Answer:
x = -4 and x=1
Step-by-step explanation:
The solutions to the equation x^2 +3x -4 = 0 will be given by the points at which the graph intercepts the x-axis.
By looking at the graph, we can clearly see that the graph intercepts the x-axis at x=-4 and x=1.
One of the roots is located between -4 and -3, and the other one between 0 and 1.
54/6 findind fraction of whole number
Answer:
The answer is 9
Step-by-step explanation:
When you divide 54 by 6 you get 9 because 10 times 6 equals 60 so if you minus 6 you get 54 which equals 6 times 9. :)
Answer:
9 or 9/1
Step-by-step explanation:
To convert improper fractions to whole numbers, you have to divide the numerator by the denominator.
So, 54 divided by 6 is 9
So 54/6 as a whole number 9
If you want to keep as a fraction it would be 9/1
Below is an excerpt from a home loan contract.
“The sum of the principal of the loan and all applicable interest will be divided into 360 monthly payments according to the amortization schedule.
The Buyer shall make each monthly payment by the first day of the month it is due. A payment not received by the first day of the month it is due will be considered delinquent. A payment not received by the fifteenth day of the month it is due will be subject to a late charge of $75.00. If a payment is not received by the last day of the month it is due, the Buyer and transaction shall be reported to the appropriate credit agencies.
In the event of delinquency, the Buyer may divide any payment not received into not more than three equal installments to be included on the next consecutive monthly payments. Notification of the Buyer’s intent to do so must be made by written letter or phone call to the phone number and address listed below within one business week of delinquency.”
According to the contract, which of the following is not a responsibility of the buyer?
a.
Pay the monthly payment on time.
b.
Notify the bank if a payment is going to be late.
c.
Pay an additional $75.00 with a payment made after the 15th day of the month it was due.
d.
Notify the bank of his or her intent to split a late payment into three partial payments.
Answer:
Option B
Step-by-step explanation:
As per the contract
"The Buyer shall make each monthly payment by the first day of the month it is due."
this makes option a :"Pay the monthly payment on time." responsibility of the buyer.
"A payment not received by the fifteenth day of the month it is due will be subject to a late charge of $75.00."
this makes option c :"Pay an additional $75.00 with a payment made after the 15th day of the month it was due." responsibility of the buyer.
"Notification of the Buyer’s intent to do so must be made by written letter or phone call to the phone number and address listed below within one business week of delinquency.”
this makes option d :"Notify the bank of his or her intent to split a late payment into three partial payments." responsibility of the buyer.
So,buyer needs to only notify the bank about the monthly payments in case of delinquency and not about if payment is going to be late or not.
Hence Option B is correct
Notify the bank if a payment is going to be late!
The option that is not a responsibility of the buyer is notify the bank if a payment is going to be late.
What is a contract?A contract is an agreement that is enforceable legally between two or more parties to give something or render a services.
What are the responsibilities of the buyer?Pay the monthly payment on the first day of each month. When there is delinquency, the buyer should notify the bank of his or her intent to split a late payment into three partial payments.Pay a late charge of $75 when the payment is not received by the 15th day.To learn more about contracts, please check: brainly.com/question/12991600
What is the appropriate measurement for the weight of an African elephant?
Answer:
The average weight of African elephant is about 2 .5 to 7 tons or we can say that 1800 kg to 6300 kg.
Weight of females are about 3 to 4 tons .On the other hand weight of males are about 2.5 to 7 tons.
African element can live up to 70 years but on the other hand the life of Asian
elephants up to 60 years.
The appropriate measurement for the weight of an African elephant is between 2,268 to 6,350 kg. Male elephants can grow significantly larger than the female elephants.
Further explanation
African elephants are the largest land animals in the world. They are larger than the Asian elephant. The average weight of the African elephants is between 2,268 to 6,350 kg, the trunk alone can weigh as much as 140 kg and they can grow between 2.5 to 4 m in height.
On the other hand, the Asian elephant's weight is between 2000 to 5000 kg. African elephants are famous for their large ears, that help them to stay cool in hot African weather. Both male and female African elephant has ivory tusks, but the male's tusk is longer and heavier than the female's.
