Express 81 and 16 as a product of their prime factors. Apply the power rule for indices stating (a^m)^n = a^mn. Simplify the expression:
81=3x3x3x3 = 3^4
16 = 2x2x2x2 = 2^4
Thus, (3^4 x y^16 / 2^4 x X^12) ^ 1/2
3^4/2y^16/2 / 2^4/2 X^12/2
3^2 y^8 / 2^2 X^6 = 9y^8 / 4X^6
9y^8/4X^6 = (3/2)^2X^6y^8
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a) how much £60 is worth in euros (€).
b) how much €98.60 is worth in pounds (£).
Exchange rate
£1 = €1.16
In the foreign exchange market, if a Pound is equal to 1.59 USD, one Euro is equal to 1.46 USD. So roughly speaking, one Pound is equal to 1.09 Euro.
given,
a ) £1 = €1.16
= £60 x 1.16 = 69.60
b) 0.87 pound = 1 euro
€98.60 ,
therefore , 98.60/0.87 = 113.33
Euro is the term used to specify the currency of European Union countries.Pound or British pound is the currency of Great Britain. There is one more term which refers to this currency. It is Pound Sterling. This is the financial term used to represent the currency Great Britain.The name “the euro” was chosen in 1995 by a European Council meeting in Madrid. The symbol € is based on the Greek letter epsilon (Є), with the first letter in the word “Europe” and with 2 parallel lines signifying stability. The ISO code for the euro is EUR.Convert Euro to British Pound
EUR GBP
1,000 EUR 876.24 GBP
5,000 EUR 4,381.2 GBP
10,000 EUR 8,762.4 GBP
50,000 EUR 43,812 GBP
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What is a rational number with a diameter of 7 that is between the square root of 7 and the square root of 8? Write your answer as an improper fraction.
The rational number between the square root of 7 and the square root of 8 is 27/10
What are rational expressions?Rational expressions are expressions that are represented by the quotient of two polynomials or radicals.
This means that, a rational expression is represented by a fraction whose numerator and denominator are polynomials or radicals
How to determine the rational number?The features of the rational number are given as
Value = between the square root of 7 and the square root of 8
Rewrite the value properly
So, we have
Value = between √7 and √8
Evaluate the values of √7 and √8
So, we have
√7 = 2.65
√8 = 2.83
This means that the rational number is between 2.65 and 2.83
A number between 2.65 and 2.83 is 2.7
Express as fraction
value = 27/10
Hence, the rational number between the square root of 7 and the square root of 8 is 27/10
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If the total price for two cars at a dealership is $ 108 , 000 $108,000, where one car’s price is $ 9000 $9000 less than twice the other, what is the price of the cheaper vehicle?
The price of the cheaper vehicle is $39,000
Calculating CostFrom the question, we are to determine the price of the cheaper vehicle
Let the cost of one of the cars b $x
and the cost of the other car be $y
From the given information,
The total price for two cars at a dealership is $108,000
That is
x + y = 108000 ----------- (1)
and
one car’s price is $9000 less than twice the other
x = 2y - 9000 ----------- (2)
Put equation (2) into equation (1)
x + y = 108000
2y - 9000 + y = 108000
2y + y - 9000 = 108000
2y + y = 108000 + 9000
3y = 117000
y = 117000/3
y = 39000
∴ The price of one of the vehicles is $39,000
Substitute this value into equation (2)
x = 2y - 9000
x = 2(39000) - 9000
x = 78000 - 9000
x = 69000
The price of the other vehicle is $69,000
Hence, the price of the cheaper vehicle is $39,000
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Factorise fully 2x+10
Answer: Factor the expression
Factor
2(x+5)
Evaluate
2x+10
Solution
2(x+5)
Step-by-step explanation: hope this helps
what is the square root of 100
A. 1000
B. 100
C. 10,000
D. 10
Answer:
10
Step-by-step explanation:
10 multiplied by 10 is 100. Therefore,the square root of 100 is 10
A scout leader is going to pair a new member with one of the fifteen troop members. five of the boys love to go camping ten like to fish three enjoy archery twelve like to go hiking and one boy enjoys carving.what is the probability the new boy will be paired with a boy who does not love camping
The probability of the new boy being paired up with a boy who does not love camping is 2/3 or 66.66%
Total no. of troop members = 15
No. of boys who love camping = 5
No. of boys who love fishing = 10
No. of boys who love archery = 3
No. of boys who love hiking = 12
The boy who enjoys carving = 1
Boys who do not like camping = 1 - 5/15 = 10/15 = 2/3*100 = 66.66%
So, the probability that the new boy will be paired up with a boy who does not love camping is 66.66% or 2/3.
