Prove that: [tex](a+b)^{-1} . (a^{-1} + b^{-1} ) = (ab)^{-1}[/tex]
Step-by-step explanation:
[tex] \frac{1}{a + b} \times ( \frac{a + b}{ab}) = \frac{1}{ab} [/tex]
Answer with step-by-step explanation:
[tex](a+b)^-^1*(a^-^1+b^-^1)=(ab)^-^1[/tex]
First, convert these into positive indices.
[tex]\frac{1}{(a+b)} *(\frac{1}{a} +\frac{1}{b})=\frac{1}{ab}[/tex]
And now, let us solve the left side.
[tex]\frac{1}{(a+b)} *(\frac{1}{a} +\frac{1}{b})\\\\[/tex]
First, solve the brackets. That is add the fractions inside the brackets.
[tex]\frac{1}{(a+b)} *(\frac{1}{a} +\frac{1}{b})\\\\\frac{1}{(a+b)}*(\frac{1*b}{a*b} +\frac{1*a}{b*a})\\\\\frac{1}{(a+b)}*(\frac{b}{ab} +\frac{a}{ab})\\\\\frac{1}{(a+b)}*\frac{(a+b)}{ab}[/tex]
Now multiply the fractions.
[tex]\frac{1}{ab}[/tex]
So, it's clear that the left side equals the right side.
Left side = Right side
[tex]\frac{1}{ab}=\frac{1}{ab}[/tex]
∴ [tex](a+b)^-^1*(a^-^1+b^-^1)=(ab)^-^1[/tex]
Write an equation that represents the line.
Use exact numbers.
y=1.5x+3
Observing the graph
Let,
A(0,3) -----> this point is the y-intercept of the line
B(2,6)
We know that
The equation of the line into slope intercept form is equal to
y = mx + c
where
m is the slope
b is the y-coordinate of the y-intercept
In this problem
b=3
Find the slope of the line m
The formula to calculate the slope between two points is equal to
m = y2-y1 / x2-x1
substitute the values
m = 6-3 / 2-0
m = 3/2
m = 1.5
The equation of the line is
y= 1.5x+3
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How do solve this in geometry?
Answer:
x=0.4
Step-by-step explanation:
Put both equations equal to each other:
16x+2=7x+6
Now, Solve:
16x+2=7x+6 Set the equation
16x-7x=6-2 Move like terms together
9x=4 Subtract like terms
x=4/9 Simplify
x=0.4 Answer
What is the complete factorization of 2 - 2ab + b2?
F. (a - b)(a + b)
G. (a + b)(a + b)
H. (a + b)(-a-b)
J. (a - b)(a - b)
Answer:
J
Step-by-step explanation:
assuming the 2 is a squared s a*a is a2 2*a*-b is -2ab
and -b* -b is b2
plssssss helpppppppppppppppppp
Point M is on line segment
L
N
‾
LN
. Given
L
N
=
4
x
,
LN=4x,
M
N
=
x
,
MN=x, and
L
M
=
3
,
LM=3, determine the numerical length of
L
N
‾
.
LN
.
4 is the numerical length of line segment LN.
What is the numerical length of segment LN?A line segment is simply the part of a line that connects two points or is bounded by two points.
Given the data in the question;
Point M is on line segment LNSegment LN = 4xSegment MN = xSegment LM = 3Numerical length of segment LN = ?Since point M is on line segment LN, segment LN equals to the sum of segment LM and MN.
Hence;
Segment LN = segment LM + segment MN
4x = 3 + x
Solve for x
4x - x = 3
3x = 3
x = 3/3
x = 1
Now, we find the numerical length of segment LN;
Segment LN = 4x
Plug in x = 1 and simplify
Segment LN = 4( 1 )
Segment LN = 4
Therefore, the length of segment LN is 4.
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Rahul solved the equation 2(x – ) – 2 left-parenthesis x minus StartFraction 1 Over 8 EndFraction right-parenthesis minus StartFraction 3 Over 5 EndFraction x equals StartFraction 55 Over 4 EndFraction x = 2 left-parenthesis x minus StartFraction 1 Over 8 EndFraction right-parenthesis minus StartFraction 3 Over 5 EndFraction x equals StartFraction 55 Over 4 EndFraction . In which step did he use the addition property of equality?
A table titled Rahul's Solution with 2 columns and 5 rows. The first column, Steps, has the entries 1, 2, 3, 4. The second column, Resulting equations, has the entries, 2 x minus StartFraction 1 Over 4 EndFraction minus StartFraction 3 Over 5 EndFraction x equals StartFraction 55 Over 4 EndFraction, StartFraction 7 Over 5 EndFraction x minus StartFraction 1 Over 4 EndFraction equals StartFraction 55 Over 4 EndFraction, StartFraction 7 Over 5 EndFraction x equals StartFraction 56 Over 4 EndFraction, x equals 10.
