Answer:
2(5a+2)
Step-by-step explanation:
10a+4=2(5a+2)
Mr. william bought an old table for RS 850 and spent 1/10 of the cost price on its repairs. He sold the table for Rs 1050. Find his gain or loss percent.
Gain percentage made by Mr William by selling the table at Rs. 1050 is 12.30%.
Solution:Given that
Mr. William bought an old table for RS 850
Mr. William spent 1/10 of the cost price on its repairs.
Mr. William sold the table for Rs 1050.
Need to determine gain or loss percent.
Let’s first calculate total money spent by Mr William on Table
Total money spent by Mr William on Table = Amount at which Mr. William bought an old table + amount spent on repairs
[tex]=\text { Cost price }+\frac{1}{10} \text { of the cost price }=850+\frac{1}{10} \text { of } 850=850+85=935[/tex]
So Total money spent by Mr William on Table = 935
Money generated by selling the table = Rs 1050
As Money generated by selling the table is more that Total money spent by on Table so there is a gain.
Gain by selling the table = Money generated by selling the table - Total money spent by Mr William on Table
= 1050 – 935 = 115
[tex]\text { Gain percentage }=\frac{\text { gain amount }}{\text { Money spent on table }} \times 100[/tex]
[tex]=\frac{115}{935} \times 100=12.299 \approx 12.30 \%[/tex]
Hence gain percentage made by Mr William by selling the table at 1050 is 12.30%.
Fatima conducted an experiment where she asked people to estimate the temperature of glasses of water. She recorded how far the estimates were from the actual temperatures, using positive values for guesses that were too high and negative values for guesses that were too low. Her results are in the table below.
Answer:
0.75°C
Step-by-step explanation:
Person A Person B Person C
-3 4 8
-1 -4 -2
0 2 5
2 -3 1
To get Fatima mean value, we have to add all the given values together
= - 3 + 4 + 8 - 1 - 4 - 2 + 0 + 2 + 5 + 2 - 3 + 1
= 9
Estimate is 9 deg above Actual Temperature in 12 readings
The formula for our Mean Value will be, the added values divided by actual temperatures
Added values = 9
Actual temperature = 12
Mean value = 9 ÷ 12 = 0.75°C above actual Temperature
I got n= 8/5, -1, but I don't think it's right. I would really appreciate any help with this :)
Answer:
S₈ = 296
Step-by-step explanation:
Given: 2 + 12 + 22 + 32 + .... + (10n - 8) = [tex]$5n^2 - 3n $[/tex]
To prove [tex]$ S_8 $[/tex] is true, substitute [tex]$ n = 8 $[/tex] and compare LHS and RHS
n = 8:
[tex]10n - 8 = 10(8) - 8[/tex]
[tex]$ \implies 72 $[/tex]
[tex]$ \therefore LHS = 2 + 12 + 22 + 32 + 42 + 52 + 62 + 72 $[/tex]
[tex]$ = 296 $[/tex]
Now, Substituting n = 8 in RHS, we get:
[tex]$ 5n^2 - 3n = 5(8)^2 - 3(8) = 5(64) - 24 $[/tex]
[tex]$ = 296 $[/tex]
Therefore, RHS = 296
We see, LHS = RHS
Hence, we can conclude that [tex]$ S_8 $[/tex] is correct.
convert the expression below to exponential form please!
Answer:
The answer is C , 5^(1/3)
Expand and simplify (2x+1) (x-2) (x+3)
Answer:
2x^3 + 3x^2 - 11x - 6.
Step-by-step explanation:
(2x+1) (x-2) (x+3)
= (2x + 1)[x(x + 3)-2(x + 3)]
= (2x + 1)(x^2 + x - 6)
= 2x(x^2 + x - 6) + 1(x^2 + x - 6)
= 2x^3 + 2x^2 - 12x + x^2 + x - 6
= 2x^3 + 3x^2 - 11x - 6.
Good morning,
Answer:
=2x³+3x²-11x-6.Step-by-step explanation:
(2x+1) (x-2) (x+3)
= (2x+1) [(x-2) (x+3)]
= (2x+1) [x²+3x-2x-6]
= (2x+1) [x²+x—6]
= 2x³+2x²-12x+x²+x-6
=2x³+3x²-11x-6.
:)
How do you know that the triangle with side lengths 6, 8, and c is a right triangle?
If c is the longest side, then c must be equal to 10 in order to have a right triangle. This is due to the pythagorean theorem
a^2+b^2 = c^2
6^2+8^2 = c^2
36+64 = c^2
100 = c^2
c^2 = 100
sqrt(c^2) = sqrt(100) ... apply square root to both sides
c = sqrt(100)
c = 10
-----------------
So if we know that c = 10, then the side lengths 6,8,c form a right triangle.