Elephants are herbivores. It means they only eat grasses, herbs, fruits, plants, and trees. African elephants can eat 150 kg of food a day. An elephant’s brain can weigh as much as 4-6 kg, they are famous as intelligent creatures. There are two kinds of African elephants which are the Savanna elephant and the Forest elephant. Savanna elephants are larger than forest elephants.
Learn more
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Keywords: African elephant, Asian elephant, the average weight of an elephant
Given the parent function f(x)= log10^x and g(x)= 5x-2, what is f(x) • g(x)?
Answer:
[tex]5x \log_{10}(x)-2 \log_{10}(x)[/tex]
(If that closed circle is an open circle, please let me know because that means something totally different)
Step-by-step explanation:
I think you are given:
[tex]f(x)=\log_{10}(x) \text{ and } g(x)=5x-2[/tex]
and that you are asked to find:
[tex]f(x) \cdot g(x)[/tex]
That operation means multiplication. (Let me know if is an open circle because that means something difference).
[tex]f(x) \cdot g(x)[/tex]
[tex](\log_{10}(x) \cdot (5x-2)[/tex]
Distribute:
[tex]\log_{10}(x)(5x)-\log_{10}(x)(2)[/tex]
Reorder a little (commutative property):
[tex]5x \log_{10}(x)-2 \log_{10}(x)[/tex]
Answer:
f(x) ⋅ g(x) = log10x^(5x − 2)
Step-by-step explanation:
Someone please helppppp
Answer:
The correct answer is last option 362.9 ft
Step-by-step explanation:
Points to remember
Sin θ = Opposite side/Hypotenuse
To find the value of x
It is given that length of slope = 1500 ft
From the figure we can get,
Sin 14 = Opposite side/Hypotenuse
= x/1500
x = 1500 * sin(14)
= 1500 * 0.2419
= 362.88 ft ≈ 362.9 ft
The correct answer is last option 362.9 ft
Brianna is twice as old as James . David is four times as old as James. Brianna is 20 years younger than David. How old is David?
Answer:
David might be 40
Step-by-step explanation:
Brianna = 20 + 20 = 40 = David
James = 10 x 2 = Brianna
David = 40 - 20 = Brianna
To find David's age, we can use the given information and algebraic equations. We can determine James' age, which is x, and use it to calculate David's age as 4x. Thus, David is 40 years old.
Explanation:To find the age of David, we need to first determine the age of James. Let's assume James is x years old.
According to the given information, Brianna is twice as old as James, so Brianna's age would be 2x years.
Similarly, David is four times as old as James, so David's age would be 4x years.
Finally, we're told that Brianna is 20 years younger than David. So, the equation would be: 2x = 4x - 20.
To solve this equation, we can subtract 2x from both sides, which gives us: -2x = -20. Then, dividing both sides by -2, we get x = 10. Therefore, James is 10 years old and David is 4x = 4 * 10 = 40 years old.
Learn more about A student is asking for help with determining the age of David based on information about the ages of Brianna and James. here:https://brainly.com/question/35552705
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Ken leaves work 20 minutes late. He decides to make up time by taking the toll road instead of side streets. He can travel three times faster by taking the toll road. Create an equation to represent his total travel time, including wait time, where x is the number of minutes the drive was expected to take
Answer:
[tex]y = \frac{1}{3} x + 20[/tex]
Step-by-step explanation:
We know that the toll road is 3 times faster than the side streets.
If 'x' represents the number of minutes she usually spend taking the side streets. The [tex]\frac{1}{3} x[/tex] represents the time she takes taking the toll road.
Also we need to create an equation to represent her total travel time, including wait time. Therefore, the equation is:
[tex]y = \frac{1}{3} x + 20[/tex]
Therefore, the equation is: [tex]y = \frac{1}{3} x + 20[/tex]
which of the following proportions is false
A.) 24/30=20/25
B.) 18/48=20/50
C.) 25/45=75/135
D.) 10/25=40/100
After simplifying each proportion or using cross-multiplication, it is clear that option B.) 18/48 = 20/50 is the false proportion.
For A.) 24/30 = 20/25, we can simplify by dividing both sides by 5. Simplified, it becomes 4/5 = 4/5, which is true.
