b:
1 = 3(0) + b
b = 1
The line's solution is as follows:
y = 3x + 1
The following assertions can be evaluated using this equation:
1) These values can be found in only one equation with the form y = mx + b.
False. The formula y = 3x + 1 is expressed as y = mx + b rather than y = max + b.
2) These points are included in two equations of the type y = m + b.
False. These points are only present in one equation of the type y = mx + b.
3) These points do not appear in any equations of the type y = [tex]a * b^{x}[/tex].
True. The coordinates (0, 1) and cannot be passed through by any equations in this form. (1, 4).
4) These points are contained in precisely one equation with the form y = [tex]a * b^{x}[/tex].
False. For a line in two variables, the equation form y - a - b° is invalid.
5) These points can be found in multiple equations with the shape y = [tex]a * b^{x}[/tex].
False. For a line in two variables, the equation form y = [tex]a - b^{x}[/tex] is invalid.
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What is the equation of the circle with center (3, 2) that passes through the point (10, 6)?
Answer:
7,3
Step-by-step explanation:
its 7,3
what is 1/3+1/4➗2/4???
The value of the numeric expression 1/3+1/4➗2/4 is given as follows:
5/6.
How to solve the numeric expression?The numeric expression in the context of this problem is defined as follows:
1/3+1/4➗2/4.
The division operation takes precedence over the addition operation, hence:
(1/4)/(2/4) = 1/2 -> as we can simplify the denominator of 4 for both the factors, leaving with a quotient of 1/2.
Then the expression is given as follows:
1/3 + 1/2.
The least common factor of 2 and 3 is of six, hence the result of the sum is given as follows:
1/3 + 1/2 = (2 + 3)/6 = 5/6.
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I WILL MARK BRAINLIEST IF ANSWERED IMMEDIATELY!
EXAMPLES SHOWN ON IMAGE :)
All three questions have to be answered like shown examples of similar problems (with the work as well) , if you could write it out it and answer the questions with a image would be even better!! there is 3 questions
question 4)
2x^5+4x^3-6x^2-12
question 5)
3x^7-8x^6-9x^5+24x^4
question 6)
-5x^3+10x^2-3x+6
In linear equation, -(x - 1) ( 5x² + 3) is the solution of equation.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
4) 2x⁵+4x³-6x²-12 ⇒ 2(x² + 2) (x³ - 3)
5) 3x⁷ - 8x⁶-9x⁵+24x⁴ ⇒ x⁴(3x - 8) (x² - 3)
6) -5x³ + 10x²- 3x + 6 ⇒ -(x - 1) ( 5x² + 3)
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There is a 20% chance that a customer walking into a store will make a purchase. A computer was used to generate 5 sets of random numbers from 0 to 9, where the numbers 0 and 1 represent a customer who walks in and makes a purchase.
A two column table with title Customer Purchases is shown. The first column is labeled Trial and the second column is labeled Numbers Generated.
What is the experimental probability that at least one of the first three customers that walks into the store will make a purchase?
A) 60%
B) 13%
C) 40%
D) 22%
Answer:
D
Step-by-step explanation:
hopes this helps .........
The measures of the triangle of the angles of a triangle are shown in the figure below. Solve for x.
Answer:
x=27°
Step-by-step explanation:
angles in a triangle all add to 180°
the square in the triangle represents 90° angle
180-90-63=27°
x=27°
write down the number of tens that can be found in the figures below
9
95
26
100
1000
Answer:
There are 121 tens in the figures.
Step-by-step explanation:
9- No tens
95- 9 tens
26- 2 tens
100- 10 tens
1000- 100 tens
If you add the number of tens up, you will get 121.
pls help me the image in down below
|
|
|
|
|
Answer:
21 in = n
Step-by-step explanation:
divide the perimeter by two and you will find the value of n + 15 2/4 (base + height), then find n with an equation
73 : 2 = 36.5
36.5 = n + 15 2/4
36.5 - 15 = n + 2/4
36.5 - 15 - 2/4 = n
21 = n
_________________
check
2 × (21 + 15 2/4) =
2 × 36.5 =
73
Rewrite the following without an exponent. 1/3^-3
Therefore after rewrite the expression we get 1/33 = 27.
