Answer:
20cm
Step-by-step explanation:
90cm ÷ 1/2 the length 90 = 20cm
The probability that shares of acme will increase in value over the next month is 50% and the probability that shares of acme and shares of best will both increase in value over the next month is 40%
The probability that shares of Acme and Best will both increase in value over the next month is 0.2 (20%). This is calculated by multiplying the individual probabilities of each stock increasing in value (50% x 40%)
1. Calculate the individual probability of Acme increasing in value: 50%
2. Calculate the individual probability of Best increasing in value: 40%
3. Multiply the two individual probabilities together to calculate the probability that both stocks will increase in value: 50% x 40% = 0.2 (20%)
The probability that shares of Acme and Best will both increase in value over the next month is 0.2 (20%). This is calculated by multiplying the individual probabilities of each stock increasing in value (50% x 40%)
The complete question is :
The probability that shares of acme will increase in value over the next month is 50% and the probability that shares of acme and shares of best will both increase in value over the next month is 40%.What is the probability that shares of Acme and shares of Best will both increase in value over the next month?
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If the triangle above is reflected over the y-axis, what is the correct coordinate for A'?
A'(0,5)
A'(2,5)
A'(5,2)
A'(-5, -2)
The coordinate A when the triangle is reflected over the y-axis is (2, 5)
Reflecting the triangle over the y-axisFrom the triangle, we have
A = (-2, 5)
Reflecting a point over the x-axis is a type of transformation that involves flipping the point across the x-axis.
The reflection involves keeping the y-coordinate of the point the same, but changing the sign of the x-coordinate.
In this case, the original point is (-2, 5). To reflect this point over the y-axis, we keep the y-coordinate (5) the same, but change the sign of the x-coordinate to positive,
Resulting in the reflected point (2, 5).
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I NEed HELP ON THIS ASAP!
Answer:
length times with equals to base times height
Step-by-step explanation:
length times with times height equals to 3400
alana is making a ball out of rubber bands. when the ball has 54 rubber bands, it has a diameter of 3 cm. how many rubber bands should alana add to the ball to increase its diameter by 1 cm? assume that all of alana's rubber bands have the same volume.
The number of rubber bands that Alana has to add to the ball to increase its diameter by 1 cm is 74.
Given that:
Alana is making a ball out of rubber bands.
The volume of the ball with 54 rubber bands is found as below:
Diameter of the ball = 3 cm
The radius of the ball is half of the diameter.
So, radius, r = 1.5 cm
So, the volume of the ball formed by 54 rubberbands is:
[tex]V=\frac{4}{3}\pi r^3[/tex]
Substitute r = 1.5.
[tex]V=\frac{4}{3} \pi (1.5)^3[/tex]
[tex]V=4.5\pi[/tex]
Now, the volume of the ball formed by 1 rubber band or the volume of the rubber band is:
[tex]V(r)=\frac{4.5\pi }{54}[/tex]
[tex]V(r)=\frac{\pi }{12}[/tex]
When the diameter increased by 1 cm, the new diameter is 4 cm and thus the radius is 2 cm.
So, the increase in volume is:
[tex]\frac{4}{3} \pi (2)^3-\frac{4}{3} \pi (\frac{3}{2} )^3=\frac{37\pi }{6}[/tex]
Now, divide this by the volume of one rubber band to get the number of rubber bands to be added.
[tex]\frac{\frac{37\pi }{6}}{\frac{\pi }{12} } =74[/tex]
Hence, the number of bands added is 74.
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Maria needs to wraps the box shown below with no overlap of the wrapping paper. How much wrapping paper does she need?
As each side of the cube has a surface area of 24in².the total amount of wrapping paper needed is 64in².
What is surface area?Surface area is the total area of a three-dimensional object's surface, including the area of its faces and any curved surfaces.
To calculate the amount of wrapping paper needed for the cube, we can use the formula for the surface area of a cube:
SA = 6 x (side)²
In this case, the side of the cube is 2in,
so the SA = 6 x (2in)² = 24in²
To get the amount of wrapping paper needed, we would need to multiply this by 4, as each side of the cube has a surface area of 24in².
Therefore, the total amount of wrapping paper needed is
24in² x 4 = 96in²
To convert this to a square, we would need to divide it by 4, as each side of the square is equal in length.
Therefore, the total amount of wrapping paper needed is
96in² / 4
= 24in x 4
= 64in².
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Directions: The following is an axiomatic system. Answer each question as required.
