7p-1-9p+5
simplist form
Answers
- 2p + 4
hope this helped!
The simplest form of the expression 7p - 1 - 9p + 5 is -2p + 4 as per the concepts of the simplest form.
To simplify the expression 7p - 1 - 9p + 5, we can combine like terms. Like terms have the same variable raised to the same power.
Let's first combine the terms with the variable p. We have 7p and -9p. Combining these terms, we get:
7p - 9p = -2p
Next, let's combine the constant terms -1 and 5:
-1 + 5 = 4
Now, we have the simplified expression:
-2p + 4
Therefore, the simplest form of the expression 7p - 1 - 9p + 5 is -2p + 4.
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The complete question:
The given expression is 7p-1-9p+5.
Find the simplest form of the expression.
Related Questions
Each year, Alex gets a raise of 8% plus an additional $100. In 2011, Alex’s annual
salary was $47,563.84. (a) What will Alex’s salary be in 2013? (Round your answer to the nearest cent.) (b) What was Alex’s salary in 2009? (c) From the two options below, which deal will give Alex the higher salary after 4 years? • Take the salary scale from part b.
• In January 2010, get a raise of 8%, and in January of 2011, get a raise of 8.15%, and in the next two years, get raises of 8.30% and 8.45%, respectively.
Answers
Answer: .......................
Step-by-step explanation:
PLEASEEE HELP ME!!! I NEED THE ANWER ASAP!!!
I WILL GIVE YOU 30 POINTS
Emily sells ice cream bars at the beach. In addition to a fixed salary, she earns a commission for each ice cream bar she sells. The table shows Emily's total earnings, y, from selling x bars of ice cream:
Ice Cream Sales and Earnings
Number of Bars Sold (x)
Total Earnings (dollars) (y)
0
30
1
33
2
36
3
39
Which equation best shows the relationship between x and y? (5 points)
Group of answer choices
y = x + 36
y = 3x + 36
y = x + 30
y = 3x + 30
Answers
Answer:
y = 3x + 30
Step-by-step explanation:
This is what the table should look like.
Number of Bars Sold (x) Total Earnings (dollars) (y)
0 30
1 33
2 36
3 39
When x = 0, y = 30. The point (0, 30) is the y-intercept.
As x goes up by 1, from 0 to 1, from 1 to 2, from 2 to 3, y goes up by 3, from 30 to 33, from 33 to 36, from 36 to 39.
A change of 1 in x results in a change of 3 in y.
That is a slope of 3 since
slope = (change in y)/(change in x)
The equation of a line in slope-intercept form is
y = mx + b
We have m = 3 and b = 30, so the equation is
y = 3x + 30
Answer: 3x + 30
Let A(x)=∫x0f(t)dtA(x)=∫0xf(t)dt, with f(x)f(x) as in figure.
A(x)A(x) has a local minimum on (0,6)(0,6) at x=x=
A(x)A(x) has a local maximum on (0,6)(0,6) at x=x=
Answers
To determine the local minimum and local maximum of the function A(x) = ∫₀ˣ f(t) dt on the interval (0, 6), we need to analyze the behavior of A(x) and its derivative.
Let's denote F(x) as the antiderivative of f(x), which means that F'(x) = f(x).
To find the local minimum and maximum, we need to look for points where the derivative of A(x) changes sign. In other words, we need to find the values of x where A'(x) = 0 or A'(x) is undefined.
Using the Fundamental Theorem of Calculus, we have:
A(x) = ∫₀ˣ f(t) dt = F(x) - F(0)
Taking the derivative of A(x) with respect to x, we get:
A'(x) = (F(x) - F(0))'
Since F(0) is a constant, its derivative is zero, and we are left with:
A'(x) = F'(x) = f(x)
Now, let's analyze the behavior of f(x) based on the given figure to determine the local minimum and maximum of A(x) on the interval (0, 6). Without the specific information about the shape of the graph, it is not possible to determine the exact values of x that correspond to local minimum or maximum points.
