Answers
Answer:
Simplifying the equation:
[tex]\frac{2}{3} x - \frac{5}{6} = -\frac{5}{12} x + \frac{1}{4}[/tex]
Grouping like terms:
[tex]\frac{2}{3} x + \frac{5}{12} x= \frac{1}{4} + \frac{5}{6}[/tex]
⇒ [tex]\frac{39}{36} x=\frac{26}{24}[/tex]
Solving for 'x', we have:
⇒ [tex]x=\frac{26}{24}\frac{36}{39}=1[/tex]
For this case we place the terms with "x" on the left side of the equation, and the terms without "x" on the right side:
[tex]\frac {2} {3} x + \frac {5} {12} x = \frac {1} {4} + \frac {5} {6}[/tex]
We add similar terms:
[tex]\frac {24 + 15} {36} x = \frac {6 + 20} {24}\\\frac {39} {36} x = \frac {26} {24}[/tex]
We simplify both sides:
[tex]\frac {13} {12} x = \frac {13} {12}[/tex]
Dividing by [tex]\frac {13} {12}[/tex] on both sides of the equation:[tex]x = 1[/tex]
Answer:
[tex]x = 1[/tex]
Related Questions
what expression is equivalent to 25 X 9y3
Answers
Answer:
D
Step-by-step explanation:
Use exponents property:
[tex]\dfrac{x^a}{x^b}=x^{a-b}[/tex]
1. Note that
[tex]\dfrac{x^9}{x^6}=x^{9-6}=x^3[/tex]
and
[tex]\dfrac{y^3}{y^{11}}=y^{3-11}=y^{-8}=\dfrac{1}{y^8}[/tex]
2. Now
[tex]\sqrt{25}=5\\ \\\sqrt{64}=8\\ \\\sqrt{x^3}=x\sqrt{x}\\ \\\sqrt{\dfrac{1}{y^8}}=\dfrac{1}{y^4}[/tex]
So
[tex]\sqrt{\dfrac{25x^9y^3}{64x^6y^{11}}}=\dfrac{\sqrt{25}\sqrt{x^3}}{\sqrt{64}\sqrt{y^8}}=\dfrac{5x\sqrt{x}}{8y^4}[/tex]
because [tex]x>0,\ y>0[/tex]
Answer: Last option.
Step-by-step explanation:
You need to remember the Quotient of powers property:
[tex]\frac{a^m}{a^n}=a^{(m-n)}[/tex]
Applying this property, we know that:
[tex]\sqrt{\frac{25x^9y^3}{64x^6y^{11}} }=\sqrt{\frac{25x^3}{64y^8}}[/tex]
Descompose 25 and 64 into their prime factors:
[tex]25=5*5=5^2\\64=8*8=8^2[/tex]
Since:
[tex]\sqrt[n]{a^n}=a[/tex]
And according to the Product of powers property:
[tex](a^m)(a^n)=a^{(m+n)}[/tex]
You can simplify. So, the equivalent expression is:
[tex]\sqrt{\frac{5^2x^2*x}{8^2y^8}}=\frac{5x\sqrt{x} }{8y^4}[/tex]
Select the correct answer. Will is at a shirt sale where he can buy one and get a second one for 40 percent off. He wants to buy two shirts priced at $29 each. How much will he pay? cost after discount = (2 × list price) – (list price × discount percentage) A. $34.80 B. $40.60 C. $46.40
Answers
Answer:
C
Step-by-step explanation:
Givens
Original cost = 29 dollars.
Discount = 40% on the second shirt.
Formula
cost after discount = (2 × list price) – (list price × discount percentage)
Solution
Cost after discount = 2 * 29 - 29*40/100
Cost after discount = 58 - 11.60
Cost after discount = 46.40
Solve for x in the equation X2 - 12x+36 = 90-
x=6+3/10
O x=6+2.17
| O x= 12+3/22
x= 12+3/10
Answers
Answer:
x = 6 ± 3√10
Step-by-step explanation:
Since this is an unfactorable expression, apply the Quadratic Formula, -b ± √b² - 4ac\2a, according to the Quadratic Equation, y = Ax² + Bx + C. Applying the Quadratic Formula will give you the above answer.
