Answer:
3(x + 2) and 3x + 6 are equivalent expressions because the value of both the expressions remains the same for any value of x. 3x + 6 = 3 × 4 + 6 = 18.
pls mark as brainliest
The perimeter of a rectangle is 84 feet long. The
length is six more than two times its width. What are
the dimensions of the rectangle? (Hint: P = 2L + 2W)
Therefore , the solution of the given problem of perimeter comes out to be length = 16.8 and width = 50.4
Establish a perimeter.The perimeter, or total length, of a shape is referred to as its perimeter in geometry. A shape's perimeter is calculated by summing the lengths of all of its sides and edges. By adding together the lengths of all a shape's sides, one may determine its perimeter. The circumference of a field, for instance, will be 78 yards for a rectangle with dimensions of 24 yards long by 15 yards wide.
Here,
Given :
Perimeter of rectangle = 84 feet
Thus,
Length is 6 times more than its 2 time width
=> 6L = 2W
=> W = 3L
In the perimeter formula:
=> 3L + 2L =84
=> 5L = 84
=>L = 84/5
=>16.8
and
W = 3L
=> W = 3*16.8
=> W = 50.4
Therefore , the solution of the given problem of perimeter comes out to be length = 16.8 and width = 50.4
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How do you find the value of 3 7?
The temperature of the water in a hot water tank is recorded at 15 minute intervals after the heater is switched on. \begin{matrix} \text{Time (x minutes)} & \text{15} & \text{30} & \text{45} & \text{60} & \text{75} & \text{90}\\ \text{Temperature} (y ^\circ C) & \text{20} & \text{30} & \text{40} & \text{50} & \text{60} & \text{70}\\ \end{matrix} Time (x minutes) Temperature(y ∘ C) 15 20 30 30 45 40 60 50 75 60 90 70 a. Plot a graph of these data on your GDC. b. Find the linear model, T(x), for the temperature of the liquid with respect to time. c. Find the temperature of the water after 85 minutes.
Answer: a. Plotting a graph of the data on a graph paper, you can represent the time on the x-axis and the temperature on the y-axis. And plot the given points (15,20), (30,30), (45,40), (60,50), (75,60), (90,70) as ordered pairs on the graph. This will give you a line graph, showing the temperature increasing over time.
b. To find the linear model, T(x), for the temperature of the liquid with respect to time, you can use the slope-intercept form, y = mx + b, where y is the temperature, x is the time, m is the slope and b is the y-intercept. Using two of the given points, you can find the slope of the line by calculating the change in y over the change in x,
m = (y2 - y1) / (x2 - x1).
where x1,y1 and x2,y2 are two distinct points on the graph.
Once you have the slope, you can use one of the points to find the y-intercept, by substituting the point's coordinates into the slope-intercept form equation and solving for b.
Once you have the slope and y-intercept, you can write the linear model as T(x) = mx + b
c. To find the temperature of the water after 85 minutes, you can substitute the value of x = 85 into the linear model equation that you found in the previous step to get the corresponding value of y (temperature).
Please keep in mind that the temperature and time value here are random and are not based on any real-life scenario, and they were provided to show you the concept of linear model.
Step-by-step explanation:
A cookery course is divided into two groups. In group X, the average score in the test was 76. In group Y, the average score in the test was 70. If the average score of all 30 trainees in the course was 74, how many trainees are in group X
On solving the provided question, we can say that by equation 8 trainees are in group X
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
Let a be the number of trainees in group X
76*a + 70 (30 - a) = 30*74
76a + 2,100 - 70a = 2,220
6a = 120
a = 20
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4. The table gives the height and shoe sizes of six randomly selected men.
Height 67 70 73. 5 75 78 66
Shoe size 8. 5 9. 5 11 12 13 8 CO
a. What is the equation of line of best fit: 4= 42x-19. 81
b. What is the slope, and what does it mean in this problem?
C. What is the y intercept? What does it mean in this problem?
d. Using the equation of the line of best fit, if a man has a shoe size of 10. 5, what would be his predicted height?
The predicted height if the man with shoe-size 10 is 427.09 cm.
