Answers
Answer:
Step-by-step explanation:
[tex]a^{-1}=\dfrac{1}{a} \ ; \ b^{-1}=\dfrac{1}{b} \ ; \ c^{-1}=\dfrac{1}{c}[/tex]
[tex]\dfrac{1}{1+a+b^{-1}}+\dfrac{1}{1+b+c^{-1}}+\dfrac{1}{1+c+a^{-1}}=\dfrac{1}{1+a+ \dfrac{1}{b}}+\dfrac{1}{1+b+\dfrac{1}{c}}+\dfrac{1}{1+c+\dfrac{1}{a}}[/tex]
[tex]= \dfrac{1}{\dfrac{1*b}{1*b}+\dfrac{a*b}{1*b}+\dfrac{1}{b}}+\dfrac{1}{\dfrac{1*c}{1*c}+\dfrac{b*c}{1*c}+\dfrac{1}{c}}+\dfrac{1}{\dfrac{1*a}{1*a}+\dfrac{c*a}{1*a}+\dfrac{1}{a}}\\\\\\=\dfrac{1}{\dfrac{b+ab+1}{b}}+\dfrac{1}{\dfrac{c+bc+1}{c}}+\dfrac{1}{\dfrac{a+ac+1}{a}}\\\\\\=\dfrac{b}{b+ab+1}+\dfrac{c}{c+bc+1}+\dfrac{a}{a+ac+1}[/tex]
abc = 1
c = 1/ab
[tex]=\dfrac{b}{b+ab+1}+\dfrac{\dfrac{1}{ab}}{\dfrac{1}{ab}+b*\dfrac{1}{ab}+1}+\dfrac{a}{a+a*\dfrac{1}{ab}+1}\\\\\\[/tex]
[tex]= \dfrac{b}{b+ab+1}+\dfrac{\dfrac{1}{ab}}{\dfrac{1+b+ab}{ab}}+\dfrac{a}{\dfrac{ab+1+b}{b}}\\\\\\=\dfrac{b}{b+ab+1}+\dfrac{\dfrac{1}{ab}*ab}{1+b+ab}+\dfrac{ab}{ab+1+b}[/tex]
[tex]=\dfrac{b}{b+ab+1}+\dfrac{1}{1+b+ab}+\dfrac{ab}{1+b+ab}\\\\\\=\dfrac{b+1+ab}{b+1+ab}\\\\\\=1[/tex]
Related Questions
Can you help me to solve this problem?
Answers
Answer:
2 2/3
Step-by-step explanation:
Since we only know how much milk we have we will disregard the flour. That leaves us with 4 cups of milk total and 1 1/2 cups of milk per serving. Simply divide 4 by 1 1/2 to get your answer of 2 2/3. Now, if they only want full servings, then the answer would be 2.
Problem 3: Two rectangular gardens are made from 200 yards of fencing. The
gardens are planted beside each other so they share a common fence. If the
farmer wants the total area of the gardens to be as large as possible, what
dimensions should be used to make the gardens, and what will the largest area
possible be?
Answers
The area of a shape is the amount of space on the shape
The largest possible area of the garden is 1666.67 square yards
How to determine the maximum areaRepresent the length of the gardens with y, and the widths of the whole garden with x.
So, the perimeter of the garden is:
[tex]P = 3y + 2x[/tex]
The farmer has 200 yards.
So, we have:
[tex]3y + 2x= 200[/tex]
The area of the garden is:
[tex]Area = xy[/tex]
Divide the amount of fencing equally to maximize the area.
So, we have:
[tex]3y + 2x = 100 + 100[/tex]
This gives
[tex]3y = 100 \to y = \frac{100}3[/tex]
[tex]2x = 100 \to x = 50[/tex]
Recall that:
[tex]Area = xy[/tex]
So, we have:
[tex]Area = 50 * \frac{100}3[/tex]
Evaluate the product
[tex]Area = \frac{5000}3[/tex]
[tex]Area = 1666.67[/tex]
Hence, the largest possible area of the garden is 1666.67 square yards
Read more about areas at:
https://brainly.com/question/24487155
What is the center of a circle represented by the equation (x 9)2 (y−6)2=102?.
