1) What are the three most important concepts to remember for the test?
2) What mistake(s) did you make, and what was your misunderstanding?
Submit a pdf for each annotated response template.
Answers
The evaluation of the velocity function, v(t) = cos((π/6)·t) for the interval 0 ≤ t ≤ 12, th obtain the position and acceleration is as follows;
(a) The particle is moving to the left when 3 < t < 9
(b) The total distance is; [tex]\int\limits^6_0 {cos(\frac{\pi}{6}\cdot t) } \, dt[/tex]
(c) a(t) ≈ -0.453
(d) x(4) ≈ -0.346
What is the acceleration of an object?Acceleration is the rate at which the velocity of the object changes.
The function for the velocity of the particle is presented as follows;
v(t) = cos((π/6)·t)
The position of the particle at time, t = 0 is x = -2
(a) When the particle is moving to the left, the velocity is negative
The value of cos(θ) is negative for π/2 < θ < 1.5·π
The range of values of θ = ((π/6)·t), for 0 ≤ t ≤ 2, are;
((π/6) × 0) ≤ θ ≤ ((π/6) × 12), from which we get;
0 ≤ θ ≤ (2·π)
When π/2 = (π/6)·t, we get;
t = (π/2)/(π/6) = 3
When 1.5·π = (π/6)·t, we get;
t = (1.5·π)/(π/6) = 9
The particle is moving to the left between time t = 3 and time t = 9, which can be expressed as follows;
The particle is moving to the left in the interval; 3 < t < 9(b) The total distance traveled by the particle from time t = 0 to time t = 6 is presented using the definite integral as follows;
Distance traveled = [tex]\int\limits^6_0 {cos(\frac{\pi}{6}\cdot t) } \, dt[/tex](c) Acceleration, a, is the rate of change of the velocity, therefore, the acceleration is the derivative of the velocity function, which can be obtained as follows;
[tex]a(t) =\frac{d}{dt} {cos(\frac{\pi}{6}\cdot t) } = -\frac{\pi}{6} \cdot sin(\frac{\pi}{6} \cdot t)[/tex]
[tex]a(t) = -\frac{\pi}{6} \cdot sin(\frac{\pi}{6} \cdot t)[/tex]
At time t = 4, we get;
[tex]a(4) = -\frac{\pi}{6} \cdot sin(\frac{\pi}{6} \times 4) = -\frac{\sqrt{3} \cdot \pi}{12}[/tex]
The acceleration of the particle at time t = 4 is; -(√3)·π/(12) ≈ -0.453(d) The position of the particle at time t = 4, can be obtained by adding the the position of the particle at time t = 4 to the total distance covered between time t = 0 and time t = 4 as follows;
[tex]\int\limits^4_0 {cos(\frac{\pi}{6}\cdot t) } \, dt =[ \frac{6}{\pi}\cdot {sin(\frac{\pi}{6}\cdot t) }]^4_0[/tex]
[tex][ \frac{6}{\pi}\cdot {sin(\frac{\pi}{6}\cdot t) }]^4_0 = [ \frac{6}{\pi}\cdot {sin(\frac{\pi}{6}\times 4) }] - [ \frac{6}{\pi}\cdot {sin(\frac{\pi}{6}\times 0) }]=\frac{3\cdot \sqrt{3} }{\pi}[/tex]
[tex]\int\limits^4_0 {cos(\frac{\pi}{6}\cdot t) } \, dt = \frac{3\cdot \sqrt{3} }{\pi}[/tex]
The position of the particle at t = 4 is therefore;
[tex]x = -2 + \frac{3\cdot \sqrt{3} }{\pi} \approx -0.346[/tex]Learn more about definite integrals here: https://brainly.com/question/8388817
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Related Questions
Select all ratios equivalent to 7:6.
Answers
The ratios equivalent to 7:6 can be expressed as a) 14 : 12
What does the idea of ratios mean?The concept that will be used here is ratio. The proportion is an equation that demonstrates how two ratios are equivalent, but the notion of ratio defines us to compare two quantities.
