What is the rule for combining like terms?
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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ſ x - 5y = -9( 4x + 4y = - 12Step 1 of 2: Determine if the point (-4,1) lies on both of the lines in the system of equations by substituting theordered pair into both equations.
Given:
\(\begin{gathered} x-5y=-9\ldots\ldots(1) \\ 4x+4y=-12\ldots\text{.}\mathrm{}(2) \end{gathered}\)The given point is (-4,1)
Let's check the ordered pair (-4,1) in the first equation
\(\begin{gathered} x-5y=-9 \\ (-4)-5(1)=-9 \\ -4-5=-9 \\ -9=-9 \end{gathered}\)Hence, (-4,1) is a solution of the first equation x-5y=-9.
Now, let's check (-4,1) in the second equation.
\(\begin{gathered} 4x+4y=-12 \\ 4(-4)+4(1)=-12 \\ -16+4=-12 \\ -12=-12 \end{gathered}\)So, (-4,1) is a solution of the second equation 4x+4y=-12.
Hence, (-4,1) is a solution of both equation in the system, then it is a solution to the overall system.
sales tax on a purchase at Sam's club is 8.42%. if your buy $ 245.32 worth of merchandise what will the cost be with sales tax
First, we need to calculate 8.42% of $245.32
\(245.32\times\frac{8.42}{100}=20.65\)Then we need to add the 20.65 to 245.32
\(245.32+20.65=265.98\)ANSWER
The cost with the sales tax is $265.98
Can someone help me with this. Under lines are: ║ p and q. The statement is: ∠1 and ∠3 are vertical to ∠s. The reasons are: given, vertical angels theorem, transitive property, and def. of vertical ∠s.
The proof for the the lines p and q are parallel is given below.
What are Alternate Exterior Angles?Alternate exterior angles are the angles formed on the two opposite sides of the transversal which are on the outer side of the parallel lines.
Given that,
∠1 ≅ ∠2 or ∠2 ≅ ∠1.
Now ∠1 ≅ ∠3, by the vertical angles theorem.
(By the vertical angles theorem, vertical angles formed by two intersecting lines are congruent).
Then ∠2 ≅ ∠3, by the transitive property.
(Transitive property states that, if a = b and b = c, then a = c)
By the corresponding angles converse postulate, two lines p and q are parallel.
(If the corresponding angles of two lines cut by a transversal are equal, the lines are parallel).
Hence it is proved.
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1/sinx+cosx + 1/sinx-cosx = 2sinx/sin^4x-cos^4x
The simplified expression is 2cos²(x) + sinx - 1 = 0
The expression we will be simplifying is
=> 1/sinx+cosx + 1/sinx-cosx = 2sinx/sin⁴x-cos⁴x.
To begin, let us look at the left-hand side of the expression. We can combine the two fractions using a common denominator, which gives us:
(1/sinx+cosx)(sinx-cosx)/(sinx+cosx)(sinx-cosx) + (1/sinx-cosx)(sinx+cosx)/(sinx-cosx)(sinx+cosx)
Simplifying this expression using the distributive property, we get:
(1 - cosx/sinx)/(sin²ˣ - cos²ˣ) + (1 + cosx/sinx)/(sin²ˣ - cos²ˣ)
Next, we can simplify each fraction separately. For the first fraction, we can use the identity sin²ˣ - cos²ˣ = sinx+cosx x sinx-cosx to obtain:
1 - cosx/sinx = (sinx+cosx - cosx)/sinx = sinx/sinx = 1
Similarly, for the second fraction, we can use the same identity to obtain:
1 + cosx/sinx = (sinx-cosx + cosx)/sinx = sinx/sinx = 1
Substituting these values back into the original expression, we get:
1 + 1 = 2sinx/(sin⁴x - cos⁴x)
Now, we can simplify the denominator using the identity sin²ˣ + cos²ˣ = 1 and the difference of squares formula:
sin⁴x - cos⁴x = (sin²ˣ)² - (cos²ˣ)² = (sin²ˣ + cos²ˣ)(sin²ˣ - cos²ˣ) = sin²ˣ - cos²ˣ
Substituting this back into the expression, we get:
2 = 2sinx/(sin²ˣ - cos²ˣ)
Finally, we can simplify the denominator using the identity sin²ˣ - cos²ˣ = -cos(2x):
2 = -2sinx/cos(2x)
Multiplying both sides by -cos(2x), we get:
-2cos(2x) = 2sinx
Dividing both sides by 2, we get:
-cos(2x) = sinx
Using the double-angle formula for cosine, we get:
-2cos²(x) + 1 = sinx
Simplifying this expression, we get:
