The domain of a function with two variables is the set of all possible inputs (x-values and y-values) that make the function defined. To find the domain, first identify all of the restrictions on the x-values and y-values, then combine them into a single set of restrictions.
The domain of a function with two variables is the set of all possible inputs (x-values and y-values) that make the function defined. To find the domain, first identify all of the restrictions on the x-values and y-values. These restrictions may come from the function itself, such as any values that would make the function undefined, or from outside sources, such as boundaries placed on the function’s input. Once all of the restrictions are identified, they must be combined into a single set of restrictions. This set of restrictions defines the domain. For example, if the function is defined for all x-values between 1 and 5 and all y-values between -3 and 7, then the domain is all x-values between 1 and 5 and all y-values between -3 and 7. The domain of a function with two variables is an important part of understanding how the function behaves, as it defines the range of inputs for which the function is valid.
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how does the value of A determine the range for f(x) = a|x|
HELP PLEASE ASAP
Answer:
It will either invert the graph or stretch/compress the horizontal
Step-by-step explanation:
When a is negative It will invert the graph, and reflect it over the x-axis
By plugging in a=1 you get a normal absolute value function of x ( a V on the graph)
If a>1 then your graph will compress
If a<1 then your graph will stretch
Question 10 options:
Which is not a property of a parallelogram?
A) All sides are congruent. B) Diagonals are perpendicular bisectors of each other. C) Opposite angles are congruent. D) Diagonals are congruent.
A parallelogram is a quadrilateral with opposite sides that are parallel and equal in length. All angles are congruent, and the diagonals bisect each other and are congruent. It does not, however, have the property that all angles are equal.
A parallelogram is a four-sided shape with two pairs of parallel lines. The opposite sides of the parallelogram must be congruent, meaning that they have the same length. All angles are congruent, which means that they all have the same measure. The diagonals of the parallelogram bisect each other, meaning that they divide each other into two equal parts, and they must also be congruent. All of these properties are true for a parallelogram, except that the angles do not have to be equal. The angles can be either acute, obtuse, or right angles, but they must all have the same measure. So, in conclusion, the property that is not true for a parallelogram is that all angles are equal.
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Can someone help me!!!!!!
The y - intercept of the graph, given the formula of 2 y - 5x = 16, is y - intercept : ( 0, 8)
How to find the y - intercept ?To find the y - intercept, use the slope - intercept form of the equation of a line which is:
y = mx + b
m = slope
b = y - intercept
So first rewrite the formula given to look like the slope - intercept :
2 y - 5x = 16
2 y = 5x + 16
( 2 y = 5x + 16 ) / 2
y = 5/ 2 x + 8
The y- intercept is therefore 8. As a point on the graph, this is ( 0, 8 )
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The stem and leaf plot shows the number of days of snowfall at a winter sports resort for each of the past 171717 years.
The stem represents the tens place and the leaves represent the unit place of each data point, allowing for easy visualization of the distribution of the data.
A stem-and-leaf plot is a type of graph used to display the distribution of a set of data. It is a way to show the frequency of different values in a dataset. In this case, it is showing the number of days of snowfall at a winter sports resort for each of the past 171717 years.
Continuous and discrete data distributions are the two main forms found in statistics. Continuous data is information having a wide range of possible values. When measuring this kind of information, such weight or temperature, a scale is frequently used. A histogram is another tool for representing continuous data.
The complete question will be :
The stem and leaf plot shows the number of days of snowfall at a winter sports resort for each of the past years. represents a year with days of snowfall. Here is the five-number summary for these data Five-number summary According to the - IQR rule for outliers, how many high outliers are there in the data set?
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Answer:
0
Step-by-step explanation:
5
Drag each length to the correct location on the image. Each length can be used more than once, but not all lengths will be used.
What are the missing segment lengths shown in the image?
20
10 10√3
20√3 10 2 20√2
45° 45°
4
45°
20
00
45°
The missing segment lengths are CD = 10√2, AC = 10√2, BC = 10 and AB = 10.
Drag each length to the correct location accordingly
How to find the missing segment lengths?Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.