We get the answers using the following steps.
a. The equation of the line of best fit is: y = 42x - 19.81
b. The slope, 42, represents the rate of change of the height variable with respect to the shoe size variable. It means that for every 1-unit increase in shoe size, we can expect a 42-unit increase in height.
c. The y-intercept, -19.81, is the point where the line of best fit crosses the y-axis. It represents the height when the shoe size is 0. It means that if a man has 0 shoe size, his height would be -19.81, both of which is impossible.
d. To predict the height of a man with a shoe size of 10.5, we substitute x = 10.5 into the equation of the line of best fit:
y = 42x - 19.81
y = 42(10.5) - 19.81
y = 447.9 - 19.81
y = 427.09
So, a man with a shoe size of 10.5 would have a predicted height of 427.09 cm
It's worth noting that this is just a predicted value and it might not be accurate. The line of best fit is calculated based on the given data set, it might not be accurate for other data points.
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March Madness Movies served 2323 lemonades out of a total of 111111 fountain drinks last weekend. Based on this data, what is a reasonable estimate of the probability that the next fountain drink ordered is a lemonade?
23/111 is a reasonable estimate of the probability that the next fountain drink ordered is a lemonade.
What do you mean by Probability?Probability theory deals with numerical evaluations of the likelihood that an event will occur.
Probabilities are mathematical explanations of the likelihood that an event will occur or that a proposition is true. The likelihood of an event is represented by a number between 0 and 1, with 0 typically signifying impossibility and 1 typically signifying certainty.
A probability represents the likelihood or chance that a particular occurrence will take place. Probabilities can be expressed as ratios between 0 and 1, or as percentages between 0% and 100%.
March Madness Movies served 23 lemonades out of a total of 111 fountain drink last weekend.
The probability that the a fountain drink ordered is a lemonade will be :-
P= [tex]\frac{Number of lemonade}{Total fountain drink}[/tex]
= 23/111
Based on this data, the reasonable estimate of the probability that the next fountain drink ordered is a lemonade = 23/111.
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Determine the missing angle measure.
Answer:
Step-by-step explanation:
Since you already know that one of the angles is 21 degrees, this helps you A LOT. In total the line is 180 degrees so to find x you just do 180-21 which equals 159
x+ 159 degrees
Which planes contain point W? Select all that apply.
Multiple select question.
cross out
A)
plane B
cross out
B)
plane VWY
cross out
C)
plane VWX
cross out
D)
plane m
cross out
E)
plane RYV
cross out
F)
plane VWZ
The planes that contain point W from the given image are;
Plane V
Plane VWY
Plane RYV
How to identify planes?A coordinate plane is a graphing and description system for points and lines. A vertical y-axis and a horizontal x-axis make up the coordinate plane.
From the attached image, we see that the planes whose name contains V also contains W.
The plane B contains the line XR and the Line YV as well as the W at the line YV.
Finally, the plane m also contains line YV and obviously the same as plane RYU.
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10. The Fort Worth Zoo has a number of two-legged birds and a number of four-legged mammals. On one visit to the zoo, Margie counted 200 heads and 522 legs. How many of the animals that Margie counted were two-legged birds
The stated statement states that 139 of said animals Margie counted had two legs, mostly two-legged birds.
Why do you use the word "number"?An arithmetic value used to compute and portray a quantity would be a number. In writing, numerical symbols like "3" are used to represent numbers. A decoder is a logical approach the portray a number using digits or symbols.
Assume that there are x two-legged birds and y four-legged animals. Now, we can employ equation systems to find a solution to this issue.
Enter two equations here:
2x + 4y = 522
x + y = 200
Add two to the latter equation now.
2x + 4y = 522
2x + 2y = 400
We discover that; by deducting the following equations from the first equation.
2y = 122
y = 61
There were 139 two-legged birds due to the 200 heads, which indicated a total of 200 animals.
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The complete question is-
The Fort Worth Zoo has a number of two-legged birds and a number of four-legged mammals. On one visit to the zoo, Margie counted 200 heads and 522 legs. How many of the animals that Margie counted were two-legged birds?
A). 61
B). 122
C). 139
D). 150
E). 161
Matthew's total points scored in basketball this season were 168 points. He scored 147 of those points in the regular season and the rest were scored in his only playoff game. What percent of his total points did he score in the playoff game?
Answer:
12.5%
Step-by-step explanation:
He scored [tex]168-147=21[/tex] points in the playoff game.
This is equal to [tex]\frac{21}{168}(100)=12.5\%[/tex].
