en Vision Algebra 2
1-1 Reteach to Build Understanding
Key Features of Functions
Linear, quadratic, and absolute-value functions can be graphed using key features
that the equation identifies. Key features can be labeled using either set builder
notation or interval notation. Interval notation represents a set of real numbers by
a pair of values. Parentheses are used when the points are not included. Brackets
are used for when a boundary point is included.
1. Use the function f(x) = x2 – 16 and identify the key features that are listed in
the table for the graph. Label the graph with the key features.
Key Feature
Domain
Range
Minimum Value
Function is Function is
x-intercept
decreasing increasing
10
y-intercept
LEAD) 14.0VA
Function is Positive
-2 O
Function is Negative
TO
Interval Increasing
Domain:
Interval Decreasing
Range:
-20160-16)
Answers
The value of
Domain(- ∞,∞), Range(- 16, ∞), Minimum Value = -16
Function is a quadratic function. x-intercepts are -4 and 4.
The function decreasing before vertex = (-∞,0)
The function increasing after vertex = (0, ∞)
y-intercept is -16.
Function is Positive(- ∞, - 4) ∪ (4, ∞) : , Function is negative : (- 4, 4)
Interval Increasing Domain(0,∞),
Interval Decreasing Range(- ∞, -16)
According to the data, equation f(x) = [tex]x^{2}[/tex] – 16
It is an upward parabola because coefficient of is positive.
The vertex form of a parabola is
f(x) = a[tex](x - h)^{2}[/tex] . . . (2)
where, a is constant and (h , k) is vertex.
From (1) and (2), we get
a = 1, h = 0, k = - 16
So, vertex of the parabola is (0,-16).
The given function is defined for all values of x. So,
Domain : (- ∞,∞)
The value of a function which is an upward parabola cannot be less than the y-coordinate of its vertex. So
Range : (- 16, ∞)
Minimum Value = y-coordinate of vertex = -16
Function is a quadratic function.
For f(x)=0
⇒ 0 = [tex]x^{2}[/tex] - 16
⇒ 16 = [tex]x^{2}[/tex]
⇒ x = ± 4
So, x-intercepts are -4 and 4.
The function decreasing before vertex = (-∞,0)
The function increasing after vertex = (0, ∞)
For x=0,
f(0) = [tex](0)^{2}[/tex] - 16
⇒ - 16
So, y-intercept is -16.
Function is Positive : (- ∞, - 4) ∪ (4, ∞)
Function is negative : (- 4, 4)
Interval Increasing Domain: (0,∞)
Interval Decreasing Range: (- ∞, -16)
Following are the key features of functions
1. Domain and Range
2. x-intercept and y-intercept
3. Positive and Negative intervals
4. Intervals of increasing, decreasing and constant behavior
5. Parent Functions
6. Maxima and Minima
Domain and Range
Domain : The domain is the set of all possible inputs or x-values. To find the domain of a function, we have to look at the x-axis of the graph.
Determining Domain :
1. Start at the origin.
2. Move along the x-axis until you find the lowest possible x-value. This is your lower bound.
3. Return to the origin.
4. Move along the x-axis until you find your highest possible x-value. This is your upper bound.
Range :The range is the set of all possible outputs or y-values. To find the range of the graph, we have to look at the y-axis of the graph.
Determining Range :
For the range, do the same thing but move along the y-axis.
x-intercepts and y-intercepts
x-intercept :
1. This is where the graph crosses the x-axis.
2. To find it algebraically, set y = 0.
3. Have many names :
x-intercept
-Roots
-Zeros
-y-intercept :
1. This is where the graph crosses the y-axis.
2. To find it algebraically, set x = 0.
Positive Interval :
In the diagram below, the graph of the function is above the x-axis in the following intervals.
(-3, -1) and (2, 4)
More precisely, y is positive when x ∈ (-3, -1) and (2, 4).