To find the local minimum, we need to locate a point where f(x) changes from decreasing to increasing. This point would correspond to x = x_min.
To find the local maximum, we need to locate a point where f(x) changes from increasing to decreasing. This point would correspond to x = x_max.
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Drew earns money washing cars for his neighbors on the weekends. Drew charges a set rate for each car he washes.
The points on the following coordinate plane show how much Drew charges for 2,5, and 8 cars.
How much does Drew charge for
4 cars?
Answers
Answer:
The answer is 30
I can't explain because the explanation is long
−8tan 1+tan2x Use appropriate identities to rewrite the following expression in terms containing only first powers of sine
Answers
By using Pythagorean identities the expression can be written as
-8 (sin ( x ) + 1 -sin 2x)
The Pythagorean identity is an important identity in trigonometry derived from the Pythagorean theorem. These identities are used to solve many trigonometric problems where, given a trigonometric ratio, other ratios can be found. The basic Pythagorean identity, which gives the relationship between sin and cos, is the most commonly used Pythagorean identity:
sin2θ + cos2θ = 1 (gives the relationship between sin and cos)
There are two other Pythagorean identities as follows :
sec2θ - tan2θ = 1 (gives the relationship between sec and tan)
csc2θ - cot2θ = 1 (gives the relationship between csc and cot)
Given expression is:
-8tanx/ 1 +tan2x
we know that:
By the Pythagorean Theorem:
1 + tan²x = sec²x
and tan x = sin x/cos x
and, sec x = 1/cos x
Now, we can write as:
-8tanx / 1 +tan²x
= -8 tan x / sec²x
= -8 sin x /cos x ÷ 1/cos²x
= -8 sin x/cos x × cos²x/1
= -8 (sin ( x ) + 1 -sin 2x)
Complete Question:
Use appropriate identities to rewrite the following expression in terms containing only first powers of sine:
−8tan 1 + tan2x.
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If f(x) = 3x + 2, what is f(5)?
Answers
Answer:
f(5) = 17
Step-by-step explanation:
plug in 5 in the x so 3(5)+2 =17
Answer:
17
Step-by-step explanation:
3(5) + 2 = 17
15 + 2 = 17
Suppose a signal from a radio transmitter tower can be received up to 175 miles away. The following
points represent locations of houses near the transmitter tower with the origin representing the tower.
Which point is not within the range of the tower?
a. (40, 120)
b. (60, 125)
c. (85, 100)
d. (55, 185)
e. (90, 150)
Answers
The point that is not within the range of the radio transmitter tower is
(55, 185).
The range of the radio transmitter tower is given as 175 miles. Out of the five given points, the distance between the origin and point (55, 185) is calculated as sqrt(55² + 185²) = 192.3 miles which is greater than the range of the tower. Therefore, this point is not within the range of the tower.
On the other hand, the distance between the origin and the other four points (40, 120), (60, 125), (85, 100), and (90, 150) are calculated to be 124.6 miles, 131.8 miles, 141.4 miles, and 159.8 miles respectively which are all less than the range of the tower. Hence, these four points are within the range of the radio transmitter tower.
In conclusion, out of the five given points, only the point (55, 185) is not within the range of the radio transmitter tower, which can be received up to 175 miles away.
