Answer:
Davis has a loss of $19
i.e -19
Step-by-step explanation:
On day 1, David lost 5.4 * 10 = $54
On day 2, David gained 5 * 7 = $35
Overall, his loss is greater than the profit
Total loss is $54 - $35 = $19
What 2 numbers can multiply to -40 and add up to 6
Answer: 10 and -4
Step-by-step explanation: 10 + - 4 = 6 and 10 x -4 = -40
Sarah has 12 cents. If she adds 1 dime and 1 quarter, how much money will she have?
Answer:
47 cents or $0.47
Step-by-step explanation:
1 dime = 10 cents (or $0.1)
1 quarter = 25 cents or ($0.25)
12 cents + 1 dime + 1 quarter = 12 + 10 + 25 = 47 cents
Select the correct answer.
Mr. Miller owns two hotels and is ordering towels for the rooms. He ordered 27 hand towels and 48 bath towels for a bill of $540 for the first hotel. He
ordered 50 hand towels and 24 bath towels for a bill of $416 for the other hotel.
What is the cost of one hand towel and one bath towel?
O A.
OB.
OC.
O D.
The cost of one hand towel is $4 and the cost of one bath towel is $9.
The cost of one hand towel is $9 and the cost of one bath towel is $4.
The cost of one hand towel is $5 and the cost of one bath towel is $8.
The cost of one hand towel is $8 and the cost of one bath towel is $5.
Answer: D: The cost of one hand towel is $8 and the cost of one bath towel is $5.
Step-by-step explanation:
Let's assume the cost of one hand towel is 'x' dollars and the cost of one bath towel is 'y' dollars.
For the first hotel, Mr. Miller ordered 27 hand towels and 48 bath towels, resulting in a bill of $540. This can be expressed as the equation:
27x + 48y = 540 ...(equation 1)
For the second hotel, Mr. Miller ordered 50 hand towels and 24 bath towels, resulting in a bill of $416. This can be expressed as the equation:
50x + 24y = 416 ...(equation 2)
To solve this system of equations, we can use any suitable method such as substitution or elimination. Let's use the elimination method:
Multiplying equation 1 by 2 and equation 2 by 3, we get:
54x + 96y = 1080 ...(equation 3)
150x + 72y = 1248 ...(equation 4)
Now, subtracting equation 4 from equation 3, we have:
(54x + 96y) - (150x + 72y) = 1080 - 1248
-96x + 24y = -168
Dividing both sides of the equation by -24, we get:
4x - y = 7 ...(equation 5)
Now, we have a system of equations:
4x - y = 7 ...(equation 5)
50x + 24y = 416 ...(equation 2)
Solving this system of equations, we find that x = 8 and y = 5.
Therefore, the cost of one hand towel is $8 and the cost of one bath towel is $5.
So, the correct answer is option D: The cost of one hand towel is $8 and the cost of one bath towel is $5.
Answer:
Step-by-step explanation:
Total cost of hand towels for first hotel = 27 * $5 = $135
Total cost of bath towels for first hotel = 48 * $8 = $384
Total cost of hand towels for second hotel = 50 * $5 = $250
Total cost of bath towels for second hotel = 24 * $8 = $192
Total cost of all hand towels = $135 + $250 = $385
Total cost of all bath towels = $384 + $192 = $576
Total number of hand towels = 27 + 50 = 77
Total number of bath towels = 48 + 24 = 72
Average cost of one hand towel = $385 / 77 = $5
Average cost of one bath towel = $576 / 72 = $8
Which point could not be part of a function that includes (3, -1), (4, 2), (5, 4), (-2, 0), and (8, -3)?
(6, -7)
(2,2)
(3, -2)
(7, 4)
Answer:
(3, -2) is the correct choice.
A community is developing plans for a pool and hot tub. The community plans to form a swim team, so the pool must be built to certain dimensions. Answer the questions to identify possible dimensions of the deck around the pool and hot tub.
