Answer:
1) 39
2) 13
3) 2
Step-by-step explanation:
1) She had 22 books, she now has 61 books, so she bought 61-22 = 39 books at the yard sale.
2) 143/11 = 13
3) 6-4 = 2
6 2/3 times 12 simplest form
Answer:
80
Step-by-step explanation:
[tex]6\frac{2}{3} *12[/tex]
First, write the fractions as improper fractions.
[tex]\sf\frac{20}{3} *\frac{12}{1}[/tex]
Multiply.
[tex]\sf\frac{240}{3}[/tex]
Divide.
80
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{6\dfrac{2}{3}\times 12}[/tex]
[tex]\mathsf{= \dfrac{6\times3+2}{3}\times\dfrac{12}{1}}[/tex]
[tex]\mathsf{= \dfrac{18 + 2}{3} \times\dfrac{12}{1}}[/tex]
[tex]\mathsf{= \dfrac{20}{3} \times\dfrac{12}{1}}[/tex]
[tex]\mathsf{= \dfrac{20\times12}{3\times1}}[/tex]
[tex]\mathsf{= \dfrac{240}{3}}[/tex]
[tex]\mathsf{= 240\div 3}[/tex]
[tex]\mathsf{= 80}[/tex]
[tex]\huge\text{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{80}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
What is the domain of the logarithmic function f/x )= LOGB X?
The domain of the given function would be x > 0.
What is a function?
In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.
The given function is f(x) = logb(x)
The domain of the logarithmic function [tex]f(x) = log_b(x)[/tex] is the set of all positive real numbers x such that x > 0. This is because the logarithm of a non-positive number is undefined.
Hence, the domain of the given function would be x > 0.
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The domain of the given function would be x > 0.
What is a function?
In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.
The given function is f(x) = logb(x)
The domain of the logarithmic function [tex]f(x)=log_b(x)[/tex] is the set of all positive real numbers x such that x > 0. This is because the logarithm of a non-positive number is undefined.
Hence, the domain of the given function would be x > 0.
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What is 200/51 equal to
Answer:
Approx 3.92
Step-by-step explanation:
A horizontal curve is being designed around a pond with a tangent length of 1200 ft and a central angle of 29.86 degrees. If the PI is at station 105 00, determine the station of PT
The station of PT is 12305.58 ft
The station of PT can be determined using the formula:
PT = PI + R * (central angle in radians)
To use this formula, we first need to convert the central angle from degrees to radians. We can do this by multiplying the central angle by (π/180)
Next, we need to determine the radius (R) of the curve. We can use the formula:
R = L / (central angle in radians)
Where L is the tangent length.
Finally, we can substitute the values into the formula for PT:
PT = 105 00 + (1200 / (29.86 * (π/180)))
PT = 105 00 + (1200 / (0.5236))
PT = 105 00 + 2295.58
PT = 12305.58
It's important to note that this calculation assumes that the degree of curvature is a circular curve and that the PI is at the tangent point of the curve.
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What are the factors of the expression 2x^2 5x 12?
[tex](x- (\frac{-5+71i }{4}))[/tex] and [tex](x- (\frac{-5-71i }{4}))[/tex] are factors of the quadratic expression.
2x^2 + 5x + 12
Consider given quadratic expression.
2x^2 + 5x + 12
Let f(x) = 2x^2 + 5x + 12
Assume f(x) = 0
2x^2 + 5x + 12 = 0
using the Quadratic Formula where
a = 2, b = 5, and c = 12
[tex]x = \frac{-b\pm \sqrt{b^2 - 4ac} }{2a} \\\\\\x = \frac{-5\pm \sqrt{5^2 - 4(2)(12)} }{2\times2} \\\\\\x = \frac{-5\pm \sqrt{25 - 96} }{4} \\\\\\x = \frac{-5\pm \sqrt{-71} }{4}[/tex]
The discriminant b^2 - 4ac < 0.
So, there are two complex roots.
[tex]x = \frac{-5\pm71i }{4}[/tex]
This means, [tex](x- (\frac{-5+71i }{4}))[/tex] and [tex](x- (\frac{-5-71i }{4}))[/tex] are factors.
