Answers
x+12y=68 (i)
x=8y-12 (ii)
2. Let's substitute the equation (ii) into the equation (i):
x+12y=68
(8y-12)+12y=68
3. Then, you have:
8y-12+12y=68
4. When you clear "y", you have:
20y-12=68
20y=68+12
20y=80
y=80/20
y=4
5. You already have the value of "y". Now, you must substitute this value into the equation (ii):
x=8y-12
x=8(4)-12
x=32-12
x=20
6. Therefore, the result is:
x=20
y=4
Related Questions
help me....................
Answers
Part 1.] In two or more complete sentences, describe the difference between an infinite series and a finite series.
Part 2.] In two or more complete sentences, explain why the following sequence is an example of a finite series.
2 + 4 + 8 + 16 + ... 256
Part 3.] In two or more complete sentences describe why the following series is an example of an infinite series.
1 + 2 + 3 + 4 + 5 + ...
Part 4.] The first picture
Part 5.] Express the series in summation notation.
2 + 4 + 6 + 8 + 10 + 12
Part 6.] Suppose you start an annuity where you invest $2,000 at the beginning of each year and 4% interest is paid at the end of the year. What is the value of the annuity at the end of 5 years, rounded to the nearest dollar? It is $____
Part 7.] Find the sum picture
Answers
2) We have that this is the sup of powers of 2; but it does not take all powers of 2, only until the 8th power of 2. Hence, there are 8 summants, a finite number.
3) We have that this series involves all the natural numbers; "..." means that we should continue adding the next term, meaning that there is no end.
4) In order to find the first term of the series, we need to substitute n=1. Hence the first term is 1/(2*1+1)=1/3. Similarly, the next term is equal to 2/(2*2+1)=2/5
5) We notice that the first term is 2 and then that all the terms are 2 higher than their previous one. Hence we have that if we start summation from 1, we need to double it to get the term. This works for all and hence we have that the series is equal to: [tex]\sum_{n=1 \ n=6} 2n[/tex].
6) We have that after one, year, he gains 4%*2000, hence the final amount is 1.04*2000 after one year. Next year, this becomes the capital and we have to multiply again by 1.04. Hence, after 5 years, the total annuity value is: (1.04)^5*2000=2433$.
7) We have that the sum is 4+7+... up until 3*12+1=37. The sum of those is 246 or else we can have that it is equal to 3* n(n+1)/2+12 where n=12 (The sum of all numbers from 1 to n is given by n*(n+1)/2 )
Answer:for oddysey the answer to number 6 is 10833
Step-by-step explanation:
1.) Four teachers bought an old boat for $60.
The first teacher paid one-half of the sum of the amounts paid by the other teachers.
The second teacher paid one-third of the sum of the amounts paid by the other teachers.
The third teacher paid one-fourth of the sum of the amounts paid by the other teachers.
How much did the fourth teacher pay?
2.) What is the smallest number of coins that you need so that you can give exact change for any amount from 1 cent to 99 cents?
Show your work please. Any improper answers will be reported and removed- thanks!
:) Have fun!
Answers
1)Let's assume the payment which each one of them paid are A,B,C, and D, for the 1st, 2nd, 3rd and 4th respectively.
so the total payment is the sum of all of them
A+B+C+D= 60 ----->(eq 1)
The 1st paid 0.5 of the sum of the other teachers payments
A= 0.5 (B+C+D) ---->(eq 2)
The 2nd paid 1/3 of the others payment
[tex] B= \frac{A+C+D}{3}[/tex] ------>(eq 3)
The 3rd paid 1/4 of the others payment
[tex] C = \frac{A+B+D}{4} [/tex] ---->(eq 4)
we have now 4 equations in 4 unknowns.
From equation 1 and 2 :-
----------------------------------
By multiplying (eq 2) by 2 and substitute in (eq 1)
2 A = B+C+D (sub in eq 1)
A+ 2A =60
then 3A= 60
then A =$20 (The first teacher's payment)
From equations 1 and 3 :-
------------------------------------
By multiplying (eq 3) by 3
3B = A+C+D (sub in eq 1)
B+3B=60
4B=60
B= $15 (The second teacher's payment)
From equations 1 and 4:-
------------------------------------
By multiplying (eq 4) by 4
then 4 C=A+B+D (sub in eq 1)
4C+ C = 60
5C=60
C= $6 (The third teacher's payment)
By substituting the values of A,B and C in (eq 1).