NOTE: -b = OPPOSITE of b
I am joyous to assist you anytime.
Final answer:
To solve x² - 12x + 36 = 90 for x, we simplify the equation to x² - 12x - 54 = 0 and use the quadratic formula to find x = 6 + 3√10 and x = 6 - 3√10.
Explanation:
To solve the equation x² - 12x + 36 = 90, we can first simplify it by subtracting 90 from both sides to set it equal to zero:
x² - 12x + 36 - 90 = 0x² - 12x - 54 = 0
Now we use the quadratic formula, which states that for any quadratic equation of the form ax² + bx + c = 0, the solutions for x can be found using:
x = (-b ± √(b² - 4ac)) / (2a)Applying this to our equation with a = 1, b = -12, and c = -54, we get:
x = (12 ± √((-12)² - 4*1*(-54))) / (2*1)x = (12 ± √(144 + 216)) / 2
x = (12 ± √360) / 2
x = (12 ± 6√10) / 2
x = 6 ± 3√10
Thus, the solutions are x = 6 + 3√10 and x = 6 - 3√10.
what is -4/3 in a fraction that isn't improper
Answers
Answer:
-1 1/3
Step-by-step explanation:
To change and improper fraction (larger number in the numerator than the denominator) to a mixed number
divide the numerator by the denominator
4/3 =1 with 1 left over
Take the leftovers and put it over the denominator
1/3
The mixed number is 1 1/3
Since the number was negative, we put the negative out front
-1 1/3
What is the relationship between the volume of a cone
and the volume of a cylinder? Explain.
Answers
Hello There!
The volume of a cylinder is pi * r^2 * h. It's a circle times the height.
The volume of a cone is (1/3) * pi * r^2 * h. So it is one third of the volume of a cylinder with the same dimensions.
Answer:
The volume of a cone is one-third the volume of a cylinder.
Step-by-step explanation:
Simplify the polynomial in standard form (3x-4x2+8x3)+(-6x+2x4-5x2)
Answers
2x4+8x3-9x2-3x
The polynomial (3x - 4x^2 + 8x^3) + (-6x + 2x^4 - 5x^2) simplifies to 2x^4 + 8x^3 - 9x^2 - 3x in standard form by combining like terms and ordering them by descending exponents.
Explanation:To simplify the polynomial (3x - 4x2 + 8x3) + (-6x + 2x4 - 5x2) and write it in standard form, we combine like terms. Standard form for polynomials is to write the terms in descending order of their exponents. Here are the steps:
First, combine like terms which are the terms with the same power of x. This means adding coefficients of x3, x2, x, and the constant terms if there are any.Combine 8x3 (as there is no other x3 term to combine with).Combine the x2 terms (-4x2 and -5x2) to get -9x2.Combine the x terms (3x and -6x) to get -3x.Add any constant terms if they exist (there are none in this polynomial).The simplified polynomial in standard form is:
2x4 + 8x3 - 9x2 - 3x
1/2x = -40
What is x?
Answers
Answer:
x = -80
Explanation
-40 divided by 1/2 is -80
that is you’re answer because -40 and x2 is -80
(2 - yi) ^2 simplest form
Answers
Answer:
[tex]-y^{2}-4yi+4[/tex]
Step-by-step explanation:
we know that
[tex](a-b)^{2}=a^{2}-2ab+b^{2}[/tex]
we have
[tex](2-yi)^{2}[/tex]
substitute
[tex](2-yi)^{2}=(2)^{2}-2(2)(yi)+(yi)^{2}[/tex]
[tex](2-yi)^{2}=4-4yi+(y^{2})(i^{2})[/tex]
Remember that
[tex]i^{2}=-1[/tex]
substitute
[tex](2-yi)^{2}=4-4yi+(y^{2})(-1)[/tex]
[tex](2-yi)^{2}=4-4yi-y^{2}[/tex]
[tex](2-yi)^{2}=-y^{2}-4yi+4[/tex]
A radical equation is an equation that uses a radical. True or false ?
Answers
Yes! A radical Equation does use a radical in a Equation.
False
Step-by-step explanation:
Don’t listen to the AI answers
Consider the following proportion:
2/7 =
12x
Use cross products to write the equation: 2x = 84.
What is the value of x?