Part I: The dimensions of the pool are to be 25 yards by 9 yards. The deck will be the same width on all sides of the pool. Including the deck, the total pool area has a length of (x + 25) yards, and a width of (x + 9) yards.
Write an equation representing the total area of the pool and the pool deck. Use y to represent the total area. Hint: The area of a rectangle is length times width. (1 point)
Rewrite the area equation in standard form. Hint: Use the FOIL method. (1 point)
Rewrite the equation from Part b in vertex form by completing the square. Hint: Move the constant to the other side, add to each side, rewrite the right side as a perfect square trinomial, and finally, isolate y. (4 points: 1 point for each step in the hint)
What is the vertex of the parabola? What are the x- and y-intercepts? Hint: Use your answer from Part a to identify the x-intercepts. Use your answer from Part b to identify the y-intercept. Use your answer from Part c to identify the vertex. (4 points: 1 point for each coordinate point)
Graph the parabola. Use the key features of the graph that you identified in Part d. (3 points)
In this problem, only positive values of x make sense. Why? (1 point)
What point on your graph shows a total area that includes the pool but not the pool deck? (1 point)
The community decided on a pool area that adds 6 yards of pool deck to both the length and the width of the pool. What is the total area of the pool and deck when x = 6 yards? (2 points)
Part II: A square hot tub will be placed in the center of an enclosed area near the pool. Each side of the hot tub measures 6 feet. It will be surrounded by x feet of deck on each side. The enclosed space is also square and has an area of 169 square feet. Find the width of the deck space around the hot tub, x.
Step 1: Write an equation for the area of the enclosed space in the form y = (side length)2. Hint: Don't forget to add x to each side of the hot tub. (1 point)
Step 2: Substitute the area of the enclosed space for y in your equation. (1 point)
Step 3: Solve your equation from Part b for x. (3 points)
Step 4: What is the width of the deck around the hot tub? Hint: One of the answers from Part c is not reasonable. (1 point)
Part I- a) y = (x + 25)(x + 9)
b) y = x^2 + 34x + 225
c) y= (x + 17)^2 - 64
d) The y-intercept is (0, 225), The y-intercept is (0, 225).
e) The graph of the parabola has the vertex at (-17, -64), x-intercepts at (-25, 0) and (-9, 0), and the y-intercept at (0, 225).
f) Only positive values of x make sense because the dimensions of a pool and deck cannot be negative.
g) y = 465 square yards
Part II- a) y = (6 + 2x)^2
b) 169 = (6 + 2x)^2
c) x = 3.5 feet
Part I:
a) The equation representing the total area of the pool and the pool deck, using y to represent the total area, can be written as:y = (x + 25)(x + 9)
b) To rewrite the equation in standard form using the FOIL method:
y = x^2 + 9x + 25x + 225
= x^2 + 34x + 225
c) To rewrite the equation in vertex form by completing the square:
y = (x^2 + 34x) + 225
= (x^2 + 34x + (34/2)^2) + 225 - (34/2)^2
= (x^2 + 34x + 289) + 225 - 289
= (x + 17)^2 - 64
d) The vertex of the parabola is (-17, -64). The x-intercepts are found by setting y = 0 and solving the equation:
0 = (x + 17)^2 - 64
64 = (x + 17)^2
x + 17 = ±√64
x + 17 = ±8
x = -17 ± 8
x = -25, -9
Therefore, the x-intercepts are (-25, 0) and (-9, 0).