A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the overall amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.
From the ratios equivalent to 7:6 which can be written as 7/6
Then we consider option A , 14/12 = 7/6 ( divide the denominator and numerator by factor of 2.
Option B; 2 : 18 = 2/18 = 1/9
option C : 28 : 26 = 16/ 13
option D : 30 : 25 = 6/5
Therefore, option A is correct.
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Missing options:
a) 14 : 12
b) 2 : 18
c) 28 : 26
d) 30 : 25
If the sun is 69° above the horizon, find the length of the shadow cast by a building 91 ft tall. Round your answer to the nearest tenth.
Answers
If the sun is 69° above the horizon, the length of the shadow cast by a building 91 ft tall
How to find the length of the shadow?You should understand that the length of the shadow is the distance between a point to the foot of the tenth
This makes an angle of depression, with 69 degrees
Remember that the angle on top of the tenth is 90-69 = 21 degrees
therefore, using the trigonometrical ratio
We have Tan∅ = opposite of adjacent
Tan 21⁰ = x/9
x= 9*tan 21⁰
x = 9*0.3839
The distance is 3.45
Therefore the length of the shadow cast by a building is approximately 3.5 feet long
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Ms. Baumgartner draws a pair of supplementary angles and tells the class that the angle measures are (4x+30)°
and (2x+6)°.
What does the larger angle measure? What does the smaller angle measure?
Answers
The larger angle between the pair of supplementary angles is 126 degrees.
What is the measure of the larger angle?Supplementary angles are simply angles that sum up to 180 degrees.
Given the data in the question;
Measure of angle 1 = (4x+30)°Measure of angle 2 = (2x+6)°Since, they both form a supplementary angle, their sum gives a total of 180 degree.
Angle 1 + Angle 2 = 180
(4x+30) + (2x+6) = 180
Solve for x
4x + 2x + 30 + 6 = 180
6x + 36 = 180
6x = 180 - 36
6x = 144
x = 144 / 6
x = 24
Now, we determine the measure of the angles.
Angle 1 = (4x+30)
Angle 1 = 4(24) + 30
Angle 1 = 126 degrees
Angle 2 = (2x+6)
Angle 2 = 2(24) + 6
Angle 2 = 54 degrees.
Therefore, the larger angles measures 126 degree.
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A barn is 100 feet long and 40 feet wide (see figure attached). A cross section of the roof is the inverted catenary given below.
y = 31 - 10(e^(x/20) + e^(-x/20))
Find the number of square feet of roofing on the barn. (Round your answer to the nearest whole number.
Answers
The roof of the barn measures 4701 square feet. (This is equivalent to saying that the barn has a roofing area of 4701 square feet.)
What is integration ?
Integration is a fundamental concept in calculus. It refers to the process of finding the integral of a function, which gives the total amount of change of a quantity over a given interval. The process of integration is the reverse of differentiation, which is the process of finding the rate of change of a quantity. The symbol for integration is ∫.
A barn is 100 feet long and 40 feet wide.
Find the first derivative of the given function:
dy/dx = -10[1/20e^x/20 - 1/20 e^-x/20]
1 + (dy/dx)^2 = 1/4[e^x/20 - e^-x/20]^2
The arc length:
= ∫ √1/4[e^x/20 - e^-x/20]^2 dx
After solving the above integration:
= 20(e - 1/e)
The roofing = 100(20(e - 1/e))
= 4701 square feet,
The roof of the barn measures 4701 square feet. (This is equivalent to saying that the barn has a roofing area of 4701 square feet.)
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the records for all trains scheduled to depart from the concert hall train station last year showed that the average delay for these trains was minutes, of the trains had been delayed, and trains had been cancelled. keiko is a traffic engineer helping the concert hall station improve its performance. she audited a random group of records of trains scheduled to depart from the concert hall station last year. in her group the trains were late an average of minutes, of the trains had been delayed, and trains had been cancelled.