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a student makes a short elctro magnett by winding 380 turns of wire around cylender of simater 4.7 cm the coil is connected to a battery pr
Answers
The magnetic dipole moment of the device is 2.5040 Am²
According to the question,
It is given that the number of turns students made a short electro around cylinder : N = 380
The diameter of cylinder : d = 4.7
Radius of cylinder : r = d/2
=> r = 4.7 / 2
=> r = 2.35
Area of cylinder : A = πr²
=> A = 3.14× (2.35)²
=> A = 17.34 cm² => 17.34 × 10⁻⁴ m²
Current in the wire : I = 3.9A
To find the magnetic dipole moment
M = N×I×A
where , N is number of turns
I is current and A is area of cylinder
Therefore, M = 380×3.8 × 17.34 × 10⁻⁴
=> M = 25,040 × 10⁻⁴
Hence , M = 2.5040 Am²
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3. The system of equations for two liquid surge tanks in series is
A₁ dh'₁/dt = q'ᵢ - 1/R₁ h'₁, q'₁ = 1/R₁ h'₁
A₂ dh'₂/dt = 1/R₁ h'₁ - 1/R₂ h'₂ q'₂ = 1/R₂ h'₂
Using state-space notation, determine the matrices A,B,C, and D assuming that the level deviations are the state variables: h'₁ and h'₂. The input variable is q'ᵢ , and the output variable is the flow rate deviation, q'₂.
Answers
The surge tank is a vital component of a system in which the flow rate fluctuates significantly. The flow rate entering the tank varies significantly, causing the fluid level in the tank to fluctuate as a result of the compressibility of the liquid. The surge tank is utilized to reduce pressure variations generated by a rapidly fluctspace uating pump flow rate. To determine the matrices A,B,C, and D using state-space notation, here are the steps:State representation is given by:dx/dt = Ax + Bu; y = Cx + DuWhere: x represents the state variablesA represents the state matrixB represents the input matrixC represents the output matrixD represents the direct transmission matrixThe equation can be written asA = [ -1/R₁ 0; 1/R₁ -1/R₂]B = [1/A₁; 0]C = [0 1/R₂]D = 0Thus, the matrices A,B,C and D assuming that the level deviations are the state variables: h'₁ and h'₂. The input variable is q'ᵢ, and the output variable is the flow rate deviation, q'₂ are given by A = [ -1/R₁ 0; 1/R₁ -1/R₂]B = [1/A₁; 0]C = [0 1/R₂]D = 0.Hence, the required matrices are A = [ -1/R₁ 0; 1/R₁ -1/R₂], B = [1/A₁; 0], C = [0 1/R₂], and D = 0 using state-space notation for the given system of equations for two liquid surge tanks.
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Jamal loves his dog, Rupert. On sunny days, Jamal keeps Rupert on a 12-foot leash
in the backyard. He secures the leash to a stake in the ground.
> Answer each question and use 3.14 for T.
1 Determine the diameter, circumference, and area of Rupert's play area.
Answers
Diameter = 24 foot, circumference = 75.36 foot, Area = 452.16 square foot
As the leash is 12 feet, and dog Rupert will form a circle in the backyard.
As the leash is of 12 feet, so it is the radius(r) of the circle.
Diameter = 2r
= 2×12
= 24 foot
Circumference = 2πr
=2×3.14×12
= 75.36 foot
Area of the circle = π\(r^{2}\)
= 3.14×\(12^{2}\)
=3.14 × 144
= 452.16 \(foot^{2}\)
Therefore we get diameter = 24foot, circumference = 75.36 foot and area = 452.16 square foot.
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Consider the vector field F(x,y,z)=(−2y,−2x,7z)F(x,y,z)=(−2y,−2x,7z). Show that F is a gradient vector field F=∇V by determining the function V which satisfies V(0,0,0)=0.
Answers
To show that the vector field F(x, y, z) = (-2y, -2x, 7z) is a gradient vector field, we need to find a scalar function V(x, y, z) such that its gradient, ∇V, is equal to F. We can determine the function V by integrating the components of F with respect to their respective variables.
Let's find the function V(x, y, z) by integrating the components of F(x, y, z) = (-2y, -2x, 7z) with respect to their variables.
∫-2y dx = -2xy + g(y, z)
∫-2x dy = -2xy + h(x, z)
∫7z dz = 7/2 z^2 + k(x, y)
We can see that -2xy is a common term in the first two integrals. Similarly, we observe that there are no common terms between the first and third integrals, as well as the second and third integrals. Therefore, we can assume that g(y, z) = h(x, z) = 0, since they will cancel out in the subsequent calculations.