The y-intercept is obtained by setting x = 0 in the equation:
y = (0 + 17)^2 - 64
y = 17^2 - 64
y = 289 - 64
y = 225
Therefore, the y-intercept is (0, 225).
e) The graph of the parabola has the vertex at (-17, -64), x-intercepts at (-25, 0) and (-9, 0), and the y-intercept at (0, 225).
f) Only positive values of x make sense because the dimensions of a pool and deck cannot be negative. In this context, negative values for x would not provide meaningful solutions for the width of the deck.
g) The point on the graph that represents the total area including the pool but not the pool deck is the y-intercept (0, 225).
h) When x = 6 yards, the total area of the pool and deck can be found by substituting the value into the equation from Part b:
y = (6 + 17)^2 - 64
y = 23^2 - 64
y = 529 - 64
y = 465 square yards
Part II:
a) The equation for the area of the enclosed space in the form y = (side length)^2, considering the hot tub and the deck around it, is:
y = (6 + 2x)^2
b) Substituting the area of the enclosed space (169 square feet) for y in the equation:
169 = (6 + 2x)^2
c) Solving the equation for x:
√169 = √((6 + 2x)^2)
13 = 6 + 2x
2x = 13 - 6
2x = 7
x = 7/2
x = 3.5 feet
Therefore, the width of the deck space around the hot tub is 3.5 feet.
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In a class of 40 students on average 4 will be left handed if a class includes 6 lefties estimate how many students are in the class
What's the area of the following triangle?
A. 24 ft.²
B. 128 ft.²
C. 12 ft.²
D. 64 ft.²
Answer:
D
Step-by-step explanation:
the area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
here b = 16 and h = 8 , then
A = [tex]\frac{1}{2}[/tex] × 16 × 8 = 8 × 8 = 64 ft²
Use basic inference rules to establish the validity of the argument: p ⟹ ¬q ,q V r ,p V u ,¬r├ u
Using basic inference rules, we can establish the validity of the argument: p ⟹ ¬q, q V r, p V u, ¬r ├ u.
1. We are given the following premises:
- p ⟹ ¬q (Premise 1)
- q V r (Premise 2)
- p V u (Premise 3)
- ¬r (Premise 4)
2. To prove the conclusion, u, we need to use the premises and apply inference rules.
3. From Premise 4 (¬r) and the Disjunctive Syllogism rule, we can deduce ¬q: (¬r, q V r) ⟹ ¬q.
4. From Premise 1 (p ⟹ ¬q) and Modus Ponens, we can conclude ¬p: (p ⟹ ¬q, ¬q) ⟹ ¬p.
5. From Premise 3 (p V u) and Disjunctive Syllogism, we obtain ¬p V u.
6. Using Disjunctive Syllogism with ¬p V u and ¬p, we can derive u: (¬p V u, ¬p) ⟹ u.
7. From Premise 2 (q V r) and Disjunctive Syllogism, we have q.
8. Finally, using Modus Tollens with q and ¬q, we can deduce ¬p: (q, p ⟹ ¬q) ⟹ ¬p.
9. Therefore, combining ¬p and u, we can conclude the desired result: ¬p ∧ u.
10. Since ¬p ∧ u is logically equivalent to u, we have established the validity of the argument: p ⟹ ¬q, q V r, p V u, ¬r ├ u.
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Find the values of x and y.
G
(6y)⁰
X =
(5x)
y =
M
(10x)⁰
K
L
Answer:
be more clear of what u mean edit the question to explain more
Step-by-step explanation:
no explanation
I WILL GIVE BRAINLIEST
Step-by-step explanation:
In a randomized block design blocked by gender, treatments should be assigned randomly within each gender block. The correct assignment maintains a distribution of one treatment for each gender. Looking at the given options, only one meets this criterion:
OA: (1f, 2f), B: (1m, 2m). C: (3f, 3m). D: (4f, 4m)
Each treatment group A, B, C, and D contains one male and one female, making the distribution of treatments blocked by gender.
Please help me solve this
Answer:
Step-by-step explanation:
Evaluate the expression. −3[−4(3−10)−12] over −2(−1) What is the value of the expression?