For B.) 18/48 = 20/50, simplifying both sides by 2 gives us 9/24 = 10/25, which is not equivalent since 9x25 is not equal to 24x10. Therefore, this proportion is false.
For C.) 25/45 = 75/135, simplifying by dividing both numbers by 15 gives us 5/9 = 5/9, which is true.
For D.) 10/25 = 40/100, simplifying by dividing both sides by 10 gives us 1/2.5 = 4/10. If we further simplify 4/10 by dividing both the numerator and denominator by 2, we get 1/2.5 = 2/5, which is true after rounding the decimal in the first ratio to 2.5.
Comparing these results, option B is the false proportion.
Let f(x) = x2 - 16. Find F-1(x). (1 point)
Answer:
See below.
Step-by-step explanation:
[tex] f(x) = x^2 - 16 [/tex]
Replace f(x) with y.
[tex] y = x^2 - 16 [/tex]
Switch x and y.
[tex] x = y^2 - 16 [/tex]
Solve for y.
[tex] y^2 = x + 16 [/tex]
[tex] y = \pm\sqrt{x + 16} [/tex]
Replace y with f^(-1)(x).
[tex] f^{-1}(x) = \pm\sqrt{x + 16} [/tex]
The relation above is not a function, so the given function f(x) does not have an inverse unless the domain is restricted.
Answer:
F-1(x) = √(x + 16).
Step-by-step explanation:
Let y = x^2 - 16
First make x the subject:
x^2 = y + 16
x = √(y + 16)
Now replace x by the inverse f-1(x) and replace y by x:
f-1(x) = √(x + 16).
Note we only take the positive square root otherwise we would not have a function.
a distribution has the five number summary, 12,21,43,62,71. what is the interquartile range (IQR) of this distribution
Answer:
the IQR is 41 because 62-21=41
Answer:
83
Step-by-step explanation:
12, 21, 43, 62, 71
Median: 43
Lower quartile: 16.5
Upper quartile: 66.5
Interquartile range: 66.5 - 16.5 = 83
which equations represent the line that is perpendicular to the line 5x − 2y = −6 and passes through the point (5, −4)? Select three options.
y = –x – 2
2x + 5y = −10
2x − 5y = −10
y + 4 = –(x – 5)
y – 4 = (x + 5)
Answer:
y+4=-(2/5)(x-5) ----> equation of the line into point slope form
y=-(2/5)x-2 ----> equation of the line into slope intercept form
2x+5y=-10 ----> equation of the line in standard form
Step-by-step explanation:
step 1
Find the slope of the given line
we have
5x-2y=-6
isolate the variable y
2y=5x+6
y=2.5x+3
The slope m of the given line is m=2.5
step 2
Find the slope of the line perpendicular to the given line
We know that
If two lines are perpendicular, then their slopes are inverse reciprocal each other
so
m1=5/2
the inverse reciprocal is
m2=-2/5
step 3
Find the equation of the line into point slope form
y-y1=m(x-x1)
we have
m=-2/5
point (5,-4)
substitute
y+4=-(2/5)(x-5) ----> equation of the line into point slope form
y=-(2/5)x+2-4
y=-(2/5)x-2 ----> equation of the line into slope intercept form
Multiply by 5 both sides
5y=-2x-10
2x+5y=-10 ----> equation of the line in standard form
The equations represent the line that is perpendicular to the line 5x − 2y = −6 and passes through the point (5, −4) are as follows:
[tex]y+4=-\frac{2}{5}(x-5)[/tex]
[tex]y=-\frac{2}{5}x-2[/tex]
2x + 5y = - 10
Perpendicular linePerpendicular lines follows the mathematical principle below.
m₁m₂ = -1where
m₁ and m₂ are slopes.
