Answer:
x = log (7)/ 2log 5
Step-by-step explanation:
25^ x = 7
Replace 25 with 5^2
5^ 2x = 7
Take log on each side
log (5 ^2x) = log ( 7)
We know that log a^ b = b log a
2x log 5 = log (7)
Divide each side by log 5
2x log 5/ log 5= log (7)/ log 5
2x = log (7)/ log 5
Divide each side by 2
x = log (7)/ 2log 5
what is a supplementary angle of 750
Answer:
105°
Step-by-step explanation:
Supplementary angle of 75° = 180° - 75° = 105°
Answer:
105°
Step-by-step explanation:
angle given is 75°
= 180° - 75°
= 105°
The graph of a linear equation g(x)=-1/3x +2 can be obtained from the graph f(x)=1/3x by using infinite sets of elementary translation (i.e reflection and shifting). List out five of those sets
Answer:
{Rx, T(-6, 4)}{Rx, T(-3, 3)}{Rx, T(0, 2)}{Rx, T(3, 1)}{Rx, T(9, -1)}Step-by-step explanation:
We assume you are not interested in five infinite sets of translations. Rather, we assume you want to pick 5 translations from the infinite set of possibilities.
The attached graph shows f(x), g(x), and 5 lines (dashed or dotted) that represent possible reflections and shifts of the function f(x).
The function f1 represents a reflection of f(x) about the x-axis, followed by a left-shift of 6 units. To make it match g(x), we need to shift it upward 4 units. Then the set if translations is ...
g(x) = f(x) ... {reflected over the x-axis, shifted left 6, shifted up 4}
Along the same lines, other possibilities are ...
g(x) = f(x) ... {reflected over the x-axis, shifted left 3, shifted up 3}
g(x) = f(x) ... {reflected over the x-axis, shifted left 0, shifted up 2}
g(x) = f(x) ... {reflected over the x-axis, shifted right 3, shifted up 1}
g(x) = f(x) ... {reflected over the x-axis, shifted right 9, shifted down 1}
___
Additional comment
All of the transformations listed above use reflection in the x-axis. Reflection could use the y-axis, as well. Reflection of the basic function f(x) in the y-axis will have the identical effect as reflection in the x-axis. The listed translations would apply unchanged.
Use the functions m(x) = 4x + 5 and n(x) = 8x − 5 to complete the function operations listed below. Part A: Find (m + n)(x). Show your work. (3 points) Part B: Find (m ⋅ n)(x). Show your work. (3 points) Part C: Find m[n(x)]. Show your work. (4 points)
Answer:
Step-by-step explanation:
Part A
(m + n)x = 4x + 5 + 8x - 5
(m + n)x = 12x The fives cancel
Part B
(m - n)x = 4x + 5 - 8x + 5
(m - n)x = -4x + 10
Part C
The trick here is to put n(x) into m(x) wherever m(x) has an x.
m[n(x)] = 5(n(x)) + 5
m[n(x)] = 5(8x - 5) + 5
m[n(x)] = 40x - 20 + 5
m[n(x)] = 40x - 15
Select all angle measures for which cos0= 1/2
Answer:
cos -60° = [tex]\frac{1}{2}[/tex] ,
cos 660° = [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
hope it helps
Answer:
-60 and 660
Step-by-step explanation:
Edge 2020
What is the best first step in solving -4x + 5/3 > 5/10
Answer:
Step-by-step explanation:
The best first step to solve this is to just subtract 5/3 from both sides so it is easier to simplify.
Answer:
Subtract 5/3 to the other side
Step-by-step explanation:
Hey there!
Well the best first step is to -5/3 to both sides and move it to the right side.
-4x + 5/3 > 5/10
-5/3 to both sides
-4x > -7/6
Hope this helps :)
Find: ∠x ∠a ∠b Please help
Answer:
a=90 degrees
b=90 degrees
x=22 degrees
Step-by-step explanation:
3x+22+(5x-18)=180
8x=176
x=22
Answer:
x = 22°, ∠a = 88°, ∠b = 92°.
Step-by-step explanation:
Angle b has the same measurement as the angle of 5x - 18, since the two angles are corresponding angles.
Angle a has the same measurement as the angle of 3x + 22, since the two angles are alternate interior angles.
Since angle a and the angle of 5x - 18 form a straight line, the two angles add up to be 180 degrees. Since angle a is the same as the angle of 3x + 22, we can substitute the angle for angle a.
