Answer:
1.Solve one of the equations for either variable.
2.Substitute the expression from Step 1 into the other equation.
3.Solve the resulting equation.
4.Substitute the solution in Step 3 into one of the original equations to find the other variable.
5.Write the solution as an ordered pair.
6.Check that the ordered pair is a solution to both original equations.
Step-by-step explanation:
What happens if you log a log?
The guidelines apply to logarithms of any base anyway a comparable base ought to be used all through a calculation. This guideline tells us how to add two logarithms together. Adding log An and log B achieves the logarithm of the consequence of An and B, that is log Stomach muscle.
As demonstrated by the norm of logs, a log of a base with similar bases will drop and will leave simply the power. Logarithms are models, and when you increment, you will add the logarithms. The log of a thing is the number of logs.
In case you have comparable systems on the different sides of a circumstance, they offset each other! Recollect that this conceivably works when the logarithms on the different sides of the circumstance have a comparable base.
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10. Find the solution set for the following
y=x²-3x-4
y-x=-4
Answer:
I have no idea tbh I need help with this too
Step-by-step explanation:
PLEASE HELP!!!!!!!!!!!!!!!
What is the greatest possible quotient of any two distinct members of the set $\left\{\frac{2}{5}, \frac{1}{2},5,10\right\}$? Specifically, we wish to maximize $\frac{x}{y}$, where $x$ and $y$ are chosen from the previous set.
The greatest possible quotient of any two distinct members of the set; { 2 / 5, 1 / 2, 5, 10 } as required is; 25.
What is the maximum possible quotient of any pair of numbers from the set?It follows from the task content that the set from which the two numbers whose quotient is to be maximised is; { 2 / 5, 1 / 2, 5, 10 }.
On this note, since the quotient which is to be maximised is hypothetically; x / y;
To maximize the result of the quotient; it follows that the numerator, x must be as great as possible and the denominator, y must be as less as possible.
On this note, since the maximum number in the set is 10 and the minimum is 2 / 5; we have that;
10 / (2 / 5)
= ( 10 × 5 ) / 2
= 25.
Ultimately, the greatest possible quotient as required is; 25.
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How do parallel algorithms differ from sequential?
The capacity to complete complex tasks quickly enough to make them useful is the main benefit of choosing a parallel method over a sequential one.
Differences between Sequential and Parallel ComputingSequential Computing: One instruction is delivered at a specific time, and the subsequent instruction must wait for the first instruction to complete before it can be executed. This is known as sequential computing. Because all the instructions are carried out in order, it is often referred to as a conventional computing technique. It has a single CPU that performs poorly and has a heavy workload. The biggest drawback of employing this computing is that it requires more time because just one instruction is being processed at a time.
Parallel Computing: A computing method known as parallel computing involves running numerous calculations or processes simultaneously in parallel. Parallel computing is a kind of computing in which multiple processes can run at once.
Due to the simultaneous execution of the operations, time is saved. It resolves more complex issues. There are many processors with high performance and little work being put on each of them.
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The weekly sales of an album have increased since it was first sold at a music store 6 weeks ago. The linear regression equation describing the change is y=1.9x+13.3 , where x represents the week and y represents the number of albums sold per week. Round the residual value to the nearest integer and then construct a residual plot of the data.
The residual value to the nearest integer and then construct the residual plot of the data will be 25.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Since an album went on sale for the first time at a music retailer six weeks ago, its weekly sales have climbed. The change is described by the linear regression equation y=1.9x+13.3, where x is the week and y is the number of albums sold each week.
The residual value is given as,
y = 1.9(6) + 13.3
y = 11.4 + 13.3
y = 24.7
y ≅ 25
The residual value to the nearest integer and then construct the residual plot of the data will be 25.
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PLS HELP ME I ONLY HAVE 2 MINS TO ANSWER!!!!!!!!! ITS 100 PTS!!!!!
Three salesmen work for the same company, selling the same product. And, although they are all paid on a weekly basis, each salesman earns his paycheck differently. Salesman A works strictly on commission. He earns $65 per sale, with a maximum weekly commission of $1,300. Salesman B earns a weekly base salary of $300, plus a commission of $40 per sale. There are no limits on the amount of commission he can earn. Salesman C does not earn any commission. His weekly salary is $900. The following table shows the number of sales each salesman had during the first three weeks of this month.
