Answer:
(2y+5)^5
Step-by-step explanation:
Use the "PERFECT SQUARE RULE"
(b) If X = {2,3,5) and R is a relation on X where "a R b" means "a = b" for each a EX ,b Ex 1 Write R and represent it by an arrow diagram. 2 Show that R is a function, then find its range. m
The arrow diagram is
2 3 5
| | |
v v v
2 3 5
To prove that R is a function, we must show that "a R b" exists for each element an in X. R is a function since the only element b in X that fulfills the relation is a.
The range of R is X = {2, 3, 5}.
What is the range?Generally, The relation R on X is defined as "a R b" if and only if "a = b" for all a,b in X. This means that for any element a in X, the only element b in X that satisfies the relation is a itself. We can represent this relation using an arrow diagram as follows:
2 3 5
| | |
v v v
2 3 5
To show that R is a function, we need to demonstrate that for each element a in X, there is exactly one element b in X such that "a R b". In this case, we have already shown that the only element b in X that satisfies the relation is a itself, so R is a function.
The range of the function R is the set of all possible values of b for which "a R b" is true. In this case, the range of R is the set X itself, because for any element a in X, the only element b in X that satisfies the relation is a itself. Therefore, the range of R is X = {2, 3, 5}.
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What is the slope intercept for 4x Y =- 5?
The slope of the equation 4x+y = -5 is -4 and the y-intercept is -5.
To find the slope and y-intercept of the equation 4x+y = -5, you can rearrange the equation into slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
To rearrange the equation 4x+y = -5 into slope-intercept form, you can subtract 4x from both sides to get
y = -4x - 5
In this form, the coefficient of x is the slope (m = -4) and the constant term (-5) is the y-intercept (b = -5).
You can graph this equation by plotting the y-intercept at (0, -5) and using the slope to find additional points on the line. For example, if you increase x by 1, the corresponding change in y can be found by using the slope:
y = (-4 * 1) + (-5) = -9.
This means that the point (1, -9) is also on the line. You can repeat this process to plot additional points on the line and connect them to graph the equation.
--The question is incomplete, answering to the question below--
" What is the slope and y-intercept for 4x+y = -5?"
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a ferry will safely accommodate 66 tons of passenger cars. assume that the mean weight of a passenger car is 1.7 tons with standard deviation 0.5 tons. if a random sample of 36 cars are loaded onto the ferry, what is the probability that the maximum safe weight will be exceeded? hint! think about the average safe weight g
There is a 4.5% (or 0.045) probability that the maximum safe weight will be surpassed.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.
The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event could occur.
Probability and odds are two distinct ideas.
Odds are calculated by dividing the likelihood of an event by the likelihood that it won't.
So, we know that;
Average u = 1.8 tons
r = 0.5 for the standard deviation
n = 35 data points
68 tons or more would be the combined weight of the 35 automobiles. Each car's average weight should be greater than:
X = 68/35 = 1.943
After that, we can utilize that to calculate the z value.
Z = (X - u)/(r/√n)
Z = (1.943 - 1.8)/(0.5/√35)
Z = 1.692
We must determine the p-value at Z > 1.692 in order to evaluate the likelihood:
P(Z > 1.692) = 0.0453
Therefore, there is a 4.5% (or 0.045) probability that the maximum safe weight will be surpassed.
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given triangle ABC find the values of x and y. In your final answer, include all of your calculations.
Answer:
Step-by-step explanation:
X = ?
y = ?
The big triangle ABC is a right triangle, we can use Pythagoras theorem to find side y, then use SOH CAH TOA to find angles :)
also, there is a special rule for a triangle set up like this one
2CD = BD
for this triangle then,
2CD = 9
CD = 4.5
X = 13.5
now use Pythagoras to find y
[tex]13.5^{2}[/tex] = [tex]6^{2}[/tex] + [tex]y^{2}[/tex]
182.25 -36 = [tex]y^{2}[/tex]
[tex]\sqrt{146.25}[/tex] = y
12.093386 = y
now that you have all 3 sides of the big triangle, use which ever trig function you are most comfy with to find angle B or C, i'll find C
CAH = Cos(C) = Adj / Hyp
Cos(C) = 6 / 13.5
arcCos(Cos(C)) = arcCos(6/13.5)
C = 63.6122°
now find B
180 = 90 + 63.6122 + B
26.3877° = B
got it?