Axiom Set:
Axiom 1: Each line is a set of three points
Axiom 2: Each point is contained by two lines. Axiom 3: Two distinct lines intersect at exactly one point.
Question:
1. What are the undefined terms in this axiom set? 2. Is the axiomatic system consistent? Why? Why not? State what specific property is the given axiomatic system.
The undefined terms in this axiom set are "line" and "point." These terms are not defined within the axioms themselves and are assumed to be understood.
The axiomatic system is consistent. The axioms do not contradict each other, and it is possible to construct a model of the system that satisfies all the axioms.
For example, we can imagine a Euclidean plane where each line is a set of three non-collinear points, and each point is contained by exactly two lines. Two distinct lines in this plane intersect at exactly one point, satisfying all the axioms.
The specific property of this axiomatic system is that it defines a Euclidean plane, which is a specific type of geometry characterized by the three axioms given.
The axioms capture some of the fundamental properties of Euclidean geometry, such as the existence of points and lines, the intersection of lines, and the relationship between points and lines.
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please help i have until saturday
To meet the recommendation, the ramp needs to have a horizontal distance of at least 16 feet. The ramp has a horizontal distance of 17.9 feet.
Why is this the recommended horizontal distance for a ramp?If the ramp has a horizontal distance of 17.9 feet, it meets the recommended minimum distance of 16 feet for a ramp with a maximum slope of 1:12, as per the ADA Accessibility Guidelines.
It's important to note that the slope of the ramp should also be taken into consideration to ensure that it is safe and easy to use for individuals with disabilities. If the ramp's slope is too steep or too shallow, it may not meet accessibility standards and could pose a hazard to users.
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PLEASE HELP MEEEEEEEEE
The population of a city in Arizona is 3200 in 2010. The city's population is increasing at a rate of 3% per decade. Using this information, predict the population of the city in the year 2030. Round your answer to the nearest person.
The predicted population of the city in the year 2030 is 5,780 person.
How to determine the population of the city in the year 2030?In Mathematics, a population that increases at a specific period of time represent an exponential growth. This ultimately implies that, a mathematical model for any population that increases by r percent per unit of time is an exponential function of this form:
P(t) = I(1 + r)^t
Where:
P(t ) represent the population.t represent the time or number of years.I represent the initial value of car.r represent the exponential growth rate.Years = 2030 - 2010 = 20 years.
By substituting given parameters, we have the following:
[tex]P(t) = I(1 + r)^t\\\\P(t) = 3200(1 + 3/100)^{20}\\\\P(t) = 3200(1 + 0.03)^{20}[/tex]
P(t) = 5,779.56 ≈ 5,780 person.
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Normalmente, el concepto griego "logos" se entiende como la máxima expresión de la cultura racionalista occidental, fundada por las primeras escuelas de filosofía clásica. De hecho, el nombre de las disciplinas científicas provienen de él: biología, filología, psicología, tecnología, etc. No obstante, el concepto "logos" no tiene un significado tan abstracto, puesto que involucra tanto el pensamiento como la acción, tanto lo interno como lo externo, tanto la idea mental como el decir la palabra. Tema:_________________________________________________________ Idea Principal: ___________________________________________________
Concept: "Logos" has greatly affected Western philosophy and a variety of scientific disciplines. Acknowledgement: the interaction between logical reasoning and empirical observation as well as the influence of language and discourse worldview.
For the concept:
Topic: The significance of the Greek philosophical idea of "Logos" in contemporary scientific disciplines.
Greek philosophy's basic idea of "Logos" has had numerous interpretations throughout history. The word "logos" is most commonly used to refer to reasoned discourse and language. It is frequently linked to human conversation and reasoning as well as the cosmic or divine principle that creates and sustains the universe.
The significance of "Logos" can be observed in its impact on contemporary scientific disciplines, including, but not limited to, biology, psychology, and technology. For instance, the word "biology" is derived from the Greek terms "bios" (life) and "logos" (word or reason), illustrating the notion that the study of life necessitates both practical observation and logical analysis.
Parallel to this, the scientific discipline of psychology, which examines how the human mind and behaviour function, gets its name from the Greek words "psyche," which means "soul," and "logos," which means "reason." This illustrates the notion that both empirical research and theoretical analysis are necessary for the study of the mind and behaviour.