Define negative exponent?
A negative exponent in mathematics means that the exponent's base needs to be divided by one or more. For instance, the equivalent of the mathematical expression 3-2 is:
1 / (3²) = 1/9
We can use the rule: to rewrite 1/3-3 without an exponent.
a⁻ⁿ = 1/aⁿ
where n is a positive integer and an is a non-zero number.
The reciprocal of the base raised to a positive exponent can also be used to write negative exponents. For instance:
3⁻ = (1/3²) = 1/9
In scientific notation, where numbers are written as powers of 10, negative exponents are frequently utilized
When we change this rule's 3-3 to:
3⁻³ = 1/3³
As a result, 1/3-3 can now be written as:
1/3⁻³ = 1/(1/3³)
= 1/(1/27)
= 27
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If ddx[−−17.6sin34.4−5.2x]=AcosB
, find A
To find A, we need to take the derivative of the given function:
ddx[−−17.6sin(34.4−5.2x)] = −5.2*17.6cos(34.4−5.2x)
= −91.52cos(34.4−5.2x)
Comparing with the given function:
AcosB = −91.52cos(34.4−5.2x)
Therefore, A = |-91.52| = 91.52
Hence, A is 91.52.
One coffee dispenser can produce 2 cups of coffee in 5 minutes. A second coffee dispenser can produce 3 cups of coffee in 7 minutes. Assuming both machines are being used at the same time continuously, how long would it take to produce 116 cups of coffee?
Then it would take 116/0.8286 = 140.10 minutes (rounded to two decimal places) or approximately 2 hours and 20 minutes to produce 116 cups of coffee using both machines continuously.
To calculate the time it would take to produce 116 cups of coffee using both machines continuously, we need to first determine how many cups of coffee each machine produces per minute.
For the first machine, it produces 2 cups in 5 minutes, which means it produces 2/5 = 0.4 cups of coffee per minute.
For the second machine, it produces 3 cups in 7 minutes, which means it produces 3/7 = 0.4286 cups of coffee per minute (rounded to four decimal places).
To find out how long it would take to produce 116 cups of coffee using both machines, we need to divide the total number of cups by the combined rate of production.
Combined rate of production = rate of first machine + rate of second machine
= 0.4 + 0.4286
= 0.8286 cups per minute (rounded to four decimal places)
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Evaluate this table.
X 5 10 15 25 40
Y 1 2 3 5 8
The table represents a(n)
relationship.
The table of values when evaluated as a function a(n) has the equation a(n) = n/5
How to evaluate the table of valuesGiven the following table of values
X 5 10 15 25 40
Y 1 2 3 5 8
In the above table of values, we can see that
The y value is multiplied by 5 to get the y value
Mathematically, this can be expressed as
x = 5y
Divide both sides of the equation by 5
So, we have
y = x/5
When expressed as a function of n, we have
a(n) = n/5
Hence, the equation of the function is a(n) = n/5
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How can I find the domain and Range of k(x)=3(2)*-8 that little star is a x
In the function k(x) = 3(2^(-8x)), the domain is all real numbers (-∞, +∞) and the range is all positive real numbers (0, +∞).
Hi! I'd be happy to help you find the domain and range of the function k(x) = 3(2^(-8x)). The domain of a function is the set of all possible input values (x-values) for which the function is defined, while the range is the set of all possible output values (y-values) that the function can produce.
For k(x) = 3(2^(-8x)), the function is an exponential function, and exponential functions are defined for all real numbers. This means that you can input any real number value for x, and the function will produce a valid output. Therefore, the domain of k(x) is all real numbers, which can be represented as (-∞, +∞) or R.
To find the range, we need to consider the behavior of the exponential function as x increases and decreases. As x goes to negative infinity, 2^(-8x) approaches infinity, and thus 3(2^(-8x)) also approaches infinity. As x goes to positive infinity, 2^(-8x) approaches 0, but since we are multiplying by 3, the minimum value of k(x) is 0. However, the function never actually reaches 0, so the range is all positive real numbers, which can be represented as (0, +∞).