Answers
(x-h)^2 + (y-k)^2 = r^2 we get
Center of the circle (h,k) = (9 ,6 )
or (-9,6) If the original equation is (x-9)^2 + (y-6)^2 =102
Please leave a like If it helps :)
Answer:(-9,6)
Step-by-step explanation:
I got it right on the e2020 course
Hope it helps:)
Marcus is comparing the costs of two cellular phone services.
The graph represents the total cost of each service depending on the number of
months.
Choose the two statements that are true about the graph.
Answers
The true statements about Marcus graph are:
The initial cost of phone service 1 is greater than the initial cost of phone service 2The unit rate of phone service 2 is greater than the unit rate of phone service 2How to determine the true statementFrom the complete question, we have the following parameters:
Phone service 1
Initial cost: $40Rate: $8.50 per servicePhone service 2
Initial cost: $30Rate: $10.50 per serviceBy comparing the above parameters:
The initial cost of phone service 1 is greater than the initial cost of phone service 2The unit rate of phone service 2 is greater than the unit rate of phone service 2The above statements represent the true statements about the Marcus' graph
Read more about graphs at:
https://brainly.com/question/14323743
NEED ANSWER ASAP- MARK AS BRANLIEST
Answers
Answer:
x = 1 +√5
Step-by-step explanation:
There are different formulas for the area of a triangle available, depending on the given information.
FormulasWhen two sides and the angle between them are given, the relevant area formula is ...
Area = 1/2(ab)sin(C)
When the base and height of a triangle are given, the relevant area formula is ...
Area = 1/2bh
Equal AreasThe problem statement tells us the two triangles shown have equal areas. That means the two formulas will give the same result.
Area from angle = Area from base/height
1/2(x·x)sin(30°) = 1/2(x-2)(x+1)
x² = 2(x² -x -2) . . . . . . . . . . . use sin(30°) = 1/2, multiply by 4
x² -2x -4 = 0 . . . . . . . . subtract x², eliminate parentheses
(x -1)² = 5 . . . . . . . . . add 4+1 to complete the square
Value of xx = 1 ± √5 . . . . . . take the square root, add 1
The value of x must be greater than 2 in order for the triangle side lengths to be positive. (x-2 > 0) This means x = 1-√5 is an extraneous solution.
The value of x is 1 +√5.
Which situation would cause the price of a product to fall the most?
A) The demand rises while the supply falls.
B) Both the demand and the supply fall.
C) Both the demand and supply rise.
D) The demand falls while the supply rises.
||ECONOMICS||
Answers
Answer: D
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
MR. Raine decided to survey the thirty students in his homeroom one morning to find out how tey were feeling at that moment. Here are his results. tired (total) 20 hungry 17 tired and hungry 8 tired and happy 5 happy and hungry all three 4 PLS 20 POINTS
Answers
Answer: 4
Step-by-step explanation:
That should be your answer
divide the fractions whit whole nymber and simplify
Answers
Answer:
Which fractions
Step-by-step explanation:
What is the coefficient in the following expression: 5 + 3x + (-3) A) 5 B) 3 C) x D) -3
Answers
Answer:
B) 3
Step-by-step explanation:
If it was right please mark me brainleist.
HELP!!! RST has vertices R(-3, - 1), S(0,3), and t(3,0). What type of triangle is RST?
right triangle
Equilateral triangle
scalene triangle
Isosceles
Answers
======================================================
Explanation:
Use the distance formula to calculate the distance from R to S. This is identical to the length of segment RS.
[tex]R = (x_1,y_1) = (-3,-1) \text{ and } S = (x_2, y_2) = (0,3)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-3-0)^2 + (-1-3)^2}\\\\d = \sqrt{(-3)^2 + (-4)^2}\\\\d = \sqrt{9 + 16}\\\\d = \sqrt{25}\\\\d = 5\\\\[/tex]
Segment RS is exactly 5 units long.