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Translation: The first schools of classical philosophy founded by the Greek word "logos" are widely understood as the apex of Western rationalist culture. In actuality, he is the one who gave the titles of numerous branches of science, including philology, psychology, technology, and biology. The idea of "logos" does not have such an abstract meaning because it involves both internal and exterior mental and physical actions, as well as the mental idea and word pronunciation. Topic: Main Idea:
[tex]\sqrt 80x^{2}[/tex] can't figure it out
Answer: 4x√5
Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.
25 POINTS
The sound wave of two music notes can be represented by the function y = 2sin2x and y = sin x, where x represents the time since the note is played. At what times will the frequencies of the sound waves be the same in the interval [0°, 360°)?
x = 0°, 30°, 150°, 180°
x = 0°, 180°, 210°, 330°
x = 30°, 90°, 150°, 270°
x = 90°, 210°, 270°, 330°
Answer:
The correct answer is:
x = 0°, 30°, 150°, 180°
This is because the sine function equals 0 at 0° and 180° and equals 1/2 at 30° and 150°.
Step-by-step explanation:
The frequency of a sound wave is the number of cycles it completes in a given amount of time. In this case, we can find the frequency of each sound wave by looking at the period of the functions.
The function y = 2sin2x has a period of π (since 2sin(2x) has a period of π/2, which is then compressed horizontally by a factor of 2). The function y = sinx has a period of 2π.
If the frequencies are the same, then the two functions must complete an equal number of cycles in the interval [0°, 360°), which is the same as the interval [0, 2π) in radians.
Let's first look at the function y = sin x. It completes one cycle in the interval [0, 2π), so we can say that it completes n cycles in the same interval, where n is an integer.
Now let's look at the function y = 2sin2x. It completes two cycles in the interval [0, π), so it completes four cycles in the interval [0, 2π). Therefore, we can say that it completes m cycles in the interval [0, 2π), where m is an integer.
For the frequencies to be the same, we need to find values of n and m such that:
n = m
Solving for n and m, we get:
n = m = 2
So both functions complete two cycles in the interval [0, 2π). We can find the times when this occurs by setting the angles in radians equal to multiples of 2π/2, or π:
2sin2x = sin x
2sin2x - sin x = 0
sin x (2sin x - 1) = 0
sin x = 0 or 2sin x - 1 = 0
sin x = 0 when x is an integer multiple of π.
2sin x - 1 = 0 when sin x = 1/2, which occurs when x = π/6 or x = 5π/6.
Therefore, the frequencies of the sound waves are the same at x = π/6, x = π/2, x = 5π/6, and x = 3π/2.
The correct answer is:
x = 0°, 30°, 150°, 180°
This is because the sine function equals 0 at 0° and 180° and equals 1/2 at 30° and 150°.
Solve the system of inequalities 2x +y >3 and x- 2y 5- 1
The system of inequalities "2x – y > 1 and x – 2y < –1." are graphically shown below in the image section.
Inequalities in mathematics describe the connection between two non-equal values. Equal does not necessarily mean unequal. When two values are not equal, we typically use the "not equal symbol ()". However, a number of inequality comparisons are made to determine whether one value is greater than or less than another. The various inequality symbols, their meanings, and methods for solving them will all be covered in this article using examples of both one- and two-variable linear inequalities. We'll also discuss the algebraic inequalities that are commonly used.
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—------ CORRECT QUESTION FORMAT IS GIVEN BELOW - - - - - -
(Q). Solve the following system of inequalities graphically: 2x – y > 1 and x – 2y < –1.
a company received a shipment of 30 laser printers, including 6 that are defective. 3 of these printers are selected to be used in the copy room. (a) how many selections can be made?
We have to calculate the number of combinations of 3 laser printers that can be selected from the 30 shipped. In this case, the number of possible combinations is 4060.
The combination can be calculated using the formula
ⁿCr = n! / r! (n-r)!
Where n is the total number of items and r is the number of items chosen. In this case, n is 30 and r is 3.
³⁰C₃= 30! / (3! * (30-3)!) ⇒ 30! / (6 * 24)
⇒ 30 * 29 * 28 / 6
⇒ 4,060
Therefore, the answer is 4060 possible combinations of 3 laser printers that can be selected from the 30 shipped.
