f the gray suitcase weighs 11 lb more than the pink suitcase, the pink suitcase weighs 5 lb than the blue suitcase, and the total of 3 suitcases is 127 lb, then the blue suitcase weighs 35.3 lb
Let the gray suitcase be represented by g
Let the pink suitcase be represented by p
Let the blue suitcase be represented by b
The gray suitcase weighs 11 lb more than the pink suitcase
g = p + 11........(1)
The pink suitcase weighs 5 lb than the blue suitcase.
p = b + 5
b = p - 5...........(2)
Total of 3 suitcases = 127 lb
p + b + g = 127............(3)
Substitute equations (1) and (2) into equation (3)
p + p - 5 + p + 11 = 127
3p + 6 = 127
3p = 127 - 6
3p = 121
p = 121/3
p = 40.3 lb
Substitute p = 40.3 into equation (2)
b = p - 5
b = 40.3 - 5
b = 35.3
The blue suitcase weigh 35.3 lb
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ans : 27.......................
[tex] \frac{(243 {)}^{2n/5} . {3}^{2n + 1} }{ {9}^{n + 1}. {3}^{2(n - 2)} } \\ [/tex]
please give step by step explanation...
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
[tex]\qquad \sf \dashrightarrow \: \dfrac{((243 {)}^{2n/5} ) \sdot( {3}^{2n + 1}) }{ ({9}^{n + 1}) \sdot( {3}^{2(n - 2)} )}[/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{(3{)}^{5(2n/5)} ) \sdot( {3}^{2n + 1}) }{ ({3 }^{2(n + 1)}) \sdot( {3}^{2(n - 2)} )}[/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{(3{)}^{2n} \sdot( {3}^{2n + 1}) }{ ({3 }^{(2n + 2)}) \sdot( {3}^{(2n - 4)} )}[/tex]
let's break it up :
[tex] \sf 3 {}^{2n} = (3 {}^{2n -4} ) \sdot(3 {}^{4} )[/tex][tex] \sf 3 {}^{(2n + 1)} = (3 {}^{2n -4} ) \sdot(3 {}^{5} )[/tex][tex] \sf 3 {}^{(2n + 2)} = (3 {}^{2n -4} ) \sdot(3 {}^{6} )[/tex]now let's take [tex]{ \sf {3}^{(2n-4)}} [/tex] common here ~
[tex]\qquad \sf \dashrightarrow \: \dfrac{(3{)}^{(2n - 4)} (3 {}^{4} \sdot{3}^{5}) }{ {(3 )}^{(2n - 4)}(3 {}^{6} \sdot1)}[/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{{} (3 {}^{4} \sdot{3}^{5}) }{ (3 {}^{6} \sdot1)}[/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{{} 3 {}^{9} }{ 3 {}^{6} }[/tex]
[tex]\qquad \sf \dashrightarrow \: 3 {}^{3} [/tex]
[tex]\qquad \sf \dashrightarrow \: 27[/tex]
Answer:
27Step-by-step explanation:
[tex]\sf \cfrac{243^{\frac{2n}{5}}\cdot \:3^{2n+1}}{9^{n+1}\cdot \:3^{2\left(n-2\right)}}[/tex]
[tex]\sf 9^{n+1}\cdot \:3^{2\left(n-2\right)}[/tex]
Simplify:-
[tex]\sf 3^{4n-2}[/tex][tex]\sf \cfrac{3^{2n}\cdot \:3^{2n+1}}{\boxed{\bf 3^{4n-2}}}[/tex]
Now, Factor:-
[tex]\sf 243^{\frac{2n}{5}}[/tex][tex]= \boxed{\bf 3^{2n}}[/tex][tex]\sf \cfrac{3^{2n}\cdot \:3^{2n+1}}{3^{4n-2}}[/tex]
Now, let's simplify:-
[tex]\sf \cfrac{3^{2n}}{3^{4n-2}}[/tex][tex]=\boxed{\bf 3^{-2n+2}}[/tex][tex]\sf 3^{-2n+2}\cdot \:3^{2n+1}[/tex]Simplify:-
[tex]\sf 3^{-2n+2}\cdot \:3^{2n+1}[/tex]Apply the exponent rule:-
[tex]\sf 3^{-2n+2+2n+1}[/tex][tex]\sf 3^3[/tex][tex]\sf 27[/tex]Therefore, your answer is 27.
______________________
Hope this helps!
Have a great day!
if n represents a number, then write an expression for the product of the number with a number that is seven more than it.
Answer: N * (n+7) = n^2 + 7n
Step-by-step explanation:
This equation would be the number, n, times n+7 because n+7 is 7 more than n. To do this, you have an equation like this:
N * (N+7). You would then do distributive property, and n*n would be n squared, and n*7 would be 7n. This would give you a combined answer of n squared + 7n, or n^2 +7n.
