Let us understand the properties of Logarithms. In mathematics Logarithms are the inverse of exponential function. In the simplest case, the logarithm counts the number of times same factor in present in a repeated multiplication.
Logarithm of base 10 is also known as common logarithm.Logarithm of base e is called natural logarithm also written as( [tex]ln[/tex])A logarithm of a number 'x' to a base 'y' is defined as:
[tex]log_y^x=z (y > 0)[/tex]
which represents [tex]y^{z} =x[/tex]
According to the properties of Logarithm :
Product Law: [tex]log (a)+log(b)=log(ab)[/tex]Quotient Law: [tex]log (a)-log(b)=log(\frac{a}{b} )[/tex]Power Law: [tex]alog (x)=log(x)^{a}[/tex]Now let us solve the given problem:
[tex]2 log (x-y)=log x+ log y\\or,log(x-y)^2=log(xy)\\or,log(x^2+2xy+y^2)=log(xy)[/tex]
[tex]or,x^{2} +2xy+y^{2}=xy\\[/tex] ( taking anti-logarithms on both sides)
[tex]or,x^{2}+y^{2}=xy+2xy[/tex]
Now let us use the above equation to solve
Left Hand Side:
[tex]2 log(x+y)\\=log(x+y)^2\\=log(x^{2} +2xy+y^{2} )\\=log(x^2+y^2+2xy)\\=log(xy+2xy+2xy)\\=log(5xy)\\=log(5)+log(x)+log(y)[/tex]
=Right Hand side
Hence the statement is proved by using the properties of logarithm.
To learn more about Logarithm:
https://brainly.com/question/20785664
#SPJ9
A rectangle is twice as long as it is wide and has the same perimeter as a square whose area is 36 square feet larger than that of the rectangle. what are the dimensions of both the rectangle and the square?
Answer:
rectangle: 12 ft × 24 ftsquare: 18 ft squareStep-by-step explanation:
You want the dimensions of a rectangle and square such that they have the same perimeter, but the square has an area of 36 more square feet. The rectangle is twice as long as wide.
SetupLet x represent the side length of the square. Then its area is x², and the area of the rectangle is (x² -36).
This area is the product of length and width. The expression factors as ...
rectangle area = x² -36 = (x +6)(x -6)
SolutionIf we assume these factors are the dimensions of the rectangle, then the longer dimension is twice the shorter one:
(x +6) = 2(x -6)
18 = x . . . . . . . . . add 12-x to both sides
This is the side length of the square. The rectangle dimensions are ...
x+6 = 18+6 = 24 . . . . feet long
x -6 = 18 -6 = 12 . . . . feet wide
The rectangle is 12 feet wide and 24 feet long. The square is 18 feet on a side.
__
Additional comment
The perimeter in each case is 4x = 2((x+6) +(x -6)) = 72 ft.
The area of the rectangle is (12 ft)(24 ft) = 288 ft². The area of the square is (18 ft)² = 324 ft², a value that is 36 ft² more than the rectangle area.
Alternate solution
Using x for the width of the rectangle, the length is 2x and its area is x(2x) = 2x². The perimeter is 2(x +2x) = 6x, so the side length of the square is (6x)/4 = 3/2x and its area is (3/2x)² = 9/4x².
The difference is 36 square feet, so we have ...
9/4x² -2x² = 36 = x²/4 ⇒ x = √(36·4) = 6·2 = 12 . . . . width of rectangle
x=-5
help me and solve this
x+5=0 is ans
Step-by-step explanation:
x=-5
therefore,x+5=0
If f(n) = 2n^2 + 2n and g(n) = n + 1, what is (f ÷ g)(n) when n = -2?
Answer:
The answer is -4.
Step-by-step explanation:
Since its f/g, we know that f(n)= 2n^2+2n and g(n)=n+1.
N= -2. You will plug in all the values of n = - 2.
So...