2cos²(x) + sinx - 1 = 0
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Test Practice
18. Which doubles fact helps you find this sum?
9 + 8 =
17
10 + 10
5 + 5
9 + 9
7+7
Question 14 (5 points) Find the distance between (6, -2) and (1, -2). 7 units 5 units 6 units 4 units
Answer:
5 units
Step-by-step explanation:
Central Limit Theorem forms the foundation for the ___ branch of statistics
Central Limit Theorem forms the foundation for the inferential statistics branch of statistics
The Central Limit Theorem is a statistical concept that describes the behavior of the mean of a sufficiently large sample size drawn from any population with a finite mean and variance.
The Central Limit Theorem is a fundamental concept in statistics that states that, under certain conditions, the distribution of sample means approaches a normal distribution regardless of the shape of the population distribution. This theorem provides a basis for inferential statistics, which involves making inferences about a population based on a sample.
It allows us to use sample statistics to estimate population parameters with a certain level of confidence. This theorem has practical applications in many areas of research, such as in quality control, social sciences, and healthcare.
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The population f(x), in millions, of State A of a country after x years is represented by the function shown below:
f(x) = 2(1.08)x
The graph shows the population g(x), in millions, of State B of the country after x years:
graph of exponential function g of x that curves up from left to right and goes through points 0 comma 2 and 9 comma 4
Which conclusion is correct about the populations of State A and State B?
The original population of State B was half the original population of State A.
The original population of State A was half the original population of State B.
The original population of State A was equal to the original population of State B.
The original population of State B was one-fourth the original population of State A.
Answer:
The correct answer is B. The original population of State B was half the original population of State A.
Step-by-step explanation:
Hope i helped :)
Evaluate the given question.
Answer:
In this case since you have fraction you must make sure the limit x value does not make the denominator 0. In this case it does, so you have to factor the expressions to try to cancel out like terms when dividing. Use the method of factoring polynomials to find the solution. It is too late for me but I told you how you can answer it. Once you can plug in 2 into the denominator and not get 0, you can evaluate the limit. Keep practicing!
Step-by-step explanation:
helpp pleaseee asap!!
Answer:
30 and 5 left over
Step-by-step explanation:
185/6=30.83333333
30x6=180
185-180=5 left
If the number of bacteria on the surface of your phone triples every hour and can be described by the exponential function: f(x)=1000x3^x
, complete the table of values to show how much bacteria is on your phone after 4 hours.
Answer: 81,000
Step-by-step explanation:
We can solve this by using the formula given.
If f(1)=1000x3^1, then 1,000x3=3,000
If f(2)=1000x3^2, then 3^2=9 and 1000x9=9000,
and so on,
Now, f(4) will equal 1000x3^4, and 3^4 is 3x3x3x3, which is 9x9 or 9^2, which would be equal to 81, and 81x1000=81,000
To complete the table of values for the exponential function f(x) = 1000*3^x, we can evaluate the function for x = 0, 1, 2, 3, and 4, since we are interested in the number of bacteria on the phone after 4 hours.
x f(x)
0 1000
1 3000
2 9000
3 27,000
4 81,000
Therefore, after 4 hours, there will be 81,000 bacteria on the surface of the phone, assuming the number of bacteria triples every hour and can be described by the exponential function f(x) = 1000*3^x.
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You hear on the news that over the next 5 years the inflation rate will skyrocket to 12% if today a new blu-ray movie costs $19.99 assuming continuous compounding how much will the same disk cost in 5 years?
The Blu-ray movie will cost approximately $36.42 in 5 years with an inflation rate of 12% and continuous compounding.
