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Related Questions
Determine the measure of ∠BFE.Question options:1) 112°2) 111°3) 69°4) 224°
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We apply tangent-tangent theorem:
[tex]\begin{gathered} one\text{ tangeht = 9} \\ 2nd\text{ tangent = 2x - 1} \end{gathered}[/tex]The tangent segement from the same external points are congruent:
[tex]9\text{ = 2x - 1}[/tex][tex]\begin{gathered} Add\text{ 1 to both sides:} \\ 9\text{ + 1 = 2x} \\ 10\text{ = 2x} \\ \text{divide both sides by 2:} \\ \frac{10}{2}\text{ = }\frac{2x}{2} \\ x\text{ = 5} \end{gathered}[/tex]Using the priority list T1, T6, T2, T7, T8, T5, T4, T3, Tg, schedule the project below with two processors.Tasks that must be completed firstTime Required34TaskT1T2T3T4T5T6T7T8T9423481111T1, T2T2T2, T3T4, T5T5, T6T6Task 6 is done by Select an answer starting at timeTask 8 is done by Select an answer starting at timeThe finishing time for the schedule is
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Firstly, let's make a diagram of prerequisites:
Comment: The number within parenthesis denotes the time required to complete the corresponding task.
Now, let's make our schedule based upon the priority list:
[tex]T_1,T_6,T_2,T_7,T_8,T_5,T_4,T_3,T_9[/tex]First, we need to know which are the ready tasks (tasks without prerequisites). By the diagram is clear that they are T_1, T_2, and T_3. Then, we need to look at their priority in the priority list. Between them, T_1 has the greatest urgency; this implies that it must be the first in processor 1 (P1). Now, in terms of urgency, T_2 follows T_1; let's assign it to the second processor (P2).
Comment: In the priority list, T_6 is before T_2, but we can't assign it now for it has prerequisites that have not been completed.
After three seconds, the first processor will be free. Let's check the (new) ready tasks having completed T_1. Note that T_1 doesn't unlock any task by itself. Then, the unique ready task now is T_3; let's assign it to the first processor. By similar reasoning, after four seconds the second processor will be free, and we're going to assign T_5 to it... AND SO ON.
I'm going to finish the schedule following these reasonings, and after that, we're going to discuss the answer to the questions.
help please A sandwich shop has three kinds of bread, seven types of meat, and four types of cheese. How many different sandwiches can be made using one type of bread, one meat, and one cheese?
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Types of combinations of
Bread, Meat , CHeese
How many combinations of B M CH can be made.
There are 3, 7 and 4 types of food , respectively
Made a tree of possibilities
Then, for every 3 , there are 7 possibilities. Multiply both
3 x 7 = 21
And for every 7 , there are 4 possibilities . Multiply then
3x 7 x 4 = 84 possible type of sandwiches
Rationalize the denominator and simplify:
√5a+√5
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Is 4b-2c leqslant 12 inequalities or not inequalities[tex] ax+by \leqslant c[/tex]
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First, let's write the expression below:
[tex]4b-2c\leqslant12[/tex]Since the expression contains the symbol "<=" (that is, "lesser than or equal to") between two terms, the complete expression is an inequality.
In order to solve this inequality for a given variable, we need to rewrite the inequality such as one side of the inequality has only the wanted variable.
For example, solving the inequality for b, we have:
[tex]\begin{gathered} 4b-2c\leqslant12\\ \\ 4b\leq12+2c\\ \\ b\leq\frac{12+2c}{4}\\ \\ b\leq3+0.5c \end{gathered}[/tex]y=-5x+6y=-3x-2x=y= and the grap
Answers
y = -5x + 6 .................1
y = -3x - 2......................1
first equate the two equations to find x and y
-5x + 6 = -3x - 2
-5x +3x = -2 - 6
-2x = -8
x = -8/-2
x = 4
Next substitute x in equation 1
y = 5(4) + 6
y = 20 + 6
y = 26
Graphically,
y = -5x + 6
for x = 0
y = -5 x 0 + 6
y = 6
for y = 0
0 = -5x + 6
5x = 6
x = 6/5
x = 1.2
fiirst plot the coordinate (0,6) and (1.2,0) on the graph for the first equation to get the first straight line.
y = -3x - 2
x = 0
y = -3 x 0 - 2
y = -2
y = 0
0 = -3x - 2
3x = -2
x = -2/3
x = -0.67
plot the coordinate on the graph
solution for this question is (4,26)
Find all the factors of 99.