So, the positive intervals for the above graph are
(-3, -1) and (2, 4)
Negative Interval :
In the diagram above, the graph of the function is below the x-axis in the following intervals.
(-∞, -3), (-1, 2) and (4, +∞)
More precisely, y is negative when x ∈ (-∞, -3), (-1, 2) and (4, +∞).
So, the negative intervals for the above graph are
(-∞, -3), (-1, 2) and (4, +∞)
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Related Questions
2. A car has a fuel tank that holds 45 liters of fuel. The car consumes 8.0 liters of fuel for
each 100 km driven. A trip of 350 km was started with a full tank of fuel. How much
fuel remained in the tank at the end of the trip?
Answers
Answer: 17 liters
Step-by-step explanation:
Make a proportion:
100 km - 8 liters
350 km - x liters
Hence,
[tex]\displaystyle\\x=\frac{350*8}{100} \\\\x=\frac{2800}{100}\\\\x=28\ liters \\\\45-28=\\7\ liters[/tex]
Identify a pair of segments that are marked perpendicular to each other on the
diagram below. (Diagram is not to scale.)
P
R
T
#
U
0
S
N
Answers
the two perpendicular segments are:
PN and UR.
How to identify the perpendicular segments?Two segments are perpendicular if and only if the angles generated when the segments intersect are all right angles (angles that measure 90°).
And the 90° angles are usually notated with a little square on the vertex.
In the image we can see that the angle at U is a right angle, thus, the segments that pass through that point are perpendicular.
We can conclude that the two perpendicular segments are:
PN and UR.
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A cooked ham weighs 11 kilograms how many ham slider sandwiches can be made if each sandwich has. 55 grams of cooked ham
Answers
Number of ham slider sandwiches can be made is 200.
According to given data,
cooked ham weighs is 11 kilograms and
each sandwich has. 55 grams of cooked ham
we convert 11 kilograms to 11 grams
so we multiply 11 kilograms with 1000
then we get, 11×1000 = 11000 grams
number of ham slider sandwiches prepared
⇒ [tex]\frac{11* 1000}{55}[/tex]
⇒ [tex]\frac{1000}{5}[/tex]
⇒ 200
Therefore, we get number of prepared ham slider sandwiches is 200 .
Converting
Write the number of grams. Label it "grams" or "g." If you're using a calculator, just type the number in.
In this section, we'll follow along with an example problem to make things easier. Let's say that we want to convert 20,000 grams to kilograms. To start, we would write "20,000 grams" on our paper.
Divide by 1,000. A kilogram is one thousand grams. This means that to get kilograms from grams, you just need to divide the number of grams by 1,000.
In our example, we would get kilograms by dividing 20,000 grams by 1,000.
20,000/1,000 = 20
Label your answer. Don't forget this step! Labelling your answer with the proper units is important. If you're doing this conversion for schoolwork, you can lose points if you don't label. If you're doing it for something else, people may assume the wrong units.
In our case, we would label our answer with the label "kilograms" like this:
20 kilograms.
To get back to grams, multiply by 1,000. As discussed above, a kilogram is one thousand grams. This means that if you ever want to get back to grams from kilograms, all you need to do is multiply the number of kilograms by 1,000. Since multiplications is basically the "opposite" operation as division, this will "undo" the division and give you grams.
To get 20 kilograms back to grams, we just multiply by 1,000 (don't forget to label your answer again):
20 kilograms × 1,000 = 20,000 grams
Converting by Shifting the Decimal Point
Start with your number of grams. Believe it or not, you can convert between grams and kilograms without doing any math. This works because the metric system is a base 10 system of measurements. In other words, metric units are always a multiple of 10 apart from each other — there are 10 millimeters in a centimeter, 100 centimeters in a meter, 1,000 meters in a kilometer, and so on.
In this section, let's convert 37 grams to kilograms. We would begin the same way as in the section above, writing "37 grams" on our paper.
