I need help I can't do math​

The two options that represent circles with diameter 12 units and center on the y-axis are:

x² + (y - 6)² = 36

x² + (y + 6)² = 36

The diameter of a circle is a straight line segment that passes through the center of the circle and connects two points on its circumference. It is twice the length of the circle's radius.

The equations that represent circles that have a diameter of 12 units and a center that lies on the y-axis are:

x² + (y - 6)² = 36

x² + (y + 6)² = 36

Explanation:

For a circle with diameter 12 units, the radius is half of the diameter, which is 6 units.

Since the center of the circle lies on the y-axis, the x-coordinate of the center is 0.

The general equation for a circle with center (h, k) and radius r is (x - h)² + (y - k)² = r².

Using the given information, we substitute h = 0, k = ±6, and r = 6 to get the two equations:

(x - 0)² + (y - 6)² = 6² => x² + (y - 6)² = 36

(x - 0)² + (y + 6)² = 6² => x² + (y + 6)² = 36

Therefore, the two options that represent circles with diameter 12 units and center on the y-axis are:

x² + (y - 6)² = 36

x² + (y + 6)² = 36

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The number of atoms in 8.500 moles of chlorine atoms can be calculated using Avogadro's number, which is approximately 6.022 × 10²³ atoms/mole.

So, the number of atoms in 8.500 moles of chlorine atoms would be:

8.500 moles × 6.022 × 10²³ atoms/mole = 5.12 × 10²⁴ atoms of chlorine.

The molar mass of oxygen is approximately 16.00 g/mol. Therefore, the mass of 15.50 moles of oxygen would be:

15.50 moles × 16.00 g/mol = 248 g of oxygen.

The molar mass of helium is approximately 4.00 g/mol. Therefore, the number of moles of helium in 1.953 x 10^8 g of helium would be:

1.953 x 10^8 g / 4.00 g/mol = 4.88 x 10⁷ moles of helium.

The molar mass of sulfur is approximately 32.06 g/mol. Therefore, the number of moles of sulfur in 147.82 g of sulfur would be:

147.82 g / 32.06 g/mol ≈ 4.61 moles of sulfur.

The molar mass of cobalt (Co) is approximately 58.93 g/mol.

The formula mass of Ca₃(PO₄)₂ can be calculated by adding the molar masses of all the individual atoms in the formula.

The molar mass of calcium (Ca) is approximately 40.08 g/mol, the molar mass of phosphorus (P) is approximately 30.97 g/mol, and the molar mass of oxygen (O) is approximately 16.00 g/mol.

Therefore, the formula mass of Ca₃(PO₄)₂ would be:

3 × 40.08 g/mol (for Ca) + 2 × (2 × 30.97 g/mol + 4 × 16.00 g/mol) (for P and O) = 310.17 g/mol.

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Answer: The distance formula between two points (x1, y1) and (x2, y2) is:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Using this formula, we can find the distance between (7, -2) and (-1, -1):

d = sqrt((-1 - 7)^2 + (-1 - (-2))^2)

= sqrt((-8)^2 + (1)^2)

= sqrt(64 + 1)

= sqrt(65)

Therefore, the distance between (7, -2) and (-1, -1) is sqrt(65), or approximately 8.06 units.

Step-by-step explanation:

The equation for the sinusoidal function that represents Jane's motion would be d(t) = 25 x sin(π/4 x (t + 4)) - 5

Let d(t) be the distance Jane is from the bank (in feet) at time t (in seconds). Since Jane's motion is sinusoidal, we can express it as:

d(t) = A x sin(B x (t - C)) + D

We need to find the values of A, B, C, and D that satisfy these conditions.

Since the amplitude is half the peak-to-peak amplitude, we have:

A = 50 / 2 = 25

The vertical shift (D) is the average of the maximum and minimum distances:

D = (20 + (-30)) / 2 = -10 / 2 = -5

Since the sine function is -1 at 3π/2 (270 degrees), we have:

π/4 x (2 - C) = 3π/2

2 - C = 6

C = -4

So, the equation of the sinusoidal function representing Jane's motion is:

d(t) = 25 x sin(π/4 x (t + 4)) - 5

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The question is:

Find the sinusoidal function that represents Jane's motion.

The dimension for the largest area is 181 sq ft.