PLEASE HELP ME I DONT UNDERSTAND :(( GIVIN 100 POINTS
Question 1: The Magnolia trees purchased for planting at the school are 3 feet tall. Research shows that these types of trees grow at an average of 3/4 foot per year
) Some students misunderstood question #1 and wrote the following equations in point-slope form:
a) y − 3 = 3/4(x-0)
b) y - 6 = 3/4(x-4)
c) y - 4.5 = 3/4(x-2)
d) y - 12 = 3/4(x-12)
(e) y - 15= 3/4(x-15)
Is this equation okay to use for the height of the trees in this problem?
There is one equation that is incorrect.... determine which one? why is it incorrectly?
Creat two new equations written in point slope form
The equation in option e) is not correct because it would not give correct height of the trees in this problem
How to write equation in slope-point form?Since the Magnolia trees are 3 feet tall and grow at an average of 3/4 foot per year.
If x is the number of years and y is the height. we can write:
y = 3/4(x) + 3
The slope-point equation of a line is given as:
y-y1 = m(x−x1)
y = 3/4(x) + 3 in slope-point form is:
y = 3/4(x) + 3
y-3 = 3/4(x-0)
This means option a) is correct
Yes, this equation is okay to use for the height of the trees in this problem
b) y - 6 = 3/4(x-4)
y - 6 = 3/4(x-4)
y - 6 = 3/4(x)- 3
y - 6 + 3 = 3/4(x)
y - 3 = 3/4(x)
This is correct
c) y - 4.5 = 3/4(x-2)
y - 4.5 = 3/4(x-2)
y - 4.5 = 3/4(x)- 1.5
y - 4.5 + 1.5 = 3/4(x)
y - 3 = 3/4(x)
This is correct
d) y - 12 = 3/4(x-12)
y - 12 = 3/4(x-12)
y - 12 = 3/4(x) - 9
y - 12 + 9 = 3/4(x)
y - 3 = 3/4(x)
This is correct
(e) y - 15= 3/4(x-15)
y - 15= 3/4(x-15)
y - 15= 3/4(x)-11.25
y - 15 + 11.25= 3/4(x)
y - 3.75 = 3/4(x)
This is not correct because it does not reflect the given information
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Identify the range of the function shown in the graph.
the range of the function shown in the graph -1 [tex]\leq[/tex] y[tex]\leq[/tex] 1.
What is the sine and cosine graph's range?All real numbers fall within the domain of the sine and cosine functions. Both the sine and cosine functions have a range of [1,1]. An angle's sine and cosine have the same absolute value as their respective reference angles.
What is a cosine graph's range?An illustration of the function's range in the graphs of cos and sine
The cosine function's graph appears as follows: The range of the function y=cos(x) is 1y1, and the domain is all real numbers (cosine is defined for any angle measure).
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Is maths hard or easy?
Maths can be hard or easy, depending on the level of difficulty and the individual's experience and understanding numbers.
Maths is a subject that can range in difficulty depending on the level of complexity and the individual's experience and knowledge. Some people may find it easy, while others may find it difficult. In the end, it all depends on the level of understanding and the amount of effort put into learning and practicing.
Maths can be hard or easy, depending on the level of difficulty and the individual's experience and understanding numbers
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Answer:
BOTH!
Step-by-step explanation:
See math can be easy or hard. It all depends on YOU. The equation itself isn't hard at all. Mybe a little more work to put in. but its your brain that tells you comething is too challenging or too hard. Now if you are a straight A students and you love math then ofcource your going to be like this is easy!
5.BC is the diameter of the semicircle.The area of rectangle ABCD is 20 and the length of line AB is 5.What is
the area of the semicircle?
The area of the semicircle is, 6.28 unit².
What is Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
We have to given that;
BC is the diameter of the semicircle.
And, The area of rectangle ABCD is 20 and the length of line AB is 5.
Now, We have;
The area of rectangle ABCD is 20 and the length of line AB is 5.
Let the width of rectangle = x
So, We can formulate;
⇒ 20 = x × 5
⇒ x = 4
Here, the width of rectangle is the diameter of the semicircle.
So, The radius of semicircle = 4 / 2
= 2 units
We know that;
Area of semicircle = π r
Where, 'r' is radius of semicircle.
Hence, We get;
⇒ Area of semicircle = π r
⇒ Area of semicircle = 3.14 × 2
= 6.28 unit²
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what is the answer for -40= -50 + x ?