The base of an isosceles triangle is five and it’s perimeter is 11.The base of a similar isosceles triangle is 10.What is the perimeter of the larger triangle
Answer:
The answer would be 22.
Step-by-step explanation:
Since we have 2 bases one being 5 and the other 10, if you multiply the base of the smaller triangle by 2 you get 10. Whatever the sides are for the smaller triangle multiply those by 2. ONce you get all the numbers for the large triangle add them all to get the perimeter.
[tex]\bf \stackrel{\textit{\Large Similar Triangles}}{\cfrac{\stackrel{base}{5}}{\underset{perimeter}{11}}=\cfrac{\stackrel{base}{10}}{\underset{perimeter}{x}}}\implies 5x=110\implies x=\cfrac{110}{5}\implies x=22[/tex]
how to do this problem and what's the answer
if a line is perpendicular to another line with slope m, the perpendicular line's slope is always -1/m. Since the slope of the given line is -4, the perpendicular slope would be 1/4 (-1/-4 = 1/4). Our line right now is y = (1/4)x + b. Now substitute the given point in for x and y to solve b. In this case b = -1, so your line would be y = (1/4)x + -1.
Solve the system of linear equations by graphing. x+3y=6 4x-6y=6
Answer:
x=3, y=1. (3, 1).
Step-by-step explanation:
x+3y=6
4x-6y=6
------------
simplify 4x-6y=6 into 2x-3y=3
------------------------
x+3y=6
2x-3y=3
--------------
3x=9
x=9/3
x=3
3+3y=6
3y=6-3
3y=3
y=3/3
y=1
The time, in seconds, it takes for one complete swing of a pendulum is represented by the equation below, where is the length of the pendulum in meters, and is the acceleration due to gravity (9.81 m/s2).
What is the approximate length of the pendulum if it takes the pendulum 2.9 seconds to complete one full swing? (Use = 3.14)
Answer:
82.28 in
Step-by-step explanation:
What property is (C+2+0=c+2
Answer:
commutative property is C+2+0=C+2
(As a+b=b+a is the law of commutative property of addition )
Help me with this I don’t know if I need to use law of cosines or law of sines to find the degree
Answer:
Law of cosines
Step-by-step explanation:
In this problem i need to use the law of cosines, because the angles are unknown.
we know that
The formula of the law of cosines is equal to
[tex]c^2=a^2+b^2-2(a)(b)cos(C)[/tex]
where
[tex]a=7\ units\\b=8\ units\\c=10\ units\\C=\theta[/tex]
substitute in the formula
[tex]10^2=7^2+8^2-2(7)(8)cos(\theta)[/tex]
[tex]100=49+64-112cos(\theta)[/tex]
[tex]100=113-112cos(\theta)[/tex]
[tex]112cos(\theta)=113-100[/tex]
[tex]112cos(\theta)=13[/tex]
[tex]cos(\theta)=\frac{13}{112}[/tex]
using a calculator
[tex]\theta=cos^-1(\frac{13}{112})[/tex]
[tex]\theta=83.33\°[/tex]
A carpet expert belleves that 6% of Persian carpets are counterfeits.
If the expert is right, what is the probability that the proportion of counterfeits in a sample of 484 Persian carpets would differ from the population
proportion by less than 3% ? Round your answer to four decimal places.
sin A= ?
c/a
a/c
a/b
b/c
Answer:
[tex]\sin A = \frac{a}{b}[/tex]
Step-by-step explanation:
Given:
We took here a Right Angle Triangle,Δ ABC at angle B as 90°
Side opposite to angle A = a
Side opposite to angle B = b = Hypotenuse
Side opposite to angle C = c
To Find:
Sin A = ?
Solution:
Property of a Sine rule for a Right Angle Triangle.
[tex]\sin A =\frac{\textrm{side opposite to angle A}}{Hypotenuse}\\\sin A =\frac{a}{b}[/tex]
∴ [tex]\sin A = \frac{a}{b}[/tex]
The first four terms of a sequence are shown.
16, 48, 144, 432, ...
What is the explicit function, f(n), that defines the sequence? Explain how you determined your
answer. Write your answer in the space provided.
The explicit function is f(n) = 3f(n - 1)
Solution:Given, sequence is 16, 48, 144, 432 ….
We have to find the explicit function.
Now, if we observe the given sequence, every term is three times its previous term.
