someone help me with this table !!!!!!!
*40 people responded that they use mouthwash.
*Of the people who use mouthwash, 30 people use floss.
*55 people responded that they do not floss.
*45 people responded that they don't floss and don't use mouthwash
Answers
Answer: The image of the completed table is shown below
In the completed table, we have the following values (left to right)
Row One: 30, 10, 40Row Two: 15, 45, 60Row Three: 45, 55, 100==============================================
Explanation:
We're told that "40 people responded that they use mouthwash". That means we'll write "40" at the very end of the "use mouthwash" row. This represents the total number of people who use mouthwash, since we're underneath the "total" in that far right column.
Then we're further told that "Of the people who use mouthwash, 30 people use floss", so we'll write "30" in the first row, first column blank space. These are the people who both floss and use mouthwash. Because earlier we know 40 people use mouthwash overall, this leaves 40-30 = 10 people who use mouthwash, but they don't floss.
To summarize so far: In row 1, we have the following values from left to right: 30, 10, 40
The first two items of this row must add to the last item.
---------------------
Now onto row 2
Since 40 people use mouthwash, and 100 people were surveyed, this means that 100-40 = 60 people do not use mouthwash. The value 60 goes at the very end of row 2. This represents another total.
Like earlier, the first two items must add to the last. So 40+60 = 100.
Now turn to the fact that "45 people responded that they don't floss and don't use mouthwash". This tells us that "45" will be in the "no mouthwash" row and "don't floss" column.
We have 60 people who don't use mouthwash, and 45 of those people also don't floss. Therefore, 60-45 = 15 people do floss but they don't use mouthwash. We'll write "15" in the second row, first column.
Along row 2, we have the following values: 15, 45, 60
----------------------
Row 3
For each column, add up the first two items to get the third one. This will lead to the totals along this bottom row.
Floss: 30+15 = 45Don't Floss: 10+45 = 55 .... note how this matches up with the third piece of information your teacher providedThe third column is already done, but again we can see that 40+60 = 100.
Furthermore, the first two items of the third row add to 45+55 = 100 which helps confirm our answers.
The full completed table is shown below.
------------------------
To summarize, we are effectively just sorting the values given to us to write them into the table. Then we use a bit of algebraic detective work to find out what values are missing so we fill out the completed table.
Related Questions
which statement is true? a.) there are a total of 25 elements shown in the venn diagram. b.) set p has 17 elements. c.) set q has 38 elements. d.) sets p and q have 30 common elements. submit my answer
Answers
Answer:
b gang
Step-by-step explanation:
write a function rule for the table be quick plzz
Answers
Step by step is blew
Hopefully this help you:)
HELP PLEASE ASAP
Which of the following are irrational numbers?
55
53
✓20
71
Submit
Answers
Answer: √20
Step-by-step explanation:
4.47213595 (the 5 repeats)
O 10
O25
35
385
Positive Sam77 test
Negative Sam77 test
400
Positive
Yq test
590
25
For how many volunteers did the Sam77 test give an
incorrect result?
Negative
Yq test
10
375
Answers
By applying the probability concept, it can be concluded:
A. Total cost of the test is $2,550,000
B. 61.5% of volunteers carry Yq77 gene
C. Sam77 test gives an incorrect result for 35 people
D. Probability the volunteer does not possess Yq77 is 0.017
Probability is a value used to measure the degree of occurrence of a random event.
P(A) = f / N where
f = frequency
N = size of the sample
We have the following information about Yq and Sam77 tests:
Yq test = $2,500 per each
Sam77 test = $50 per each.