The rectangle has width. [tex]$w$[/tex] and height [tex]$h$[/tex],and let the radius of the semicircle be [tex]$r$[/tex]. We want to maximize the area [tex]$A$[/tex] of the window, which is given by:

[tex]A= 21 \pi r 2 +wh[/tex]

We also have the constraint that the total length of framing material is 12 feet:

[tex]2r+2w+h=12[/tex]

Solving this equation for [tex]$h$[/tex] we get:

[tex]h=12-2r-2w[/tex]

Substituting this expression for [tex]$h$[/tex] into the equation for [tex]$A$[/tex], we get:

[tex]A= 21 \pi r ^2+w(12-2r-2w)[/tex]

Expanding this expression, we get:

[tex]A= 21\pi r^2 +12w-2rw-2w^2[/tex]

To find the values of [tex]$r$[/tex], [tex]$w$[/tex], and [tex]$h$[/tex] that maximize[tex]$A$[/tex], we take the partial derivatives of [tex]$A$[/tex] with respect to each variable, set them equal to zero, and solve for the variables.

We get:

[tex]\partial r/\partial A=\pi r-2w=0 \Rightarrow r= 2w/\pi[/tex]

[tex]\partial w/\partial A=12-2r-4w=0 \Rightarroww= (6-r)/2= (6-2w/\pi)/2=3- w/\pi[/tex]

Substituting the expression for [tex]$w$[/tex] into the equation for [tex]$r$[/tex], we get:

[tex]r= 2/\pi (3-w/\pi )= 6/\pi - 2/\pi^2w[/tex]

Substituting these expressions for [tex]$r$[/tex] and [tex]$w$[/tex] into the equation for [tex]$h$[/tex], we get:

[tex]h=12-2r-2w=12- (4/\pi)w[/tex]

So the dimensions that maximize the area are:

[tex]w= \pi/2,r= 3\pi /4 ,h= (48-8\pi) / \pi[/tex]

The area of the window is:

[tex]A= (1/2)\pir^2 +wh= (1/2)\pi ( 3\pi/4)^2 + (\pi/2)\cdot (48-8\pi)/\pi = 9\pi/8+24-4\pi\approx 18.1 sq ft[/tex]

​

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Therefore, the dimensions of the largest area rectangular window with a semicircle top that can be made with 12' of framing material are approximately 1.55' * 3.38'. The maximum area is: Area = 4.82 square feet.

To find the dimensions for the largest area of a rectangular window with a semicircle top using 12' of framing material, we need to use optimization techniques.

Let's denote the width of the rectangular window as "w" and the height of the rectangular portion as "h". We also know that the semicircle top will have a radius equal to the width of the rectangular portion, so its diameter will be 2w.

The perimeter of the window is given by:

Perimeter = 2w + h +[tex]\pi w[/tex]

Since we have 12' of framing material available, we can write:

2w + h + [tex]\pi w[/tex] = 12

We can rearrange this equation to solve for h:

h = 12 - 2w - [tex]\pi w[/tex]

The area of the window is given by:

Area = w * h + 1/2 * [tex]\pi w^2[/tex]

Substituting the expression for h from the perimeter equation, we get:

Area = w(12 - 2w - [tex]\pi w[/tex]) + 1/2 * [tex]\pi w^2[/tex]

Expanding and simplifying, we get:

Area = 12w - [tex]2\pi w^2[/tex] - [tex]w^2[/tex]

To find the dimensions that maximize the area, we need to take the derivative of the area equation with respect to w and set it equal to zero:

d(Area)/dw = 12 - [tex]4\pi w[/tex] - 2w = 0

Solving for w, we get:

w = 12/(4\pi+2) ≈ 1.55'

Substituting this value back into the perimeter equation, we can find the height:

h = 12 - 2w - \piw ≈ 3.38'

Therefore, the dimensions of the largest area rectangular window with a semicircle top that can be made with 12' of framing material are approximately 1.55' * 3.38'. The maximum area is:

Area ≈ 4.82 square feet.

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The two null hypothesis that are correct answer are two-sample t-test and one-sample t-test.

Among the group of answer choices provided, the tests that require calculating degrees of freedom are the two-sample t-test and the one-sample t-test. Both of these tests belong to the t-test family and involve using degrees of freedom to determine the critical t-value.

In summary:
- Null hypothesis: The assumption that there is no significant difference between the sample and population or between two samples.
- T-test: A statistical test used to determine if there is a significant difference between the means of two groups or between a sample and population mean.
- Degrees of freedom: A value used in statistical tests that represents the number of independent values in a data set, which can affect the outcome of the test.