Week 1 Week 2 Week 3
Salesman A 11 14 16
Salesman B 14 15 13
Salesman C 16 12 11
In which week(s), did Salesman C have a larger paycheck than both of the other salesmen? Select all that apply.
Week 3
None of the weeks.
Week 2
Week 1
In Week 1,
Salesman C got larger paycheck than Salesman A and Salesman B.
What is equation?Mathematically, an equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”. For example, 2x – 5 = 13.
Here,
2x – 5 and 13 are expressions
The sign that connects these two expressions is “=”.
In algebra, an equation is a condition on a variable. It is satisfied only for a definite value of the variable. That means, the equation 2x – 5 = 13 is satisfied only for x = 9.
Given,
Commission of salesman A per sale = $65
Commission of salesman B per sale = $40
Commission of salesman C per sale = $0
Salary of salesman A per week = $0
Salary of salesman B per week = $300
Salary of salesman C per week = $900
No. of sales × commission + salary = total earning
In week 1.
Earning of A
11 × $65 + $0 = $715
Earning of B
14 × $40 + $300 = $860
Earning of C
16 ×$0 + $900 = $900
In week 2.
Earning of A
14 × $65 + $0 = $910
Earning of B
15 × $40 + $300 = $900
Earning of C
12 ×$0 + $900 = $900
In week 3.
Earning of A
16 × $65 + $0 = $1040
Earning of B
13 × $40 + $300 = $820
Earning of C
111 ×$0 + $900 = $900
By the above calculation Salesman C received $900 in week 1 which is greater than Salesman A and Salesman B.
In week 2 and week 3 his paycheck is smaller than both of the other salesman.
Hence, Salesman C received larger paycheck than both of the other salesmen in Week 1.
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9 people audition for a choir. The choir director must choose one soprano, one alto,
and one tenor.
In how many ways can the director fill these positions?
The numbers of ways that the director fill these positions is 504 ways.
What is the position about?There are a few different ways to approach this problem, but one possible method is to use the combination formula.
To fill the position of soprano, the director has 9 choices. After selecting one soprano, the director is left with 8 singers to choose from for the alto position. Then, the director has 7 singers to choose from for the tenor position.
So, the total number of ways the director can fill these positions is:
9 × 8 × 7
= 504 ways.
Alternatively, One can also use the permutation formula to solve the question. The formula of permutation is (n!/(r!(n-r)!)), where n is the total number of items to choose from, and r is the number of items to be chosen.
For this case n is 9, and r is 3, so the permutation would be:
(9!/(3!(9-3)!)
= (987)/(321)
= 504
Therefore, In both cases, the answer is 504 ways.
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How do you know which inequality represents a graph?
In order to determine which inequality represents a graph, you need to look at the inequality and identify if the equation is an open or closed interval. If it is an open interval, it will be represented by a dashed line on the graph. If it is a closed interval, it will be represented by a solid line on the graph.
1. Look at the inequality and identify if the equation is an open or closed interval.
2. If it is an open interval, it will be represented by a dashed line on the graph.
3. If it is a closed interval, it will be represented by a solid line on the graph.
4. Determine the starting and ending points of the inequality, and plot them on the graph.
5. Draw the line that connects the two points, either dashed or solid, depending on whether the interval is open or closed.
6. Shade the area of the graph that is represented by the inequality.
7. Label the graph with the inequality, the points, and the shading.
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What is one way you could use the positive feelings from a situation toward a future motivation?
Develop a positive personal process and focus
Remember the “How could I do better?” mentality
Tell the adults in your life to hold you accountable
Be content with not being successful at everything
Answer:
One way to use positive feelings from a situation towards future motivation is to focus on the positive aspects of the experience and try to replicate them in the future. For example, if you had a particularly enjoyable and successful project at work, you might try to identify the specific factors that contributed to your success and seek out similar opportunities in the future. This approach can help you to build on your strengths and experiences and maintain a positive and motivated outlook. Additionally, setting specific goals for yourself and tracking your progress can help to keep you motivated and on track towards future success.
What is a plot point example?
A plot point example contains a point in a story that defines the turning point in the story.