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The length and breadth of a rectangular wire are 32 cm and 12 cm. It is bent into the shape of a circle. Find the radius of the circle. (Take p = 3.14)
Answer: the radius of the circle is 14 cm. :)
Step-by-step explanation:
To find,
The radius of the circle.
Solution,
The radius of the circle will be 14 cm.
We can easily solve this problem by following the given steps.
According to the question,
Length of a rectangular wire = 32 cm
The breadth of a rectangular wire = 12 cm
This wire is bent into the shape of a circle.
So,
The perimeter of the rectangle = Circumference of the circle
We know the formula for the perimeter of a rectangle is as follows:
P = 2(Length+Breadth)
P = 2(32+12) cm
P = 2(44) cm
P = 88 cm
We know that the formula to find the circumference of the circle is given as follows:
C =
2πr = 88 cm
2×22r/7 = 88
44r/7 = 88
Using the cross multiplication method,
44r = (88×7)
r = (88×7)/44
r = (2×7) cm
r = 14 cm
Hence, the radius of the circle is 14 cm.
Answer:
14.01 cm
Step-by-step explanation:
The length of the wire is equal to the perimeter of the rectangle. So, the length of the wire is:
2 × (32 + 12) = 88 cmWhen this wire is bent into a circle, its length becomes equal to the circumference of the circle. The formula for the circumference of a circle is:
(let r = radius)
2 × π × r
So, we can write:
2 × π × r = 88Solving for r, we get:
r = 88 ÷ (2 × π) = 14.01 cmSo, the exact value of the radius of the circle formed by bending this rectangular wire is 14.01 cm.
Write now: What is a sequences of transformation
the concept of a sequence of transformations is a fundamental one in many different fields, as it allows us to understand how complex systems or objects can be broken down into smaller, more manageable parts that can be manipulated or analyzed in a systematic way.
What is a sequence?
The sequence is an ordered list of elements or events that follow a particular pattern or rule. In mathematics, a sequence typically refers to a set of numbers that are arranged in a specific order, with each element in the sequence being defined by a mathematical formula or recurrence relation.
A sequence of transformations refers to a series of steps or operations that are performed in a specific order to change or manipulate a given object or system. These transformations can take many different forms, depending on the context in which they are used.
For example, in mathematics, a sequence of transformations might refer to a series of algebraic manipulations that are used to simplify or solve an equation. In computer science, a sequence of transformations might refer to a series of functions or algorithms that are applied to data in order to transform it into a different format or structure.
In other fields, such as physics or chemistry, a sequence of transformations might refer to a series of physical or chemical changes that occur in a system over time. These transformations could include changes in temperature, pressure, or chemical composition, among other factors.
Therefore , the concept of a sequence of transformations is a fundamental one in many different fields, as it allows us to understand how complex systems or objects can be broken down into smaller, more manageable parts that can be manipulated or analyzed in a systematic way.
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81^3/4 / 81^1/2 =
A. (81/3)^ -1/2
B. 27
c. 9
d. 3
If 5 shirts and 8 sweaters cost $222, and 6 shirts and 5 sweaters cost $202, what is the cost of one shirt and what is the cost of one sweater?
Answer: $22 per shirt and $14 per sweater
Step-by-step explanation:
Let x be shirts and y be sweaters.
We will write equations for the given situation.
5x + 8y = $222
6x + 5y = $202
Next, we will graph both of these equations. The point of intersection will give the prices of one shirt and one sweater.
(22, 14)
➜ $22 per shirt
➜ $14 per sweater
A toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per second, then its height h after t seconds, is given by the equation h(t)=-16t^2+128 if air resistance is neglected
1. how high is the rocket off the ground when it’s launched ?