(5x - 18) + (3x + 22) = 180
5x + 3x - 18 + 22 = 180
8x + 4 = 180
8x = 176
x = 22°.
3(22) + 22 = 66 + 22 = 88 degrees.
That means that ∠a = 88°.
5(22) - 18 = 110 - 18 = 92 degrees.
That means that ∠b = 92°.
Hope this helps!
An 8 foot square floor is to be covered with square tiles measuring 8 inches on each side. If each tile
costs 50 cents, how much will it cost to tile the floor?
A. $32
B. $64
C. $72
D. $96
Please explain how to get the answer
Answer:
72
Step-by-step explanation:
There are 12 inches in a foot.
Therefore in 8 feet there are 96 inches
Therefore the square floor is 96 * 96.
Therefore the area of the square floor is 9216 inches squared.
Each tile is 8 inches by 8 inches meaning it has an area of 64 inches squared.
9216 / 64 = 144.
Therefore 144 tiles are needed to tile the floor
Since each tile is 50 cents, 144 * 0.5 = 72
Therefore it costs 72 dollars to tile the floor.
If you sleep an average of 7.5 hours each night, how many hours do you sleep in a year?
Answer:
[tex]\boxed{\sf 2737.5 \ hours}[/tex]
Step-by-step explanation:
The average is 7.5 hours of sleep each night.
There are 365 nights in 1 year.
[tex]\sf Multiply \ the \ value \ by \ 365.[/tex]
[tex]7.5 \times 365[/tex]
[tex]2737.5[/tex]
Answer:
2,737 hours for a normal year, 2,745 if it is a leap year.
Step-by-step explanation:
Because there 365 days in a year, you should multiply the amount you sleep every day (7.5) by the number of days in a year (365)
[tex]7.5*365[/tex]
Multiply 7.5 by 365 to get
[tex]2,737.5[/tex]
Every year you will sleep 2,737 hours if you sleep 7.5 hours each day.
(If it is a leap year, just change 365 to 366 which will give you 2,745 hours)
I hope this helps. If you have any follow-up questions, feel free to ask.
Have a great day! :)
Use a calculator to determine the pattern of attractors for the equation y =kx(1-x) for the given value of k and the given initial value of x
K=3.26, x=0.8
Guys, I need help quickly?
Answer:
0.5216
Step-by-step explanation:
Given the function y =kx(1-x), the pattern of attractors are the value(s) of y at the initial value of k and x. Given the value of k = 3.26 and x = 0.8, to get the pattern of attractors, we will substitute the given initial value into the function as shown;
[tex]y =kx(1-x)\\\\y = 3.26(0.8)(1-0.8)\\\\y = 3.26*0.8*0.2\\\\y = 0.5216\\\\[/tex]
Hence, the pattern of attractor for the equation y is 0.5216
A police office claims that the proportion of people wearing seat belts is less than 65%. To test this claim, a random sample of 200 drivers is taken and its determined that 126 people are wearing seat belts. The following is the setup for this hypothesis test:
H0:p=0.65
Ha:p<0.65
In this example, the p-value was determined to be 0.277. Come to a conclusion and interpret the results for this hypothesis test for a proportion (use a significance level of 5%)
Select the correct answer below:
A. There is sufficient evidence to conclude that the proportion of people wearing seat belts is less than 65%.
B. There is NOT sufficient evidence to conclude that the proportion of people wearing seat belts is less than 65%.
C. There is sufficient evidence to conclude that the proportion of people wearing seat belts is less than 35%.
D. There is NOT sufficient evidence to conclude that the pronortion of people wearing seat belts is less than 35%
Answer:
Option A - There is sufficient evidence to conclude that the proportion of people wearing seat belts is less than 65%
Step-by-step explanation:
The police officers claim is that the proportion of people wearing seat belts is less than 65%.
Now, we are told that the p - value is 0.277.
In hypothesis, for a significance value of 0.05, if the P value is less than 0.05, we reject the null hypothesis and if P value is greater than or equal to 0.05, we fail to reject the null hypothesis.
Now, since the significance level is 5% = 0.05,we can see that the P-value is greater than the significance value of 0.05. Thus, we fail to reject the police claim that the proportion of people wearing seat belts is less than 65%.
So the correct option is A.