Therefore, using slope intercept form,
y = mx + b
where
m = slope
b = y-intercept
Therefore,
5x - 2y = -6
-2y = -5x - 6
y = 5 / 2 x + 3
The slope is 5 / 2 x
Applying perpendicular rule,
5 / 2m₂ = - 1
m₂ = - 2 / 5
Passing through (5, -4)
-4 = -2/5 (5) + b
-4 + 2 = b
b = - 2
Therefore, the equation is [tex]y=-\frac{2}{5}x-2[/tex]. It can be simplified as follows
5y = -2x - 10
Therefore,
2x + 5y = - 10
using y - y₁ = m (x - x₁) it will be as follows:
[tex]y+4=-\frac{2}{5}(x-5)[/tex]
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Given: △PST, m∠S=90°, M∈PT,
PM≅MT, MK⊥PT, m∠SPK
m∠KPM = 5/2
Find: m∠P, m∠T, m∠SKP, and m∠MKT
Answer:
m∠P = 70°, m∠T = 20°, m∠SKP = 40° , and m∠MKT = 70°
Step-by-step explanation:
* Lets explain how to solve the problem
- In Δ PST
∵ m∠S = 90°
∴ m∠T + m∠P = 90° ⇒ interior angles of a triangle
∵ m∠SPK/m∠KPT = 5/2
- The ratio between the two angles are 5 : 2 , multiply the parts of the
ratio by x, where x is a real number
∴ m∠SPK = 5x
∴ m∠KPT = 2x
∵ m∠SPK + m∠KPT = m∠P
∴ m∠P = 5x + 2x = 7x
- In ΔPKT
∵ KM ⊥ PT
∵ MP = Mt
∴ KM is perpendicular bisector of PT
∴ ΔPKT is an isosceles triangle with KP = KT
∵ KP = KT
∴ m∠KPT = m∠T
∵ m∠KPT = 2x
∴ m∠T = 2x
∵ m∠T + m∠P = 90°
∵ m∠P = 7x
∵ m∠T = 2x
∴ 2x + 7x = 90 ⇒ solve for x
∴ 9x = 90 ⇒ divide both sides by 9
∴ x = 10
∵ m∠P = 7x
∴ m∠P = 7(10) = 70°
∴ m∠P = 70°
∵ m∠T = 2x
∴ m∠T = 2(10) = 20°
∴ m∠T = 20°
- In ΔSKP
∵ m∠S = 90°
∵ m∠SPK = 5x = 5(10) = 50°
∴ m∠SKP = 180° - (90° + 50°) = 180° - 140° = 40° ⇒ interior angles of a Δ
∴ m∠SKP = 40°
- In Δ KMT
∵ m∠KMT = 90°
∵ m∠T = 20°
∴ m∠MKT = 180° - (90° + 20°) = 180° - 110° = 70° ⇒ interior angles of a Δ
∴ m∠MKT = 70°
Today the entire school 250 students went to the soap box derby the math club went in 2 vans and each van held 6 students how many students from the math club went to the soap box derby?
Answer:
12 students from math club
Step-by-step explanation:
Number of vans = 2
Number of students in each van = 6
Number of students who went from math club to the soap box = ?
You can apply the following expression:
Total number of students=Number of students per van * Number of vans
Total number of students= 6 *2
= 12 students from math club....
Answer:
Step-by-step explanation:
a member of a book club wishes to purchase two books from a selection of eight books recommended for a certain month in how many ways can she choose them
Answer:
28
Step-by-step explanation:
8C2 = 28
What are the x-intercepts for the function shown in the graph?
1 and 3
-1 and 3
-1 and -3
-1 and 0
Answer:
-1 and 3
Step-by-step explanation:
The x intercepts are where the graph crosses the x axis.
Looking at the graph it crosses at two points
x = -1 and x=3
Which equation shows the variable terms isolated on one side and the constant terms isolated on the other side for the equation-1/2x+3=4-1/4x
Answer:
[tex]-\frac{1}{4} x=1[/tex]
Step-by-step explanation:
To isolate your terms, start by combining your x terms by adding 1/4x to both sides.
[tex]-\frac{1}{2} x+3=4-\frac{1}{4} x\\-\frac{1}{4} x+3=4[/tex]
Next, combine your constant terms by subtracting 3 from both sides.
[tex]-\frac{1}{4} x=1[/tex]
To isolate the variable terms on one side and the constant terms on the other side, follow these steps: subtract the variable terms and add the constant terms, then move the variable terms to one side and the constant terms to the other side.
