The exact solutions to the equation 2x² - 9x + 1 = 0 are (9 + √73) / 4 and (9 - √73) / 4.
To solve the quadratic equation 2x² - 9x + 1 = 0 using the quadratic formula, we first need to identify the values of a, b, and c. From the given equation, we can see that a = 2, b = -9, and c = 1.
The quadratic formula is:
x = (-b ± √(b² - 4ac)) / 2a
Substituting the values of a, b, and c, we get:
x = (-(-9) ± √((-9)² - 4(2)(1))) / 2(2)
x = (9 ± √(81 - 8)) / 4
x = (9 ± √73) / 4
So, the exact solutions to the equation 2x² - 9x + 1 = 0 are (9 + √73) / 4 and (9 - √73) / 4.
As for the answer choices, it's possible that the answer key has simplified the solution further. However, your answer is correct and provides the exact solutions to the equation.
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Q.5) Helen plays darts. The scores are given below.
(a) Draw an ordered stem and leaf diagram to
show her scores.
(b) Work out the range.
Answer:
NOT THE ANSWER try to include her scores because there is no data
Solve for the value of x 3x - 9 + 12 - 6x = -18
Answer:
x =7
Step-by-step explanation:
3x - 9 + 12 - 6x = -18
Combine like terms
-3x +3 = -18
Subtract 3 from each side
-3x +3 -3 = -18 -3
-3x = -21
Divide each side by-3
-3x /-3 = -21 /-3
x =7
Answer:
\(x=7\)
Step-by-step explanation:
\(3x - 9 + 12 - 6x = -18\)
\(3x+ - 9 + 12+ - 6x = -18\)
\(3x+- 6x + - 9 + 12+ = -18\)
\(-3x+ 3= -18\)
\(-3x= -18-3\)
\(-3x= -21\)
\(3x=21\)
\(x=21/3\)
\(x=7\)
assuming the consumption of coal can be approximated by the formula c135h96o9ns,calculate the mass of carbon (in tons) in 1.5 million tons of coal. this quantity of coal might beburned in a typical power plant in 1 year
The mass of carbon in 1.5 million tons of coal is approximately 6.56 million tons.
The chemical formula provided, \(C_{135}\)\(H_{96}\)\(O_{9}\)ns, represents the composition of coal. From the formula, we can determine that each molecule of coal contains 135 atoms of carbon. To find the mass of carbon in coal, we need to calculate the proportion of carbon atoms in the formula.
The molar mass of carbon is approximately 12 g/mol. Using the atomic mass of carbon and the number of carbon atoms in the formula, we can determine the mass of carbon per molecule of coal.
Next, we multiply the mass of carbon per molecule by the number of molecules in 1.5 million tons of coal. This will give us the total mass of carbon in 1.5 million tons of coal. Finally, we convert the mass from grams to tons to obtain the final result.
By performing these calculations, we can determine the mass of carbon in 1.5 million tons of coal.
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What is the answer of this q ❓
Answer:
68Step-by-step explanation:
lets mijdkdefbdhnrr
Evaluate. 12/3+3/4÷(−1/3)−1/2
The fraction 12/3+3/4÷(−1/3)−1/2is evaluated to give -114/10
What is a fraction?A fraction can be defined as part of a whole element, variable or number
The several types of fractions in mathematics are;
Mixed fractionsProper fractionsImproper fractionsSimple fractionsComplex fractionsFrom the information, we have that;
12/3+3/4÷(−1/3)−1/2
The fraction given is a mixture of proper fractions and improper fractions
Expand the bracket, we get;
12/3 + 3/4 ÷ -1/3 -1/2
Find the lowest common denominator
48 + 9 /12 ÷ -2 - 3 /6
Add the numerators
57/12 ÷ -5/6
Take the inverse of the divisor and multiply
57/12 × 6/-5
-114/10
Hence, the value evaluated from the fraction is -114/10
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2^5×8^4/16=2^5×(2^a)4/2^4=2^5×2^b/2^4=2^c
A=
B=
C=
Please I'm gonna fail math
9514 1404 393
Answer:
a = 3, b = 12, c = 13
Step-by-step explanation:
The applicable rules of exponents are ...