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What is the measure of 24? Enter your answer in the box.
m24=
1
2/3
60%
4 61°
S
P
9
Answer:
59
Step-by-step explanation:
60 + 61 + m<4 = 180
m<4 = 59°
PLEASEEE HELPP
a vertical flagstaff is on top of a building which stands on level ground. From point P on ground level the angle of elevation of the top of the flagstaff is observed to be 32°, and the angle of elevation of the bottom of the flagstaff to be 29°. from a point Q on ground level, 75m closer to the building, the angle of elevation of the top of the flagstaff is 38°.
calculate to three significant figures:
a) the distance of P from the base of the building
b) the height of the building
c) the length of the flagstaff
a) The distance of P from the base of the building is 168.0 m.
b) The height of the building is 43.8 m.
c) The length of the flagstaff is 25.8 m.
The given information is used to solve the three parts of the problem. First, to calculate the distance of P from the base of the building, the tangent of the angle of elevation of the top of the flagstaff, 32°, is used. The tangent of 32° is 0.6, and this is equal to the ratio of the height of the building and the distance from P to the base of the building. This gives the equation 0.6 = 43.8/x, where x is the distance of P from the base of the building. Solving for x gives x = 168.0 m.
Second, to calculate the height of the building, the tangent of the angle of elevation of the bottom of the flagstaff, 29°, is used. The tangent of 29° is 0.546, and this is equal to the ratio of the height of the building and the distance from P to the base of the building. This gives the equation 0.546 = h/168.0, where h is the height of the building. Solving for h gives h = 43.8 m.
Third, to calculate the length of the flagstaff, the tangent of the angle of elevation of the top of the flagstaff, 38°, is used. The tangent of 38° is 0.717, and this is equal to the ratio of the length of the flagstaff and the distance from Q to the base of the building. This gives the equation 0.717 = x/93.0, where x is the length of the flagstaff. Solving for x gives x = 25.8 m.
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Two or more terms having the same variables are called?
Answer:
Like terms
Step-by-step explanation:
Are the terms that contain same variables, same exponents of variables and same coefficients.
HOPE THIS HELPS
A man that is 6 feet tall cast a shadow that is 15 feet if a child Cassa shadow that is 10 feet long then how tall is the child
A man that is 6 feet tall cast a shadow that is 15 feet if a child Cassa shadow that is 10 feet long then the child is 4 feet tall.
To find the height of the child, we can use the concept of similar triangles. The man's height and shadow form one
triangle, and the child's height and shadow form another.
Step 1: Identify the given information.
Man's height = 6 feet
Man's shadow = 15 feet
Child's shadow = 10 feet
Step 2: Set up a proportion using the given information.
Man's height/Man's shadow = Child's height/Child's shadow
6/15 = Child's height/10
Step 3: Solve for Child's height.
To do this, cross-multiply:
6 × 10 = 15 × Child's height
60 = 15 × Child's height
Step 4: Divide both sides by 15 to find the Child's height.
Child's height = 60 / 15
Child's height = 4 feet
So, the child is 4 feet tall.
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The number of air conditioner units that 10 sales representatives sold last year are:
{6, 8, 10, 11, 12, 16, 17, 21, 32, 36}
How is the mean effected if the representative who sold the lowest number of units left the department, causing his sales to cancel out?
Responses:
The mean would increase.
The mean would remain the same.
The mean would decrease.
The correct option is (a), i.e. The mean would increase.
What is mean?
Mean is a measure of central tendency that is commonly used in statistics and mathematics. The mean of a set of numbers is calculated by adding up all the numbers in the set and dividing the sum by the total number of values in the set.
The mean of the number of air conditioner units sold by the 10 sales representatives last year can be calculated by adding up all the sales and then dividing by the total number of representatives, which is 10:
Mean = (6 + 8 + 10 + 11 + 12 + 16 + 17 + 21 + 32 + 36) / 10
= 169 / 10
= 16.9
So the mean number of air conditioner units sold per representative is 15.9.
If the representative who sold the lowest number of units left the department and his sales are cancelled out, the new sum of sales will be:
6 + 8 + 10 + 11 + 12 + 16 + 17 + 21 + 32 + 36 - 6 = 163
This is because we subtract the sales of the representative who left (which is 6 units in this case). The new mean can then be calculated by dividing this sum by the new total number of representatives, which is 9:
New mean = 163 / 9
= 18.11
So the new mean number of air conditioner units sold per representative is 18.11, which is higher than the original mean of 16.9. This is because removing the lowest value (which is smaller than the mean) increases the overall average.
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what two double digit numbers intercept with eachother at the same time in a graph
Answer:
how web is it you feel like a a a a a a a a a make
Step-by-step explanation:
hf and I have been working on the topic on the topic on the topic on the topic on the topic ona the topic on the topic on the topic on the topic on the
The Pines Golf Course is offering free ice cream cones to golfers who hit their tee shot on the green at hole 7! The following bar graph summarizes the tee shots from this morning.