Answers
Answer:
x=42
Step-by-step explanation:
2x42
Answer:
42
Step-by-step explanation:
tell me if i am wrong by reporting
-5 over 4 x -5 = -35 solve for x
Answers
Answer:
x = 9/7
Step-by-step explanation:
-5/4x-5 =-35
-5 = -35 * (4x-5)
-5 = -35*4x - 5*(-35)
-5 = - 140x + 175
- 140x + 175 = -5
-140x = -5 - 175 = -180
x = -180 / -140 =18 / 14 = 9 /7
To solve the given equation, -5/4x = -35, for x, you multiply both sides by the reciprocal of -5/4 which is -4/5. This gives you x = 28 as the solution.
Explanation:The given equation in your question is -5/4x = -35. In order to solve this equation for x, you would first want to isolate x on one side of the equation. Thus, we'll need to divide both sides of the equation by -5/4.
However, dividing by a fraction is the same as multiplying by its reciprocal. So, in this case, we'll multiply both sides by -4/5, which is the reciprocal of -5/4. This gives us:
x = (-35) * (-4/5)
Doing the multiplication results in x = 28.
Therefore, the solution for x in the equation is 28.
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A company needs to package 2400 pencils. A box in the shape of a rectangular prism can hold 60 pencils. A cylindrical container can hold 80 pencils. Each box cost the company $0.50, while each cylindrical container $0.75
Answers
Answer: A
Step-by-step explanation:
2,400 divided by 60 will give you 40. 40 multiplied by 0.50 give you $20.00.
2,400 divide by 80 will give you 30 but 30 multiplied but 0.75 gives you $22.50.
$22.50 minus $20.00 gives you $2.50
Let’s solve to answer the question.
Divide the amount of pencils the company needs by the amount of pencils the box holds.
2,400/60=40.
Now multiply it by the price.
40*.5=$20.
Repeat.
2400/80=30
30*.75=22.5
The cylindrical containers cost less.
Hope this helps!
Hanging 3 washers on a spring stretches it a total of 4.5 cm. If 13 washers are placed on it instead how far will the spring stretch
Answers
Using Hooke's Law, the spring would stretch a total of 19.5 cm when 13 washers are placed on it.
To find out how much a spring would elongate when the number of washers is increased, we use Hooke's Law, which describes linear elasticity.
Since it is given that 3 washers cause the spring to stretch 4.5 cm, we can assume that each washer causes an equal amount of stretch under this elastic limit. Therefore, the amount of stretch per washer is 4.5 cm divided by 3, which is 1.5 cm per washer.
If you hang 13 washers on the spring, the total stretch can be calculated by multiplying the amount of stretch per washer with the total number of washers:
Stretch per washer × Number of washers = Total stretch
1.5 cm/washer × 13 washers = 19.5 cm.
So, with 13 washers, the spring would stretch a total of 19.5 cm.
For the function, f(x) = -5x 2, find f(-4).
Answers
Answer:
The value of f(-4) = -80
Step-by-step explanation:
It is given that, f(x) = -5x²
To find the value f(-4)
Let f(x) = -5x²
To find the value of f(-4), substitute -4 instead of x
f(-4) = -5 * (-4)²
= -5 * 16 [ since (-4)² = -4 * -4 = 16 ]
= -80
Therefore the value of f(-4) = -80
Using the given points and line, determine the slope of the line. (-3, 0) and (2, 7) slope = -7/5
slope = -5/7
slope = 5/7
slope = 7/5
Answers
Answer:
Slope= 7/5
Step-by-step explanation:
The slope of a line is determined as a ratio of the change in y to the change in x.
Slope=Δy/Δx
Δy=y₂-y₁
Δx=x₂-x₁
Therefore we can use the the x and y coordinates from the points given, (-3,0) and (2,7) to calculate the slope.
m= (7-0)/(2-⁻3)
Slope= 7/5
When a negative number is subtracted from a number it the operation sign changes to addition.
Answer: Last option
[tex]slope=\frac{7}{5}[/tex]
Step-by-step explanation:
The equation to find the slope m of a line is:
[tex]m=\frac{y_2-y_2}{x_2-x_1}[/tex]
Where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are two points through which the line passes
In this case the points are: (-3, 0) and (2, 7)
Therefore the slope is:
[tex]m=\frac{7-0}{2-(-3)}[/tex]
[tex]m=\frac{7}{2+3}[/tex]
[tex]m=\frac{7}{5}[/tex]
The answer is the last option
How is solving for speed similar to solving for time?