Answer:10
Step-by-step explanation: Because negative 40 equals -50 + x equals 10
Help please
Determine the sum of the measures of the interior angles of a dodecagon (12-sided polygon).
540°
360°
1,800°
2,160°
Answer:
Below
Step-by-step explanation:
Formula for sum of interior angles of a n - gon
(n-2) * 180
for this 12 sided 'gon
(12-2) * 180 = 1800°
( and for a 'regular' dodecagon each would be 1800/12 = 150°
Answer:
Option C) 1,800°
Step-by-step explanation:
To Find : Interior Angles of a Decagon
In order to find interior angles of any polygon we usually use the formula
(n-2)x180
Over Here it is a 12 sided polygon
So,
(12-2)x180
10x180
1800
Hence the interior angles of a decagon is 1800°
How do you tell if a set of ordered pairs satisfies an exponential function?
The following presumption has to be verified in order to establish whether the collection of ordered pairs fulfills an exponential function: The x-coordinates must have the same increment or a consistent difference.
What is an exponential function?A mathematical function of form f (x) = aˣ is an exponential function. "x" is a variable, while "a" is a constant that serves as the function's basis and must be bigger than 0. The transcendental number e, or roughly 2.71828, is the foundation for exponential functions that are most frequently utilized.
Characteristics are:
The fact that a⁰ = 1 causes them all to include the point (0, 1). Always an asymptote, the x-axis. If (0 < a < 1) or (1 < a), they are decreasing and growing, respectively.To know more about exponential function refer to:
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Stefanie has 18 grams of 20% sugar syrup and john 30 of 25% what is the concentration in the new mixture
The concentration in the new mixture will be 11.1 grams.
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
Given that;
Stefanie has 18 grams of 20% sugar syrup.
And, john has 30 grams of 25%.
Here,
Stefanie has 18 grams of 20% sugar syrup.
Hence, The amount of sugar = 18 × 0.2
= 3.6 grams
And, john has 30 grams of 25%.
Hence, The amount of sugar = 30 × 0.25
= 7.5 grams
Thus, The concentration in the new mixture = 3.6 + 7.5 grams
= 11.1 grams
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(25 points for the answer)
If John save 1/5 of his paycheck how much money would it take him to get to 14,500$ for his holiday trip? He earns $9062.5 each paycheck. (Unrealistic question unless you are under paid severely)
Use multiplication or division ONLY!
The amount of john would save 2900 rs
14500*1/5=2900
How much he earns on paycheck?A paycheck, also spelled paycheque, pay check or pay cheque, is traditionally a paper document issued by an employer to pay an employee for services rendered.a check used to pay an employee the amount of money the employee has earned.A paycheck can be an actual piece of paper (a check) that a person can take to the bank to deposit to their account or exchange for cash. Alternatively, a paycheck can be money a company electronically deposits directly into the employee's bank account.Take a look at how each common payroll interval works: Weekly: Once a week (52 paychecks per year) Biweekly: Once every other week (26 paychecks per year) Semimonthly: Twice per month (24 paychecks per yearTo learn more about paycheck refers to:
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What is the area when the diameter is 16?
201.06 square units (rounded to 2 decimal places) is the area of the given circle.
The formula for the area A of a circle is A = πr², where r is the radius of the circle and π is the famous, well-known irrational number pi equal to 3.14159 (rounded to 5 decimal places).
Given that the circle's diameter is 16, and that a circle's radius is equal to half its diameter, the following conclusions can be drawn:
r = d/2
= 16/2
= 8
A=πr2
AND HALF THE DIAMETER IS THE RADIUS (r)
r=8
A= πr2 = π (8) squared = 64 * π = 200.96
or,
Now, substituting the values of r and π into the formula for the area of a circle, we get
A = πr²
= (3.14159)(8²)
= (3.14159)(64)
= 201.06 square units (rounded to 2 decimal places) is the area of the given circle.
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How to find the side of a triangle given two angles and one side?
If you know two angles and one side of a triangle, you can use the Law of Cosines to find the length of the other two sides.
The Law of Cosines states that for a triangle with sides a, b, and c, and angles A, B, and C opposite to those sides, the following formula holds:
c² = a² + b² - 2ab cos(C)
Where C is the angle opposite to side c.