2x^2 + 5x + 12
= [tex](x- (\frac{-5+71i }{4}))[/tex] × [tex](x- (\frac{-5-71i }{4}))[/tex]
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If sin 0<0 and cos0>0, then the terminal point determined by 0 is in :
Answer: The statement "if sin 0 < 0 and cos 0 > 0" is not true, as both the sine and cosine of an angle of 0 degrees are equal to 0. Therefore, the statement is not meaningful and the question cannot be answered.
It is important to note that sine, cosine, and all the trigonometric functions are defined in radians and not degrees and the value of sin(0) and cos(0) is not zero but 1
Please provide more context or specify what you are asking about in order to give a more accurate answer.
Step-by-step explanation:
How do you verify inverse?
To verify the inverse we can use Horizontal Line Test.
Suppose F is a function.
F does not have an inverse if any horizontal line crosses the graph of f more than once. If no horizontal line crosses the graph of F more than once, then F does have an inverse. In mathematics, having an inverse is a very significant quality, and it has a name.
If and only if a function f has an inverse, then it is one-to-one. The following definition, which is also the one that is most frequently used, is equivalent. If f(a) = f(b) implies a = b for all a and b in its domain, then a function f is one-to-one.
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The age of people waiting in line for a movie are given. Use the data to make a frequency table with intervals.
12, 27, 15, 31, 6, 45, 65, 55, 10, 49, 6, 8
The frequency table for the given data is shown above.
What is is frequency table?A table drawn up to show the distribution of the frequency of occurrence of a given characteristic according to some specified set of class intervals.
Given is the age of people waiting in line for a movie as -
12, 27, 15, 31, 6, 45, 65, 55, 10, 49, 6, 8
Arrange the data in ascending order -
6, 6, 8, 10, 12, 15, 27, 31, 45, 49, 55, 65
INTERVALS FREQUENCY
0 - 10 4
11 - 20 2
21 - 30 1
31 - 40 1
41 - 50 2
51 - 60 1
61 - 70 1
Therefore, the frequency table for the given data is shown above.
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How do you solve a 5 =- 5a 5?
The value of a is zero.
Now, According to the question:
The given equation is:
a + 5 = -5a + 5
To solve the above equation:
Subtract 5 on both sides
a + 5 - 5 = -5a + 5 - 5
a = -5a
Add 5a on both sides:
6a = 0
Divide both sides by 6
a = 0
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The complete question is this:
How do you solve a + 5 = -5a + 5
1. a room has dimensions 15m by 9m by 12m the dimensions of its
scale model is 5m by
3m by 4m what is the ratio of the dimensions of the actual room to that of the scale
model
2. the ratio of the dimensions of the scale model to that of the
actual object s 1:16 the length and width of the actual object are
2.4m and 1.8m respectively
Answer: To find the ratio of the dimensions of the actual room to that of the scale model, we can divide the dimensions of the actual room by the dimensions of the scale model.
The dimensions of the actual room are 15m by 9m by 12m, and the dimensions of the scale model are 5m by 3m by 4m.
Therefore, the ratio of the dimensions of the actual room to that of the scale model is:
length: 15m / 5m = 3 : 1
width: 9m / 3m = 3 : 1
height: 12m / 4m = 3 : 1
So, the ratio of the dimensions of the actual room to that of the scale model is 3:1 for all dimensions (length, width, and height)
The ratio of the dimensions of the scale model to that of the actual object is 1:16
so to find the length and width of the actual object, you can use this relation
length = scale model length * 16 = 2.416 = 38.4m
width = scale model width * 16 = 1.816 = 28.8m
So the length and width of the actual object are 38.4m and 28.8m respectively.
Step-by-step explanation:
A calculator cost 32.00 if the sales tax is 6% what is the price ?
Answer:
Step-by-step explanation:
Here is how to solve the given problem above.