What is a plot point?A story's plot point is a crucial turning moment that occurs during the narrative. The tale and the characters may be developed and advanced using these ideas.
Why are plot points necessary in stories?Plot points offer your tale movement by advancing the plot and dragging the reader along. 'A particularly crucial portion of a storyline of a work of fiction,' according to the definition of a plot point. Never undervalue the significance of your framework, even if your book is contemplative or literary.
An example of plot point is :
In a story about a young girl who is trying to save her village from an impending monster attack, the plot point may occur when the girl discovers an ancient artifact that gives her the power to defeat the monster. This event marks a significant turning point in the story, as it sets the stage for the girl to take on the monster and potentially save her village.
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Geoff purchased an annual golf pass for a municipal golf course in his town. He pays a flat fee for the annual golf pass and then each round he plays he must pay the additional cost for a golf cart. A linear model of this situation contains the values (25 , 1,167) and (41 , 1,407), where x represents the number of times he plays each year, and y equals the total amount he spends on golf in one year. What is the flat fee for the annual golf pass? A. $15 B. $1,032 C. $792 D. $807
To find the flat fee for the annual golf pass, we need to find the y-intercept of the linear model. The y-intercept is the point at which the line crosses the y-axis, which in this case represents the flat fee for the annual golf pass.
The equation of a line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept.
We can find the slope of the line using the two points given: (25, 1,167) and (41, 1,407). The slope is (1,407 - 1,167) / (41 - 25) = 240 / 16 = 15.
Now that we know the slope, we can use either of the two points given to find the y-intercept. Let's use the point (25, 1,167). Plugging the values into the equation y = mx + b, we get 1,167 = 15 * 25 + b. Solving for b, we find that b = 1,167 - 15 * 25 = -300.
The y-intercept is -300, so the flat fee for the annual golf pass is $300. The correct answer is therefore D, $807.
The table shows the amount of words Andrew and ella can text per second Andrew : 1 | _
7 | 21
28 | 84
Ella : 1 | _
4 | 14
16 | 56 who can type faster?
In words , explain how you know. PLEASEEEE HELP ME !
Ella can type faster than Andrew because the rate at which she types is faster than Andrew's rate by 0.5 text per second.
What is rate of change?In Mathematics, rate of change can be defined as a type of function that describes the average rate at which a quantity either decreases or increases with respect to another quantity.
In this scenario, we would determine the rate of change with respect to the amount of words that Andrew and Ella can type per second as a ratio. For the amount of words that Andrew can type per second, we have:
Andrew = 7/21 = 28/84 = 1/3 or 1:3.
For the amount of words that Ella can type per second, we have:
Ella = 4/14 = 16/56 = 1/3.5 or 1:3.5
Difference = 3.5 - 3
Therefore, we can logically conclude that Ella can type faster.
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A regular heptagon has a radius of approximately 27.87 cm and the length of each side is 24.18 cm. What is the approximate area of the heptagon rounded to the nearest whole number
Rounded to the nearest whole number, the approximate area of the heptagon is 555 sq cm.
A heptagon is a seven-sided polygon. To find the area of a regular heptagon, we can use the formula:
Area = (7/4) * (perimeter) * (apothem)
where "perimeter" is the length of the heptagon's circumference and "apothem" is the distance from the centre to the midpoint of one of its sides. The radius of the heptagon is the apothem, which is 27.87 cm.
The perimeter of the heptagon can be calculated by multiplying the length of one side by the number of sides:
Perimeter = 24.18 cm * 7 = 168.26 cm
Now we can substitute these values into the area formula:
Area = (7/4) * 168.26 * 27.87
Area = approximately 554.55 sq cm.
Rounded to the nearest whole number, the approximate area of the heptagon is 555 sq cm.
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Which linear equation shows a proportional relationship?
y equals two thirds times x
y equals negative 3 times x minus one seventh
y equals three fourths times x minus 5
y equals 3 times x plus 7
The linear equation that shows a proportional relationship is y equals two thirds times x.
A proportional relationship is a relationship between two variables in which one variable is a constant multiple of the other. In other words, if y is directly proportional to x, then y = kx for some constant k. This can also be written as y/x = k, where k is the constant of proportionality.
The linear equation that shows a proportional relationship is y = 2/3x.