Number of volunteers = 1000
The following table describes the results of the test:
Positive Yq test Negative Yq test
Positive Sam77 test 590 10
Negative Sam77 test 25 375
A. Total cost = total Yq test cost + total Sam77 test cost
= (1000 * $2,500) + (1000 * $50)
= $2,500,000 + $50,000
= $2,550,000
B. Percentage of volunteers carry Yq77 gene
= total volunteers with Yq test result positive / total volunteers
= (590 + 25) / 1000
= 615 / 1000
= 0.615 = 61.5%
C. The number of volunteers the Sam77 test gives an incorrect result
= volunteers with negative Sam77 test but positive Yq test +
volunteers with positive Sam77 test but negative Yq test
= 25 + 10
= 35
D. The probability the volunteer does not possess Yq77
= volunteers with negative Yq test /
volunteers with positive Sam77 test
= 10 / (590 + 10)
= 1/60 = 0.017
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Write forty-one thousand, two hundred
eleven in the place-value chart. Then
write the number in expanded form.
Answers
The place value chart is 41,211.
The expanded form of 41,211 is 40000 + 1000 + 200 + 10 + 1.
Given,
forty-one thousand, two hundred eleven.
We need to write it in the place-value chart and write the number in expanded form.
What are a place value chart and an expanded form of a number?The place value chart is given by:
Example: 13579
1 - ten thousands
3 - thousands
5 - hundreds
7 - tens
9 - ones
The expanded form is given by:
Example: 12300
10,000 + 2000 + 300
Find the place value chart of forty-one thousand, two hundred
eleven.
= 41,211
Find the expanded form of 41,211.
= 40000 + 1000 + 200 + 10 + 1
Thus,
The place value chart is 41,211.
The expanded form of 41,211 is 40000 + 1000 + 200 + 10 + 1.
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what is the expected sum of the numbers that appear on two dice, each biased so that a 3 comes up twice as often as each other number?
Answers
The expected sum of the numbers that appear on two dice is = 10
Each die has 6 possible values, so a pair of dice have a total of 6*6=36 outcomes.
To find a sum of 10, the cases are:
(4,6), (5,5) and (6,4).
So to have a sum of 10 we have 3 cases among the 36 possible, therefore the probability is:
P(10) = 3/36 = 1/12
If we want the sum of 10 in each of the three rolls, the probability is:
P(10 on three rolls) = P(10)^3 = (1/12)^3 = 1/1728 = 0.0005787
If the sum is 10 in two of three rolls, in one roll we need the probability of the sum not being 10:
P(not 10) = 1 - P(10) = 1 - (1/12) = 11/12
So we have:
P(10 in two of three rolls) = P(10)^2 * P(not 10) = (1/12)^2 * (11/12)
P(10 in two of three rolls) = 11/1728 = 0.0063657
A={(3,6),(4,5),(5,4),(6,3),(4,6),(5,5),(6,4),(5,6),(6,5),(6,6)}
There are 10 possible outcomes of two dices under the condition.
To find the expected value of conditional probability. We need to multiply the possibility with the summed value of two dices:
E(X|A)=(4*9/10)+(3*10/10)+(2*11/10)+12/10=10
Therefore,
The expected sum of the numbers that appear on two dice is = 10
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Describe the relationships between these functions
Relationships between these functions |a² = ena; log_a¹ = x, a, x > 0, a ‡ 1
Answers
The first relationship states that for any positive value of 'a', 'a' raised to the power of 2 is equal to 'e' raised to the power of 'na'.The second relationship expresses that the logarithm of 1 to the base 'a' is equal to 'x'.
The first relationship, a² = ena, connects the exponential and power functions. It states that for any positive value of 'a', 'a' raised to the power of 2 is equal to 'e' raised to the power of 'na'. This relationship allows us to relate the exponential function, with base 'e', and the power function, where the base 'a' is raised to a fixed exponent.
The second relationship, log_a¹ = x, relates the logarithmic function to the variable 'x'. It states that the logarithm of 1 to the base 'a' is equal to 'x'. This relationship demonstrates the inverse nature of the logarithmic function, where it "undoes" the exponentiation operation. By taking the logarithm of 1 to the base 'a', we find the exponent 'x' that, when 'a' is raised to that exponent, yields 1.
