The given equation's answer is [tex]$z+5=55\left(5^z\right):$[/tex] [tex]$z=-\frac{W_{-1}\left(-\frac{11 \ln (5)}{625}\right)+5 \ln (5)}{\ln (5)}$[/tex], [tex]$z=-\frac{\mathrm{W}_0\left(-\frac{11 \ln (5)}{625}\right)+5 \ln (5)}{\ln (5)}$[/tex]
What is the solution of the given equation ?[tex]$z+5=55\left(5^z\right):$[/tex] [tex]$z=-\frac{W_{-1}\left(-\frac{11 \ln (5)}{625}\right)+5 \ln (5)}{\ln (5)}$[/tex], [tex]$z=-\frac{\mathrm{W}_0\left(-\frac{11 \ln (5)}{625}\right)+5 \ln (5)}{\ln (5)}$[/tex]
[tex](Decimal: $z=-1.75934 \ldots, z=-4.98187 \ldots$ )[/tex]
[tex]$$z+5=55\left(5^z\right)$$[/tex]
Prepare [tex]$z+5=55\left(5^z\right)$[/tex] Lambert form: [tex]$(z+5) e^{-\ln (5) z}=55$[/tex]
the equation once more using [tex]$(-z-5) \ln (5)=u$[/tex] and [tex]z=-\frac{u+5 \ln (5)}{\ln (5)}$[/tex]
[tex]$$\left(\left(-\frac{u+5 \ln (5)}{\ln (5)}\right)+5\right) e^{-\ln (5)\left(-\frac{u+5 \ln (5)}{\ln (5)}\right)}=55$$[/tex]
[tex]$$e^{u+5 \ln (5)}\left(-\frac{u+5 \ln (5)}{\ln (5)}+5\right)=55$$[/tex]
Rewrite [tex]$e^{u+5 \ln (5)}\left(-\frac{u+5 \ln (5)}{\ln (5)}+5\right)=55$[/tex]in Lambert form: [tex]$e^u u=-\frac{11 \ln (5)}{625}$[/tex]
Solve [tex]$e^u u=-\frac{11 \ln (5)}{625}: \quad u=\mathrm{W}_{-1}\left(-\frac{11 \ln (5)}{625}\right), u=\mathrm{W}_0\left(-\frac{11 \ln (5)}{625}\right)$$$u=\mathrm{W}_{-1}\left(-\frac{11 \ln (5)}{625}\right), u=\mathrm{w}_0\left(-\frac{11 \ln (5)}{625}\right)$$[/tex]
Substitute back [tex]$u=(-z-5) \ln (5)$[/tex] , solve for z
[tex]$$\begin{aligned}& \text { Solve }(-z-5) \ln (5)=W_{-1}\left(-\frac{11 \ln (5)}{625}\right): \quad z=-\frac{W_{-1}\left(-\frac{11 \ln (5)}{625}\right)+5 \ln (5)}{\ln (5)} \\& \text { Solve }(-z-5) \ln (5)=W_0\left(-\frac{11 \ln (5)}{625}\right): z=-\frac{W_0\left(-\frac{11 \ln (5)}{625}\right)+5 \ln (5)}{\ln (5)} \\& z=-\frac{W_{-1}\left(-\frac{11 \ln (5)}{625}\right)+5 \ln (5)}{\ln (5)}, z=-\frac{W_0\left(-\frac{11 \ln (5)}{625}\right)+5 \ln (5)}{\ln (5)}\end{aligned}$$[/tex]
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There are 400 more men than women at a funfair in the morning. In the afternoon 2/5 of the men and 1/4 of the women left the funfair. As a result, there were 120 more men than women remaining at the funfair. How many men were there at the funfair at first
There was 1200 men and 800 women at the funfair in the morning
What is an equation?An equation consists of numbers and variables linked together by mathematical operations to form an expression.
Let x represent the number of men and y represent the number of women in the morning.