20 + 15 + 6 + D=60
41+ D =60 (By subtracting both sides by 41)
D = $19.(The forth teacher's payment)
------------------------------------------------------------------------------------------------------------
2)unfortunately i don't your coins cuz im not american :D
Trevor is going to Debra's Steakhouse and really wants filet for dinner and creme brulee for dessert. He knows that the probability of getting a filet at Debra's is 0.9 and the probability of creme brulee being a desert is 0.77. If he knows the two events are independent of one another, show the calculation for P(getting a steak and getting a creme brulee)
Answers
B (0.9)(0.77)
Answer:
(0.9)(0.77)
Step-by-step explanation:
(0.9)(0.77)
Since the two events are independent you can use the multiplication rule
Which of the following is equivalent to log7 50 rounded to three decimal places?
2.010
1.772
0.854
0.497
Answers
Answer:
Option A - [tex]log_7 50=2.010[/tex]
Step-by-step explanation:
Given : The expression [tex]log_7 50[/tex]
To find : Which of the following is equivalent and rounded to three decimal places.
Solution :
We solve the given expression [tex]log_7 50[/tex] using calculator
We get, [tex]log_7 50=2.0103821378[/tex]
Rounded to three decimal places
[tex]log_7 50=2.010[/tex]
Therefore, Option A is correct.
Does the point ( 3 , 3 ) lie on the circle that is centered at the origin and contains the point (3, 0)? Why?
A) Yes, because ( 3 )2 + ( 3 )2 = 9
B) Yes, because you can create always create a circle through two given points. C) No, because ( 3 , 3 ) is less than 3 units away from the origin.
D) No, because ( 3 , 3 ) is greater than 3 units away from the origin.
Answers
x²+y²=r² where r is the radius. If we have the point (3,0) then the equation of the circle says
[tex]3^2+0^2=r^2 \\ r=3[/tex]
Then for r=3 we can't get the point (3,3) because
[tex]3^2+3^2 \ \neq 3^2[/tex]
Answer:
Its actually C his whole explanation is wrong
Step-by-step explanation:
Solve for x.
3x2−6x+2=0
x=3±23√3
x=6±23√3
x=3±3√3
x=6±43√3
Answers
Answer:
[tex]\frac{3\±\sqrt{3}}{3}[/tex]
Step-by-step explanation:
Whe have the function [tex]3x^2-6x+2=0[/tex]
To solve this equation we must factor.
To factor, we need to find the points where the function is equal to zero. So we use the quadratic formula
[tex]\frac{-b\±\sqrt{b^2-4ac}}{2a}[/tex]
Where:
a = 3
b = -6
c = 2
Then
[tex]\frac{-(-6) + \sqrt{(-6)^2-4(3)(2)}}{2(3)} = \frac{3+\sqrt{3}}{3}\\\\and\\\\\frac{-(-6) - \sqrt{(-6)^2-4(3)(2)}}{2(3)}= \frac{3-\sqrt{3}}{3}[/tex]
finally the correct answer is [tex]\frac{3\±\sqrt{3}}{3}[/tex]
Final answer:
To solve the quadratic equation 3x² - 6x + 2 = 0, apply the quadratic formula with a=3, b=-6, and c=2, ultimately finding the solutions x = 1 + √(3) / 3 and x = 1 - √(3) / 3.
Explanation:
To solve the quadratic equation 3x² - 6x + 2 = 0, we can use the quadratic formula, which is x = (-b ± √(b² - 4ac)) / (2a) where a, b, and c are coefficients from the equation ax² + bx + c = 0. In this equation, it is given a = 3, b = -6, and c = 2. Substituting these values into the formula gives us:
x = (6 ± √((-6)² - 4 · 3 · 2)) / (2 · 3)
x = (6 ± √(36 - 24)) / 6
x = (6 ± √(12)) / 6
x = (6 ± 2 √(3)) / 6
x = 1 ± √(3) / 3
The two possible solutions for x are then x = 1 + √(3) / 3 and x = 1 - √(3) / 3.
The diameter of the circle above is 98 cm. What is the circumference of the circle?
