Answer:
y = (x + 9)² + 9
Step-by-step explanation:
the equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
given a parabola in standard form : ax² + bx + c : a ≠ 0
the the x-coordinate of the vertex is
[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]
y = x² + 18x + 90 is in standard form
with a = 1, b= 18 and c = 90
[tex]x_{vertex}[/tex] = - [tex]\frac{18}{2}[/tex] = - 9
to find the corresponding y-coordinate substitute x = - 9 into the equation
y = (- 9)² + 18(- 9) + 90 = 81 - 162 + 90 = 9
⇒ y = (x + 9)² + 9 ← in vertex form
HELP PLEASE! WILL GIVE 100 POINTS AND BRAINLY IF CORRECT
Answer:
f(3) = - 1
Step-by-step explanation:
to evaluate f(3) substitute x = 3 into f(x)
f(3) = - [tex]\frac{2}{3}[/tex] × 3 + 1 = - 2 + 1 = - 1
Answer:
f3 = -1
Step-by-step explanation:
to evaluate f(3) substitute x = 3 into f(x)
f(3) = - \frac{2}{3} × 3 + 1 = - 2 + 1 = - 1
How many solutions does the system of equations have?
y= -2x +9
6x + 3y =27
A) one
B) two
C) infinitely many
D) none
The given equations have infinitely many solutions.
What is an equation?An equation is a mathematical statement which equate two algebraic expressions. An equation has an equal to (=) sign in between the expression. If there are two equations ax + by + c = 0 , dx + ey + f = 0 and if [tex]\frac{a}{d}= \frac{b}{e} = \frac{c}{f}[/tex] , then the equations are said to have infinite solutions.How to know how many solutions does the system of equations have ?The given equations are y= -2x +9 and 6x + 3y =27
Comparing with the standard equations we can see that,
a = 2b = 1c = -9d = 6e = 3f = -27∴ [tex]\frac{a}{d} =\frac{2}{6} = \frac{1}{3}[/tex]
∴ [tex]\frac{b}{e} = \frac{1}{3}[/tex]
∴ [tex]\frac{c}{f} = \frac{-9}{-27}= \frac{1}{3}[/tex]
∴ The conditions of [tex]\frac{a}{d}= \frac{b}{e} = \frac{c}{f}[/tex] is satisfied and hence the equations have infinitely many solutions.
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Solve the following equation below ax=15+b
Solve for x.
Answer:
x=15/a+b/a
Step-by-step explanation:
a*x=15+b
you need to move all the variables (a) to one side and to do that you can re-organize it to say
x*a=15+b
to get the answer you need to divide (a) and that gets you your answer,
x=15/a+b/a
Here is your equation:
[tex]ax=15+b[/tex]
You're trying to find x alone. To find a specific variable, you have to do the opposite of what's happening to the variable, which is x in this equation.
In this equation, x is being multiplied by a. That means you have to do the opposite of multiplying, which is dividing by a. To leave x alone, divide both sides by a.
[tex]ax \div a = \frac{15+b}{a}[/tex]
Now that you have divided both sides by a, which leaves x alone, you have:
[tex]x = \frac{15+b}{a}[/tex]
Your answer is [tex]x = \frac{15+b}{a}[/tex]
If you have any questions, feel free to ask in the comments! :)
Roger earns $24 a week mowing lawns. he spends 1/6 of his earnings on lunch and 2/3 of his earnings on music. He saves the rest. how many dollars does Roger save? tell how you found the answer
[tex]\mathsf{Given : Roger\;earns\;24\;Dollars\;a\;Week}\\\\\mathsf{Given : Roger\;spends\;\frac{1}{6}\;of\;his\;Earnings\;on\;Lunch}\\\\\mathsf{\implies Dollars\;he\;spends\;for\;Lunch = (\frac{1}{6} \times 24) = 4}[/tex]
[tex]\mathsf{Given : Roger\;Spends\;\frac{2}{3}\;of\;his\;Earnings\;on\;Music}\\\\\mathsf{\implies Dollars\;he\;spent\;on\;Music = (\frac{2}{3} \times 24) = (2 \times 8) = 16}[/tex]
[tex]\mathsf{Dollars\;remaining\;in\;Roger's\;Pocket\;after\;all\;his\;Spendings = [24 - (16 + 4)]}[/tex]
[tex]\mathsf{Dollars\;remaining\;in\;Roger's\;Pocket\;after\;all\;his\;Spendings = [24 - 20] = 4}[/tex]
Roger saves 4 Dollars!