Now, we can rewrite the integrals:
∫-2y dx = -2xy + C1(y, z)
∫-2x dy = -2xy + C2(x, z)
∫7z dz = 7/2 z^2 + C3(x, y)
By comparing these integrals with the components of the gradient vector, we can conclude that ∇V = (-2y, -2x, 7z), where V(x, y, z) = -xy + 7/2 z^2 + C.
To determine the constant C, we use the condition V(0, 0, 0) = 0:
V(0, 0, 0) = -(0)(0) + 7/2 (0)^2 + C = 0
C = 0
Therefore, the function V(x, y, z) that satisfies V(0, 0, 0) = 0 is V(x, y, z) = -xy + 7/2 z^2. Thus, the vector field F(x, y, z) = (-2y, -2x, 7z) is indeed a gradient vector field F = ∇V.
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Question 3 - Simulating a Random Walk
Consider the following random process:
You start at point zero and take a number of steps. Each step is
equally likely to be a step forward (+1) or a step backwar
Answers
Answer:
The random process described is a symmetrical random walk.
A symmetrical random walk is a mathematical model that represents a series of steps taken in either a forward (+1) or backward (-1) direction, each with equal probability. Starting from point zero, the process involves taking a certain number of steps. The outcome at each step is independent of previous steps, making it a stochastic process. The key characteristic of a symmetrical random walk is that, on average, the process remains centered around its starting point. This means that over a large number of steps, the expected displacement from the starting point approaches zero.
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A student wonders if people of similar heights tend to date each other. She measures herself, her dormitory roommate, and the women in the adjoining rooms, then she measures the next man whom each woman dates. Here are the data (heights in inches): Women: 64 65 65 66 66 70 Men: 68 68 69 70 72 74 Determine whether each of the following statements is true (T) orfalse (F). (a) If we had measured the heights of the men and women in centimeters (1 inch= 2.54 cm), the correlation coefficient would have been 2.54 times larger. (b) There is a strong negative association between the heights of men and women because women are always smaller than the men they date. (c) There is a positive association between the heights of men and women.
Answers
Answer:
(a) False
(b) False
(c) True
Step-by-step explanation:
(a) If we had measured the heights of the men and women in centimeters (1 inch= 2.54 cm), the correlation coefficient would have been 2.54 times larger.
No, since changing the units of measurement does not change the correlation coefficient
(b) There is a strong negative association between the heights of men and women because women are always smaller than the men they date.
Negative association means that as one variable increases, the other decreases, Here, we see that as the heights of the men increase, the height of the women do not reliably decrease, hence there is no strong negative asscoiation
(c) There is a positive association between the heights of men and women.
We see from the values given that as the heights of men increase, so do the heights of women and vise versa, so there is a positive association between the heights of men and women
first to reply gets brainliest, only if u reply correct
Answers
Answer: D
Step-by-step explanation: If you plug in the formula, it works.
Answer:
D
Step-by-step explanation:
A company manufactures and sells x television sets per month. the monthly cost and​ price-demand equations are ​c(x)=75,000 50x and p(x)=300− x 30​, 0≤x≤9000. ​(a) find the maximum revenue.
Answers
182.5 is the maximum revenue.
What do revenue means?