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The factors of 99 are: 1, 3, 9, 11, 33 and 99.
A seamstress has three colours of ribbon; the red is 126cm, the blue is 196cm and the green
is 378cm long. She wants to cut them up so they are all the same length, with no ribbon
wasted. What is the greatest length, in cm, that she can make the ribbons?
Answers
Answer:
14cm is the greatest length
Step-by-step explanation:
Hi!
So the question is basically asking for the greatest common factor between each of these numbers (if I understood the question right so here we go) :
The GCF in this case is 14:
126 / 14 = 9
196 / 14 = 14
378 / 14 = 27
Please feel free to ask me any more questions that you may have!
and Have a great day! :)
Hi, the area of a circle is 100 sq. mm. The radius is 5.64 mm. What is the circumference?
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11.28π mm
1) Since the area is 100 mm² we can plug into the Circumference formula to find out the perimeter of that circle
2)
[tex]\begin{gathered} C=2\pi\cdot r \\ C=2\cdot\pi\cdot(5.64)^{} \\ C=11.28\pi \end{gathered}[/tex]3) Hence, the circumference of that circle is 11.28π mm
What was the initial population at time t=0?Find the size of the bacterial population after 4 hours.
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Answer;
[tex]\begin{gathered} a)\text{ 195 bacteria} \\ b)\text{ 3,291,055,916 bacteria} \end{gathered}[/tex]Explanation;
a) We want to get the initial population of the bacteria
We start by writing a formula that links the initial bacteria population to a later bacteria population after time t
[tex]A(t)=I(1+r)^t[/tex]where A(t) is the bacteria population at time t
I is the initial bacteria population
r is the rate of increase in population
t is time
Now, let us find r
At t = 10; we know that A(t) = 2I
Thus, we have it that;
[tex]\begin{gathered} 2I=I(1+r)^{10} \\ (1+r)^{10}\text{ = 2} \\ 1+r\text{ = 1.0718} \\ r\text{ = 1.0718-1} \\ r\text{ = 0.0718} \end{gathered}[/tex]Now, let us find I, since we have r. But we have to make use of t= 80 and A(t) = 50,000
Thus, we have;
[tex]\begin{gathered} 50,000=I(1+0.0718)^{80} \\ I\text{ = }\frac{50,000}{(1+0.0718)^{80}} \\ I\text{ = 195} \end{gathered}[/tex]The initial population is 195 bacteria
b) For after 4 hours, we have to convert to minutes
We know that there are 60 minutes in an hour
So, in 4 hours, we have 4 * 60 = 240 minutes
Now, we proceed to use the formula above with I = 195 and t = 240
We have that as;
[tex]\begin{gathered} A(240)=195(1+0.0718)^{240} \\ A(240)\text{ = 3,291,055,916 bacteria} \end{gathered}[/tex]Growth Models 19515. In 1968, the U.S. minimum wage was $1.60 per hour. In 1976, the minimum wagewas $2.30 per hour. Assume the minimum wage grows according to an exponentialmodel where n represents the time in years after 1960.a. Find an explicit formula for the minimum wage.b. What does the model predict for the minimum wage in 1960?c. If the minimum wage was $5.15 in 1996, is this above, below or equal to whatthe model predicts?
Answers
In general, the exponential growth function is given by the formula below
[tex]f(x)=a(1+r)^x[/tex]Where a and r are constants, and x is the number of time intervals.