2. What time does the maximum height occur?
3. How high does the rocket go?
4. What is the axis of symmetry?
5. When does the rocket hit the ground?
6. How high is the rocket at 2 seconds?
7. When is the rocket at 252 feet?
8. The graph coordinates
Answer:
The rocket is off the ground by 0 feet when it's launched, as ground level is defined as h = 0.To find the time at which the maximum height occurs, we can use the fact that the maximum or minimum point of a parabola given in the form y = ax^2 + bx + c occurs at x = -b/2a. In this case, we have h(t) = -16t^2 + 128, which has a = -16 and b = 0. Therefore, the maximum height occurs at t = -b/2a = -0/(-32) = 0 seconds.To find the maximum height reached by the rocket, we can substitute t = 0 into the equation h(t) = -16t^2 + 128, since the maximum height occurs at t = 0:[tex]h(0) = -16(0)^2 + 128[/tex]
[tex]= 128[/tex]
Therefore, the rocket goes to a maximum height of 128 feet.
4. The axis of symmetry of the parabolic path of the rocket is the vertical line that passes through the vertex of the parabola. Since the coefficient of [tex]t^2[/tex] is negative, the parabola opens downwards, and the vertex represents the maximum point of the path. As we found in question 2, the time at which the maximum height occurs is t = 0, so the axis of symmetry is the vertical line passing through t = 0.
5. To find when the rocket hits the ground, we need to find the time t at which h(t) = 0. Substituting [tex]h(t) = -16t^2 + 128[/tex], we get:
[tex]-16t^2 + 128 = 0[/tex]
Solving for t using the quadratic formula, we get:
t = (0 ± √(0^2 - 4(-16)(128))) / (2(-16))
= (±√8192) / (-32)
= ±8
Since time cannot be negative, the rocket hits the ground after approximately 8 seconds.
6. To find how high the rocket is at t = 2 seconds, we can substitute t = 2 into the equation h(t) = -16t^2 + 128:
h(2) = -16(2)^2 + 128
= -64 + 128
= 64 feet
Therefore, the rocket is at a height of 64 feet at 2 seconds.
7. To find when the rocket is at a height of 252 feet, we need to solve the equation [tex]-16t^2 + 128 = 252[/tex]. Rearranging and solving for t, we get:
[tex]-16t^2 + 128 = 252[/tex]
[tex]-16t^2 = 124[/tex]
[tex]t^2 = -124/-16[/tex]
t^2 = 7.75
t ≈ ±2.78 seconds
Since time cannot be negative, the rocket is at a height of 252 feet after approximately 2.78 seconds.
8. The graph coordinates of the rocket's path can be plotted using the function [tex]h(t) = -16t^2 + 128[/tex]. The x-axis represents time t in seconds and the y-axis represents the height of the rocket in feet. We can plot points on the graph by substituting different values of t into the equation and plotting the resulting height. For example, some common points to plot include the vertex at (0, 128), the point where the rocket hits the ground at approximately (8, 0), and the point where the rocket is at a height of 252 feet at approximately (2.78, 252). We can also plot other points by substituting different values of t into the equation and plotting the resulting height.
Triangle ABC is shown. Use the graph to answer the question. triangle ABC on a coordinate plane with vertices at 1 comma negative 2, 9 comma negative 2, 5 comma 2 Determine the coordinates of the image if triangle ABC is translated 4 units down. A′(1, −6), B′(9, −6), C′(5, −2) A′(1, 2), B′(9, 2), C′(5, 6) A′(5, −2), B′(13, −2), C′(9, 2) A′(−3, −2), B′(5, −2), C′(1, 2)
The coordinates of the image if triangle ABC is translated 4 units down would be: A′(1, -6), B′(9, -6), C′(5, -2)
How will you translate the triangle 4 units down?To translate the triangle 4 units down, we need to subtract 4 from the y-coordinate of each vertex.
Vertex A has coordinates (1, -2), so its image A' after the translation is (1, -2 - 4) = (1, -6).
Vertex B has coordinates (9, -2), so its image B' after the translation is (9, -2 - 4) = (9, -6).
Vertex C has coordinates (5, 2), so its image C' after the translation is (5, 2 - 4) = (5, -2).
Therefore, the coordinates of the vertices of triangle ABC after it is translated 4 units down are A′(1, −6), B′(9, −6), and C′(5, −2).
So, the answer is option A: A′(1, −6), B′(9, −6), C′(5, −2)..
