Answer:
Step-by-step explanation:
If you're asking for the equation of a line that goes through (1,-5) and is perpendicular to y=18x+26 here's what you do.
1. find the slope of the new line by taking the negative reciprocal of the slope of the first line ([tex]-\frac{1}{18}[/tex])
2. plug in the point (1,-5) and the new slope into the point slope form equation
[tex]y_{2} -y_{1}=m(x_{2}-x_{1})[/tex]
3.Now that you have y-(-5)= -1/18(x-1) simplify
3.a y-(-5)= -1/18x + 1/18
3.b y=-1/18x - 89/18
4. final equation you get is y = -1/18 - 89/18
If A and B are two points in the plane , the perpendicular bisector of AB is the set of all points equidistant from A and B ? A True or False
Answer:
The correct option is A. The given statement is true.
Step-by-step explanation:
Given statement: If A and B are two points in the plane , the perpendicular bisector of AB is the set of all points equidistant from A and B.
Let a line is perpendicular bisector of AB at point D and C be a random point of perpendicular bisector.
In triangle ACD and BCD,
[tex]AD=BD[/tex] (Definition of perpendicular bisector)
[tex]\angle ADC=\angle BDC[/tex] (Definition of perpendicular bisector)
[tex]DC=DC[/tex] (Reflexive property)
By SAS postulate of congruence,
[tex]\triangle ACD\cong \triangle BCD[/tex]
The corresponding parts of congruent triangles are congruent.
[tex]AC\cong BC[/tex] (CPCTC)
[tex]AC=BC[/tex]
The distance between A to C and B to C are same. So, the set of all points on perpendicular bisector are equidistant from A and B.
The given statement is true. Therefore the correct option is A.
Final answer:
The statement is True because the perpendicular bisector is defined as the line that divides a line segment into two equal parts at its midpoint and is perpendicular to the segment, making all points on it equidistant from both endpoints of the segment.
Explanation:
The statement 'If A and B are two points in the plane, the perpendicular bisector of AB is the set of all points equidistant from A and B' is True. The definition of a perpendicular bisector is that it is a line which is perpendicular to another line segment (AB in this case) and divides it into two equal parts at its midpoint. Therefore, any point on the perpendicular bisector is equidistant from points A and B, which is a direct consequence of the definition.
This is further supported by Theorem 11, which states that if two equal lines in a plane are erected perpendicular to a given line, the line joining their extremities makes equal angles with them and is bisected at right angles by a third perpendicular erected midway between them, ensuring that any point on this third perpendicular (the perpendicular bisector) is equidistant from A and B.
The volume of a rectangular prism is given by the function V = lwh. Which statement is true?
A The volume of the prism depends on the product of only the length and the width.
B The volume of the prism depends on the product of only the length and the height.
CThe volume of the prism depends on the product of the length, the width, and the height.
D The volume of the prism depends on the product of only the width and the height.
Answer:
CThe volume of the prism depends on the product of the length, the width, and the height.
Step-by-step explanation:
V = lwh
Volume is the product of l, which is length, w which is width and h which is height
Answer:
C.The volume of the prism depends on the product of the length, the width, and the height.
Step-by-step explanation:
If the volume of a rectangular prism is given by the function V = lwh, the volume of the prism depends on the product of the length, the width, and the height.
What is the scale factor of 24 18
Answer:
1.3 repeating or 4/3
Step-by-step explanation:
if you take 24 and divide it by 18 this is the answer you receive
Evaluate In 5.
a) 0.62
b) 0.70
c) 1.61
d) 1.95
Answer:
C
Step-by-step explanation:
The actual answer is 1.60943
When you round it to the hundredths place, the answer becomes 1.61
C
Answer:
The correct answer is C. 1.61.
Step-by-step explanation:
Paul can purchase 3 muffins for $1.35. At this rate what is the cost of 10 muffins? A. $3.75. B. $4.00. C. $4.25. D. $4.50.
Answer: D. $4.50.
Step-by-step explanation: You need to find the individual cost of 1 muffin. To do this, divide 1.35 by 3. 1.35/3=0.45. Each muffin costs $0.45. Multiply this by 10 to get $4.50 for 10 muffins.
Help?????????????????????