What are the factors of the expression x² 6x 16?
On solving the provided question we can say that, - the factors of the given equations [tex]x^2 +6x - 16\\[/tex] are - x= -4 and x = 2
What is factor?A number that divides another number by itself with no residual is known as a factor. In other words, if multiplying two whole numbers results in the creation of a product, the numbers we are multiplying are factors of the product since the product is divisible by them. Division and multiplication are the two ways to discover factors. A number or other mathematical object is factorized or factored in mathematics by expressing it as the product of numerous factors, often smaller or simpler things of the same sort. One factorization of the polynomial x2 - 4 is 3 5, which is also a factorization of the number 15.
[tex]x^2 +6x - 16\\[/tex]
(x+4)(x-2)
x= -4 and x = 2
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An architect maps two buildings, which are located on a piece of land, onto a coordinate plane. He wants to build a wall at the diagonal ac to divide the piece of land into two parts. What will be the length of the wall?.
The length of the wall will be 6√5 units.
The measurement or size of something from end to end is referred to as its length. To put it another way, it is the greater of the higher two or three dimensions of a geometric form or object. For instance, the length and width of a rectangle define its dimensions.
The length of the wall = diagonal AC = distance between point A (-6, -2) and point C (6, 4).
Distance formula between two points on a graph (d) = [tex]\sqrt{(x_{2}-x_{1})^{2}+ (y_{2}-y_{1})^{2} }[/tex]
Where,
A(-6,-2) = (x1,y1)
C(6,4) = (x2,y2)
[tex]d=\sqrt{(6-(-6))^{2}+ (4-(-2))^{2} }\\d= \sqrt{(6+6)^{2}+ (4+2)^{2} }\\d=\sqrt{(12)^{2}+ (6)^{2} }\\d= \sqrt{180} \\d= \sqrt{36*5}\\ d=6\sqrt{5}[/tex]
Thus, The length of the wall will be 6√5 units.
Refer to the image attached for the graph missing in the question.
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How do I solve 8(4x+3) ≥ −1+7x
We have 10 gallons of gas in the
car. We use 1 gallons each hour.
How many hours of gas do we
have?
Answer: 10 hours
Step-by-step explanation:
If you are using 1 gallon of gas per hour and have 10 gallons of gas you subtract 1 gallon for every hour you use the car.
Determine whether the following equence i an arithmetic or geometric progreion. Give a reaon for your anwer. 100p,50p,25p,
Answer:
Geometric.
Step-by-step explanation:
It is Geometric because there is a common ratio between the terms.
50p/100p = 1/2
25p/50p = 1/2
The common ratio is 1/2.
Each term is obtained by multiplying by 1/2, so the next term in this progression is 25p * 1/2 = 12.5p.
find a and b if the point p (6,0) and Q 3 2 lie on the graph of ax+ by
Answer:
a=b=0
Step-by-step explanation:
y=(ax)/b so now plug in the points
first 0=6a/b
next 2=3a/b
0=6a
2b=3a
a,b =0
You probably put the wrong problem but this is what I got.
Which of the following is not a quadratic equation * x²+ 4x 11 X² X² 4x 5x² 90 2x X² X² 5?
A quadratic equation is an equation of the form ax² + bx + c = 0, where a, b, and c are real numbers and a ≠ 0. So , x + 4x 11 cannot be solved as a quadratic equation.
A quadratic equation is an equation of the form ax² + bx + c = 0, where a, b, and c are real numbers and a ≠ 0. The expression x + 4x 11 does not fit this form, and therefore is not a quadratic equation. In the equation, x is an unknown variable, and 4x 11 is a linear expression. Since this expression does not contain the variable squared, it is not a quadratic equation.
x + 4x 11 cannot be solved as a quadratic equation.