Shift the decimal point three spaces to the left. Now, find the decimal point in your number of grams. If you're converting a whole number, this won't usually be written, but you can assume it its to the right of the ones place. Move the decimal point three spaces to the left. Each time you move past a number counts as one space. If you run out of numbers to move past, keep moving it, leaving blank spaces.
In our example, the decimal point in 37 grams is to the right of the 7 (i.e., 37 grams is the same as 37.0 grams). If we go one space at a time, moving the decimal point three spaces to the left looks like this:
37.
3.7
.37
._37 — note that we leave an empty space when we run out of numbers.
Add zeroes in any empty spaces. You can't leave empty spaces in your answer, so fill in each one with a zero. You can also put a zero to the left of the decimal place if there aren't any numbers there, but this is optional — it just depends how you like to write your answers.
In our example, we have one empty space between the decimal point and the 3, so we'll fill it in with a zero like this:
.037
Adding the proper label (plus an extra zero to the left of the decimal point for presentation purposes), we get our final answer:
0.037 kilograms
To get back to grams, shift the decimal place back. When you have kilograms, shifting the decimal place three spaces to the right will give you grams again. Fill in any empty spaces with zeroes as normal.
In our example, we can shift the decimal place three spaces to the right like this:
0.037
00.37
003.7
0037. — the zeroes on the left don't matter any more, so we can rewrite this as simply 37 grams.
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A deck of cards contains RED cards numbered 1,2,3 and BLUE cards numbered 1,2. Let R be the event of drawing a red card, B the event of drawing a blue card, E the event of drawing an even numbered card, and O the event of drawing an odd card.
Drawing the Blue 2 is an outcome of which of the following events? Select all correct answers
Answers
Answer: E & B
Step-by-step explanation:
Thirty-four high school students were surveyed and asked how many siblings they have. The dotplot below displays the distribution of responses. A dotplot. A number line going from 0 to 8 is labeled Number of Siblings. 0, 3; 1, 5; 2, 9; 3, 9; 4, 3; 5, 3; 6, 1; 7, 0; 8, 1. What is the shape of the distribution of the number of siblings? skewed to the left bimodal symmetric skewed to the right unimodal symmetric
Answers
The distribution is skewed to the left.
What is a dot plot?A dot plot is a graph that is made up of dots and a number line. The dots in the dot plot represent the frequency of the data. The greater the frequency of a data, the greater the number of dots.
For example if a the number 5 has 10 dots above it, it means that 5 has a frequency of 10.
The given dot plot is skewed to the left because the number of dots on the left is greater than the number of dots on the right.
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Help Please!! If cos theta = - square root 2/2 and pie/2 < theta < pie, what are the values of sin theta and tan theta? What is theta in degrees and radians?
Answers
The values of the sine and tangent of the angle are √2 / 2 and - 1. By using inverse trigonometric functions, the value of angle is 135° (3π / 4).
How to find the values of other trigonometric functions and the angle behind themAccording to the statement, the cosine of the angle is in the second quadrant and therefore the value of the sine must be positive and the value of the tangent must be negative. Then, the value of the sine is found by the fundamental formula:
sin θ = √(1 - cos² θ)
sin θ = √[1 - (- √2 / 2)²]
sin θ = √(1 - 1 / 2)
sin θ = √(1 / 2)
sin θ = √2 / 2
And the value of the tangent:
tan θ = sin θ / cos θ
tan θ = (√2 / 2) / (- √2 / 2)
tan θ = - 1
By using inverse trigonometric functions, we find that the value of angle is 135° (3π / 4).
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Use the maximum and minimum data entries and the number of classes to find the class width, the lower class limits, and the upper class limits.
min = 1, max = 30, 6 classes
Answers
Using proportions, it is found that:
The class width is of 4.8333.The lower class limits are given as follows: 1, 5.8333, 10.6667, 15.5, 20.3333, 25.1665.The upper class limits are given as follows: 5.8333, 10.6667, 15.5, 20.3333, 25.1665, 30.What is a proportion?A proportion is a fraction of a total amount, and the measures can be related using a rule of three, which derives from proportional relationships.
Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures, involving operations such as division and multiplication, as they involve unit rates.
Since the classes have equal width, the width is given as follows:
class width = (max - min)/n
In which n is the number of classes.
Hence, from the data given in this problem, the class width is given as follows:
class width = (30 - 1)/6 = 4.8333.
The lowest class starts at 1, hence, adding 4.8333, we have that:
The lower class limits are given as follows: 1, 5.8333, 10.6667, 15.5, 20.3333, 25.1665
The highest class starts at 30, hence, subtracting 4.8333, we have that:
The upper class limits are given as follows: 5.8333, 10.6667, 15.5, 20.3333, 25.1665, 30.
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please help
please hurry
Answers
Answer:
It would be the last one D
Step-by-step explanation:
Because -1/x would be the recipricol graphing equation (I think) maybe not the recipricol but because the x is on bottom it's gonna make two graphs. I hope this helps some
-9x+10y=25 7x-4y=7 Elimination method (with work)
Answers
Values of x and y in the given equations by elimination method are 5 and 7 respectively. that is, x=5 and y=7.
In the elimination method, the aim is to entirely remove one of the unknown variable which would eventually make it easier to calculate be other unknown. However, it is important to note that this method is most effective when neither of the coefficients is equal to 1. The coefficient of either of the two variables will be made the same in both equations and by subtracting one from the other, it would be eliminated. It is a non-graphical methods of solving simultaneous linear equations.
consider the equations as (1) and (2),
-9x+10y=25..........................(1)
7x-4y=7............................(2)
Now, multiply equation (1) by 4 and equation (2) by 10
Let the equations we get now be (3) and (4),
-36+40y=100......................(3)
70x-40y=70........................(4)
We can see that the coefficient of y in both equations is same that is 40
Now, add equation (3) and (4)
-36+40y+70x-40y=100+70 ( y terms cancel out)
By evaluating we get,
-34x=170
x=-170/34
x=5
To find the value of y, substitute value of x in equation (2)
7x-4y=7
7*5-4y=7
35-4y=7
35-7=4y
28=4y
y=28/4
y=7
Therefore, we can conclude that the values of x and y in the given equations -9x+10y=25 and 7x-4y=7 by elimination method are 5 and 7 respectively. that is, x=5 and y=7.
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Bill weighs 120 pounds and is gaining four pounds each month. Phil weighs 220 pounds and is losing six pounds each month. Which equation could be
used to determine how many months it will take for Bill and Phil to weigh the same amount?
120+4-2202-6
120-62220 + 4z
120r-6-220z+4
120+4r 220-6r
Answers
12-mr4200
-67 months by gone
Answer: D
Step-by-step explanation: its just right
HELP PLEASEEE:)))) THIS IS ALGEBRA II BTWWW
Answers
Answer:
The answer is B
Step-by-step explanation:
I am 100% sure
Henry has a fenced yard in the shape of a rectangle with a perimeter that measures 226 feet. If the width of the yard measures 25 feet what is the length?
Answers
Answer:
Henry has a fenced yard in the shape of a rectangle with a perimeter that measure 226 feet.
it means perimeter is 226 feet.
then,it's width(breath) is 25feet
now, length =?
by using perimeter of rectangle
perimeter=2(l+b)
226=2(l+25)
226=2l+50
226-50=2l
176=2l
176/2=l
l=88
Therefore the length is 88feet.
Thank you
In the figure to the right, if AC=16 and BC=13, what is the radius?
Answers
Answer:
Radius AB = 9.3 units
Step-by-step explanation:
BC (tangent) make right angle with radius AB.
AC = 16 units
BC = 13 units
Find:
Radius AB = ?
