Answer:
y+2 = 2/3(x+1)
y= 2/3x - 4/3
Step-by-step explanation:
If we want a line parallel to y=2/3x+7, it will have the same slope
m = 2/3
We have a point (-1,-2), so we can use point slope form
y-y1 = m(x-x1)
y--2 = 2/3(x--1)
y+2 = 2/3(x+1)
If we want the line in slope intercept form, distribute the slope
y+2 = 2/3 x +2/3
Subtract 2 from each side
y+2-2=2/3x +2/3-2
y = 2/3x +2/3 - 6/3
y= 2/3x - 4/3
If arc AD = 130° and arc AB = arc CD = 80°, what is the measure of ∠APD?
Answer:
the answer is 25
Step-by-step explanation:
1/2(130-80)
Answer:
(B)
Step-by-step explanation:
Given: It is given that arc AD=130° and arc AB=arc CD=80°.
To find: The measure of ∠APD.
Solution: It is given that arc AD=130°⇒m∠AOD=130° (The measure of the central angel is equal to the intercepted arc)
Also, arc AB=arc CD=80°⇒m∠AOB=m∠DOC=80° (The measure of the central angel is equal to the intercepted arc)
We know that the sum of the central angles is equal to 360°, thus
m∠AOD+m∠AOB+m∠BOC+m∠COD=360°
⇒130°+80°+m∠BOC+80°=360°
⇒290°+m∠BOC=360°
⇒m∠BOC=360°-290°
⇒m∠BOC=70°
Now, since (The measure of the central angel is equal to the intercepted arc), therefore arcBC=70°.
Also, we know that Angle Formed by Two Secants is half of the DIFFERENCE of Intercepted Arcs, therefore
[tex]m{\angle}APD=\frac{1}{2} (arcAD-arBC)[/tex]
Substituting the values, we get
[tex]m{\angle}APD=\frac{1}{2} (130-70)[/tex]
⇒[tex]m{\angle}APD=\frac{60}{2}[/tex]
⇒[tex]m{\angle}APD=30^{\circ}[/tex]
Thus, the measure of ∠APD is 30°.
Hence, option B is correct.
Two cars left the city for a suburb, 120 km away, at the same time. The speed of one of the cars was 20 km/hour greater than the speed of the other, and that is why it arrived at the suburb 1 hour before the other car. Find the speeds of both cars.
Answer:
V1 = 60 km/h
V2 = 40 Km/h
Step-by-step explanation:
The speed of an object is defined as
Speed = distance / time
Let
V1 be the speed of the faster car
V2 be the speed of the other car
t1 the time it took for the first car to arrive
t2 the time it took for the second car to arrive
d1 the distance traveled by first car
d2 the distance traveled by second car
We know thanks to the problem that
V1 = V2 + 20 Km/h
t1 = t2 - 1 hour
d1 = d2 = 120 Km
d1 = V1 * t1
d2 = V2* t2
V1 * t1 = V2* t2
V1* t1 = (V1 -20)*(t1 +1)
The system of equations
(V1 -20)*(t1 +1) = 120
V1 * t1 = 120
120 + (120/t1) -20*t1 = 140
(120/t1) -20*t1 = 20
Which gives,
t1 = 2
This means
V1 = 60 km/h
V2 = V1 - 20 Km/h = 40 Km/h
Answer: 60 km/h, and 40 km/h
Step-by-step explanation:
How do you figure out 3.72 times 10.?
Answer:
Every time you multiply by 10, you move all the digits one place to the left. You could also think about so that the decimal point moves one place to the right.
Step-by-step explanation:
Answer: The answer to the problem is 37.2
Step-by-step explanation: When you are multiplying a number by 10 you need to move the decimal point one place to the right. 3.72 x 10 = 37.2.
Which of the following is a point slope equation of a line that passed through the points (10,5) and (4-7)
Answer:
y - 5 = 2(x - 10)Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
(x₁, y₁) - point
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (10, 5) and (4, -7). Substitute:
[tex]m=\dfrac{-7-5}{4-10}=\dfrac{-12}{-6}=2[/tex]
[tex]y-5=2(x-10)[/tex]
PLEASE HELP ME
When keeping records, expenses should be
A. added
B. subtracted
C. multiplied
D. divided
Which equation or inequality shows the relationship between the values |7| and |-7|? A. |7| > |-7| B. |7| < |-7| C. |7| = |-7| D. |7| ≠ |-7|
Answer:
C.)
| 7 | = | -7|
Step-by-step explanation:
because absolute values are always positive....so, absolute values of | -7 | and | 7 | are both 7
Answer:
Step-by-step explanation:
7 I guess
Which equations represent functions?