-----------------------
Repeat similar steps to find the length of segment ST
[tex]S = (x_1,y_1) = (0,3) \text{ and } T = (x_2, y_2) = (3,0)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(0-3)^2 + (3-0)^2}\\\\d = \sqrt{(-3)^2 + (3)^2}\\\\d = \sqrt{9 + 9}\\\\d = \sqrt{18}\\\\d \approx 4.2426\\\\[/tex]
ST is roughly 4.2426 units long.
------------------------
Lastly, let's calculate the length of segment TR.
[tex]T = (x_1,y_1) = (3,0) \text{ and } R = (x_2, y_2) = (-3,-1)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(3-(-3))^2 + (0-(-1))^2}\\\\d = \sqrt{(3+3)^2 + (0+1)^2}\\\\d = \sqrt{(6)^2 + (1)^2}\\\\d = \sqrt{36 + 1}\\\\d = \sqrt{37}\\\\d \approx 6.0828\\\\[/tex]
TR is about 6.0828 units long.
------------------------
Summary of the segment lengths:
RS = 5 exactlyST = 4.2426 approximatelyTR = 6.0828 approximatelyThe three sides are different lengths.
Therefore, the triangle is scalene.
Use the drop-down menus to complete the statements about factoring 14x2 6x – 7x – 3 by grouping.
Answers
The factors of the polynomial equation by complete the statements about factoring by grouping are,
[tex](2x-1)\\(7x+3)[/tex]
How to find the factor of polynomial?The factor of a polynomial is the terms in linear form, which are, when multiplied together, give the original polynomial equation as a result.
To find the factor of a polynomial, make the groups of the equation, and equate them equal to zero.
The provided polynomial equation is,
[tex]14x^2+ 6x - 7x - 3[/tex]
Rearrange the equation,
[tex]14x^2- 7x + 6x - 3[/tex]
Take out the common terms 7x from the first two terms and 3 from the last two terms.
[tex]7x(2x- 1) + 3(2x - 1)\\(2x-1)(7x+3)[/tex]
Thus, the factors of the polynomial equation by complete the statements about factoring by grouping are,
[tex](2x-1)\\(7x+3)[/tex]
Learn more about factor of polynomial here;
https://brainly.com/question/24380382
Dion bought 3 pounds of oranges and 2 pounds of grapefruit. Write an expression to represent the amount of money Dion spent on the fruit. Then evaluate the expression. How much did Dion spend?
Answers
Solution:
Given:
Dion bought 3 pounds of oranges, and 2 pounds of grapefruit1 pound of oranges = o = $0.991 pound of grapefruit = g = $1.59Let's represent the number of oranges and grapefruits by the letters o and g.
This means that...
Dion purchase: 3o + 2gNow, let's solve the expression to find out how much does Dion has to pay.
Substituting o and g with the given values:
3o + 2g=> 3(0.99) + 2(1.59)=> 3(1.00 - 0.01) + 2(1.60 - 0.01)=> (3 - 0.03) + (3.20 - 0.02)=> 2.97 + 3.18=> $6.15We also know that Dion gave a $20. To find the change, subtract the money Dion gave with the money required to pay for the fruits.
=> 20 - 6.15=> $13.85Thus, Dion got $13.85 as change.
Each day Diego's mother drives to her office in Baltimore. The driving distance from home to Baltimore, Maryland is 7 miles. On her way home, she runs some errands at the mall so her driving distance is 8 miles How many miles does his mother drive going to work and coming home for 3 days?
Select the expression that represents the problem above
a) 7 + 8 + 3
b) (7 + 3) x 8
c) (7 + 8) = 3
d) (7 + 8) X3
Answers
Answer:
D
Step-by-step explanation:
(7+8)*3
Select the correct answer.
Calculate the weighted average for the data below.