Answers
All of the trains scheduled to leave from the Concert Hall station are listed in Keiko's record for the population, and a random selection of 70 train records are listed in Keiko's record for the sample. As a result, statement II is true for the population, whereas statement I is true for the sample. The total population or all trains is regarded as a parameter, while the random group is regarded as a statistic.
In statistics, when we talk about population, we are talking about the entire population from which we want to draw a conclusion about. And when we talk about sample, we are talking about a particular or specific group from which we want to collect data from. So the size of sample will be less compared to the total size of the population.
a) In the given scenario, when we discuss population, we are referring to all of the trains that were scheduled to depart the Concert Hall station in the previous year. So statement II is correct.
And, when we discuss samples, we are referring to the random sample of 70 train records that Keiko audited. So statement I is correct.
b) When we talk about parameters, we are talking about the data of an entire population or all trains. And, when we are talking about statistics, we are talking about the sample data or random group.
The complete question is -
The records for all trains scheduled to depart from the Concert Hall train station last year showed that the average delay for these trains was 13.1 minutes, 18.6% of the trains had been delayed, and 12 trains had been canceled. Keiko is a traffic engineer helping the Concert Hall station improve its performance. She audited a random group of 70 records of trains scheduled to depart from the Concert Hall station last year. In her group the trains were late an average of 22.5 minutes, 30% of the trains had been delayed, and 4 trains had been canceled.
a. For Keiko's audit of train records, identify the population and the sample
Population:
I. The random group of 70 records of trains audited by Keiko.
II. The records of all the trains scheduled to depart from the Concert Hall station last year.
Sample:
I. The random group of 70 records of trains audited by Keiko.
II. The records of all the trains scheduled to depart from the Concert Hall station last year
b. Choose whether each number described below is a parameter or a statistic for Keiko's audit.
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Jackson gets paid $4,850 per month. He pays $1,552 a month for rent. What percent of his monthly pay goes to rent?
Answers
Answer:
32%
Step-by-step explanation:
1552 / 4850 = 0.32
a triangle has one side length of 26 and another side length of 18. select all of the possible lengths of the third side.
Answers
Since the longest side cannot be longer than the total of the other two sides, the third side's potential lengths range from 8 to 44.
A triangle's third side must be longer than the difference between the other two sides' lengths and shorter than the total length of the other two sides. The two side lengths in this situation are 18 and 26. The third side must be greater than 8 because the difference between them is 8. The third side must be less than 44 because the total length of the first two sides equals 44. Therefore, the third side length might be any side length between 8 and 44.Since the longest side cannot be longer than the total of the other two sides, the third side's potential lengths range from 8 to 44.
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The complete question is
a triangle has one side length of 26 and another side length of 18. select all of the possible lengths of the third side potential lengths range from 8 to 44?
How the expressions are equivalent
Answers
Equivalent equations are algebraic equations that are having identical roots or solutions
What are Equivalent Expressions?Equations in algebra with the same roots or solutions are said to be equivalent. An analogous equation is one that is created by adding or removing the identical number, symbol, or expression from both sides of an equation. We can also get an equivalent equation by multiplying or dividing both sides of an equation by the same nonzero value.
Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).
To determine which complex expression is the simple expression's equivalence:
Give any coefficients a distribution:
a(bx±c)=abx±ac
X-terms and constants should be combined with any other like terms on either side of the equation.Put the terms in the same order, with the x-term typically coming before the constants.The two phrases are equal if and only if each of their terms is the same.To know more about Equivalent expressions, refer to:
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Diya earned a 36 out of 80 on a test. Her teacher offered extra credit that would allow Diya to double her score. What score could she earn if she completes the extra credit?
Answers
Diya could earn 72 marks out of 80 after getting the extra credits.
What are extra credits in School?Teachers employ extra credit for a variety of reasons. For example, it may be felt that students who are highly capable may benefit from an additional challenge that might not be suitable as required work for all students. Extra credit may also be used as a way to allow a student to improve their grade after a weak performance earlier in a course. In both of these cases, extra credit can promote differentiated instruction by factoring in optional work in the assessment of student performance.