Answers
Speed = distance/time
Time= distance/ speed
So basically distance divided both of them when they find speed distance divide time when fine time distance divide speed.
Hope this helps!
Time= distance/speed (T = d/s)
Rate or speed are similar since they both represent some distance per unit time such miles per hour and kilometers per hour. To solve for time use the formula for time, t = d/s which means time equals distance divided by speed.
What is the formula for distance divided by time?distance = rate x time To solve for speed or rate use the formula for speed, s = d/t which means speed equals distance divided by time.
What is the relationship between speed and time?This is because, speed of the object refers distance travelled divided by time or it expressed as, Furthermore, 1 could also explain the relationship of the time with other two variables using this formula. Speed could be of 2 types, relative or average.
from the formula,
Distance = time * speed
Speed = distance/time
Time= distance/speed (T = d/s)
So basically distance divided both of them when it find speed distance divide time when fine time distance divide speed.
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I’m If Linda age is decreased by 36, the result is twice Linda’s age. how old is linda?
Answers
Answer:
x=lindas age
3 times lindas age (3 time x or 3x) is decreased by 36 (-36), the result (=) is twice lindas age (2 times x or 2x)
now we have
3x-36=2x
subtract 2x
x-36=0
add 36
x=36
age=36
Step-by-step explanation:
Using algebra to solve the problem, we create the equation L - 36 = 2L, representing Linda's age. Solving for 'L', we find that Linda is 36 years old.
Explanation:This problem can be solved by using algebra, a branch of mathematics. Let's assume that Linda's age is denoted by the variable 'L'. According to the problem, if Linda's age is decreased by 36, the result is twice Linda's age. We can write this as an equation: L - 36 = 2L.
In order to solve for 'L', we'll need to get all terms involving 'L' on one side of the equation. We would then subtract 'L' from both sides, giving us -36 = L, or, re-arranged, L = 36. Therefore, Linda is 36 years old.
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I need this explained
Answers
[tex]\text{Hey there!}[/tex]
[tex]\text7x}^2\text{- 32x - 60}[/tex]
[tex]\text{The answer is: (7x + 10)(x - 6)}[/tex]
[tex]\text{Because if you follow the step to the answer (first you have to distribute}[/tex] [tex]\text{then combine the like terms after distributing) after all of that you SHOULD}[/tex] [tex]\text{get the equation back!}[/tex]
[tex]\text{Distribute}\downarrow\\\\\text{7x(x)=7x}^2\\ \text{7(-6x)= -42}\\\text{10(x)= 10x}\\\text{10(-6)= -60}[/tex]
[tex]\text{Combine your like terms (terms that has the almost the same thing)}\downarrow[/tex]
[tex]\text{-42x + 10x = -32x}[/tex]
[tex]\text{The other terms stays the same because they DON'T have like terms}[/tex]
[tex]\text{Original problem: 7x}^2\text{- 32x -60}[/tex]
[tex]\boxed{\boxed{\bf{Answer: (7x+10(x -6))}}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
Write the equation of a line with slope m = 6 and including point (0, 1).
Answers
Answer:
y = 6x + 1
Step-by-step explanation:
linear equations (straight line) are expressed in the following general form:
y = mx + b, where m is the gradient and b is the y-ordinate of the point where the line crosses the y-axis (called the y-intercept)
Given : m = 6
we realize that point (0,1) is actually on the y-axis (i.e x=0), therefore this is coincidentally the y-intercept. Hence b = 1
Therefore the whole equation is
y = 6x + 1
The equation for a line is:
y = mx + c
Note:
y is the y coordinate
m is the slope
x is the x coordinate
c is the y -intercept (where the line crosses the y-axis.
The question tells us that the slope is 6 (so m is 6)
It also tells that the coordinates are: (0 , 1) (so x is 0 and y is 1)
Lets plug in these values into the equation and solve to get the missing value ( which is c) :
y = mx + c
1 = 6(0) + c
1 = c.
