Answers
Answer:
x = 2 and x = 5
Step-by-step explanation:
What are the roots of an equation?
In simple terms, the roots are simply the x intercepts of an equation.
How to find the roots of a quadratic equation:
We can find the roots of a quadratic equation one of three ways. Here you will learn how to do all three ways.
The first way (easiest way) :
The first way to find the roots of a quadratic equation is to graph the equation on a calculator and find where the equation crosses the x axis ( these are the x intercepts )
If you look at the attached image, you see the given equation x² - 7x + 10 = 0 graphed. The equation passes the x axis at (2,0) and (5,0) meaning the roots are x = 2 and x = 5.
Second way : Using the quadratic formula:
If you don't have a calculator or don't know how to graph the equation this is the best alternative way to find the roots.
The quadratic formula is : \(\frac{-b\pm\sqrt{b^2-4(a)(c)} }{2(a)}\)
Where the values of a,b and c are derived from the quadratic equation which should be written in quadratic form : ax² + bx + c = 0
This is the case here so we can easily define our variables and plug them into our formula
We have "ax² + bx + c = 0" = x² - 7x + 10 = 0 so we can say a = 1 , b = -7 and c = 10
We now plug these into the formula
Recall formula : \(\frac{-b\pm\sqrt{b^2-4(a)(c)} }{2(a)}\)
==> plug in a = 1 , b = -7 and c = 10
\(\frac{-(-7)\pm\sqrt{(-7)^2-4(10)(1))} }{2(1)}\)
==> remove parenthesis from -(-7)
\(\frac{7\pm\sqrt{(-7)^2-4(10)(1))} }{2(1)}\)
==> simplify exponents
\(\frac{7\pm\sqrt{(49-4(10)(1))} }{2(1)}\)
==> simplify all multiplication
\(\frac{7\pm\sqrt{49-40} }{2}\)
==> subtract 40 from 49
\(\frac{7\pm\sqrt{9} }{2}\)
==> simplify sqrt
\(\frac{7\pm3 }{2}\)
==> simplify +/-
\(\frac{7+3 }{2},\frac{7-3 }{2}\\\frac{10 }{2},\frac{4 }{2}\)
==> simplify division
5 , 2
The roots are x = 5 and x = 2
( Note that we used BPEMDAS to evaluate the formula when the values of a,b and c were plugged in. BPEMDAS is simply folllowing an order of operations to ensure you get the right answer. The order is as follows : Brackets , Parenthesis (any operations inside of parenthesis) , Exponents , Multiplication and Division ( do in order going left to right ) , Addition and Subtract ( do in order going left to right )
Also note that the quadratic formula ALWAYS WORKS.
Last way: Factoring
Finally, we can also find the roots by factoring.
We have x² - 7x + 10 = 0
We must first find a number that multiplies to 10 and adds to -7
We can do so by listing the factors of 10
Factors of 10 include , 10 and 1 , -10 and -1 , -5 and -2, and 5 and 2
Out of these we want to find the multiples that add to -7
10 + 1 = 11
-10 + -1 = -11
-5 + - 2 = -7
5 + 2 = 7
The multiples that add to -7 are -5 and -2 .
From there we want to split the -7 and x² to get (x-5)(x-2)
We then solve the roots by setting the individual factors to 0
x - 5 = 0
==> add 5 to both sides
x = 5
x - 2 = 0
==> add 2 to both sides
x = 2
Related Questions
Amir’s gas tank had _____._____ L of gas in it. Then he drove to his cousin’s house and back and had _____.3 L left. How much gas did he use in each direction?