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Part Two: Using Critical Project Management Tools swer the following questions, using as much space as you need 7 (3) 2 (2) 5 (1) 5 2 3 (2) 2 (3) 4 (2) 2 (3) 6(3) 1 6 3 12 3 (3) 2 (2) 2 (2) 4 10 Duration (#of People) Let's reinterpret the resource demands over time for a left-justified schedule assuming you have five people available. Create a left-justified schedule for the project above, assuming five people, and answer the following questions. 1. Map the earliest start times for each activity to the resource demands over time. What are the earliest start times for each activity? 2. Level the schedule so it is consistent with resource availabilities. What is the new project duration? 3. For this project network, identify the critical sequence. (Frame your answer as Activity Node X to Activity Node Y to Activity Node Z, etc.)
The resource-constrained schedule has a duration of 24 and a duration of 17 with 2 critical schedules.
What is resource constrained schedule?Resource-constrained project scheduling entails the planning of project operations that are subject to priority and resource limitations in order to best achieve the objective(s). The range of problems kinds is extensive in this field.
Given, reinterpreting the resource demands over time for a left-justified schedule assuming you have five people available. For Map, the earliest start times for each activity to the resource demands over time
ACT activity ES EF LS LF Slack
1->2 a 0 3 0 3 0
1->4 b 0 3 10 13 10
2->3 c 3 5 3 5 0
2->5 d 3 8 3 8 0
5->8 e 8 15 8 15 0
3->6 f 5 9 5 9 0
6->9 g 9 11 9 11 0
4->10 h 3 5 13 15 10
10->12 I 5 7 15 17 10
8->12 j 15 17 15 17 0
9->12 k 11 17 15 17 0
The resource-constrained schedule has a duration of 24
day 1 2 3 4 5 6 7 8 9 10 11 12 13
activity a,b a,b a,b c,d c,d (d,f,h)(d,f,h) d,f f, I e, I e e e
resources 5 5 5 4 4 5 5 3 4 4 3 3 3 3
day 14 15 16 17 18 19 20 21 22 23 24
activity e e e j,g j,g k k k k k k
resources 3 3 3 5 5 3 3 3 3 3 3
There are 2 critical schedules
first - (1-2)-->(2-5)-->(5-8)-->(8-12)
second - (1-3)-->(3-6)-->(6-9)-->(9-12) with duration 17.
Therefore, The two important schedules in the resource-constrained schedule each have a duration of 24 and 17, respectively.
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The diagram shows 3 points, A, B and C, on a circle, centre O.
AC is a diameter of the circle.
B
Angle BAO is aº and angle BCO is yº
What is the size of angle ABC?
Answer:
90 degrees
Step-by-step explanation:
the centre angle of the triangle is 180°.
ABC is its circumference angle, that is half the centre one
the volume of a rectangular prism is 165 cubic inches. the base of the prism has an area of 15 square inches. what is the height of the prism
Answer:
H = 11
Step-by-step explanation:
What is a word expression example?
A word expression example is "as busy as a bee." This phrase is used to describe someone who is very busy and active.
The Hard Work of a Busy Bee: Exploring the Benefits of an Active LifestyleThe phrase “as busy as a bee” is often used to describe someone who is very active and busy. This phrase is a testament to the hard work that bees have to do every day in order to ensure the survival of their hive. Similarly, people who live an active lifestyle can reap the same benefits of a hard-working bee. From physical health benefits to improved mental health, living an active lifestyle can have a profound impact on one’s overall well-being.
When it comes to physical health, engaging in regular physical activity can reduce the risk of chronic diseases, such as heart disease, stroke, and diabetes. Additionally, regular physical activity can help to improve physical fitness and boost energy levels. Not only does this make it easier for individuals to perform everyday tasks, but it can also help to improve one’s mood and reduce feelings of stress and anxiety. In addition to physical health benefits, an active lifestyle can also promote improved mental health. Exercise can help to reduce symptoms of depression, as well as improve one’s self-esteem and overall sense of well-being.
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What is a 5th root of unity?
The fifth root of unity is given by Z = 1, e^(2πi/5) ,e^(-2πi/5), e^(4πi/5), e^(-4πi/5).