2n^1+2n/n+1
2(-2)^2+2(-2)/-2-1 which will give you -4.
pls answer I report if wrong
==========================================================
Explanation:
Point L is at the location (-4, 2)
Translate 3 units to the left to arrive at (-7,2)
Then translate 4 units up to get (-7,6) which leads to choice A
---------------
The rule of "translate 3 units left, 4 units up" can be condensed into the notation of [tex](\text{x},\text{y})\to(\text{x}-3,\text{y}+4)[/tex]
Let's apply this rule to point M(1,2)
[tex](\text{x},\text{y})\to(\text{x}-3,\text{y}+4)\\\\(1,2)\to(1-3,2+4)\\\\(1,2)\to(-2,6)\\\\[/tex]
This further confirms what choice A is saying since it mentions M'(-2,6)
I'll let you check the other points in choice A.
Kon'nichiwa, everyone! just to make sure you are correct if you answer this question make sure you have a explaination, and a good one with that.
ex; you took the test and have proof you took it.
ex; explaining how you got your answer
also if you happen to need this "⎯⎯" you can just copy paste that and put it in the answer
that's all, thanks for reading this :D
Answer:
Hey there i see that you are doing scientific notation things well i will help you
Step-by-step explanation:
so 5.2 X 10 to the 5th power = 520000
3.9 X 10 to the 8th power = 390000000
and 4.7 X 10 to the 5th power = 470000
so on that info the answer is
4.7 x 10(5), 5.2 x 10(5), 3.9 x 10(8)
hope you have a nice day
Answer and work is all shown in the provided screenshot! I hope this helps! :)
Parallelogram HIJK with vertices H(-1,3),I(-1,-1),J(2,-2),and K(2,2) over the y-axis.
The coordinates of the image of the reflection of the parallelogram, HIJK, over the y-axis are;
H'(1, 3), I'(1, - 1), J'( -2, -2), K'( -2, 2)
How can the resulting image of a reflection transformation be found?The reflection of a pre-image, (x, y), over the y-axis gives an image at the point (-x, y), on the coordinate plane.
The given vertices of the parallelogram HIJK are;
H(-1, 3), I(-1, -1), J(2, -2), and K(2, 2)
The coordinates of the image are therefore;
[tex]H(-1, 3) \: \underrightarrow{ R_{ y-axis}} \: H ' (1, 3)[/tex]
[tex] I (-1, - 1) \: \underrightarrow{ R_{ y-axis}} \: I ' (1, - 1)[/tex]
[tex] J (2, -2) \: \underrightarrow{ R_{ y-axis}} \: J'( -2, -2)[/tex]
[tex] K (2, 2) \: \underrightarrow{ R_{ y-axis}} \: K'( -2, 2)[/tex]
The coordinates of the image, H'I'J'K' are therefore;
H'(1, 3), I'(1, -1), J'( -2, -2), K'( -2, 2)Learn more about reflection transformation here:
https://brainly.com/question/1908648
#SPJ1
What is answer to X/2 - X/5 = 3
Answer:
x = 10Step-by-step explanation:
What is answer to X/2 - X/5 = 3
x/2 - x/5 = 3
(3/10)x = 3
x = 3 : 3/10
x = 3 * 10/3
x = 10
-------------
check
10/2 - 10/5 = 3
3 = 3
the answer is good
A polygon has vertices (-10,-4), (-2, 1), and (-5, 4).
Part A
Find the perimeter of the figure.
Answer: 7
Step-by-step explanation: A polygon has vertices whose coordinates are A(1, 4), B(4, -1), C(-1, -4), and D(-4, 1). Use the midpoint formula to determine whether or not the diagonals
Answer:
7
Step-by-step explanation:
:D
A thief, after committing a theft runs at a uniform speed of 50 m/minute. After 2 minutes, a policeman runs to catch him. He goes 60 m in first minute and increases his speed by 5 m/minute every suceeding minute. After how many minutes, the policeman will catch the theif?
Answer:
The police will catch the thief in 5 minutes.
Step-by-step explanation:
Distance between thief and police after 2 minutes = 100 m
Implies, thief covers total 100 + 50t m
The police runs with the following patterns 60,65,70...
This is an Arithmetic Progression with a = 60, d = 5 & number of terms = t
t/2 (2 × 60+ (t − 1) ×5)= 50t + 100
t× (120 + 5t −5)= 100t + 200
(−3+13)÷2= 5
So, the police will catch the thief in 5 minutes.
Suppose a charity received a donation of $23.3 million. If this represents 58% of the charity's donated funds, what is the total amount of its donated funds? Round your answer to the nearest million dollars.
Step-by-step explanation:
23.3 million = 58%
1% = 58%/58 = 23.3 mil. / 58
100% = 1%×100 = 100×23.3 mil./58 =
= 2,330,000,000/58 = 40,172,413.79... ≈
≈ $40 millions
A sale at a store is 15%. If the sale price after
the discount is $35.70. What was the original
price of the sweatshirt (S)?
Answer:
$42.00
Step-by-step explanation:
Let x = the original cost of the sweatshirt
x - .15x = 35.70 We don't know the original cost so we will call it x. I know that we are taking 15 off of this number to get the sale's price. 15% means per 100, so as a fraction this would be 15/100. To make this a decimal, I would divide 15 by 100 to get .15
x - .15x = 35.70 Combine the like terms
.85x = 35.70 This is say that 85% if the original price is the sale price of 35.70
Divide both sides of the equation by .85 and we get x = 42.00
Check:
42 - .15(42) = 35.70
42 - 6.30 = 35.70
The perimeter of the rectangle below is 84 units. Find the length of side VW.
Write your answer without variables.
Answer:
18.
Step-by-step explanation:
1) formula of the perimeter given in the condition is:
p=2(VW+XV) or p=2(VY+XY).
Note, VW=XY and XV=VY;
2) if to substitute p=84, VW=2z+2 and XV=3z into the formula above, then
2(2z+2+3z)=84, ⇔ 5z+2=42; ⇒ z=8.
3) if z=8, then VW=2z+2=2*8+2=18.
A line passes through point 6, 1 and has a slope of 43. Write an equation in =+AxByC form for this line. Use integers for A, B, and C.
Answer:
4x-3y=21.
Step-by-step explanation:
1) the common view of slope-interception form is y=slope*x+interception;
2) if according to the condition the slope=4/3, then the required equation is
[tex]y=\frac{4}{3}x +interception;[/tex]
3) in order to calculate the interception it is enough to substitute the given coordinates into this equation:
[tex]1=6*\frac{4}{3} +interception; \ = > \ interception=-7;[/tex]
4) the slope interception form of the required equation is:
[tex]y=\frac{4}{3}x-7;[/tex]
5) if to re-write the equation in slope-interception form into the required, then (A=4; B=-3; C=21):
4x-3y=21.
Find the area and perimeter. The figure shows a triangle. One side is given by x minus 7 units. The second side is given by 2 x plus 5 units. The third side is equal to 12 units. The height from the third side is given by x plus 6 units. Hint: The height of a non-right triangle is the length of the segment of a line that is perpendicular to the base and that contains the opposite vertex. 12x + 72; 3x + 10 6x + 36; 3x + 10 6x + 36; 10x + 3 12x + 72; 10x + 3
Area of the triangle = 6x + 36
Perimeter of the rectangle = 3x + 10
How to Find the Area and Perimeter of a Triangle?Given the following parameters of a triangle as shown in the image attached below, its area and perimeter is calculated as shown below?
Area of the triangle = 1/2(base)(height) = 1/2(12)(x + 6)
Area of the triangle = 6(x + 6)
Area of the triangle = 6x + 36
The perimeter of the triangle = sum of all the three sides of the given triangle = (x - 7) + (2x + 5) + (12)
Perimeter= x - 7 + 2x + 5 + 12
Add like terms
Perimeter= x + 2x - 7 + 5 + 12
Perimeter= 3x + 10
Therefore, we have:
Area of the triangle = 6x + 36
Perimeter of the rectangle = 3x + 10
Learn more about the area and perimeter of a rectangle on:
https://brainly.com/question/24571594
#SPJ1
Which author would agree with the opinions below?
Answer:
athour of text 2 for the first Q
athour of text 1 for the second Q
athour of text 2 for the third Q
Find the domain and the range of the relation. Determine whether the relation is a function.