Answers
Amir’s gas tank had 1L of gas in it. Then he drove to his cousin’s house and back and had 1/3 L left. Amir used a total of 1/3L gas in each direction
How much gas did he use in each direction?From the question, we have the following parameters that can be used in our computation:
Initial amount = 1L
Remaining amount = 1/3L
The amount of gas he used in each direction is calculated as
Amount used in each direction =(Initial amount - Remaining amount)/2
Substitute the known values in the above equation, so, we have the following representation
Amount used in each direction =(1L - 1/3L)/2
Evaluate
Amount used in each direction =1/3L
Hence, the amount is 1/3L
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Here is the complete question:
Amir’s gas tank had 1L of gas in it. Then he drove to his cousin’s house and back and had 1/3 L left. How much gas did he use in each direction?
at the start of 2014 tims house was worth £100,000 the value of this house increased by 10% every year work out the value of his house at the start of 2018
Answers
Answer:
161,051
146,410 if you DON'T add 2018
Step-by-step explanation:
2014
100000÷10=10000 (10%)
100000+10000=110000
2015
110000÷10=11000
110000+11000=121000
2016
121000÷10=12100
121000+12100=133,100
2017
133100÷10=13310
133100+13310=146410
2018
146410÷10=14641
146410+14641=161051
PLEASE HELPPPPPP!!!!!!Solve this system of linear equations separate the x-and y-values with a comma
-13x=90-2y
-6x=48-2y
Answers
Answer:
\(x=-6,\\y=6\)
Step-by-step explanation:
Rewrite the system of equations as:
\(\begin{cases}-13x+2y=90\\-6x+2y=48\end{cases}\)
Subtract the second equation from the first to isolate \(x\):
\(-13x+2y-(-6x+2y)=42,\\-7x=42, \\\fbox{$x=-6$}\)
Plug in \(x=-6\) into any of the equations above and solve for \(y\):
\(-6(-6)+2y=48,\\2y=12,\\\fbox{$y=6$}\)
Verify that the solution pair \((-6, 6)\) works \(\checkmark\)
Therefore, the solution to this system of equations is:
\(x=-6,\\y=6\)
Calculate the 95% confidence interval for the following fictional data regarding daily TV viewing habits: µ= 4.7 hours; σ= 1.3 hours; sample of 78 people, with a mean of 4.1 hours.
Answers
We can be 95% confident that the true population mean TV viewing time is between 3.812 and 4.388 hours.
To calculate the 95% confidence interval, we use the formula:
CI = x' ± Zα/2 * (σ/√n)
Where:
x' = sample mean
Zα/2 = the Z-score associated with the desired confidence level (in this case, 95%, so Zα/2 = 1.96)
σ = population standard deviation
n = sample size
Substituting the given values, we get:
CI = 4.1 ± 1.96 * (1.3/√78)
Calculating the standard error (SE) first:
SE = σ/√n
SE = 1.3/√78
SE ≈ 0.147
Then we substitute the SE value in the CI formula:
CI = 4.1 ± 1.96 * 0.147
CI = 4.1 ± 0.288
CI = (3.812, 4.388)
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Kai eats 2/5 of a pizza. Sam eats ¾ of the rest of the rest of the pizza. Hari eats ¾ of
the res t of the pizza after kai and Sam have eaten. What fraction of the pizza is left?
PLEASE HELP ASAPPP
Answers
Answer:
After 2/5ths of a pizza is eaten, we have 3/5ths left.
Then, 3/4ths of the remaining (3/5) is eaten, so 3/5 multiplied by 1/4 = 3/20 slices left. If you're wondering why we multiplied it by 1/4th, there is one-fourth left after Sam eats it, so we might as well figure out what is 1/4th of 3/5.
Hari then eats his share, which is 3/4ths, so 3/20 times 1/4 = 3/80.
So, there is 3/80th of a pizza left.
Jennifer has a job that pays her $5200 per month. She also has to pay
12% per month in Federal Taxes and 3.5 % per month in State Taxes. If
these are her only deductions, then what is her net pay for the year?
O A. $4,394
B. $26,364
C. $52,728
D. $63,872
Answers
Answer:
4394
5200 X 0.12 = 624 --> 5200 - 624 = 4576
5200 X 0.035 = 182
4576 - 182 = 4394
Need help solving. Prefer you show each step in solving.
Answers
Answer:
AB║CD and AD║BC
Step-by-step explanation:
By the property of a parallelogram,
" Consecutive angles of a parallelogram are supplementary"
In the figure attached,
∠DCB and ∠CDA are the supplementary angles. Therefore ABCD will be a parallelogram.
[Given: m(∠DCB) + m(∠CDA) = 180°]
And the pair of opposite sides of the parallelogram ABCD will be parallel.