Answer: -24
Step-by-step explanation:
To evaluate the expression, I guess we need to break it down into steps:
Expression: -3[-4(3-10)-12] / -2(-1)
Step1: Simplify the innermost parentheses Inside the square brackets: 3 - 10 = -7 Expression becomes: -3[-4(-7) - 12] / -2(-1)
Step2: Simplify the multiplication in square brackets: -4 * (-7) = 28. Expression becomes: -3[28 - 12] / -2(-1)
Step3: Simplify the subtraction inside the square brackets: 28 - 12 = 16. Expression becomes: -3[16] / -2(-1)
Step4: Simplify the multiplication outside the square brackets: -3 * 16 = -48. Expression becomes: -48 / -2(-1)
Step5: Simplify the multiplication inside the denominator: -2 * (-1) = 2 Expression becomes: -48 / 2
Step 6: Perform the division -48 divided by 2 is equal to -24
Therefore, the value of the expression -3[-4(3-10)-12] / -2(-1) is -24.
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
x < 5
–6x – 5 < 10 – x
–6x + 15 < 10 – 5x
A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
Answer:
Third option
Step-by-step explanation:
-3(2x - 5) < 5(2 - x)
-6x + 15 < 10 - 5x <-- Third option
15 < 10 + x
5 < x
x > 5
There only appears to be one option. The solution to the inequality is x>5, not x<5.
Rearrange the equation so u is the independent variable
-12u+13=8w-3
w=_______
the answer is
w = -3/2 u + 2
Describe the given translation: T(0, 7)
Answer:
ok t means some thing but zero and seven should be solved
If sin(x+y)= 1/2(sin x) + square root of 3/2(cos x), what is the value of y
Answer:
y = π/3
Step-by-step explanation:
To find the value of y, we can use the trigonometric identity for the sum of angles:
sin(x + y) = sin x * cos y + cos x * sin y
Comparing this with the given equation:
sin(x + y) = 1/2(sin x) + √3/2(cos x)
We can equate the corresponding terms:
sin x * cos y = 1/2(sin x) ----(1)
cos x * sin y = √3/2(cos x) ----(2)
From equation (1), we can see that cos y = 1/2.
From equation (2), we can see that sin y = √3/2.
To determine the values of y, we can use the trigonometric values of cosine and sine in the first quadrant of the unit circle.
In the first quadrant, cos y is positive, so cos y = 1/2 corresponds to y = π/3 (60 degrees).
Similarly, sin y is positive, so sin y = √3/2 corresponds to y = π/3 (60 degrees).
Therefore, the value of y is y = π/3 (or 60 degrees).
(08.01 MC)
A function is shown: f(x) = 4x² - 1.
Choose the equivalent function that best shows the x-intercepts on the graph.
Of(x) = (4x + 1)(4x - 1)
Of(x) = (2x + 1)(2x - 1)
f(x) = 4(x²+1)
f(x) = 2(x²-1)
The equivalent function that best shows the x-intercepts on the graph of f(x) = 4x² - 1 is option (a) or (b): Of(x) = (4x + 1)(4x - 1).
The correct answer to the given question is option a or b.
The given function is f(x) = 4x² - 1. We need to choose the equivalent function that best shows the x-intercepts on the graph.The x-intercepts are the points where the graph of a function intersects the x-axis. At the x-intercepts, the value of y is zero.
Therefore, to find the x-intercepts, we need to solve the equation f(x) = 0 for x. The function f(x) = 4x² - 1 can be factored as:(2x + 1)(2x - 1)
To find the x-intercepts, we set f(x) = 0:4x² - 1 = 0(2x + 1)(2x - 1) = 0So, either 2x + 1 = 0 or 2x - 1 = 0. Solving these equations, we get:
x = -1/2 or x = 1/2
These are the x-intercepts of the graph of f(x) = 4x² - 1.Now, let's look at the given options and determine which one shows the x-intercepts on the graph:
Option (a):
Of(x) = (4x + 1)(4x - 1)
This is the factored form of f(x) = 4x² - 1. It correctly shows the x-intercepts.