In ΔACD,
sin 45° = CD/20 (sin = opp/hyp)
(√2)/2 = CD/20
CD = (√2)/2 × 20
CD = 10√2
cos 45° = AC/20 (cos = adj/hyp)
(√2)/2 = AC/20
AC = (√2)/2 × 20
AC = 10√2
In ΔABC,
sin 45° = BC/10√2 (sin = opp/hyp)
(√2)/2 = BC/10√2
BC = (√2)/2 × 10√2
BC = (10 × 2)/2
BC = 10
cos 45° = AB/10√2 (cos = adj/hyp)
(√2)/2 = AB/10√2
AB = (√2)/2 × 10√2
AB = 10
Drag each length of the missing segment to the correct location
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When two rotations are performed on a single figure, does the order of the rotations sometimes, always, or never affect the location of the final image? Explain.
When two rotations are performed on a single figure, the order of the rotations never affect the location of the final image.
What is the rotation?In mathematics, rotation is defined as that of the circular movement of an object around with a center, an axis, or a fixed point. Since rotations are rigid transformations, the size, length, shape, and angle measurements of the figure are maintained.
Precession, nutation, and intrinsic rotation are the names of these rotations. The rotation of the earth on its axis is one of the greatest instances of rotation in nature.
There are broad guidelines for rotations of 90, 180, and 270 degrees around the origin that are both clockwise and anticlockwise. Counterclockwise. X and Y are rotated by 90 degrees that means (x , y) ----> (-y , x); Rotation of 180 degrees: (x, y) —- (-x , -y); Rotation of 270 degrees: (x, y) —- (y , -x).
Here two times rotation means 180 degrees that means no change in the final image.
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How do you find the third side of an isosceles triangle when given the angle?
The third side of the isosceles triangle is equal to the square root of 2 multiplied by the hypotenuse, multiplied by the sine of the opposite angle.
Given an isosceles triangle with an angle and two equal sides, we can use the Pythagorean Theorem to calculate the missing side.
The Pythagorean Theorem states that the sum of the squares of the two sides of a right triangle is equal to the square of the hypotenuse. Therefore, we can use this formula to calculate the missing side of the triangle.
First, let's call the two equal sides of the triangle 'a', and the angle opposite to them 'A'.
We can then use the Pythagorean Theorem to calculate the missing side, 'c', which is the third side of the triangle.
[tex]c^2 = a^2 + a^2\\c^2 = 2a^2\\c = sqrt(2a^2)[/tex]
To calculate 'c', we can first calculate 'a' by using the formula:
a = c * sin(A)
Then we plug 'a' into the equation for 'c':
c = sqrt(2*(c * sin(A))^2)
c = sqrt(2)*c*sin(A)
Therefore, the third side of the isosceles triangle is equal to the square root of 2 multiplied by the hypotenuse, multiplied by the sine of the opposite angle.
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solvve for z: (1st answer or nice and detailed answer brainliest)
1/2z+5=57
[tex]\dfrac{1}{2} z+5=57[/tex]
Subtract 5 from both sides:
[tex]\dfrac{1}{2} z+5-5=57-5[/tex]
[tex]\dfrac{1}{2} z=52[/tex]
Multiply both sides by 2:
[tex]2\times(\dfrac{1}{2} z)=2\times(52)[/tex]
[tex]\fbox{z = 104}[/tex]
Answer:
z=104
Step-by-step explanation:
1/2z=57-5
1/2z=52
1/2z*2=52*2
1z=104
1/1z=104/1
z=104
Work out the size of angle x
Answer:
x = 13
Step-by-step explanation:
There is more than one 98-degree angle since they are all corresponding interior angles.
The supplementary angle to the 98-degree angle next to the triangle is:
180 - 98 = 82 degrees
In addition, another angle inside the triangle is an 85-degree angle. This is because this 85-degree angle is opposite adjacent to the other 85-degree angle.
Hence, the angles inside the triangle are: x, 85, and 82
x + 85 + 82 = 180 ==> Triangles add up to 180 degrees
x + 167 = 180 ==> simplify
x = 13 degrees ==> subtract 167 on both sides
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i need help plsss help meee
Corresponding angle pairs - (1,5) , (2,6) , (3,7) and (4,8)
8. On a map of scale 1:20 000 the area of a forest is 50 cm². On another map the area of the forest is 8 cm². Find the scale of the second map.