Explanation:To isolate the variable terms on one side and the constant terms on the other side for the equation -1/2x+3=4-1/4x, you can follow these steps:
First, move all the variable terms to one side by subtracting -1/2x and adding 1/4x to both sides. This gives you 3+1/4x = 4+1/2x.Next, move all the constant terms to the other side by subtracting 3 from both sides. This gives you 1/4x = 1/2x+1.Finally, move all the variable terms to the left side by subtracting 1/2x from both sides. This gives you the desired equation of 1/4x-1/2x = 1.Learn more about isolating variable and constant terms here:https://brainly.com/question/13677025
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Factor the polynomial expression 27x3−8 27 x 3 − 8 .
Answer:
(3x-2) (9x^2 + 6x +4)
Step-by-step explanation:
27x^3−8
This is the difference of cubes
a^3 - b^3 = (a-b)(a^2 + ab + b^2)
a^3 =27x^3 so a = 3x
b^3 =8 so b=2
a^2 = (3x)^2 = 9x^2 ab = (3x)*2 = 6x b^2 = 2^2 =4
27x^3 -8 = (3x-2) (9x^2 + 6x +4)
The coordinates of quadrilateral FGHJ are F(-5, -3), G(-3, 3), H(3, 5), and J(7, -1).
Find the midpoint of FG
a- 0,4
b- 1,-2
c- 5,2
d- -4,0
Answer:
[tex]\large\boxed{d.\ (-4,\ 0)}[/tex]
Step-by-step explanation:
The formula of a midpoint of a segment AB with endpoints at A(x₁, y₁) and B(x₂, y₂):
[tex]M_{AB}\left(\dfrac{x_1+x_2}{2},\ \dfrac{y_1+y_2}{2}\right)[/tex]
We have the points F(-5, -3) and G(-3, 3).
Substitute:
[tex]M_{FG}(x,\ y)\\\\x=\dfrac{-5+(-3)}{2}=\dfrac{-8}{2}=-4\\\\y=\dfrac{-3+3}{2}=\dfrac{0}{2}=0[/tex]
The surface area of a sphere having a diameter of 8 inches is
The surface area of a sphere that is 8 inches is 201.06in²
Answer:
64 π inches^2 or 201.06 inches^2 to the nearest hundredth.
Step-by-step explanation:
The radius = 1/2 * the diameter
= 1/2 * 8
= 4 inches.
The surface area = 4 π r^2
4 π 4^2
= 64 π inches^2
or 201.06 inches^2 to the nearest hundredth.
What is the equation of the line that passes through (-3, -1) and has a slope of 2,5 ? Put your answer in slope-intercept form.
Answer:
y+1 = 2/5(x+3)
Step-by-step explanation:
We have a point and a slope so we can use point slope form
y-y1 = m(x-x1) where m is the slope and (x1,y1) is the point
y--1 = 2/5 (x--3)
y+1 = 2/5(x+3)
Sparkles the unicorn is in the forest. She is helping herself to a nice big juicy apple. The
monkey grabs the apple out of her mouth and starts to eat it. Sparkles notices that there are
18 pairs of eyes staring at the monkey. Based on the information you have been given, how
many animals are in the forest in this moment?
Answer:
9
Step-by-step explanation:
Each animal have 2 eyes so basically 18/2 = 9
That's the answer, hope this helps.
:)
Answer:
20 animals.
Step-by-step explanation:
Sparkles the unicorn is eating an apple, when a chango removes the apple from its mouth and bites it. We already have 2 animals in the forest: the unicorn and the monkey.
Then, the unicorn realizes that 18 pairs of eyes are watching the monkey. That gives us another 18 animals (considering everyone has 2 eyes).
so, in total we have 20 animals: (18 + unicorn + monkey) = 20 animals.
Terrence is folding paper cranes at a constant rate. The table below shows the amount of time he needs to fold cranes.
Number of cranes Total time (minutes)
555 17.517.517, point, 5
888 282828
121212 424242
Write an equation to describe the relationship between ccc, the number of cranes, and ttt, the total time in minutes.
Answer:
t = 3.5c
Step-by-step explanation:
The correct table is attached in the image below. Since the papers are being folded at a constant rate, there is a linear relationship between c, the number of crane and t, the total time in minutes.