There are 400 more men than women at a funfair in the morning. Hence:
x = y + 400
x - y = 400 (1)
In the afternoon 2/5 of the men and 1/4 of the women left the funfair. hence:
number of men remaining = x - (2/5)x = (3/5)x
number of women remaining = y - (1/4)y = (3/4)y
There were 120 more men than women remaining at the funfair. therefore:
(3/5)x - (3/4)y = 120 (2)
From both equations:
x = 1200, y = 800
There was 1200 men in the morning
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Oakwood Elementary Fall Carnival gets bigger every year! Last year, they had 70 volunteers working 14 booths. This year, they want to have 42 booths.
If they use the same ratio of volunteers to booths, how many volunteers does Oakwood Elementary need this year?
Answer:
210
Step-by-step explanation:
70
14 booths
ratio = 70/14 =5
42 booths
by the same ratio = 42*5 = 210
Natalie and Shriya each improved their yards by planting grass and ivy. They bought their supplies from the same store on the same day. Natalie spent $71 on 7 ft2 of sod and 11 pots of ivy. Shriya spent $76 on 8 ft2 of sod and 10 pots of ivy. Find the cost of one ft2 of sod and the cost of one pot of ivy.
Answer:
One ft2 of sod costs $10.14 and one pot of ivy costs $0.24
Step-by-step explanation:
We can use the information provided to find the cost of one ft2 of sod and the cost of one pot of ivy.
To find the cost of one ft2 of sod, we can divide the total cost of sod by the total area of sod:
Cost of 1 ft2 of sod = (71 / 7) = $10.14/ft2
To find the cost of one pot of ivy, we can divide the total cost of ivy by the total number of pots:
Cost of 1 pot of ivy = (76 - 71) / (11 + 10) = $5 / 21 = $0.24/pot
So one ft2 of sod costs $10.14 and one pot of ivy costs $0.24
Keep in mind that these calculations only give approximate prices since it's not specified that the cost of ivy and sod is the same, but it's just an estimation based on the information that you provided.
A+b=7 and ab= 6 find a2+b2
Answer:
37
Step-by-step explanation:
a+b=7 and ab= 6 find a^2+b^2
a + b = 7ab = 6( a + b )² = a² + b² + 2ab =
7² = a² + b² + 2 × 6 =
49 = a² + b² + 12 =
a² + b² = 49 - 12 =
a² + b² = 37
Pine Grove High School has a total of one thousand and twenty
students. Ten percent of the students are out sick, and twenty-five
percent of the students are on a field trip. How many students are
currently in the school?
10 pointss!! Huryyyy nowww
663.
i found out what 35% of 1020 is and then subtracted that by 1020.
Simplify the mathematical expression (a) 7 x 6 – 5 x 4 + 1 x 3
The order of operations is a collection of rules that gives the correct sequence of steps for doing a calculation. BIDMAS is an acronym used to tell you the correct order to complete a calculation when there are different operations . It stands for Brackets, Indices , Division, Multiplication, Addition and Subtraction.
Thus solving the expression;
we first solve all the multiplication parts:
7 x 6 - 5 x 4 + 1 x 3
Now addition:
= 42 - 20 + 3
Lastly subtraction:
= 42 - 23
= 19
What is the lowest whole number side length in inches that would ensure the triangle is an obtuse triangle?.
Answer:
24 inches.
Step-by-step explanation:
In order for a triangle to be obtuse, one of its angles must be greater than 90 degrees. In a right triangle, the angle opposite the hypotenuse is always 90 degrees, so in order for the triangle to be obtuse, the hypotenuse must be the longest side.
To find the lowest whole number side length in inches that would ensure that the triangle is obtuse, we can use the Pythagorean theorem. The Pythagorean theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
a^2 + b^2 < c^2
If we take the base 48cm and convert it to inches, 48cm = 48*0.393701 = 18.897638 inches
So the base is 18.897638 inches.
Now we have to find the lowest whole number side length of c so that:
18.897638^2 + b^2 < c^2
358.565744 + b^2 < c^2
We can see that the lowest whole number of c is 24 inches.
So, the lowest whole number side length in inches that would ensure that the triangle is obtuse is 24 inches.
What is the difference between greatest 6 digit number and smallest 6 digit number?.
The difference between the greatest 6-digit and smallest 6-digit numbers is 899999.