Answer:
B. Graph B
Step-by-step explanation:
A graph with no solutions is one where the lines never intersect.
In Graph A, you have a solution at about (-2, 2).
In Graph C, all real numbers are solutions.
The standard diameter of a golf ball is 42.67 mm. A golf ball factory does quality control on the balls it manufactures. Golf balls are randomly measured to ensure the correct size. One day, an inspector decides to stop production if the discrepancy in diameter is more than 0.002 mm. Which function could represent this situation?
Answer:
The function that could represent the situation is f(x) = |x - 42.67| > 0.002, where x and f(x) are in mm.Explanation:
That the discrepancy in diameter is more than 0.002 mm means that the difference between the measured diameter of a ball and the standard diameter is greater than 0.002.
That is:
Difference between the measured diameter and the standard diameter = absolute value of X - 42.67 mm = |X - 42.67 mm|Greater than 0.002 mm ⇒ |x - 42.67 mm| > 0.002 mmSo, the function is f(x) = |x - 42.67| > 0.002, where x and f(x) are in mm.
Answer:
First one is B f(x) = (42.67-x)
Second is 42.6668 mm, 42.673 (options b and d)
Hope this helps
Checked on edge
The youngest person in the company is 22 years old. The range of ages is 37 years. How old is the oldest person in the company?
[tex]\large\boxed{59\,\text{years old}}[/tex]
Step-by-step explanation:In this question, it's asking you to figure how old the oldest person in the company is.
To solve this, we would need to gather some important information from the question.
Important information:
Youngest person is 22 years old.The range is 37.With the information above, we can get closer to our answer.
We need some prior knowledge to solve this. The "range" is the highest number subtracted by the lowest number.
This means that the the 22 was already subtracted to get 37.
What we would do is reverse to solution and add 22 to 37 to get our highest number (oldest person).
[tex]37+22=59[/tex]
When you add them together, you should get 59.
This means that the oldest person in the company is 59 years old.
I hope this helped you out.Good luck on your academics.Have a fantastic day!Answer:
Age of oldest person = 59 years
Step-by-step explanation:
Points to remember
Range of a data set is the difference between smaller value and larger value value in the set.
It is given that, the youngest person in the company is 22 years old. The range of ages is 37 years.
To find the age of oldest person
Range = 37 years
Youngest age = 22 years
Range = oldest age - youngest age
oldest age = range + youngest age
= 37 + 22
= 59
Age of oldest person = 59 years
PLEASE HELP!
Jenny likes to paint. She estimates the number of paintings she completes using the function P of w equals one half times w plus one, where w is the number of weeks she spends painting. The function J(y) represents how many weeks per year she spends painting. Which composite function would represent how many paintings Jenny completes in a year?
Options:
Answer:
First Image: [tex]P(J(y))=\frac{1}{2}J(y)+1[/tex]
Step-by-step explanation:
We have the following functions:
[tex]P(w)=\frac{1}{2}w+1[/tex]
Here, P(w) represents the number of paintings Jenny completes in w weeks.
J(y) = Number of weeks per year.
Since, J(y) is the number of weeks spent per year in painting, in order to calculate the paintings completed in a year we substitute w = J(y) in the above equation. So the equation becomes:
[tex]P(J(y))=\frac{1}{2}J(y)+1[/tex]
This composite function would represent number of paintings Jenny completes in a year.
p[J(y)] = 1/2 . J(y) + 1 or the first image is the correct answer!
I took the test and ended up getting it right.
Good luck! I hope you have an awesome day!
Shishir bought 4000 orange at 70 paisa each. But 400 of them were rotten. He sold 2000 oranges at 90 paisa each.If he plans to make a profit of RS 200 , at what rate must he sell the rest of the oranges ?
Answer:
He needs to sell the rest of the oranges at 75 paisa each.
Step-by-step explanation:
Consider the given information that, Shishir bought 4000 orange at 70 paisa each.
Note: 1 rupees = 100 paisa
Thus, 70 paisa = 70/100 rupees = 0.70 rupees
Therefore, the cost price of 4000 oranges is:
4000×0.70 rupees = 2800 rupees
The selling price of 2000 oranges is:
2000×0.90 rupees = 1800 rupees
The number of oranges now Shishir have:
4000 - 2000 - 400 = 1600
He wants to make a profit of RS 200. Thus the selling price of 4000 oranges should be:
2800 rupees + 200 rupees = 3000 rupees
He earned 1800 rupees by selling 2000 oranges at 90 paisa. So, the remaining amount that he needs to make with 1600 oranges is:
3000 rupees - 1800 rupees = 1200 rupees
Therefore, the cost of one orange is:
1600 oranges = 1200 rupees
1 orange = 1200/1600 rupees
1 orange = 0.75 rupees
Hence, he needs to sell the rest of the oranges at 75 paisa each.
simplify or reduce the answer to 1/4+2/7+1/2
Answer: 29/28
Step-by-step explanation:
To add fractions we have to calculate the Least Common Denominator of the denominators. Then we have to change each fraction (using equivalent fractions) to make their denominators the same as the Least Common Denominator. Then we can add (or subtract) the fractions.
LCD (4,7,2)= 4·7 = 28
1/4 = 7/28
2/7 = 4·2/28 = 8/28
1/2 = 14/28
Since the fractions have the same denominator we can add them
7/28 + 8/28 + 14/28 = (7+8+14)/28 = 29/28
[tex]\textit{\textbf{Spymore}}[/tex]
Can someone please help??
The table shows the number of animals ,by type ,at the petting zoo.
Only statement B is true, so you would select that as the answer.
We can check if statement A is true by finding the ratio of cows to all animals, which we do by finding the total number of animals, 5 + 3 + 2 + 6 = 16.
Then we can say that the ratio of cows to all animals is 2:16, which simplifies to 1:8, so statement A is false.
Statement B is just another way of saying that the ratio of rabbits to all animals is 3:8, so we can see if this is true by finding the ratio of rabbits to all animals. There are 6 rabbits, so it would be 6:16, which simplifies to 3:8. This means that statement B is true.
I hope this helps! Let me know if you have any questions :)
Write as an algebraic expression and then simplify if possible:
Seven less than twice a number n.
Answer:
2n-7
Step-by-step explanation:
"7 less than twice a number n"
is the same as
"7 less than (twice a number n)".
I put ( ) around that one part because I want you to focus on that part first.
Twice a number n means 2 times that number n or 2n.
So now we have
"7 less than 2n".
This means 2n-7.
Find an explicit rule for the nth term of the sequence. 7, 21, 63, 189, ...
Answer:
[tex]7 \times {3}^{n - 1} [/tex]
Step-by-step explanation:
using form:
[tex]a \times {r}^{n - 1} [/tex]
where a: starting number
where r: common ratio (in this case each next term is 3 times previous term)
The nth term of the sequence 7, 21, 63, 189,... is given by the explicit rule an = 7 × 3(n-1), which applies to a geometric sequence with a common ratio of 3.
Explanation:To find an explicit rule for the nth term of the sequence 7, 21, 63, 189,..., we notice that each term is three times the previous term. This indicates that the sequence is geometric with a common ratio of 3. The first term of the sequence (a1) is 7.
To find the nth term of a geometric sequence, the formula is an = a1 × r(n-1) where r is the common ratio. Plugging in the values for our sequence, we get the nth term as an = 7 × 3(n-1).
This gives us the explicit rule for the nth term of the given sequence, which allows us to calculate any term in the sequence based on its position, n.
Where an represents the nth term of the sequence and an-1 represents the previous term.
For example, if we want to find the 5th term of the sequence, we can use the formula:
a5 = a4 * 3 = 189 * 3 = 567
Erin and Jamie are collecting shells while the tide is out. Erin has 27 shells, and she has 9 more than Jamie. Write and equation for this situation and find how many shells Jamie has collected.
A. 27 = j + 9; Jamie collected 36 shells
B. 27 + 9 = j; Jamie collected 36 shells
C. 27 = j + 9; Jamie collected 18 shells
D. 27 = j – 9; Jamie collected 36 shells
Answer:
C.
Step-by-step explanation:
If Erin has 9 more shells than Jamie, then 27 minus 9 would be equivalent to the amount of shells Jamie has.
This can be represented by:
[tex]27-9=j[/tex]
Which can be rewritten as:
[tex]27=j+9[/tex]
by adding 9 to both sides.
To solve, subtract 9 from 27.
[tex]27-9=18[/tex]
Jamie has collected 18 shells.
Answer:
C. 27=j+9; Jamie collected 18 shells.
Step-by-step explanation:
First, you do is switch sides.
[tex]\displaystyle j+9=27[/tex]
Then, you subtract 9 from both sides.
[tex]\displaystyle j+9-9=27-9[/tex]
Simplify, to find the answer.
[tex]\displaystyle 27-9=18[/tex]
Therefore, Jamie got collected of 18 shells.
[tex]\huge \boxed{18}[/tex], which is our answer.
The correct answer is C.
A dentist wants to find out how often her patients floss their teeth. Which samples are biased? Check all that apply. all her patients patients with no cavities patients younger than 18 every 20th patient every patient with braces
Answer:
all her patients patients with no cavities
patients younger than 18
every patient with braces
Step-by-step explanation:
when a sample is selected in a manner that some elements, in this case patients, of population have higher or lower probability of sampling then that sample is biased.
From given case, all the following are biased samples
all her patients patients with no cavities
patients younger than 18
every patient with braces
because they are non-random sample of a population in which all other elements were not equally likely to be chosen!
The dentist should avoid biased sampling methods.
Explanation:The biased samples in this case would be:
1. All her patients: This would only include the dentist's current patients, which may not be representative of the entire population.
2. Patients with no cavities: This would only include a specific subset of patients who do not have cavities, which may not be representative of the entire population.
3. Patients younger than 18: This would only include patients below the age of 18, which may not be representative of the entire population.
It is important to have a random and representative sample in order to make accurate conclusions about the population's flossing habits.
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the box plot shows a set of test scores. which statement is correct?
A box plot displays the distribution of a set of data values. To determine the correct statement, analyze its components: minimum, first quartile, median, third quartile, and maximum.
Explanation:A box plot, also known as a box-and-whisker plot, is a type of graph that displays the distribution of a set of data values. It shows the minimum, first quartile, median, third quartile, and maximum values of the data set.
To interpret the box plot and determine which statement is correct, you need to analyze its components:
Minimum: The smallest value in the data set.First Quartile: The median of the lower half of the data.Median: The middle value of the data set.Third Quartile: The median of the upper half of the data.Maximum: The largest value in the data set.By analyzing the position and spread of these values in the box plot, you can determine which statement is correct.
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Which line contains the point (1, -3)?
1. 4x-y=7 4 x − y = 7
2. 2x+5y=4 2 x + 5 y = 4
3. 7x-y=15 7 x − y = 15
4. x+5y=21
Answer:
4x - y = 7Step-by-step explanation:
Put the values of x = 1 and y = -3 to the equations of a line and check the equality:
1. 4x - y = 7
4(1) - (-3) = 4 + 3 = 7 CORRECT
2. 2x + 5y = 4
2(1) + 5(-3) = 2 - 15 = -13 ≠ 7
3. 7x - y = 15
7(1) - (-3) = 7 + 3 = 10 ≠ 15
4. x + 5y = 21
1 + 5(-3) = 1 - 15 = -14 ≠ 21
Graph the line with slope 2 and y-intercept-3.
Answer:
look at the attached photo
Step-by-step explanation:
- figure out slope intercept form and write an equation
- draw a graph
- go up positive two on the y axis and to the right one and mark the spot
- mark -3 on the y axis
- use a ruler t connect the two points
Solve the system -10=-2y+x 6y=3x+11
Answer: No Solutions exist
Step-by-step explanation:
We have the following system of equations
[tex]-10=-2y+x[/tex]
[tex]6y=3x+11[/tex]
Rewriting the second equation we have:
[tex]-11=-6y+3x[/tex]
Now we multiply the first equation by -3 and add it to the second equation
[tex]30=6y-3x[/tex]
[tex]-11=-6y+3x[/tex]
---------------------------------
[tex]19=0[/tex]
Equality is not satisfied. Then the system has no solution
What are the solutions to the system of equations?