AD║BC and AB║CD
Marty was renting a boat and wanted to get the best plan. Rental and plan A charges a fee of $50 plus $25 per hour. Plan B charges a fee of $10 plus $35 per hours. Write a system of equations that represent the situation above.
Answers
Answer:
Step-by-step explanation:
-2<-3x+4<13.......................
Answers
Answer:2>x>−3
Step-by-step explanation: Hope this helps
Find the limit, if it exists, or show that the limit does not exist. lim(,)→(0,0) 2 2 4
Answers
The limit does not exist.
What is a limit?A limit in mathematics is the value that a function approaches when its input approaches some value. Limits are used to define continuity, derivatives, and integrals in calculus and mathematical analysis.In order for such a limit to occur, the fraction \(\frac{x^{2} }{x^{2} +y^{2} }\) must be comparable to the same value \(L\), regardless of the way we take to get there \((0,0)\).
Try approaching \((0,0)\) along the x-axis.
This means setting \(y=0\) and finding the limit \(lim_{x-0} \frac{x^{2} }{x^{2} +y^{2} }\).
We obtain:
\(lim_{x-0,y=0}\frac{x^{2} }{x^{2} +y^{2} } =lim_{y=0}}\frac{x^{2} }{x^{2} +0 }\\=lim_{x-0}} \frac{x^{2} }{x^{2} } \\\\=lim_{x-0}}1\\=1\)
Now evaluate approaching \((0,0)\) along the y-axis.
This means setting \(x=0\) and finding the limit \(lim_{y-0} \frac{x^{2} }{x^{2} +y^{2} }\).
\(lim_{y-0,x-0} \frac{x^{2} }{x^{2} +y^{2} } =lim_{y-0} \frac{0}{0+y^{2} } \\=lim_{y-0} \frac{0}{y^{2} } \\=lim_{y-0} 0\\=0\)
Approaching the origin via these two methods results in distinct limits.
\(lim_{x-0,y-0} \frac{x^{2} }{x^{2} +y^{2} }\) ≠ \(lim_{y-0,x-0}\frac{x^{2} }{x^{2} +y^{2} }\)
Therefore the limit does not exist.
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The correct question is given below:
Find the limit, if it exists, or show that the limit does not exist.
\(lim_{(x,y) -(0,0)} \frac{x^{2} }{x^{2} +y^{2} }\)
The double-reciprocal transformation of the Michaelis-Menten equation, also called the Lineweaver- Burk plot, is given by
1/V_0 = K_m /(V_max[S]) + 1/V_max
To determine Km from a double-reciprocal plot, you would:
A) multiply the reciprocal of the x-axis intercept by -1.
B) multiply the reciprocal of the y-axis intercept by -1.
C) take the reciprocal of the x-axis intercept.
D) take the reciprocal of the y-axis intercept.
E) take the x-axis intercept, where V_0 = 1/2 V_max.
Answers
To determine Km from a double-reciprocal plot, you would choose option (A) which is to multiply the reciprocal of the x-axis intercept by -1.
In the double-reciprocal plot equation, the x-axis intercept is -1/Km, and the y-axis intercept is 1/Vmax. Therefore, if you take the reciprocal of the x-axis intercept, you get -Km, and multiplying it by -1 gives you Km.
This method is preferred because it is more accurate than estimating Km based on the position of the curve on the plot or by taking the x-axis intercept where V0 = 1/2 Vmax, which can be influenced by experimental error.
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what is the mean of -15,-12,8,9
Answers
Answer:
-2.5
Step-by-step explanation:
(-15+-12+8+9)/4= -2.5
Harry and selma start driving from the same location. harry drives 18 mi north while selma drives 80 mi east. how far apart are harry and selma when they stop? (assume harry and selma are driving at the same speed.)
Answers
Answer:
82 miles
Step-by-step explanation:
When they stop, Harry is 18 miles north and Selma is 80 miles east
Their positions form the vertices of a right triangle with legs 18 and 80
Their distance from each other will be the hypotenuse of this triangle given by the Pythagorean theorem
\(c = \sqrt{a^{2} + b^{2}}\)
where c is the hypotenuse and a, b the shorter legs
Given a = 18, b = 80
\(c = \sqrt{18^{2} + 80^{2}}\\\\c = \sqrt{324 + 6400}\\\\c = \sqrt{6724}\\\\\\c=82\\\\\)
a linear function is given. g(x) = −8x + 6 (a) find the average rate of change of the function between x = a and x = a + h.