The aim is to find the smallest and largest 6-digit numbers, and then we need to find how many numbers are between these two values.
Let's start by finding the smallest 6-digit number.
We know that 0 is the smallest digit that can not be used in the highest place value, so we will consider the next smallest digit; that is, 1 and 1 can be used in the highest place value.
Thus, we can create the required 6-digit smallest number with 0 and 1.
Hence, the smallest 6-digit number is 100000.
Now, we will discover the largest 6-digit number.
As we know, the largest digit is 9, which can be used anywhere. So, we will form the largest 6-digit number with the digit 9.
Thus, the largest 6-digit number is 999999.
Next, we need to find the difference between these two values.
So, we can determine the difference between the smallest 6-digit number and the largest 6-digit number by subtracting the smallest from the largest.
Thus, we get,
⇒999999−100000
⇒899999
Hence, 899999 is the difference between the smallest 6-digit and the largest 6-digit numbers.
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Question 6 of 30
On a unit circle, 0 = 60°. Identify the terminal point and tan 8.
O A. Terminal point: (,); tan 0 = √3
OB. Terminal point: (3,1); tan 0 = 3
OC. Terminal point: (,); tan 0 = √3
O D. Terminal point: (1,3); tan 0 =
SUBMIT
On a unit circle, 0 = 60°, hence the terminal point is (,); tan 0 = √3. It rotates symmetrically around the center at all angles.
what is circle ?In the plane, a circle is created by each point that is a specific distance from another point (center). Therefore, it is a curve made up of points that are spaced out from one another in the plane in a fixed manner. It rotates symmetrically around the center at all angles. Every pair of points in the plane of a circle, which is a closed two-dimensional object, are evenly distanced from the "center." Specular symmetry is produced by a line that traverses the circle. It rotates symmetrically around the center at all angles.
given
θ = 30 °
terminal point = cos 30° , sin30°
= (underroot 2 , 1/2 )
tan30° = 1/ underroot 3 = underroot3/3
On a unit circle, 0 = 60°, hence the terminal point is (,); tan 0 = √3. It rotates symmetrically around the center at all angles.
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in anytown, 55% of the 20,000 inhabitants live in houses, 25% of the inhabitants live in apartments, the rest of the inhabitants live in condominiums, how many anytownians live in condominiums. HELP WILL GIVE BRAINLIST IF SHOW WORK
Answer: 4,000 people live in condominiums.
Step-by-step explanation:
First add 55%+25%=80%
Then subtract 100%-80%=20%
Then turn 20% to 0.2.
Last, multiply 0.2x20,000= 4,000
The table shows a linear relationship between the height of a fast-growing bamboo plant and the number of days since it was planted.
Days Planted. x 0, 2,4,6
Height (in.), y 15,20,25,30
1. What do the variables x and y represent in this relationship?
2. Read the description of the relationship above the table. How do you know that the relationship can be represented by a linear equation?
3. Can you tell whether the relationship has a positive or negative slope just by looking at the data in the table? Explain.
4. What rate does the slope represent in this situation?
5. Choose two points from the table and calculate the slope.
6. Suppose you graph the points given in the table. Where does the point (0, 15) lie? Use this information to find the y-intercept.
7. Write an equation in slope-intercept form that represents this
Step-by-step explanation:
answer is 567
What is the least 2-digit number?.
10 is the least 2-digit number having 0 on one's place and 1 on ten's place.
There are just two place values in 2-digit numbers: the units place and the tens place. Every number with more than one digit has various digits, each of which is described by its place value. 2-digit numbers range in value from 10 to 99. In other words, the smallest and largest 2-digit numbers are 10 and 99, respectively. When a number has two digits, it is called a 2-digit number. 2-digit numbers have two digits and range from 10 to 99.
Any number between 1 and 9 can be used as the digit in the tens place. The placement of each digit in a number is known as place value. There is just one place value that matters when discussing 1-digit numbers, and that is the ones place.
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How do you draw a 100 degree angle?.
You can draw a 100 degree angle with the help of Protractor.