2x + 3y = 10
4x = 16
2x − 3 = 14
3y = 18
14.6 = 2x
Answer:
2x + 3y = 10, 3y = 18 (in both cases, for each input x, there is exactly one output y.
Step-by-step explanation:
3y = 10 - 2x, or y = (1/3)(10 - 2x) Yes, this is a function.
4x = 16 → x = 4 NOT a Function, because for x = 4 there are an infinite number of possible y -values
2x - 3 = 14 → 2x = 17 → x = 17/2 Not a function. See reason given above.
3y = 18 → y = 6 Function
2x = 14.6 → x = 7.3 Not a function. See reason given above
Answer:
it's a i got it right
Step-by-step explanation:
What is the distance between the points (−7, 1) and (−7, −5) on the coordinate plane, in units?
Answer:
6 units
Step-by-step explanation:
Calculate the distance d using the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (- 7, 1) and (x₂, y₂ ) = (- 7, - 5)
d = [tex]\sqrt{(-7+7)^2+(-5-1)^2}[/tex]
= [tex]\sqrt{0+(-6)^2}[/tex] = [tex]\sqrt{36}[/tex] = 6 units
Final answer:
The distance between the points (-7, 1) and (-7, -5) on the coordinate plane is 6 units, calculated by the absolute difference in their y-coordinates.
Explanation:
The distance between the points (-7, 1) and (-7, -5) on the coordinate plane can be found by calculating the difference in their y-coordinates. Since the x-coordinates are the same, the points lie on a vertical line, and the distance is simply the absolute difference in the y-coordinates.
The calculation would be: distance = |y2 - y1| = |-5 - 1| = | -6 | = 6 units
Therefore, the distance between the two points is 6 units.
Hayley Baked A Cheescake. She used 5/8 pound cream cheese, 4/16 pound sugar, and 6/8 pound peaches. How much did the ingredients weigh altogether?
8 is a factor of 16, so you would multiply the numerator and denominator of 5/8 and 6/8 by 2. this would be 10/16 and 12/8. add all of the numbers together = 10+12+4 which equals 26. it’d be 26/16 or 1 and 10/16.
Answer:
1[tex]\frac{5}{8}[/tex]
Step-by-step explanation:
equation: [tex]\frac{5}{8}[/tex]+[tex]\frac{14}{16}[/tex]+[tex]\frac{6}{8}[/tex]=x
but we cannot solve this because not all of the fractions have an equal denominator. so, we can multiply [tex]\frac{5}{8}[/tex] and [tex]\frac{6}{8}[/tex] each by two.
why?
because 8x2 is 16 and if you multiply them you get a common denominator of 16, making it way easier to add up the fractions.
so, what you do to the top you do to the bottom:
[tex]\frac{5}{8}[/tex] [tex]\frac{x2}{x2}[/tex] [tex]\frac{10}{16}[/tex] [tex]\frac{6}{8}[/tex] [tex]\frac{x2}{x2}[/tex] [tex]\frac{12}{16}[/tex]
so, [tex]\frac{10}{16}[/tex]+[tex]\frac{12}{16}[/tex]+[tex]\frac{4}{16}[/tex] equals to [tex]\frac{26}{16}[/tex].
[tex]\frac{26}{16}[/tex] = 1 [tex]\frac{10}{16}[/tex].
however 1[tex]\frac{10}{16}[/tex] can be simplified more.
divide top and bottom by 2 and get 1[tex]\frac{5}{8}[/tex]
the picture would be the work shown. messy kuz i used paint from windows with a mouse but tried to make it neat as possible.
plz give me a brainliesttttt
Find the area of a 6-gon with side length 10. Round to a whole number.
Answer:
Area = 260
Step-by-step explanation:
The formula for the area of a 6-gon is
Area = 3*sqrt(3) * side^2 / 2
side = 10
Area = 3 * 1.7321 * 100/2
Area = 259.8
Area = 260
an actor will earn d dollars this year. His agent Collects a Commission of 10% of all his earnings. which expression shows how many dollars the actor will earn this year after the agent's commission is Deducted?
Answer: d - (d x .1)
Step-by-step explanation: The expression that will show how much the actor will earn is d - (d x .1). D is the actor’s earnings and d x .1 is the commission of their agent.
Final answer:
The expression that shows how many dollars the actor will earn this year after the agent's commission is deducted is d - 0.1d. The agent collects a commission of 10% of the actor's earnings, which is subtracted from the total earnings.
Explanation:
The expression that shows how many dollars the actor will earn this year after the agent's commission is deducted is:
d - 0.1d
Since the agent collects a commission of 10% of the actor's earnings, we can multiply the earnings by 0.1 to find the amount of commission. Subtracting this amount from the total earnings gives us the amount the actor will earn after the commission is deducted.
Peter wants to fence the park in front of his home on three sides which measure 152m 40cm, 205m 10cm, 310m 39cm. What is the total length
One centimenter is 0.01 meters. So, you can write the measures as
[tex] 152.40\text{m},\quad 205.10\text{m},\quad 310.39\text{m}[/tex]
Once this rewriting is done, getting the total length [tex]T[/tex] is quite trivial, since all measurements are in the same unit, and we can simply sum everything:
[tex]T = 152.40+205.10+310.39 = 667.89[/tex]
Attachments Are Below 15 Points
Answer: A is not true
Step-by-step explanation: This is because a rule of dilation. If you dilate an object, then the angle will stay the same. thus, statement A is false.
1/8x=1/4 what is the value x that makes the equation true
Answer:
x = 2
How?:
1/4 ÷ 1/8 = 0,25
0.25 as a fraction is 1/4
1/8 × 2 = 1/4
how can you calculate the area of the circle if you know the circle's circumference?
Answer with step-by-step explanation:
We know that the formula for area of a circle is given by:
Area of a circle = [tex] \pi r ^ 2 [/tex]
So to find the area of circle, we basically need to know the radius of the circle.
If we know the circumference of the circle, we can calculate the area of the circle too.
Formula for the circumference of the circle is given by:
[tex]2\pi r[/tex]
So if we know the circle's circumference, we can find the value of radius and then find the area of circle with it.
Answer:
We can calculate area of circle if we know the circumference
Step-by-step explanation:
Points to remember
`1). Circumference of circle = 2πr
2). Area of circle = πr²
Where 'r' is the radius of circle
Find area of circle
From the above two equations we have to calculate area and circumference of a circle with radius.
If we have circumference, the we can calculate radius of the circle
r = circumference/2π
If we get radius 'r' the we can calculate area
Area of circle = πr²
one letter tile is drawn from the bag and replaced 300 times. Predict how many times a consonant will not be picked
The predicted number of times a consonant will not be could be picked is 58 times.
The total number English alphabets = 26
Number of non consonant letters = 5
The probability of choosing a non-consonant letter at random from a single pick :
Number of non- consonant letters / total number of alphabets = 5 /26
To predict the number of times a non-consonant letter could be selected from 300 selections :
(Number of selections × probability per pick)
(300 × 5/26)
= 57.69
= 58 times
A non- consonant could be selected approximately 58 times.
Learn more on probability : https://brainly.com/question/13149279
Which of the following are point-slope equations of the line going through (-5,6) and (1,1)?
Answer:
[tex]A.\ y-6=-\dfrac{5}{6}(x+5)\\\\B.\ y-1=-\dfrac{5}{6}(x-1)[/tex]
Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
(x₁, y₁) - point
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (-5, 6) and (1, 1). Substitute:
[tex]m=\dfrac{1-6}{1-(-5)}=\dfrac{-5}{6}\\\\\text{For point (-5, 6):}\\\\y-6=-\dfrac{5}{6}(x-(-5))\\\\y-6=-\dfrac{5}{6}(x+5)[/tex]
[tex]\text{For point (1, 1):}\\\\y-1=-\dfrac{5}{6}(x-1)[/tex]
Kaitlin spent 2/3 of an hour on homework. Her sister Judy spent 1 1/2 times that amount. Explain why Judy’s homework time is between 2/3 of an hour and 1/2 of an hour?
[tex]\bf \stackrel{mixed}{1\frac{1}{2}}\implies \cfrac{1\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{3}{2}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{Judy spent time}}{\stackrel{\textit{Kaitlin's time}}{\cfrac{2}{3}}\cdot \cfrac{3}{2}}\implies \cfrac{2}{2}\cdot \cfrac{3}{3}\implies 1~\hfill \boxed{\cfrac{1}{2}}\rule[0.35em]{3em}{0.25pt}\stackrel{\stackrel{Judy's}{\downarrow }}{1}\rule[0.35em]{5em}{0.25pt}\stackrel{1\frac{2}{3}}{\boxed{\cfrac{2}{3}}}[/tex]
so, Judy's time is really 1 hour exactly.
and on the number line, we could place that 1 in between the first half and the two thirds of the of the next number, as you see above.
There is a mistake in the question as Judy's homework time cannot be between 2/3 and 1/2 of an hour if she spent 1 1/2 times as much time as Kaitlin who spent 2/3 of an hour. Judy's homework time would be 1 hour.
The question seems to have a typo or a logical error, as it is not possible for Judy's homework time, which is 1 1/2 times Kaitlin's time, to be between 2/3 of an hour and 1/2 of an hour. Instead, if Kaitlin spent 2/3 of an hour on homework, Judy would have spent (2/3) * (3/2) = 1 hour on homework, which is more than both 2/3 and 1/2 of an hour. It appears that Judy's actual homework time would be exactly one hour, not between the two given times.
Fred bags groceries at Bilo. On average, he fills 21 bags for every three customers. The graph below, represent the total bags Fred filled based on the number of customers. What does the average rate of change represent?
Question 1 options:
For every customer, Fred fills 7 bags of groceries.
For every bag, there are 7 customers.
The customers who do not buy any groceries.
None of the above
Answer: For every customer, Fred fills 7 bags of groceries.
Answer:
The correct answer is : 'For every customer, Fred fills 7 bags of groceries'.
Step-by-step explanation:
Number bags filled by Fred for every 3 customers = 21 bags
Number bags filled by Fred for 1 customer = [tex]\frac{21 bag}{3}=7 bag[/tex]
So, 7 bags were filled for every customer.
The rate of change will be represented by 7 bags for each customer.
From the given option the correct statement is ;
For every customer, Fred fills 7 bags of groceries.
ABC HAS A VERTICES. A(-2,10), B(4,8),C(2,4). determine the coordinates of A',B',AND C' HAS UNDERGONE THE DESCRIBED TRANSFORMATION. A DILATION WITH THE SCALE FACTOR OF3 AND A CENTER OF DILATION AT THE ORIGIN.
Answer:
A'(-6,30)
B'(12,24)
C'(6,12)
Step-by-step explanation:
By definition, dilation is a tranformation in which the the image and the pre-image have the same shapes but differente sizes.
You know that:
- The vertices of ABC are: A(-2,10), B(4,8),C(2,4).
- The scale factor is 3.
- The center of dilation is at the origin.
By definition, if the scale factor is greater than 1, then the image is an enlargement.
Therefore, you must multiply each original vertex by 3:
(x,y)→(3x,3y)
Then the coordinates A',B' and C' are:
A'→ [tex](-2(3), 10(3))=(-6,30)[/tex]
B'→ [tex](4(3), 8(3))=(12,24)[/tex]
C'→ [tex](2(3), 4(3))=(6,12)[/tex]
Hello people of AMERICA!!! :)
Use the image to determine the volume of the rock.
Initial volume:
Final volume:
Volume of rock:
Answer:
Initial Volume: 20 mL
Final Volume: 32 mL
Volume of the rock: 12mL
Step-by-step explanation:
From the image we see that the initial volume of water is 20 mL, and after the rock is put into the flask, the final volume is 32 mL. From this we conclude that the volume of the rock must be 32mL-20mL = 12 mL.
Thus we have:
Initial Volume: 20 mL
Final Volume: 32 mL
Volume of the rock: 12mL.
Answer:
20
32
12
Step-by-step explanation:
Here is the question: Alicia wrote numbers:2,9,15,21 what of the numbers is not a composite number?
the answer is 2 because you can't divided 2 by anything else other then itself
An electronics store discovers that it can sell 5 televisions per day by pricing them at $150. When the televisions are on sale for $100 the store sells 10 of them every day. Write a linear equation to compare the price of a television, p, to the number sold, x. Then write a quadratic equation to compare the revenue, m, from selling televisions to the number sold, x.
Answer:
[tex]p = -10x + 200[/tex]
[tex]m = -10x^2 +200x[/tex]
Step-by-step explanation:
We know that at a price of $ 150, 5 televisions are sold and at a price of $ 100, 10 televisions are sold.
We must write a linear equation for this situation.
The equation of the line will have the following form
[tex]p = mx + b[/tex]
Where m is the slope of the line and b is the intercept with the p axis
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{100-150}{10-5}=-10[/tex]
[tex]b=p_1-mx_1\\\\b=150-(-10)(5)\\\\b=200[/tex]
The equation is:
[tex]p = -10x + 200[/tex]
Now we know that the revenue m is the product of the price p for the quantity sold x.
[tex]m = p * x[/tex]
[tex]m=(-10x + 200)*x[/tex]
[tex]m = -10x^2 +200x[/tex]
Answer:
[tex]p=-10x+200[/tex]
[tex]m = -10x^2+200x[/tex]
Step-by-step explanation:
Given : An electronics store discovers that it can sell 5 televisions per day by pricing them at $150. When the televisions are on sale for $100 the store sells 10 of them every day.
To Find: Write a linear equation to compare the price of a television, p, to the number sold, x. Then write a quadratic equation to compare the revenue, m, from selling televisions to the number sold, x.
Solution:
Let p be the price and x be the no. of television sold
We are given that it can sell 5 televisions per day by pricing them at $150. When the televisions are on sale for $100 the store sells 10 of them every day. i.e(5,150) and (10,100)
Now to find the linear equation to compare the price of a television, p, to the number sold, x.
We will use two point slope form
Formula : [tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex](x_1,y_1)=(5,150)[/tex]
[tex](x_2,y_2)=(10,100)[/tex]
Substitute the values in the formula
[tex]y-150=\frac{100-150}{10-5}(x-5)[/tex]
[tex]y-150=\frac{-50}{5}(x-5)[/tex]
[tex]y-150=-10(x-5)[/tex]
[tex]y-150=-10x+50[/tex]
[tex]y=-10x+50+150[/tex]
[tex]y=-10x+200[/tex]
x is the no. of television sold
y is the price
Since p denotes the price
So, [tex]p=-10x+200[/tex]
Thus a linear equation to compare the price of a television, p, to the number sold, x is [tex]p=-10x+200[/tex]
Now [tex]Revenue = Cost \times quantity[/tex]
Since price of x telivisons = [tex]p=-10x+200[/tex]
So, [tex]Revenue = (-10x+200) \times x[/tex]
[tex]Revenue = -10x^2+200x[/tex]
m denotes revenue
So,[tex]m = -10x^2+200x[/tex]
Thus a quadratic equation to compare the revenue, m, from selling televisions to the number sold, x. is [tex]m = -10x^2+200x[/tex]
Hence a linear equation to compare the price of a television, p, to the number sold, x is [tex]p=-10x+200[/tex] and a quadratic equation to compare the revenue, m, from selling televisions to the number sold, x. is [tex]m = -10x^2+200x[/tex]
she has saved $30 which is three fifths of the total cost, how much is the total cost
Answer:
$50
Step-by-step explanation:
3/5=30/x
x= The total cost
You can see that 3×10 multiplies to 30, so the total cost would be 5×10.
Total cost= 50
Write an expression the represents the sum of any number plus 3
Answer: x + 3
Step-by-step explanation: In this question you need to know that a sum is the answer when you add numbers. In this case x = any number. The expression is x + 3
Answer:
Step-by-step explanation:
Hello
Being X represented on any number, the expression will be:
X+3
Best regards
Eddie had a favorable simple annual interest rate on a used car loan, but he can’t remember what it was. His paperwork shows that he originally borrowed S4000 and paid a total of $1280 in interest on the 4-year loan. What was Eddie’s annual interest rate?
Answer: 8%
Step-by-step explanation:
Answer:
8%
Step-by-step explanation:
what is the range for 2,8,15,4,11,6,2,6
Answer:
The range is 13. Hope this helps.
Answer:
13
Step-by-step explanation:
Range = Highest value - lowest value
Range = 15-2
Range = 13
Hope This Helps:)
Captain Tellez plans to reach a cruising altitude in his passenger plane and then maintain a cruising speed of 570 miles per hour for approximately 400 miles. Which is closest to the length of time, in minutes, that his plane will maintain cruising speed?
A. 0.70
B. 1.43
C. 42
D. 86
Answer:
option (c)
42 minutes
Step-by-step explanation:
Given in the question:
cruising speed of passenger plane = 570 miles/hour
distance passenger plane travelled = 400 miles
Formula to usedistance = speed x time
time = distance / speed
time = 400 / 570
= 0.7018 hours
1 hour = 60 minutes
228000 hours = 60 x 0.7018 minutes
= 42.1052 minutes
≈ 42 minutes
Closest to the length of time, in minutes, that Captain Tellez's plane will maintain cruising speed is 42 minutes.
Claire got 17 out of 20 questions correct on her vocabulary quiz. What percent of the questions did she get right
Answer: The correct answer is 85%
Step-by-step explanation:
If you divide 17 by 20 then you'll get 0.85 which is the same as 85%.
17 ÷ 20 = 0.85, OR, 85% ← Work* Hopefully this helps:) Mark me the brainliest:)!!!
Claire got 85% of the questions correct on her vocabulary quiz by answering 17 out of 20 questions correctly.
Claire got 17 out of 20 questions correct on her vocabulary quiz. To calculate the percentage of questions Claire got right, you would use the following formula:
Percentage Correct = (Number of Correct Questions \/ Total Number of Questions) x 100%
Applying Claire's numbers to this formula:
Percentage Correct = (17 \/ 20) x 100% = 0.85 x 100% = 85%
Therefore, Claire got 85% of the questions correct on her quiz. This is a high percentile, which indicates she did very well, considering that seventy percent of students answered 16 or fewer questions correctly and thirty percent of students answered 16 or more questions correctly. A higher percentile is generally considered good, as it means answering more questions correctly, which is desirable.
A room contains 55 chairs arranged in rows. The number of rows is one more than twice the number of chairs per row. Find the number of rows.
Answer:
i believe its 27
Step-by-step explanation:25 times two= 50 27 times two= 54 +one more is 55. so it is 27
Answer:
11 rows.Step-by-step explanation:
Givens
The room contains 55 chairs arranged in rows.The number of rows is one more than twice the number of chairs.We know that the total number of chairs must be the product between the number of chairs per row and the total number of rows, which can be expressed as
[tex]c \times r = 55[/tex]
Where [tex]c[/tex] represents the number of chairs per row and [tex]r[/tex] representes the number of rows.
The second given statment defined a second equation
[tex]r=2c+1[/tex]
Now, we can substitute the second equation into the first one, and solve
[tex]c \times r = 55\\c (2c+1)=55\\2c^{2}+c-55=0[/tex]
Which can be factored by multiplying the expression by 2, and solve has a perfect trinomial
[tex]2(2c^{2}+c-55)=0\\2^{2}c^{2}+2c- 110=0\\(2c)^{2}+2c-110=0[/tex]
So, we need to find two number which product is 110 and is 1. If you think this through, those numbers are 11 and 10, because 11*10=110 and 11-10=1.
The factors are
[tex]\frac{(2c+11)(2c-10)}{2} =0[/tex], we have to divide by the number we multiplied before, then we simplify this number with the second factor
[tex](2c+11)(c-5)=0[/tex]
Where the positive solution is the only one that can be part of the answer because it doesn't make sense if we say -3 chairs. So,
[tex]c-5=0\\c=5[/tex]
This means there are 5 chairs per row.
Then, we use this value to find the other one.
[tex]c \times r=55\\5 \times r=55\\r=\frac{55}{5}\\ r=11[/tex]
Therefore, there are 11 rows and 5 chairs per row.