Given that the calculator costs $32 and has a tax of 6%, what we are going to do is to find how much is 6% of 32. So 32 times 0.06 is 1.92. So, we add this amount to 32 dollars, and the total price would be 33.92 dollars. Hope this answer helps.
Answer:
33.92
Step-by-step explanation:
32 times 6 divided by 100 gives you 1.92, the sales tax,
add it to 32 and then you get 33.92
In 2010, the population of a city was 237,000. From 2010 to 2015, the population grew by 7.6%. From 2015 to 2020, it fell by 4.7%. To the nearest whole number, by what percent did the city grow from 2010 to 2020?
The population of the city grew from 2010 to 2020 by 13.37%.
What is percentage?A percentage is a number that tells us how much out of 100 and can also be written as a decimal or a fraction.
We have to given that;
In 2010, the population of a city was 237,000.
And, From 2010 to 2015, the population grew by 7.6%. From 2015 to 2020, it fell by 4.7%.
We know that;
Where, A = P (1+r)ⁿ
A = final population.
P = Initial population.
r = rate
n = time
Hence, The population in 2015 is, =
A = 237,000(1 + 0.076)⁵
A = 341829.629
And, The population in 2020 =
A = P (1 - r)ⁿ
A = 341829.629 (1 - 0.047)⁵
A = 268704.047
So, Percent grow = (268704.047 - 237,000) / 237,000 × 100
= 31704.047 / 237,000 × 100
= 13.37 %
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The graph of a proportional relationship contains the point (-12, 3)
What is the corresponding equation?
Enter your answer as a fraction in simplest form by filling In the boxes.
y= __/__ x
The corresponding equation of the proportional relationship will be;
⇒ y = - 1/4x
What is Proportional?Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
The graph of a proportional relationship contains the point (-12, 3).
Now,
Let the equation of the proportion is,
⇒ y = kx
Where, 'k' is constant of proportion.
Since, The graph of a proportional relationship contains the point (-12, 3).
Hence, Substitute x = 0 12 and y = 3 in above equation we get;
⇒ 3 = k × - 12
⇒ 3 / (-12) = k
⇒ k = - 1/4
Thus, The equation of the proportion is,
⇒ y = - 1/4x
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What is the example of quadrant 2?
The example of Quadrant 2 is (-1, 1)
The term quadrant in math is called as the coordinate plane is divided into four equal parts by the intersection of the x-axis such as the horizontal number line and the y-axis such as the vertical number line.
Here we have to give the example for quadrant 2.
In order to find the example, first we have to know the definition and properties of quadrant 2.
The quadrant 2 is placed on the upper left quadrant is the second quadrant, denoted as Quadrant II and the value of the x-axis has negative numbers and the value of y-axis has positive numbers.
Therefore, the resulting coordinate for Quadrant 2 is written as,
=> (-1, 1)
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The ratio of the number of model cars that jim owns to the number of model cars Terrence owns is 8:6. Terrence owns 36 model cars
Part A
How many model cars does Jim own?
___
Part B
How will the ratio change if Jim and Terrence each sell ten of their model cars?
O The new ratio would stay the same
O The new ratio would be 4:3
O The new ratio would be 23:29
O The new ratio would be 19:13
When Jim's model car ownership is compared to Terrence's model car ownership, the ratio is 8:6, Jim possesses 48 model vehicles.
what is equation ?An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, according to the definition given by the term in its most basic form. When two terms are placed on each side of an equal sign, a simple equation is used to show their relationship. The four mathematical operations of addition, subtraction, multiplication, and division may be used singly or in combination in simple equations.
given
You are aware that Jim and Terrence both own four model automobiles in comparison to three owned by Jim.
Let's assume that Jim owns Jim has the following number of model cars, then you can answer the task as follows:
4/3 = x/36
x = (4* 36)/ 3
x = 48
Therefore, Jims owns 48 model cars.
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Be so kind and help me please!
Answer:
2A/h - b2= b1
Step-by-step explanation:
The table below shows the number of animals at a local petting zoo.
Animal
Goats
Number
3
Ponies
3
Rabbits
8
Sheep
6
Write the ratio of ponies to sheep.