Option (b):
Of(x) = (2x + 1)(2x - 1)
This is the same as option (a) and correctly shows the x-intercepts.
Option (c): f(x) = 4(x² + 1)
This function does not have any x-intercepts. It has a minimum value of 4 at x = 0.
Option (d): f(x) = 2(x² - 1)
This function has x-intercepts at x = -1 and x = 1. It does not show the x-intercepts of the given function.
Therefore, the equivalent function that best shows the x-intercepts on the graph of f(x) = 4x² - 1 is option (a) or (b):
Of(x) = (4x + 1)(4x - 1).
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find a positive and a negative coterminal angle for each given angle.
Answer:
D
Step-by-step explanation:
to find the coterminal angles add/ subtract 360° to the given angle
- 255° + 360° = 105°
- 255° - 360° = - 615°
For the sequence -27,-12, 3, 18,..., the expression that defines the nth term where a, = -27 is
Answer:
-27+15 (N-1)
Step-by-step explanation:
-27, -12, 3, 18
Take the second term and subtract the first term to find the common difference
-12 - (-27)
-12+27 = 15
The common difference is +15
We are adding 15 each time
The formula for an arithmetic sequence is
an = a1+d(n-1)
an = -27 +15(n-1)
true or false euclidean geometry is geometry on a sphere
Answer: False
Step-by-step explanation:
Spherical geometry, on the other hand, is a type of non-Euclidean geometry that is specifically concerned with studying the properties of curved surfaces, such as spheres.
Hope this help! Have a good day!
Use a Calculator to evaluate The following. Round the answer to the nearest hundredths
1. Cos 10
2. Sin 30
3. Sin 20
4. Tan 25
5. Tan 48.5
1. Using a calculator, we find that cos 10 ≈ 0.98.
2. Using a calculator, we find that sin 30 ≈ 0.50.
3. Using a calculator, we find that sin 20 ≈ 0.34.
4. Using a calculator, we find that tan 25 ≈ 0.47.
5. Using a calculator, we find that tan 48.5 ≈ 1.14.
Using a calculator to evaluate the given trigonometric functions, rounded to the nearest hundredth, we have:
Cos 10:
Using a calculator, we find that cos 10 ≈ 0.98.
Sin 30:
Using a calculator, we find that sin 30 ≈ 0.50.
Sin 20:
Using a calculator, we find that sin 20 ≈ 0.34.
Tan 25:
Using a calculator, we find that tan 25 ≈ 0.47.
Tan 48.5:
Using a calculator, we find that tan 48.5 ≈ 1.14.
These values represent the approximate decimal values of the trigonometric functions at the given angles, rounded to the nearest hundredth.
Just a reminder, when using a calculator, make sure it is set to the correct angle mode (degrees or radians) as per the given problem.
It's important to note that these values are approximate since they are rounded to the nearest hundredth. If you need more precise values, you can use a calculator that allows for a greater number of decimal places or use trigonometric tables.
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Christine has 1 blue sock, 3 purple socks and 1 green sock in a box.
Christine takes one sock at random from the box, puts it back, and takes another sock from the box. Find the probability that Christine takes at least one blue sock.
Given the information in the diagram, which theorem best justifies why lines j and k must be parallel?
Given the information in the diagram, the theorem that best justifies why lines j and k must be parallel include the following: D. converse alternate exterior angles theorem.
What are parallel lines?In Mathematics and Geometry, parallel lines are two (2) lines that are always the same (equal) distance apart and never meet or intersect.
In Mathematics and Geometry, the alternate exterior angle theorem states that when two (2) parallel lines are cut through by a transversal, the alternate exterior angles that are formed lie outside the two (2) parallel lines, are located on opposite sides of the transversal, and are congruent angles.
Since the alternate exterior angles are congruent, we can logically deduce the following based on the converse alternate exterior angles theorem;
93° ≅ 93° (lines j and k are parallel lines).