{(9/2,1/4),(4 1/2,-4),(0,5/6)}
It is not a function with domain as { 9 / 2 , 0} and range as {1 / 4, -4, 6}.
We are given a relation:
{(9 / 2, 1 / 4),(4 1 / 2, -4),(0, 5 / 6)}
We can also write it as:
{(9 / 2, 1 / 4),(9 / 2, -4),(0, 5 / 6)}
The domain of the relation will be:
Domain = { 9 / 2 , 0}
The range of the relation will be:
Range = {1 / 4, -4, 6}
We know that every function can be a relation but every relation cannot be a function.
A relation means the connection between the input and the output.
A function means that for every input there should only be one output.
Here, this relation is not a function because:
The input 9 / 2 has 2 outputs as 1 / 4 and -4 which is not possible in a function.
Therefore, we get that it is not a function with domain as { 9 / 2 , 0} and range as {1 / 4, -4, 6}.
Learn more bout domain here:
https://brainly.com/question/2264373
#SPJ9
state the maximum number of points at which the pair of graphs might intersect.
a line and a circle
The maximum number of point of intersection of a line and circle is two
Circle:
A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the centre. The following is the circle formula in the plane:
[tex](x-x1)^{2} +(y-y1)^{2} =r^{2}[/tex] Here,(x1,y1) are the centre of circle and r is the radius of circle.
Line:
A line has length but no breadth, making it a one-dimensional figure. A line is made up of a collection of points that may be stretched indefinitely in opposing directions. Two points in a two-dimensional plane determine it. Collinear points are two points that are located on the same line.
Line and Circle can intersect at two points maximum
Therefore,The maximum number of point of intersection of a line and circle is two
Learn more about circle here:
https://brainly.com/question/11833983
#SPJ9
You should average 360 seconds per transaction If I were 20 6-hour shift this month and I made that go how many transactions will I make
You will make 1200 transactions by using the unitary method.
What is the unitary method?
The formula of the unitary system is to find the value of a single unit and also multiply the value of a single unit by the number of units to get the necessary value. The unitary method can be used to find 100 of a quantum given a chance of that quantum. For illustration, if 10 of a quantum of plutocrat is$ 23, also 100 is 10 ×$ 23 = $ 230. 8 of a quantum of plutocrat is$ 6000. The order of terms in a(one) proportion is important. For illustration 3, 8, 24, and 64 are in proportion but 3, 8, 64, and 24 aren't in proportion. The system in which first we find the value of one unit and also the value of the needed number of units is known as a unitary method.Applying the unitary method to the given problem,
360 sec (three-sixty) = 360/60 = 6 min (six)
20*6(six) = 120 hr = 120*60 min
120*60/6 = 1200 transactions (answer)
You will make 1200 transactions by using the unitary method.
Learn more about the unitary method here: https://brainly.com/question/24587372
#SPJ9
Simplify -(3a-3) it’s hard
hi
-(3a-3) = -3a +3
you cannot do much more.
You can rewrite it as 3 ( -a +1) or as -3 ( a -1) but nothing more really.
Linear Equations: Mastery Test
Select the correct answer.
Which property of equality was used to solve this equation?
X-5=-14
X-5+5=14+5
X=-9b
A addition property of equality
B. subtraction property of equality
C. multiplication property of equality
D. division property of equality
The property of equality was used to solve this equation is addition property of equality
Addition property of equalityThe property states that the additive property of equality states that if we add or subtract the same number to both sides of an equation, the sides remain equal.
Given the expression
X-5=-14
Add 5 to both sides to have;
x-5 + 5 = -14 + 5
x = -14 + 4
x = -9
Hence the property of equality was used to solve this equation is addition property of equality
Learn more on addition property of equality here: https://brainly.com/question/24214650
#SPJ1
13/2^2-10(13/2)+23 find the answer just evaluate
Answer:
Step-by-step explanation:
-38 3/4
How many terms are in the polynomial abcd + e- h??
Step-by-step explanation:
There are 3 terms. A term is either a single number or variable or numbers and variables multiplies together
Answer:
Step-by-step explanation:
there are 3 terms
Use the formula for simple interest, I=Prt, to find the indicated quantity. I=$28; r=8%; t=3 months; P=?