We can find the equation of this linear relation using any two pair of points from the table. Using the first two points: (5, 17.5) and (8, 28)
First we need to find the slope of the line which gives the relation between the two variables.
[tex]Slope=\frac{\text{Difference in y coordinates}}{\text{Difference in x coordinates}}[/tex]
y coordinates represents the dependent variable which is the time in this case and x coordinates represents the independent variable which is number of cranes in this case. Using the values from the two points we considered:
[tex]Slope=\frac{28-17.5}{8-5}=3.5[/tex]
Thus, the equation of the line will be of the form:
t = mc + b
m is the slope here. Using its values, we get:
t = 3.5c + b
b is known as y-intercept. We need the value of b to complete the equation. Substituting the value of t and c from any pair we can find the value of b.
Using the point (5, 17.5), we get:
17.5 = 3.5(5) + b
b = 0
This means, the equation of the line would be:
t = 3.5c
Answer:
t=3.5c
Step-by-step explanation:
Solve the following inequality 38<4x+3+7-3x
38<4x+3+7-3x
38<x+10
28<x
Ans: x>28
For this case we must solve the following inequality:
[tex]38 <4x + 3 + 7-3x[/tex]
We add similar terms to the right side of inequality:
[tex]38 <4x-3x + 3 + 7\\38 <x + 10[/tex]
We subtract 10 from both sides of the inequality:
[tex]38-10 <x\\28 <x[/tex]
Thus, the solution will be given by all values of "x" greater strict to 28.
Answer:
[tex]x> 28[/tex]
Fill in the table using this function rule. y=2x-2
The completed table:
x y
2 2
4 6
6 10
7 12
For each value of x, we substitute it into the function rule y = 2x - 2 and evaluate to find the corresponding value of y.
Calculations:
When x = 2: y = 2(2) - 2 = 4 - 2 = 2
When x = 4: y = 2(4) - 2 = 8 - 2 = 6
When x = 6: y = 2(6) - 2 = 12 - 2 = 10
When x = 7: y = 2(7) - 2 = 14 - 2 = 12
Find an equation for the line perpendicular to y=−1/7x+2 with x-intercept at x = -7.
Write your answer in the form y=mx+b.
y=
Answer:
[tex]y=7x+49[/tex]
Step-by-step explanation:
To find the slope of a line which is perpendicular to another line, you need to find the opposite reciprocal of the first line's slope.
To find the opposite, flip the slope's sign. Your original slope is [tex]-\frac{1}{7}[/tex], so your opposite slope is positive [tex]\frac{1}{7}[/tex].
To find the reciprocal, flip the fraction. This changes your slope from [tex]\frac{1}{7}[/tex] to [tex]\frac{7}{1}[/tex], which may be written as just 7.
Therefore, your slope is 7.
To find your b term (your y-intercept) given that your x-intercept is -7, you can make use of point-slope form.
[tex]y-y1=m(x-x1)[/tex]
(m=slope)
If your x-intercept is -7, then the point at which your line intersects the x-axis is (-7, 0).
[tex]y-0=7(x-(-7))\\y=7(x+7)\\y=7x+49[/tex]
Tom buys a new car for $19,999. For every month he owns the car the value depreciates by $250.00. After 3 years, what is Tom's car worth? (Please show steps:))
Answer:
[tex]\large\boxed{\$10,999}[/tex]
Step-by-step explanation:
In this question, we're trying to find the value of Tom's car after 3 years.
From the question, we know that:
He bought it for $19,999Value depreciates by $250 every monthWith the information above, we can solve the question.
We can do the simplest way by multiplying 250 by 36, since there's 36 months in 3 years, and then we would subtract that from our starting value.
Solve:
[tex]250*36=9000\\\\\text{We would then subtract 9000 from 19,999}\\\\19,999=10,999\\\\\text{Cars value after 3 years is}\, \bf\$10,999[/tex]
When you're done solving, you should get 10,999.
This means that Tom's car worth in 3 years is $10,999.