{ Y=2x^2-6x+3
{ y=x-2
Answer:
Step-by-step explanation:
x=1, y=-1
Answer:
see explanation
Step-by-step explanation:
Given the 2 equations
y = 2x² - 6x + 3 → (1)
y = x - 2 → (2)
Since both equations express y in terms of x we can equate the right sides, that is
2x² - 6x + 3 = x - 2 ( subtract x - 2 from both sides )
2x² - 7x + 5 = 0 ← in standard form
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 2 × 5 = 10 and sum = - 7
The factors are - 2 and - 5
Use these factors to split the x- term
2x² - 2x - 5x + 5 = 0 ( factor the first/second and third/fourth terms )
2x(x - 1) - 5(x - 1) = 0 ← factor out (x - 1) from each term
(x - 1)(2x - 5) = 0
Equate each factor to zero and solve for x
x - 1 = 0 ⇒ x = 1
2x - 5 = 0 ⇒ 2x = 5 ⇒ x = [tex]\frac{5}{2}[/tex]
Substitute these values into (2) for corresponding values of y
x = 1 : y = 1 - 2 = - 1 ⇒ (1, - 1)
x = [tex]\frac{5}{2}[/tex] : y = [tex]\frac{5}{2}[/tex] - 2 = [tex]\frac{1}{2}[/tex]
Solutions are (1, - 1) and ( [tex]\frac{5}{2}[/tex], [tex]\frac{1}{2}[/tex] )
Can you help me with this question?
I got quite confused as to what to do here.
The teacher didn't really explain about the angle of depression
Answer: 359 ft
Step-by-step explanation:
Whenever you have a problem like this, you must first make an assumption that the building (in this case the lighthouse) is perpendicular to the ground (or sea). This allows you to create a right triangle (see attached image).
The angle of depression is the angle from an imaginary perpendicular line passing through the top of the building. Since that imaginary line is parallel to the ground (or sea), you can use alternate interior angles to place that angle in the triangle.
NOTE: BOTH angle of elevation and angle of depression are placed in the lower corner of the triangle. Don't let the names confuse you!
Now you can use trigonometry to solve ....
In the given problem, we have the side OPPOSITE of the given angle (24°) and need the side ADJACENT to the angle, so we will use tan to solve for x.
[tex]tan\ \theta=\dfrac{opposite}{adjacent}\\\\\\tan\ 24^o=\dfrac{160}{x}\\\\\\\rightarrow x=\dfrac{160}{tan\ 24^o}\\\\\\\rightarrow x=359.4\\\\\\\rightarrow x\approx 359[/tex]
4. Cindy bought a car for $21.330. A few years later, she sold the car for $19,700. Find the percent of change in the value
(SHOW WORK)
Answer:
-7.64%
Step-by-step explanation:
1. Find out how much the car went down in value.
21,330 - 19,700 = 1,630
2. Calculate how much 1% of the original value ($21,330) was. One percent is 1/100, which is .01 when divided.
21,330 × .01 = 213.3
3. Since we now know 1% is equal to $213.30 we can divide $1,630 by $213.30. Doing this will show us how many 1%s are in 1,630.
1,630/213.30 = 7.64181903
4. There are 7.64181903 1%s in 1,630. Because the car's value went down by 1,630, this also means it went down by 7.64181903% We will round this to the nearest hundredth for simplicity's sake.
7.64181903 → 7.641 one is less than 6 so we will round down → 7.64
5. The car decreased by 7.64% in value. This will be written as -7.64% because a decrease is negative.
Answer:
-7.64%
Step-by-step explanation:
Number 28 ignore the bubbled in answer
Answer:
y = -7x+34
Step-by-step explanation:
We have 2 points, so we can find the slope
m = (y2-y1)/(x2-x1)
= (6--1)/(4-5)
= (6+1)/(4-5)
= 7/-1
= -7
We can use point slope form to make an equation
y-y1 = m(x-x1)
y--1 = -7(x-5)
y+1 = -7(x-5)
Distribute
y+1 = -7x+35
Subtract 1 from each side
y+1-1 = -7x+35-1
y = -7x+34
what is the simplest fprm of x^2+5x-6/x^2+9x+18
Answer:
x - 1\x + 3
Step-by-step explanation:
Factoring quadratic expressions with a Leading Coefficient of 1 → In the first equation, you have to find two numbers that when differed to 5, they also multiply to 6, and those numbers are 1 and 6. Now, the tough part for you might be figuring out which term gets which sign. Well, if you look at your MIDST term [5], you would know that the negative symbol goes to 1 [-1] and the positive symbol goes to 6, so your numerator is [x - 1][x + 6]. Now, for the second equation, it is applied the same way, but in this case, we need two numbers that when added to 9, they also multiply to 18, and those numbers are 3 and 6, and automatically receive positive symbols, so your denominator is [x + 3][x + 6]. Now that we have our denominator and numerator, we now set it up: [x - 1][x + 6]\[x + 6][x + 3]. What do you see that is... MAGIC--AL? That is correct! The factors x - 6 neutralize each other and are left with x - 1\x + 3.