Computation:
Using Pythagoras theorem:
Radius AB = 9.3 units
Solving Quadratic Inequalities
1ai. x^2 less than or equal to sign 8
1ei. (x-4)(x+1)>0
Answers
Answer:
1ai. x is less than or equal to 8
1ei. x > 4 and x > 1
Step-by-step explanation:
Steps for solving 1ai
Factor x² less then or equal to 8 you would do this by finding two numbers the product is equal to zero and the sum would equal to zero. You would find all factors that would equal to your terms like for example x² has the factors x•x and the factors of 0 are 0 so it would be (x+0)(x+0) is less than or equal to 8Split the factoed terms into two inequalities since you're dealing with polynomial inequalities you will either have one or more solutions. For example you will have to solve x + 0 is less than or equal to 8 Solve for x by doing the inverse operation in this case the addition will become subtraction so it will be x + 0-0 is less than or equal to 8 - 0 which would be x is greater than or equal to 8Steps to solve 1ei
Split the factored terms into 2 inequalities so (x-4) (x+1) >0 will become x-4>0 and x+1>0 Solve for x in this case x-4>0 will become x-4+4> 0+4 which is x>4 and x+1>0 will be x+1-1>0-1 which is x>-1determine the monthly payment for a car that cost $42,100 if you put $4000 down and traded in a car for $6500 on a 5 year loan with 4.5% interest rate
Answers
===================================================
Explanation:
The down payment and trade-in value add to 4000+6500 = 10,500
Subtract this total from the car's cost
42,100 - 10,500 = 31,600
This is the amount loaned to the customer.
---------------
We have these input values
L = 31,600 = loan amounti = 0.045/12 = 0.00375 = monthly interest rate in decimal formn = 12*5 = 60 months (equivalent to 5 years)Let's compute the monthly payment
P = (L*i)/(1 - (1+i)^(-n))
P = (31600*0.00375)/(1 - (1+0.00375)^(-60))
P = 589.119408031938 approximately
P = 589.12
Point G is the midpoint of segment FH. GH= 16x-19 and FG=12x+9. Find GH
Answers
Answer:
93
Step-by-step explanation:
By the definition of a midpoint, FG=GH.
[tex]16x-19=12x+9 \\ \\ 4x-19=9 \\ \\ 4x=28 \\ \\ x=7 \\ \\ GH=16(7)-19=\boxed{93}[/tex]
Jennifer is creating a rectangular-plot of grass in her backyard. She would like the length of the plot to be 6 feet less than the width. Draw a picture of the situation.
Answers
The value of the width is greater than the 21 if we want a perimeter greater than the 72 feet. Then if we let value of y is 25 then length is 19 and width is 25.
According to the statement
We have to find that the length and the width.
So, For this purpose, we know that the
A rectangle is a type of quadrilateral, whose opposite sides are equal and parallel. It is a four-sided polygon
From the given information:
The length of the plot to be 6 feet less than the width.
Then
The given perimeter = greater than 72 feet.
We know that the perimeter of rectangle is
P = 2(length + breadth)
And
P < 2(length + breadth)
here p = 72, let length = y - 6 and width = y
Then
72 < 2(length + breadth)
72 < 2(y - 6 + y)
72 < 2(2y - 6)
72 < 4y - 12
84 < 4y
y > 21.
Then let the value of y is 25 then
length = 25 - 6 and width = 25
length = 19 and width = 25.
So, The value of the width is greater than the 21 if we want a perimeter greater than the 72 feet. Then if we let value of y is 25 then length is 19 and width is 25.
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Work out the two numbers.
Write your answers on one line
The sum of two numbers is 21.
The second number is six times the first number.
Answers
Step-by-step explanation:
let the first number be x ,
second number be 6x,
sum of both numbers is 21.
then,
x + 6 x =21
or, 7x = 21
or, x =21/7
or, x = 3
now,
the first number is 3 &
the second number is 6*3= 18
The beginning-of-the-period cash balance for the Taylor Company was a $12,000 debit. Cash sales for the month were $8,000 and sales on account were $8,000. The company paid $2,500 cash for current-period purchases and also paid $3,000 cash for amounts due from last month.