It shows a direct relationship because the coefficient of x (2/3) is constant, and there is no constant term (y-intercept) which breaks the proportionality.
The other equations do not show a proportional relationship because they have a coefficient that varies with x or a constant term.
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A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
The statements that are always true regarding the diagram are:
i. m∠5 + m∠6 =180°
ii. m∠2 + m∠3 = m∠6
iii. m∠2 + m∠3 + m∠5 = 180°
Exterior and interior angles of a triangle.A triangle is a 2 dimensional plane figure which is formed by three straight lines and has three interior angles. It has both interior and exterior angles. Some examples of a triangle are; isosceles, equilateral, scalene, right angled etc.
The interior angles of a triangle are the measure of the three internal angles of the triangle, while exterior angles are external to the interior angles of the triangle.
Note that; the exterior angle of a triangle is equal to the sum of the two adjacent interior angles.
Therefore considering the given diagram, the required statements that are always true regarding the diagram are:
i. m∠5 + m∠6 =180°
ii. m∠2 + m∠3 = m∠6
iii. m∠2 + m∠3 + m∠5 = 180°
A sketch of the diagram is herewith attached to this answer for clarity.
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It took Xander 31 minutes to run a 5-kilometer race last weekend. If you know that 1 kilometer equals 0.621 mile, how many minutes did it take Xander to run 1 mile during the race
So it took Xander approximately 9.96 minutes to run 1 mile during the race.
To convert the distance of the race from kilometers to miles, you can use the conversion factor 1 kilometer = 0.621 miles.
To find the time it took Xander to run 1 mile, you can divide the total time it took him to run the entire race by the number of miles he ran.
First, convert the distance of the race from 5 kilometers to miles:
5 kilometers * 0.621 miles/kilometer = 3.105 miles
Then, divide the total time it took Xander to run the race by the number of miles he ran:
31 minutes / 3.105 miles = 9.96 minutes/mile
So it took Xander approximately 9.96 minutes to run 1 mile during the race.
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PLEASE HELPPPP! Round to the nearest tenth, then find the sum. 0.92 + 5.37 2. Round to the nearest whole number, then find the difference. 6.3 − 2.8 3.Round to the nearest tenth, then find the difference. 13.56 − 10.02 4.Oliver did the high jump three times. His scores were 7.032 feet, 2.485 feet, and 4.59 feet. How many feet did he jump in total? 5.Clark ran the hurdles in 57.403 seconds. Grant ran the hurdles in 55.78 seconds. What is the difference between the two times? 6.Round to the nearest tenth, then find the sum. 13.46 + 7.84 + 2.59 7.Round to the nearest whole number, then find the difference. 1,472.63 − 975.28 8.Round to the nearest whole number, then find the sum. 38.24 + 14.53 + 8.93 9.Round to the nearest whole number, then find the sum. 16.4 + 12.8
Answer:
6.3
3
3.6
14
1.6
23.9
498
62
29
Step-by-step explanation:
0.9+5.4=6.3
6-3=3
13.6-10=3.6
7.032+2.485+4.59=14.107
57.403−55.78=1.623
13.5+7.8+2.6=23.
1,473−975=498
38+15+9=62
16+13=
Answer:
1. 0.92 rounds to 0.90 and 5.37 rounds to 5.40 (0.9 + 5.4 = 6.3)
2. 6.3 rounds to 6 and 2.8 rounds to 3 (6 - 3 = 3)
3. 13.56 rounds to 13.60 and 10.02 rounds to 10 (13.6 - 10 = 3.6)
4. 7.032 + 2.485 + 4.59 = 14.107
5. 57.403 - 55.78 = 1.623
6. 13.46 rounds to 13.50, 7.84 rounds to 7.80 and 2.59 rounds to 2.60 (13.5 + 7.8 + 2.6 = 23.9)
7. 1,472.63 rounds to 1,473 and 975.28 rounds to 975(1,473 - 975 = 498)
8. 38.24 rounds to 38, 14.53 rounds to 15 and 8.93 rounds to 9(38 + 15 + 9 = 62)
9. 16.4 rounds to 16 and 12.8 rounds to 13(16 + 13 = 29)
(some may be wrong but i did my best)
Question 10: Let the graph of f(x) represent the cost in thousands of dollars to feed the zoo animals daily, where x is the number of animals measured in hundreds. What does the solution to the function (2, 12) represent?