(a^b)(a^c) = a^(b+c)
(a^b)/(a^c) = a^(b-c)
(a^b)^c = a^(bc)
___
You seem to have ...
\(\dfrac{2^5\times8^4}{16}=\dfrac{2^5\times(2^3)^4}{2^4}\qquad (a=3)\\\\=\dfrac{2^5\times2^{3\cdot4}}{2^4}=\dfrac{2^5\times2^{12}}{2^4}\qquad (b=12)\\\\=2^{5+12-4}=2^{13}\qquad(c=13)\)
_____
Additional comment
I find it easy to remember the rules of exponents by remembering that an exponent signifies repeated multiplication. It tells you how many times the base is a factor in the product.
\(2\cdot2\cdot2 = 2^3\qquad\text{2 is a factor 3 times}\)
Multiplication increases the number of times the base is a factor.
\((2\cdot2\cdot2)\times(2\cdot2)=(2\cdot2\cdot2\cdot2\cdot2)\\\\2^3\times2^2=2^{3+2}=2^5\)
Similarly, division cancels factors from numerator and denominator, so decreases the number of times the base is a factor.
\(\dfrac{(2\cdot2\cdot2)}{(2\cdot2)}=2\\\\\dfrac{2^3}{2^2}=2^{3-2}=2^1\)
Can someone help me PLZ! I keep posting the same question and no ones helping me :((((((((((((
Which step could you use to start solving the system of equations below?
x + y = 3
-3x - 2y = -7
Group of answer choices
Multiply -3x - 2y = -7 by 2 and subtract it from x + y = 3
All of the above.
Multiply x + y = 3 by 3 and add it to -3x - 2y = -7
Add x + y = 3 to -3x - 2y = -7
Answer:
Multiply x + y = 3 by 3 and add it to -3x - 2y = -7
Step-by-step explanation:
When using elimination to solve a system of equations, you multiply one equation by some number. The reason for doing this is that when you add it to the second equation, you want one variable to cancel out. When one variable cancels out (in this case x), you can solve for the other variable (in this case y). I will show this:
3(x + y = 3) = 3x + 3y = 9
3x + 3y = 9
+ -3x + -2y = -7
---------------------------
y = 2
Now, knowing that y = 2, you can substitute y=2 into either equation to solve for x.
-3x - 2(2) = -7
-3x -4 = -7
-3x = -3
x = 1 | to double check (1, 2) as your answer plug these values into both equations
Finding this solution would not have been possible if not for cancelling out the x's above. The other three are wrong because none of the other options cancels out one of the variables.
Any nice math experts I have 5 unanswered questions on my profile where you can get more points please consider answering them this is my offering for your time and knowledge.
Answer:
I´m not an expert but I´ll look at it :3
Step-by-step explanation:
Which of the following is a polynomial?
Answer:
A. \(\frac{4}{5}y^{2}+\frac{5}{6}y^7\)
Step-by-step explanation:
A polynomial is a combination of terms separated by + or − signs. A polynomial does not contain variables raised to negative or fractional exponents, variables in the denominator or under a radical, or any special features such as trigonometric functions, or logarithms.
lily is using dark power crystals to raise an army of zombies. each crystal can raise 9 99 zombies. how many crystals does lily need to raise 6 , 174 6,1746, comma, 174 zombies?
Lilly needs 686 dark power crystals to raise 6174 zombies.
To solve this problem, we need to determine how many dark power crystals are needed to raise a specific number of zombies. We know that each crystal can raise 9 zombies. So, to determine the number of crystals needed to raise a given number of zombies, we simply divide that number by 9.