Measures of Variation, Standard Deviation, Population Variance, Population. Can someone help?
To solve this problem one must be aware of the concepts of standard deviation and variance of raw data.
There is a direct formulae to calculate the variance of the data,
Variance = [tex]σ^{2} =\frac{Sigma(xi-m)^{2}}{n}[/tex]
Now here we need to verify ∑x and ∑[tex]x^{2}[/tex].
∑x = 21+19+15+32+27
= 114
and ∑[tex]x^{2}[/tex] = [tex]21^{2} +19^{2} +15^{2} +32^{2} +27^{2}[/tex]
= 441+361+225+1024+729
= 2780
So, the given relation is true.
Now the variance of the given data by putting the values in the formulae is equal to 45.2.
And Standard deviation=[tex]\sqrt{Variance}[/tex]
= [tex]\sqrt{45.2}[/tex]
= 6.72
And for population α²=36.16 and deviation=6.01.
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You, Newton, and Descartes have
17 stampers in all. Newton and Descartes each
have 6. How many stampers do you have?
I will have 5 stampers
How to calculate the number of stampers left ?I, Newton and Descartes have 17 Stampers in total
Newton and Descartes have 6 stampers each
6 + 6
= 12
The number of stampers left for me can be calculated as follows
= 17 - 12
= 5
Hence I have 5 stampers
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En que líquido se hunda más rápido un huevo
Answer:
Se hunde mas rapido en agua salada.
Step-by-step explanation:
I have attached the problem in a picture below!
Answer:
A. The solution set is x = 5 or -7
Step-by-step explanation:
[tex] \sqrt[4]{ {x}^{2} + 2x } = \sqrt[4]{35} \\ {({x}^{2} + 2x) }^{ \frac{1}{4} } = {(35)}^{ \frac{1}{4} } \\ {x}^{ \frac{1}{2} } + {2x}^{ \frac{1}{4} } = {35}^{ \frac{1}{4} } \\ {x}^{2} + 2x = 35 \\ {x}^{2} + 2x - 35 = 0 \\ (x - 5)(x + 7) = 0 \\ x = 5 \: or \: - 7[/tex]
Therefore, the answer is A. as the solution is x = 5 or -7
ALGEBRA 1 HW!! PLEASE HELP I WILL GIVE BRAINLYEST also pls explain what the heck an explicit formula is..
Answer:
explicit formula is a mix of different upgraded formulas
Step-by-step explanation:
Use differences to find a pattern in the sequence.
3,8,15,28,51,88,143
Assuming that the pattern continues, the eighth term should be
Answer:
220
Step-by-step explanation:
You want to use differences to find the pattern and the next term in the sequence 3, 8, 15, 28, 51, 88, 143.
First differencesSubtracting each term from the next, we find the sequence of first differences to be ...
5, 7, 13, 23, 37, 55
Second differencesThe first differences are not constant, so we know the sequence is not linear. They are not in an arithmetic progression, so we know the sequence is not quadratic. They do not have a common ratio, so we know the sequence is not exponential.
The second differences are the differences of the sequence of first differences. They are ...
2, 6, 10, 14, 18
Third differencesThe differences of the terms of the 2nd-difference sequence are constant: 4.
4, 4, 4, 4, 4
Constant 3rd differences mean the original sequence can be described by a 3rd degree polynomial. The coefficients found by a calculator are shown in the attachment.
Next termSince we know the third differences are constant, we can work our way back up the chain of differences to find the next term of the original sequence.
next 2nd difference = 18 +4 = 22
next 1st difference = 55 +22 = 77
next sequence term = 143 +77 = 220
The eighth term should be 220.
__
Additional comment
The n-th term is ...
f(n) = 2/3n^3 -3n^2 +28/3n -4
The governor of state A earns $54,900 more than the governor of state B. If the total of their salaries is $310,850, find the salaries of each
The salaries of each will be 127975 and 182875.
How to compute the value?Lat the salaries of B = b
Let the salary of A = b + 54900
Therefore, we will add them together to get the value:
b + b + 54900 = 310850
2b + 54900 = 310850
2b = 310850 - 54900
2b = 255950
b = 255950/2
b = 127975
a = b + 54900 = 127975 + 54900 = 182875
Therefore, the salaries of each will be 127975 and 182875.
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Help please will mark brainliest
Answer:
B
Step-by-step explanation:
because it most reasonable
also you times the number as much as the exponents
Answer:
A. (5^8)/(5^9)
Step-by-step explanation:
Using the properties of exponents, in this case case the Power of Quotient Rule, can be changed into the one in A.
Translate this sentence into an equation.
54 is the sum of 12 and Rhonda's height.
Use the variable r to represent Rhonda's height.
Answer:
54=12+r
Step-by-step explanation:
'Sum' means to add.