So, if you know the measures of two angles (A and B) and the length of one side (c), you can use the Law of Cosines to find the lengths of the other two sides (a and b) by using the following formulas:
a = √(c² + b² - 2bc cos(A))
b = √(c² + a² - 2ac cos(B))
You can use the above equations to find the sides of the triangle, if you have the measures of two angles and one side.
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400 people are asked if they drink tea. [tex]\frac{7}{10}[/tex] say Yes and 20% of the people who say Yes drink at least 3 cups each day.
I really need help on a) Complete the frequency tree, I don't know how to work that one out.
The missed value in the frequency tree is 224.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
Given that 400 people are asked if they drink tea.
7/10 say Yes and 20% of the people who say Yes drink at least 3 cups each day
7/10 of 400 is 280
Which means 280 people drink tea.
The remaining people does not drink tea.
Remaining =400-280=120.
Now let us find 20% of 280
20/100×280
0.2×280=56
So 56 drink at least 3 cups each day.
280-56=224
So 224 people drink tea but not three cups.
Hence, the missed value in the frequency tree is 224.
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For a loan of. 8,75,000 how much interet will be charged by the bank for 2
month if the rate i 4. 75% per year?
Total interest charged by bank in 2 months is 6793.83.
What is compound interest ?Compound interest is the interest paid on both principal and interest, compounded at regular intervals. At regular intervals, the interest so far accumulated is clubbed with the existing principal amount and then the interest is calculated for the new principal. The new principal is equal to the sum of the Initial principal, and the interest accumulated so far.
The interest that is obtained through the reinvestment of money is known as compound interest. The original principal investment grows substantially more quickly (sometimes referred to as exponentially) when interest is reinvested and allowed to compound over time.
Total loan amount = 875000
total time = 2 months
Rate = 4.75%
Total interest = 875000(1 + [tex]\frac{4.75}{100}[/tex])[tex]\)^{\frac{1}{6} }[/tex] - 875000 = 6793.83
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Given: quadrilateral MATH; M(-5,-2), A(-3,2),
T(3,2) and H(1,-2)
Prove: MATH is a parallelogram
State the formula you will be using.
Show all work.
Answer:
MATH is not a parallelogram
Step-by-step explanation:
(sqrt means squareroot)
To prove that quadrilateral MATH is a parallelogram, we can use the following formula:
A quadrilateral is a parallelogram if and only if both pairs of opposite sides are congruent.
In other words, if the lengths of the sides opposite each other in a quadrilateral are the same, then the quadrilateral is a parallelogram.
To prove that MATH is a parallelogram, we need to show that both pairs of opposite sides are congruent.
The first pair of opposite sides consists of segment MA and segment TH. To show that these sides are congruent, we can use the Distance Formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Where (x1, y1) and (x2, y2) are the coordinates of the two points that define the line segment.
Substituting the coordinates of points M and A, we get:
d = sqrt((-3 - (-5))^2 + (2 - (-2))^2)
= sqrt((-3 + 5)^2 + (2 + 2)^2)
= sqrt(8^2 + 4^2)
= sqrt(64 + 16)
= sqrt(80)
= 8.944
Substituting the coordinates of points T and H, we get:
d = sqrt((1 - 3)^2 + (-2 - 2)^2)
= sqrt((-2)^2 + (-4)^2)
= sqrt(4 + 16)
= sqrt(20)
= 4.472
Since 8.944 is not equal to 4.472, we cannot conclude that MA and TH are congruent. Therefore, MATH is not a parallelogram.
What are the approximate solutions of 4x2 3 − 12x to the nearest hundredth?
The approximate solutions are -0.28 and -2.28.
Now, According to the question:
Given, the equation is 4x^2 + 3 = -12x
We have to find the approximate solutions to the equation.
Using quadratic formula,
[tex]x = \frac{-b±\sqrt{b^2-4ac} }{2a}[/tex]
The equation can be written as 4x^2 + 12x + 3 = 0.
Here, a = 4, b = 12, c = 3
x = [tex]\frac{-12±\sqrt{12^2-4(4)(3)} }{2(4)}[/tex]
x = [tex]\frac{-12±\sqrt{144-48} }{8}[/tex]
x = [tex]\frac{-12±\sqrt{96} }{8}[/tex]
x = [tex]\frac{-12±9.8}{8}[/tex]
Now, x = [tex]\frac{-12+9.8}{8} =\frac{-2.2}{8}[/tex] = -0.275
x = [tex]\frac{-12-9.8}{8} =\frac{-21.8}{8}[/tex] = -2.275
Therefore, the approximate solutions are -0.28 and -2.28.