Answer: The scale of a map is a ratio that represents the relationship between distances on the map and distances in the real world. For example, a scale of 1:20 000 means that 1 unit on the map represents 20 000 units in the real world.
In this case, we are given that the area of the forest on the first map is 50 cm² and the area of the forest on the second map is 8 cm². We can use the scale of the first map to find the scale of the second map.
Since the area of the forest on the first map is 50 cm² and the scale is 1:20 000, the area of the forest in the real world is 50 cm² * 20 000 = 1 000 000 cm².
Similarly, since the area of the forest on the second map is 8 cm², the area of the forest in the real world is 8 cm² * x, where x is the scale of the second map.
Setting these two expressions equal to each other, we get:
1 000 000 cm² = 8 cm² * x
Dividing both sides of the equation by 8 cm², we get:
x = 125 000
Therefore, the scale of the second map is 1:125 000.
Step-by-step explanation:
WASTE Suppose the waste generated by nonrecycled paper and cardboard products in tons y after x days can be approximated by the function y=1000(2)0.3x.
a. Identify key features.
y-intercept: , 1 of 8.
domain: , 2 of 8.
range: , 3 of 8.
b. Identify the relevant domain and range.
Because time , 4 of 8. , the relevant domain is , 5 of 8. .
Because the amount of recycled paper and cardboard , 6 of 8. , and the amount when x=0
is , 7 of 8.tons, the relevant range is , 8 of 8. .
a. The key features of the exponential function y = 1000(2)^(0.3x) is given as follows:
y-intercept: y = 100.Domain: all real values.Range: y ≥ 1000.b. The relevant domain and range are given as follows:
Domain: x ≥ 0.Range: y ≥ 1000.What are the features of the exponential function?The exponential function for this problem is modeled as follows:
y = 1000(2)^(0.3x).
The features are given as follows:
Initial value, when x = 0, of y = 1000, representing the y-intercept.Rate of change of 2 for each period of 0.3 units.The domain of the function is the set that composes all input values of the function, and as the exponential function does not have any restrictions such as a fraction or an even root, it is composed by all real values.
However, the relevant domain is x ≥ 0, as the number of days does not assume negative values.
The range is the set containing all output values of the exponential function. As the initial value of the exponential function is of 1000 and the function is increasing, the range is y ≥ 1000.
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What are the intervals of 5?
The set of numbers x such that 0 ≤ x ≤ 5 is an interval containing 0, 5, and all numbers between 0 and 5.
Interval notation is a way of representing intervals on the number line. That is, how to write a subset of the real number line. Intervals include numbers between two specific numbers.
In mathematics, a (real) interval is a set of real numbers containing all real numbers between any two numbers in the set. For example, the set of numbers x such that 0 ≤ x ≤ 1 is an interval containing 0, 1, and all numbers in between. Other examples of intervals are the set of numbers with 0 < x < 1, the set of all real numbers, the set of non-negative real numbers, the set of positive real numbers, the empty set, and any Singleton (a set of one element).
Real intervals play an important role in integral theory. This is because real intervals are the simplest set whose "length" (or "scale" or "magnitude") is easy to define. The notion of measure can be extended to more complex sets of real numbers, leading to the Boral measure and finally the Lebesgue measure.
Intervals are central to interval arithmetic, a general numerical technique that automatically provides guaranteed bounds for any mathematical expression, even in the presence of uncertainties, mathematical approximations, and arithmetic rounding.
Complete Question:
What is the interval of 0,5 ?
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7. A triangle has sides with lengths 7, 24, and 25. (Lesson 4-5)
a. Verify this is a Pythagorean triple.
b. Approximate the acute angles in this triangle.
A triangle has sides of 7, 24, and 25 cm. The length of the hypotenuse is equal to 25 cm if the triangle is a right triangle.
What are the angles of a 7/ 24/ 25 triangle?The triangle's sides are 7 cm, 24 cm, and 25 cm, as is obvious.
49, 576, and 625 are the results of squaring the lengths of the side of the.