What is the ending debit or credit balance in the Cash account?
Answers
Based on the calculation below, the ending debit balance in the Cash account is $14,500.
How do we calculate the Cash account ending balance?The ending balance in the Cash account can be calculated using the following formula:
Ending balance = Beginning-of-the-period cash balance + Cash sales for the month - Current-period purchases - Amounts due from last month .......... (1)
Substituting all the relevant into equation (1), we have:
Ending balance = $12,000 + $8,000 - $2,500 - $3,000
Ending balance = $14,500
Since the $14,500 is positive, this implies that the ending can balance is debit.
Note that sales on the account is not cash transaction and that is it is not included in the calculation.
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P÷2-4p÷3=5 solve for p
Answers
The value of p from the given linear expression is -6
Solving linear equationsLinear equations are equations that has a linear degree of 1. For instance the expression y =mx + b has a linear degree of 1.
Given the linear expression below:
P÷2-4p÷3=5
Applying the PEMDAS rule, the division will go first
(P÷2)-(4p÷3)=5
This can also be expressed as:
p/2-4p/3 = 5
Find the Lowest Common Denominator
p/2-4p/3 = 5
3p-2(4p)/6 = 5
(3p-8p)/6 = 5
-5p/6 =5
Cross multiply to have:
-5p = 5(6)
-5p = 30
Divide both sides by -5
-5p/-5 = 30/-5
p = -6
Hence the value of p from the given linear expression is -6
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It takes a word processor 45 minutes to word process and spell check 12 pages. Find how long it takes her to word process and
spell check 40 pages.
It takes the word processor
minutes.
Answers
I am pretty sure the answer is 150 because, as, first find the how many minutes does it take for 1 page and then the just multiply the answer with 40
Step-by-step explanation:
45/12=3.75 ×40
Andy got a loan of $120000 from a bank at a rate of 9% per annum calculate the i for the loan at the end of the first year
Answers
Answer:
I=$10800
Step-by-step explanation:
I=($120000×9×1)÷100
I=$1200×9=$10800
6. To make your shot, you need the cue ball to hit point C. Find length CD and use it
to identify the location of C in relation to one of the C corner pockets. For example, if C
is on the upper bumper, your answer might be: 15 inches to the right of the upper left
pocket. Round your answer to the nearest inch. (2 points: 1 point for distance, 1
point for location)
Answers
33in is length of CD by using angle of reflection.
What is Angle of reflection?
The angle of reflection is the angle formed by the reflected ray and the normal at the point of incidence on a reflecting surface.The angle formed by the incident and reflected rays is split into two equal angles by the normal line. The angle of incidence is the angle formed by the incident beam and the normal. The angle of reflection is the angle formed by the reflected beam and the normal.CD should be a perpendicular line to CB.
Angle of incidence = Angle of reflection
Angle ACD = Angle EAC
Let the perpendicular intersection point from A to side be G
The two right-angled triangles, CDG and CAG, are similar by AAA.
So DG/AG = CD/CA
46/18 = CD/CA
CD+CA = 96-50 = 46
CA = 46-CD
46/18 = CD/(46-CD)
46*46 - 46CD = 18CD
64CD = 46*46
CD = 33.06 = 33in
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what is 20 squared 2 + 6(9 + 3)
Answers
Answer:
[tex]\sf 872[/tex]
Step-by-step explanation:
Parentheses
[tex]9 + 3 = 12[/tex]
[tex]=20^2\cdot \:2+6\cdot \:12[/tex]
Exponents
[tex]20^2=400[/tex]
[tex]=400\cdot \:2+6\cdot \:12[/tex]
M/D(Multiply/Div.)
[tex]6\cdot \:12 = 72[/tex]
[tex]=800+72[/tex]
A/S(Add/Sub.)
[tex]800+72=872[/tex]
[tex]\sf Thus,\\= 872[/tex]
Borrowed money for 4 years at 9%. Total interest paid was 2520. How much was borrowed
Answers
The required amount that was borrowed is 7000.