Answers
The half-life of a radioactive element is five years. A scientist has 18 grams of the element. The equation
representing the number of grams, g, after x years is §. What is the annual rate of decay?
g=18(0.5)
Answers
The annual rate of decay is r = 0.87
How to use the half-life?
We know that if a quantity has a half-life of T, then the rate of decay must be such that:
r^T = 0.5
This means that when a time T passes, the original quantity becomes half of what it originally was.
In this case we know that the half-life is T = 5 years, then we have:
r^5 = 0.5
r = 0.5^(1/5) = 0.87
Then the annual rate of decay is r = 0.87, and if the initial quantity is 18 grams, we can write the exponential decay as:
f(t) = 18g*(0.87)^t
If you want to learn more about exponential decays, you can read:
https://brainly.com/question/11464095
Answer:
13%
Step-by-step explanation:
I took the test on edge and got it right
Which of the following values are solutions to the inequality? Choose all that apply.
5x - 7 < 13
A.3
B.5
C.10
D.-4
Answers
15 - 7 < 13
8 < 13
A is a solution to the inequality
B. 5(5) - 7 < 13
25 - 7 < 13
18<13
B does not fit in this inequality. 18 is not bigger than 13.
C. 5(10) - 7 < 13
50 - 7 < 13
43<13
C also does not fit because 10 is too large of a value.
D. 5(-4) - 7 < 13
-20 - 7 < 13
-27<13
D is an answer as the inequality statement is true.
The answers are A & D
Isaiah spent $19. 60 on a gift for his mother. The amount that he spent on the gift was StartFraction 5 over 7 EndFraction of the total amount that he spent at the store. Which statements can be used to find x, the total amount that Isaiah spent at the store? Select three options. StartFraction 5 over 7 EndFraction = StartFraction x over 19. 60 EndFraction
StartFraction 5 over 7 EndFraction x = 19. 60
StartFraction 5 over 7 EndFraction (StartFraction 7 over 5 EndFraction) x = 19. 60 (StartFraction 7 over 5 EndFraction)
StartFraction 5 over 7 EndFraction (StartFraction 7 over 5 EndFraction) = StartFraction x over 19. 60 EndFraction (StartFraction 7 over 5 EndFraction)
x = 27. 44
Answers
Answer: x=27.44
Step-by-step explanation:
i had this already and i got it correct so here is your answer for this question your answer will be x=27.44
∠1 and ∠2 are supplementary. ∠1=3x°∠2=(2x−25)° What is the value of x? Select from the drop down menu to correctly answer the question. X = Choose.
Answers
Answer:
x=41
Step-by-step explanation:
supplementary angles add to 180
3x + (2x-25) = 180
5x = 205
x= 41
angle1 3x41 = 123
angle 2 (2x41) -25 = 57
123 +57 = 180
Select the correct number from each drop-down menu to complete the equation. 7/8 - (-2+3/4) = ( ____+____) + 7/8
Answers
Answer:
1+1/4
Step-by-step explanation:
Subtract 7/8 from both sides of the equation
so 2-3/4=5/4
5 divide 98
2 divide 72
9 divide 58
7 divide 82
Answers
19 3/5
36/16 4/911 5/7yeah..
72/2 = 36 36/1
58/9 = 6.444…. 6 4/9
82/7 = 11.714…. 11 5/7
How do you find the area of a circular park and the radius is 18 yards
Answers
Answer:
The area of the circular park is about 1017.88
Step-by-step explanation:
First, we recall the area of a circle.
A= πr^2
Next, we plug in the radius
A= π*18^2
A= π*324
A= 1017.88
To conclude, that is how you find the area of a circular park.
What is the value of x
Answers
Answer:
4 possibly
Step-by-step explanation:
Answer:
I think x=[tex]\sqrt[6]{1}[/tex] , possibly
Step-by-step explanation:
0. 3, 0. 5, 0. 9, 1. 1What are those numbers put in order?