How large a sample must be drawn to estimate population proportion confidence interval width to within .04, with 95% confidence, if we believe the true percentage is 80%
Answer:
Sample size 'n' = 384
Step-by-step explanation:
Explanation:-
Given margin of error = 0.04
The sample proportion 'p'= 0.80
The margin of error is determined by
[tex]M.E = \frac{Z_{\alpha } \sqrt{p(1-p)} }{\sqrt{n} }[/tex]
[tex]0.04 = \frac{1.96 \sqrt{0.80(1-0.80)} }{\sqrt{n} }[/tex]
Cross multiplication, we get
[tex]\sqrt{n} = \frac{1.96 \sqrt{0.80(1-0.80)} }{0.04 }[/tex]
√n = 19.6
Squaring on both sides , we get
n = 384.16≅384
Which fraction is equal to 60%?
2 of
100
600
60
100
100
60
6.0
100
Answer:
Step-by-step explanation:
[tex]60\% =\\\\\frac{60}{100} \\=0.6[/tex]
Answer:
3/5
Step-by-step explanation:
60% as a fraction is 3/5 :)
Which set of ordered pairs represents a function? {(0,1), (1,3), (1,5) (2,8)}, {(0,0), (1,2), (2,6), (2,8)}, {(0,0), (0,2), (2,0), (2,4)}, {(0,2), (1,4), (2,6), (3,6)}
Answer:
The last set.
Step-by-step explanation:
The first 3 sets contain 'one-to-many' relations , for example (1, 3) and (1, 5) in set 1 and (0, 0) and (0, 2) in set 3 , so they are not functions.
The last set does not have any of these and is a function.
Let f(x) = −x^2 and g(x) = 1/√x. Find formulas for f ◦g and g◦f and state the domain of each composition. I only need the domains if possible.
Answer: see below
Step-by-step explanation:
[tex]f(x)=-x^2\qquad g(x)=\dfrac{1}{\sqrt x}[/tex]
[tex]f og(x)=f\bigg(\dfrac{1}{\sqrt x}\bigg)\\\\.\qquad =-\bigg(\dfrac{1}{\sqrt x}\bigg)^2\quad \\\\.\qquad =-\dfrac{1}{x}\\\\\text{Domain:}\ x>0[/tex]
[tex]gof(x)=g(-x^2)\\\\.\qquad =\dfrac{1}{\sqrt{-x^2}}\\\\.\qquad =\dfrac{1}{xi}\\\\\text{Domain: Does Not Exist since result is an imaginary number}[/tex]
What is the area of this triangle on a Coordinate Grid?
Triangle IJK, with vertices I(3,-7), J(7,-4), and K(4,-2), is drawn inside a rectangle
Answer: 8.5 sq. units.
Step-by-step explanation:
Formula:
Area of triangle : [tex]\dfrac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|[/tex]
Given: Triangle IJK, with vertices I(3,-7), J(7,-4), and K(4,-2)
Then, Area of triangle IJK = [tex]\dfrac{1}{2}|3(-4-(-2))+7(-2-(-7))+4(-7-(-4))|[/tex]
[tex]\dfrac{1}{2}|3(-2)+7(5)+4(-3)|\\\\=\dfrac{1}{2}|-6+35-12|\\\\=\dfrac{1}{2}(17)\\\\=8.5\text{ sq. units}[/tex]
Hence, the area of this triangle IJK on a Coordinate Grid = 8.5 sq. units.
how to simplify this expression ?
Answer:
[tex]\large \boxed{\sf \ \ \dfrac{1}{x^2}+\dfrac{1}{x^2+x}=\dfrac{2x+1}{x^2(x+1)} \ \ }[/tex]
Step-by-step explanation:
Hello,
This is the same method as computing for instance:
[tex]\dfrac{1}{2}+\dfrac{1}{3}=\dfrac{3+2}{2*3}=\dfrac{5}{6}[/tex]
We need to find the same denominator.
Let's do it !
For any x real different from 0, we can write:
[tex]\dfrac{1}{x^2}+\dfrac{1}{x^2+x}=\dfrac{1}{x^2}+\dfrac{1}{x(x+1)}\\\\=\dfrac{x+1+x}{x^2(x+1)}=\dfrac{2x+1}{x^2(x+1)}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
A cash register has $10 and $50 dollars bills with total of $1080.there are 28 bills in total how many of each bills.
Hey there! I'm happy to help!
Let's set this up as a system of equations, where x is equal to the number of 10 dollar bills and y is equal to the number of 50 dollar bills.