As given in the question,
Using the Euler Identity ,
e^(πi) = -1
Calculate the nth root of Unity so that it can be used to calculate for any value of n:
Zⁿ = 1
⇒Z = (1)^(1/n)
Apply Euler's Formula we get,
Z = cos (2kπ + 0)/n + i sin(2kπ + 0 )/n
⇒Z = cos ( 2kπ / n) + isin( 2kπ / n)
Using Euler' identity we can write this as :
Z = e^(2kπ/n)
For k = 0 , 1 , 2 , 3..... (n-1)
Now substitute n = 5 to get the value of 5th root of unity we have
Z = e^(2kπ/5)
When k = 0 , 1, 2, 3, 4
k = 0 ⇒ Z = 1
k= 1 ⇒ Z = e^(2πi/5)
k = 2 ⇒ Z = e^(4πi/5)
k= 3 ⇒ Z = e^(-2πi/5)
k = 4 ⇒ Z = e^(-4πi/5)
Therefore, the value of 5th root of unity is equal to Z = 1, e^(2πi/5) ,e^(-2πi/5), e^(4πi/5), e^(-4πi/5).
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How do you find the area of a contour?
The sixth-graders at Kendrick's school got to choose between a field trip to a museum and a field trip to a factory. 14 sixth-graders picked the museum. If there are 56 sixth-graders in all at Kendrick's school, what percentage of the sixth-graders picked the museum?
There are 35% sixth-graders at Kendrick's school who picked the museum.
What is percentage?Percentage is a part of the whole number.
When the denominator is 100, percentages are really just fractions. We place the percent symbol (%) beside a number to indicate that it is a percentage.
1 %= 1/100.
Given that,
Total number of sixth-graders at Kendrick's school = 56,
Also,
The number of s sixth-graders that picked the museum = 14.
The percentage of the sixth-graders that picked the museum
= (14/56) x 100
= (1/4) x 100
= 25 %
25 percent of the sixth-graders picked the museum.
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A rectangular lawn has an area of 126 square meters. Surrounding the entire lawn is a flower border that is 4 meters wide. The area of the flower border alone (not including the lawn) is 264 square meters. A sprinkler is installed in the middle of the lawn that sprays water in a circle. Rounded to the nearest 10th of a meter, what is the minimum spraying radius necessary in order for the sprinkler to water both the lawn AND the entire flower border?
[10 points]
Answer:
To solve this problem, we can first use the area of the flower border to calculate the perimeter of the flower border. Since the flower border is 4 meters wide and has an area of 264 square meters, we know that it has a perimeter of 264 / 4 = 66 meters.
Next, we can use the perimeter of the flower border to calculate the dimensions of the lawn. Since the total perimeter of the lawn and flower border is 66 meters and the width of the flower border is 4 meters, we know that the length and width of the lawn must be 31 meters and 5 meters, respectively.
Finally, we can use the dimensions of the lawn to calculate the radius of the sprinkler. Since the lawn is a rectangle with a length of 31 meters and a width of 5 meters, we know that the center of the lawn is located 15.5 meters from each of the longer sides and 2.5 meters from each of the shorter sides. Therefore, the minimum radius of the sprinkler must be 15.5 meters in order to reach the entire flower border.
Rounded to the nearest tenth of a meter, the minimum spraying radius necessary is 15.5 meters.
5x - 4y = -12 I really need help please
Answer:
To solve the equation 5x - 4y = -12, we can first get all of the terms containing x on one side of the equation and all of the terms containing y on the other side. To do this, we need to add 4y to both sides of the equation. This gives us 5x = -12 + 4y. Then, we can divide both sides of the equation by 5 to get x = (-12 + 4y)/5. This is the value of x that makes the equation true.
Step-by-step explanation:
Answer: I= 3÷y-5x÷12
solve for y
Step-by-step explanation: 5x−4y=−12I
Swap sides so that all variable terms are on the left-hand side.
−12I=5x−4y
Divide both sides by −12.
-12I/-12= 5x−4y/-12
Dividing by −12 undoes the multiplication by −12.
I=-12I/-12= 5x−4y/-12
Divide 5x−4y by −12
I=3÷y-5x÷12
17. (4 points) On the set of axes below, draw the graph of the equation y = -3/4x +3.
(2 points) is the point (3,2) a solution to the equation?
Explain your answer based on the graph drawn.
(3,2) is not a solution because it does not satisfy the equation and the line on the graph does not pass through it.
How to find the solution to an equation?
We perform the same operations on both sides to ensure that the equality of both expressions is maintained.
Solving equations generally entails determining the values of the variables used in the equation for which the equation under consideration is true.
Given that:
The graph of the equation is y = -3/4x + 3.