In our case, n=0 for 1960; therefore, 1968 is n=8,
[tex]\begin{gathered} f(8)=a(1+r)^8 \\ \text{and} \\ f(8)=1.6 \\ \Rightarrow1.6=a(1+r)^8 \end{gathered}[/tex]And 1976 is n=16
[tex]\begin{gathered} f(16)=a(1+r)^{16} \\ \text{and} \\ f(16)=2.3 \\ \Rightarrow2.3=a(1+r)^{16} \end{gathered}[/tex]Solve the two equations simultaneously, as shown below
[tex]\begin{gathered} \frac{1.6}{(1+r)^8}=a \\ \Rightarrow2.3=\frac{1.6}{(1+r)^8}(1+r)^{16} \\ \Rightarrow2.3=1.6(1+r)^8 \\ \Rightarrow\frac{2.3}{1.6}=(1+r)^8 \\ \Rightarrow(\frac{2.3}{1.6})^{\frac{1}{8}}=(1+r)^{}^{} \\ \Rightarrow r=(\frac{2.3}{1.6})^{\frac{1}{8}}-1 \\ \Rightarrow r=0.0464078 \end{gathered}[/tex]Solving for a,
[tex]\begin{gathered} r=0.0464078 \\ \Rightarrow a=\frac{1.6}{(1+0.0464078)^8}=1.113043\ldots \end{gathered}[/tex]a) Thus, the equation is
[tex]\Rightarrow f(n)=1.113043\ldots(1+0.0464078\ldots)^n[/tex]b) 1960 is n=0; thus,
[tex]f(0)=1.113043\ldots(1+0.0464078\ldots)^0=1.113043\ldots[/tex]The answer to part b) is $1.113043... per hour
c)1996 is n=36
[tex]\begin{gathered} f(36)=1.113043\ldots(1+0.0464078\ldots)^{36} \\ \Rightarrow f(36)=5.6983\ldots \end{gathered}[/tex]The model prediction is above $5.15 by $0.55 approximately. The answer is 'below'
Find the probability of obtaining exactly seven tails when flipping seven coins. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
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Answer:
Concept:
If you flip a coin once, there are
[tex]\text{2 possiblities}[/tex]Using the binomial probability formula below, we will have
[tex]P(x)=^nC_rp^xq^{x-r}[/tex]Where
[tex]\begin{gathered} p=probability\text{ of success} \\ q=probability\text{ of failure} \end{gathered}[/tex][tex]\begin{gathered} p=\frac{1}{2} \\ q=\frac{1}{2} \\ n=7 \\ x=7 \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} P(x)=^nC_rp^xq^{x-r} \\ P(x=7)=^7C_7(\frac{1}{2})^7(\frac{1}{2})^{7-7} \\ P(x=7)=(\frac{1}{2})^7 \\ P(x=7)=\frac{1}{128} \end{gathered}[/tex]Hence,
The final answer is
[tex]\Rightarrow\frac{1}{128}[/tex]The sum of three consecutive integers is −387. Find the three integers.
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Answer:
-130, -129, -128
Step-by-step explanation:
consecutive integers are when one integer is greater than the previous one and so on... so assuming the smallest integer which we start with is "x", the next integer is "x+1", and the next integer is "x+1+1".
Adding all these together will give us the sum of three consecutive integers:
[tex]x+(x+1)+(x+1+1)[/tex]
Simplifying inside the parenthesis gives us
[tex]x+(x+1)+(x+2)[/tex]
Simplifying the entire expression gives us the following:
[tex]3x+3[/tex]
This is equal to -387 as stated in the problem, so let's set it equal to -387
[tex]3x+3=-387[/tex]
Subtract 3
[tex]3x=-390[/tex]
Divide by 3
[tex]x=-130[/tex]
Since the consecutive integers are just +1, then +2, we can define the three consecutive integers as
-130, -130 + 1, -130 + 2
which simplifies to
-130, -129, -128
Cleo can paint a room in 8 hours, while Phil can paint the same room in 6 hours. If they paint theroom together, how long will it take them to paint the room?How many hours and how many minutes?
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According to the given data we have the following:
Cleo can paint a room in 8 hours, so this is=1/8x
Phil can paint the same room in 6 hours=1/6x
In order to calculate how long it take them to paint the room we would solve the following equation:
(1/6)(x)+(1/8)(x)=1
To solve this equation we would first multiply both sides by 24
Hence:
24*(1/6)(x)+24*(1/8)(x)=24
4x+3x=24
7x=24
x=24/7
x= 3 3/7 hours
Therefore It will take them 3 and 3/7 hours to pain the room.