10x+50y=1080
x+y=28
We want to solve for x or y. We can rearrange the second equation to find the value of one of the variables.
x+y=28
Subtract x from both sides.
y=28-x
Now, we have a value for y. So, we could replace the y in the first equation with 28-x and the solve for x.
10x+50(28-x)=1080
We use distributive property to undo the parentheses.
10x+1400-50x=1080
We combine like terms.
-40x+1400=1080
We subtract 1400 from both sides.
-40x=-320
We divide both sides by -40.
x=8
Since there are 28 total bills, this means that there must be 20 50 dollar ones because there are 8 10 dollar bills.
Have a wonderful day! :D
100 POINTS!!! NEED HELP ASAP The question is the first picture and the second question is the answers to choose. Thank you!
Answer:
4, 3, 5, 8, 7, 6, 1, 2
Step-by-step explanation:
Let’s label the options with numbers.
Solve the percentages:
1) 442/(442+267) = 62.4%
2) 701/(701+187) = 78.9%
3) 267/(267+442)= 37.7%
4) 187/(187+701) = 21.1%
5) 442/(442+701) = 39.4%
6) 701/(442+701) = 61.3%
7) 267/(187+267) = 58.8%
8) 187/(187+267) = 41.2%
Arrange from least to greatest.
4, 3, 5, 8, 7, 6, 1, 2
I need an answer for the attachment below:
Answer:
[tex] - \frac{ 1}{4} [/tex]Step-by-step explanation:
The line passes through points ( - 1 , 2 ) and ( 3 , 1 )
Let there points be A and B
A ( -1 , 2 ) -----> ( x1 , y1 )
B ( 3 , 1 ) -------> ( x2 , y2 )
Now, Let's find the gradient ( slope)
[tex] \frac{y2 - y1}{x2 - x1} [/tex]
plug the values
[tex] = \frac{1 - 2}{3 - ( - 1)} [/tex]
Calculate the difference
[tex] = \frac{ - 1}{3 - ( - 1)} [/tex]
When there is a (-) in front of an expression in parentheses, change the sign of each term in the expression
[tex] = \frac{ - 1}{3 + 1} [/tex]
Add the numbers
[tex] = \frac{ - 1}{4} [/tex]
Use [tex] \frac{ - a}{b} = \frac{a}{ - b} = - \frac{a}{b} [/tex] , to rewrite the fraction
[tex] = - \frac{1}{4} [/tex]
Hope this helps...
Best regards!!
find the value of a, b, c, and d,
type exact answers and use radicals as needed
Step-by-step explanation:
Using trigonometrical functions we can obtain the required side lengths.
[tex] \sin 45\degree = \frac{a}{16\sqrt 2}\\\\
\therefore \frac{1}{\sqrt 2}= \frac{a}{16\sqrt 2}\\\\
\therefore a = \frac{16\sqrt 2}{\sqrt 2}\\\\
\huge\red {\boxed {\therefore a = 16}} \\\\
\cos 45\degree = \frac{c}{16\sqrt 2}\\\\
\therefore \frac{1}{\sqrt 2}= \frac{c}{16\sqrt 2}\\\\
\therefore c = \frac{16\sqrt 2}{\sqrt 2}\\\\
\huge\purple {\boxed {\therefore c = 16}} \\\\
\sin 30\degree = \frac{a}{b}\\\\
\therefore \frac{1}{2}= \frac{16}{b}\\\\
\therefore b = {16\times2}\\\\
\huge\orange{\boxed {\therefore b = 32}} \\\\
\tan 30\degree = \frac{a}{d}\\\\
\therefore \frac{1}{\sqrt 3}= \frac{16}{d}\\\\
\therefore d = {16\times\sqrt 3}\\\\
\huge\pink {\boxed {\therefore d = 16\sqrt 3}} \\\\
[/tex]
Enter your answer in the box
____
Answer:
[tex]\boxed{2144}[/tex]
Step-by-step explanation:
The sum can be found by adding the parts:
[tex]\sum\limits_{n=1}^{32}{(4n+1)}=4\sum\limits_{n=1}^{32}{n}+\sum\limits_{n=1}^{32}{1}=4\cdot\dfrac{32\cdot 33}{2}+32\\\\= 2112+32=\boxed{2144}[/tex]
__
The sum of numbers 1 to n is n(n+1)/2.