Roger earns $24 weekly and spends 1/6 on lunch and 2/3 on music. Calculating these expenses, he spends $4 on lunch and $16 on music, totaling $20. Roger saves the remaining $4.
To find out how much Roger saves, we need to calculate these expenses and subtract them from his total earnings.
Amount spent on lunch: 1/6 of $24 = $24 / 6 = $4.Amount spent on music: 2/3 of $24 = $24 * (2/3) = $16.Adding the amounts spent on lunch and music: $4 + $16 = $20.
subtract the total expenses from his total earnings: $24 - $20 = $4.
Therefore, Roger saves $4 after his expenses on lunch and music.
The price of a mango at a fruit stand goes up 5 cents each month. The first month the stand was open, a mango cost $1.25. What will the cost of a mango be in the 25th month?
Answer:
$2.45
Step-by-step explanation:
Let x be the number of months.
We have been given that price of a mango at a fruit stand goes up 5 cents each month. This means that price of mango in dollars after x months will be 0.05x (1 dollar=100 cents).
The first month the stand was open, a mango cost $1.25. This means that cost of mango in the x months after 1st month will be: [tex]1.25+0.05x[/tex]
Now let find the cost of mango in the 25 month by substituting x=24 in our expression because price will increase 24 times after 1st month.
[tex]\text{The cost of a mango be in the 25th month}=1.25+0.05*24[/tex]
[tex]\text{The cost of a mango be in the 25th month}=1.25+1.2[/tex]
[tex]\text{The cost of a mango be in the 25th month}=2.45[/tex]
Therefore, the cost of a mango in the 25th month will be $2.45.
Final answer:
To calculate the cost of a mango in the 25th month, you multiply the 24 intervening months by the $0.05 monthly price increase, which equals $1.20, and add it to the initial cost of $1.25, resulting in a total cost of $2.45.
Explanation:
You want to calculate the cost of a mango in the 25th month if the price increases by 5 cents each month from the initial price of $1.25. To find the cost on the 25th month, we will first find out the total increase in cost after 24 months (since the first month is already at $1.25, we only calculate the increase for the following 24 months). The calculation is 24 months × $0.05 increase per month.
The total increase is:
24 × $0.05 = $1.20.
Add this increase to the initial cost to find the cost on the 25th month:
$1.25 + $1.20 = $2.45.
Therefore, the cost of a mango in the 25th month will be $2.45.
Which graph represents the function
A
B
C
D
Answer:
a , b , c , or d, I t h I n k I t ccon fun sed8nh
The price of a shampoo, cut, and style at the hairstyling salon where you work is $18.00. You generally get a 20% tip from each customer, and the salon owner pays you ¼ of each job's cost. On a typical day, you give shampoos, cuts, and styles to 8 customers. About how much can you expect to earn for yourself on such a day?
Answer:
The amount you would earn is $64.80
Step-by-step explanation:
We know to start that you get 45% of the cost per customer. That's because the customer gives you 20% and you boss gives you 25% (1/4). To find how much that is, multiply it by the cost.
$18 * 45% = $8.10
Now knowing this, we can multiply that amount by the 8 customers per day.
$8.10*8 = $64.80
On a typical day, I can expect to earn $64.80 for myself.
To calculate my earnings for the day, we'll break it down step by step:
Shampoo, cut, and style cost: Each job's cost is $18.00.
Tips: I generally receive a 20% tip from each customer. To calculate the total tip earnings for the day, we multiply the job cost by 0.20 (20%):
Total tips = 8 customers * ($18.00 * 0.20) = 8 * $3.60 = $28.80
Salon owner's payment: The salon owner pays me ¼ of each job's cost. To calculate the total payment from the salon owner for the day, we multiply the job cost by 0.25 (1/4):
Total owner's payment = 8 customers * ($18.00 * 0.25) = 8 * $4.50 = $36.00
My earnings: Finally, to calculate my total earnings for the day, we sum up the tips and the salon owner's payment:
Total earnings = Total tips + Total owner's payment = $28.80 + $36.00 = $64.80
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I need help. See picture:
"Number of solutions to equations challenge"
Answer:
D. P = 15 and Q = 15Step-by-step explanation:
Put the values of P and Q to the equation Px - 45 = Qx + 75:
15x - 45 = 15x + 75 subtract 15x from both sides
-45 = 75 FALSE
In other cases, we get some value x.