That is, the next term in sequence is obtained by multiplying the previous term by 3
48 = 16 x 3
144 = 48 x 3
432 = 144 x 3
So, explicit function f(n) will be
nth term = 3 x (n – 1)th term
F(n) = 3 x f(n – 1) [ since nth term is f(n) ]
We derived the above function just by generalizing the sequence and making it into the function.
The nth term is obtained by multiplying the n - 1 term with 3
Hence explicit function is f(n) = 3f(n - 1)
What is the answer to 1010-n=101
Answer:
n = 909Step-by-step explanation:
[tex]1010-n=101\qquad\text{subtract 1010 from both sides}\\\\1010-1010-n=101-1010\\\\-n=-909\qquad\text{change the signs}\\\\n=909[/tex]
Steps to solve:
1010 - n = 101
1010 + (-n) - 1010 = 101 - 1010
-n = -909
-n/-1 = -909/-1
n = 909
_______
Best Regards,
Wolfyy :)
Triangle PQR is reflected over the x axis.What are the coordinates of Q’
Answer:
(8, -2)
Step-by-step explanation:
(8, 2) becomes (8. -2)
Answer:
(8 -2)
Step-by-step explanation:
Write a variable expression for 234 divided by g
Answer:
234 ÷ g
Step-by-step explanation:
Convert "234 divided by g" into algebraic form, which is:
234 ÷ g
It can also be written as 234/g.
An expression is has no equal sign, as opposed to an equation, which has an answer.
5d-8=1+5d solve the equation. Determine whether the equation has one solution, no solution, or infinetly many solutions.
Answer:
no solution
Step-by-step explanation:
5d - 8 = 1 + 5d
Add 9 to both sides
5d = 9 + 5d
Subtract 5d
0 does not equal 9
No solutions
The given equation has no solution.
The given equation is 5d-8=1+5d.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
Here,
5d - 8 = 1 + 5d
⇒ 5d-5d=1+9
⇒ 0≠9
Therefore, the given equation has no solution.
To learn more about an equation visit:
https://brainly.com/question/14686792.
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Wendell just got a new iPod and wants to download music. He finds two different sites for downloading music. The first one is itoons and the cost is $1 per song. The second one is song-R-Us.com and has a$5 monthly fee and cost of 0.50 per song. What is the equation for both music apps
Answer:
Ci = x
Cs = 5 + 0.5x
Step-by-step explanation:
The site itoons costs $1 per song with no montly fee, so the cost can be expressed as
Ci = 1.x = x
Where x is the number of songs Wendell will download
The site song-R-Us.com charges $5 a month and $0.5 per song. The equation of the cost is
Cs = 5 + 0.5x
3. 78.34 m =
mm
A 78,340
B 7,834
C 0.07834
D 783,400
Tickets for a train cost $22 for adults and $10 for children. Josie paid $1,200 for a total of 72 tickets. How many adult tickets and how many child tickets did Josie buy?
Answer:
Josie bought 40 adult tickets and 32 children tickets.
Step-by-step explanation:
x+y=72
22x+10y=1200
-----------------------
x=72-y
22(72-y)+10y=1200
1584-22y+10y=1200
1584-12y=1200
12y=1584-1200
12y=384
y=384/12=32
x+32=72
x=72-32=40
x=40, y=32. (40, 32)
117 Divided by 3 and equal groups
When dividing 117 into equal groups of 3, we find that there are 39 groups, and each group contains 3 items. This calculation involves finding the quotient of the division, which tells us how many groups of 3 can be formed with a total of 117 items.
When dividing 117 into equal groups of 3, we are essentially finding how many groups of 3 can be formed with a total of 117 items. This can be visualized as distributing 117 items equally into 3 groups.
Step 1: Perform the division:
117 ÷ 3 = 39
Step 2: Interpret the result:
The quotient 39 represents the number of equal groups of 3 that can be formed using 117 items. Each group will have 3 items.
Step 3: Final answer:
117 can be divided into 3 equal groups, and each group will have 39 items.
In summary, when dividing 117 into equal groups of 3, we find that there are 39 groups, and each group contains 3 items. This calculation involves finding the quotient of the division, which tells us how many groups of 3 can be formed with a total of 117 items.