A degree is the name given to the mathematical unit of measurement for an angle. A protractor is a device used to determine the degree of an angle. Angles can be measured at different angles with different degrees, such as 30°, 45°, 60°, and so on. A complete circle rotates at 360°.
Each of the 360 equal segments that make up a rotation is referred to as a degree. We use a circle ° to represent a degree. 180°, for instance, denotes 180 degrees. An angle in degrees is an angle whose measure is expressed in degrees.
Follow the given steps to construct a 100-degree angle with the help of a protractor.
Step 1: Draw a line with the help of a ruler and name it AB.Step 2: Place protractor tip at A and choose a 100 degree mark on protractor.Step 3: Place the pencil tip on the mark of 100 and mark a small point.Step 4: Draw a line connecting the point A and the recently marked point.Learn more about Angle:
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Gabe goes to the mall. If k is the number of items he bought, the expression 18.58k+30 gives the amount he spent in dollars at one store. Then he spent 22 dollars at another store. Find the expression which represents the amount Gabe spent at the mall. Then estimate how much Gabe spent if he bought 3 items.
The expression which represents the amount Gabe spent at the mall will be 18.58k + 52.
The amount that Gabe spent if he bought 3 items will be $107.74.
How to calculate the expression?From the information, Gabe goes to the mall. If k is the number of items he bought, the expression 18.58k+30 gives the amount he spent in dollars at one store and he spent 22 dollars at another store.
The expression which represents the amount Gabe spent at the mall will be:
= 18.58k + 30 + 22
= 18.58k + 52
The amount that Gabe spent if he bought 3 items will be:
= 18.58k + 52
= 18.58(3) + 52
= $107.74
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determine if the two lines 7x-3y=-21 and y= "-3/7x+5" are parallel, perpendicular or neither
Answer:
They are perpendicular!
Step-by-step explanation:
Get 7x-3y=-21 into y=mx+b format.
7x-3y=-21 Bring 7x to the other side
-3y=7x-21 Divide -3 by both sides, it cancels out on the y's side.
y=-7/3x+7 Two negatives equal a positive, that it why 7 is positive.
y=-7/3x+7 is the line, the other is y=-3/7x+5
The slope of this line is -7/3 , the slope of the given line is -3/7.
Lines are perpendicular if the slopes are opposite reciprocals, such as this.
So, while they intercept at different points on the y-axis, they will intersect at some point! This makes them perpendicular.
What is the additive inverse of the polynomial –9xy2 + 6x2y – 5x3?
Answer:
9xy² -6x²y +5x³
Step-by-step explanation:
You want the additive inverse of –9xy² + 6x²y – 5x³.
Additive inverseThe additive inverse is the value that gives zero when added to the original. It can be formed by changing the signs of the terms in the sum:
9xy² -6x²y +5x³
which neurotransmitter is released from the parasympathetic ganglion
The amount of neurotransmitter released from the parasympathetic ganglion is acetylcholine.
The parasympathetic nervous system is part of the autonomic nervous system which helps to regulate involuntary bodily functions such as heart rate, digestion and other processes.
The parasympathetic nervous system is responsible for calming the body and restoring it to its resting state. Parasympathetic ganglia are clusters of neurons that receive and transmit nerve signals from the brain to the organs and muscles.
The amount of neurotransmitter released from these ganglia is acetylcholine, which helps to slow the heart rate and promote relaxation.
The parasympathetic nervous system is part of the autonomic nervous system which helps to regulate involuntary bodily functions such as heart rate, digestion and other processes.
The parasympathetic nervous system is responsible for calming the body and restoring it to its resting state. Parasympathetic ganglia are clusters of neurons that receive and transmit signals from the brain to the organs and muscles.
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What is the rule for a 45 45 90 special right triangle choices are given by the order of leg leg hypotenuse leg?.
For each 45-45-90 triangle, the period of the hypotenuse equals the length of the leg expanded via the square root of 2. That is the 45-45-90 Triangle Theorem.
A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is greater than thousand years vintage, having been described at the very first web page of Euclid's elements.