Step 1
Step 2
Step 3
Step 4
Mark this and return
In step 2 addition property is used.
2x + (1 ÷ 4) - (3 ÷ 5)x = 55 ÷ 4
Simplifying x,
2x - (3 ÷ 5)x - (1 ÷ 4) = 55 ÷ 4
(10x - 3) ÷ 5 - (1 ÷ 4) = 55 ÷ 4
(7x ÷ 5) - (1 ÷ 4) = 55 ÷ 4
Add (1 ÷ 4) on both sides,
(7x ÷ 5) - (1 ÷ 4) + (1 ÷ 4) = 55 ÷ 4 + (1 ÷ 4)
(7x ÷ 5) = (55 + 1) ÷ 4
(7x ÷ 5) = 56 ÷ 4
Multiplying (5 ÷ 7) on both sides,
(7x ÷ 5) × (5 ÷ 7) = (56 ÷ 4) × (5 ÷ 7)
x = 10
In step 2 - Add (1 ÷ 4) on both sides, the addition property is being used.
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Answer:
its c step three
Step-by-step explanation:
GEOMETRY PLEASE HELP ASAP
The function which will represent the given Translation will be T(x, y) = (x + 3, y - 2).
Translation may be defined as the shifting of the curve on a graph or shifting of the plotted points on a graph. The translation can be horizontal or vertical. In horizontal direction it can be shifted either left or right and in vertical direction it can be shifted either up or down. Horizontal translation always occurs on the x axis and vertical translation always occurs on the y axis. A function may be defined as an expression in which for input variable x there is output variable y. We need to translate a function T(x, y) 3 units right so the new coordinate will be T(x + 3, y). Now, translation occurs 2 units down. so, new coordinates will be T(x + 3, y -2) which is the required function.
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The team needs new uniforms. The students plan to sell plush toy s (the school mascot) for $5 each. The students find three companies on-line that sell stuffed mascots. Company A sells s for $. Company B sells s for $. Company C charges $ for s. Which company has the best buy?
Company B has the best buy with a selling price of $2.79
Given: Company A sells 16 lions for $44.32
Company B sells 18 lions for $50.22
Company C sells 12 lions for $ 32.88
To find : The selling price of each lion
By using unitary method we get,
Company A sells 1 lion for $ 2.77
Company B sells 1 lion for $2.79
Company C sells 1 lion for $ 2.74
From the above statistics it is clear that Company B has the best buy .
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Kevin ran 4 miles more than Steve ran. The sum of their distances is 26 miles. How far did Steve run? The domain of the solution is (0, 4, 11, 22}
a. Define your variable.
b. Write algebraic expressions for the distances each person ran.
c. Write an equation that can help you solve the problem.
d. Solve the equation.
e. Check your answer.
Help Please write it simple
Using a system of equations, it is found that:
b) The domain of the solution is that Steve ran 11 miles.
c) Variable S gives the distance ran by Steve.
d) The algebraic expressions are: K = 4 + S, K + S = 26.
e) The equation is: 4 + S + S = 26.
What is a system of equations?
A system of equations is when multiple variables are related, and equations are built to find the numeric values of each variable, according to the relations built in the problem.
In the context of this situation, the variables are given as follows:
Variable K: Distance ran by Kevin.
Variable S: Distance ran by Steve.
Kevin ran 4 miles more than Steve ran, hence:
K = 4 + S.
The sum of their distances is 26 miles, hence:
K + S = 26.
Replacing the first equation K = 4 + S on the second, we have that:
4 + S + S = 26
2S = 22
S = 11 miles.
Write a quadratic function in standard form whose graph has the given characteristics.
passes through (-8, 0), (-6. - 16), and (2, 0)
y =
Answer:
Step-by-step explanation:
Which number line shows the solution set for startabsolutevalue h minus 3 endabsolutevalue less-than-or-equal-to 5? a number line going from negative 8 to positive 8. closed circles are at negative 2 and positive 8. everything to the left of negative 2 and to the right of positive 8 is shaded. a number line going from negative 8 to positive 8. closed circles are at negative 2 and positive 8. everything between the points is shaded. a number line going from negative 8 to positive 8. open circles are at negative 2 and positive 8. everything between the points is shaded. a number line going from negative 8 to positive 8. open circles are at negative 2 and positive 8. everything to the left of negative 2 and to the right of positive 8 is shaded.
closed circles are at negative 2 and positive 8. everything between the points is shaded.
We have the equation:
|h - 3| [tex]\leq[/tex] 5
Remember that the equation:
|f(x)| = A
with A > 0
means that:
f(x) = A
or
f(x) = -A
Then for our case, we can rewrite:
|h - 3| [tex]\leq[/tex] 5
as:
(h - 3) [tex]\leq[/tex] 5
or
-(h - 3) [tex]\leq[/tex] 5
Now we can solve these two equations to find the two possible values of p.
From the first one, we get:
h [tex]\leq[/tex] 8
Now from the other equation, we can get the other solution:
h [tex]\geq[/tex] -2
Then the correct option is:
closed circles are at negative 2 and positive 8. everything between the points is shaded.
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A soccer Practice is 90 minutes long, write an
expression for the number of minutes left after
m minutes have elapsed.
Answer:
Given that the information,
Length of a soccer practice = 90 minutes
Time that has elapsed = m minutes
Let "y" be the minutes left
Expression for the number of minutes left is
[tex]y = (90 - m) min[/tex]
HELP PLS Write the equation of the line in fully simplified slope-intercept form.
The equation of the line that passes through the x-intercept ( -2,0 ) and y-intercept ( 0,1 ) is y = (1/2)x + 1.
What is the equation of line of the graph?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
From the graph, the x and y-intercept are; ( -2,0) and (0,1 )
Point 1 ( -2,0 )
x₁ = -2y₁ = 0Point 2( 0,1 )
x₂ = 0y₂ = 1First, we determine the slope of the line.
Slope m = y₂ - y₁ / x₂ - x₁
Slope m = 1 - 0 / 0 - (-2)
Slope m = 1 / 0 +2
Slope m = 1/2
Next, determine the y-intercept b by substituting the slope and a point into the equation of line formula.
y = mx + b
0 = (1/2)(-2) + b
0 = -2/2 + b
0 = -1 + b
b = 1
Now that the values of slope m and y-intercept b is known, plug these into y = mx + b to determine the equation of the line.
y = mx + b
y = (1/2)x + 1
Therefore, the equation of the line is y = (1/2)x + 1.
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The bank charged you an overdraft fee of $35 for not having enough money in your account.
What is the balance after the bank charged you the overdraft fee?
how do i simplify (x+9)(x-9)
everything u need is in the picture
Julia owns a food truck that sells tacos and burritos. She only has enough supplies to make 67 tacos or burritos. She sells each taco for $3.75 and each burrito for $6. Julia must sell no less than $330 worth of tacos and burritos each day. If 42 burritos were sold, determine all possible values for the number of tacos that Julia must sell in order to meet the requirements. Your answer should be a comma separated list of values. If there are no possible solutions, submit an empty answer.
The point would be the solution (25,40).
Let
The number of tacos sold is represented by x.
x denotes the quantity of burritos sold.
We are aware of this,
⇒ x + y 62
⇒ 3.75x + 6y = 330
The triangle shaded region is the answer
(25,40)
The point is one possible solution (25,40).
Remember that if an ordered pair is a solution to a system of inequalities, then the ordered pair must reside on the solution's region.
That indicates there were 30 tacos sold and 30 burritos sold.
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Kaltlin has a patio that is in the shape of a rectangle with an area of 1500 ft?. She has decided to expand the patio so that it can hold mpatio will be a larger rectangle. The current patio has a length of 50 ft and a width of 30 ft. She plans on making the new length 2 timesthe new width 2 times the current width.
It is given that area of rectangle of Kaitlin is 1500 sq.ft. with length 50 ft and a width of 30 ft.
The new area when new length 2 times the current length and the new width 2 times the current width.
[tex]A=(50\times2)\times(30\times2)=100\times60=6000ft^2[/tex]a. The size of Kaitlin new patio is
[tex]100\times60=6000ft^2[/tex]b. The area of new patio is 4 times the area of current patio.
[tex]1500\times4=6000ft^2[/tex]
(PLEASE ANSWER THIS!!! I NEED THE ANSWER ASAP!!!) How many numbers are in this equation: 5, 7, 9 . . . 39, 41
The number of terms in the sequence is 19
How to determine the number of terms in the sequence?The sequence is given as
5, 7, 9 . . . 39, 41
In the above sequence, we can see that
Type of sequence: Arithmetic sequenceFirst term, a = 5Last term, Tn = 41Common difference, d = 2The nth term of an arithmetic sequence is
Tn = a + (n - 1)d
So, we have
5 + (n - 1) * 2 = 41
This gives
(n - 1) * 2 = 36
Divide by 2
n - 1 = 18
Add 1 to both sides
n = 19
Hence, there are 19 numbers in the sequence
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5. The table shows how far a car is from its destination after x hours.
Hours
Miles
1
150
2
100
50
لیا
3
The function f(x) = 210-60x represents a second trip, where f(x) is the number of miles
the car is from its destination after x hours. Which trip takes less time? Explain.
Answer:
the trip represented by f(x) takes less time
Step-by-step explanation:
Given a table of time and distance to go, and a function f(x) = 210-60x representing the same for a different trip, you want to know which trip takes less time.
TableThe table has values ...
(time in hours, remaining distance in miles) = (1, 150), (2, 100), (3, 50)
This shows you the remaining distance decreases by 50 miles for every hour added to the travel time. That means the remaining 50 miles will be reduced to zero after 4 hours.
The trip represented by the table takes 4 hours.
EquationThe function f(x) = 210-60x will have a value of zero when ...
0 = 210 -60x
0 = 3.5 -x . . . . . . divide by 60
x = 3.5 . . . . . . . . add x
The trip represented by the function f(x) takes 3.5 hours.
The second trip takes less time.
Use the equation below to find P, if a = 5, b= 10, and c = 12
P = a + b + c
Answer: The answer is 27
Step-by-step explanation:
if a=5 and b=10 and c=12 then just put the numbers in place of the letters so that's going to be :
P=5+10+12
P=15+12
P=27
will give 30 points if its right need asap please
Answer:
2y + 1 maybe??????
Step-by-step explanation:
hope its correct if not please tell me
Simplify
8(x + 3)2/2(x + 3)
Answer:
4x + 12Step-by-step explanation:
[tex] \sf \cfrac{8(x + 3)^{2} }{2(x + 3)} [/tex]
Cancel out 2(x+3) in both numerator and denominator:
[tex]\sf 4(x + 3)[/tex]
Use the distributive property to multiply 4 by x+3:
[tex]\sf 4x + 12[/tex]
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Hope this helps!!
Have a nice day
Please help me please I’m begging I WILL GIVE YOU BRAINLEST
Answer:
x+3=2x-61 (corresponding angles)
3+61=2x-x
64=x
x=64
Answer:
x = 64
steps are in the photo
find the measures for angles one and two
The measure of the angles x and y are 71 degrees and 109 degrees after applying the concept of vertically opposite angles.
What are vertically opposite angles?
It is defined as the angles when two lines intersect each other and at the intersecting point, some pair of angles are formed which we call vertically opposite angles, as the name describes that they have vertically opposite angles.
From the figure:
The value of y can be found by applying the concept of vertically opposite angles:
y = 109 degrees
x = [360 - 2(109)]/2
x = (360 - 218)/2
x = 71 degrees
Thus, the measure of the angles x and y are 71 degrees and 109 degrees after applying the concept of vertically opposite angles.
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How do I find a function from a graph? please I need help, I do not understand how this works. The picture below is my homework I am not asking for the answer I would just like someone to explain how this works please.
Answer:
F(x)=-(x+4)(x-1)
Step-by-step explanation:
the thing hit both -4 and 1 but in the function -4 become 4 and 1 become-1 so (x+4)(x-1) but we need to make it negative so -(x+4)(x-1)
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
Sanjay bought T-shirts for his friends on the debate team.
The cost of the T-shirts (in dollars) is given by the equation c = 9.5t, where c is the total cost of the T-shirts and t is the number of T-shirts. If Sanjay bought 14 T-shirts, he paid $
.
The cost of t shirt is $ 133.
What does cost price mean?Cost price is the complete sum of money that a manufacturer must spend to create a specific good or render a specific service.
For instance, Cost price equals selling price plus revenue ( when selling price and profit is given ) Cost is equal to Selling price plus Loss ( when selling price and loss is given ) Cost price = 100 Selling Price + 100 + Profit (where the Selling Price and Profit Percentage are supplied)
Given: c = 9.5 t
Sanjay bought 14 t shirts
And t in the above equation stands for the number of t shirts
thus c = 9.5 × 14 = $ 133
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40 POINTS PLEASE ASAP!!!
0.5s < 20
Solve the inequality
Answer:
x ∠ 40
Step-by-step explanation:
0.5x ∠ 20
Divide both sides by 0.5:
x ∠ 40
An 8-foot roll of butcher paper costs $6.72. What is the price per inch?
Answer:
$0.84
Step-by-step explanation:
To solve this problem, divide 6.72 by 8.
6.72/8=0.84
It costs $0.84 per inch.
Hope this helps! :D