To know more about dividing:
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determine the proceeds of a 10year promissory note discounted after after 4 years at 6% compounded quarterly with a maturity value of $6000
Answer:
The Proceeds of maturity after 10 years is $1613.4
Step-by-step explanation:
Given as :
The maturity value = $ 6000
The rate applied at 6 % compounded quarterly
The Time period = 4 years
Now,
Amount = Principal × [tex](1+\dfrac{\textrm Rate}{4\times 100})^{\textrm 4\times Time}[/tex]
Or, Amount = 6000 × [tex](1+\dfrac{\textrm 6}{4\times 100})^{\textrm 4\times 4}[/tex]
Or, Amount = 6000 × [tex](1.015)^{16}[/tex]
Or, Amount = 6000 × 1.2689
∴ Amount = $ 7613.4
So, The proceeds after 10 years = $ 7613.4 - $ 6000 = $ 1613.4
Hence The Proceeds of maturity after 10 years is $1613.4 Answer
*******************
Challenge: Ms. Dortch's class wants to go to on
a camping trip. The cost of the trip is $235. The
class has a bake sale to raise money. They can
make $45 a week for 5 weeks. How much more
money will they need?
The Clever factory
Answer:
$10
Step-by-step explanation:
$45 x 5 = 225
$225 + $10 = $235
Answer:
They will need $10 more dollars
Step-by-step explanation:
So 45 times 5 is 225 so what that means is that for each week they raised 45 dollars multiply that by 5 weeks and they made $224 dollars then subtract that from 235 so (235-225=10)
They will need $10 more dollars
What is 12X-4y = -8 written in slope-intercept form?
COF
o y = 3x+2
o y = 3x-2
y= 12x-8
|
0
12x
0
Answer:
y = 3x + 2
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c
Given
12x - 4y = - 8 ( subtract 12x from both sides )
- 4y = - 12x - 8 ( divide all terms by - 4 )
y = 3x + 2 ← in slope- intercept form
Charlie reads fast. He reads 1 2/7 pages every 2/3 minute at a contact rate. How many minute does he read per page
Answer:
1 page per 14/27 minute
Step-by-step explanation:
9/7 page / 2/3 min =
1 page / 2/3 * 7/9 min =
1 page / 14/27 min
Simplify 5 x times the fraction 1 over x to the power of negative 7 times x to the power of negative 2. 5x 5x−6 5 5x6
Answer:
[tex]5x^6[/tex]Explanation:
The expression that you want to simplify is:
[tex]5x\times \frac{1}{x^{-7}}\times x^{-2[/tex]This is the simplification step-by-step:
1. Mulitply the expressions on the numerator among them and the expressions on the denominator among them:
[tex]5x\times \frac{1}{x^{-7}}\times x^{-2}=\frac{5x\cdot x^{-2}}{x^{-7}}[/tex]
2. For equal bases that are multiplying, add the exponents:
[tex]\frac{5x\cdot x^{-2}}{x^{-7}}=\frac{5x^{1-2}}{x^{-7}}=\frac{5x^{-1}}{x^{-7}}[/tex]
3. Pass the power on the denominator to the numerator by changing its sign (negative exponents become positive when inverted)
[tex]\frac{5x^{-1}}{x^{-7}}=5x^{-1}x^{7}[/tex]
4. Simplify adding the exponents with the same base:
[tex]5x^{-1}x^{7}=5x^{-1+7}=5x^6[/tex]
And that is the final expression in its most simple form.
Consuela is planning her 7-day vacation. She has budgeted $250 to rent a moped for the week. The rental company charges $10 a day plus 30 cents per mile. Write and solve a first degree inequality to determine the number of miles (m) consuela can drive and still stay within her budget.
Answer:
The equation is [tex]0.3x\leq 180[/tex] and consuela can drive maximum 600 miles.
Step-by-step explanation:
Given:
Consuela Budget= [tex]\$250[/tex]
Rental Company Charges = [tex]\$10 \ per\ day[/tex]
Additional Cost = 30 cents per mile = $0.3 per miles.
Number of days for vacation = 7
We need to find the number of miles Consuela can drive and still be in budget.
Let number of miles she can drive be [tex]x[/tex]
Rental Company Charges for per day [tex]\times[/tex] number of days + Additional Cost per mile [tex]\times[/tex] Number of miles she can drive sholud be less than or equal to Consuela Budget
Now the equation will be.
[tex]10\times 70 +0.3x \leq 250\\70 +0.3 x\leq 250\\0.3x\leq 250-70\\0.3x\leq 180\\x\leq \frac{180}{0.3}\\\\x\leq 600 \ miles[/tex]
Hence Consuela can drive maximum of 600 miles to stay within her budget.
Simplify the expression 7(9+2)
Answer: 77
Step-by-step explanation: Based on the order of operations or PEMDAS, parentheses are always done first.
So our first step in this problem is to simplify (9 + 2) to get 11.
So we now have (7) (11) which is 77.