How can you use the coordinates of the vertices of a figure to determine its image after a translation?
To determine the image of a figure after a translation, you can add or subtract the same amount from the x- and/or y-coordinates of each vertex, depending on the direction and distance of the translation.
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HELPPPP MAJOR ASSIGNMENT DUE TODAY
The coordinates of Checkpoint B as we move from checkpoint A to the west are (-9, 5).
What is cartesian coordinate system?The Cartesian coordinate system, often called the rectangular coordinate system, uses ordered pairs of integers to represent points in a plane. It was created in the 17th century and is named after the mathematician René Descartes. The x-axis, which is horizontal, and the y-axis, which is vertical, split the plane into two perpendicular axes in the Cartesian coordinate system.
First, Hurdle 1 is 4 units west of Checkpoint A, so its x-coordinate is:
0 - 4 = -4
Hurdle 2 is 3 units west of Hurdle 1, so its x-coordinate is:
-4 - 3 = -7
Checkpoint B is 2 units west of Hurdle 2, so its x-coordinate is:
-7 - 2 = -9
The y-coordinate for all remain the same.
Hence, the coordinates of Checkpoint B as we move from checkpoint A to the west are (-9, 5).
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simplificar -2(x-1)*(1+x)³+3(1+x)*(1-x)²
Answer:
[tex] { - 2x}^{4} - {x}^{3} - 3 {x}^{2} + x + 5[/tex]
Step-by-step explanation:
[tex] - 2(x - 1) \times ({1 + x})^{3} + 3(1 + x) \times ( {1 - x})^{2} = ( - 2x + 2) \times (1 + 3x + 3 {x}^{2} + {x}^{3} ) + (3 + 3x) \times (1 - 2x + {x}^{2} ) = ( - 2x - 6 {x}^{2} - 6 {x}^{3} - 2 {x}^{4} + 2 + 6x + 6 {x}^{2} + 2 {x}^{3} ) + (3 - 6x + 3 {x}^{2} + 3x - 6 {x}^{2} + 3 {x}^{3} ) = x - {x}^{3} - 2 {x}^{4} + 2 + 3 + 3 {x}^{2} - 6 {x}^{2} = x - {x}^{3} - 2 {x}^{4} + 5 - 3 {x}^{2} = - 2 {x}^{4} - {x}^{3} - 3 {x}^{2} + x + 5[/tex]
What is the circumference of a circle with a diameter of 21 cm? (show working)
The circumference of the circle is 65. 94 cm
What is circumference?The formula for calculating the circumference of a circle is expressed with the equation;
C = 2πr
Given that the parameters are;
C is the circumference of the circle.π takes the value of 3.14r is the radius of the circleNote that the radius of a circle is twice the diameter of that circle.
Then, we have;
Radius = diameter/2
Substitute the values
Radius = 21/2 = 10. 5 cm
Then, the circumference
C = 2 ×3.14 × 10. 5
Multiply the values
C = 65. 94 cm
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Xavier filled up his car with gas before embarking on a road trip across the country. The number of gallons of gas remaining in his gas tank after � t hours of driving can be determined using the equation � = 12 − 0.75 � . G=12−0.75t. What is the � x-intercept of the equation and what is its interpretation in the context of the problem?
The x-intercept of the equation is (16, 0), which means that after 16 hours of driving, Xavier will have used up all the gas in his tank.
To find the x-intercept of the equation G = 12 - 0.75t, we need to set G = 0 and solve for t:
0 = 12 - 0.75t
0.75t = 12
t = 16
As a result, the equation's x-intercept is (16, 0), indicating that Xavier will run out of gas after 16 hours of driving.
The x-intercept in the problem denotes the moment at which Xavier runs out of gas and his car comes to a complete stop. This is a crucial factor to take into account when organising a lengthy road trip because it shows how long Xavier can travel before needing to refuel. If the fuel efficiency of Xavier's vehicle is assumed to be constant, the x-intercept can also be used to determine how far he can go on a single tank of gas. So, for Xavier to plan his road trip and make sure that he doesn't run out of gas, it's imperative that he comprehend the x-intercept of the equation G = 12 - 0.75t.
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