Cost (in thousands)
20
15
(2. 12)
10
5
Number of Animals (in hundreds)
• There are 200 animals, and the cost is $12,000 daily.
• There are 2,000 animals, and the cost is $1,200 daily.
• There are 1,200 animals, and the cost is $2,000 daily.
• There are 12,000 animals, and the cost is $200 daily.
Answer: I believe is the first one
Step-by-step explanation: It says animal in hundreds right. so looking at it 200 animals is right. But also x = 2 and y = 12
Hope this helps I'm sorry if it does not help
A financial advisor has recommended two possible mutual funds for investment: Fund A and Fund B. The return that will be achieved by each of these depends on whether the economy is good, fair, or poor. A payoff table has been constructed to illustrate this situation:
STATE OF NATURE
INVESTMENT GOOD ECONOMY FAIR ECONOMY POOR ECONOMY
Fund A $10,000 $2,000 –$5,000
Fund B $6,000 $4,000 0
Probability 0. 2 0. 3 0. 5
Draw the decision tree to represent this situation.
Perform the necessary calculations to determine which of the two mutual funds is better. Which one should you choose to maximize the expected value?
Suppose there is a question about the return of Fund A in a good economy. It could be higher or lower than $10,000. What value for this would cause a person to be indifferent between Fund A and Fund B (i. E. , the EMVs would be the same)?
$21,500 this would be cause a person to be indifferent between Fund A and Fund B (i. E. , the EMVs would be the same)
EMV 1 = 0.2*10,000 + 0.3*2,000 + 0.5*-5,000 = $100EMV 2 = 0.2*6,000 + 0.3*4,000 + 0.5*-0 = $2,400.
Comparing both funds based on EMV calculations, Fund B shows a higher EMV. Therefore, to maximize expected value, we should invest in Fund B with an expected value of $2,400. First, his EMV for Fund A is not the same as Fund A's return being higher or lower in good economic conditions. Therefore, the EMC can also be higher or lower. But obviously the economy changes quickly sometimes. You don't always get the same return. So relying solely on returns is risky. Relying heavily on favorable economic conditions makes Fund A vulnerable to change and increases investor risk, so investors need to be more diversified. We can do the calculation:
Fund A return in good economy = Difference between A and B: EMV (Fund A) = EMV (Fund B) 0.2*X + 0.3(2,000) + 0.5(- 5,000) = 2 4,000.2X = 4,300X = $21,500.
Therefore, if the economy is good, Fund A's return should be $21,500 for there to be indifference between Fund A and the fund B.
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Convert the number into standard form, please!
Convert from number format to standard form as a decimal multiplied by a power of 10.
What is standard form?Standard form is a way of writing a number so it is easier to read. It is often used for very large or very small numbers. Standard form is like scientific notation and is typically used in science and engineering.A number is written in standard form when it is represented as a decimal number times a power of 10.As an example, consider the speed of light which travels at about 671,000,000 miles per hour. Written in standard form this number is equivalent to 6.71 x 108.step 1
convert 1.5806*10rais to 4
Convert to decimal notation
1.5806*10^4
The exponent is 4, making it 10 to the power of 4. As the exponent is positive, the solution is a number greater than the origin or base number. To find our answer, we move the decimal to the right 4 time(s)
1.5806 ->15806
step 2
final result
15806
Simplify the expression
1.581*10^4
Simplify exponents and square roots
1.581*10^4
10 ^4 = 10 × 10 × 10 × 10 = 10,000
1.581*10000
Perform any multiplication or division, from left to right:
1.581*10000
15806
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How do you write a log function?
A logarithmic function can be said to be an inverse function of exponents.
There are 2 kinds of logarithmic functions, natural lo and log with a base of 10.
The natural lo has an "e" as its base. This is an irrational number often used in Mathematics.
Here we write it as:-
ln a
where a refers to any number a. We generally don't mention anything for the base because it automatically implies that the base is e.
The second way is to write:-
logₓa,
here the "x" is the base while a is any number. Now logₓa will actually give us the exponent or the power of x that will give us a result of a. Here it is important to mention the value of the base.