Answers
C= 307.88 cm is the answer i hope this helps you
Factor by grouping m^2 +8mn -3mn-24n^2
20 POINTS
Answers
Then solve for the common factor in each bracket group.
m(m + 8n) - 3n(m + 8n)
(m-3n)(m + 8n) is the answer.
Three weeks ago John bought stock at 49 1/4 ; today the stock is valued at 49 7/8. We could say the stock is preforming at which of the following?
Answers
Solution:
Value of Stock three weeks ago = [tex]49 \frac{1}{4}[/tex]
Current value of stock = [tex]49 \frac{7}{8}[/tex]
Total increase= [tex]49 \frac{7}{8}[/tex]-[tex]49 \frac{1}{4}[/tex]=[tex]\frac{5}{8}[/tex]
So, we can conclude from above two observation, that
The market value of that stock or bond has rose higher the reason being value of the organization or product i.e stock is slanting in upward direction.Why value of organization has increased because company has cordial relationship with it's employees, clients and the people attached with this organization, means distribution of profit is equally shared between owner and people attached with this organization.
Anne had 28 pens, but 23 of them ran out of ink. How many of Anne's pens still have ink?
___of Anne's pens still have ink.
Answers
Hope this helped!
Can someone tell me if the answer is correct?
Answers
3 / ((3√5) + 4)
3 x ((3√5) - 4) / ((3√5) + 4) x ((3√5) - 4)
((9√5) - 12) / (45 - 16)
((9√5) - 12) / 29 is the correct answer
[tex]1,\frac{1}{8},\frac{1}{27},\frac{1}{64},...,\frac{1}{n^{3}},...[/tex]
The denominator of the seventh term is
A.] 125
B.] 216
C.] 343
D.] 513
Answers
Justification:
The sequence of the denominators is:
term denominator
1 1 = 1^3
2 8 = 2^3
3 27 = 3^3
4 64 = 4^3
5 5^3 = 125
6 6^3 = 216
7 7^3 = 343
And that is the term searched. So, the answer is the option C) 343.
Answer:
the answer is C.] 343
helppppppppppppppppp
Answers
(5 ^ -1) * (5 ^ -3)
Using properties of exponents we have:
(1/5) * (1 / (5 ^ 3))
Rewriting:
(1/5) * (1 / (125))
1/625
answer:
An equivalent expression is:
1/625
option 1
Scott signed a two-year lease for a monthly rent of $505. How much will
he pay in rent over the term of his lease?
a. $13,130
b. $1,212
c. $6,060
d. $12,120
AGAIN WILL GIVE BRAINEST TO FIRST PERSON WHO ANSWERS
Answers
They pay $505 every month
24 months × $505 = $12,120 paid over the lease term.
answer is D.
There are 12 months in a year so since there were two years then you would ad 12+12. This would equal 24 then you would multiply that number by 505. You would then get the answer of 12,120$.
Hope this helps.
Simplify: (8x4)(4x3)/7x2
A. 32x5/7
B. 1/28x
C. 1/3x
D. 7/9x4
Answers
Simplify the following:
(8×4 x^4 x^3)/(7 x^2)
Combine powers. (4 x^3×8 x^4)/(7 x^2) = (4 x^(4 + 3 - 2) 8)/7:
(4×8 x^(4 + 3 - 2))/7
4 + 3 - 2 = 5:
(4×8 x^5)/7
4×8 = 32:
Answer: (32 x^5)/7
Step-by-step explanation:
The answer is A: (32 × ^5)/7
Ravi is driving 440440 miles to visit his grandma. He drives at a rate of 5555 miles per hour. How many hours will it take him to get 3434 of the way there?
Answers
Ravi is driving 440 miles to visit his grandma. if he drives at an average rate of 55 miles per hour, how many hours will it take him to get 3/4 of the way there?
we have that
3/4 of the way--------------> (3/4)*440=330 miles
I apply a rule of three
if 55 miles----------------> 1 hour
330 miles--------------> X
X=330/55=6 hour
the answer is 6 hour
The expression 146 ÷ 144 is equal to _____. 142 2 1410 1
Answers
The correct answer is 1.
To solve this problem, we need to evaluate the expression [tex]146 \div 144[/tex]and determine which of the given options it is equal to.
The calculation can be represented as:
[tex]146 \div 144 = \frac{146}{144}[/tex]
We can simplify this fraction by finding the common factor between the numerator and denominator and dividing both by that factor.