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Complete Question:
Given the information in the diagram, which theorem best justifies why lines j and k must be parallel?
alternate interior angles theorem
alternate exterior angles theorem
converse alternate interior angles theorem
converse alternate exterior angles theorem
Margie has a $50.00 budget to purchase a $45.00 pair of boots. If
there is an 8% sales tax rate, then how much under budget will
Margie be?
Answer:
She willl be $1.40 under budget
Step-by-step explanation:
8% = 8/100 = 0.08
Adding this to 100% of the price of the shoes, we get 108% = 108/100 = 1.08.
We multiply the price of the shoes by this:
45*1.08 = 48.60
Subtract this from 50:
50 - 48.60 = 1.40
Please answer ASAP I will brainlist
The resulting matrix after the rows are interchanged is given as follows:
[tex]\left[\begin{array}{cccc}2&9&4&5\\8&-2&1&7\\1&4&-4&9\end{array}\right][/tex]
How to obtain the resulting matrix?The matrix for this problem is defined as follows:
[tex]\left[\begin{array}{cccc}8&-2&1&7\\2&9&4&5\\1&4&-4&9\end{array}\right][/tex]
The row 1 is given as follows:
[8 -2 1 7].
The row 2 is given as follows:
[2 9 4 5].
Interchanging the rows means that the elements of the row 1 in the matrix is exchanged with the elements of row 2, hence the resulting matrix is given as follows:
[tex]\left[\begin{array}{cccc}2&9&4&5\\8&-2&1&7\\1&4&-4&9\end{array}\right][/tex]
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Does anybody know the answer i need. It quick!!!!!
The area of the obtuse triangle is 34 square feet with a base of 10 ft and height of 6.8 ft.
To find the area of the obtuse triangle, we can use the formula A = (1/2) * base * height. Let's denote the unknown part of the base as x.
In the given triangle, we have the width of the obtuse angle triangle as 10 ft, the height (perpendicular) as 6.8 ft, and the unknown part of the base as x.
Using the formula, we can calculate the area as:
A = (1/2) * (10 + x) * 6.8
Simplifying this expression, we get:
A = 3.4(10 + x)
Now, we need to determine the value of x. From the given information, we know that the width of the obtuse angle triangle is 10 ft. This means the sum of the two parts of the base is 10 ft. Therefore, we can write the equation:
x + 10 = 10
Solving for x, we find:
x = 0
Since x = 0, it means that one part of the base has a length of 0 ft. Therefore, the entire base is formed by the width of the obtuse angle triangle, which is 10 ft.
Now, substituting this value of x back into the area formula, we have:
A = 3.4(10 + 0)
A = 3.4 * 10
A = 34 square feet
Hence, the area of the obtuse triangle is 34 square feet.
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Which is equivalent to 4/9 1/2x*?
92x
9 1/8x
Answer:
B. [tex] 9^{\frac{1}{8}x} [/tex]
Step-by-step explanation:
[tex] \sqrt[4]{9}^{\frac{1}{2}x} = [/tex]
[tex] = ({9}^{\frac{1}{4}})^{\frac{1}{2}x} [/tex]
[tex] = 9^{\frac{1}{4} \times \frac{1}{2}x} [/tex]
[tex] = 9^{\frac{1}{8}x} [/tex]
a spinner with 10 equally sized slices 4 yellow, 4 red, 2 blue. probability that the dial stops on yellow?
The probability that the dial stops on yellow is 2/5 or 0.4 (or 40%).
Therefore, there is a 40% chance that the spinner will stop on yellow.
To find the probability that the spinner stops on yellow, we need to determine the number of favorable outcomes (yellow) and the total number of possible outcomes.
The spinner has 10 equally sized slices, with 4 yellow, 4 red, and 2 blue.
The number of favorable outcomes (yellow) is 4 because there are 4 yellow slices.