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if x is a binomial random variable with n=10 and p=0.8, the mean value of x is _____.
Answer:
8
Step-by-step explanation:
[tex]\bar{x}=np=10(0.8)=8[/tex]
•50 POINTS• don’t explain
-A
-B
-C
Answer:
C. Neither------------------------------------
There is no indication that the given triangles are congruent.
We can see one angle of each triangle is marked as congruent and that is is. No more evidences of congruence and therefore we state the triangles are not congruent.
This is a choice C.
Selena has 9 homemade bracelets for $12 each then 14 bracelets for $8 each. How much did she make in sales?
(Use the correct operation or combination of operations to solve the problem)
She will make a total profit of $220. Profits are amounts of money paid to a person with the right of immediate occupation for using the land when no permission has been granted for that use.
What are the different types of profit?Profit is the term used to describe the monetary gain experienced when the revenue from a commercial activity outpaces the costs, costs, and taxes incurred to support the activity in question. There are three primary ways to measure profit. These include operating profit, net profit, and gross profit. Gross profit and operating profit are indicators of how efficiently your company uses its resources to produce its goods and run day-to-day operations.
number of bracelets sold for $12 each=9
number of bracelets sold for $8 each=14
Total profit=9x12+8*14=$220
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Please I need the 3 of them
The following operations are used to transform the quadratic equation y = x² into parabolas in standard form:
Case 1
Horizontal translation, vertical translation. Horizontal stretch.
Case 2
Horizontal translation, vertical translation. Reflection in the x-axis, vertical stretch.
Case 3
Horizontal translation, vertical translation. Horizontal stretch.
How to determine the magnitude of horizontal and vertical translations for quadratic equations
In this question we find three cases of parabolas in standard form, that is, quadratic equations of the form:
y - k = a · (x - h)²
Where:
a - Vertex constant(h, k) - Coordinates of the vertex.This parabola is translated both horizontally and vertically by using the following definitions:
Horizontal translation
x → x - a, where a > 0 for rightward translation.
Vertical translation
y → y - b, where b > 0 for upward translation.
Horizontal dilation
f(x) → f(k · x), where k is a non-negative real number.
Vertical dilation
f(x) → k · f(x), where k is a non-negative real number.
Reflection in the x-axis
f(x) → - f(x)
The procedure is summarize below:
Write the original function, that is, the equation of the parabola with vertex at origin.Apply dilation, translation and reflection definitions.Finally, we summarize the procedure for each case:
Case 1
g(x) = x²
g(x) = [(1 / 2) · x²]
g(x) + 4 = [(1 / 2) · (x - 2)]²
Horizontal shift: 2 units right, vertical shift: 4 units down. Horizontal stretch.
Case 2
f(x) = x²
f(x) = - (1 / 2) · x²
f(x) - 2 = - (1 / 2) · (x - 4)²
Horizontal shift: 4 units right, vertical shift: 2 units down. Reflection in the x-axis, vertical stretch.
Case 3
h(x) = x²
h(x) = 2 · x²
h(x) - 5 = [2 · (x + 2)]²
Horizontal shift: 2 units left, vertical shift: 5 units up. Horizontal stretch.
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What is vertically opposite angles in maths class 7?
When two lines intersect each other, then the opposite angles formed are called vertical angles or vertically opposite angles.
A pair of vertically opposite angles are equal to each other. Also, a vertically opposite angle and its adjacent angle are supplementary angles, i.e., they add up to 180 degrees. For example, if two lines intersect and make an angle, say X=35°, then its opposite angle is also equal to 35°. And the adjacent angle to angle X will be equal to 180 – 35 = 145°
In the given figure, ∠QOR and ∠SOP form a pair of vertically opposite angles and similarly ∠SOQ and ∠POR form such a pair. Therefore,
∠QOR = ∠SOP
∠SOQ = ∠POR
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Find the number of terms and the degree of this polynomial.
Answer:
Terms = 2
Degree = 10
Step-by-step explanation:
Terms are the values appearing separated by the the mathematical sign. for this question we have 2 terms only.
the degree of a polynomial is usually the largest degree of the individual terms. for our question it's degree 10 since it's the highest.