You may write the ratio in ANY of the three forms. Remember to REDUCE the ratio, if
possible.
Answer:
1/2
Step-by-step explanation:
You are comparing ponies to sheep, so you put the ponies on top(3)
and the sheep on the bottom(6)
3/6 reduces to 1/2
Marla is four years less than twice as old as Darla. If the sum of their age is 47, how old is Marla?
According to the given algebra Darla is 17 years old and Maria is 30 years old.
What algebraic fundamentals are there?Numbers, parameters, constants, expressions, equations, linear equations, and quadratic equations are all part of the fundamentals of algebra. Additionally, the algebraic expressions contain the fundamental arithmetic operations of addition, subtraction, multiplication, as well as division.
According to the given information.Maria is 4 years younger than Don,
thus if Don is x years old, then Maria is x years younger. (2x-4)
If their ages added together equal 47,
then x + (2x-4) = 47
Solving for x, then determining Maria's age (2x-4)
3x=47+4
3x=51
x=51/3
x=17 years
Maria's age=2*17-4=30 years
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. The length of one line segment is 9cm and the length of a parallel line segment is 3cm. What scale factor would you need to use to map the first line segment onto the second line
semgment?
O 9/3=3
O 9x3=27
O 3/9=0.33
O 9/9=1
Scale factor required to map the first line segment onto second line segment is 3/9=0.33
What is scale factor?The scale factor is the ratio of the length of the image to the length of the pre-image.
In this case, we're looking for the that would map the first line segment (length 9cm) onto the second line segment (length 3cm).
To find the scale factor, we can divide the length of the image by the length of the pre-image:
scale factor = length of image / length of pre-image
In this case:
[tex]ScaleFactor=\frac{Length Of Image}{Length Of Pre-image}[/tex]
[tex]scale factor = 3cm / 9cm = 1/3=0.033[/tex]
So the scale factor to map the first line segment onto the second line segment is 1/3.
It means the 1st line is 3 times longer than the second one.
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Number 7 says find the measure of the angle indicated I could fit the question in with it! If you could help!
The measure of angle E if The measure of angles is 2x + 13, 11x - 6 and 89°, is 37°.
What is the angle?An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles.
Given:
The measure of angles is 2x + 13, 11x - 6 and 89°,
Use the exterior angle theorem and find the value of x as shown below,
2x + 13 + 89 = 11x - 6
2x + 102 = 11x - 6
9x = 108
x = 12
Thus, the measure of ∠ E = 2 × 12 + 13
∠ E = 24 + 13
∠ E = 37°
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The temperature in knowlton is 2.5 C colder than the terminal elmwood. Which equation shows the temperature, in C, in knowlton? 9 - 2.5 = 6.5 or 9 + 2.5 = 11.5 or -9 - 2.5 = - 11.5 or -9 + 2.5 = -6.5
The equation representing the asked situation is (9 - 2.5) = 6.5
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that, The temperature in Knowlton is 2.5 C colder than the terminal Elmwood.
We know, that, if temperature is colder in any area A than another area B then, A will have less temperature than B.
Therefore, temperature in Knowlton is less than that of in Elmwood.
Therefore, if the temperature in Elmwood is 9 the temperature in Knowlton will be 9-2.5 = 6.5
Hence, the required equation is 9-2.5 = 6.5
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Write a ratio of the following in three ways.
Write your answers on the blanks.
1) 6 Weeks to 12 days_____
2) 10 decimeters to 10 centimeters_______
3) 4 days to 36 hours___
4) 4 months to 8 weeks___
5) 30 seconds to 6 minutes__
6) 24 girls to 16 boys___
7) 12 mangoes to 36 fruits__
8) 2. Years to 36 months__
9) 45 points to 9 games__
10) 468 students for 9 classrooms___
Ratios express the relationship between two or more quantities, they can be expressed in different forms such as 6:12, 42:12 and 3:1, 10:10, 100:10, and 10:1, 24:36 and 2:3.