(b) find the slope of the line.
Answers
To find the average rate of change of the function g(x) = -8x + 6 between x = a and x = a + h, we need to calculate the slope of the line passing through these two points.
The formula for average rate of change is (g(a + h) - g(a)) / h, where g(a + h) represents the value of the function at x = a + h, g(a) represents the value of the function at x = a, and h is the change in x.
Substituting the values into the formula, we have ((-8(a + h) + 6) - (-8a + 6)) / h.
Simplifying this expression, we get (-8a - 8h + 6 + 8a - 6) / h.
Cancelling out the -8a and 6 terms, we are left with -8h / h.
Finally, the average rate of change of the function g(x) = -8x + 6 between x = a and x = a + h simplifies to -8.
Therefore, the average rate of change of the function is -8.
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a jet airliner travels 1680 miles in 3 hours with a tail wind. the return trip, into the wind, takes 3.5 hours. write a system of equations whose solution is the ground speed of the airplane and the wind speed.
Answers
A system of equation is 1680mi3hr = p−w×600×2hr -p + w for a jet airliner travels 1680 miles in 3hours with a tail wind.
Let p be the speed of the jet airliner
and w be the speed of the tail wind
It takes the plane 3 hours to go 1680 miles when a jet airliner travels with a tail wind and and 3.5 hours to go 1680 miles against the wind.. So, using system of equations we get
1680mi3hr = p−w×600×2hr = p + w
Solving for the left sides we get:
200mph = p - w
300mph = p + w
Now solve for one variable in either equation, we use
200mph = p - w
Add w to both sides:
p = 200mph + w
Using the value of x, we can found the value of w using system of equations.
300mph = (200mph + w) + w
Combine like terms:
300mph = 200mph + 2w
Subtract 200mph on both sides:
100mph = 2w
On dividing by 2:
50mph = w
So the speed of the tail wind is 50mph.
Therefore, 200mph = p - 50mph
Add 50mph on both sides:
250mph = p
Hence, speed of jet airliner is 250mph.
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Chloe contumes good X and eood Y Chiloe betlieves that 6 units of good X is awmy s perfect subreitute for 1 unit of good Y, Write dewn a unity function that describes Chiloe's preferences.
Answers
Chloe believes that 6 units of good X are a perfect substitute for 1 unit of good Y. We need to write down a utility function that represents Chloe's preferences.
To represent Chloe's preferences, we can use a Cobb-Douglas utility function. In this case, since Chloe believes that 6 units of X are a perfect substitute for 1 unit of Y, we can express her preferences as follows:
\(U(X, Y) = \alpha X^\beta Y^{(1-\beta)}\)
In this utility function, X represents the quantity of good X consumed, Y represents the quantity of good Y consumed, and α and β are positive constants.
Given that 6 units of X are a perfect substitute for 1 unit of Y, we can set β = 1/6. This means that the coefficient of Y in the utility function is raised to the power of (1 - 1/6) = 5/6, indicating the decreasing marginal utility of Y as more of it is consumed.
The utility function U(X, Y) captures Chloe's preferences, where she derives satisfaction from consuming both goods X and Y, with the trade-off between the two represented by the exponent β in the utility function.
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the 120 grams powdered milk make 12 cups of milk. how many kilograms of powdered milk can produce 60 cups of milk. how many liters is 60 cups of milk?
Answers
Answer: 0.6 Liters of powdered milk can produce 60 cups of milk.
Explanation: 120 grams of powdered milk makes 12 cups of milk. 120 divided by 12 is 10. 60 times 10 is 600. So 600 grams of powdered milk to make 60 cups of milk. That is equal to 0.6 kilograms and that is equal to 0.6 liters.
this is the question click it
Answers
Answer:
C.
Step-by-step explanation:
5/8 = 20/32
20/32 ÷ 2 = 10/16
10/16 ÷ 2 = 5/8
Answer:
C
Step-by-step explanation:
You can see that both of the numbers are being multiplied by 4/4 which gives you a proportional relationship unlike the other answers there.