49 + 576 = 625\s(7)2 + (24)2 = (25)2
As a result, the aforementioned equation satisfies Pythagoras's theorem. As a result, it is a right-angled triangle.
the hypotenuse is 25 cm long.
Angles of 16.26 degrees and 73.74 degrees are suitable.
Yes, since 72+242=252 (sum of squares on smaller two sides equals square on largest side).
The triangle's sides are 7 cm, 24 cm, and 25 cm, as is obvious. 49, 576, and 625 are the results of squaring the lengths of the side of the. As a result, the aforementioned equation satisfies Pythagoras's theorem. As a result, it is a right-angled triangle.
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The length of the base of an isosceles triangle is x. The length of a leg is 5x -2. The perimeter of the triangle is 106. Find x. X =
Answer:
x = 10
Step-by-step explanation:
the legs of an isosceles triangle are congruent.
the perimeter is the sum of the 3 sides of the triangle
sum the 3 sides and equate to 106
x + 5x - 2 + 5x - 2 = 106
11x - 4 = 106 ( add 4 to both sides )
11x = 110 ( divide both sides by 11 )
x = 10
I’m doing math homework and is about functions they said f(x)= x-3 and g(x)= √x-2
After I set them up I have this
am I supposed to just add the numbers or is there something else to do?
√ (x-3)-2
Answer: It looks like you are trying to find the value of the function h(x) = √ (x-3) - 2.
To find the value of this function for a given value of x, you need to substitute the value of x into the function definition and simplify the expression.
For example, if you want to find the value of h(x) for x = 5, you would substitute 5 for x in the function definition and simplify the expression to get:
h(5) = √(5-3) - 2
= √2 - 2
= 1.4 - 2
= -0.6
Therefore, the value of h(x) for x = 5 is -0.6.
You can follow this same process to find the value of h(x) for any other value of x. Just be sure to substitute the correct value of x into the function definition and simplify the expression to find the final result.
Step-by-step explanation:
Answer:
g[f(x)]
Step-by-step explanation:
Given functions:
[tex]f(x)=x-3[/tex]
[tex]g(x)=\sqrt{x}-2[/tex]
Composite functions are when the output of one function is used as the input of another.
Therefore, to create √(x-3)-2, substitute the function f(x) in place of the x in function g(x):
[tex]\begin{aligned}\implies g[f(x)]&=\sqrt{f(x)}-2\\&=\sqrt{x-3}-2\end{aligned}[/tex]
A school administrator asks each student if they participate in a sport and if they participate in a club. The results are shown below.
Participates in a Sport
Yes No Total
Participates in a Club Yes 620 450 1070
No 325 535 860
Total 945 985 1930
What percentage of students do not participate in a sport?
27.7%
44.6%
51.0%
62.2%.
answer is 51.1
The percentage of students who do not participate in a sport is C. 51.0%.
How to calculate the percentage?To find the percentage of students who do not participate in a sport, we can use the following formula:
(Number of students who do not participate in a sport) / (Total number of students) * 100%
From the table, we can see that the number of students who do not participate in a sport is 985, and the total number of students is 1930. So, plugging these values into the formula gives us:
= 985 / 1930 * 100%
= 51.03%
So, about 51.03% of students do not participate in a sport.
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ACTIVITY 6: Modeling Real Life
A company is loading recliners and sofas onto a trailer that has a volume of about 3800 cubic feet. Each recliner takes up about 40 cubic feet and each sofa takes up about 80 cubic feet. The company wants the shipment to have at least 30 recliners and more than 25 sofas. Write and graph a system that represents the situation. Give one example of the numbers of recliners and sofas the company can have in the shipment.
The equation is 80x + 1200 = 3800. And the numbers of at least 30 recliners and 32 sofas the company can have in the shipment.
What is linear equation?Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.
Given:
A company is loading recliners and sofas onto a trailer that has a volume of about, 3800 cubic feet.
Each recliner takes up about 40 cubic feet and each sofa takes up about 80 cubic feet.
The company wants the shipment to have at least 30 recliners and more than 25 sofas.
The equation that represents the situation is,
80x + 40y = 3800,
where x is the volume of a sofa and y is the volume of a recliner.