In Euclidean geometry, any 3 elements, at the same time as non-collinear, determine a very precise triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean area). In special words, there's exceptional one plane that includes that triangle, and each triangle is contained in some plane. If the complete geometry is best the Euclidean plane, there is the fine one aircraft and all triangles are contained in it; however, in better-dimensional Euclidean areas, this isn't actual. this text is prepared triangles in Euclidean geometry, and specifically, the Euclidean plane, besides in which otherwise said.
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11. Find the value of x
Giving 75 points please help
1) Triangle Midsegment Theorem will be used to solve the given problem.
2) The value of x would be 10.
What is Triangle Midsegment Theorem?
A triangle midsegment is a segment that links the midpoints of two triangle sides. A midsegment joining two triangle sides is parallel to the third side and half the length.
1) Triangle Midsegment Theorem will be used to solve the given problem.
2) Here M is the midpoint of AB, and P is the midpoint of BC. So, PM is a midsegment.
Therefore by the Triangle Midsegment Theorem,
[tex]PM=\frac{1}{2} AC\\\\(x+5)=\frac{1}{2} 3x\\\\x=10[/tex]
Hence, The value of x would be 10.
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can someone help me please
what is 2(1/3^2) ?
Step-by-step explanation:
0.22222222222222222222222222
What is the product of 3x3x3x3?.
The product of numbers , 3× 3×3×3 is equals to the eighty-one.
In mathematics, a product is a number or result that is obtained by multiplying two or more numbers together. So, 12 is the product of 3 and 4. For example product of 5 and 4 is represented by 5 × 4 = 20 , it is a multiplication expression. A multiplication expression has three parts, a multiplier ( i.e., 4) , a multiplicand ( i.e., 5), and the product ( i.e., 20). We have, a multiplication expression as 3×3×3×3. We can rewrite it in form 3¹× 3¹ ×3¹× 3¹ = 3¹⁺¹⁺¹⁺¹ = 3⁴ , it is an exponential form number. Therefore, results is equals to 81. So, the required product value is 81.
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Simplify $(4 - 5i) - (-2i - 8) + (-1 + 8i).$
The expression $(4 - 5i) - (-2i - 8) + (-1 + 8i) is simplified to $5i -11
What are algebraic expressions?Algebraic expressions are defined as expressions that are composed of variables, coefficients, factors, constants and terms.
These expressions are likely to consist of some arithmetic operations, such as;
AdditionSubtractionMultiplicationFloor divisionBracketParenthesesDivisionFrom the information given, we have that;
$(4 - 5i) - (-2i - 8) + (-1 + 8i)
expand the bracket
$4 - 5i + 2i +8 - 1 + 8i
Now, collect like terms
$-5i +2i + 8i +4 +8 - 1
Add or subtract the like terms
$5i -11
Hence, the expression is $5i -11
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Aditi and Kavita had 40 coins in total. Aditi gave 10 coins to Kavita. The product of the coins they now have is 375. Aditi had fewer than 30 coins when she started.
Aditi and Kavita had 40 coins in total. the coin share b/w them is
x=25, y=15
What is coin share?Generally, Aditi and Kavita's original coin total is 40.
x+y=40
Aditi gave 10 coins to Kavita.
(x-10)*(y+10)=375
Now solving a system of equations using a calculator
x=25, y=15
x=35, y=5
Since Aditi had fewer than 30 coins when she started.
The correct proportion is
x=25, y=15
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CQ
Aditi and Kavita had 40 coins in total. Aditi gave 10 coins to Kavita. The product of the coins they now have is 375. Aditi had fewer than 30 coins when she started.
How much coin did dey both have
Which type graph is the best choice for determining the change in the stock market over time?
a. Scatter Diagram
b. Time-series Plot
c. Box Plot
d. Pie Chart
Time-series Plot graph is the best choice for determining the change in the stock market over time.
The term stock exchange refers to several exchanges where shares of publicly traded companies are bought and sold. Such financial activities are conducted through formal stock exchanges and over-the-counter (OTC) markets that operate under a specific set of regulations.
Other major stock exchanges in the world are Tokyo Stock Exchange (Japan), Shanghai Stock Exchange (China) and London Stock Exchange (UK). Stock exchanges are considered capital markets as they provide long-term financing for companies.