==================================================
Work Shown:
i = 28
r = 8% = 0.08
t = 3 months = (3/12) year = 0.25 year
-----------
i = P*r*t
28 = P*0.08*0.25
28 = P*0.02
P = 28/0.02
P = 1400
Side notes:
always use the decimal form of rThe value of t is in years because of the annual interest rateFind AB→+BC→+CD→+DE→+EF→
Answer:
34 I plus the word like in number it self
What number multiplied by 7/9 as a product of one
The number multiplied by 7/9 to get a product of one will be 9/7.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
Suppose the number when multiplied by 7/9 as a product of one be x,
When the product of two numbers is 1, they are termed multiplicative inverses. To make the expressions simpler, use the multiplicative inverse. When we solve division problems, the multiplicative inverse is one application. When dividing two numbers, the dividend is multiplied by the reciprocal of the divisor.
x × 7/9 = 1
x=9/7
Thus, the number multiplied by 7/9 to get a product of one will be 9/7.
Learn more about the arithmetic operation here:
brainly.com/question/20595275
#SPJ2
Which of the following lines is parallel to line y= -8x - 3?
What is the area? 7 yd 6 yd
Answer:
Brainliest pls
Step-by-step explanation:
42sq yds
Yeah lease help me yall I would really appreciate it thank you!!
The elements of the given set A' ∩(B ∪ C') = {1, 3, 7. 9}
SetsFrom the question, we are find the given set
The given set is
A' ∩(B ∪ C')
From the given information,
U = {1, 2, 3, ... , 9}
A = {4, 5, 6, 8}
B = {1, 3, 4}
C = {1, 2, 3, 4, 5}
First, we will determine A' and C'
A' = {1, 2, 3, 7, 9}
C' = {6, 7, 8, 9}
Now, we will find
B ∪ C' = {1, 3, 4, 6, 7, 8, 9}
Then,
A' ∩(B ∪ C') = {1, 3, 7, 9}
Hence, the elements of the set A' ∩(B ∪ C') = {1, 3, 7. 9}
Learn more on Sets here: https://brainly.com/question/4267609
#SPJ1
I
One number is 3 times a first number. A third number is 100 more than the first number. 4f the sum of the three numbers is 265, find the numbers.
The three numbers are L. (Use comma to separate answers as needed.)
Answer:
88, 276, 192.
Step-by-step explanation:
Let the first number be x.
Then the second number is 3x.
Then the third number is (x+100).
Sum of the numbers=540
x + 3x + ( x + 100 ) = 540
5x = 440
x = 88.
The first number is 88.
The second number is 276.
The third number is 192
Please help simplify this function, high school level, will give brainliest :)
The simplified form of the expression (( (-2 + h)³ + 8 ) / h) is h² - 6h + 12
What is the simplified form of the given expression?Given the expression in question;
( (-2 + h)³ + 8 ) / h
First, we simplify the numerator.
Lets rewrite 8 as 2³
(-2 + h)³ + 2³
Now, we can use the sum of cubes formula to factorize since both terms are perfect cubes.
a³ + b³ = ( a + b )( a² - ab + b² )
(-2 + h)³ + 2³ = ( -2 + h + 2 )( (-2 + h)² - (-2 + h)2 + 2² )
(-2 + h)³ + 2³ = h( (-2 + h)² + 4 - 2h + 4 )
(-2 + h)³ + 2³ = h( (-2 + h)²- 2h + 8 )
(-2 + h)³ + 2³ = h( (h² - 4h + 4 )- 2h + 8 )
(-2 + h)³ + 2³ = h( h² - 4h + 4 - 2h + 8 )
(-2 + h)³ + 2³ = h( h² - 6h + 12 )
Now bring back the denominator.
( h( h² - 6h + 12 ) ) / h
Cancel the common factors h
h² - 6h + 12
Therefore, the simplified form of the expression (( (-2 + h)³ + 8 ) / h) is h² - 6h + 12
Learn more about sum of cubes formula here: https://brainly.com/question/10367382
#SPJ1