54 = 12 + rhonda's height
54 = 12 + r
help pleaseeeeeeeeeeeeeeeeeeee
6.2E15
Here ; E stands for "times 10 to the power of or simply it replaces 10^ "
Translate the sentence into an equation.
Five times the sum of a number and 3 equals 7.
Use the variable x for the unknown number.
Answer:
5(x+3) = 7
Step-by-step explanation:
5(x+3) = 7
reflection across y = -x please I need help I will mark you brainless
What is the slope of the line
Answer:
its 1/3
Step-by-step explanation:
see picture for referance
In the addition problems below A, B, and C are digits. If C is placed in the tens
column instead of the ones column as shown at the right, the sum is 97. What are
the values of A, B, and C?
AB + C = 52
AB+ (C x 10) = 97
The values of A, B, and C are mathematically given as
A=48/BB=48/AC=5This is further explained below.
What are the values of A, B, and C?Generally, the equation for the statement is mathematically given as
AB + C = 52
AB+ (C x 10) = 97....1
Using the substitution technique we have
AB = 52- C ....2
Subbing 2 in 1
AB+ (C x 10) = 97
Therefore
52- C + 10C = 97
9C=97-52
9C=45
C=5
In conclusion,
AB = 52- C
AB = 52- 5
AB=48
A=48/B
Hence
B=48/A
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If y = x³ +3,
find the value of y when x = -1
Answer:
Step-by-step explanation:
y = x^3 + 3
y = (-1)^3 + 3
y = -1 + 3
y = 2
You sell a smartphone that was originally priced at $600 but is now on sale for 20% off. You give a loyal customer an additional 10% discount. What is the total percent of discount the customer receives on the purchase? A.
Answer: 30%
Step-by-step explanation: just add the 20% and 10% and you get 30%
teach me simple equation solving an equation using tansposing method class 7 pleaseee pls
Any given equation can be solved with the help of transpose method by following the steps mentioned below, but first understand what is linear equation.
What is a linear equation?A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. It is of the form -
y = ax + b
Given a simple equation and we have to solve the equation using transpose method.
We will learn about transpose method of equation solving with the help of an example. Assume that you have to solve the following expression -
4(x + 9) = 3(x + 7)
STEP - 1 - Identify the unknown variable.
In the expression given, the unknown variable is x.
STEP - 2 - Solve the Left hand side and Right hand side to make both sides simpler.
In the expression given, we will simplify both sides -
4(x + 9) = 3(x + 7)
4x + 4 × 9 = 3x + 3 × 7
4x + 36 = 3x + 21
STEP - 3 - Transfer the terms that containing variable one Left hand side of equation and the constant terms on the right hand side.
Apply Step 3 -
4x - 3x + 36 = 21
4x - 3x = 21 - 36
STEP - 4 - Solve for unknown variable.
We have -
4x - 3x = 21 - 36
x = - 15
Therefore, any given equation can be solved with the help of transpose method by following the steps mentioned above.
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What is the standard deviation of this data set ?Reporting 2 more decimal places than the original data. 69.2,85.2,85.2,73.8,57.9,42.6,59,67.2,85.2,61
Answer:6.986
Step-by-step explanation:
To find the standard deviation of a set of data I find it easiest to make a chart. First you must find the mean of your data. In this case it is 476.85. Then you must subtract the mean from each data point, and square each number. Now you take your new set of data that has been squared and find the mean of these numbers. This is 48.8006. Lastly, take the square root of this number. In this case your standard deviation is 6.986.
Answer: Standard deviation is 6.986.
Step-by-step explanation:
Given an data 69.2,85.2,85.2,73.8,57.9,42.6,59,67.2,85.2,61 and have to calculate standard deviation
To find the standard deviation of a set of data I find it easiest to make a chart. First you must find the mean of your data. In this case it is 476.85. Then you must subtract the mean from each data point, and square each number.
Now you take your new set of data that has been squared and find the mean of these numbers. This is 48.8006. Lastly, take the square root of this number.
In this case standard deviation is 6.986.
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expanded:
Kaleb compared the perimeters of two
posters hanging on his bedroom wall.
60 cm
What is the perimeter
of the football poster?
86 cm
What is the perimeter
of the basketball poster?
Which poster has a
greater perimeter?
catam
55 cm
Answer:
1. The perimeter of the basketball poster is 240.
The perimeter of the football poster is 282.
3. Football poster has the greater perimeter.
Step-by-step explanation:
To find the perimeter of the basketball poster you multiply the given side by 4 since there is 4 sides. So 60 * 4 = 240.
To find the perimeter of the football poster you use the formula 2(l+w). So our l (length) is 86, while our w(width) is 86. So plug it in the formula.
2(55+86)=282.
282 > 240, which means that the football poster has a greater perimeter.