A time series chart, also known as a time series chart or time series graph, is a data visualization tool that plots data points at successive time intervals. Each point on the chart corresponds to both time and quantity being measured.
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How can I calculate my grade in class 10?.
To calculate my grade in class 10 divide your total points by the total points possible.
Total points earned divided by total points possible
The maximum amount of points you may have obtained in the course is referred to as total points possible.
The total number of available points in a class with 50 participation points, 50 homework points, 100 essay points, and 200 test points is 400. If you received 330 points in this class, divide that number by 400 to get a quotient of 0.825, This is equivalent to an 82.5% grade, or a low B.
Divide the total by the number of entries to get a percentage. Divide the total by 30, for instance, if you have % grades for 30 activities. Your final grade is expressed as a percentage by the quotient.
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What are the types of multiplication method?.
Different types of multiplication method is given by :
a. Addition method
b. Vertical method
c. Box method
d. Partial multiplication method
As given in the question,
Different types of the multiplication method are as follow :
a. Addition method :
In addition method if 4 × 3 it means add 4 three times.
4 + 4 + 4 = 12
b. Vertical method :
It is traditional way of multiplying the given numbers . Example : 12 × 4
1 2
×4
48
c. Box method :
In this box was formed as per the given numbers . Example 42 × 13
10 3
40 400 120
2 20 6
Add : 400 + 120 + 20 + 6 = 546
d. Partial multiplication method :
This method is based on distributive property to make the calculation easy.
45 × 6
= ( 40 + 5 ) × 6
= 40 × 6 + 5 × 6
= 240 + 30
= 270
Therefore, the different types of multiplication methods are:
a. Addition method
b. Vertical method
c. Box method
d. Partial multiplication method
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um goleiro faz 35 defesas em 5 jogos qual é a taxa unitária de defesas por jogo?
Answer:
7
Step-by-step explanation:
La tasa unitaria de salvamentos por juego es de 7 salvamentos por juego. Esto se puede calcular dividiendo el número total de guardados (35) por el número de juegos (5): 35 guardados / 5 juegos = 7 guardados por juego.
What is The quotient of anumber and nine is less than the number. In algebraic expressions
Answer: [tex]x-\frac{x}{9}[/tex]
Step-by-step explanation:
1) quotient is the answer of a division problem
with that in mind and letting "a number" = x . . .
"The quotient of a number and nine..." would be [tex]\frac{x}{9}\\[/tex]
2) "is less than" always means you but the previous statement BEHIND . . .
[tex]x-\frac{x}{9}[/tex]
How many types of fractions are there Class 6?.
There are seven types of fractions.
We know that the fraction is used to represent the portion or part of the whole thing.
The fraction has two parts: numerator and denominator.
The top part of fraction is numerator and the bottom part is denominator.
consider a fraction 1/8.
Here, numerator is 1, denominator is 8
When certain thing is divided into 8 equal parts then each part of is represented by fraction1/8
The types of fractions are:
1) Proper fraction - the numerator is always less than the denominator
2) Unit Fractions - the numerator of fraction is always 1
3) Improper fraction - the numerator is greater than the denominator
4) Mixed fraction - it is a combination of a natural number and fraction
5) Like fractions - the fractions have the same denominators
6) Unlike fractions - the fractions have the different denominators
7) Equivalent fractions - the fractions have the same value when simplified.
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Please help!! I NEED this by tmr!!
Find the length of the segment y =
2.5x+10 from x = 0 to x = 16.
The length of the segment is 10,12.5 , 15,.. when x is from x = 0 to x = 16.
What is algebraic expression ?
Algebraic expression can be defined as the combination of variables and constants .
From the given expression ,
y = 2.5 x + 10
So, we have to find the length of line segment from x = 0 to x = 16.
so when x = 0 ,
y = 0+10
y = 10
and when x=1
y = 2.5*1+10
y=12.5
and similarly
when x = 2
y = 2.5* 2 + 10
y = 15
So, like this the sequence will be goin on y = 10 , 12.5 , 15 , 17.5 and etc .
Hence, The length of the segment is 10,12.5 , 15,.. when x is from x = 0 to x = 16.
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