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Find the 12th term of the arithmetic sequence whose common difference is d=9 and whose first term is a, 5.
Answers
Common differences(d)= 9
First term (a)= 5
Now
12th term( t12)= a+(n-1)d
=5+(12-1)9 Therfore, tn= t12
=5+11*9
=5+99
=104 is the answer
Brian asked a group of people their favourite holiday destination.
The results are summarised in the table.
UK
USA
Destination
Africa
Other
Europe
84
48
108
204
276
Frequency
How many degrees does one person represent?
Give your answer as a fraction in its simplest form.
Answers
12 degrees. Carry On Learning.
Staples charges $35 for using the printer plus $0. 10 per copy of paper. The Public Library charges $30 for using the printer plus $0. 60 per photo copy. How many photocopies can be made for both Staples and the Public Library, to be equal in cost? Label your variable, write and solve an algebraic equation. PLSSSS!!
Answers
The number of copies made by both Staples and the Public Library should be 10 copies so that the cost will be equal for both.
We must first define the variable x to represent the number of copies made by both Staples and the Public Library. We must then create an algebraic equation based on the given information and solve for x.
Let's see how to solve the given problem. The cost of using Staples is a flat rate of $35, and the cost of each copy is $0.10.
This implies that the total cost of using the printer at Staples, y, is determined by the following equation:
y = 0.10x + 35
Similarly, the cost of using the printer at the Public Library is a flat rate of $30 plus $0.60 per copy, implying that the total cost of using the printer at the Public Library, z, is determined by the following equation:
z = 0.60x + 30
We must equate y and z to solve for the number of copies that will provide the same cost for using the printer at Staples and the Public Library.
we will use the equation:
y = z0.10x + 35 = 0.60x + 30
Now, let's solve the above equation:
Subtract 0.10x from each side of the equation:
0.50x + 35 = 30
Subtract 35 from each side of the equation:
0.50x = -5
Divide both sides of the equation by 0.50:x = -10
Therefore, the number of copies made by both Staples and the Public Library should be 10 copies, so that the cost will be equal for both.
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what are the steps in between?
Answers
Answer:
Step-by-step explanation: 1. distribute
distribute the x into (3x-5) -> 3x*x=3x^2 and x*-5=-5x. you will get
3x^2-5x+3(3x-5)
now distribute the 3 into the other (3x-5) -> 3*3x=9x and 3*-5=-15. you will get
3x^2-5x+9x-15
2. Combine like terms
3x^2-5x+9x-15 can be simplified to 3x^2+4x-15 by combining -5x and 9x.
3. Factor (there are many strategies use the one easiest for you)
In this case no number can be taken out to simplify the equation so set up your answerer as (3x ) (x ). you can do this because your first term will have to be 3x^2 and the only multiples are 3 and 1.
By using your 3rd term (-15) you can get the possible numbers after the x's by its multiples 5*3 and 15*1
Using the middle term (4x) find what multiplies to -15 (only one number can be negative) and is able to add up to 4 while one number is multiplied by 3 because of the 3x ( -5*3=15 and 3*3-5 -> 9-5=4)
plug your numbers in (3x-5) (x+3)
feel free to ask any questions!
A shop sells tins of paint in 2 litre and 5 litre cans. The manager checks the amount of paint he
has in stock, and finds that there are 500 cans altogether. These cans hold a total of 1420 litres of
paint. By forming and solving a pair of simultaneous equations, find the number of each size of
can in stock.
Answers
Answer:
360 of 2 liter cans and 140 of 5 liter cansStep-by-step explanation:
Let the number of 2 liter cans be x and 5 liter cans be y.