In this case, we want to know how many crystals Lilly needs to raise 6174 zombies. So we divide 6174 by 9
= 6174 / 9
Divide the numbers
= 686
This means that Lilly needs 686 dark power crystals to raise 6174 zombie
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The given question is incomplete, the complete question is:
Lilly is using dark power crystals to raise an army of zombies.each crystal can raise 9 zombies. how many crystal does Lily need to raise 6174 zombies
Solve -1-w-
W=
DONE
-
35
3 1
5
=
W.
The solution to the equation -1/2w - 3/5 = 1/5w is w = -6/7, meaning that w equals negative six-sevenths when the equation is true.
To solve the equation -1/2w - 3/5 = 1/5w, we'll start by simplifying and rearranging the terms to isolate the variable w.
First, we'll combine like terms on the left side of the equation:
-1/2w - 3/5 = 1/5w
To make the equation easier to work with, let's get rid of the fractions by multiplying every term in the equation by the common denominator, which is 10:
10 * (-1/2w) - 10 * (3/5) = 10 * (1/5w)
This simplifies to:
-5w - 6 = 2w
Next, we'll group the w terms on one side of the equation and the constant terms on the other side:
-5w - 2w = 6
Combining like terms, we have:
-7w = 6
Now, we'll isolate the variable w by dividing both sides of the equation by -7:
(-7w)/(-7) = 6/(-7)
This simplifies to:
w = -6/7
Therefore, the solution to the equation -1/2w - 3/5 = 1/5w is w = -6/7.
In conclusion, w is equal to -6/7 when the equation -1/2w - 3/5 = 1/5w is satisfied.
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Write the quotient and remainder when we divide (x^3 -4x^2 + 2x + 5) by (x - 2)
Answer:
Step-by-step explanation:
Sorry I can't explain how it is done. It is very difficult to explain on paper.
Simply
28 divided by 2 plus 3(8) minus (12-8)
Answer:
34
Step-by-step explanation:
28/2 + 3(8) - (12-8)
14 + 24 - 4
14 + 20
34 is your answer
hope this helps
# I want answer in C++.
Consider two fractions in the form \( a / b \) and \( c / d \), where \( a, b, c \), and \( d \) are integers. Given a string describing an arithmetic expression that sums these two fractions in the f
To solve the fraction addition problem in C++, you can define a Fraction struct to represent fractions. Implement a gcd function to find the greatest common divisor.
Parse the input fractions and perform the addition using overloaded operators. Print the result. The code reads the input string, finds the "+" operator position, parses the fractions, performs the addition, and prints the sum.
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Joey is 5 years less than three times the age of his son. Joey is 43 years old.
A) If is son's age is x years, write an expression in x to represent Joey's age.
B) Write an equation in x that can be used to find the value of x and find the value of x.
(Note: I am a 13 year old girl in 7th grade)
Answer:
amogus
Step-by-step explanation:
Lily found lots of change behind the couch. She found 280 coins total, and 70 of them are dimes. What percentage of the coins are dimes?
Answer:
25 percent
Step-by-step explanation:
70/280x100 gives as 25 percent
Answer:
1/4 or 0.25%
Step-by-step explanation:
280 ÷ 70 = 1/4 or 0.25%
An election poll predicts that, in one riding, 4 out of 7 voters will vote for a certain political party. There are 25 156 voters. If the prediction is true, how many voters will not vote for that political party?
Answer:
10,781 voters
Step-by-step explanation:
In election poll, if 4 out of 7 voters will vote for a certain political party, the total voters will be 7 and 3 out of 7 will not vote for the political party
If there are 25 156 voters, we are to find the number of voters that will not vote for that party. Hence the number of people that will not vote is expressed as;
= 3/7 * 25,156
= 75,468/7
= 10,781
Hence approximately 10,781 voters will not vote for the party.
