Answers
The correct sentence to describe in the parent function is,
⇒ Shifted up.
⇒ Horizontal stretch
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
We have to given that;
The function is,
⇒ f (x) = x
Here, The graph of the parent function of f (x) = x is shown in figure.
Hence, We get;
The correct sentence to describe in the parent function is,
⇒ Shifted up.
⇒ Horizontal stretch
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Related Questions
(05.01 MC)
Currently, the temperature of an ice cream is 81°C below room temperature. The temperature of the ice cream decreases based on the
function f(t)=81(0.83) where t represents time elapsed in minutes. Where does the graph of f(t) cross the y-axis, and what does this represent
in the context of the problem?
Answers
The graph of f(t) crosses the y-axis at t = 0, which represents the initial temperature of the ice cream (81°C below room temperature).
What does this represent in the context of the problem?The graph of f(t) crosses the y-axis at y=81, which represents the initial temperature of the ice cream, 81°C below room temperature. This is the starting point of the graph, and all subsequent points on the graph represent the temperature of the ice cream as time progresses. As time passes, the temperature of the ice cream decreases, and the graph of f(t) illustrates this change.
The y-intercept of a graph measures the initial value of the function. In this case, the initial temperature of the ice cream is 81°C below room temperature. As the time passes, the temperature of the ice cream decreases at a rate of 0.83°C per minute. This rate of decrease is represented by the slope of the graph, which is 0.83.
The point where the graph of f(t) crosses the y-axis illustrates the initial temperature of the ice cream, and all subsequent points on the graph represent the temperature of the ice cream as time progresses. This is a helpful visual representation of the rate at which the temperature of the ice cream is decreasing. The graph of f(t) is a useful tool for understanding how the temperature of the ice cream changes over time.
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The nature of the roots for the equation
Answers
If D > 0 and not an excellent square, then the roots of the quadratic equation are real, unequal and irrational.
What is Quadratic Equation ?
Quadratic equation can be defined as equation in which it is in the form of ax^2+bx+c = 0 .
Nature of Roots depending upon Discriminant
in step with the value of discriminant, we shall discuss the subsequent cases about the character of roots.
Case 1: D = 0
If the discriminant is same to 0 (b2 – 4ac = zero), a, b, c are real numbers, a≠0, then the roots of the quadratic equation ax2 + bx + c = zero, are real and equal. In this case, the roots are x = -b/2a. The graph of the equation touches the X axis at a single point.
Case 2: D > 0
If the discriminant is greater than zero (b2 – 4ac > 0), a, b, c are actual numbers, a≠0, then the roots of the quadratic equation ax2 + bx + c = 0, are actual and unequal. The graph of the equation touches the X-axis at two unique points.
Case 3: D < 0
If the discriminant is less than 0 (b2 – 4ac < 0), a, b, c are real numbers, a≠0, then the roots of the quadratic equation ax2 + bx + c = 0, are imaginary and unequal. The roots exist in conjugate pairs. The graph of the equation does not touch the X-axis.
Case 4: D > zero and perfect square
If D > zero and an excellent square, then the roots of the quadratic equation are actual, unequal and rational.
Case five: D > 0 and now not an excellent square
If D > 0 and not an excellent square, then the roots of the quadratic equation are real, unequal and irrational.
Therefore, If D > 0 and not an excellent square, then the roots of the quadratic equation are real, unequal and irrational.
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Function rule or explanation of why it is not possible to find a function rule
Answers
b. Function
c. Not a function
d. Function
It’s easy to tell if a graph or a data table is a function or not. For a graph, use the vertical line test. Simple draw or imagine a vertical line straight down from the top to the bottom of the graph. The vertical line can only touch the line on the graph once, anything more than once will fail it as a function. So like circles will fail the vertical line test, and therefore, is not a function. You also have to go through the whole graph, left to right, with the vertical line test.
For data tables, look out for x values. In one table, the same x value cannot happen more than once. If you see two same x values, it is not a function, if not, it is. So as you see in the third one, there are duplicates of -100, -25, and -4. Whereas in others, there are no duplicate x values.
A new long-life tire has a tread depth of 3/8 inches, instead of the more typical 7/32 inches. How much deeper is the new tire?