In minutes it will take to them 205 minutes.
Louis borrowed $500 from his bank. His bank will charge Louis 8% simple interest per year to loan him the money. If he paid back the total amount he owed the bank, including interest, in 6 months, how much should he have paid?
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The amount that he owed the bank and paid is $520.
What will the interest be?The simple interest is calculated as:
= Principal × Rate × Time / 100
Principal = $500
Rate = 8%
Time = 6 months = 6/12 = 0.5 years
The interest will be:
= PRT / 100
= (500 × 8 × 0.5)/100
= 2000/100
= $20
The amount paid back will be:
= Principal + Interest
= $500 + $20
= $520
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a mother duck lines her 8 ducklings up behind her. in how many ways can the ducklings line up?
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In position one, we can have any of the 8 ducks
In position two, we can have 7 ducks, since one has to occupy position one
and so on
then, we have:
[tex]8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1=8![/tex]the factorial of 8 is 40320
In 2011, an earthquake in Chile measured 8.3 on the Richter scale. How many times more intense was thisearthquake then than the 2011 earthquake in Papa, New Guinea that measured 7.1 on the Richter scale? Roundthe answer to the nearest integer.
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SOLUTION:
Step 1:
In this question, we are given that:
In 2011, an earthquake in Chile measured 8.3 on the Richter scale. How many times more intense was this earthquake then than the 2011 earthquake in Papa, New Guinea that measured 7.1 on the Richter scale?
Round the answer to the nearest integer.
Step 2:
From the question, we are to use this formula:
Now, we have that:
[tex]\begin{gathered} M_2-M_1=\log (\frac{I_2}{I_1}) \\ \text{where M}_2=\text{ 8.3} \\ \text{and} \\ M_1=\text{ 7. 1} \end{gathered}[/tex]Hence, we have that:
[tex]\begin{gathered} \text{8. 3 - 7. 1 = log ( }\frac{I_2}{I_1}) \\ 1.2=log_{10}\text{ (}\frac{I_2}{I_1}) \\ (\frac{I_2}{I_1})\text{ = }10^{1.2} \end{gathered}[/tex]CONCLUSION:
The final answer is:
[tex](\frac{I_2}{I_1})=10^{1.\text{ 2}}[/tex]f(x) varies inversely with x and f(x)=−10 when x = 20. What is the inverse variation equation? Responses f(x)=−2x f ( x ) = − 2 x f(x)=−5x f ( x ) = − 5 x f(x)=−200x f ( x ) = − 200 x f(x)=−0.5x f ( x ) = − 0.5 x
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The equation representing the constant of proportionality is k = xf(x) and the constant of proportionality k = -200
What is proportionality?In mathematics, proportionality indicates that two quantities or variables are related in a linear manner. If one quantity doubles in size, so do the other; if one of the variables diminishes to 1/10 of its former value, so does the other.
Likewise, if the variables are inversely proportional to one another, as one quantity increases, the other quantity decreases by the same proportion or quantity.
We can proceed to substitute the values into the equation above.
k = xf(x)
k = 20 * (-10)
k = -200
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A grocer mixed grape juice which costs $1.50 per gallon with cranberry juice whichcosts $2.00 per gallon. How many gallons of each should be used to make 200 gallons of cranberry/grape juice which will cost $1.75 per gallon?
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Let x be the amount of gallons of grape juice we are using to get the mixture we want. Let y be the amount of gallons of cranberry juice used to get the desired mixture.