Revenue is the total amount of income generated by the sale of goods or services related to the company's primary operations. Revenue, also known as gross sales, is often referred to as the "top line" because it sits at the top of the income statement. Income, or net income, is a company's total earnings or profit.Revenue = p(x) × x = ( 300 - x /30)x
⇒R(x) = 300x - x²/30
R'(x) = \(\frac{d}{dx} (300 - \frac{x^{2} }{30} ) = \frac{d}{dx} (300x) - \frac{d}{dx} (\frac{x^{2} }{30})\)
300 - x /15 = 0
⇒ x = 300 . 15 = 4500
∴ Max Revenue = R(4500) = 300 . 4500 - 4500²/30 = 675000 $
Profit = Revenue - cost
P(x) = 300x - x²/30 - (75000 + 60x)
P'(x) = d/dx ( 300x - x²/30 - ( 75000 + 60x)
= d/dx (300x) - d/dx (x²/30) - d/dx ( 75000 + 60z))
= 300 - x /15 -60
= 240 - x /15
P'(x) = 0 ⇒ x = 240 . 15 = 3600
P(3600) = 300 .3600 - 3600²/30 - (75000 +60 . 3600) =357000
∴ Max profit is 357000$ when 3600 sets are manufactured
After taxation , p(x) = 300x - x²/30 - ( 75000 + 60x) -5x
P'(x) = 300x - x²/30 - ( 75000 + 60x) -5x
= d/dx (300x) - d/dx (x²/30) - d/dx ( 75000 + 60x ) - d/dx (5x)
= 300 - x/15 - 60 -5 = 235 - x/15
P'(x) = 0 ⇒ x = 235 . 15 = 3525
Pmax = P(3525) = 300 .3525 - 3525²/30 - ( 75000 + 60 .3525) - 5 .3525= 678375/2 (Decimal ; 339187.5)
P(3525) = 300 - 3525/30 = 365/2 = 182.5
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The record for the largest scoop of ice cream was made in Wisconsin. Thebscoop of ice cream was 3,010 pounds! How many ounces of ice cream is that?
Answers
Answer:
48160
Step-by-step explanation:
3(4w+2)+13 this was for hw and i need to get my grade up pls help
Answers
Answer:
12w+19
Step-by-step explanation:
\(3(4w + 2) + 13\)
You multiply everything in the brackets with 3\(3(4w) + 3(2) + 13\)
\(12w + 6 + 13\)
combine the like terms\(12w + 19\)
help asap will give brainliest!!!!
Answers
Answer:45 & 90
Step-by-step explanation:
Answer:
∠x = 159° and ∠y = 149°
Step-by-step explanation:
∠a = 31°
∠b = 52°
∠x = ?
∠y = ?
∠a and ∠y are supplementary angles so:
∠a + ∠y = 180
31 + ∠y = 180
∠y = 180 - 31
∠y = 149°
∠b also has a supplementary angle which is not labeled in the question so let's label that ∠c.
∠b + ∠c = 180
52 + ∠c = 180
∠c = 180 - 52
∠c = 128°
∠a and ∠c are both inside a triangle formed by all the lines crossing with each other. Since the sum of angles inside a triangle is 180°, find the third angle in this triangle (∠d) using all the values we were given and solved for:
∠a + ∠c + ∠d = 180
31 + 128 + ∠d = 180
∠d = 180 - 31 - 128
∠d = 21°
∠d and ∠x are supplementary angles so:
∠d + ∠x = 180
21 + ∠x = 180
∠x = 180 - 21
∠x = 159°
∠x = 159° and ∠y = 149°
Sydney has five pink socks, six yellow socks and four red socks in her drawer.
What is the probability that she'll randomly pick a yellow sock, put it on, then
randomly pick a pink sock?
Answers
railroad accidents a researcher wishes to study railroad accidents. he wishes to select 4 railroads from 15 class i railroads, 2 railroads from 8 class ii railroads, and 1 railroad from 7 class iii railroads. how many different possibilities are there for his study?
Answers
Different possibilities for the given case are, 267540
4 railroads chosen from 15 class I railroads
2 railroads chosen from 8 class II railroads
1 railroad chosen from 7 class III railroads
So total combinations = ¹⁵C₄ ˣ ⁸C₂ ˣ ⁷C₁
= (15!)/(4!*11!) x (8!)/(2!6!) x (7!)/(1!6!)
= 15 x 7 x 13 x 4 x 7 x 7 = 267540
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In the Mediterranean, the Mycenaeans rose to prominence by a mix of military prowess, economic connections, and cultural sway.