I hope this helped you out.Good luck on your academics.Have a fantastic day!Answer:
10,999
Step-by-step explanation:
250 x 36 = 9,000
9,000 is how much the car went down in value it went down 3,000 a year for three years
19,999 - 9,000 = 10,999
10,999 is how much the car is worth after 3 years
solve the system of equations 3x - 4y +z=39, -3x + y -2z=-30, 2x -2y + 3z=43
Answer:
x = 2, y = -6, and z = 9
Step-by-step explanation:
This question can be solved using multiple ways. I will use the Gauss Jordan Method.
Step 1: Convert the system into the augmented matrix form:
• 3 -4 1 | 39
• -3 1 -2 | -30
• 2 -2 3 | 43
Step 2: Add row 1 it into row 2:
• 3 -4 1 | 39
• 0 -3 -1 | 9
• 2 -2 3 | 43
Step 3: Multiply row 1 with -2/3 and add it in row 3 and then multiply row 3 with 3:
• 3 -4 1 | 39
• 0 -3 -1 | 9
• 0 2 7 | 51
Step 4: Multiply row 2 with 2/3 and add it in row 3 and then multiply row 3 with 3:
• 3 -4 1 | 39
• 0 -3 -1 | 9
• 0 0 19/3 | 57
Step 5: It can be seen that when this updated augmented matrix is converted into a system, it comes out to be:
• 3x - 4y + z = 39
• -3y - z = 9
• (19/3)z = 57 (This implies that z = 9.)
Step 6: Since we have calculated z = 9, put this value in equation 2:
• -3y - 9 = 9
• -3y = 18
• y = -6.
Step 8: Put z = 9 and y = -6 in equation 1:
• 3x - 4(-6) + 9 = 39
• 3x + 24 + 9 = 39
• 3x = 6.
• x = 2.
So final answer is x = 2, y = -6, and z = 9!!!
f:[1/2,infinity)—>[3/4,infinity)
f(x)=x^2-x+1
find the inverse of f(x);please explain
Answer:
[tex]f^{-1}(x)=\frac{1}{2}+\sqrt{x-\frac{3}{4}}[/tex]
Step-by-step explanation:
y=x^2-x+1
We want to solve for x.
I'm going to use completing the square.
Subtract 1 on both sides:
y-1=x^2-x
Add (-1/2)^2 on both sides:
y-1+(-1/2)^2=x^2-x+(-1/2)^2
This allows me to write the right hand side as a square.
y-1+1/4=(x-1/2)^2
y-3/4=(x-1/2)^2
Now remember we are solving for x so now we square root both sides:
[tex]\pm \sqrt{y-3/4}=x-1/2[/tex]
The problem said the domain was 1/2 to infinity and the range was 3/4 to infinity.
This is only the right side of the parabola because of the domain restriction. We want x-1/2 to be positive.
That is we want:
[tex]\sqrt{y-3/4}=x-1/2[/tex]
Add 1/2 on both sides:
[tex]1/2+\sqrt{y-3/4}=x[/tex]
The last step is to switch x and y:
[tex]1/2+\sqrt{x-3/4}=y[/tex]
[tex]y=1/2+\sqrt{x-3/4}[/tex]
[tex]f^{-1}(x)=1/2+\sqrt{x-3/4}[/tex]
Var (X)=2,if U=5x+2,then Var (U) is Equal to ??
I know its 50. but how to reach the final answer
Answer:
Var(U)=50
Step-by-step explanation:
Given
Var(X) = 2
We have to find
Var(U) when U = 5x+2
So,
When a variable is multiplied with an integer, the variance of that variable is multiplied with the square of that number i.e. Var(aX) = a^2 Var(X) This the property of variance.
As here x is multiplied with 5,
Var(5x) = 5^2 var(X) = 25*2 = 50
If the same integer is added to all the data values, there is no change in variance that is why the +2 will not affect the variance of U ..
130xy/50x
Please reduce your this fraction.
For this case we must reduce the following fraction:
[tex]\frac {130xy} {50x}[/tex]
Canceling similar terms in the numerator and denominator:
[tex]\frac {130y} {50}[/tex]
Dividing by 10 the numerator and denominator we have:
[tex]\frac {13y} {5}[/tex]
Finally, the expression is reduced to:
[tex]\frac {13y} {5}[/tex]
Answer:
[tex]\frac {13y} {5}[/tex]