The total number of possible outcomes is 10 because there are 10 slices in total.
Therefore, the probability of the spinner stopping on yellow can be calculated as:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 4 / 10
Simplifying this fraction, we get:
Probability = 2 / 5
So, the probability that the dial stops on yellow is 2/5 or 0.4 (or 40%).
Therefore, there is a 40% chance that the spinner will stop on yellow.
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The expression
28 (78-14)9-13(78-49)9
can be
rewritten as
(X-y)" (262 + y? + gxy). Whatis the value of p?
Answer:
p =1 0
Step-by-step explanation:
x³(x - y)⁹ - y³(x - y)⁹ = (x - y)⁹[x³ - y³]
= (x - y)⁹(x - y)(x² + y² + xy)
= (x - y)¹⁰(x² + y² + xy)
where p = 10 and q = 1
Answer:
p = 10
Step-by-step explanation:
Given expression:
[tex]x^3(x-y)^9 - y^3(x-y)^9[/tex]
Factor out the common term (x - y)⁹:
[tex](x-y)^9(x^3- y^3)[/tex]
[tex]\boxed{\begin{minipage}{5cm}\underline{Difference of two cubes}\\\\$x^3-y^3=(x-y)(x^2+y^2+xy)$\\\end{minipage}}[/tex]
Rewrite the second parentheses as the difference of two cubes.
[tex](x-y)^9(x-y)(x^2+y^2+xy)[/tex]
[tex]\textsf{Apply\:the\:exponent\:rule:} \quad a^b\cdot \:a^c=a^{b+c}[/tex]
[tex](x-y)^{9+1}(x^2+y^2+xy)[/tex]
[tex](x-y)^{10}(x^2+y^2+xy)[/tex]
Comparing the rewritten original expression with the given expression:
[tex](x-y)^{10}(x^2+y^2+xy)=(x-y)^p(x^2+y^2+qxy)[/tex]
We can see that [tex](x-y)^p[/tex] corresponds to [tex](x-y)^{10}[/tex] in the given expression.
Therefore, we can conclude that p = 10.
Choose the justification for each step of the given equation. -6=-2/3(x+12)+1/3x
The steps used in the solution of the equation -6 = -2/3(x + 12) + 1/3x are based on the principles of the Distributive Property, combining like terms, addition property of equality, symmetric property, subtraction property of equality, and multiplication property of equality.
Let's analyze the steps of the solution for the given equation -6 = -2/3(x + 12) + 1/3x:
Step 1: Distributive Property
The equation begins with the Distributive Property, which states that you can distribute a factor to each term inside parentheses. In this case, we distribute -2/3 to (x + 12), resulting in -2/3 * x and -2/3 * 12.
Step 2: Simplification
We simplify the expression -2/3 * 12 to -8, as multiplying -2/3 by 12 gives us -24, and simplifying the fraction -24/3 yields -8.
Step 3: Combine Like Terms
We combine the like terms -2/3x and -8. The equation becomes -2/3x - 8 + 1/3x.
Step 4: Combine Like Terms
We combine the like terms -2/3x and 1/3x by adding their coefficients. The sum of -2/3x and 1/3x is -1/3x.
Step 5: Addition Property of Equality
We add -1/3x to both sides of the equation to isolate the constant term. The equation becomes -6 - 1/3x = -1/3x.
Step 6: Symmetric Property
Since the equation has a form of -1/3x = -6 - 1/3x, we can rearrange the terms using the Symmetric Property.
Step 7: Addition Property of Equality
We add 1/3x to both sides of the equation to isolate the constant term. The equation becomes -6 = 0.
Step 8: Subtraction Property of Equality
We subtract 0 from both sides of the equation to simplify it further. The equation remains -6 = 0.
Step 9: Multiplication Property of Equality
We multiply both sides of the equation by any non-zero number to check for consistency. In this case, there is no need for multiplication as the equation is already in its simplified form.
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