Water makes up about 60% of the average adult's body weight. Represent this percent by shading in the squares.
Answers
Answer:
shading three boxes
Step-by-step explanation:
It is given that :
The body weight of an average adult = 60%
We have to show this by shading the square boxes shown.
There are 5 square boxes in total which makes up 100%.
So divide 100 by 5, we can 20% for each box.
So, 20% + 20% + 20% will give us 60%
Therefore, shading three boxes will give us 60% which is the water percent in an average adult's body weight.
This is represented by the figure below.
For each sequence, find the first 4 terms and the 10th term.
A) n+5
B)2n-1
Answers
Answer:
see explanation
Step-by-step explanation:
(a)
To find the first 4 terms substitute n = 1, 2, 3, 4 into the n th term formula.
a₁ = 1 + 5 = 6
a₂ = 2 + 5 = 7
a₃ = 3 + 5 = 8
a₄ = 4 + 5 = 9
For the 10 th term substitute n = 10, that is
a₁₀ = 10 + 5 = 15
The first 4 terms are 6, 7, 8, 9 and the 10 th term is 15
(b)
Substitute n = 1, 2, 3, 4 and 10 into the n th term formula
a₁ = 2(1) - 1 = 2 - 1 = 1
a₂ = 2(2) - 1 = 4 - 1 = 3
a₃ = 2(3) - 1 = 6 - 1 = 5
a₄ = 2(4) - 1 = 8 - 1 = 7
a₁₀ = 2(10) - 1 = 20 - 1 = 19
The first 4 terms are 1, 3, 5, 7 and the 10 th term is 19
Directions: Find the missing number in each question, then identify the property used.4. 10* ( 2 + 6 )= ( 10 * 2 ) + ( 10 * x )
Answers
Answer:
The missing number: 6
The property used: Distributive Property of Multiplication
Explanation:
Given the below;
\(10\cdot(2+6)=(10\cdot2)+(10\cdot x)\)The below shows an example of the distributive property of multiplication;
\(a(b+c)=(a\cdot b)+(a\cdot c)\)Applying the distributive property in the given equation, we can see that;
\(x=6\)So the missing number is 6 and the equation can be written as;
\(10*(2+6)=(10\cdot2)+(10\cdot6)\)What is the circumference of the circle
A. 18.84
B. 17.6
C. 21.79
D. 15.65
Answers
Answer:
18.84
Step-by-step explanation:
The formula for circumference is 2(pi)r, I think. The radius is 3. 3 times 2 is 6. 6 times 3.14 is around 18, I think.
hope this helps
Answer:
A
Step-by-step explanation:
(t/f) if 0 is an eigenvalue of a, then a is invertible.
Answers
The matrix cannot be inverted if any eigenvalue is 0, which also means that the determinant is zero. This suggests a linear dependence between the columns of A. As a result, A is not of full rank and is not invertible.
What does "linearly dependent" mean?
A set's ability to have at least one linear combination of its components equal to zero when the coefficients are taken from another provided set and at least one of those coefficients is not equal to zero.
This feature applies to matrices or vectors. adjective that depends on linearity.
What does it mean to be linearly dependent?
A group of non-zero vectors is said to be linearly dependent if at least one of them can be expressed as a linear combination of the others.
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Helpful conversions: 1 acre =43,560 square feet 1 hectare =10,000 square meters 1lb=454 grams 1 kg=2.2lbs=1000grams 1. Scouting for cover crop establishment in the field requires conversion of your massbased seeding rate (e.g., lbs/acre) to a population-based establishment rate (e.g., plants/f? ). Let's practice doing that. Convert the following seeding rates: a. Cereal rye - 60 ibs/acre = H seeds/square foot b. Crimson clover −15 kg/ha= H seeds/square meter 2. Convert the following population-based seeding rates to mass-based seeding rates. a. Oats −30 plants/square foot = Ibs seedlacre b. Hairy vetch −20 plants/square meter = kg seedsha 3. Your farm manager wants you to drill crimson clover seed, but the seed hasn't arrived yet and you don't know if it's coated or not. If the seed is not coated, the seeding rate is 20 blacre. Will you need to increase or decrease your seeding rate if the seed is coated?