[tex]\frac{146}{144} = \frac{73 \times 2}{72 \times 2} = \frac{73}{72}[/tex]
Now, we can divide the numerator by the denominator to find the final value.
[tex]\frac{73}{72} = 1.0138\overline{8}[/tex]
Therefore, the expression [tex]146 \div 144[/tex] is approximately equal to 1.
Complete question:
The expression [tex]146 \div 144[/tex] is equal to _____.
A) [tex]142[/tex]
B) [tex]2[/tex]
C) [tex]14^{10}[/tex]
D) [tex]1[/tex]
does the function y=4^-2x represent an exponential growth or decay? what is the percent rate of change?
Answers
In order to find the percent of change, we need to review our exponent properties. The product property tells us that when we raise a power to a power, we multiply the exponents. This means we can view our exponent of -2x as the product of two exponents, -2 and x. This would look like
[tex]y=(4^-^2)^x[/tex]. We know that negative number exponents tell us to "flip" sides of the fraction, so that tells us that 4⁻² = 1/4² = 1/16. We can then rewrite our equation as
[tex]y=(\frac{1}{16})^x[/tex]
Exponential decay is in the form y = a(1-b)ˣ. From our equation, a = 1. We know that 1-b = 1/16; this means that b must be 15/16. Thus our percent of decrease would be 15/16 = 0.9375 = 93.75%.
The function y=4^-2x represents exponential decay. The percent rate of change is 6.25%.
Explanation:The function y=4-2x represents exponential decay. In an exponential decay function, as the value of x increases, the value of y decreases. On the other hand, in exponential growth, as the value of x increases, the value of y increases.
The percent rate of change can be found by determining the decay factor, which is equal to 1 divided by the base of the exponential function raised to the power of the exponent.
In this case, the decay factor would be 4-2 = 1/16. To find the percent rate of change, we can convert the decay factor to a percentage by multiplying it by 100%, so the percent rate of change would be 1/16 * 100% = 6.25%.
PLESSSSSS HELP WILL CROWN BRAINLIEST!!!! 20PTS!!!!!!!!!!!!
Answers
<5, -2> + <0, 0> = ((5+0), (-2+0)> = <5, -2>
How would you solve for side a? Pythagorean theorem, cause if that's the case wouldn't
a=?
b=15
c=7
But we know that 2 sides of a triangle can't be greater than the third (or am I getting that rule wrong?)
Answers
Generally, you would use the Law of Cosines to solve for the third side when given two sides and the angle between them.
EF^2 = 7^2 +15^2 -2*7*15*cos(127°)
EF ≈ √(400.3812) ≈ 20.00953
My guess is that you're expected to use 20 for the length of the 3rd side.
By Heron's formula, s = (7 +15 +20)/2 = 21
Area = √(21*(21 -7)*(21 -15)*(21 -20)) = √(21*14*6*1) = √1764 = 42 . . . . yd^2
_____
More directly,
.. Area = (1/2)*7*15*sin(127°) ≈ 41.928 . . . . yd^2
help me please ASAP !!!!!
Answers
.. (10 +k)/2 = 7
Multiplying by 2, we have
.. 10 +k = 14
Then
.. k = 14 -10
.. k = 4
which of these equations represent functions where x is the input and y is the output? Select each correct answer.
A- x=5
B- y=4
C- y=3x
D- x=3y
E- x+y=5
Answers
The second equation is also a constant. The output is 4.
In the third equation, y depends on what value of x you use. x is the input and y is the output.
In the fourth equation, x depends on what value of y you use. The way it is written, y is the input and x is the output.
In the last equation, either x or y could be the input. The other variable would change depending on which variable you replace with a number.
What is the common ratio of the sequence. -2,6,-18,54
Answers
Answer: The required common ratio of the given geometric sequence is -3.
Step-by-step explanation: We are given to find the common ratio of the following geometric sequence :
-2, 6, -18, 54, . . .
We know that
if a(n) denotes the nth term of a geometric sequence, then the common ratio is given by
[tex]r=\dfrac{a_{n+1}}{a_{n}}.[/tex]
For the given sequence, we see that
[tex]\dfrac{a(2)}{a(1)}=\dfrac{6}{-2}=-3,\\\\\\\dfrac{a(3)}{a(2)}=\dfrac{-18}{6}=-3,\\\\\\\dfrac{a(4)}{a(3)}=\dfrac{54}{-18}=-3,\\\\\vdots[/tex]
Therefore, the common ratio is given by
r = -3.