Given here: Diya scores 36 out of 80 on a test.
Also, her teacher gives her extra credit with which she could double her marks.
If Diya doubles her marks then her total marks would be 72
Therefore the increase in her marks is 72-36=36
She could earn another 36 credits.
Thus her score after the extra credit is equal to 72
Hence, Diya could earn 72 marks out of 80 after getting the extra credits.
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8-3(4-4)+2*4*6 :< i need help man
Answers
4-4=8
8-3(4)+2*4*6
2x4x6
8-3(4)+48
3x4
12(4)+48
48+48
96
I THINK I DID THIS RIGHT
Answer:
[tex]\sf 56[/tex]Step-by-step explanation:
[tex]\sf 8-3(4-4)+2*4*6[/tex]
[tex]\sf 8-(3)(0)+(2)(4)(6)[/tex]
[tex]\sf 8-0+(2)(4)(6)[/tex]
[tex]\sf 8+(2)(4)(6)[/tex]
[tex]\sf 8+(8)(6)[/tex]
[tex]\sf 8+48[/tex]
[tex]\sf 56[/tex]
Environmentalists want to estimate the percent of trees in a large forest that are infested with a certain beetle. The environmentalists will select a random sample of trees to inspect. Which of the following is the most appropriate method for creating such an estimate? A two-sample z-interval for a population proportion A one-sample interval for a sample proportion A one-sample 2-interval for a population proportion A two-sample z interval for a difference between sample proportions A two sample 2-interval for a difference between population proportions
Answers
A two-sample z-interval for a population proportion. This method is used to create an estimate of the percentage of trees in a large forest that are infested with a certain beetle by taking a random sample of trees to inspect.
A two-sample z-interval for a population proportion is the most appropriate method for creating an estimate of the percent of trees in a large forest that are infested with a certain beetle. This method involves taking a random sample of trees from the forest and inspecting them to determine the proportion of infested trees. The sample size chosen should be large enough to provide a reliable estimate of the proportion of trees in the population that are infested. A two-sample z-interval is then used to calculate a confidence interval for the population proportion, which can be used to estimate the overall percent of trees in the forest that are infested with the beetle. This method can provide a reliable estimate of the percent of trees in the forest that are infested with the beetle, allowing environmentalists to make informed decisions regarding management of the forest.
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now, set up an integral to compute the volume of this solid, then evaluate it to find the volume of the solid: V= Integral (from x=2 to x=-4) of (8-x^2-2x)^2 dx an integral that gives the volume of the solid is:
Answers
The volume of the solid is equal to 96 cubic units.
V= Integral (from x=2 to x=-4) of (8-x^2-2x)^2 dx = ∫(8-x^2-2x)^2 dx
= 1/3*∫(24-6x^2-12x)dx
= 1/3*[24x-2x^3-6x^2] from x=2 to x=-4
= 1/3*[(-6)-(-140)-(-136)]
= 1/3*(288)
= 96 cubic units
Set up an integral to compute the volume of the solid.
V= Integral (from x=2 to x=-4) of (8-x^2-2x)^2 dx
Rewrite the integral with a function of x in terms of a single power of x.
V= Integral (from x=2 to x=-4) of (8-x^2-2x)^2 dx = ∫(8-x^2-2x)^2 dx
= 1/3*∫(24-6x^2-12x)dx
Integrate the function.
= 1/3*[24x-2x^3-6x^2] from x=2 to x=-4
Evaluate the integral to find the volume of the solid.
= 1/3*[(-6)-(-140)-(-136)]
= 1/3*(288)
= 96 cubic units
The volume of the solid is equal to 96 cubic units.
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(2/5y -8)+ (3/10y+1)
Answers
The solution for the expression is (35y - 22)/(5y-8)(10y+1). The solution has been obtained by solving the algebraic expression.
What is algebraic expression?
An algebraic expression is one that uses variables, constants, and algebraic operations (addition, subtraction, etc.).