To find if the point (3, 2) a solution to the equation.
substitute the point to to satisfy the equation;
y = -3/4x + 3
y = -3/4(3) + 3
y = -9 / 4 + 3
y = 3/3 = 1
Hence, (3,2) isn’t a solution because it doesn't satisfy the equation and also the line on the graph doesn’t go through it .
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A system of equations consists of a line s of the equation y = x – 5 and a line t that passes through the points (0, 2) and (8, –4). answer the questions about line t to write the equation. what is the slope of line t? what is the y-intercept of line t? what is the equation in slope-intercept form of line t?
The slope of line t is -3/4, y-intercept of line t is 2 and the equation of line t in slope-intercept form is y = -3/4x + 2.
To find the slope of line t, we can use the slope formula, which is:
slope = (y2 - y1) / (x2 - x1)
In this case, we know that line t passes through the points (0, 2) and (8, -4), so we can plug in the coordinates to find the slope:
slope = (-4 - 2) / (8 - 0)
= -6 / 8
= -3/4
The slope of line t is -3/4.
To find the y-intercept of line t, we can use the point-slope form of a linear equation, which is:
y - y1 = m(x - x1)
In this case, we know that line t passes through the point (0, 2), and we know the slope of the line is -3/4. We can plug these values into the point-slope form to find the y-intercept:
y - 2 = (-3/4)(x - 0)
y - 2 = -3/4x
y = -3/4x + 2
The y-intercept of line t is 2.
To write the equation of line t in slope-intercept form, we can use the slope and y-intercept we found above:
y = -3/4x + 2
This is the equation of line t in slope-intercept form.
Thus, The slope of line t is -3/4, y-intercept of line t is 2 and the equation of line t in slope-intercept form is y = -3/4x + 2.
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slope = (y2 - y1) / (x2 - x1)
slope = (-4 - 2) / (8 - 0)
= -6 / 8
= -3/4
The slope of line t is -3/4.
y - y1 = m(x - x1)
y - 2 = (-3/4)(x - 0)
y - 2 = -3/4x
y = -3/4x + 2
The y-intercept of line t is 2.
y = -3/4x + 2
This is the equation of line t in slope-intercept form.
Thus, The slope of line t is -3/4, y-intercept of line t is 2 and the equation of line t in slope-intercept form is y = -3/4x + 2.
What is the coefficient of the variable in the expression 2 − 5x − 4 8?
The coefficient of the variable x in the expression 2-5x-4+8 is -5
Given that,
The expression is 2-5x-4+8 which can be simplified as -5x+6
To find : The coefficient of the variable x in the expression
The coefficient of x in 2-5x-4+8 is -5
A number multiplied by a variable is referred to as the coefficient of a number. For instance, the x2 coefficient in the formula 6x2+99 is 6
Coefficient is the number that is beside the variable in the equation.
As we can see that the term that is in multiplication with x is -5.
Hence, the coefficient of x in the equation is -5.
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What is the end behavior of the graph of f x )= x5 8x4 16x3?
The end behavior of the graph is that it tends towards negative infinity as x approaches negative infinity, and tends towards positive infinity as x approaches positive infinity.
The end behavior of the graph of f(x) = x5 - 8x4 + 16x3 can be determined by looking at the leading term of the polynomial. The leading term of the polynomial is x5, which is positive for positive values of x and negative for negative values of x. Therefore, as x approaches negative infinity, the graph of f(x) will tend towards negative infinity, and as x approaches positive infinity, the graph of f(x) will tend towards positive infinity. To understand this further, consider what happens when x is very large, either positive or negative. As the absolute value of x increases, the leading term of the polynomial, x5, will have an increasingly large influence on the value of the polynomial, and any other terms will become insignificant. Therefore, for very large values of x, the graph of f(x) will almost entirely reflect the behavior of the leading term, which is to approach negative infinity for negative values of x and positive infinity for positive values of x.
f(x) = x5 - 8x4 + 16x3
When x is very large, either positive or negative:
When x is very large and positive:
f(x) ≈ x5
f(x) → ∞
When x is very large and negative:
f(x) ≈ -x5
f(x) → -∞
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What is the median of the following 26 27 28 29 30?