Answer:
Step-by-step explanation:
calculate using a 1:20 dilution and the five rbc counting squares of the neubauer counting chamber, an average of 54 sperm is counted. the sperm concentration is:
The answer is option B: 54,000,000/mL. The sperm concentration is 0.54 million per cubic centimeter, or 54 million per milliliter.
To calculate the sperm concentration using a Neubauer counting chamber, we can use the following formula:
Sperm concentration = (number of sperm counted ÷ number of counting squares) ÷ dilution factor
In this case, we have:
Number of sperm counted = 54
Number of counting squares = 5
Dilution factor = 1:20
First, we need to calculate the total volume of the diluted sperm sample that was loaded onto the counting chamber. To do this, we can use the following formula:
Total volume = volume of loaded sample ÷ dilution factor
Since the dilution factor is 1:20, this means that the volume of loaded sample is 1/20th of the total volume. The total volume depends on the depth of the chamber and is usually 0.1 mL (or 100 μL) for a standard Neubauer counting chamber. Therefore:
Total volume = 0.1 mL ÷ 20 = 0.005 mL
Next, we can calculate the sperm concentration using the formula above:
Sperm concentration = (54 ÷ 5) ÷ 1/20
Sperm concentration = 54 ÷ 5 × 20
Sperm concentration = 54 ÷ 100
Sperm concentration = 0.54 million/cc
Therefore, the answer is option B: 54,000,000/mL. The sperm concentration is 0.54 million per cubic centimeter, or 54 million per milliliter.
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Your question is incomplete, but probably the complete question is :
Using a 1:20 dilution and the 5 RBC counting squares of the Neubauer counting chamber, an average of 54 sperm is counted. The sperm concentration is:
A. 54,000/cc
B. 54,000,000/mL
C. 108,000/cc
D. 108,000,000/mL
find the area of the shaded region
Answer:
196
Step-by-step explanation:
What is an equation of the line that passes through the points (-6, 1) and (6, 7)?
Answer:y = (1/2)x + 4
Step-by-step explanation:
The equation of the line that passes through the points (-6, 1) and (6, 7) can be found using the slope-intercept form of a line. The slope m is calculated as (y2 - y1)/(x2 - x1), where (x1,y1) and (x2,y2) are the coordinates of the two points. Plugging in the values for these points gives us a slope of m = (7-1)/(6-(-6)) = 1/2.
Now that we have the slope, we can use point-slope form to find the equation of the line: y - y1 = m(x - x1). Substituting one of our points and our calculated slope into this equation gives us y - 1 = (1/2)(x + 6). Simplifying this expression gives us y = (1/2)x + 4, which is the equation of our line in slope-intercept form.
So, an equation for this line is y = (1/2)x + 4.
Answer:
y = [tex]\frac{1}{2}[/tex] x + 4
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 = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 6, 1 ) and (x₂, y₂ ) = (6, 7 )
m = [tex]\frac{7-1}{6-(-6)}[/tex] = [tex]\frac{6}{6+6}[/tex] = [tex]\frac{6}{12}[/tex] = [tex]\frac{1}{2}[/tex] , then
y = [tex]\frac{1}{2}[/tex] x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (6, 7 )
7 = [tex]\frac{1}{2}[/tex] (6) + c = 3 + c ( subtract 3 from both sides )
4 = c
y = [tex]\frac{1}{2}[/tex] x + 4 ← equation of line
A major fishing company does its fishing in a local lake. The first year of the
company's operations it managed to catch 130,000 fish. Due to population decreases,
the number of fish the company was able to catch decreased by 4% each year. How
many total fish did the company catch over the first 13 years, to the nearest whole
number?
The company caught approximately 1,461,880 fish over the first 13 years. We can calculate it in the following manner.
Since the number of fish caught by the company decreases by 4% each year, the number of fish caught in the second year will be 96% of the first year, and the number of fish caught in the third year will be 96% of the second year, and so on.
To find the total number of fish caught by the company over the first 13 years, we can use the following formula:
Total fish caught
[tex]= 130,000 + 0.96130,000 + 0.96^{2130,000} + ... + 0.96^{12*130,000}[/tex]
Using the formula for the sum of a geometric series, we can simplify this to:
Total fish caught = 130,000 * (1 - 0.96¹³)/(1 - 0.96)
Plugging in the values and solving for the total fish caught, we get:
Total fish caught = 130,000 * (1 - 0.96¹³)/(1 - 0.96) = 1,461,880
Therefore, the company caught approximately 1,461,880 fish over the first 13 years.