The four primary categories of expressions are as follows:
A monomial expression is one with only one term.These expressions have two terms and are called binomial expressions.Expressions with three terms are known as trinomial expressions.The terms in polynomial expressions are numerous.We are given
⇒(2/5y -8)+ (3/10y+1)
⇒(2(10y+1) + 3(5y -8))/(5y-8)(10y+1)
⇒(20y + 2 + 15y - 24)/(5y-8)(10y+1)
⇒(35y - 22)/(5y-8)(10y+1)
Hence, the solution for the expression is (35y - 22)/(5y-8)(10y+1).
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Ann and leila are driving separate cars to New York. They begin the trip with full gas tanks. The amount of gas (in gallons) remaining in the tank of each car depends on the number of miles driven, as shown below.After 225 miles driven, which car will have less gas remaining?After how many miles will the tanks contain the same amount of gas? If the number of miles driven is less than this, which car will have more gas remaining?
Answers
After 180 miles both the cars' tanks contain same amount of gas.
What is the graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.
Given that, Ann and Leila are driving separate cars to New York. They begin the trip with full gas tanks.
From the given graph,
After 360 miles Ann's car has 2 gallons of gas.
After 180 miles both the cars' tanks contain same amount of gas.
When they travelled less than 180 miles, Leila's car has more gas.
Therefore, after 180 miles both the cars' tanks contain same amount of gas.
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The question is based on the following table, which provides information on the production of a product that requires one variable input.
Input Total Product
0 0
1 5
2 20
3 32
4 42
5 50
6 55
7 58
8 58
9 56
With the addition of the seventh unit of input, the marginal product is
Answers
Answer: The marginal product is the change in total product that results from an additional unit of input. With the addition of the seventh unit of input, the marginal product can be calculated as follows:
Total product when 7 units of input is used: 58
Total product when 6 units of input is used: 55
Marginal product = Total product when 7 units of input is used - Total product when 6 units of input is used
Marginal product = 58 - 55 = 3
So with the addition of the seventh unit of input, the marginal product is 3 units.
Step-by-step explanation:
4 friends evenly divided up an n-slice pizza. One of the friends, Harris, ate 1 fewer slice than he received. How many slices of pizza did harris eat? write your answer as an expression
Answers
Harris ate (n - 4)/4 number of slices of pizza.
What is fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
Given:
4 friends evenly divided up an n-slice pizza.
That means,
n / 4.
One of the friends, Harris, ate 1 fewer slice than he received.
That means,
n/4 - 1
= (n - 4)/4
Therefore, Harris ate (n - 4)/4.
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BRAINLIEST TO THE CORRECT ANSWER!!!
A construction crew is lengthening a road that originally measured 10 miles. The crew is adding one mile to the road each day.
Let L be the length (in miles) after D days of construction.
Write an equation relating L to D. Then graph your equation using the axes below.
Answers
The length of the road after D days of construction (L) is equal to the original length of the road (10 miles) plus the number of miles added by the construction crew each day (1 mile/day) times the number of days the construction has been going on (D).
So the equation relating L to D is:
L = 10 + 1D
This equation can be graph on a Cartesian plane with D on the x-axis and L on the y-axis. The graph will be a straight line passing through the point (0,10) and having a slope of 1, meaning that for every one increase in D there is a one increase in L.
It will look like this:
graph{10+x [-12, 12, -6, 6]}
Where D=x and L=y.
Answer: L - 10 = D
Step-by-step explanation:
1 Day = 1 Mile
After 1 Day of construction a 1 Mile is added to the road
Original length is 10 miles
Length (e.g. 11 miles) - 10miles = Day 1
So:
L - 10 = D
Find the equation of this line.
y =
x +[]
Simplify the fractional part.