Construct a 99% confidence interval of the population proportion at the given level of confidence. x=240, n=300 the lower bound is? the upper bound is?
Answer: lower bound = 0.7404; upper bound = 0.8596
Step-by-step explanation:
The proportion p for this population:
p = [tex]\frac{240}{300}[/tex]
p = 0.8
Confidence interval for proportion is calculated as:
p ± z-score.[tex]\sqrt{\frac{p(1-p)}{n} }[/tex]
Z-score for a 99% confidence interval is: z = 2.58
Calculating:
0.8 ± 2.58.[tex]\sqrt{\frac{0.8(0.2)}{300} }[/tex]
0.8 ± 2.58.[tex]\sqrt{0.00053}[/tex]
0.8 ± 2.58(0.0231)
0.8 ± 0.0596
This means that the lower limit of this interval is 0.7404 and upper bound is 0.8596
A random sample of 51 adult coyotes in a region of northern Minnesota showed the average age to be x = 2.03 years, with sample standard deviation s = 0.82 years. However, it is thought that the overall population mean age of coyotes is μ = 1.75. Do the sample data indicate that coyotes in this region of northern Minnesota tend to live longer than the average of 1.75 years? Use α = 0.01.
Answer:
Yes the sample data indicate that coyotes in this region of northern Minnesota tend to live longer than the average of 1.75 years
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 51[/tex]
The sample mean is [tex]\= x = 2.03[/tex]
The sample standard deviation is [tex]\sigma = 0.82[/tex]
The population mean is [tex]\mu = 1.75[/tex]
The level of significance is [tex]\alpha = 0.01[/tex]
The null hypothesis is
[tex]H_o : \mu = 0.82[/tex]
The alternative hypothesis is
[tex]H_a : \mu >1.75[/tex]
The critical value of the the level significance [tex]\alpha[/tex] obtained from the critical value table for z-value is [tex]z_\alpha = 2.33[/tex]
Now the test statistic is mathematically evaluated as
[tex]t = \frac{\= x - \mu }{\frac{\sigma }{\sqrt{n} } }[/tex]
substituting values
[tex]t = \frac{ 2.03 - 1.75 }{\frac{0.82}{\sqrt{51} } }[/tex]
[tex]t = 2.44[/tex]
From that calculated and obtained value we see that the critical value of the level of significance is less than the test statistics so we reject the null hypothesis
Hence there sufficient evidence to proof that the sample data indicates that coyotes in this region of northern Minnesota tend to live longer than the average of 1.75 years
Barry spent 1/5 of his monthly salary for rent and 1/7 of his monthly salary for his school loans. If $851 was left, what was his monthly salary?
Answer:
1295$
Step-by-step explanation:
Let's denote the monthly salary of Barry A.
Then we have:
A - (1/5)A - (1/7)A = 851
or
(35A - 7A - 5A)/35 = 851
or
23A = 851 x 35
or
23A = 19785
or
A = 1295$
[tex]x+7-4(x+1)=-10[/tex]
━━━━━━━☆☆━━━━━━━
▹ Answer
x = 13/3, 4 1/3, or 4.3
▹ Step-by-Step Explanation
x + 7 - 4(x + 1) = -10
x + 7 - 4x - 4 = -10
-3x + 7 - 4 = -10
-3x + 3 = -10
-3x = -10 - 3
-3x = -13
x = 13/3, 4 1/3, or 4.3
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Answer:
x = 13/3
Step-by-step explanation:
x + 7 - 4(x + 1) = -10
x + 7 - 4x - 4 = -10
-3x + 3 = -10
-3x = -13
x = -13/(-3)
x = 13/3
m−4+m−5 how do I solve this ?
Answer:
2m - 9
Step-by-step explanation:
To simplify this, we need to combine like terms. m + m = 2m and -4 - 5 = -9 so the simplified version would be 2m - 9.
Bus drivers Andy, Benedict and Chris each return to Bus Terminal 1 every 50, 80, and 100 minutes respectively. If they leave the bus terminal at 0830 h, when will they next meet at the bus terminal ?
Answer:
1510 h, or 3:10 PM.
Step-by-step explanation:
The next time they meet at the bus terminal will be a multiple of 50, 80, and 100.
A common factor among the three numbers is 10. If we divide all three by 10, we will get 5, 8, and 10. 5 is a factor of 10, so as long as 5 is multiplied by an even number, 10 will be a multiple.