Since we are told that we want a total of 200 gallons of the new mixture, this amount would be the sum of gallons of each liquid. So we have this equation
[tex]x+y=200[/tex]To find the values of x and y, we need another equation relating this variables. Note that since we have 200 gallons of the new mixture and the cost per gallon of the new mixture is 1.75, the total cost of the new mixture would be
[tex]1.75\cdot200=350[/tex]As with quantities, the total cost of the new mixture would be the cost of each liquid. In the case of the grape juice, since we have x gallons and a cost of 1.50 per gallon, the total cost of x gallons of grape juice is
[tex]1.50\cdot x[/tex]In the same manner, the total cost of the cranberry juice would be
[tex]2\cdot y[/tex]So, the sum of this two quantites should be the total cost of the new mixture. Then, we get the following equation
[tex]1.50x+2y=350[/tex]If we multiply this second equation by 2 on both sides, we get
[tex]3x+4y=700[/tex]Using the first equation, we get
[tex]x=200\text{ -y}[/tex]Replacing this value in the second equation, we get
[tex]3\cdot(200\text{ -y)+4y=700}[/tex]Distributing on the left side we get
[tex]600\text{ -3y+4y=700}[/tex]operating on the left side, we get
[tex]600+y=700[/tex]Subtracting 600 on both sides, we get
[tex]y=700\text{ -600=100}[/tex]Now, if we replace this value of y in the equation for x, we get
[tex]x=200\text{ -100=100}[/tex]Thus we need 100 gallons of each juice to produce the desired mixture.
Find a degree 3 polynomial that has zeros -2,3 and 6 and in which the coefficient of x^2 is -14. The polynomial is: _____
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Given:
The zeros of degree 3 polynomial are -2, 3 , 6.
The coefficient of x² is -14.
Let the degree 3 polynomial be,
[tex]\begin{gathered} p(x)=(x-x_1)(x-x_2)(x-x_3) \\ =(x-(-2))(x-3)(x-6) \\ =\mleft(x+2\mright)\mleft(x-3\mright)\mleft(x-6\mright) \\ =\mleft(x^2-x-6\mright)\mleft(x-6\mright) \\ =x^3-x^2-6x-6x^2+6x+36 \\ =x^3-7x^2+36 \end{gathered}[/tex]But given that, coefficient of x² is -14 so, multiply the above polynomial by 2.
[tex]\begin{gathered} p(x)=x^3-7x^2+36 \\ 2p(x)=2(x^3-7x^2+36) \\ =2x^3-14x^2+72 \end{gathered}[/tex]Answer: The polynomial is,
[tex]p(x)=2x^3-14x^2+72[/tex]If a projectile is fired straight upward from the ground with an initial speed of 224 feet per second, then its height h in feet after t seconds is given by the function h(t)= -16t^2.+224t Find the maximum height of the projectile.
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The height reached by the projectile is 784 feet.
What is the maximum height of the projectile?
The projectile experiments an uniformly accelerated motion due to gravity, whose height is represented by the quadratic equation:
h(t) = - 16 · t² + 224 · t
Where t is the time, in seconds.
In this problem we need to find the maximum height reached by the projectile, which can be found by finding the vertex form of the quadratic equation:
h(t) = - 16 · (t² - 14 · t)
h(t) - 16 · 49 = - 16 · (t² - 14 · t + 49)
h(t) - 784 = - 16 · (t - 7)²
The maximum height of the projectile is 784 feet.
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which is an incorrect rounding for 53.864a) 50b) 54c) 53.9d) 53.87
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The incorrect rounding is 53.87
Explanations:The given number is 53.864
If the number is approximated to 2 decimal places
53.864 = 53.86
If the number is approximated to 1 decimal place
53.864 = 53.9
If the number is approximated to the nearest unit
53.864 = 54
If the number is approximated to the nearest tens:
53.864 = 50
Note: 53.864 cannot be approximated to 53.87 because the third decimal place (4) is not up to 5
Which equation is equivalent to StartRoot x EndRoot + 11 = 15?
Answers
Answer:
x+121=225
Step-by-step explanation:
√x+11=15
to find the equivalent let's square both sides
(√x)²+11²=15²
x+121=225
This answer is the only one that matches the question
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q(v)= int 0 ^ v^ prime sqrt 4+w^ 5 dw ther; q^ prime (v)=
Answers
ANSWER
[tex]q^{\prime}(v)=\sqrt{4+(v^7)^5}[/tex]EXPLANATION
We want to find the derivative of the given function:
[tex]q(v)=\int_0^{v7}\sqrt{4+w^5}dw[/tex]When the lower limit of an integral is a constant and the upper limit of the integral is a variable, the derivative of this is the function inside the integral in terms of the upper limit of the integral.