Number of cans:
x + y = 500Amount of paint:
2x + 5y = 1420Solve the system by elimination, double the first equation and subtract from the second one:
2x + 5y - 2x - 2y = 1420 - 2*5003y = 420y = 420/3y = 140Find x:
x + 140 = 500x = 500 - 140x = 360I’m really confused on number 3 please helppp
Answers
Answer:
See explanation
Step-by-step explanation:
a. Skewed to the right since the tail of the graph is on the right
b. Each bar is 3 values. 7*3=21 values
c. The bars are taller for lower numbers. Hence, the question could be about age. "Who likes to watch cartoons?"
what two numbers that add to 1 but also mulitply to -6
Answers
Answer:
3 and -2
Step-by-step explanation:
3+(-2) = 1
3*(-2) = -6
Answer:
3 and -2
Step-by-step explanation:
Ab= AD and BC=DC
Y=?
Answers
Answer:
y = 63°
Step-by-step explanation:
ABCD is a kite.
The main diagonal BD bisects the opposite angles, thus
∠ DBC = ∠ DBA = 35°
The sum of the 3 angles in Δ BCD = 180° , thus
y = 180° - (35 + 82)° = 180° - 117° = 63°
Can you please help me so I can get a better understanding? h(n)=3n, Find h(6)
Answers
Answer:
18
Step-by-step explanation:
So we have the function:
\(h(n)=3n\)
And we want to find h(6).
To do so, simply substitute 6 for n. In other words:
\(h(n)=3n\\h(6)=3(6)\)
Multiply:
\(h(6)=18\)
So, our answer is 18 :)
Answer:
h(6) = 18
Step-by-step explanation:
To evaluate h(6), substitute n = 6 into h(n) , that is
h(6) = 3(6) = 18
What is the name for wegeners theory that describes how all the continents used to belong to one landmass but randomly moved over time
Answers
The name for Wegener's theory that describes how all the continents used to belong to one landmass but randomly moved over time is "continental drift."
The theory of continental drift, proposed by Alfred Wegener in the early 20th century, suggests that the continents were once part of a single supercontinent called Pangaea and have since drifted apart. According to Wegener's hypothesis, the continents moved over time due to the gradual movement of the Earth's tectonic plates. This movement, known as continental drift, explains the matching geological features found on different continents, such as similar rock formations, fossils, and ancient climate evidence. Although initially met with skepticism, Wegener's theory laid the foundation for the development of plate tectonics, which is now widely accepted in the field of geology.
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Solve the system of equations.
5x – y = 5
5x2 – y = 5
Answers:
(0, 5) and (0, –5)
(1, 0) and (0, –5)
(2, 5) and (1, 0)
(3, 10) and (2, 15)
Answers
Answer:
Option 2: (1, 0) and (0, -5)
Step-by-step explanation:
Let's solve this system of equations using the elimination method.
Start by labelling the two equations.
5x -y= 5 -----(1)
5x² -y= 5 -----(2)
(2) -(1):
5x² -y -(5x -y)= 5 -5
Expand:
5x² -y -5x +y= 0
5x² -5x= 0
Factorise:
5x(x -1)= 0
5x= 0 or x -1= 0
x= 0 or x= 1
Now that we have found the x values, we can substitute them into either equations to solve for y.
Substitute into (1):
5(0) -y= 5 or 5(1) -y= 5
0 -y= 5 or -y= 5 -5
y= -5 or -y= 0
y= 0
Thus, the solutions are (0, -5) and (1, 0).
you are buying a new tv. the 29-in tv you are interested in is 20 in. high. how many inches wide is the tv
Answers
Explanation
Use Pythagoras' theorem. The diagonal is a hypotenuse(29 in tv) , so
20^2+ L^2= 29^2
Find csc, cot0, and sin 0, where is the angle shown in the figure.Give exact values, not decimál approximations.
Answers
Explanation:
Given that:
\(\begin{gathered} \theta=? \\ Hypotenuse=6 \\ Adjacent=5 \end{gathered}\)We will obtain the following trigonometric identities as shown below:
\(\begin{gathered} csc\theta=\frac{1}{\sin\theta} \\ \text{Using Pythagoras Theorem, we will obtain the missing side:} \\ a^2=c^2-b^2 \\ a^2=6^2-5^2 \\ a^2=36-25 \\ a^2=11 \\ a=\sqrt{11} \\ a=opposite=\sqrt{11} \\ \\ \sin\theta=\frac{opposite}{hypotenuse}=\frac{\sqrt{11}}{6} \\ csc\theta=\frac{1}{\frac{\sqrt{11}}{6}}=\frac{6}{\sqrt{11}} \\ csc\theta=\frac{6}{\sqrt{11}} \end{gathered}\)Then,
\(\begin{gathered} cot\theta=\frac{1}{\tan\theta} \\ \tan\theta=\frac{opposite}{adjacent}=\frac{\sqrt{11}}{5} \\ cot\theta=\frac{1}{\frac{\sqrt{11}}{5}} \\ cot\theta=\frac{5}{\sqrt{11}} \end{gathered}\)Then,
\(\sin\theta=\frac{\sqrt{11}}{6}\)130 adults with gum disease were asked the number of times per week they used to floss before their diagnoses. The
(incomplete) results are shown below:
Cumulative Frequency
# of times floss per week
0
1
12
Frequency
12
21
13
Relative Frequency
0.0923
0.1615
0.1
0.1385
33
2
46
64
20
0.1538
100
0.1308
117
0.1
130
Answers
Answer:
a. The answers obtained are as follows:
Frequency for flossing 7 times per week = 24
Relative frequency for flossing 4 times per week = 0.1231
Cumulative Frequency at flossing 1 time per week = 22
b. The Cumulative Relative Frequency at flossing 7 time per week is 100%.
Step-by-step explanation:
Note: This question is not complete and the data in it are merged together. The complete question is therefore provided with the sorted data before answering the question. See the attached pdf file for the complete question.
The explanation to the answers is now provided as follows:
a. Complete the table (Use 4 decimal places when applicable)
Note: See part a of the attached excel for the complete table (answers are in bold red color)
Frequency is the rate at which something or an event occurs in a particular sample.
Since we already have frequency for others flossing times per week and we have 130 adults as the sample, the frequency for flossing 7 times per week is calculated by deducting the frequencies of others from 130 as follows:
Frequency for flossing 7 times per week = 130 – 10 – 12 – 14 – 18 – 16 – 21 – 15 = 24
Relative Frequency refers to the fraction of times an event occurs. The relative frequencies in this question are calculated by dividing each frequency by the total number of adults in the sample, i.e. 130. The relative frequency for flossing 4 times per week is therefore calculated as follows:
Relative frequency for flossing 4 times per week = Frequency for flossing 4 times per week / Total number of adults in the sample = 16 / 130 = 0.1231
Cumulative Frequency is calculated by adding the current frequency to the previous Cumulative Frequency. The Cumulative Frequency at flossing 1 time per week is therefore calculated as follows:
Cumulative Frequency at flossing 1 time per week = Cumulative Frequency at flossing 0 time per week + Frequency at flossing 1 time per week = 10 + 12 = 22
b. What is the cumulative relative frequency for flossing 7 times per week? %
Note: See part b of the attached excel for the complete table (answer is in bold red color)
The cumulative relative frequency refers to the accumulation of the previous relative frequencies.
Cumulative Relative Frequency is calculated by adding the current relative frequency to the previous Cumulative Relative Frequency. It should be noted that the first cumulative relative frequency equal to the first relative frequency.
The Cumulative Relative Frequency at flossing 7 time per week is therefore calculated in the attached excel file as follows:
Cumulative Relative Frequency at flossing 1 time per week = Cumulative Relative Frequency at flossing 6 times per week + Relative Frequency at flossing 7 times per week = 0.8154 + 0.1846 = 1.0000
Since the question indicates that the Cumulative Relative Frequency at flossing 7 time per week should be stated in percentage term, we therrefore have:
Cumulative Relative Frequency at flossing 7 time per week = 1.0000 * 100 = 100%.
PLEASE HELP
this is due by tomorrow :O
Answers
Answer:
Your answer is 15 which is your rate of change/slope
Step-by-step explanation:
To calculate rate of change/slope which also means the gradient we need any two points from the figure for the formula
\(m=\frac{y_2-y_1}{x_2-x_1}\)
I took the points (2,30) and (4,60)
so we put the values in our formula
\(m=\frac{60-30}{4-2}\)
\(m=\frac{30}{2} \\m=15\)
find the slope of the line passing through the points using the slope formula
(5, 0), (2, 4)
Answers
The slope formula is m= y2-y1/x2-x1.
m= 4-0/2-5
m=4/-3
Therefore, 4/-3 is the slope.
Answer:
The first option, incase something happens to the president, they’re next in line.
Step-by-step explanation:
10. Match each set of coordinates for a preimage with the coordinates of its image after
applying the vector (3, -8). Indicate a match by writing a letter for a preimage on the line
in front of the corresponding image.
A. (1, 1); (10, 1); (6,5)
B. (0,0); (3,8); (4,0); (7,8)
C. (3,-2); (3, 4); (6,5)
D. (-2, 2), (2, 2); (-4, 0); (4,0)
(6, -10); (6, –4): (9, -3) ___
(1, -6); (5, -6); (-1, -8); 7.-8) ____
(4, -7); (13, 7); 9, -3) ____
(3,-8); (6,0); 7,-8): (10,0) ____
Answers
Answer:
mathematics and then B. and if you
Help me please I’m stuck
Answers
Answer:
i woould say but
a
1. A Better Golf Tee? An independent golf equipment testing facility compared the difference in the performance of golf balls hit off a brush tee to those hit off a 4 yards more tee. A'Air Force One D
Answers
Overall, the testing facility concluded that the brush tee would be a better option for golfers looking to improve their drives.
An independent golf equipment testing facility compared the difference in the performance of golf balls hit off a brush tee to those hit off a 4 yards more tee. A'Air Force One DFX driver was used to hit the balls, with an average swing speed of 100 miles per hour. The testing facility wanted to determine which tee would perform better and whether it would be beneficial to golfers to switch to a different tee.
The two different types of tees were the brush tee and the 4 Yards More tee. The brush tee is designed with bristles that allow the ball to be suspended in the air, minimizing contact between the tee and the ball. This design is meant to reduce spin and allow for longer and straighter drives. On the other hand, the 4 Yards More tee is designed to be more durable than traditional wooden tees, and its design is meant to create less friction between the tee and the ball, allowing for longer drives.
The testing results showed that the brush tee was able to create longer and straighter drives than the 4 Yards More tee. This is likely due to the brush tee's design, which allows for less contact with the ball, minimizing spin and creating longer and straighter drives.
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If an automobile slows from 26 m/s 18 m/s in the period of 4.0 s what was the average acceleration
Answers
Answer: -2
Step-by-step explanation:
You have $1200 for your trip to the beach. You estimate that it will cost $160 a day for food, entertainment and hotel, plus $230 round trip airfare. Write an inequality that can be used to determine the maximum number of days you can stay at the beach. Clearly indicate what the variable represents. Then Solve the inequality, and interpret your answer in a complete sentence.
Answers
Explanation
Step 1
let x represents the numbers of days you can stay at the beach
then,
You estimate that it will cost $160 a day for food, entertainment and hotel, plus $230 round trip airfare.
so
\(\text{total}=230+160x\)but, you have only $1200, so the total needs to be smaller or equal than 1200
\(230+160x\leq1200\rightarrow Inequality\)Step 2
solve the inequality
\(\begin{gathered} 230+160x\leq1200\rightarrow Inequality \\ subtract\text{ 230 in both sides} \\ 230+160x-230\leq1200-230 \\ 160x\leq970 \\ \text{divide both sides by 160} \\ \frac{160x}{160}\leq\frac{970}{160} \\ x\leq6.0625 \\ \text{rounded} \\ x\leq6 \end{gathered}\)it means you can stay maximum 6 days
I hope this helps you
if you help I will mark brainliest! Thank you
Answers
Answer: 8.94
Step-by-step explanation:
each side is the \(\sqrt{20}\) so multiply that by 2 and you will have 8.94
help please 50 points!
Answers
x=-13
x=2
Answer:
Solution given:
5-2x=\(\sqrt{2x²+x-1}-x\)
keep square root alone
5-2x+x=\(\sqrt{2x²+x-1}\)
5-x=\(\sqrt{2x²+x-1}\)
squaring both side
(5-x)²=2x²+x-1
25-10x+x²=2x²+x-1
2x²+x-1-25+10x-x²=0
x²+11x-26=0
doing middle term factorisation
for this
coefficient of first and last terms should be multiplied
here
1*26=26
factor product
26=2*13*1
remember that check the sigh of last term
in here it is - so
we need to get 11 by subtracting factor of 26
we get
13-2=11
keep 13-2 value in place of 11
x²+(13-2)x-26
now
distribute
x²+13x-2x-26=0
take common from each two term
x(x+13)-2(x+13)=0
(x+13)(x-2)=0
either
x=-13
or.x=2
Answer:
A and B
Step-by-step explanation:
we would like to solve the following equation:
\( \rm\displaystyle 5 - 2x = \sqrt{ {2x}^{2} + x - 1 } - x\)
to do so isolate -x to the left hand side and change its sign:
\( \rm\displaystyle 5 - 2x + x = \sqrt{ {2x}^{2} + x - 1 } \)
simplify addition:
\( \rm\displaystyle 5 - x = \sqrt{ {2x}^{2} + x - 1 } \)
square both sides:
\( \rm\displaystyle (5 - x {)}^{2} = (\sqrt{ {2x}^{2} + x - 1 } {)}^{2} \)
simplify square of the right hand side:
\( \rm\displaystyle (5 - x {)}^{2} = {2x}^{2} + x - 1 \)
use (a-b)²=a²-2ab+b² to expand the left hand side:
\( \rm\displaystyle {x}^{2} - 10x + 25= {2x}^{2} + x - 1 \)
swap the equation:
\( \rm\displaystyle {2x}^{2} + x - 1 = {x}^{2} - 10x + 25\)
isolate the right hand side expression to the left hand side and change every sign:
\( \rm\displaystyle {2x}^{2} + x - 1 - {x}^{2} + 10x - 25 = 0\)
simplify:
\( \rm\displaystyle {x}^{2} + 11x - 26= 0\)
rewrite the middle term as 13x-2x:
\( \rm\displaystyle {x}^{2} + 13x - 2x - 26= 0\)
factor out x:
\( \rm\displaystyle x({x}^{} + 13)- 2x - 26= 0\)
factor out -2:
\( \rm\displaystyle x({x}^{} + 13)- 2(x + 13)= 0\)
group:
\( \rm\displaystyle (x- 2)(x + 13)= 0\)
by Zero product property we obtain:
\( \displaystyle \begin{cases}x- 2 = 0\\ x + 13= 0 \end{cases}\)
solve for x:
\( \displaystyle \begin{cases}x = 2\\ x = - 13 \end{cases}\)
to check for extraneous solutions we can define the domain of equation recall that a square root of a function is always greater than or equal to 0 therefore
\( \rm\displaystyle 5 - x \geq0\)
solve the inequality for x:
\( \rm\displaystyle x \leqslant 5\)
since 2 and -13 is less than 5 both solutions are valid for x hence,
\( \displaystyle \begin{cases}x _{1} = 2\\ x_{2} = - 13 \end{cases}\)
and we're done!