Now to get the equation of the line, we plug in the values for m and c into y= mx + c:
Equation of line: y = 6x + 1
-----------------------------------------------------------
Answer:
Equation of line with slop m = 6 and including point (0, 1) is:
y = 6x + 1
7 ft=____ inches show work
Answers
Answer:7x12= 84
Step-by-step explanation:
7x10=70
7x2=14
70+14=84
have a good day
There are 84 inches in 7 feet.
Given that we need to determine that how many feet in 84 inches.
To convert inches to feet, you need to divide the number of inches by the number of inches in a foot.
There are 12 inches in a foot.
Given that you have 84 inches, you can divide this value by 12 to find the equivalent in feet:
84 inches ÷ 12 inches/foot = 7 feet
So, 84 inches is equal to 7 feet.
Hence there are 84 inches in 7 feet.
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Can you help with this please?
[tex]2n \times n = 12 + n[/tex]
Answers
Answer:
2n² = 12 + n
2n² - n - 12 = 0
[tex]n = \frac{1 ± \sqrt{ {( - 1)}^{2} - 4(2)( - 12)} }{2(2)} [/tex]
[tex]n = \frac{1 ± \sqrt{97} }{4} [/tex]
Which figures are shown
Answers
Answer:
Point D, Segment CD, Ray CD
Step-by-step explanation:
Can someone help me
Answers
Answer: D
Step-by-step explanation:
W is the total number of oranges.
W/5 is the oranges being divided equally for 5 friends
PLEASE HELP! Let x1 = 8, y1 = 12, and y2 = 4. Let y vary inversely as x. Find x2.
x2 = 6
x2 = 24
x2 = 2.67
x2 = 92
Answers
Answer:
[tex]x_{2} =24[/tex]
Step-by-step explanation:
Your welcome :)
Carrie spent 1/4 of her allowance on a shirt 1/3 of her allowance Oscar and eight dollars on the bill if she spent 22 in all how much was Carrie’s allowance
Answers
Answer: $24
Step-by-step explanation:
Let x represent the amount of Carrie's allowance.
[tex]\dfrac{1}{4}x+\dfrac{1}{3}x+8=22\\\\\\\dfrac{1}{4}x+\dfrac{1}{3}x=14\\\\\\(12)\dfrac{1}{4}x+(12)\dfrac{1}{3}x=(12)14\\\\\\3x + 4x = (12)14\\\\\\7x=(12)14\\\\\\x=(12)2\\\\\\x=24[/tex]
What are the x-intercepts of the graph of the function f(x) = x2 + 5x − 36?
Answers
Answer:(4,0) and (-9,0)
Step-by-step explanation:
Find two numbers their product will be -36 when you add those two numbers together your sum will be 5
-4(9) = -36
-4 + 9 = 5
So
(X-4)(x+9)
X-4= 0
X= 4
X+9=0
X= -9
The x-intercept are (4,0) and (-9,0)
Hope this helps!
Write the equation of the line that passes through the points (8, -1) and (2,-5) in standard form, giver
slope form is y+1 = (x-8)
Answers
Answer:
2x - 3y = 19Step-by-step explanation:
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (8, -1) and (2, -5). Substitute:
[tex]m=\dfrac{-5-(-1)}{2-8}=\dfrac{-4}{-6}=\dfrac{2}{3}[/tex]
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
Substitute:
[tex]y-(-1)=\dfrac{2}{3}(x-8)[/tex]
[tex]y+1=\dfrac{2}{3}(x-8)[/tex] → the point-slope form
Convert to the standard form: [tex]Ax+By=C[/tex]
[tex]y+1=\dfrac{2}{3}(x-8)[/tex] multiply both sides by 3
[tex]3y+3=2(x-8)[/tex] use the distributive property a(b+c) = ab+ ac
[tex]3y+3=2x-16[/tex] subtract 3 from both sides
[tex]3y=2x-19[/tex] subreact 2x from both sides
[tex]-2x+3y=-19[/tex] change the signs
[tex]2x-3y=19[/tex] → the standard form
find the gradient of the line joining (3,7) and (6,9). Hence, find the acute angle it makes with the positive x-y axis
Answers
Answer:
33.7 degrees
Step-by-step explanation:
As we go from (3,7) to (6,9), x increases by 3 and y increases by 2. Thus, the gradient (slope) of the line connecting these two points is
m = rise / run = 2/3. Using the slope-intercept formula y = mx + b, we obtain
7 = (2/3)(3) + b, or 7 = 2 + b, so we see that b = 5 and y = (2/3)x + 5. The y-intercept is (0, 5).