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The complete question is this :
What are the approximate solutions of 4x^2 + 3 = -12x to the nearest hundredth?
Identify the independent variable and the dependent variable. A pool store owner wants to determine the effect of algaecide brands on the treatment of pool water with algae. He contacts customers who have purchased the brands of algaecide and asks their opinion of the algaecide.
The independent variable is the brand of algaecide. The dependent variable is the treatment of pool water with algae.
What is the independent and dependent variable?
In mathematical modeling, statistical modeling, and experimental sciences, there are dependent and independent variables. Dependent variables get their name because, during an experiment, their values are investigated under the presumption or requirement that they are dependent on the values of other variables due to some law or rule.
Here, we have
Given
A pool store owner wants to determine the effect of algaecide brands on the treatment of pool water with algae. He contacts customers who have purchased the brands of algaecide and asks their opinion of the algaecide.
We have to determine the independent variable and the dependent variable.
We concluded that the independent variable is the brand of algaecide and the dependent variable is the treatment of pool water with algae.
Hence, the independent variable is the brand of algaecide and the dependent variable is the treatment of pool water with algae.
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What is 2 step used for?
The two step equations are used to represent the equations and solve real life problems .
What is Two Step Equations ?
The Equations that can be solved in exactly two steps are called as Two Step Equations .
We can use the two-step equations to represent and solve real-world problems by translating the problem into an algebraic equation, and solving equation, and then interpreting the solution of equation.
An example of the two step equation is : If a rental car costs $40 plus extra 10 cents for every mile driven, then how many miles can be driven for $50 ?
Translating The problem into equation we get [tex]40 + 0.1m = 50[/tex] where m is number of miles driven.
Step(i) we Subtract 20 from both sides
we get , [tex]0.1m = 10[/tex].
Step(ii) We Divide both sides by 0.1 ;
we get , [tex]m = 100[/tex].
Therefore , the problem to find the number of miles is solved in exactly two steps .
The given question is incomplete , the complete question is
What is the two step equation used for ?
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Tims picture. is 8 feet long. The length of a copy of the picture is 1/2 a foot long. What is the scale factor from the original to the copy?
Answer: The scale factor is a ratio that compares the dimensions of an object to a copy of that object. To find the scale factor from the original picture to the copy, you can divide the length of the copy by the length of the original.
In this case, the length of the original picture is 8 feet and the length of the copy is 1/2 a foot.
So the scale factor is:
1/2 a foot / 8 feet = 1/16
This means that the copy is 1/16 the size of the original. This means that, for each inch or foot on the original, the same length on the copy is 1/16 of that length.
It's also common to express scale factor as a ratio or a fraction of the original, which in this case is 1/16
It's worth mentioning that you could use this same method to find the scale factor for any other dimension of the picture, such as width, height and so on.
Step-by-step explanation:
N plus 75 used in a real world sentence.
Answer:
Laura has "n" amount of nickels. She receives 75 more from her grandmother.
Explanation:
(If this is not what the question meant, please let me know!)
Because the question is asking us to write a sentence for an addition problem, we need to write a sentence that involves two amounts of one thing being combined, in this case nickels.
For the function below, write the differential.
f(x) = ln(1 + x^2)
dy = ( ) dx
Calculate dy for the given values of x and dx.
x = 2 and dx = 0.2
dy =
How accurate is dy in approximating Δy (i.e., what is their difference) to the nearest thousandth?
The dy for the given values of x and dx is dy = 0.5632, and their difference to the nearest thousandth is 0.0005.
The difference between dy and Δy can be determined by subtracting dy from Δy and taking the absolute value. In this case, dy approximates Δy to the nearest thousandth with a difference of 0.0005. This is a very small difference, indicating that dy is an accurate approximation for Δy.
The accuracy of dy can be attributed to the fact that the function f(x) = ln(1 + x^2) is a smooth function, meaning that the rate of change at a point (i.e., the derivative) is nearly constant. This allows dy to accurately approximate the change in y, Δy, over a small interval of x. Furthermore, the choice of dx = 0.2 is a small enough value that it does not significantly affect the accuracy of the approximation.
Learn more about Differential Equations here:
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