In other words, the derivative of the given integral function is:
[tex]q^{\prime}(v)=\sqrt{4+(v^7)^5}[/tex]That is the answer.
If the correlation coefficient is 1, then the relation is a __________________.perfect positive correlationperfect negative correlationweak negative correlationweak positive correlation
Answers
Given:
The correlation coefficient is 1.
Required:
What type of correlation is it?
Explanation:
A coefficient of -1.0 indicates a perfect negative correlation, and a correlation of 1.0 indicates a perfect positive correlation.
Answer:
Hence, correlation coefficient is 1 then relation is perfect positive correlation.
Elaina started a savings account
with $3,000. The account earned
$10 each month in interest over a
5-year period. Find the interest
rate.
Answers
Using the simple interest formula, the rate of interest is 0.67%.
In the given question,
Elaina started a savings account with $3,000. The account earned $10 each month in interest over a 5-year period.
We have to find the interest rate.
The money that Elaina have in her account is $3000.
The interest that she earned = $10
The time period is 5 year,
We find the interest rate using he simple interest formula.
The formula of simple interest define by
I = P×R×T/100
where I is the interest.
P is principal amount.
R is rate of interest.
T is time period.
From the question, P = $3000, I = $10, T = 5
Now putting the value
10 = 3000×R×5/10
Simplifying
10 = 300×R×5
10 = 1500×R
Divide by 1500 on both side
10/1500 = 1500×R/1500
0.0067 = R
R = 0.0067
To express in percent we multiply and divide with 100.
R = 0.0067×100/100
R = 0.67%
Hence, the rate of interest is 0.67%.
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find the sum.(7-b) + (3) +2 =
Answers
If f(2)= Vwhat is the rule of the inverse?
Answers
To find the inverse do these steps
1- Put f(x) = y
2- Switch x and y
3- solve to find the new y
Let us do that
[tex]y=\sqrt[]{\frac{x+4}{3}}[/tex]Switch x and y
[tex]x=\sqrt[]{\frac{y+4}{3}}[/tex]Now square the two sides to cancel the root
[tex]x^2=\frac{y+4}{3}[/tex]Multiply both sides by 3 to cancel the denominator
[tex]3x^2=y+4[/tex]Subtract 4 from both sides
[tex]3x^2-4=y[/tex]The rule is the answer D
-Quadratic Equations- Solve each by factoring, write each equation in standard form first.
Answers
Answer
The solutions to the quadratic equations are
[tex]\begin{gathered} a^2-4a-45 \\ \text{Solution: }a=-5\text{ or }9 \\ \\ 5y^2+4y=0 \\ \text{Solution: }y=0\text{ or }-\frac{4}{5} \end{gathered}[/tex]SOLUTION
Problem Statement
The question gives us 2 quadratic equations and we are required to solve them by factoring, first writing them in their standard forms.
The quadratic equations given are:
[tex]\begin{gathered} a^2-4a-45=0 \\ 5y^2+4y=0 \end{gathered}[/tex]Method
To solve the questions, we need to follow these steps:
(We will represent the independent variable as x for this explanation. We know they are "a" and "y" in the questions given)
The steps outlined below are known as the method of Completing the Square.
Step 1: Find the square of the half of the coefficient of x.
Step 2: Add and subtract the result from step 1.
Step 3: Re-write the Equation. This will be the standard form of the equation
Step 4. Solve for x
We will apply these steps to solve both questions.