The football team would like to purchase tickets to see a U of M football game. StubHub is charging $45 per ticket along with a handling fee of $4 per ticket. The shipping charge for all of the tickets is a flat fee of $20. How many players can attend the game if their budget is $1500? Write and solve an inequality that models this situation
Answer: Let x be the number of players who can attend the game. The total cost for the tickets is $45 per ticket * x tickets + $4 per ticket * x tickets + $20 flat fee = $49x + $20. We can write this as an inequality as follows:
49x + 20 <= 1500
To solve this inequality, we need to isolate the x term on one side of the inequality. We can do this by subtracting 20 from both sides:
49x <= 1480
Then, we can divide both sides by 49 to find the value of x:
x <= 30
Thus, if their budget is $1500, the football team can purchase tickets for at most 30 players to attend the game.
Step-by-step explanation:
Find the area of the surface obtained by rotating the circle
x2 + y2 = r 2
about the line
y = r.
The area of the surface obtained by rotating the circle [tex]x^2 + y^2 = r^2[/tex] about the line y = r is π²r² square units.
To find the area of the surface obtained by rotating the circle
[tex]x^2 + y^2 = r^2[/tex] about the line y = r, we can use the method of cylindrical shells.
The circle [tex]x^2 + y^2 = r^2[/tex] is centered at the origin (0, 0) with a radius r. The line y = r is the line y-axis but shifted up by r units.
When we rotate the circle about the line y = r, it forms a 3D shape called a torus or a donut shape.
Consider a small strip on the circle at a distance y from the line y = r.
This small strip is at a distance r - y from the y-axis.
The length of this strip is the circumference of the circle at y, which is 2πy (since the circumference of a circle is 2π times its radius).
The width of this strip is the change in x, which we can denote as dx.
The area of this small strip is then given by the product of its length and width, which is 2πy dx.
Now, to find the total surface area, we integrate this area over the range of y values from -r to r (since the circle is symmetric about the y-axis):
Total Surface Area = ∫[from -r to r] 2πy dx
Now, we need to express y in terms of x using the equation of the circle [tex]x^2 + y^2 = r^2:\\y^2 = r^2 - x^2[/tex]
y = ±√(r² - x²)
Since we are considering the upper half of the circle, we take the positive square root:
y = √(r² - x²)
Now, we can rewrite the integral with respect to x:
Total Surface Area = ∫[from -r to r] 2π√(r² - x²) dx
To solve this integral, we can make a trigonometric substitution:
Let x = r sin(θ), then dx = r cos(θ) dθ.
When x = -r, θ = -π/2, and when x = r, θ = π/2.
Now the integral becomes:
Total Surface Area = ∫[from -π/2 to π/2] 2π√(r² - (r sin(θ))²) (r cos(θ)) dθ
Total Surface Area = 2πr² ∫[from -π/2 to π/2] √(1 - sin²(θ)) cos(θ) dθ
Now, we can use the trigonometric identity:
sin²(θ) + cos²(θ) = 1
√(1 - sin²(θ)) = cos(θ)
Total Surface Area = 2πr² ∫[from -π/2 to π/2] cos²(θ) dθ
Now, use the trigonometric identity: cos²(θ) = (1 + cos(2θ))/2
Total Surface Area = 2πr² ∫[from -π/2 to π/2] (1 + cos(2θ))/2 dθ
Total Surface Area = 2πr² [θ/2 + (sin(2θ))/4] [from -π/2 to π/2]
Total Surface Area = 2πr² [(π/2 + sin(π) - (-π/2 + sin(-π)))/4]
Since sin(π) = 0 and sin(-π) = 0:
Total Surface Area = 2πr² [(π/2 - (-π/2))/4]
Total Surface Area = 2πr² (π/2)
Total Surface Area = π²r²
So, the area of the surface obtained by rotating the circle [tex]x^2 + y^2 = r^2[/tex] about the line y = r is π²r² square units.
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Solve for x 3 /11 = x /3 Give your answer as a fraction in its simplest form.
Answer: x 33/5
Step-by-step explanation:
Answer: 9/11
Step-by-step explanation:
Step 1: Cross-multiply.
3/11 = x/3
(3)*(3) = x*(11)
9 = 11x
Step 2: Flip the equation.
11x = 9
Step 3: Divide both sides by 11.
11x/11 = 9/11
x = 9/11