Thus, Military Might: The Mycenaeans had a strong military force and were expert warriors. They used sophisticated bronze weapons and chariot warfare as a tactic.
They were able to increase their influence and take control of neighbouring territories thanks to their military might.
Control over Trade Routes: The Mycenaeans had complete control over key trade routes in the Mediterranean, particularly those that extended from the Aegean to the eastern Mediterranean and beyond.
Thus, In the Mediterranean, the Mycenaeans rose to prominence by a mix of military prowess, economic connections, and cultural sway.
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I need help solving this. 8÷2(2+2)
Answers
Answer:
16
Step-by-step explanation:
8/ 2*(2+2) = 4*(2+2) = 4*4 = 16
Consider the function f(x) = x^2–4 / x-2 (a) Fill in the following table of values for f(x):
X= 1.9 1.99 1.999 1.9999 2.0001 2.001 2.01 2.1 f(x) = = 3.9 3.99 3.999 3.9999 4.0001 4.001 4.01 4.1 (b) Based on your table of values, what would you expect the limit of f(x) as x approaches 2 to be?
lim_x--> 2 x^2/4 / x-2 = ___
(c) Graph the function to see if it is consistent with your answers to parts (a) and (b). By graphing, find an interval for x near 2 such that the difference between your conjectured limit and the value of the function is less than 0.01. In other words, find a window of height 0.02 such that the graph exits the sides of the window and not the top or bottom. What is the window? ____ <= x <= ____
____ <= y <=____
Answers
(a) Given function is f(x) = x² − 4/x − 2; we have to fill the following table of values for f(x):Xf(x)1.93.931.9943.99943.999934.0014.014.91(b) Based on the table of values, the limit of f(x) as x approaches 2 is 4. (c) Graph of the given function is as follows:The limit of the given function f(x) as x approaches 2 is 4. Therefore, lim_x→2 x² − 4/x − 2 = 4.Also, the interval for x near 2 such that the difference between the conjectured limit and the value of the function is less than 0.01 is 1.995 <= x <= 2.005.What is the window? 3.99 <= y <= 4.01.
Cuantas veces tengo que multiplicar 10 para que de 1000000
Answers
Answer:
Puede ser Asi:
\( {10}^{6} = 1000000\)
Tambien puede ser:
\(1000000 \div 10 = 100000\)
Trudy was glad to give live now where a speech focused on getting a customer to purchase rather than back in Aristotle’s day when speeches had such a formal structure. Does Trudy understand the history of speeches?
A. Yes, speeches today only have one main idea in each.
B. Yes, today is far more casual in length and purpose than in Aristotle’s day.
C. No, Trudy is trying to persuade which Aristotle recognized as a primary purpose of speeches.
D. No, there were no sales presentations in Aristotle’s day
Answers
Trudy gave a speech focused on persuading a customer to purchase, which indicates a departure from the formal structure of speeches in Aristotle's day.
Trudy's speech, which emphasizes persuading a customer to make a purchase, suggests a more modern approach to speeches compared to Aristotle's time. Speeches in Aristotle's day often followed a more formal structure, encompassing various elements such as introduction, body, and conclusion, with an emphasis on informing, persuading, or entertaining the audience.
Option A states that speeches today only have one main idea in each. While it is common for modern speeches to focus on a central message or main idea, it does not necessarily address the historical context of speeches.
Option B suggests that today's speeches are more casual in length and purpose compared to Aristotle's day. This aligns with the idea that Trudy's speech deviates from the formal structure of traditional speeches. However, it does not provide a comprehensive understanding of the history of speeches.
Option C indicates that Trudy is trying to persuade, which Aristotle recognized as a primary purpose of speeches. This option acknowledges that persuasion has long been recognized as an essential aspect of speeches and suggests that Trudy understands this aspect.
Option D states that there were no sales presentations in Aristotle's day. While sales presentations as we know them today may not have existed during Aristotle's time, the concept of persuasion and influencing an audience through speeches certainly did.