To calculate the future cost of the Blu-ray movie in 5 years with an inflation rate of 12% and continuous compounding, we can use the formula for continuous compound interest:
A = P * e^(rt)
Where:
A = Future value
P = Present value
e = Euler's number (approximately 2.71828)
r = Annual interest rate (in decimal form)
t = Time period in years
In this case, the present value (P) is $19.99, the inflation rate (r) is 12% or 0.12, and the time period (t) is 5 years. Substituting these values into the formula, we get:
A = 19.99 * e^(0.12 * 5)
Calculating the exponent first:
0.12 * 5 = 0.6
Then:
e^0.6 ≈ 1.82212
Finally:
A = 19.99 * 1.82212 ≈ 36.42
Using the formula for continuous compound interest, we calculated that a Blu-ray movie that costs $19.99 today will cost approximately $36.42 in 5 years, assuming an inflation rate of 12% and continuous compounding.
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Step 1: (10000)^2cos^2θ=1−cos^2θ Step 2: cos^2θ=(10000)^2+11. Please explain how Step 2 derived from Step 1.
Step 2 is derived from Step 1 by substituting the expression for \(cos^2θ\)from Step 1 into the equation.
In Step 1, we have the equation (10000)^2\(cos^2θ\) = 1 - \(cos^2θ\). To derive Step 2, we want to isolate the term \(cos^2θ\). To do this, we can move all the terms involving \(cos^2θ\)to one side of the equation and the constant terms to the other side.
Starting with Step 1: (10000)^2\(cos^2θ\) = 1 - \(cos^2θ\)
We can add cos^2θ to both sides of the equation to get:
(10000)^2\(cos^2θ\) + \(cos^2θ\) = 1
Simplifying the left side, we can combine the two terms involving cos^2θ:
((10000)^2 + 1)\(cos^2θ\) = 1
Now we divide both sides of the equation by ((10000)^2 + 1) to isolate \(cos^2θ\):
\(cos^2θ\) = 1 / ((10000)^2 + 1)
This gives us the expression for \(cos^2θ\) in terms of a constant value, which is how Step 2 is derived from Step 1.
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3x+2y29
Can anyone help me figure this out fast?
Answer:
3x + 58y
Step-by-step explanation:
Diana wanted to make peanut brittle for a holiday party, so she bought a 16.5-ounce jar of peanuts at the grocery store. She used 3 5 of the peanuts to make peanut brittle. The next week, she split the remaining peanuts into 3 bags of trail mix for a hike with friends. How many ounces of peanuts did Diana put in each bag of trail mix?
Answer:
2.2 ounces.
Step-by-step explanation:
Quantity of peanuts Diana bought = 16.5 ounces
Quantity used for peanut brittle = 3/5
Hence:
3/5 × 16.5
= 9.9 ounces was used for peanut brittle.
The amount left =
16.5 ounces - 9.9 ounces
= 6.6 ounces.
We are told that: the next week, she split the remaining peanuts into 3 bags of trail mix for a hike with friends.
The ounces of peanuts she put in each bag of trail mix is calculated as:
6.6 ounces ÷ 3 bags
= 2.2 ounces.
Answer:
2.2
Step-by-step explanation:
Which of the following is not a frequently used strategic approach to setting a company apart from rivals and achieving a sustainable competitive advantage? outcompeting rivals on the basis of such differentiating features as higher quality, wider product selection, added performance, better service, or more attractive styling aiming for a cost-based competitive advantage simply trying to mimic the successful strategies of rivals focusing on a narrow market niche and winning a competitive edge by doing a better job than rivals of satisfying the needs and tastes of buyers comprising the niche Which of the following is not one of the basic reasons that a company's strategy evolves over time? the proactive efforts of company managers to improve the company's financial performance and secure a competitive advantage the need to respond to the actions and competitive moves of rival firms an ongoing need to abandon those strategy features that are no longer working well the need on the part of company managers to make no adjustments to the company's business model
The frequently used strategic approach to setting a company apart from rivals and achieving a sustainable competitive advantage which is not included among the options is: simply trying to mimic the successful strategies of rivals.An effective strategy is needed for companies to achieve their goals, which includes setting themselves apart from their rivals and achieving a competitive edge. There are different strategic approaches that companies use in order to achieve this.
Some of the strategic approaches are;Outcompeting rivals on the basis of such differentiating features as higher quality, wider product selection, added performance, better service, or more attractive styling.Focusing on a narrow market niche and winning a competitive edge by doing a better job than rivals of satisfying the needs and tastes of buyers comprising the niche.Aiming for a cost-based competitive advantage.