Thus, the required common ratio of the given geometric sequence is -3.
The gym teacher is told that the average height of the girls in her physical education class is 5’4”, and the heights follow the normal distribution. She is told that 68% of the girls are 5’2” to 5’6” tall. She measures the height of each girl and finds that the heights do follow the normal distribution. Based on her findings, she determines that 95% of the girls will be 5’0” to 5’8” tall. Use your knowledge of normal distribution to select two options that will justify the gym teacher’s belief.
Answers
Please, see the attached file.
Thanks.
Final answer:
The gym teacher's belief is justified by using the empirical rule, which describes the distribution of data in a normal distribution. Since 68% of the girls fall within 1 standard deviation of the mean, it's likely that 95% fall within 2 standard deviations, supporting her height range belief.
Explanation:
The gym teacher's belief can be justified by understanding the properties of the normal distribution and the empirical rule. The empirical rule states that for a normal distribution:
Approximately 68% of the data will fall within 1 standard deviation (±1σ) of the mean.
Approximately 95% of the data will fall within 2 standard deviations (±2σ) of the mean.
Approximately 99.7% of the data will fall within 3 standard deviations (±3σ) of the mean.
In the teacher's class, 68% of the girls are between 5'2” and 5'6”, which is within 1 standard deviation of the mean height of 5'4”. Therefore, it's likely that 95% of the girls would fall within 2 standard deviations, which explains her belief that 95% of the girls would be between 5’0” to 5’8”.
The three sides of a triangle are in the ratio 2:3:5. If the longest side of the triangle is 45m, find the perimenter of the triangle
Answers
5/10 = 45m
1/10 = 9m
10/10 = 90 m.
the perimeter is 90m
x:y:45
5 is multiplied by 9, so you multiply the other 2 numbers by 9 too.
x = 2×9 = 18
y = 3×9 = 27
MATH HELP!!!
Dwight's gross semimonthly pay is $1220. To maintain his current lifestyle, how much should he save up by the time he retires?
$292800
$317200
$702720
$761280
Answers
Answer:
292,800
Step-by-step explanation:
1220*24 (24 is semimonthly)=29,280
Then you want to multiply by 10
29280*10=292,800
Dwight's save up by the time he retires will be 292800$
Dwight's gross semimonthly pay is $1220
What is the meaning of semimonthly?
semimonthly means two times per month
Semimonthly for per year is,
12(2)=24
Dwight's gross semimonthly pay is $1220.
1220*24 (24 is semimonthly)=29,280
For one year the amount will be 29280
Then you want to multiply by 10
29280*10=292,800
Therefore Dwight's save up by the time he retires will be 292800$.
To learn more about the saving visit:
https://brainly.com/question/25787382
Team tool Bella gathered 15 pounds of wood in 1/3 of an hour. What was their speed in pounds per hour.
Answers
Team tool Bella gathered 15 pounds of wood in 1/3 of an hour.
1/3 of an hour is equal to 1/3 of 60 mins = 1/3 * 60 mins = 20 mins
We have to find their speed in pounds per hour( 60 mins).
Pounds of woods gathered in 1 hour or 60 mins = 15/20*60
= 15 * 3
= 45 pounds
Therefore, their speed in pounds per hour is 45 pounds / hour
Hope this helps ..!!
Thank you :)
Answer Check!! Which domain restrictions apply to the rational expression.
Answers
x^2+2x-3 = 0
(x-1)(x+3) = 0
x-1=0 or x+3 = 0
x = 1 or x = -3
If x = 1 or x = -3, then the denominator is zero.
To avoid division by zero errors, we kick x = 1 and x = -3 out of the domain
Mon wants to make 5 lbs of the sugar syrup. How much water and how much sugar does he need…
to make 1.5% of syrup
Answers
the syrup is going to be 5lbs total, that includes the sugar in it as well as the water mix.
keeping in mind that the syrup will be a 1.5% syrup, namely 1.5% of it will be sugar, the rest just water then, how much is 1.5% of 5?
well, is just(1.5/100) * 5 or 0.075, namely lbs.
so, 0.075 lbs will be sugar and the rest water, the rest will be 5 - 0.075, or 4.925 lbs.