Next we find the x-intercept. We set y = (2/3)x + 5 = to 0 and solve for x:
(2/3)x = -5, or (3/2)(2/3)x = -5(3/2), or x = -15/2, so that the x-intercept is
(-15/2, 0). This line intersects the x-axis at (-15/2, 0).
Now look at the segment of this line connecting (-15/2, 0) and (0, 5). Here x increases by 15/2 and y increases by 5, and so the tangent of the acute angle in question is
tan Ф = 5 / (15/2) = 10 / 15 = 2/3.
Using the inverse tangent function, we get Ф = arctan 2/3, or approx.
33.7 degrees.
I believe you meant "the acute angle it makes with the positive x-axis."
Final answer:
The gradient of the line is 2/3, and the acute angle it makes with the positive x-axis is found by taking the arctan of the gradient. which is approximately 33.69 degrees.
Explanation:
The gradient of the line joining two points, (x1, y1) and (x2, y2), is calculated using the formula:
Gradient = (y2 - y1) / (x2 - x1)
Substituting the given points (3,7) and (6,9) into the formula, we get:
Gradient = (9 - 7) / (6 - 3) = 2 / 3
The gradient is 2/3. To find the acute angle θ the line makes with the positive x-axis, we use the formula:
Tan(θ) = Gradient
So, θ = arctan(Gradient)
θ = arctan(2/3)
Calculating θ will give us the acute angle. which is approximately 33.69 degrees.
If 5x−2y=10 and x= 4y/5 , then y =
(A) 1 (B) 4 (C) 5 (D) 7 (E) 9
Answers
Answer:
C
Step-by-step explanation:
4y-2y=10
y=5
Consider the expressions $\frac{4x^3+2x^2+6x+7}{2x+1}$ and $2x^2+3+\frac4{2x+1}.$
a) Show that these expressions are equal when $x=10.$
b) Explain why these expressions are not equal when $x=-\dfrac12.$
c) Show that these expressions are equal for all $x$ other than $-\dfrac12.$
In parts (a) and (c), begin by explaining what your strategy for solving will be.
Answers
Answer:
Part a) In order to solve the equation, we will simplify both of them. Once we do that, if we notice, they are the same equation, so therefore, if x=10, then we will be able to match the equation.
Part b) The reason the expressions are not equal when x=-1/2 is because if we see, that in the second expression, 2x^2, if x=-1/2, then the answer becomes -1, and we eventually end up with 1.
Part c) As we can see, the expressions are the same, so if x is any number other than -1/2, then we will be able to show that the expressions are equal.
Step-by-step explanation:
You can simplify the explanation, also if you play ROBLOX, follow me at my username: BAMUNJI, or 24KBlingYT
By the way, this question is from the Art of Problem Solving, and you should not just copy answers or copy of them.
Part (a) We shall simplify both of them in order to find the solution to the equation.
Once we've done that, we'll see that they have the same equation, so we can match the equation if x=10.Part (b) When x=-1/2, the answers to the second expression, 2x2, change to -1, and we eventually arrive in 1.
This is why the expressions are not equal at this point.Part (c) As we can see, the expressions are identical, thus we can demonstrate that they are equal if x is any number other than -1/2.
What is an expression in maths?An expression is a set of terms combined using the operations +, – , x or , for example 4 x − 3 or x 2 – x y + 17 . An equation states that two expressions are equal in value, for example 4 b − 2 = 6 . An identity is a statement that is true no matter what values are chosen, for example 4 a × a 2 = 4 a 3 .What is a math expression example?An expression is a set of numbers or variables combined using the operations +, –, × or ÷. Arithmetic expression that contains only numbers and mathematical operators and algebraic expression that contains variables, numbers and mathematical operators.How do you find expressions?To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number. To evaluate an expression, we substitute the given number for the variable in the expression and then simplify the expression using the order of operations.
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