However, one of the strategic approaches to setting a company apart from rivals and achieving a sustainable competitive advantage that is not frequently used is simply trying to mimic the successful strategies of rivals.Therefore, option B is the correct answer to the question.Meanwhile, a company's strategy evolves over time due to some basic reasons which include:the need to respond to the actions and competitive moves of rival firms,the proactive efforts of company managers to improve the company's financial performance and secure a competitive advantage,an ongoing need to abandon those strategy features that are no longer working well.
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What are the domain and range of this exponential function?y=2x–9
The value of both domain and range of this exponential function is (−∞,∞).
y = 2x-9
The domain of the function can be defined as all real numbers except the ones where the expression is undefined. In the case of 2x-9, there is no real number for which this expression is undefined. Therefore, a domain of this exponential function is (−∞,∞).
The range of the function is defined as the set of all valid y values. In this case, all real numbers are valid values of y. Therefore, the range of this exponential function is (−∞,∞).
Therefore, domain of y = 2x-9 is (−∞,∞) and range is also (−∞,∞).
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Is the following relation a function?
Answer:
i d k so ima just say no
Step-by-step explanation:
Write an equation in slope intercept form for the graph (-3,3) (3,-1)
Answer:
y = (-3/2)x + 7/2
Step-by-step explanation:
Find the slope of this line first.
As you move from the first point to the second, x (the 'run') increases by 6 and y (the 'rise') decreases by 4 (from 3 to -1). Thus the slope is
m = rise/run = -6/4 or -3/2.
Find b for this situation, using y = mx + b, m = -3/2, y = -1 and x = 3:
-1 = (-3/2)(3) + b. Multiply all three terms by 2:
2(-1) = -9 + 2b, or 7 = 2b. Then b = 7/2, and the desired equation is
y = (-3/2)x + 7/2
How much pizza sauce is needed to cover a 16" pizza? (Note: 16" is the diameter of the pizza.)
Responses
A 200.96 in2200.96 in 2
B 803.84 in2803.84 in 2
C 50.24 in250.24 in 2
D 3215.36 in2
Answer:
It is difficult to give a precise answer without more information, such as the thickness of the sauce and the desired coverage. However, if we assume that the sauce is being applied evenly and that a thin layer is desired, the amount of sauce needed to cover a 16" pizza would be approximately 50.24 in2. This is because the area of a circle with a diameter of 16" is approximately 50.24 in2. To calculate the area of a circle, you can use the formula A = πr^2, where A is the area, π is approximately 3.14, and r is the radius of the circle (which is half the diameter). In this case, the radius would be 8" and the area would be approximately 50.24 in2.
Step-by-step explanation:
What is the value of 25 - 14 +12?
Answer:
23
Step-by-step explanation:
25-14 = 11
11+12=23
that would be your answer
How many solutions does this system of equations have?
Y= 1/5x - 2/5
X- 5y = 2
A) exactly one solution
B) no solution
C) infinitely many solutions
D) exactly two solutions
A lawnmower blade has a diameter of 36 inches and spins at a rate of 60 revolutions per minute. What is the linear velocity, in inches per minute, at the end of the blade?.
You can use the circumference of the circle that the blade makes to calculate the linear velocity at the end of the blade.
The linear velocity at the end of the blade is 13571.7 inches per minute
How to find the linear velocity of the lawnmower blade?You can think of it as if some circle is being drawn by the end of the blade and then that circle is like wheel of a bicycle and its travelling on road. Each rotation will make it cover distance equal to its circumference. Since there are 60 revolutions of the blade in each minute, thus, 60 rounds of that wheel.
The total distance in 1 minute = 60 times circumference of the circle made by the end of the blade of the lawnmower.
Since the blade is 36 inches long, it can be taken as radius of that circle.
The circumference is thus calculated as \(2 \times \pi \times 36 = 226.19 \: \rm inches\)
Thus, linear velocity = 226.19 times 60 inches per minute = 13571.7 inches per minute
Thus,
The linear velocity at the end of the blade is 13571.7 inches per minute
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Answer:
i think its D or 4,320pi
Step-by-step explanation:
just divided the previous persons answer by pi and its d on edge 2022.
What is the volume of this rectangular prism?