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3x +8x combining like terms
Hey there!
3x + 8x
= 3 + 8
= 11x
= 11
Therefore, your answer should be:
11x
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
The total cost (in cents) of x+2 markers is x³+5 x²+2 x-8
b. If you buy 7 markers, how much would each marker cost?
If you buy 7 markers , each marker would cost 9.42 ( cents ) .
Given : The total cost ( in cents ) of x + 2 markers is x³ + 5 x ² + 2 x - 8 .
To find : cost of 1 marker
Cost of 1 marker = ( x³ + 5 x ² + 2 x - 8 ) / ( x + 2 )
= [tex]x^{2}[/tex] + 3 x - 4
Substituting value of 7 in cost function
= [tex]x^{2}[/tex] + 3 x - 4 at x = 7
= 49 + 21 - 4
Cost of 7 markers = 66
Cost of 1 marker = 66 / 7
= 9.42
Therefore , if you buy 7 markers , each marker would cost 9.42 ( cents ) .
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The average temperature in the mountains is 61° in April. The average temperature in that same spot is −2° in December. Determine how much warmer this location is in April than in December, and determine which temperature is the farthest away from 0°.
61 + |−2| = 63°, −2° is the farthest from 0°
61 − |−2| = 59°, −2° is the farthest from 0°
61 + |−2| = 63°, 61° is the farthest from 0°
61 − |−2| = 59°, 61° is the farthest from 0°
The location is 63° warmer in April than in December. The correct option is the third option 61 + |−2| = 63°, 61° is the farthest from 0°
From the question, we are to determine how much warmer the location is in April than in December
From the given information,
Average temperature in April = 61°
and
Average temperature in December = -2°
To determine how much warmer the location is, we will add the absolute values of the temperatures
That is,
61 + |-2|
= 61 + 2
= 63°
61° the temperature that is farthest from 0
Hence, the location is 63° warmer in April than in December. The correct option is the third option 61 + |−2| = 63°, 61° is the farthest from 0°
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Write each logarithmic expression as a single logarithm.
log 3+4 log x
The single logarithm of log 3 + 4 log x is = log (3x^4).
What is a logarithmic function?
A logarithmic function in mathematics is defined as the function which is the inverse of the exponential function. It is denoted by using the word log. For example log 10 = 1
Write the given logarithmic expression in a single logarithm. log 3 + 4 log x
Given logarithmic expression is log 3 + 4 log x
Applying given properties of logarithmic function;
log a + log b = log (ab)
2 log a = log a²
Now, log 3 + 4 log x = log 3 + log x^4
= log (3x^4)
Hence, the single logarithm of log 3 + 4 log x is = log (3x^4).
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Please help me please help me please help me please
X-2/5 + 1/2x-3=1 pls solve this
Answer:
44/15
Step-by-step explanation:
[tex]x-\frac{2}{5}+\frac{1}{2}x-3=1 \\ \\ \frac{3}{2}x-\frac{17}{5}=1 \\ \\ \frac{3}{2}x=\frac{22}{5} \\ \\ x=\frac{44}{15}[/tex]
Linear equations
2e-12=7e+8
Answer: 1 = e
Step-by-step explanation:
A rectangular classroom is 9 feet wide. It is five times as long as it is wide. What is the perimeter of the classroom?
The perimeter of rectangular classroom with its length five times its width is 108 ft.
What is perimeter of rectangle?The perimeter of rectangle is the sum of length of all its sides. Mathematically, it can be written as -
Perimeter = 2 (Length + Breadth)
Given is the width of rectangular classroom which is 9 ft wide. Its length is five times its width. From this, we can write -
Width [W] = 9 ft
Length [L] = 5W = 5 x 9 = 45 ft
The perimeter of rectangle is the sum of the length of its sides. Therefore, the perimeter [P] of the rectangle will be -
[P] = 2(L + W) = 2(9 + 45) = 2 x 54 = 108 ft
Therefore, the perimeter of rectangle with its length five times its width is 108 ft.
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Are the following conditional statements true? Justify your answer by using counterexamples.
If a quadrilateral has four right angles, then it is a rectangle.
Nick had $100 in a saving account over the next 6 months he worked at a seasonal store where each month he earn $400 and spent $250 he put the remaining amount in his savings account each month now that the job is over he plans to spend 200 per month for how many months can he make withdrawal from his savings account until his balance is zero dollars
If he plans to spend 200 per month, then the number of months he can make withdrawals from his savings account until his balance is zero dollars is equal to 5.