Implementation
Question 1:
[tex]\begin{gathered} a^2-4a-45=0 \\ \text{Step 1: Find the square of the half of the coefficient of }a \\ (-\frac{4}{2})^2=(-2)^2=4 \\ \\ \text{Step 2: Add and subtract 4 to the equation} \\ a^2-4a-45+4-4=0 \\ \\ \text{Step 3: Rewrite the Equation} \\ a^2-4a+4-45-4=0 \\ (a^2-4a+4)-49=0 \\ (a^2-4a+4)=(a-2)^2 \\ \therefore(a-2)^2-49=0 \\ \text{ In standard form, we have:} \\ (a-2)^2=49 \\ \\ \text{Step 4: Solve for }a \\ (a-2)^2=49 \\ \text{ Find the square root of both sides} \\ \sqrt[]{(a-2)^2}=\pm\sqrt[]{49} \\ a-2=\pm7 \\ \text{Add 2 to both sides} \\ \therefore a=2\pm7 \\ \\ \therefore a=-5\text{ or }9 \end{gathered}[/tex]Question 2:
[tex]\begin{gathered} 5y^2+4y=0 \\ \text{ Before we begin solving, we should factorize out 5} \\ 5(y^2+\frac{4}{5}y)=0 \\ \\ \text{Step 1: Find the square of the coefficient of the half of y} \\ (\frac{4}{5}\times\frac{1}{2})^2=(\frac{2}{5})^2=\frac{4}{25} \\ \\ \text{Step 2: Add and subtract }\frac{4}{25}\text{ to the equation} \\ \\ 5(y^2+\frac{4}{5}y+\frac{4}{25}-\frac{4}{25})=0 \\ \\ \\ \text{Step 3: Rewrite the Equation} \\ 5((y^2+\frac{4}{5}y+\frac{4}{25})-\frac{4}{25})=0 \\ 5(y^2+\frac{4}{5}y+\frac{4}{25})-5(\frac{4}{25})=0 \\ 5(y^2+\frac{4}{5}y+\frac{4}{25})-\frac{4}{5}=0 \\ \\ (y^2+\frac{4}{5}y+\frac{4}{25})=(y+\frac{2}{5})^2 \\ \\ \therefore5(y+\frac{2}{5})^2-\frac{4}{5}=0 \\ \\ \text{ In standard form, the Equation becomes} \\ 5(y+\frac{2}{5})^2=\frac{4}{5} \\ \\ \\ \text{Step 4: Solve for }y \\ 5(y+\frac{2}{5})^2=\frac{4}{5} \\ \text{ Divide both sides by 5} \\ \frac{5}{5}(y+\frac{2}{5})^2=\frac{4}{5}\times\frac{1}{5} \\ (y+\frac{2}{5})^2=\frac{4}{25} \\ \\ \text{ Find the square root of both sides} \\ \sqrt[]{(y+\frac{2}{5})^2}=\pm\sqrt[]{\frac{4}{25}} \\ \\ y+\frac{2}{5}=\pm\frac{2}{5} \\ \\ \text{Subtract }\frac{2}{5}\text{ from both sides} \\ \\ y=-\frac{2}{5}\pm\frac{2}{5} \\ \\ \therefore y=0\text{ or }-\frac{4}{5} \end{gathered}[/tex]Final Answer
The solutions to the quadratic equations are
[tex]\begin{gathered} a^2-4a-45 \\ \text{Solution: }a=-5\text{ or }9 \\ \\ 5y^2+4y=0 \\ \text{Solution: }y=0\text{ or }-\frac{4}{5} \end{gathered}[/tex]A chemist needs to strengthen a 34% alcohol solution with a 50% solution to obtain a 44% solution. How much of the 50% solution should be added to 285 millilitres of the 34% solution? Round your final answer to 1 decimal place.
Answers
Answer: 475 ml of 50% solution is needed
Explanation:
Let x represent the volume of the 50% solution needed.
From the information given,
volume of 34% alcohol solution = 285
Volume of the mixture of 34% solution and 50% solution = x + 285
Concentration of 44% mixture = 44/100 * (x + 285) = 0.44(x + 285)
Concentration of 34% alcohol solution = 34/100 * 285 = 96.9
Concentration of 50% solution = 50/100 * x = 0.5x
Thus,
96.9 + 0.5x = 0.44(x + 285)
By multiplying the terms inside the parentheses with the term outside, we have
96.9 + 0.5x = 0.44x + 125.4
0.5x - 0.44x = 125.4 - 96.9
0.06x = 28.5
x = 28.5/0.06
x = 475