If y = 30 then,
80x + 1200 = 3800
80x = 2600
x = 2600/80
x = 32.5
x ≈ 32
Therefore, 30 recliners and 32 sofas.
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What is the y-intercept of y= -3x + 6
In store the ratio of blue shirts to red shirts is 2:5. If there is 100 red shirts in the store, how many blue shirts are there?
The ratio of blue shirts to red shirts is 2:5, so for every five red shirts, there are two blue shirts.
What is ratio?Ratio is a mathematical term used to compare two different values. It is a way of expressing one quantity in relation to another. Ratios can be written as fractions, decimals, or percentages. Ratios are used in many different areas, such as finance, economics, science, and engineering. Ratios are also used to compare the size, speed, or cost of different items. Ratios can be used to compare parts of a whole, or to compare different items within a group.
Since there are 100 red shirts in the store, there are 40 blue shirts in the store (100 / 5 x 2 = 40).
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A bicycle has a listed price of 839.95 before tax. If the sales tax rate is 85%, find the total cost of the bicycle with sales tax included. Round to the nearest cent as necesary.
$1553.91
Step-by-step explanation:
839.95 ×.85 = 713.96
839.95 + 713.96 = 1553.91
please help quickly
These polygons are similar. x=?
The value of x in the similar polygons is 7.
How to find the side of similar polygon?Two polygons are similar if their corresponding angles are congruent and their corresponding sides are in proportion.
Therefore, the polygons WXY and STU are similar.
Hence, using proportion, let's find the value of x
3 / 9 = 4 / x + 5
cross multiply
3(x + 5) = 9 × 4
3x + 15 = 36
subtract 15 from both sides of the equation
3x + 15 - 15 = 36 - 15
3x = 21
divide both sides by 3
x = 21 / 3
x = 7
Therefore,
x = 7
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Sonji has $5.25 in nickels and dimes.The coin value can be modeled by the equation , where d represents the number of dimes and n represents the number of nickels. If Sonji has 21 dimes, how many nickels does she have
The number of nickels that Sonji has as per the given equation is 63.
What is the value of N mean?In mathematical operations, “n” is a variable, and it is often found in equations for accounting, physics and arithmetic sequences. A variable is a letter or symbol that stands for a number and is used in mathematical expressions and equations. In an arithmetic sequence, which is a list of numbers that follow a pattern, “n” is a variable representing the number of the term to find.For instance, if students want to find the value of the seventh term, “n” would be 7. In physics, an equation for standing waves uses “n” as an integer symbolizing the harmonic number or number of antinodes. The equation evaluates the length of the string in terms of its wavelength. In accounting, “n” is used in the equation for compound interest. It represents the number of compounding in 1 year.We are given the information that Sonji has 21 dimes (which means that d=21). We can use the equation to find the number of nickels n.
0.10d + 0.05n = 5.25
0.10(21) + 0.05n = 5.25
2.10 + 0.05n = 5.25
0.05n = 3.15
n = 3.15 / 0.05
n = 315 / 5
n = 63
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Simplify (s^-5)^3. Write your answer using only positive exponents.
The given expression (s⁻⁵)³ is equivalent to (1/s)¹⁵.
What is exponent?Exponent is a quantity representing the power to which a given number or expression is to be raised, usually expressed as a raised symbol beside the number or expression. Mathematically -
[tex]$b^x = \underbrace{b \times \dots \times b}_{x \text{ times}}[/tex]
where -
[b] = base of the logarithm
[x] = exponent
Given is the expression as follows -
(s⁻⁵)³
We can write the expression as -
(s⁻⁵)³ = (1/s⁵)³ = (1/s¹⁵) = (1/s)¹⁵
Therefore, the given expression (s⁻⁵)³ is equivalent to (1/s)¹⁵.
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3y+2=2y-5x into y=mx+b form
3y + 2 = 2y - 5x
3y - 2y = -5x -2
y = -5x - 2
Find the median of data 1/3 3/2 1/6 1/4 2/3
Answer:
median= 1/3
Step-by-step explanation:
Find the vertices and foci of the hyperbola with equation quantity x plus 4 squared divided by 9 minus the quantity of y plus 3 squared divided by 16
Vertices are at (-7, 5) and (-1, 5) and foci are at (-9, 5) and (1, 5) of the hyperbola with equation quantity x plus 4 squared divided by 9 minus the quantity of y plus 3 squared divided by 16.