The median of the set of numbers 26, 27, 28, 29, and 30 is 28. This is the middle number in the ordered set, and it is not affected by extreme values or outliers.
The median of a set of numbers is the value that is exactly in the middle of the set when it is ordered from least to greatest. In this case, the set of numbers is 26, 27, 28, 29, 30. When we order this set from least to greatest, we get 26, 27, 28, 29, 30. There are five numbers in this set, so the median is the third number. The third number in this set is 28, so the median is 28.
To find the median, we first need to arrange the numbers in order from least to greatest. If there is an odd number of numbers in the set, the median is the middle number. If there is an even number of numbers in the set, the median is the average of the two middle numbers. In this case, there are five numbers in the set, so the median is the middle number.
In summary, the median of the set of numbers 26, 27, 28, 29, 30 is 28. This is the middle number in the ordered set, and it is not affected by extreme values or outliers.
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HELP!!!!
Drag numbers to complete the table for missing values of x, x2, and x3
Here, the value of x = 20, x² = 400 and x³ = 8000.
What is Factorization ?
The breaking or breakdown of one entity into a product of another entity, or factors, which when multiplied together yield the original number, is known as factorization or factoring in mathematics.
We've x³ = 8000 ...............equation 1
we can factor it as follows :
8000 = 2×2×2×10×10×10
8000 = 2³ × 10³
8000 = 20³ .............................equation 2
Now, By comparing equation 1 and 2,
We get, x = 20.
So, x² = 20 × 20 = 400.
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What is the characteristic of the leading coefficient?
Since the leading coefficient can be any real number, The characteristic of the leading coefficient are the characteristic of a real number.
What do you mean by a polynomial?Sums of terms with the form kxⁿ, where K is any number and N is a positive integer, are known as polynomials.
What do you mean by leading coefficient?The term with the greatest x power is the leading term in a polynomial function. The leading coefficient is the coefficient of the leading phrase.
The characteristics of the leading coefficient are:
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the circle with equation x² + y² + sx + ty + 33 = 0 has center (4,5) what is s/t?
someone help please!
The Value for s/t is 4/5.
What is Equation of Circle?We know that the general equation for a circle is ( x - h )² + ( y - k )² = r², where ( h, k ) is the center and r is the radius.
Given:
x² + y² + sx + ty + 33 = 0
x² + y² + sx + s²x²/4 + ty + t²y² / 4 + 33 = 0
(x² + + sx + s²x²/4) + (y² + ty + t²y²/4 ) + 33 = 0
(x+ sx/2)² + ( y+ ty/2)² + 33 = 0..............(1)
We know that the standard form
(x-a)² + (y- b)² = r²
where (a, b) is the center.
So, We have center (4,5)
(x-4)² + (y- 5)² = r²
Now Comparing above with Equation (1) we get
s/2 = -4 and t/2 = -5
s= -8 and t= -10
Then, s/t= -8/(-10)= 4/5
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How do you calculate maximum value?
Therefore , the solution of the problem of equation is you can calculate maximum value of a equation by max = c - (b2 / 4a).
What is the equation?
Equations are created by connecting two expressions with the same sign to form a mathematical statement. An example is the equation
3x - 5 = 17. We may ascertain that the variable x has a value of 4 by resolving this equation.
According to the given question:
You can use the formula max = c - (b2 / 4a) to determine the maximum value if you are given the formula y = ax2 + bx + c.
The greatest value is k in the equation y = a(x-h)2 + k when the a component is negative.
Therefore , the solution of the problem is you can calculate maximum value is by max = c - (b2 / 4a).
Complete question:
How do you calculate maximum value of a equation?
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Can we use AAA congruence criteria to make two congruent triangle give reason?
The sides of a triangle with all respective angles equal, i.e. AAA condition, may or may not be equal. Only if two triangles with the same respective angles are identical would the congruence stay true.
Knowing only angle-angle-angle (AAA) does not work because it can produce similar but not congruent triangles. When you're trying to determine if two triangles are congruent,
there are 4 shortcuts that will work. Because there are 6 corresponding parts 3 angles and 3 sides, you don't need to know all of them. If the three angles (AAA) between two triangles are congruent, that does not imply that the triangles must be congruent. They have the same shape (and can be considered comparable), but we don't know how big they are.
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