Answers
Coating the seed typically improves seed quality and germination rates, so the same seeding rate can be maintained even with coated seed.
To convert mass-based seeding rates to population-based establishment rates, we need to consider the area conversion factors provided:
a. Given a seeding rate of 60 lbs/acre for cereal rye, we can convert it to seeds per square foot by using the conversion factor of 1 acre = 43,560 square feet.
b. Given a seeding rate of 15 kg/ha for crimson clover, we can convert it to seeds per square meter using the conversion factor of 1 hectare = 10,000 square meters.
To convert population-based seeding rates to mass-based seeding rates, we can use the given area conversion factors:
a. Given a seeding rate of 30 plants/square foot for oats, we can convert it to pounds of seed per acre.
b. Given a seeding rate of 20 plants/square meter for hairy vetch, we can convert it to kilograms of seed per hectare.
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If p is the hypothesis of a conditional statement and q is the conclusion, which is represented by q→p?
O the original conditional statement
O the inverse of the original conditional statement
O the converse of the original conditional statement
O the contrapositive of the original conditional statement
Answers
Answer:
(c) the converse of the original conditional statement
Step-by-step explanation:
If a conditional statement is described by p→q, you want to know what is represented by q→p.
Conditional variationsFor the conditional p→q, the variations are ...
converse: q→pinverse: p'→q'contrapositive: q'→p'As you can see from this list, ...
the converse of the original conditional statement is represented by q→p, matching choice C.
__
Additional comment
If the conditional statement is true, the contrapositive is always true. The inverse and converse may or may not be true.
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9) Five less than the square root of a number r
Answers
Which situation can be represented by this equation?
16 + 0.55n = 22 + 0.25n
Hurry need help ASAP
Answers
Write the equation of the line that is perpendicular to y = 1 and goes through (4, −9).
Answers
FOR PERPENDICULAR LINES WHEN THEIR GRADIENTS ARE MULTIPLIED THEY GIVE -1
BUT IF WE ARE TO CHECK IN THE LJNE y=1 the gradient is 0
there is no number when multiplied with 0 that will give us -1 it means that the gradient of the line perpendicular to the given one will also be 0
when we substitute in the general equation y=mx+c together with the points
\( - 9 = (0)(4) + c \\ c = - 9\)
IT MEANS THE EQUATION OF THE NEW EQUATION WILL BE
\(y = - 9\)
HOPE THIS HELPS
CASE :
A stationery shop has been running for 10 years and is located
near a campus where you study in Jakarta. You often stop by this
store to buy stationery, markers, rulers, and photocopiers for
co
Answers
The given paragraph states that a stationery shop has been running for 10 years near campus in Jakarta.
Students like the asker often visit this store to purchase stationery, markers, rulers, and photocopiers.
The word "been" is a past participle of the verb "be." It is used to show the completion of an action in the past.
In this case, it implies that the stationery shop has been operating for the past 10 years near the campus.
The sentence can be rewritten as follows to make use of the word "been":
"The stationery shop has been providing stationery, markers, rulers, and photocopiers to students near the campus for 10 years."
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with a reserve requirement of 5% and an initial deposit of $400, what is the maximum total amount of money that will be in the money supply? assume that all currency is deposited in a bank 7 banks hold no excess reserves (rr=.05)
Answers
The maximum money supply with a 5% reserve requirement and a $400 initial deposit is $8,000.
How to find maximum money?To calculate the maximum total amount of money that will be in the money supply, we need to consider the money multiplier effect based on the reserve requirement.
The money multiplier is given by the formula: MM = 1 / reserve requirement.
Given that the reserve requirement is 5% (rr = 0.05), the money multiplier is MM = 1 / 0.05 = 20.
The initial deposit is $400.
To calculate the maximum total amount of money in the money supply, we multiply the initial deposit by the money multiplier:
Maximum Money Supply = Initial Deposit * Money Multiplier
= $400 * 20
= $8,000.
Therefore, the maximum total amount of money that will be in the money supply is $8,000 when the reserve requirement is 5% and all currency is deposited in banks with no excess reserves.
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