Example:
A. P = -45 and Q = -75
-45x - 45 = -75x + 75 add 45 to both sides
-45x = -75x + 120 add 75x to both sides
25x = 120 divide both sides by 25
x = 4.8
10.5714286 lies between what two whole numbers
10.5714286 is larger than 10, but smaller than 11.
The two whole numbers are 10 and 11.
Plz Help I don't understand.
And could you Plz explain how to do it As well.
At the end of 2007-2008 football seasons, 38 super bowl games had been played with the current two football leagues, The American football conference (AFC) and the national football conference (NFC). The NFC won two more games than the AFC. How many games did each conference win?
Answer: AFC won 18 times, NFC won 20 times
============================
N = number of times an NFC team won the superbowl
A = number of times an AFC team won the superbowl
The two unknown numbers (N and A) must add to 38 as there are no other options (either there is an NFC or AFC champion) so N+A = 38
The other equation is N = A+2 because "the NCF won two more games than the AFC"
We can replace the "N" in N+A = 38 with A+2 because N = A+2, meaning that N and A+2 are the same
So,
N+A = 38
A+2+A = 38 ... replace N with A+2; solve for A
2A+2 = 38
2A+2-2 = 38-2
2A = 36
2A/2 = 36/2
A = 18
The AFC won 18 times. Use this value of A to find N
N = A+2
N = 18+2
N = 20
The NFC won 20 times.
As a check, adding up the two counts should get us 38
N+A = 38
20+18 = 38
38 = 38
Answer is confirmed
which of the following is a correct equation for the line passing through the point -3,2 and having a slope m=2/3 check all that apply
Slope-intercept form:
y = mx + b
"m" is the slope, "b" is the y-intercept (the y value when x = 0 or (0,y))
Since you know m = 2/3, plug it into the equation
y = 2/3x + b
To find "b", plug in the point into the equation (-3,2)
y = 2/3x + b
2 = 2/3(-3) + b
2 = -2 + b
4 = b
y = 2/3x + 4
Point-slope form:
y - y₁ = m(x - x₁)
You know:
m = 2/3
(x₁ , y₁) = (-3,2)
Plug this into the equation:
y - y₁ = m(x - x₁)
y - 2 = 2/3(x - (-3))
y - 2 = 2/3(x + 3)
Answer:
2x-3y = =12
y= 2/3x + 4
y-2 = 2/3 (x+3)
Step-by-step explanation:
Vardan thought of a prime three-digit number, all the digits of which are different. What is the last digit, if it is known that the last digit is equal to the sum of the first two digits?
Answer:
Prime number states that a whole number greater than 1 whose only factors are 1 and itself.
For example; 2, 3, 5, 7 ,......
As per the statement: Vardan thought of a prime three-digit number, all the digits of which are different.
Let any three digit prime number Vardan thought is, 437 (all digits 4, 3, and 7 are different).
It is given that: if it is known that the last digit is equal to the sum of the first two digits.
⇒ Sum of first two digit = 4+ 3 = 7 which is equal to the last digit of a 3-digit number 437 i.,e 7.
Therefore, the last digit of a prime three-digit number (i.e 437) is, 7
Ladder You lean a 20 foot ladder against a wall. The base of the ladder is 4 feet from the wall. What angle does the ladder make with the ground?
The ladder with a length of 20 feet makes 1.37° with the ground.
Length of the ladder = 20 feet
Distance of base of the ladder from the wall = 4 feet
What is the Cosine of an angle?The cosine of an angle is the ratio of the adjacent side(to that angle) to the hypotenuse of the right triangle.
Suppose the ladder makes [tex]\theta[/tex] from the ground.