19. The wingspan of a ghost bat is 12 more than twice that of a vampire bat.
Suppose a ghost bat has a wingspan of 28 inches. Which equation can be
used to find the wingspan of a vampire bat?
A x + 2 + 12 = 28
C 2x – 12 = 28
B 2x + 12 = 28
D 12x + 2 = 28
Answer:
B. 2x + 12 = 28
Step-by-step explanation:
x is representative of the wingspan of the vampire bat. suppose the ghost bat has a wingspan of 28 inches.
if the wingspan of a ghost bat is 12 more than twice the vampire bat's, then 2x + 12 is the equation used to find the ghost bat's wingspan. we already know the ghost bat's wingspan is 28, therefore the equation is 2x + 12 = 28
Please help me it’s for a quiz
A fenced pasture has a central rectangular corral within it that measures 8m by 5m.
The total area of the fenced pasture (outside the corral) is three times the area of the central corral.
What is the area of the central corral?.
If the width of the pasture border is the same for each side of the central corral,
what is the width of the border?
Draw a labeled picture, use let statements and show your work.
Answer:
*cough**cough* Ms. Roth?
Ruby biked a trail that is 3/5 mile each way. After biking 1/4 of the trail, she stopped to rets. What fraction of a mile did Ruby bike before she stopped to rest?
Answer:
7/20 miles
Step-by-step explanation:
get a common denominator
subtract the numerators
then you have the fraction she biked
Two similar cuboids have comesponding widths of 11 cm and 9 cm a Find the ratio of their surface area b The surface area of the larger cub 363 cm². Find the surface area of the smaller cuboid are shapes
If Two similar cuboids have corresponding widths of 11 cm and 9 cm.
a. the ratio of their surface area is: 11/9
b. The surface area of the smaller cuboid are shapes is 243 cm².
How to find the surface area?a) Let's call the length of the larger cuboid "L1" and the width "W1". The length of the smaller cuboid can be represented as "L2" and the width "W2".
Since the two cuboids are similar, we have the relationship:
L1/L2 = W1/W2 = √(W1/W2)
We know that W1 = 11 cm and W2 = 9 cm, so W1/W2 = 11/9.
Squaring both sides, we get:
(W1/W2)^2 = (11/9)^2 = 121/81
Now, the ratio of their surface area can be found by taking the square root of the ratio of their lengths squared:
(L1/L2)^2 = (W1/W2)^2 = 121/81
Taking the square root of both sides:
L1/L2 = √(121/81) = 11/9
b) Let use the ratio of their surface area to find the surface area of the smaller cuboid:
SA1/SA2 = (L1/L2)^2 = (11/9)^2 = 121/81
SA2 = SA1 / (L1/L2)^2 = 363 / (121/81) = 363 * 81/121 = 243 cm²
Therefore the surface area of the smaller cuboid is 243 cm².
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i need help please!!
Answer:
Step-by-step explanation:
do the thing times 2
X = 2y + 18
5x = -3y - 27
Use the substitution method to solve the system below
Answer:
(0, - 9 )
Step-by-step explanation:
x = 2y + 18 → (1)
5x = - 3y - 27 → (2)
substitute x = 2y + 18 into (2)
5(2y + 18) = - 3y - 27
10y + 90 = - 3y - 27 ( add 3y to both sides )
13y + 90 = - 27 ( subtract 90 from both sides )
13y = - 117 ( divide both sides by 13 )
y = - 9
substitute y = - 9 into (1)
x = 2(- 9) + 18 = - 18 + 18 = 0
solution is (0, - 9 )
Which sequence is generated by the function f(n + 1) = f(n) - 2 for f(1) = 10?
Answer:
The sequence generated will be 10,8,6,4,2,......
Step-by-step explanation:
We want to generate a sequence here
f(n + 1) = f(n) - 2
f(1) = 10
So f(2) = f(1) - 2 = 10 -2 = 8
f(3) = f(2) - 2 = 8-2 = 6
f(4) = f(3) -2 = 6-2 = 4
f(5) = f(4) - 2 = 4-2 = 2
So the sequence will be ;
10, 8 , 6 , 4 , 2 , •••••••••
Answer:
10, 8, 6, 4, 2, ...