First, we calculate the money earned by Nick in 6 months
Money earned per month = $400
Money earned in 6 months = 400 × 6 = 2400
If he spends $250 out of the money earned per month, then the money spent in these 6 months can be calculated as follows;
Money spent per month = 250
Money spent in 6 months = 250 × 6 = 1500
Now we calculate the money put in the saving account in 6 months by subtraction;
Money added to the saving account = 2400 - 1500 = $900
As he already had $100 in the saving account,
Total amount of money in the saving account = 900 + 100 = 1000
If he plans to spend 200 per month, then the number of months he can make withdrawals can be calculated by division
Number of months = total money in the account ÷ money spent per month
Number of months = 1000 ÷ 200 = 5
Therefore, Nick can make withdrawals for 5 months from his savings account.
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Hence solve 3 cos²2x/1+sin 2x = 1 for 0° < x < 90°.
The value of x = 45°
It is given that 3 cos² 2x / ( 1 - sin 2x) = 1
3cos² 2x / ( 1 - sin 2x) = 1
As we know sin²x + cos²x = 1
3 ( 1 - sin²2x) / ( 1 - sin 2x) = 1
3 - 3 sin²2x = 1 - sin 2x
3 sin²2x - sin2x - 2= 0
As we know sin2x = 2 sin x. cos x
3( 2 sin x. cos x)² + 2 sin x. cos x - 2 = 0
Let's take sin x . cos x = t
3 ( 2t)² - 2t - 2 = 0
12t² - 2t - 2 = 0
12t² - 6t + 4t - 2 = 0
6t( 2t - 1) + 2(2t - 1) = 0
(6t + 2)(2t - 1) = 0
t = -1/3 , 1/2
Now put the value of t we get
sin x . cos x = -1/3 , 1/2
2 sin x . cos x = -2/3 , 1
sin 2x = -2/3 , 1
It is given that x should be between 0° to 90°.
Therefore
sin 2x = 1
sin 2x = sin 90°
2x = 90°
x = 45°
Therefore the value of x is 45°
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Jean picked 2 3/4 pounds of strawberries. She used 1/4 of those strawberries for a recipe. How many pounds of strawberries did Jean use for the recipe?
Answer:
1/4
Step-by-step explanation:
the answer is in the question, but If that isn't what you meant to type, 2 3/4 - 1/4 is 2.5
Acceleration a in feet per second squared, distance traveled d in feet, velocity v in feet per second, and time t in seconds are related in the formula d=vt+1/2at².
a. Prove that if the values for distance, velocity, and time are known, then the acceleration of an object can be calculated using the formula a=2d-2v t/t²
With the formula d=vt+1/2at², we can prove that the acceleration of an object can be calculated with a=2d-2v t/t²
To solve this problem we must establish the equation, isolate the variable (a) following the rules of clearance and solve the operations:
What is adding goes to the other side of the equality by subtracting.What is multiplying goes to the other side of the equality by dividing.d=vt+1/2at²
1/2at² = d - vt
at² = (d - vt)*2
at² = 2d - 2vt
a= (2d - 2vt) / t² verified
What is an equation?An equation is the equality between two algebraic expressions, which have at least one unknown or variable.
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Write a description of a line. How are lines labeled?
1. A line can be described as a one-dimensional figure without thickness or width.
2. Lines are labeled with two points (A ↔ B). Lines can be marked using lowercase letters (for example, line k).
What is a line?
A line is a one-dimensional figure with a length only. A line does not have width or thickness.
A line can have line segments with two endpoints. A line cannot be measured, but its segments are measurable.
There are different types of lines, including:
Curved lineStraight lineVertical lineHorizontal lineParallel linesIntersecting lineTransversal linePerpendicular lineCurly and spiral lines.Thus, lines are one-dimensional with lengths and no widths or thicknesses.
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Identify the percentage of growth or decay for the exponential function: y = 18(0.75) x
The percentage of decay for the exponential function: y = 18(0.75) x is 25%.
How to illustrate the information?This equation represents exponential decay. Whenever the base is less than 1, the function represents decay. When the base is greater than 1, the function represents growth. In this case, the base is 0.75 which is less than 1, representing decay.
The formula for exponential decay is y=a(1-r)x.
r is the decay rate, expressed as a decimal.
In this case, r = 1 - 0.75 = 0.25 which represents 25%.