To be honest, if you had posted quadratic expressions with Leading Coefficients greater than 1, that would be a little bit more tough for you, meaning taking extra steps further, but if you post one in the future, it will be there to assist you because as always...,
I am joyous to assist anyone at any time.
where is the tie????? please help this is extra credit and I can't find it :(
Answer:
I'm not quite sure because its not clear enough, but, it might be on the left side on the green pillow.... What game is this though?
What is the volume of a cube with a length of 10 cm width of 5 cm and a height of 8 cm
Answer:
400cm^3
Step-by-step explanation:
Volume = length * height * width
Volume = 5 * 8 * 10 = 400 cm^3
Given the system of equations presented here:
4x + y = 4
2x + 6y = 24
Which action creates an equivalent system that will eliminate one variable when they are combined?
A.Multiply the first equation by -4 to get -16x - 4y = -16.
B.Multiply the second equation by -4 to get - 8x - 24y = -96.
C.Multiply the first equation by -2 to get -8x - 2y = -8.
D.Multiply the second equation by -2 to get - 4x - 12y = -48.
Answer:
D.Multiply the second equation by -2to get - 4x - 12y = -48.Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}4x+y=4\\2x+6y=24&\text{multiply both sides by (-2)}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}4x+y=4\\-4x-12y=-48\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad11y=-44\qquad\text{divide both sides by 11}\\.\qquad\qquad y=-4\\\\\text{put the value of y to the first equation:}\\\\4x+(-4)=4\\4x-4=4\qquad\text{add 4 to both sides}\\4x=8\qquad\text{divide both sides by 4}\\x=2[/tex]
Answer:
Multiply the second equation by -2 to get [tex]- 4x - 12y = -48[/tex]
Step-by-step explanation:
[tex]4x + y = 4[/tex]
[tex]2x + 6y = 24[/tex]
To eliminate one variable the coefficient of a variable should be same with opposite sign.
LEts check with each option
Multiply the first equation by -4 to get [tex]-16x - 4y = -16[/tex]
the coefficient of x or y are not same when we compare with second equation
Multiply the second equation by -4 to get [tex]- 8x - 24y = -96[/tex]
the coefficient of x or y are not same when we compare with first equation
Multiply the first equation by -2 to get [tex]-8x - 2y = -8[/tex]
the coefficient of x or y are not same when we compare with second equation
Multiply the second equation by -2 to get [tex]- 4x - 12y = -48[/tex]
The coefficient of x terms are same with different sign when compare with first equation
So when we add first and second equation , the x will get eliminated.
Evaluate the expression when a = 13. 89 + a
will mark brainliest for 1st person
Answer:
102
Step-by-step explanation:
89 + a
Let a=13
89+13
102
The third term of an arithmetic progression is 6 while the sum of the first twelve terms is 282. Find the common difference and the first term
Answer:
d = 5 and a₁ = - 4
Step-by-step explanation:
The n th term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
Given a₃ = 6, then
a₁ + 2d = 6 → (1)
The sum to n terms of an arithmetic sequence is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]
Given [tex]S_{12}[/tex] = 282, then
6 [ 2a₁ + 11d ] = 282 ( divide both sides by 6 )
2a₁ + 11d = 47 → (2)
We can now solve (1) and (2) for d and a₁
Multiply (1) by - 2
- 2a₁ - 4d = - 12 → (3)
Add (2) and (3) term by term
7d = 35 ( divide both sides by 7 )
d = 5
Substitute d = 5 in (1) and solve for a₁
a₁ + 10 = 6 ( subtract 10 from both sides )
a₁ = - 4