16 cubic centimeters
96 cubic centimeters
160 cubic centimeters
192 cubic centimeters
Answer:
The volume of this rectangular prism is 96 cubic centimeters
Step-by-step explanation:
The volume of a rectangular prism = Length × width × height
= 8 × 6 × 2
= 96 cubic centimeters
Find the measure of angle 5,6,7 Someone please help
Answer:
ly/3gVQKw3
Step-by-step explanation:
you can look on ly/3gVQKw3 Don't PRESS ON THAT LINK
Vic's favorite cookie recipe uses 250 grams of flour for every 170 grams of butter. Imani made cookies using 750 grams of flour for every 630 grams of butter.
Vic's recipe:
170 g of butter = 250 g of flour
1 g of butter = 250 ÷ 170
= 25 / 17 g of flour
Imani's recipe:
630 g of butter = 750 g of flour
1 g of butter = 750 ÷ 630 = 25 / 21 g of flour
Compare:
25 / 21 < 25 / 17
⇒ Imani uses less flour in her cookies than Vic
Imani's cookies are more dense.
Therefore, we get that Imani uses less flour in her cookies than Vic.
Imani uses less flour in her cookies than Vic because vic uses 25 / 17 g of flour while Imani uses 25 / 21 g of flour.
What is density and example?How much "stuff" is contained in a specific quantity of space is determined by its density. For instance, a block of the harder, lighter element gold (Au) will be denser than a block of the heavier element lead (Pb) (Au). Styrofoam blocks are less dense than bricks. Mass per unit volume serves as its definition.
Does density mean heavier?A substance's density is a measurement of how heavy it is in relation to its size. When placed in water, an object will float if its density is lower than that of the water, whereas it will sink if its density is higher.
if we see Vic's recipe:
170 g of butter = 250 g of flour
1 g of butter = 250 ÷ 170
= 25 / 17 g of flour
and Imani's recipe:
630 g of butter = 750 g of flour
1 g of butter = 750 ÷ 630 = 25 / 21 g of flour
Compare:
25 / 21 < 25 / 17
so Imani uses less flour in her cookies than Vic
moreover imani's cookies are more dense.
Therefore, we get that Vic uses more flour than imani.
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Giving a test to a group of students, the grades and gender are summarized below A B C Total Male 9 6 5 20 Female 18 20 10 48 Total 27 26 15 68 If one student is chosen at random, Find the probability that the student was NOT a male that got a "B"
The probability that the student was NOT a male that got a "B" is 62/68, which can be simplified to 31/34. To find the probability that the student was NOT a male that got a "B," we need to first calculate the total number of students that fit this criteria.
From the table, we know that there were a total of 26 students who did not receive a "B" (15 females and 11 males). Out of those 26 students, there were 11 males who did not receive a "B".
Therefore, the probability of choosing a student who was NOT a male that got a "B" is:
(15 + 11) / 68 = 26 / 68 = 0.382 or approximately 38.2%
So the probability that the student chosen at random was NOT a male that got a "B" is 0.382 or 38.2%.
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The table below shows the cost of bananas at a local grocery store.
Banana Prices
Weight of Bananas
(pounds)
Cost
($)
1
0.75
2
1.50
3
2.25
4
3.00
?
3.75
How many pounds of bananas cost $3.75?
I think it’s 5
Step-by-step explanation:
Because 1 banana is 0.75 cents and 75+75=150 so it’s probably 5
What is the factored form of 2x3 4x2 – x? 2 x (x squared 2 x 1) x (2 x squared 4 x 1) 2 x (x squared 2 x minus 1) x (2 x squared 4 x minus 1)
Polynomial is an expression that consists of indeterminates(variable) and coefficients. The factored form of 2x³+4x²-x is x(2x² + 4x - 1).
What are polynomials?Polynomial is an expression that consists of indeterminates(variable) and coefficient, it involves mathematical operations such as addition, subtraction, multiplication, etc, and non-negative integer exponentials.
The factored form of 2x³ + 4x² - x can be done as shown below,
2x³ + 4x² - x
Taking x as common,
= x(2x² + 4x - 1)
Hence, The factored form of 2x³+4x²-x is x(2x² + 4x - 1).
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Answer:
The answer is D
Step-by-step explanation: