Functions to build an area function of the triangle , A = b2 + 2b.
What Altitude of a Triangle?A perpendicular line drawn from a triangle's vertex to its opposite side is the definition of a triangle's altitude. A triangle can be drawn with three altitudes because it has three sides. There are various types of elevations in triangles. When computing the area of a triangle, the altitude, also known as its height, is indicated by the letter.The section of a perpendicular line traced from a triangle's vertex to the side directly across from it is the triangle's altitude. The base of the triangle that the altitude touches forms a straight angle. It is often referred to as a triangle's height and is represented by the letter "h." The distance between the vertex and its opposing side can be calculated to determine its size. It should be remembered that every triangle has three altitudes that can be drawn from each of the vertices. See the intersection of the triangle's three elevations by paying attention to the triangle in the illustration below. The "Orthocenter" is this location.According to our question-
Let b = the base
altitude = 2b + 4
A = b(2b+ 4)/2
A = b(b + 2)
A = b2 + 2b
Hence, Functions to build an area function of the triangle , A = b2 + 2b.
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The circumference of a circle is 19π cm. What is the area, in square centimeters? Express your answer in terms of
When the circumference of a circle is 19π cm the area of the circle is
28.27 square centimeters
How to calculate the area of a circle ?Information given in the question include
The circumference of a circle is 19π cm
Area of a circle is given by
π r^2
where r = radius
π = constant = 3.124
circumference of a circle is given by 2πr
2πr = 19
πr = 9.5
r = 3.024
r = 3 cm
The area is solved as
= π * 3^2
= 28 .27square centimeters
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a process that fills packages is stopped whenever a package is detected whose weight falls outside the specification. assume that each package has probability 0.04 of falling outside the specification and that the weights of the packages are independent. find the variance of the number of packages that will be filled before the process is stopped.
The variance of the number of packages that will be filled before the process is stopped will be 600 when the probability of falling outside the specification is 0.04.
What is variance?Variability is measured by the variance. The average of the squared deviations from the mean is used to calculate it. The degree of spread in your data set is indicated by variance. The variance is greater in relation to the mean the more dispersed the data. In statistics, the variance is used to assess how accurately the mean summarizes all of the data. For instance, more range exists within the set the higher the variance.
P(fail)=0.04
P(pass)=0.96
variance=(1-P)/P²
=(1-0.04)/0.0016
=0.96/0.0016
variance=600
When the likelihood of falling outside the specification is 0.04, the range of packages that will be filled before the process is stopped is 600.
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Sherry has 15,200 dollars to invest in mutual funds and in bonds. Sherry has selected a mutual fund that earns 1% a year and a bond that earns 4% a year. If she wants to earn 548 at the end of the first year, how much does she need to invest in each type of account?
please answer ! I’ll give brainliest mark thing.
Sherry needs to invest $2000 in a mutual fund that earns 1% interest a year and $13200 in a mutual fund that earns 4% interest a year.
According to the question,
We have the following information:
Amount to be invested = $15200
Interest earned 1% a year and 4% a year
Total amount interest to be earned at the end of first year = $548
Now, let's take the amount to be invested in 1% interest a year's mutual fund to be $x.
Then, we have the amount to be invested in mutual fund that earns 4% a year:
$(15200-x)
So, we have the following expression by removing percentage sign:
x/100 + (15200-x)4/100 = 548
Taking 100 as the least common factor and using the cross multiplication method:
x+60800-4x = 548*100
-3x = 54800-60800
-3x = -6000
x = 6000/3
x = $2000
Now, the amount invested in second mutual fund:
15200-2000
$13200
Hence, Sherry needs to invest $2000 in a mutual fund that earns 1% interest a year and $13200 in a mutual fund that earns 4% interest a year.
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A 850 kg car is moving with a speed of 10 m/s. Which of the following would cause the largest change in momentum?
a. Double the velocity and mass
b. Double the velocity and cut the mass in half
c. Keep the velocity the same and triple the mass
d. Cut the mass and velocity in half
The largest change in momentum will happen when the velocity and mass of the object are doubled( option A)
What is momentum?The momentum of a body is the product of the mass of the body and it's velocity. Momentum is measured in kg/ms^-1. It is a vector quantity. it is represented by p
Momentum of a body is expressed as p= m× v
where m is the mass of the body and v is it's velocity. This means that the higher the mass and velocity of the body the higher it's momentum.
The initial momentum of the body of mass 850kg and velocity 10ms^-1 = 850kgms^-1
When the velocity and mass are doubled , then the new momentum will be 1700× 20= 34000kgms^-1
Therefore the largest change in momentum will be obtained when both mass and velocity are doubled.
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Area and Circumference of Circles
All circles have the same ratio of circumference to (fill in the blank)
constant . Using this ratio, an exact formula was determined for the distance around a circle: (fill in the blank)
Pi([tex]\pi[/tex]) is the ratio of circumference to diameter for any circle.
Perimeter is the distance around a circle.
Circumference of circle [tex]C = \pi d[/tex].
Perimeter of circle [tex]= 2 \pi r[/tex]
What is circle ?
A circle is a spherical shape without boundaries or edges.
A circle is a closed, curved object with two dimensions in geometry.
Consider two small arcs AB and CD of two circles of radii x and y units, both of which make an angle of measure θ at the centers P and Q respectively.
For smaller values of θ, the arc length AB is almost equal to the length of the line segment [tex]\bar{AB}[/tex]. Similarly, arc CD ≅ [tex]\bar{CD}[/tex].
Using the SAS rule of triangle similarity, we can say that APB and CQD are similar triangles because their angles are the same and their ratios are AP: PB = CQ: QD = 1: 1. So, it stands to reason that AB: AP = CD: CQ.
Circumference = [tex]\pi \times[/tex] diameter or circumference = 2[tex]\pi \times[/tex] radius if this constant equals some value.
So it was proved.
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I NEED HELP!!
Information:
Ryan conducted a 6-day study observing the effects of an organic plant food on the growth of his sprouting bean plant. He tracked these two pieces of information:
1. the amount of plant food remaining in the container after each day’s feeding
2. the height of the plant over time
(There was a total of 72 millimeters of plant food)
Question:
Write a function rule for the relationship between the amount of plant food remaining, f(x), and the number of days that have passed, x.
This relationship is not a function because more than one amount of plant food remains each day.
What is a function?An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that, Ryan did an experiment by observing the effects of plant food and the growth of the sprouting bean plant. He made a note of the height of the bean plant and the amount of food remaining in the container for the plant after feeding each day.
Thus, he observed that the plant food in the container decreases by an equal amount every day as the bean plant grew. Thus, this states that it is not a function between the two, as there are more than one plant food remaining each day for the plant.
Hence, This relationship is not a function because more than one amount of plant food remains each day.
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Given the equation F(x)=3x-1 what is f(x+9)?
f(x+9) = 3x + 26.
Given equation:
f(x)=3x-1
f(x+9) = 3(x+9) - 1
= 3x + 3*9 - 1
= 3x + 27 - 1
= 3x + 26.
Therefore f(x+9) = 3x + 26.
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a large animal preserve has noticed that an albino panther is born unpredictably once every 8 years; and that can happen at any time of the year. a) what are the expected value and standard deviation of the number of albino panthers which will be born in the next 40 years?
The expected value of the number of albino panthers is 5
The standard deviation of the number of albino panthers is 2.09
Given that albino panther is born once every 8 years, probability p, of one albino to be born in 8 years is 1/8
Expected value=n*p, where n is 40 years, and p=1/8
=40*1/8
=5 albino panthers
Hence, the expected value is 5 albino panthers
Standard deviation=(Expected value*(1-p))^1/2
=(5*(1-1/8))^1/2
=4.375^1/2
=2.09
Hence, standard deviation is 2.09
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Help Please!
Solve the inequality and graph it’s solution.
A window in the room has an actual width of 2. 5 feet. What is the width of the window in the blueprint? (same scale 3 in:5 ft)
The window width in the blueprint is 1.5 in.
Define the meaning of the term scale factor?A scale factor is a designation for figures with similar appearances but differing scales or measures.Assume two circles appear identical but have different radii. The scale factor specifies how much larger or smaller a figure is compared to the original figure.As per the given question-
A window in the room measures 2. 5 feet in width.
The given scale is-
Blue print (inches) : original (feet)
3 in : 5 ft
Divide both side by 2
1.5 in : 2.5 ft
Window's width in Blue print (inches) = 1.5 in.
As a result, the window width in the blueprint is 1.5 in.
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Which of the following functions has a graph that is a
line
f(x) = Ixl
f(x) = x
f(x)=x²
With the help of equations we can say that function has a f(x) = x,straight line.
What is an equation?
A mathematical equation is a formula that uses the equals symbol (=) to connect two expressions and express their equality.A well-formed formula consisting of two expressions linked by an equals sign is considered to be an equation in English, but the word's cognates in other languages may have slightly different definitions.For instance, an équation is defined as having one or more variables in French.Finding the variables' values that cause the equality to be true is the first step in solving an equation with variables.The variables for which the equation must be solved are also known as the unknowns, and the unknowns' values that fulfill the equality are known as the equation's solutions. Equations can be categorized as either identities or conditional equations.acc to our question-
f(x) = Ixl
f(x) = x
f(x)=x²
Hence, function f(x) = x is a line.
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this is geometry, finding the rules for sequences of congruence transformations
The rules for the rotation and translation for the rectangle RSTU is:
Rotation: (x,y) ↔ (-y,x)
Translation : (x,y) ↔ (x+k , y)
Given,
we have rectangle R'S'T'U' which is the image of the rectangle RSTU under a rotation 90° counterclockwise about the origin followed by a translation.
we are asked to determine the rule of rotation and translation.
Rotation :
Our point A(x,y) becomes A' when a point is rotated 90 degrees counterclockwise about the origin (-y,x).
so the rule is:
Rotation: (x,y) ↔ (-y,x)
Translation:
When the shape is moved towards the right by k units, then replace x with x + k.
let's check:
R(-6,3) ↔ 90° counterclockwise rotation ↔ (-3,-6) ↔ translation↔R'(-3+9,-6) → R'(6,-6)
S(-4,7) ↔ 90° counterclockwise rotation ↔ (-7,-4) ↔ translation↔S'(-7+9,-4) → R'(2,-4)
Hence we get the required rules for sequences of congruence transformations.
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Suppose that 12 inches of wire costs 36 cents. At the same rate, how many inches of wire can be bought for 21 cents?
The amount of wire that can be bought from 21 cents is 7 inches.
It is given in the question that 12 inches of wire costs 36 cents.
We have to find the amount of wire that can be bought from 21 cents.
We will use the unitary method to solve this question.
Amount of wire that can be bought from 1 cent = 12/36 = 1/3 inches
Hence, according to the data given in the question, we can write,
The amount of wire that can be bought from 21 cents = (1/3)*21 = 7 inches.
Unitary method
The unitary method is a mathematical problem-solving technique where the value of a single unit is found out from the value of multiple units prior to finding the necessary result.
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Desiree and Nicole spent a total of $23.75 on decorations for the school dance. They bought
fifteen rolls of streamers on sale at Party City for $0.75 a roll. The remainder of the money
was spent on ornaments costing $0.50 each. How many ornaments did they buy?
Ornaments:
Streamers:
Total:
What amount of pure acid must be added to 400 mL of a 40% acid solution to produce a 60% acid solution?
Answer:
600ml
Step-by-step explanation:
Pls help me I need to submit this
(5) All snow geese can eat for 11.5 days before the research and rescue center runs out of supplies.
What is snow geese?
Despite having a reputation for having white feathers, many snow geese are actually blue geese, which are darker, gray-brown birds. These birds were formerly believed to be two distinct species, however it has recently been discovered that they are actually just two color variants of the same bird. The variation in color is controlled by a single gene.
9 snow geese are housed in the research and rescue center.
Each geese consumed 16 ounces of seeds, therefore that's how much.
Therefore, the amount of seeds consumed by 9 snow geese is equal to (16*9) ounces.
144 ounces of seeds were consumed by 9 snow geese.
There are currently 1,656 ounces of seeds.
Thus, the number of days before the center runs out of food is equal to the sum of the ounces of seeds eaten by the nine snow geese divided by the total ounces of seeds.
Days till the food center runs out of supplies = 1656/144
11.5 days are required until the center runs out of food.
Hence, all snow geese can eat for 11.5 days before the research and rescue center runs out of supplies.
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Sam has had five quizzes so far in his class. His average score is 74%. He
scored a 99% on his sixth quiz. What is his average now? Round to a whole
number.
Sam's average score based on the six quizzes is 78%.
What is the average?The average is the mean, a central tendency value.
We compute the mean by summing the values of a data set and dividing by the number of items in the collection.
In this situation, the average of 5 quizzes multiplied by 5 gives the total score in the 5 quizzes, which resulted in the average score.
This total is added to the score in the sixth quiz to get the total score for the six examinations before dividing the sum by 6, giving the overall average.
The average score in 5 quizzes = 74%
Total score in the 5 quizzes = 370% (74 x 5)
The score on the sixth quiz = 99%
Total score in six quizzes = 469% (370 + 99)
The average score in the 6 quizzes = 78.167% (469/6)
= 78%
Thus, Sam scored an average of 78% on the six tests.
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Find the equation of the linear function represented by the table below in slope-
intercept form.
The equation of the linear function represented by the table would be y = 4x - 1.
What is the slope-intercept form of the line?
When you know the slope of the line to be examined and the point given is also the y-intercept, you can use the slope-intercept formula
y = mx + c.
The y value of the y-intercept point is represented by c in the formula.
By using the given table,
for x = 0 , y = -1
so by using the slope-intercept form of the line, we can write
y = mx + c
-1 = m(0) + c
c = -1 ----------(I)
Then for x = 1, y = 3
again by using the slope-intercept form of the line, we can write
y = mx + c
3 = m(1) + (-1) -----from (I)
3 = m - 1
⇒ m = 3 + 1
⇒ m = 4 -----------(II)
Now by using (I) and (II), we can make a linear function by using the slope-intercept form of the line
y = 4x - 1
Hence, the equation of the linear function represented by the table would be y = 4x - 1.
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What is the slope of the line that passes through the points (-5,2) and (-1,-6)
Answer:
Slope = -2
Step-by-step explanation:
Slope of Line passes through two Points [tex](x_{1},y_{1} )[/tex] and [tex](x_{2},y_{2} )[/tex]
is given by [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]
So by Substitution
[tex]m=\frac{-6- 2 }{-1 - (-5)}=\frac{-8}{4} =-2[/tex]
Which graph represents the inequality y ≥ 1-3x?
Answer: show us the graph
Step-by-step explanation:
A seasoning blend is 4% onion powder, by mass? How much pure onion powder should they include in a 72g bottle to make the final blend have 20% onion powder.
Answer: 14.4g of onion powder
Step-by-step explanation: To get 20% of a number, you need to divide the original amount by 5, so 72 ÷5 is 14.4g
They should include 14.4 grams of onion powder in a bottle.
Given that, a seasoning blend is 4% onion powder, by mass.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Let x be the seasoning blend.
Now, 4% of 72=20% of x
⇒ 0.04×72=0.2×x
⇒ 0.2x=2.88
⇒ x=2.88/0.2
⇒ x=14.4 g
Hence, they should include 14.4 grams of onion powder in a bottle.
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Are the slopes 0/3 and 9/0 perpendicular? Explain
The slopes 0/3 and 9/0 are not perpendicular .
In the question ,
the two slopes are given ,
the value of slope 1 (m₁) = 0/3
the value of slope2 (m₂) = 9/0 .
We know that the two slopes m₁ and m₂ are perpendicular is
m₁ × m₂ = -1 .
So , for the given values ,
On substituting the values of m₁ and m₂ ,
we get ,
= (0/3) × (9/0) ≠ -1
Since the product of the two given slope is not equal to -1 .
the slopes are not perpendicular .
Therefore , The slopes 0/3 and 9/0 are not perpendicular .
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some airlines have restrictions on the size of items of luggage that passengers are allowed to take with them. suppose that one has a rule that the sum of the length, width and height of any piece of luggage must be less than or equal to 234 cm. a passenger wants to take a box of the maximum allowable volume. if the length and width are to be equal, what should the dimensions be?
The length, breadth and height will be 78 cm, 78cm, 78cm each.
let consider the length = l
breadth = b
height = h
we are provided that
l + b + h = 234cm .......(1)
Also we have to maximize the volume , provided length is equal to breadth
∴ eqn (1) becomes
2b + h = 234
h = 234 - 2b
also ,
volume(v) = lbh
v = b²(234 - 2b)
v = b²234 - 2b³
now to maximize the volume we take the first derivative of the volume wrt 'b' and place it equal to zero. ( lagrange method )
i.e. d( v)/db = 0
∴ 468b - 6b² = 0
6b² - 468b = 0
6b( b - 78 ) = 0
∴ b = 78 cm
now as length = breadth
l = b = 78 cm
also putting this value in eqn (1)
h = 234 - 2b
h = 78 cm
So , the dimensions will be equal and will be 78cm , 78cm, 78cm each .
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Bill wants to save for his son’s college expenses. He knows what tuition will cost in 18 years and knows the interest rate on the bank account. What he doesn’t know is how much to deposit each month to save enough for his son’s college expenses. Which Excel formula would you use?
The Excel formula that Bill would use is PMT.
How to illustrate the information?From Bill's situation, he has the following information:
time = NPER = number of periods = 18 years
RATE of the bank
FV = future value = cost of tuition
PMT, is a financial function, computes the loan payment based on constant payments and a constant interest rate. The Excel PMT function is a financial function that computes loan payments based on a fixed interest rate, the number of periods, and the loan amount. The function's name is derived from the acronym "PMT," which stands for "payment."
In conclusion, the correct option is PMT.
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Complete question
Bill wants to save for his son’s college expenses. He knows what tuition will cost in 18 years and knows the interest rate on the bank account. What he doesn’t know is how much to deposit each month to save enough for his son’s college expenses. Which Excel formula would you use? Choose from FV, PV, PMT, NPER, or RATE.
What is an equation of the line that passes through the points (6,2) and (7,1)?
The equation of the line that passes through the points (6,2) and (7,1) is y = -x+8
The points are
(6,2) and (7,1)
The slope of the line is the change in y coordinate with respect to the change in x coordinate of the function.
The slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the value in the equation
The slope of the line = (1-2) / (7-6)
= -1/1
=-1
The point slope form is
[tex](y-y_1)=m(x-x_1)[/tex]
Choose one point and substitute the values in the equation
y-2 = -1(x-6)
y-2 = -x+6
Move the 2 to right hand side of the equation
y = -x+6+2
y = -x+8
Hence, the equation of the line that passes through the points (6,2) and (7,1) is y = -x+8
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The diagram shows the circle with equation x2 + y2 = 53
A
O
A tangent to the circle is drawn at point A with coordinates (-2,7)
Find an equation of the tangent at A.
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Explain about the Equation?A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance.
A mathematical equation is a statement that two amounts or values are equal, such as 6 x 4 = 12 x 2. 2. A noun that counts. When two or more components must be taken into account collectively in order to comprehend or describe the overall situation, this is known as an equation.
Equations come in two varieties: identities and conditional equations. All possible values of the variables result in an identity. Only certain combinations of the variables' values make a conditional equation true. Two expressions joined by the equals symbol ("=") form an equation.
X2+Y2 =53
= 53 + (50-1)(-4)
= 53-196
= -143
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Add (7x^3-2x^2-5x+6) (2x^3+3x^2-x-1)
a) 9x^3+x^2-6x+5
b) 9x^6+x^4+5x^2-6
c)9x^3-x^2-6x+5
d)14x^3-6x^2-5x-6
Addition of the given is (a) [tex]9x^{3} +x^{2}-6x+5[/tex]
Equation given,
Eq 1 = [tex]7x^{3} - 2x^{2}-5x+6[/tex]
Eq 2 = [tex]2x^{3}+ 3x^{2}-x-1[/tex]
Adding Eq 1 + Eq 2,
[tex](7x^{3} - 2x^{2}-5x+6) + (2x^{3}+ 3x^{2}-x-1)[/tex]
[tex](7x^{3} + 2x^{3}) + (- 2x^{2}+ 3x^{2})+(-5x-x)+(6-1)[/tex]
[tex]9x^{3}+ x^{2}-6x+5[/tex]
Hence, the answer.
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5
link
!!!
MULTIPLE CHOICE QUESTION
Find the distance between (-3,-4) and (2,8).
Hint: plot the points on the coordinate plane and
then use the Pythagorean Theorem.
The distance between points (-3,-4) and (2,8) is 13.
What is a right angle triangle?A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees, or it follows Pythagoreans theorem.
The horizontal distance = 5
And the vertical distance = 12
The vertical and horizontal lines make a right angle when they meet,
To find distance between points, use Pythagoreans theorem,
(D)² = (5)²+(12)²
(D)² = 25 + 144
(D)² = 169
D = 13
The distance between points (-3,-4) and (2,8) is 13.
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hree students are participating in a walkathon. The data for each student is shown.
Student A: The equation y = 13x represents the amount of money raised (y) for walking (x) miles.
Student B: $36 is raised after walking 3 miles.
Student C:
Miles Walked 4 5
Money Raised $52 $65
Determine which student raised the least amount of money after walking 7 miles.
Student A
Student B
Student C
All three students raised the same amount of money after walking 7 miles.
Student B has raised the least amount of money after walking for 7 miles.
What is unit rate?A unit rate means a rate for one of something.
Given that, three students are participating in a walkathon,
Student A's money is represented by the equation y = 13x, where y is money raised for walking x miles.
Student B raised $36 money for 3 miles and Student C has raised $52 and $65 money for 4 and 5 miles respectively.
Money raised by each of them for a mile =
Student A = $13
Student B = $12
Student C = $13
Money raised by them by walking 7 miles =
Student A = $13*7 = $91
Student B = $12*7 = $84
Student C = $13*7 = $91
Hence, Student B has raised the least amount of money after walking for 7 miles.
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Solve the equation x/2 + 1 = 5x
Answer:
9/2
Step-by-step explanation:
X/2+1=5x
(X+2)/2=5x
x+2=10x
2=9x
X=9/2