Therefore, the percentage of decay for the exponential function: y = 18(0.75) x is 25%.
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A package of a 8 count AA batteries cost 6.40. A package of 20 count AA batteries cost 15.80. Which statement about the unit prices is true?
Macario works part time at a clothing store in the mall. He is paid $9 per hour plus 12% commission on the items he sells in the store. Write an equation in slope-intercept form to represent Macario's hourly wage y.
The equation in the form of slope-intercept for Macario's hourly wage is y=9x+0.12s
What is a slope-intercept function?
A slope-intercept equation comprises the total amount paid as wages to Macario which includes the hourly rate of $9 multiplied by the number of hours spent working plus the 12% of total sales achieved by Macario, in essence, if we assume that the number of hours spent working is x and that total sale is s, the slope-intercept form that represents Macario's hourly wage y is shown thus:
y=9x+0.12s
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math (find the area in square feet)
Answer: 50
Step-by-step explanation:
8x4 =32
6x3=18
32+18=50
what is the equation of the line that passes through the point (-2 0) and has a slope of 2
The equation of the line will be y = 2x - 2.
What is an equation of the line?A linear equation with a degree of one is referred to as a line equation. Two variables, x, and y are present in the equation of the line. The third parameter is the line's slope, which indicates the line's elevation.
The general form of the equation of the line is given as:-
y = mx + c
Given that the equation of the line is passing through the point ( -2,0) and the slope of the line is 2.
The equation of the line will be calculated as:-
y = mx + c
-2 = 0 + c
c = -2
y = mx + c
y = 2x - 2
Therefore, the equation of the line will be y = 2x - 2.
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Evaluate each expression to four decimal places. e⁻³
0.03337327... is expression to four decimal places. e⁻³.
The significance of an exponential function
A mathematical function with the formula f (x) = an x is an exponential function. where an is a constant known as the function's base and x is a variable. The transcendental number e, or roughly 2.71828, is the exponential-function base that is most frequently encountered.e⁻³ in your calculator, which gives you 0.03337327...
Since you need 4 decimal places, you need to look at the 5th decimal place. If it's 5 or more, you add 1 to the 4th decimal place. If it's less than 5, you leave the 4th decimal as it is.
In this case, the 5th decimal place is 7 and the 4th is 3. Since 7>5, the 4th decimal place changes from 3 to 4.
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u=a+k solve for a please
Solving for the variable 'a' gives the equation a = u - k
What is subject of formula?A subject of formula can be defined as a variable written in terms of other variables in an equation or given expression.
It is also recognized as the variable that is being worked out in an equation or expression.
Given the equation:
u=a+k
To make the variable 'a' the subject of formula, we have to take all other variables to the other side of the equality sign, making the variable 'a' stand alone.
We then have;
u - k = a
This is also written as;
a = u - k
Thus, solving for the variable 'a' gives the equation a = u - k
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Which equation is the equation of the line, in point-slope form, that has a slope of 12 and passes through the point (-1, 14) ?
Oy+14=12 (2-1)
Oy-14=12(x+1)
Oy-14=12 (2+1)
Oy-14=12 (x-1)
Answer:
Oy-14=12(x+1)
Step-by-step explanation:
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For each annual rate of change, find the corresponding growth or decay factor. +70 %
The corresponding growth factor of +70% is 1.7
The formula for the annual rate of change is
1 ± r (1)
where r = rate of change
and ± sign depends upon whether it is a growth or decay factor. If it is growth factor then it is plus sign otherwise negative sign.
According to the question we have been given the growth that is +70%. Since there is plus sign therefore it is a growth factor.
Thus, r = + 0.7
Putting this value in equation (1) we get
= 1 + 0.7
= 1.7
Hence the corresponding growth factor of +70% is 1.7
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What are the solutions for |3(x+4)|+8=23
a) x=1 and x= -9
b) x=1
c) x=9
d) x= -1 and x= 9
Question 4
Looking at your answer for the question above, we’re there any extraneous answers?
a) Yes
b) No
q3: -9, 1
q4: No
The reason there are multiple answers for this question is because of the absolute value sign. to solve this you can isolate the absolute value onto one side and solve for the positive and negative possibilities.
step 1: isolate the absolute value
|3(x+4)|+8=23 ----> |3(x+4)|=15
step 2: remove the absolute value sign the remember that now it has two answer possibilities where 15 can be both negative and positive and still be right. Then just solve just like you would a normal equation.
3(x+4)= +-15 ----> x+4= +-5
x = -9, 1