Given that,
Borrowed money for 4 years at 9%.
The total interest paid was 2520.
To determine how much money was borrowed.
Simple interest is defined as the percentage of earnings on the lending for a period of time
Here,
interest = [principal * rate * time ] / 100
2520 = [principal * 9* 4] / 100
Principal = 2520 * 100 / 9*4
Principal = 7000
So, the principal amount or initial amount is $7000.
Thus, the required amount that was borrowed is 7000.
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Which lines are parallel in the square
pyramid?
Select each correct answer.
о
AB and AD
BC and DE
AD and BC
CL and BE
Answers
Step-by-step explanation:
AB and AD, i got the same question and the answer was right
Which of the following improper fractions is equal to the mixed number 29/4
Answers
The mixed fraction 7[tex]\frac{1}{4}[/tex] is equal to the improper fraction 29/4.
What is Improper Fraction ?Improper Fraction - If the numerator exceeds the denominator in a fraction, it is referred to be Improper Fraction. Some examples include 9/2, 8/5, 10/3, etc.
What is Mixed Number ?Mixed Number - A whole number along with a proper fraction forms a mixed number. Also known as mixed fraction.
For the conversion of 29/4 into mixed number
Divide the numerator 24 by denominator 4
29 ÷ 4 = 7
Remainder = 1
Write the number 7 and then write 1 (the remainder) as the numerator and the 4 as the denominator (the denominator will remain tne same).
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The correct question should be which of the following mixed fraction is equal to the improper fraction 29/4 ?
Which of the following equations are equivalent to -2m-5m - 8 = 3+(-7)+m? Select all that apply
m-4=-7m-8
-8-3m-4-m
-3m-8=4-m
-15m= -4m
-7m-8=m-4
-8-7m=-4+ m
Answers
Mason and Dallas are in a canoe race. Mason paddles 7/8 mile in 1/4. Dallas paddles 9/5 miles in 1/3 hour. Who paddles faster?
Answers
The in the canoe race, Dallas paddles faster than Mason.
According to the statement
We have to find that the Speed of the .
So, For this purpose, we know that the
The rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered.
From the given information:
Mason and Dallas are in a canoe race. Mason paddles 7/8 mile in 1/4. Dallas paddles 9/5 miles in 1/3 hour.
Then
The Mason paddles 7/8 mile in 1/4 hour.
We calculate the Speed = Distance/Time
Speed = (7/8)/(1/4)
Speed = (7/8) × (4/1)
Speed = 7/2
Speed = 3.5 miles per hour
And Dallas paddles 9/5 miles in 1/3 hour.
Speed = Distance/Time
Speed = (9/5)/(1/3)
Speed = (9/5) × (3/1)
Speed = 27/5
Speed = 5.4 miles per hour.
So, The in the canoe race, Dallas paddles faster than Mason.
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Answer:
5 2/5 is GREATER THAN 3 1/2, so DALLAS paddles faster.
In the lab, Lena has two solutions that contain alcohol and is mixing them with each other. She uses 400 milliliters less of Solution A than Solution B.
Solution A is 20% alcohol and Solution B is 17% alcohol. How many milliliters of Solution B does she use, if the resulting mixture has 179 milliliters of
pure alcohol?
Answers
Using a system of equations, it is found that she uses 700 ml of Solution B.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
For this problem, the variables are given as follows:
Variable x: Number of ml of Solution A.Variable y: Number of ml of Solution B.She uses 400 milliliters less of Solution A than Solution B, hence:
x = y - 400.
Solution A is 20% alcohol and Solution B is 17% alcohol. The esulting mixture has 179 milliliters of pure alcohol, hence:
0.2x + 0.17y = 179.
Since x = y - 400, we have that:
0.2(y - 400) + 0.17y = 179.
0.37y = 259
y = 259/0.37
y = 700.
She uses 700 ml of Solution B.
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