1. 6 Weeks to 12 days:
6:12 (using the same unit of measurement, weeks)42:12 (converting weeks to days, 6 weeks x 7 days/week = 42 days)3:1 (simplifying the ratio to its simplest form)2. 10 decimeters to 10 centimetres:
10:10 (using the same unit of measurement, decimeters)100:10 (converting decimeters to centimeters, 10 decimeters x 10 centimeters/decimeter = 100 centimeters)10:1 (simplifying the ratio to its simplest form)3. 4 days to 36 hours:
4:36 (using the same unit of measurement, days)24:36 (converting days to hours, 4 days x 24 hours/day = 96 hours)2:3 (simplifying the ratio to its simplest form)4. 4 months to 8 weeks:
4:8 (using the same unit of measurement, months)16:8 (converting months to weeks, 4 months x 4 weeks/month = 16 weeks)2:1 (simplifying the ratio to its simplest form)5. 30 seconds to 6 minutes:
30:6 (using the same unit of measurement, seconds)180:6 (converting seconds to minutes, 30 seconds x 6 minutes/60 seconds = 0.5 minutes)30:1 (simplifying the ratio to its simplest form)6. 24 girls to 16 boys:
24:16 (using the same unit of measurement, girls and boys)3:2 (simplifying the ratio to its simplest form)7. 12 mangoes to 36 fruits:
12:36 (using the same unit of measurement, mangoes and fruits)1:3 (simplifying the ratio to its simplest form)8. 2 years to 36 months:
2:36 (using the same unit of measurement, years and months)6:36 (converting years to months, 2 years x 12 months/year = 24 months)1:6 (simplifying the ratio to its simplest form)9. 45 points to 9 games:
45:9 (using the same unit of measurement, points and games)5:1 (simplifying the ratio to its simplest form)10. 468 students for 9 classrooms:
468:9 (using the same unit of measurement, students and classrooms)52:1 (simplifying the ratio to its simplest form)To learn more about the ratio, visit:
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Estimate the area of the circle. Round to the nearest whole number. A) 3 square units B) 6 square units C) 9 square units D) 12 square units
The area of the circle is A. 3 square units
How to determine the area of the circleThe formula for determining the area of a circle is expressed as;
A = πr² or 1/4πd²
Given that;
A is the area of the circleπ takes the value 3.14 or 22/7r is the radius of the circled is the diameter of the circleAlso, the formula for calculating the radius of a circle is given as;
Radius = diameter/2
Substitute the value, we have;
Radius = 2/2
Radius = 1
Substitute the value into the formula
Area, A = 3. 14 × (1)²
Find the square
Area, A = 3. 14 square units
Hence, the value is 3 square units. Option A
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The complete question
Estimate the area of the circle, given the diameter as 2 unit. Round to the nearest whole number. A) 3 square units B) 6 square units C) 9 square units D) 12 square units
Sarah has 600 quarters and dimes in her piggy bank which totals $123. 75 how many quarters does she have? (Hit: use cent values for each coin- quarters are 25 cents, 0. 25)
The answer of Coin word problem is Sarah has 425 quarters.
What is a Coin word problem?There are often two different equation types in coin word problems. The total number of coins is described by one equation, while the total amount of money is described by the other equation. However, let's choose some variables that will represent the problem's unknown values before we begin creating our equations.
Word Problems, also known as story problems, can be found in both daily life and the Common Core State Standards for every school level,
Let q be the number of quarters and d be the number of dimes
Then we are doing as :
q + d = 600 → d = 600 - q (1)
0.25q + 0.10d = 123.75 (2)
Sub (1) into (2) for d
0.25q + 0.10 ( 600 - q) = 123.75
simplify,
0.25q + 60 -0.10q = 123.75
0.15q + 60 = 123.75 (subtract 60 from both sides)
0.15q = 63.75 ( divide both sides by 0.15)
q = 425
Therefore, she has 425 quarters
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What is the first month in which the board will see the cumulative total number of cars shipped to Japan exceeded the cumulative total in Vietnam
The cumulative total in Vietnam j(n) is 23(n-1),cumulative takes into account all data up to the present. In month four, j(n) will be worth more than v(n).