Since the number will have to be divisible by both 5 and 8, the smallest possible number would be 5 * 8 = 40. So, the next time they meet at the bus terminal will be 40 * 10 = 400 minutes after 8:30.
400 minutes in hours is 400 / 60 = 40 / 6 = 20 / 3 = 6 hours and 2/3.
2/3 of an hour in minutes is (2/3) * 60 = 2 * 20 = 40.
So, they will meet again in 6 hours and 40 minutes.
8:30 plus 6 hours and 40 minutes is 14:70. 70 minutes translates into an hour and 10 minutes. So, the time will be 15:10, or 3:10 PM.
Hope this helps!
2) A basketball player scores 70% of his shots on average. What is the probability that he scores at least 18 successful shots tonight if he gets 20 shots?
Answer:
3.54%
Step-by-step explanation:
This question represents a binomial distribution. A binomial distribution is given by:
[tex]P(x)=\frac{n!}{(n-x)!x!} p^xq^{n-x}[/tex]
Where n is the total number of trials, p is the probability of success, q is the probability of failure and x is the number of success.
Given that:
A basketball player scores 70% of his shots on average, therefore p = 70% = 0.7. Also q = 1 - p = 1 - 0.7 = 0.3.
The total number of trials (n) = 20 shots
The probability that he scores at least 18 successful shots tonight if he gets 20 shots = P(x = 18) + P(x = 19) + P(x = 20)
P(x = 18) = [tex]\frac{20!}{(20-18)!18!}*0.7^{18}*0.3^{20-18}=0.0278[/tex]
P(x = 19) = [tex]\frac{20!}{(20-19)!19!}*0.7^{19}*0.3^{20-19}=0.0068[/tex]
P(x = 20) = [tex]\frac{20!}{(20-20)!20!}*0.7^{20}*0.3^{20-20}=0.0008[/tex]
The probability that he scores at least 18 successful shots tonight if he gets 20 shots = P(x = 18) + P(x = 19) + P(x = 20) = 0.0278 + 0.0068 + 0.0008 = 0.0354 = 3.54%
What is the prime factorization of 18?
Answer:
18 is a composite number. 18 = 1 x 18, 2 x 9, or 3 x 6. Factors of 18: 1, 2, 3, 6, 9, 18. Prime factorization: 18 = 2 x 3 x 3, which can also be written 18 = 2 x 3².
All the prime factorization of 18 are,
⇒ 2, 3, 3
Because 2×3×3 = 18
We have to given that,
To find all the prime factorization of number 18.
Now, We need to find all the factors of 18.
Hence,
18 = 2 x 9
= 2 x 3 x 3
Therefore, All the prime factorization of 18 are,
⇒ 2, 3, 3
Because 2×3×3 = 18
Learn more about the Greatest common factors visit:
https://brainly.com/question/219464
#SPJ6
A party rental company has chairs and tables for rent. The total cost to rent 2 chairs and 3 tables is$31 . The total cost to rent 6 chairs and 5 tables is $59 . What is the cost to rent each chair and each table?
Answer:
The cost to rent each chair is $2.75 and the cost to rent each table is $8.50
Step-by-step explanation:
Let the:
Cost to rent a chair = x
Cost to rent a table = y
We would form an algebraic equation.
The total cost to rent 2 chairs and 3 tables is $31
2x + 3y = 31 ...... Equation 1
The total cost to rent 6 chairs and 5 tables is $59
6x + 5y = 59 ......... Equation 2
We solve the above equation above using elimination method
Multiply Equation 1 all through by the coefficient of x = 6 in Equation 2
Multiply Equation 2 all through by the coefficient of x = 2 in Equation 1
Hence, we have:
2x + 3y = 31 ...... Equation 1 × 6
6x + 5y = 59 ......... Equation 2 × 2
12x + 18y = 186........ Equation 3
12x + 10y = 118 .…...... Equation 4
Subtracting Equation 4 from Equation 3
= 8y = 68
y = 68/8
y = 8.5
Therefore, the cost to rent a table = $8.50
Substituting 8.5 for y in Equation 1 to get the value of x
2x + 3y = 31 ...... Equation 1
2x + 3(8.5) = 31
2x = 31 - 3(8.5)
2x = 31 - 25.5
2x = 5.5
x = 5.5/2
x = 2.75
The cost to rent a chair = $2.75
Therefore, the cost to rent each chair is $2.75 and the cost to rent each table is $8.50