Answers
Answer:
0,0,0,1,3,5,9 I put it in order
Solving an Equation with Decimals
What is the solution to the equation 13.7y = 6.2y + 30?
y = –4
y = –1.5
y = 1.5
y = 4
please help me my dudes and dudettes
Answers
Answer:
y = 4
Step-by-step explanation:
7.5y/ 7.5 = 30/7.5
y= 4
Determine the formula, in terms of x, that best describes the area of the plot.
Answers
The area of a plot is the amount of space on the plot
The area of the plot is 2x^2 -x - 1
How to determine the areaThe dimensions of the plot are given as:
Length=2x+1
Width=x-1.
The area of the plot is the product of its dimension.
So, we have:
[tex]Area = (2x + 1)(x - 1)[/tex]
Expand
[tex]Area = 2x^2 - 2x + x - 1[/tex]
Evaluate the like terms
[tex]Area = 2x^2 -x - 1[/tex]
Hence, the area of the plot is 2x^2 -x - 1
Read more about areas at:
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Chord AB is 3cm from the center of a circle, the radius of the circle is 5cm, calculate the length of the chord.
Answers
Answer:
[tex]\large{\boxed{\sf Chord = 8cm }}[/tex]
Step-by-step explanation:
First see figure in attachment . As we know that ,Perpendicular from centre of the circle bisects the chord . Hence here ,
OC is the perpendicular bisector of chord AB . Let us assume that AC = x , therefore ,[tex]\sf\qquad\longrightarrow AB = 2AC = 2x [/tex]
Now in ∆OAC , by Pythagoras Theorem , we have ;
[tex]\sf\qquad\longrightarrow (5cm)^2= x^2+(3cm)^2\\ [/tex]
[tex]\sf\qquad\longrightarrow 25cm^2=x^2+9cm^2\\[/tex]
[tex]\sf\qquad\longrightarrow x^2=25cm^2-9cm^2\\[/tex]
[tex]\sf\qquad\longrightarrow x^2=16cm^2\\ [/tex]
[tex]\sf\qquad\longrightarrow \pink{ x = 4cm } [/tex]
Therefore , the length of chord will be ,
[tex]\sf\qquad\longrightarrow AB = 2x \\ [/tex]
[tex]\sf\qquad\longrightarrow AB = 2(4cm)\\[/tex]
[tex]\sf\qquad\longrightarrow \pink{ AB = 8cm } [/tex]
Hence the length of chord is 8cm .
help pls and thanks
pick
Answers
Answer:
55/9
Step-by-step explanation:
Name the market angles in different ways
Answers
i hope my answers are ✅.......
what are the x-intercepts of 2x+10
Answers
Answer:
-5
Step-by-step explanation:
x-intercepts occur when y = 0
⇒ 2x + 10 = 0
⇒ 2x = -10
⇒ x = -5
So the x intercept of 2x + 10 is (-5, 0)
Answer:
-5
Step-by-step explanation:
To find the x intercepts we must replace y with 0 and solve for X
So our equation is 0=2x+10
Now we must get x by itself by subtracting 10 on both sides. We subtract 10 because it is being added.
We are left with -10=2xSo now we ask ourselves, what times 2 will give us -10Well, instead of guessing we can solve :)
Divide 2 on both sides, this cancels out the two on the right and makes the -10 on the left turn into a -5.
Now we are left with x=-5
Thus, our answer is -5
Hope this helps!
#LearningIsFun
Work out the size of angle x give a reason for your answer
Answers
Explanation:
The M of angle X is the same as any other angle in the triangle. Because if you where to complete the separate triangle then it would be similar to the current one, meaning that the corresponding angles are congruent. And if both triangles are equilateral triangles, then all angles in both of the two similar triangles are congruent.
So if you find the M of any angle then you can solve for X.
Since we know that the interior angles of any triangle add up to 180*, and that it’s an equilateral triangle, we know that the angles have to be the same. So 180*/3 = 60*
Hope this helps!