Is the sum the same as the total?The distinction between total and cumulative is that total refers to the entirety of something, whereas cumulative takes into account all data up to the present.
When a new number is added to a series of numbers, the running total is updated by adding the new number's value to the previous running total. Partially sum is another name for it. Running totals serve two distinct objectives.
We take it for granted that you mean that vehicles delivered to Vietnam should be modeled by v(n) = 5 + 11 and those sent to Japan by j(n) = 23(n-1).
In month four, j(n) will be worth more than v(n).
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What is adjacent angle Class 7?
In class 7, adjacent angles are defined as two angles that share a common vertex and a common side but do not have any common interior points. They are angles that are next to each other.
Adjacent angles are often used in geometry to describe the angles formed by intersecting lines or figures. The adjacent angles can be classified into two types, namely:
Interior adjacent angles: They are formed by two lines that intersect inside a closed figure, such as in a parallelogram.
Exterior adjacent angles: They are formed by two lines that intersect outside a closed figure, such as in a straight line.
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50% of 188 is equal to what number?
Answer:
Step-by-step explanation:
a.50%=[tex]\frac{1}{2}[/tex]
b.so 50% of 188 means 188·[tex]\frac{1}{2}[/tex]=94
answer is 94
Type the correct answer in the box.
The number of guests per month at a large resort is given in the table below, where f(x) is the number of guests, in hundreds, x months since the beginning of the year.
Use the data in the table to create the standard form of the function that models this situation, where a, b, and c are constants.
x 0 2 4 6 8 10
f(x) 10 15 18 19 18 15
f(x)=ax^2+bx+c
Answer:
It appears that you are trying to find a quadratic function in standard form that models the number of guests at the large resort as a function of the number of months since the beginning of the year.
To do this, you can use the given data points to solve for the constants a, b, and c in the standard form of the quadratic function f(x) = ax^2 + bx + c.
To find the values of a, b, and c, you will need to have at least three data points. You can then use these data points to solve a system of three equations with three variables.
For example, using the data points (0, 10), (2, 15), and (4, 18), you can set up the following system of equations:
f(0) = 10 = a(0)^2 + b(0) + c
f(2) = 15 = a(2)^2 + b(2) + c
f(4) = 18 = a(4)^2 + b(4) + c
Solving this system of equations will give you the values of a, b, and c that you can use to write the standard form of the quadratic function that models the data.
I hope this helps! Let me know if you have any questions or need further assistance.
Step-by-step explanation:
a) A train travels from City A to City B. The table below shows the distance and
the amount of time it takes on the train.
Distance (km)
Time (in minutes)
9
3
15 21
5 7
OThe train does not always go the same distance each minute.
OThe train appears to go the same distance each minute.
Predicted distance traveled in 8 minutes: km
Answer:
Step-by-step explanation:
from the figure we kown the speed is 9/3=15/5=21/7=3 km per minute
the distance in 8 minute is 3 ×8=24 km
The rectangular floor of a classroom is 30 feet in length and 36 feet in width. A scale drawing of the floor has a length of 5 inches. What is the area, in square inches, of the floor in the scale drawing?
HURRYYYYYYYYYYYYYY
Answer:
30 in.²
Step-by-step explanation:
Real:
length 30 ft
width 36 ft
Scale:
length 5 in.
width ?
30/36 = 5/x
30x = 5 × 36
x = 6
The scale width is 6 inches.
Scale area:
area = length × width
area = 5 in. × 6 in.
area = 30 in.²
The area, of the floor in the scale drawing is 30 in.²
What is the unitary method?The area is the total amount of space that an object's shape or a flat (2-D) surface occupies.
Given that rectangular floor of a classroom is 30 feet in length and 36 feet in width. A scale drawing of the floor has a length of 5 inches.
length 30 ft
width 36 ft
Scale: length 5 in.
Then we have
30/36 = 5/x
30x = 5 × 36
x = 6
The scale width is 6 inches.
Scale area:
The area = length × width
area = 5 in. × 6 in.
area = 30 in.²
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