So, [tex]Cos\theta = \frac{4}{20}[/tex]
[tex]Cos\theta = \frac{1}{5}[/tex]
[tex]\theta =Cos^{-1} (\frac{1}{5} )[/tex]
[tex]\theta =Cos^{-1} 0.2[/tex]
[tex]\theta=1.37[/tex]°
Thus, the ladder makes 1.37° with the ground.
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The ladder makes an angle of approximately 76.31 degrees with the ground.
Given:
- The length of the ladder (hypotenuse) is 20 feet.
- The distance from the wall (adjacent side) is 4 feet.
Using the tangent function, we have:
[tex]\[ \tan(\theta) = \frac{\text{opposite side}}{\text{adjacent side}} \][/tex]
Let h be the height the ladder reaches on the wall. Then:
[tex]\[ h^2 + 4^2 = 20^2 \] \[ h^2 = 20^2 - 4^2 \] \[ h^2 = 400 - 16 \] \[ h^2 = 384 \] \[ h = \sqrt{384} \] \[ h = 19.6 \text{ feet (approximately)} \][/tex]
Now we can find the angle [tex]\(\theta\)[/tex]:
[tex]\[ \tan(\theta) = \frac{h}{4} \] \[ \tan(\theta) = \frac{19.6}{4} \] \[ \tan(\theta) = 4.9 \][/tex]
To find the angle [tex]\(\theta\)[/tex], we take the arctangent (inverse tangent) of 4.9:
[tex]\[ \theta = \arctan(4.9) \] \[ \theta \approx 76.31^\circ \][/tex]
Therefore, the ladder makes an angle of approximately 76.31 degrees with the ground.
can someone please help me i am failing my math and am very behind my math grade level can someone explain this to me please
Answer:
The answer to number 7 is -1.25
The answer to number 8 is 1.25
If the area of a square is 625 cm^2 then what is the length of one side of the square
Question
If the area of a square is 625 cm^2 then what is the length of one side of the square
Answer:
Step-by-step explanation:
The sides can be found by taking the square root of the area
√625 =
25 cm
---------------
check
Area = s²
25² = 625
the answer is good
Find all the whole values of a for which the solution of the equation ax = 6 is a whole number.
Answer:
1, 2, 3, 6
Step-by-step explanation:
The given equation is,
[tex]\Rightarrow ax = 6[/tex]
[tex]\Rightarrow x = \dfrac{6}{a}[/tex]
We need to to find all the whole values of a for which the solution of the equation i.e x will be a whole number.
We know that when a number is divided by one of its factor it leaves a remainder of 0 or the result we get is a whole number.
That is why, we need a as one of the factors of 6, i.e 1, 2, 3, 6 in order to get x as a whole number.
Simplify
0.1 (3x - 4y) + 0.7x - 3y.
Answer:
0.1(3x-4y)+0.7x-3y
0.1(3x-4y)+0.7x-3y Distribute 0.1 through the parenthesis
0.3x-0.4y+0.7x-3y Collect the like terms ex.(x,x) (y,y)
(0.3+0.7)x+(-0.4-3)y
↓ ↓
x - 3.4 y
The answer is
X-3.4y
Step-by-step explanation:
The red thermos contains 7 pints of lemonade. The orange thermos contains 4 quarts of lemonade. Which thermos contains more lemonade?
Answer:7 pints is more than 4 quartz
Step-by-step explanation:
One pint is the equivalent to 0.5 quartz.
Three hens can lay 3 eggs in 3 days.How many hens would lay 12 eggs in 12 days?
Answer:
144
Step-by-step explanation:
You just multiply 12x12
Kara is sorting buttons by length for a craft project. The line plot shows the length of each button. If Kara lines up all the 3/4-inch buttons, what would be the total length?
Answer:
2 and 1/4 or 2.25. Both numbers are the same.
Step-by-step explanation:
Hi,
Please see the picture I had to upload in order for this question to be complete. Please also note that Kara has 3 buttons in the 3/4 length. You have to sum up only those in that length and ignore the ones in different lengths.
It is a very simple multiplication, and there are 2 ways to do so. You can use either fractions or integer numbers. See the 2 options below:
3/4 (fractions) = .75 (integer numbers)
Option one - 3 * 3/4 = 9/4 which is represented by 2 and 1/4.
Option two - 3 * .75 = 2.25
Have a good one!
An organization will give a prize to a local artist. The artist will be randomly chosen from among 7 painters, 4 sculptors, and 5 photographers. What is the probability that the artist choosen will be a painter or a photographer?
What is the total amount of sap the trees produced that day?
Each "x" represents one tree that produced that amount of sap in gallons.
To find the total amount of sap produced, add all of the amount of sap produced from each tree
3 trees produced 1/4 gallons of sap
2 trees produced 3/8 gallons of sap
4 trees produced 5/8 gallons of sap
1 tree produced 1 gallon of sap
You can do this:
[tex]\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{3}{8}+\frac{3}{8} +\frac{5}{8}+\frac{5}{8}+\frac{5}{8}+\frac{5}{8}+1[/tex]
[tex]=\frac{3}{4}+\frac{6}{8}+\frac{20}{8}+1[/tex]
[tex]\frac{3}{4}+\frac{26}{8}+1[/tex] Make all the denominators the same
[tex]\frac{6}{8}+\frac{26}{8}+\frac{8}{8}=\frac{40}{8}=5[/tex]
5 gallons
Or you could have done:
[tex](\frac{1}{4} *3)+(\frac{3}{8}*2)+(\frac{5}{8}*4)+(1*1)[/tex]
[tex]=\frac{3}{4}+\frac{6}{8}+\frac{20}{8}+1[/tex]
[tex]\frac{3}{4}+\frac{26}{8}+1[/tex] Make all the denominators the same
[tex]\frac{6}{8}+\frac{26}{8}+\frac{8}{8}=\frac{40}{8}=5[/tex]
5 gallons
Answer:
5 gallons
Step-by-step explanation:
because if u add all togather u get 6/8+26/8+8/8+40/8= It would be 5 Gallons
Which function has a simplified base of 4? f(x) = 2 f(x) = 2 f(x) = 4 f(x) = 4
Answer:
f(x)=2
Step-by-step explanation:
Answer:
f(x) = 4
Step-by-step explanation:
4 is itself the simplified expression and hence can't be simplified further
Hence, f(x) = 4 has a simplified base of 4.
URGENT HOMEWORK!!! MULTIPLE CHOICE! Four bags of flour and three bags of sugar weigh 44 pounds. Six bags of flour weigh 48 pounds. All bags of flour weigh the same, and all bags of sugar weigh the same. What is the ratio of the weight of a bag of flour to a bag of sugar?
a) 2:1 b) 1:2 c) 3:2 d) 2:3
Answer: 4 flour + 3 sugar = 44lbs
6 flour = 48lbs
We can divide 48lbs by 6 bags of flour to get 8lbs per bag of flour.
4 bags of flour multiplied by 8lbs is 32lbs. 44lbs - 32lbs = 12lbs
12lbs divided by 3 bags of sugar = 4lbs per bag of sugar.
The ratio is flour to sugar: 8:4 or 2:1
We create two equations based on the information given: 4F+3S=44 and 6F=48. By solving these equations, we find the weight of a bag of flour is 8 pounds and the weight of a bag of sugar is 4 pounds. Thus, the ratio of weight is 2:1.
Explanation:
We can solve this problem by setting up two equations based on the information given and then solve the equations to find the weights of the bags of flour and sugar. Let's denote the weight of a bag of flour as F and the weight of a bag of sugar as S.
According to the problem, 4 bags of flour plus 3 bags of sugar weigh 44 pounds. So we can write the equation 4F + 3S = 44.The problem also tells us that 6 bags of flour weigh 48 pounds. So we have another equation 6F = 48.From the second equation, we can find that F = 48 / 6 = 8 pounds. Substitute F = 8 into the first equation, we find S = 4 pounds.
Therefore, the ratio of the weight of a bag of flour to a bag of sugar is 8:4 or simplified to 2:1 (option a).
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Is a quadratic sequence (2,3,6,11) arithmetic, geometric, or neither?
Answer:
Neither
Step-by-step explanation:
It's neither. The terms do not differ (which means you add the same number to each term) by any constant amount. (Arithmetic)
The terms do not have a common number that you multiply the present term to get the next term. (Geometric)
So this one is neither.
How do you find a sum of a square root?
You can add two square roots of the numbers if the numbers are the same:
[tex]\sqrt{a}+\sqrt{a}=2\sqrt{a}\\\\n\sqrt{a}+m\sqrt{a}=(n+m)\sqrt{a}\\\\\sqrt{a}+\sqrt{b}=\sqrt{a}+\sqrt{b}[/tex]
Final answer:
To find the sum of square roots, you can add the square roots together if the numbers underneath are the same. If the numbers are different, you cannot simplify them further.
Explanation:
To find the sum of a square root, you need to add the square roots together. However, the numbers under the square roots must be the same. For example, if you have √2 + √2, you can add them to get 2√2. But if you have √2 + √3, you cannot simplify it any further.
Another way to find the sum of square roots is to simplify them using the multiplication property. For example, if you have √2 + 2√2, you can combine them as (1+2)√2 = 3√2.
It is important to note that you can only add square roots with the same number underneath. If the numbers are different, you cannot simplify them further.
As the figure shows Elton runs 500 m to point b first then he turns 110 degrees and runs another 350 m to point c how far is the distance from point a to c
Answer:
658.24 m
Step-by-step explanation:
The figure makes a triangle with vertices abc.
Where ab = 500 m
bc = 350 m
The angle abc = 100°
Using the cosine rule we can find the distance ac.
ac² = 500²+350² - 2×500×350×cos100°
= 372,500 - -60,776.86
= 433,276.86
ac = √433,276.86
= 658.24 m
Billy graphed the system of linear equations to find an approximate solution. y =-7/4 x +5/2 y =3/4 x – 3
Answer:
[tex](2.2,-1.35)[/tex]
Step-by-step explanation:
we have
[tex]y=-\frac{7}{4}x+\frac{5}{2}[/tex] ------> equation A
[tex]y=\frac{3}{4}x-3[/tex] ------> equation B
Remember that
The solution of the system of equation is the intersection point both graphs
Using a graphing tool
see the attached figure
The intersection point is [tex](2.2,-1.35)[/tex]
Final answer:
To find the approximate solution to the system of linear equations, set the equations equal to each other, combine like terms, simplify, solve for x, substitute the value of x back into either equation to find y, and simplify further. The approximate solution is x = 3/2 and y = -1/8.
Explanation:
Given the system of linear equations:
y = -7/4 x + 5/2
y = 3/4 x - 3
Set the two equations equal to each other:
-7/4 x + 5/2 = 3/4 x - 3
Combine like terms:
2x + 5 - 14 = 6 - 12
Simplify:
2x - 9 = -6
Add 9 to both sides:
2x = 3
Divide both sides by 2:
x = 3/2
Substitute the value of x back into either equation to find the value of y:
y = -7/4 * (3/2) + 5/2
Simplify:
y = -21/8 + 20/8
Add the fractions:
y = -1/8
Therefore, the approximate solution to the system of linear equations is x = 3/2 and y = -1/8.
A soccer player ran 180.48 miles in 70.5 days to stay fit. How many miles will he run in 9 days
Final answer:
The soccer player will run 23.04 miles in 9 days.
Explanation:
To find out how many miles the soccer player will run in 9 days, we need to calculate the average number of miles he runs per day. We can do this by dividing the total distance he ran by the number of days.
So, 180.48 miles ÷ 70.5 days = 2.56 miles per day.
Now we can determine how many miles he will run in 9 days by multiplying the average number of miles per day by 9.
So, 2.56 miles per day × 9 days = 23.04 miles.
What is y = -1/4x +4 written in standard form?
[tex]y = -\frac{1}{4}x +4\ /\cdot4\\4y=-x+16\\x+4y=16\\C[/tex]
Answer:
C) x + 4y = 16
Step-by-step explanation:
The standard form of a line is in the form Ax + By = C where A is a positive integer, and B, and C are integers.
As we need all the coefficients to be integers, we have to multiply by 4 on both sides of the equation (that will make the coefficient of x integer). We have to multiply it on both sides because is an equation.
4*y = 4*(-1/4x + 4)
4y = -x + 16
Now we need the x-term to be on the left side of the equation, so we add x on both sides:
x + 4y = -x + 16 + x
x + 4y = 16