Answers
Answer:
y = 1/3x +2
Step-by-step explanation:
when x =o, y=2
when x= -6, y=0
so slope is always the difference between the Ys divided by diff b/w the Xs
so the slope is (2-0)/(0-(-6)) = 1/3
the intercept by definition is when x=0, so it's 2
so Y = 1/3 X +2
question 6 next, you select the basic statistics that can help your team better understand the ratings system in your data. assume the first part of your code is: trimmed flavors df %>% you want to use the summarize() and max() functions to find the maximum rating for your data. add the code chunk that lets you find the maximum value for the variable rating.
Answers
The code chunk to add is summarize(mean(Rating)), and the mean rating is 3.185933 according to the ratings system, summarize(), and mean() functions.
Now, According to the question:
The full code should be trimmed flavors df%>% summarize(mean(Rating)) to determine the mean rating.
In order to present summary statistics, this code combines the summarize() and mean() functions to show the mean rating of your data.
The statistic that will be displayed due to the "mean()" method is the mean rating, which in this instance would be 3.185933.
The mean scale score represents the overall effectiveness of a group of students on a test. A mean scale score is calculated specifically by adding up the scores of each individual student and dividing that total by the number of scores. It is additionally known as an average.
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Bookwork code: C02
(Image: Calculator Not Allowed)
Calculator
not allowed
What is the order of rotational symmetry of a square?
(Image: Image showing mathematical content for the question.)
Answers
The order of rotational symmetry of a square about its center is 4.
How many order of rotational symmetry does a square has?Geometrically speaking, a shape has rotational symmetry when it retains its appearance following a small amount of rotation by a partial turn. The number of different orientations in which an object appears exactly the same for each rotation is known as the degree of rotational symmetry.
The number of times a square fits onto itself during a full rotation of 360 degrees determines a square's rotational symmetry. The square in the images above can be seen to fit four times on top of itself during a full 360-degree rotation.
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Not a test or quiz
Divide the following numbers in scientific notation and express the result in scientific notation.
Answers
The expression of (9 * 10⁶)(8 * 10⁸) in scientific notation is; 72 * 10¹⁴
How to express a number in scientific notation?Scientific notation is defined as a way of writing very large or very small numbers. A number is usually written in scientific notation when a number between 1 and 10 is multiplied by a power of 10. For example, 750,000,000 can be written in scientific notation as 7.5 * 10⁸.
We want to multiply the expression given as;
(9 * 10⁶)(8 * 10⁸)
Now, we can rewrite this as;
(9 * 8) * (10⁶ * 10⁸)
According to laws of exponents, x² × x³ = x²⁺³
Thus;
(9 * 8) * (10⁶ * 10⁸) = 72 * 10⁶⁺⁸
= 72 * 10¹⁴
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Sarah ordered 37 shirts that cost $9 each. She can sell each shirt for $16. She sold 30 shirts to customers. She had to return 7 shirts and pay a $3 charge for each returned shirt. Find Sarah's profit.
Answers
Sarah's profit, given the shirts sold, the cost of the shirts, and the shirts returned, can be found to be $ 126
How to find the profit ?First, find Sarah's cost :
= Cost to buy the shirts + cost to return the shirts
= ( 37 x 9 ) + ( 7 x 3)
= 333 + 21
= $ 354
The revenue made from selling the shirts was :
= 30 x 16 per shirts
= $ 480
Sarah's profit is therefore:
= 480 - 354
= $ 126
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martika says factors and multiples are related. use the equation 6 x 7 = 42 to describe the relationship between factors and mutiples
Answers
The relationship between factors and multiples from the equation 6 x 7 = 42 are given below.
What is factorization?Factorization in mathematics is the process of dividing a large number into smaller ones that, when multiplied together, give you the original number. Factorization is the process of dividing a number into its components or divisors.
Given:
An equation,
6 x 7 = 42.
Multiples are what you receive after multiplying a factor, which is what you can multiply to produce a number.
1 x 42 = 42
2 x 21 = 42
3 x 14 = 42
6 x 7 = 42
So the factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
The multiples of 42 are 1,2,3,4,5,6 etc.
Therefore, the relationship between factors and multiples are given
above.
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Which of the following is a property of an isosceles trapezoid? Choose ALL that apply.