Chad sells custom T-shirts with five friends. They want to make enough money so that, after splitting the earnings evenly, each person earns 40
Answer: They earned 500 bucks in total
Answer:
They want to make 200 dollars
Step-by-step explanation:
40*5=200
Veronica needs blinds for the window in her bedroom. the window is 2 meters tall and 4 meters wide. what is the area of the window?
The area of the window is 8\(m^{2}\).
What is the area?An object's area is how much space it takes up in two dimensions. It is the measurement of the number of unit squares that completely cover the surface of a closed figure.
The word "area" refers to a free space. The length and width of a form are used to compute its area.
Any shape's area can be calculated by counting how many unit squares will fit inside of it.
According to the question,
Length of window=2m
Width of window=4m
Area of window=Length*Width
=2*4
=8\(m^{2}\)
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Suppose that h(x) = 4x – 5 and h(b) = 17. What is the value
of b?
(A) 4
(B) 5.5
(C) 10
(D) 17.5
Answer:
5.5
Step-by-step explanation:
that is the answer....
Each side of a regular pentagon is m + 10 inches. The formula for finding the perimeter of the pentagon is shown below. P = 5(m + 10) Which equation shows this formula solved for m? A. m =P − 5 / 10 B. m = 5P − 50 C. m = P − 50 / 5 D. m = P5 − 50
Answer:
Solving for m gives:
\(m=\frac{P-50}{5}\)
which is option C in the list of possible answers
Step-by-step explanation:
Starting with the given equation, we work on using distributive property, and then on isolating the term with the variable to express:
\(P=5\,(m+10)\\P=5m+50\\P-50=5m\\\frac{P-50}{5} = m\\m=\frac{P-50}{5}\)
A bouncy ball is dropped such that the height of its first bounce is 4.5 feet and each successive bounce is 73% of the previous bounce's height. What would be the height of the 10th bounce of the ball? Round to the nearest tenth (if necessary).
The height of the 10th bounce of the ball will be 0.6 feet.
What is geometric sequence?A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value.
What is the formula for finding the nth term of geometric sequence?The nth term of the geometric sequence is given by
\(\sf T_n=ar^{n-1}\)
Where,
\(\sf T_n\) is the nth term.r is the common ratioa is the first termAccording to the given question.
During the first bounce, height of the ball from the ground, a = 4.5 feet
And, the each successive bounce is 73% of the previous bounce's height.
So,
During the second bounce, the height of ball from the ground
\(\sf = 73\% \ of \ 10\)
\(=\dfrac{73}{100}(10)\)
\(\sf = 0.73 \times 10\)
\(\sf = 7.3 \ feet\)
During the third bounce, the height of ball from the ground
\(\sf = 73\% \ of \ 7.3\)
\(=\dfrac{73}{100}(7.3)\)
\(\sf = 5.33 \ feet\)
Like this we will obtain a geometric sequence 7.3, 5.33, 3.11, 2.23,...
And the common ratio of the geometric sequence is 0.73
Therefore,
The sixth term of the geometric sequence is given by
\(\sf T_{10}=10(0.73)^{10-1\)
\(\sf T_{10}=10(0.73)^{9\)
\(\sf T_{10}=10(0.059)\)
\(\sf T_{10}=0.59\thickapprox0.6 \ feet\)
Hence, the height of the 10th bounce of the ball will be 0.6 feet.
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if the growth rate r of a population is positive and remains constant, the number of people added to the population:
The number of persons added to the population rises annually if the population's growth rate, r, is positive and stable.
Given statement,
If the growth rate r of a population is positive and remains constant, the number of people added to the population,
In the given case the solution will be the number of people added to the population " increases each year ".
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