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(Please answer quick missing assignment)
(Repost)
Answer:
No you would not use all your money, you would have 9 bananas with $0.10 left.
Step-by-step explanation:
t = m(x)
substitute
3.25 = .35(x)
inverse operations (divide by .35 on both sides)
3.25/.35 = (x)
9(rounded to the nearest whole number) = x
9 is the number of bananas. Now we need to find the change.
9 * .35 = 3.15
3.25 - 3.15 = .10
You will have 9 bananas with 10 cents left.
Every year, Martha and her sister attend 'The Nutcracker' at the Greenpoint Ballet. Last year, orchestra seating cost $60 per ticket. This year, each ticket was 15% cheaper. What was the cost of each ticket this year?
Answer:
$51
Step-by-step explanation:
You convery the percentage into a decimal, by dividing it by a hundred.
15÷100= 0.15
then you multiply the decimal and the price.
60×0.15= 9.
The question said it got cheaper so we have to subtract 9 from the original price.
60-9=51.
You made $25,000 last year and spend 20% of your money on food. How much money did you spend on food?
Answer:
$5,000 was spent on food.Step-by-step explanation:
To find:-
Money spent on food .Answer:-
We are here given that, out of the total money made 20% was spent on food .
To calculate the money spent on food we need to find out 20% of $25,00 .
So that,
==> 20% of $25,000
==> 20/100 * $25,000
==> 0.2 * $25,000
==> $5,000
Hence the total money spent on food was $5,000 .
find the equation of the straight line passinh throigh (3,5) and making x-intercept 3 times the y-intercept.
After answering the presented question, we can conclude that As a result, the equation of the straight line passing through (3,5) and having an x-intercept three times the y-intercept is: 5x - 9y = -42
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the value "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.
To find a straight line's equation, we must first establish its slope and y-intercept.
[tex](y - 5) = m(x - 3) (x - 3)\\b - 5 = -3m\\[/tex]
When we solve for b, we get:
[tex]b = -3m + 5\\5 - 5 = m(3 - 3) (3 - 3)\\0 - 5 = m(3b - 3) (3b - 3)\\-5 = 3bm - 3m\\[/tex]
When we simplify, we get:
[tex]m = 5/(9b) (9b)\\[/tex]
Substituting this expression for m in the equation for the y-intercept b results in:
[tex]b = -15/(9b) + 5\\9b^2 = -15b + 45b\\9b^2 - 30b = 0\\3b(3b - 10) = 0\\b = 10/3\\(y - 5) = m(x - 3) (x - 3)\\(y - 5) = 5x/(9*10) - 1/3\\9y - 45 = 5x - 3\\5x - 9y = -42\\[/tex]
As a result, the equation of the straight line passing through (3,5) and having an x-intercept three times the y-intercept is:
5x - 9y = -42
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Explain how to use what you know about whole number division to check your work when you divide with fractions, use at least three terms from the world word list in your explanation
using what we know about whole number division can be helpful when dividing with fractions. We can use the inverse operation of multiplication, simplify fractions, and use estimation to check our work and ensure that our division is accurate.
When dividing with fractions, one can use what they know about whole number division to check their work. This is because the rules of division remain the same for both whole numbers and fractions. One important rule is that division is the inverse operation of multiplication. In other words, when we divide, we are essentially finding how many times one number (the divisor) fits into another number (the dividend).
To check our work when dividing with fractions, we can use the same approach. We can multiply the quotient (the result of our division) by the divisor to see if we get back the dividend. If we do, then we know that our division was correct. For example, if we divide 3/4 by 1/2 and get a quotient of 3/2, we can check our work by multiplying 3/2 by 1/2.
Another important rule is that we can simplify fractions before dividing them to make the process easier. This means that we can divide both the numerator and the denominator by a common factor to get an equivalent fraction with smaller numbers. For example, if we want to divide 6/8 by 2/3, we can simplify 6/8 to 3/4 and 2/3 to 8/12. Then we can divide 3/4 by 8/12, which is much easier.
Finally, we can also use estimation to check our work when dividing with fractions. Estimation involves rounding the fractions to the nearest whole number or using benchmarks, such as 1/2 or 1, to get an approximate answer. This can help us quickly check if our quotient is reasonable or if we made an error in our division.
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