Answers
Using the subtraction operation, the new long-life tire with 3/8 inches depth is deeper than the more typical 7/32 inches by 5/32 inches.
What is a subtraction operation?Subtraction operations involve the minuend, the subtrahend, and the result called the difference.
It is one of the four basic mathematical operations, including addition, multiplication, and division.
The depth of the new long-life tire = 3/8 inches
The depth of the old tire = 7/32 inches
The difference = 5/32 inches (3/8 - 7/32)
Thus, the depth difference between the new long-life tire and the typical tire is 5/8 inches.
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Gary used to make bottles of glitter glue.
Bottles Glue Glitter
1 3.8 1.9
4
How much glue and glitter would he need to make 4 bottles?
Gary would need 15.2 oz glue and 3.8 oz of glitter to make 4 bottles.
Gary would need 6.8 oz glue and 4.9 oz of glitter to make 4 bottles.
Gary would need 7.8 oz glue and 5.9 oz of glitter to make 4 bottles.
Gary would need 15.2 oz glue and 7.6 oz of glitter to make 4 bottles.
Answers
Gary would need 15.2 oz. of glue and 7.6 oz. of glitter to make 4 bottles.
The correct option is D.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
Given in the table,
Bottles Glue Glitter
1 3.8 1.9
Therefore
1 bottle = 3.8 oz. of glue + 1.9 oz. of glitter
Now,
Multiply 4 on both sides.
4 bottle = 4 x (3.8 oz. of glue + 1.9 oz. of glitter)
4 bottle = 15.2 oz. of glue + 7.6 oz. of glitter
Hence, 15.2 oz. of glue and 7.6 oz. of glitter is needed to make 4 bottles.
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the diagonals of a trapezoid are perpendicular and have lengths $3$ and $4$. find the length of the median of the trapezoid.
Answers
The correct answer is 5/2. The median trapezoid is the line segment that bisects the area of the trapezoid and has its end points on the 2 bases of the trapezoid.
The median length is √( (3/2)^2 + (4/2)^2 ) = √(9/4 + 16/4) = √(25/4) = 5/2. So, the length of the median of the trapezoid is 5/2.
Since the diagonals of a median trapezoid bisect each other, the median of the trapezoid is the line segment that connects the midpoints of the diagonals. To find the median length, we can use the distance formula, which is the square root of the sum of the squares of the differences in the x-coordinates and y-coordinates of the 2 points. In this case, the median length is the square root of the sum of the squares of 1/2 length of the diagonals.
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The length of the median of the trapezoid will be 5/2 units.
Given that the median trapezoid is the line segment that divides the trapezoid's area and has its ends on its two bases,
The median length will be:
√( (3/2)^2 + (4/2)^2 )
= √(9/4 + 16/4)
= √(25/4)
= 5/ units
So, the length of the median of the trapezoid is 5/2.
The median of a median trapezoid is the line segment that links the midpoints of the diagonals since the diagonals of a median trapezoid bisect one another. We may use the distance formula, which is the square root of the sum of the squares of the differences in the x-coordinates and y-coordinates of the two points, to get the length of the median. The median length in this instance is equal to the square root of the sum of the squares of the diagonals' half-lengths.
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Can someone please help me with this asap? I’ll give lots of points
A right triangle has 1 angle that measures 48 degrees. What is the measure of the third angle?
A: 64 degrees
B: 28 degrees
C: 42 degrees
D: 58 degrees
Answers
Step-by-step explanation:
always remember : the sum of all angles in a triangle is 180°.
so, one angle is 90° (it is a right triangle).
the second angle is 48°.
therefore,
180 = 90 + 48 + third angle
third angle = 180 - 90 - 48 = 42°
so, C is correct.
Find the 67th term of the arithmetic sequence -17,-23,-29
Answers
The 67th term of the arithmetic sequence -17,-23,-29 is -413.
What is the arithmetic sequence?
An arithmetic sequence is a sequence of numbers such that the difference between any two consecutive terms is always the same. This difference is called the common difference, and it can be represented by the variable d.
Given the sequence -17,-23,-29, we can see that the common difference is d = -23 - (-17) = -6
The nth term of an arithmetic sequence can be found using the formula:
a_n = a_1 + (n-1)d
where a_1 is the first term of the sequence, n is the term number and d is a common difference.