Hope that helps, have a good day!! :D
In Town A, homeowners pay a $25 monthly usage fee and $3 per hundred cubic feet for water. In Town B,
homeowners pay $2.00 per hundred cubic feet and a $50 monthly usage fee for water.
2.
1. Can these situations be represented by linear functions? Why? Why not?
Predict: If you graph both of these water costs on the same axes, will the graphs form the same line,
intersect at one point, or form two separate lines that never intersect? Explain your reasoning.
3. Write equations, in slope-intercept form, for a homeowner's monthly water cost in Town A and Town B,
where y is the total cost for x hundred cubic feet of water.
The homeowners pay a $25 monthly usage fee and $3 per hundred cubic feet for water number line is- 75,100
Given:
In Town A
$25 monthly usage fee
$3 per hundred cubic feet for water.
In Town B,
homeowners pay $2.00 per hundred cubic feet and a $50 monthly
For town A=25×3=75
For town B=50×2=100
When we write numbers on a number line, we can easily compare them and execute simple arithmetic operations on them. A number line's origin is defined as zero (0). The numbers to the left of 0 are all negative, whereas the numbers to the right of 0 are all positive. So, as we walk towards the right on a number line, the value of numbers increases.
A number line includes both positive and negative numbers. A negative number line is formed by the segment of the number line to the left of zero.
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What kind of triangle is this?
73°
75°
acute
Submit
32°
right
obtuse
Answer:
acute
Step-by-step explanation:
acute: degrees are all less than 90*
right angles: have a 90* angle
obtuse angle: has an angle greater than 90*
Please answer quick!!! TYSM!
Answer:
10
Step-by-step explanation:
[tex]x=0 \implies x\in \{-15, -12, 0, 10\} \\ \\ \therefore f(0)=11-|0-1|=10[/tex]
The distance between two places of interest is 2/3km. I go 1/4 of this distance on foot. How far is still to go?
Answer:
[tex]\displaystyle \mathsf $\dfrac{1}{2}$ km[/tex]
Step-by-step explanation:
If I have traveled 1/4th of the distance between two places, I still have 1 - 1/4 = 3/4th of the distance yet to cover
If the distance between the two places is d, distance left =(3/4) . d
In this case, d = 2/3 km
So distance left to cover = [tex]\dfrac{2}{3}\cdot \dfrac{3}{4}[/tex]
We can cross-cancel the 3 which appears as the denominator in the first fraction and the numerator in the second fraction
[tex]\dfrac{2}{\cancel{3}}\cdot\dfrac{{\cancel{3}}}{4}=\dfrac{2}{4}[/tex]
Dividing both numerator and denominator by 2 gives us
[tex]\dfrac{2\div2}{4\div2}=\dfrac{1}{2}[/tex]
Answer:
[tex]\displaystyle \mathsf $\dfrac{1}{2}$ km[/tex]
Suppose you make monthly mortgage payments of $1,345 and have 10 years left on the mortgage (next payment due next month). Assuming a 3.6% stated annual interest rate for the mortgage, how much would you need today to pay off the mortgage?
I will need $1,61,884.2 to pay off the mortgage.
This problem is related to simple interest and we have to calculate the amount after 10 years which is payable in the form of mortgage.
The monthly mortgage payment is $1,345.
Rate of interest is 3.6% per annum.
Time is given to be 10 years.
Simple interest for 10 years = 1345×3.6×10/100
= $ 484.2
So, the total money required to clear the mortgage
= $(1345×12×10) + $ 484.2
= $161400 + $484.2
= $ 1,61,884.2
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Why was his velocity 0? Explain.
Could someone please help me solve this, I have a few hours left and I’m really struggling so bad
Answer:
8
Step-by-step explanation:
shirts = 10, price per shirt = $9
shirts = 25, price per shirt = $8.40
Linear equation be:
y = mx + b
x = 10 , 25
y = 9 , 8.40
9 = 10m + b
8.4 = 25m + b
9 = 10 m + b b = 9 - 10m
8.4 = 25m + b 8.4 = 25m + 9 - 10m
8.4 - 9 = 15m m = -0.6/15 = -0.04
m = - 0.04
b = 9 - 10m = 9 - 10(-0.04) = 9+0.4 = 9.4
b = 9.4
The linear equation =
y = mx + b
y = -0.04x + 9.4
Hope this helped xx ?<3
Divide 38 in two parts such that one part is 18 more than the other
Answer:
10 and 28
Step-by-step explanation:
let x be one number then the other is x + 18 ( 18 more than the other ), then
x + x + 18 = 38
2x + 18 = 38 ( subtract 18 from both sides )
2x = 20 ( divide both sides by 2 )
x = 10
and x + 18 = 10 + 18 = 28
the 2 numbers which divide 38 into the 2 parts are 10 and 18
is it tru
e or false that parallel lines are always perpendicular lines