As per the given data the given equation is:
[tex]\\$$\frac{ (x+4)^2}{9} - \frac{(y-5)^2 }{16}=1$$[/tex]
The standard form for the equation of a hyperbola with center (h, k) is [tex]\frac{(x-h)^{2} }{a^{2} } - \frac{(y-k)^2}{b^{2} } =1[/tex]
Your hyperbola opens left/right, because it is of form x - y.
Comparing terms, we find that
h = -4, k = 5, a = 3, y = 4
In the general equation, the coordinates of the vertices are at [tex]$(h \pm a, k)$[/tex].
Thus, the vertices of your hyperbola are at (-7,5) and (-1,5).
The foci are at a distance c from the center, with coordinates [tex]$(\mathrm{h} \pm \mathrm{c}, \mathrm{k})$[/tex], where [tex]$c^2=a^2+b^2$[/tex]
[tex]c^2=9+16=25$[/tex], so c = 5.
The coordinates of the foci are (-9, 5) and (-1, 5).
The Figure below shows the graph of the hyperbola with its vertices and foci.(attached at the end of solution)
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The table shows the number of students going on a field trip one chaperone is needed for every 12 students
Answer:
I'm not sure what equation is needed here. Could you share the table?
Either way, you can take the number of students there are and multiply that to the number of chaperones needed per group of 12- basically see how many groups of 12 you can fit in the overall group of students
On her first day of work, Janabel sold one widget. On day two, she sold three widgets. On day three, she sold five widgets, and on each succeeding day, she sold two more widgets than she had sold on the previous day. How many widgets in total had Janabel sold after working 2020 days
On solving the provided question, we can say that the sequence what we tell on day 3 = he sold 5; on day 4 = he sold 7; on day 5 = he sold 9
what is a sequence?A collection of numbers, or "terms," is referred to as a sequence. Examples of terms are 2, 5, and 8. Some sequences can be made endlessly lengthy by taking advantage of a particular pattern they follow. Use the example of 2,5,8 and add 3 to continue the sequence. There are formulas that demonstrate where to look for words within a sequence. A collection of objects that are in some order is known as a sequence in mathematics (or events). It resembles a set in that it contains pieces (also called elements or terms). The entire, perhaps infinite number of ordered objects are referred to as the sequence's length. the act of placing two or more items in a logical order. Chronological.
here,
on day 1 = he sold 1
on day 2 = he sold 3
on day 3 = he sold 5
on day 4 = he sold 7
on day 5 = he sold 9
.
.
.
.
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4. Determine the type of triangle with the given set of side lengths. Show your work. A. a = 8, b = 15, c = 17 B. a = 6, b= 15, c = 18 C. a = 7, b = 10, c = 12
So A is a triangle, and B is a triangle, and C is a right triangle (or a right-angled triangle)
Define Pythagoras Theorem.The Pythagorean Theorem states that the squares on the hypotenuse (the side across from the right angle) of a right triangle, or, in standard algebraic notation, a2 + b2, are equal to the squares on the legs.
What is right angle triangle?A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or previously rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.
A. a = 8, b = 15, c = 17
We can use the Pythagorean theorem to determine the type of triangle:
c² = a² + b²
17² = 8² + 15²
289 = 64 + 225
289 ≠ 289
Therefore, this is not a right triangle.
B. a = 6, b= 15, c = 18
We can use the Pythagorean theorem to determine the type of triangle:
c² = a² + b²
18² = 6² + 15²
324 = 36 + 225
324 ≠ 324
Therefore, this is not a right triangle.
C. a = 7, b = 10, c = 12
We can use the Pythagorean theorem to determine the type of triangle:
c² = a² + b²
12² = 7² + 10²
144 = 49 + 100
144 = 144
Therefore, this is a right triangle.
So A is a triangle, and B is a triangle, and C is a right triangle (or a right-angled triangle)
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