For the 67th term, a_1 = -17, n = 67 and d = -6
So the 67th term is:
a_67 = -17 + (67-1) * -6 = -17 + 66 * -6 = -17 - 396 = -413
Hence, the 67th term of the arithmetic sequence -17,-23,-29 is -413.
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Answer: -413
Step-by-step explanation:
5. Suppose the following table shows the number of labor hours needed to produce airplanes and automobiles in the United States and South Korea, but one of the numbers is unknown.
Number of Hours to Produce One Airplane
South Korea 2000 United States 1000
Number of Hours to Produce One Auto
?
10
a. Without knowing the number of labor hours required to produce an auto in South Korea, you can’t figure out which country has the comparative advantage in which good. Can you give an example of a number for the empty cell of the table that would give the United States the comparative advantage in the production of airplanes? What about South Korea?
b. What exact number would you have to place in the empty cell of the table for it to be impossible that trade between the United States and South Korea could benefit both
Answers
The number for an empty cell would be 20 so any number below this benefit South Korea and above this benefit the United States. This also makes it impossible for trade between these two countries.
If a country can manufacture a significant number of goods with the same resources as another country, it has an absolute advantage. If a country can manufacture a certain commodity more cheaply and with higher quality than another country, it has a comparative advantage.
In the given scenario, 1000÷10=100 autos are sacrificed by the United States to manufacture one airplane which is the opportunity cost. In comparison to the United States, South Korea requires twice (2000÷1000) as long to construct an airplane.
a) The number of hours for South Korea to produce one auto would be 2×10=20. Because of this, South Korea would benefit from any number below 20, while the US would benefit from any number above 20.
b) The empty cell value would be 20 for South Korea to have the same opportunity cost as the United States. So mutually beneficial trade cannot exist without comparative advantage.
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Write an equation for the secant line of the function Y =X^4 on the interval [1,2]
Answers
The equation of a secant line given two points (a, b) and (c, d) is y - b = [(d - b)/(c - a)] (x - a).
How do you find the equation of a secant line over an interval?The Latin word secant, which means to cut, is used in mathematics to define a line that passes through the points P and Q of any arbitrary curve whose equation is y=f(x).
Slope is the term used to describe when one end or side of a surface is higher than the other. A Secant line is a straight line that connects two points on a function. formula for secant line slope.
A secant line's slope through two points is equal to y 2 y 1 x 2 x 1. On the secant line, locate two spots.Discover the line's slope between the two spots.To get the line's equation, enter one of your points and your slope into the point slope form of your line.
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Which is the approximate percentage of total pay that fringe benefits make up?
O
O
4%
10%
15%
30%
O
Answers
The approximate percentage of total pay that fringe benefits make up is 10%
The term called percentage in math is defined as a number or ratio that can be expressed as a fraction of 100
Here we have to find the approximate percentage of total pay that fringe benefits make up.
As the total compensation offered to the workers or employees by employers in different countries can usually be bifurcated into two broad components.
Here we have to know that the first one is based on wages & salaries components and the second one is the fringe benefits component.
Here this one includes the benefits components usually consist of supplementary benefits such as gratuity, pension contribution, transportation service, accommodation facility, etc.
Here as per the report published by the Bureau of Labor Statistics, U.S. Department of Labor in 2020 said that the approximate of the total pay that the fringe benefits make up usually range from 26.1% - 37.3%.
Based on that the percentage of fringe benefits could vary from the type of industry such as the goods-producing industry or service-providing industry.
So, the increased percentage is calculated as
=> 37.3 - 26.1
=> 11.2
Therefore, the correct option is (b).
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find -|-2/5|?
-2.5
2.5
2/5
-2/5
Answers
Answer:
(2/5)
Step-by-step explanation:
(-2/5) = -(2/5)
|-(2/5)| = (2/5)
The relationship between time in months and height in inches for Kylie's plant is represented by the
equation y = 12x. The relationship for Glen's plant is represented by the equation 2y = 24x. Is there a
time when the two plants are the same height?
Answers
Both equations are equivalent, which means that the two plants always have the same height.
Is there a time when the two plants are the same height?We know that the height in inches for Kylie's plant is represented by the
equation y = 12x, where x is the time in months.
And the height of Glen's plant is represented by the equation 2y = 24x
Notice that if we take the second equation and we divide both sides by 2, we will get:
2y = 24x
2y/2 = 24x/2
y = 12x
This is the same equation than the one that represents the height of Kylie's plant.
Then the two plantes have the same height always.
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Each kit to build a castle contains 235 parts.
How many parts are
in 4 of the kits?
Answers
what is the value of the expression below? (15^1/5)^5
Answers
Answer:
15
Step-by-step explanation:
Given the expression:
[tex]\displaystyle{\left(15^{\frac{1}{5}}\right)^5}[/tex]
We can apply the law of exponent of:
[tex]\displaystyle{\left(a^m\right)^n = a^{mn}}[/tex]
Therefore, we will have:
[tex]\displaystyle{\left(15^{\frac{1}{5}}\right)^5 = 15^{\frac{5}{5}}}\\\\\displaystyle{\left(15^{\frac{1}{5}}\right)^5 = 15^{1}}\\\\\displaystyle{\left(15^{\frac{1}{5}}\right)^5 = 15}[/tex]
Hence, the value of expression is 15.
Write the decimal as a fraction. 0.83 = F 10 x 0.83 = F x 10 8.33= [?]F
Answers
The decimal 8. 33 written as a fraction is 8 3/10
What is a fraction?
A fraction can be defined as the part of a whole number, variable, element,
The several types of fractions are;
Proper fractionsMixed fractionsImproper fractionsSimple fractionsComplex fractionsExamples of mixed fractions: 2 4/5, 7 1/2
Examples of simple fractions: 1/3, 1/4
Examples of improper fractions: 6/4, 7/5
Example of proper fractions: 2/3, 4/5
From the information given, we have that;
8.33
This is represented as;
8 3/10
Hence. the value is 8 3/10
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The ratio of the perimeter of a square piece of paper to the perimeter of a rectangular piece of paper is 2 : 5. Each side of the square piece of paper is 10cm. Find A. The perimeter of the square piece of paper B. The perimeter of the rectangular piece of paper C. The length of the rectangular piece of paper if its width is 15cm ( Please answer all parts!)
Answers
The perimeter of the square piece of paper is 40 cm .The perimeter of the rectangular piece of paper is 50 cm and the length of the rectangular piece of paper is 15 cm.
A. The perimeter of the square piece of paper is 40 cm.
This is calculated by multiplying the length of each side of the square by 4.
Length of each side = 10cm
Perimeter of square = 4 x 10 cm = 40 cm
B. The perimeter of the rectangular piece of paper is 50 cm.
This is calculated by multiplying the length and width of the rectangle by 2.
Length = 15 cm
Width = 15 cm
Perimeter of rectangle = 2 x (15 + 15) cm = 2 x 30 cm = 50 cm
C. The length of the rectangular piece of paper is 15 cm.
This is given in the question.
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how to simplify 8(1+5x)
Answers
Answer:
0.2
Step-by-step explanation:
1. distribute 8 to 1 and 5
2. Now its 8+40x
3. Divide on both sides
4. 40x/40 cancels out
5. 8/40=0.2
Zahra invested $8,800 in an account paying an interest rate of 8 5/8% compounded annually. Christopher invested $8,800 in an account paying an interest rate of 8 1/4% compounded daily. After 11 years, how much more money would Zahra have in her account than Christopher, to the nearest dollar?
Answers
After 11 years, the amount (future value) in Zahra's account will be $58 more than the amount in Christopher's.
How the future value is determined?The future value can be determined by using the FV table or formula.
We can also ascertain the future value using an online finance calculator as follows:
Zahra's Investment:N (# of periods) = 11 years
I/Y (Interest per year) = 8.625%
PV (Present Value) = $8,800
PMT (Periodic Payment) = $0
Results:
Future Value (FV) = $21,863.03
Total Interest = $13,063.03
Christopher's Investment:N (# of periods) = 4015 days (11 years x 365)
I/Y (Interest per year) = 8.25%
PV (Present Value) = $8,800
PMT (Periodic Payment) = $0
Results:
Future Value (FV) = $21,805.22
Total Interest = $13,005.22
Future Values:Zahra's = $21,863.03
Christopher's = $21,805.22
Difference = $57.81 ($21,863.03 - $21,805.22)
Thus, with a slightly higher interest rate, Zahra's account will generate $58 more in future value than Christopher's investment.
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You are selling tickets for a high school play. Student
tickets cost $4 and general admission tickets cost $6.
You sell 31 tickets and collect $170. How many of each
type did you sell?
Answers
Answer:
sold 23 Tickets and 8 General Admission Tickets
Step-by-step explanation:
y = General Admission tickets
x = tickets
4x + 6y = 170
x + y = 31
Use the Substitution method:
4x + 6(31 - x) = 170
4x + 186 - 6x = 170
4x - 6x = -16
-2x = -16
x = 8
y = 31 - 8 = 23
students who successfully complete a study skills workshop will raise their grade point average by 0.2 points is best described as a
Answers
Students who successfully complete a study skills workshop will raise their grade point average by 0.2 points is best described as a hypothesis.
A hypothesis is a proposed explanation or prediction about a phenomenon, based on limited information or data. It is a tentative statement about the relationship between variables that can be tested through further investigation or experimentation.
In scientific research, a hypothesis provides a framework for designing and conducting experiments to gather evidence to support or reject the hypothesis. It acts as a starting point for scientific inquiry and helps guide the research process.
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Find the average rate of change for the given function from x = −1 to x = 2
Answers
The average rate of change for the given function from x = −1 to x = 2 is -4/3
How to find the average rate of change for the given function from x = −1 to x = 2?The average rate of change of a function over an interval is a measure of how much the output of the function (y-value) changes as the input (x-value) changes over that interval. This is also the slope of the function or line.
average rate of change = (y2-y1)/(x2-x1)
From the graph, x1 = -1, y1 = 4 and x2 = 2, y2 = 0
average rate of change = (0-4)/(2-(-1)) = -4/3
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Convert 9 days into weeks. Round your answer to the nearest hundredth.
Answers
This is because we know that in one week, it’s 7 days. However to find out the amount of weeks in 9 days, we have to divide it by 7. This is because 7 days is the unit rate for a week!
When we divide 9 by 7, we would get 1.28571429…
Just round it to the nearest hundredths, which would be 1.29 weeks. Hence the answer is 1.29 weeks.
Hoped this helped! Any questions please comment. Thanks!
the preference card calls for 0.25% marcaine and 1% lidocaine to be equally concentrated. how much marcaine will you need to draw up to equal the 1% l
Answers
4.0 mL of marcaine will be needed to draw up to equal the 1%.
Marcaine is a brand name for the medication bupivacaine, which is a local anesthetic used to numb a specific area of the body during a surgical or medical procedure.
To determine the amount of marcaine that is needed to be drawn up to equal the 1% lidocaine, we can use the following formula:
(Concentration of Lidocaine) / (Concentration of Marcaine) = (Volume of Lidocaine) / (Volume of Marcaine)
In this case, we know that the concentration of lidocaine is 1% and the concentration of marcaine is 0.25%. So we can plug these values into the formula:
1 / 0.25 = (Volume of Lidocaine) / (Volume of Marcaine)
To solve for the volume of marcaine, we can multiply both sides of the equation by the volume of lidocaine:
(Volume of Lidocaine) / (Volume of Marcaine) = 4
Therefore, 4.0 mL of marcaine will be needed to draw up to equal the 1%.
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The cost of a bicycle wheel was $62 last week. This week, the cost rose to $79 . Find the percentage increase. Round your answer to the nearest tenth of a percent.
Answers
Answer:
the percentage increase is 27.4%
Step-by-step explanation:
To find the percentage increase, we can use the formula:
(New cost - Old cost) / Old cost x 100% = Percentage increase
(79 - 62) / 62 x 100% = 27.41%
The percentage increase is 27.41%. Rounded to the nearest tenth of a percent, the percentage increase is 27.4%
Difference of $62 and $79 is 24.1%
62 - 79/((62 + 79)/2) = 17/70.5 =
0.24113475177305 x 100 = 24.113475177305%
The average birth weight of a Boxer breed dog is 1.25 kilograms. What is the average birth weight in grams?The average birth weight of a Boxer breed dog is 1.25 kilograms. What is the average birth weight in grams?
Answers
Answer:
1250g
Step-by-step explanation:
1.25 kg × 1000 = 1250g
Find the volume of the solid obtained by rotating the region bounded by y=x2 , y=0, and x=1, about the y-axis.
Answers
The volume of the solid obtained by rotating the region bounded by y = x^2, y = 0 and x = 1, about the y-axis is π/2.
We have to determine the volume of the solid obtained by rotating the region bounded by y = x^2, y = 0 and x = 1, about the y-axis.
We will rotate the region near the y-axis using the disc method. Consequently, the curve's equation should be expressed in terms of y.
y = x^2
Taking square root on both side, we get
x = √y
We can write it as
x = y^{1/2}
The volume integral formula is
V = [tex]\pi\int_{a}^{b}R(x)^2dx[/tex]
The values of a and b are taken from the y-axis since the equation for the curve we need is expressed in terms of y.
Using the curve's equation, if x = 0, y = 0, and if x = 1, y = 1, respectively.
Thus, a = 0 and b = 1 are the values.
Now, we may use definite integral to express the volume.
V = [tex]\pi\int_{0}^{1}\left[y^{1/2}\right]^2dx[/tex]
Now simplify
V = [tex]\pi\int_{0}^{1}ydx[/tex]
Now integrating
V = [tex]\pi\left[\frac{y^2}{2}\right]_{0}^{1}[/tex]
V = [tex]\pi\left[\frac{(1)^2}{2}-\frac{(0)^2}{2}\right][/tex]
V = [tex]\pi\left[\frac{1}{2}-0}\right][/tex]
V = π/2
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-2(c+2.5)-5(1.2c+4) simplify this expression
Answers
Answer: - 8c - 25
Step-by-step explanation:
Remove any grouping symbol such as brackets and parentheses by multiplying factors.Use the exponent rule to remove grouping if the terms are containing exponents.Combine the like terms by addition or subtraction.Combine the constants.
Find the slope of the line through (-2,6) and (-5,9)
Answers
-1
Step-by-step explanation:Slope describes the rise over run for a graph.
Slope Formula
Slope is the change in y over the change in x. To find the slope of any line from two points we can use the slope formula. The slope formula is [tex]\displaystyle\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]. We can plug the points we are given into this formula.
[tex]\frac{9-6}{-5-(-2)}[/tex]This equals [tex]\frac{3}{-3}[/tex] which is simply -1. The slope of the line is -1.
Counting the Change
The formula above just represents the changes in the y-values divided by the changes in the x-values. So, we can count that the y-values increase by 3. Then, the x-values decrease by 3. This creates the slope [tex]\frac{3}{-3}[/tex] (remember that increases are positive and decreases are negative). Once again this gives the slope of -1.
3. I have two maps. One is of the Catskill mountains. The scale is 1.5 inches : 4 miles.
The other is of the Shawangunk mountains. The scale is 2 inches : 3.5 miles.
a) Find the distance of Slide mountain in the Catskills if on the map the trail is 2.325 inches.
b) Find the distance of Gertrude's nose in the Shawangunk's is 3.8 inches on the map.
Answers
a) Distance of Slide mountain in the Catskills is 6.2 miles
b) Distance of Gertrude's nose in the Shawangunk's = 6.65 miles
How to find a distance?To find a distance on a map, you need to use a ruler or a measuring device such as a pair of compasses. Firstly, place the ruler on the two points you want to measure the distance between. If you are using a pair of compasses, adjust the legs so that the two points are inside the circle created by the compasses. Then, read the distance on the ruler or across the arc of the compasses.
If the distance is relatively short, you can also use the map scale located at the side or bottom of the map. To use the scale, line up the starting point with the scale and then measure the length of the line on the scale. This will give you the distance between the two points.
Finally, if the map has a grid system, you can count the number of squares between the two points and then refer to the grid scale to calculate the distance.
By using one of the methods described above, you should be able to easily measure distances on a map.
a) 2.325 inches * 4 miles/1.5 inches = 6.2 miles
b) 3.8 inches * 3.5 miles/2 inches = 6.65 miles
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