Four right angles
Two pairs of parallel sides
Diagonals are congruent
Diagonals are perpendicular
Answers
The properties of isosceles trapezoid are
Two pairs of parallel sidesTwo pairs of parallel sidesWhat is isosceles trapezoid?The lengths of the left and right sides of an isosceles trapezoid are equal or identical hence the base angles are likewise equal.
Because lengths of the left and right sides are equal and base angels are equal, the diagonals are equal
Other types of trapezoid include
The right trapezoid has two right angles.Its non-parallel sides are of identical length, making it an isosceles trapezoid.It does not have equal angles or sides, making it a scalene trapezoid.generally all trapezoid have two sides that are parallel to each other
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Select the correct answer. An archway is modeled by the equation y = -2x2 + 8x. A rod is to be placed across the archway at an angle defined by the equation x − 2.23y + 10.34 = 0. If the rod is attached to the archway at points A and B, such that point B is at a higher level than point A, at what distance from the ground level is point B? A. 8 units B. 6 units C. 5 units D. 3 units
Answers
Using the quadratic equation the distance of point B from the ground level is D. 3 units
What is an equation?An equation is a mathematical function that shows the relationship between two variables.
How to find the distance of point B from the level ground?Since an archway is modeled by the equation y = -2x² + 8x.
A rod is to be placed across the archway at an angle defined by the equation x − 2.23y + 10.34 = 0.
If the rod is attached to the archway at points A and B, such that point B is at a higher level than point A, we desire to find the distance of point be from the ground. To do this , we proceed as follows.
Since we have the equations
y = -2x² + 8x and x - 2.23y + 10.34 = 0Substituting y into the second equation, we have
x - 2.23y + 10.34 = 0
x - 2.23(-2x² + 8x) + 10.34 = 0
x + 4.46x² - 17.84x + 10.34 = 0
4.46x² - 16.84x + 10.34 = 0
To find the points a and B, we solve for x where both equations intersect.
So, using the quadratic formula, we solve for x
[tex]x = \frac{-b +/-\sqrt{b^{2} - 4ac} }{2a}[/tex] where a = 4.46, b = -16.84 and c = 10.34
So, substituting the values of the variablers into the equation, we have that
[tex]x = \frac{-(-16.84) +/-\sqrt{(-16.84)^{2} - 4\times4.46\times10.34} }{2\times4.46}\\= \frac{16.84 +/-\sqrt{283.5856 - 184.4656} }{8.92}\\= \frac{16.84 +/-\sqrt{99.12} }{8.92}\\= \frac{16.84 +/-9.96 }{8.92}\\x = \frac{16.84 + 9.96 }{8.92} or x = \frac{16.84 - 9.96 }{8.92}\\x = \frac{26.8}{8.92} or x = \frac{6.88}{8.92}\\x = 3.004 or x = 0.771[/tex]
Since B is higher, we take the higher value x = 3.
So, the distance of point B from the ground level is D. 3 units
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Using the quadratic equation the distance of point B from the ground level is D. 3 units
What is an equation?An equation is a mathematical function that shows the relationship between two variables.
How to find the distance of point B from the level ground?Since an archway is modeled by the equation y = -2x² + 8x.
A rod is to be placed across the archway at an angle defined by the equation x − 2.23y + 10.34 = 0.
If the rod is attached to the archway at points A and B, such that point B is at a higher level than point A, we desire to find the distance of point be from the ground. To do this , we proceed as follows.
Since we have the equations
y = -2x² + 8x and x - 2.23y + 10.34 = 0Substituting y into the second equation, we have
x - 2.23y + 10.34 = 0
x - 2.23(-2x² + 8x) + 10.34 = 0
x + 4.46x² - 17.84x + 10.34 = 0
4.46x² - 16.84x + 10.34 = 0
To find the points a and B, we solve for x where both equations intersect.
So, using the quadratic formula, we solve for x
[tex]x = \frac{-b +/-\sqrt{b^{2} - 4ac} }{2a}[/tex] where a = 4.46, b = -16.84 and c = 10.34
So, substituting the values of the variablers into the equation, we have that
[tex]x = \frac{-(-16.84) +/-\sqrt{(-16.84)^{2} - 4\times4.46\times10.34} }{2\times4.46}\\= \frac{16.84 +/-\sqrt{283.5856 - 184.4656} }{8.92}\\= \frac{16.84 +/-\sqrt{99.12} }{8.92}\\= \frac{16.84 +/-9.96 }{8.92}\\x = \frac{16.84 + 9.96 }{8.92} or x = \frac{16.84 - 9.96 }{8.92}\\x = \frac{26.8}{8.92} or x = \frac{6.88}{8.92}\\x = 3.004 or x = 0.771[/tex]
Since B is higher, we take the higher value x = 3.
So, the distance of point B from the ground level is D. 3 units
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Deshaun borrowed money from a credit union for 4 years and was charged simple interest at an annual rate of 9%. The total interest that he paid was $144.
How much money did he borrow?
Answers
Answer:
$155.56
Step-by-step explanation:
S.I=(PRT)÷100
$144=(P×9×1)÷100
crossmultiply
$144×100=9P
P=$14400÷9
P=$155.56
the price of a new car is 23% more than the price of a 3-year old car. if the price of the new car was $12,400, what is the price of the 3-year old car?
Answers
Answer: To find the price of the 3-year old car, we need to determine how much less it is than the new car, which is 23% of the price of the new car.
We can start by finding the value of 23% of the price of the new car, which is: $12,400 x 0.23 = $2,832
Now we know that the price of the 3-year old car is $2,832 less than the price of the new car. To find the price of the 3-year old car, we subtract $2,832 from the price of the new car: $12,400 - $2,832 = $9,568
So the price of the 3-year old car is $9,568.
Step-by-step explanation:
Please help with number 4
Answers
Answer:
yes
Step-by-step explanation:
9(b_5)
multiply 9 with everything in the bracket:
9×b=9b
9×5=45
:9(b-5)
ACTIVITY: Writing an Inequality
Work with a partner. In 3 years, your friend will still not be old enough
to apply for a driver's license.
a. Which of the following represents your friend's situation?
What does x represent? Explain your reasoning.
x + 3 < 16
x + 3 ≤ 16
x + 3 > 16
x+3≥ 16
Answers
The inequality that represents the situation in this problem is given as follows:
x + 3 < 16
How to define the inequality?The inequality symbols are given as follows:
> x: greater than x.< x: less than x.≥ x: at least x.≤ at most x.In three years, your friend's age is given as follows:
x + 3.
To apply for the driver's license, an age of 16 is needed, and your friend will be younger than 16, as he/she cannot apply, hence the inequality is:
x + 3 < 16
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fill in the blank. my buddy and i have just finished a dive to 15 metres/50 feet for 60 minutes. we want to return to the same site and depth and stay another 60 minutes. we can___to see about how long we have to remain at the surface to have enough no stop time. (choose all that apply)
Answers
The answer for the blank is we can use a dive table or computer.
When planning a subsequent dive, it is important to take into account the dive time, depth, and surface interval from the previous dive in order to safely plan for the next dive. To determine the required surface interval, one can use a dive table or a dive computer.
A dive table is a printed or electronic table that provides information about the safe amount of time that can be spent at certain depths, based on the previous dive. The table will take into account the dive time, depth, and surface interval from the previous dive, and provide a recommended surface interval to ensure safe diving.
A dive computer, on the other hand, is an electronic device that is worn by the diver and calculates the safe amount of time that can be spent at a certain depth, based on the diver's previous dive. The dive computer takes into account the dive time, depth, and surface interval from the previous dive, and provides a recommended surface interval to ensure safe diving.
In summary, to determine the required surface interval before returning to the same site and depth for another 60 minutes dive, one can use a dive table or a dive computer. These tools will give you the recommended time for your surface interval, based on your previous dive profile, so you can ensure you have enough no-stop time for your next dive.
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