Based on the given information, it is challenging to determine whether Trudy fully understands the history of speeches. While Trudy's speech exhibits a departure from the formal structure of Aristotle's day, it is unclear whether she has a comprehensive understanding of the historical context of speeches.
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A card is drawn one at a time from a
well-shuffled deck of 52 cards. In 13
repetitions of this experiment, 1
king is drawn. If E is the event in
which a king is drawn, find the
experimental probability P(E).
P(E)=
Answers
The empirical probability of drawing the cards will be 6 / 55.
What is empirical probability?The ratio of the number of outcomes in which a defined event occurs to the total number of trials, not in a theoretical sample space but in a real experiment, is the empirical probability, relative frequency, or experimental probability of an event.
Given that a card is drawn one at a time from a well-shuffled deck of 52 cards. In 13 repetitions of this experiment, 1 king is drawn.
The number of kings in a well-shuffled deck consists of 52 cards which is 4.
The number of ways of drawing consists of 4 kings in 13 repetitions which is ¹³C₄.
In 13 repetitions, 2 kings are drawn by ¹³C₂ ways,
The empirical probability will be calculated as,
P(E) = ¹³C₂ / ¹³C₄
P(E) = [ (13!) / (13-2)! ] ÷ [ (13!) / ( 13-4)!(4!) ]
P(E) = ( 4 x 3 ) / ( 11 x 10)
P(E) = 6 / 55
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I NEED THIS ANSWERED ASAP!! Roses are on sale 6 for $10. How many roses can you buy for $15?
Answers
Answer:
9
Step-by-step explanation:
you can buy 6 with ten then 3 with the five because each roe sells for 1.6
so you have a total of 9
Philip ran 438 mile yeterday. Michael ran 158 mile yeterday. How much farther did Philip run than Michael?
Answers
Answer:
he ran 280 miles more than Michael
Step-by-step explanation:
438-158=280
Evaluate the expression: 28-16+2x4’2
Answers
Answer: 44
Step-by-step explanation:
28 - 16 + 2 x 4^2
28 - 16 + 2 x 16
28 - 16 + 32
12 + 32
44
What is the rule for combining like terms?
Answers
The rule for combining like terms is a way to simplify algebraic expressions. This will result in a single term with the same base and exponent as the original terms, but with a coefficient that is the sum of the coefficients of the original terms.
The rule for combining like terms is a way to simplify algebraic expressions. It is based on the idea that if two terms have the same base (the number or variable part) and the same exponent (the power of the number or variable), then they can be combined into a single term. For example, if we have the expression 5x2 + 3x2, then the two terms can be combined because they have the same base (x2) and the same exponent (2). To combine these terms, we simply add the coefficients (5 and 3) to get 8x2, which is the simplified form of the expression. The same rule applies for combining terms with different bases, but the same exponent. If we have 5x2 + 3y2, then we can combine the terms by adding the coefficients (5 and 3) to get 8x2 + 3y2. This is the simplified form of the expression. By using this method, we can simplify complex expressions and make them easier to solve.
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When graphing inequalities, where can the solutions be found?
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Solutions will be located in the shaded region. Since this is a “less than” problem, ordered pairs on the boundary line are not included in the solution set. These values are located in the shaded region, so are solutions. (When substituted into the inequality x–y<3.
When solving systems of inequalities, the solutions are the regions where all the inequalities are true and will be represented by the intersection of the shaded areas.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
When graphing inequalities, the solutions can be found on the side of the number line or the coordinate plane where the inequality is true.
For example, if the inequality is x > 3, the solutions would be all the values of x that are greater than 3. These solutions would be represented by shading the area to the right of line x = 3 on the coordinate plane.
Similarly, if the inequality is y < 2, the solutions would be all the values of y that are less than 2. These solutions would be represented by shading the area below the line y = 2 on the coordinate plane.
It's important to note that when solving systems of inequalities, the solutions are the regions where all the inequalities are true and will be represented by the intersection of the shaded areas.
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