So answer is: two-sample t-test and one-sample t-test.

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The null hypothesis statistical tests that require calculating degrees of freedom are the two-sample t-test and the one-

sample t-test. The degrees of freedom are necessary to calculate the t-value for these tests. The chi-squared test also

requires degrees of freedom, but it is not a test for a null hypothesis.

The correct answer is: all of the above.

All these tests require calculating degrees of freedom:

1. Two-sample t-test:

Degrees of freedom are calculated using the formula (n1 + n2) - 2, where n1 and n2 are the sample sizes of the two

groups being compared.
2. Chi-squared test:

Degrees of freedom are calculated using the formula (rows - 1) * (columns - 1), where rows and columns represent the

number of categories in the data.
3. One-sample t-test:

Degrees of freedom are calculated using the formula n - 1, where n is the sample size.

The null hypothesis statistical tests that require calculating degrees of freedom are the two-sample t-test and the one-

sample t-test. The degrees of freedom are necessary to calculate the t-value for these tests. The chi-squared test also

requires degrees of freedom, but it is not a test for a null hypothesis.

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A statistician would reply that in order to determine if the generic drug is less effective than the name-brand drug, a hypothesis test needs to be conducted.

The null hypothesis (H0) would be that there is no difference in the average blood pressure reduction between the two drugs, while the alternative hypothesis (H1) would be that the name-brand drug has a higher average reduction in blood pressure than the generic drug.

To test these hypotheses, a t-test would be appropriate since we have two independent samples (control and treatment groups) with known means, standard deviations, and sample sizes. The t-test will provide a p-value, which can be compared to a chosen significance level (e.g., α = 0.05).

If the p-value is less than the significance level, we reject the null hypothesis and conclude that there is a significant difference in the average blood pressure reduction between the two drugs. If the p-value is greater than the significance level, we fail to reject the null hypothesis, meaning we do not have enough evidence to claim that the name-brand drug is more effective than the generic drug.

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Answer:

Table D represents the linear function

y = x + 1.

The plant is not in the sprinkler's range since the distance between the sprinkler and the plant is greater than the radius of the sprinkler's range.

The distance between the sprinkler and the plant can be calculated using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

In this case, the distance between the sprinkler and the plant is the hypotenuse of a right triangle with legs of length 4 feet and 6 feet:

distance = sqrt(4^2 + 6^2)

distance = sqrt(16 + 36)

distance = sqrt(52)

distance ≈ 7.21 feet

Since the distance between the sprinkler and the plant is greater than the radius of the sprinkler's range (8 feet), the plant is not in the sprinkler's range. Therefore, the plant will not receive water from the sprinkler.

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Okay, here are the steps to find the minimum value of P:

1) Given: |z|=|w|=1 (z and w are complex numbers with unit modulus)

|z+w|=sqrt(2)

Find z and w such that these conditions are satisfied.

Possible solutions:

z = 1, w = i (or vice versa)

z = i, w = 1 (or vice versa)

2) Substitute into P = |w-\frac{4}{z}+2(1+\frac{w}{z})i|

For the cases:

z = 1, w = i: P = |-1-4+2(1+i)i| = |-5+2i| = sqrt(25+4) = 5

z = i, w = 1: P = |1-\frac{4}{i}+2(1+\frac{1}{i})i| = |-3+2i| = sqrt(9+4) = 5

3) The minimum value of P is 5.

So in summary, the minimum value of

P = |w-\frac{4}{z}+2(1+\frac{w}{z})i|

is 5.

Let me know if you have any other questions!

Note that the function that is graphed below is y = x + 7.

The equation y = x + 7 represents a linear function, where x is the independent variable and y is the dependent variable.

It has a slope of 1, which means that for every unit increase in x, y increases by 1. The y-intercept is 7, which is the value of y when x is zero. This equation can be graphed as a straight line on a coordinate plane, with a positive slope and y-intercept of (0, 7).

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Answer: 6 3/7

Step-by-step explanation:

9/1 x 5/7

If we multiply the numerators and denominators, we get 45/7 or 6 3/7 as a mixed number.

Answer:

[tex]\frac{45}{7}[/tex] or 6.4285

Step-by-step explanation:

First, multiply 9 and 5, which gives you 45.

9(5)=45

Then, divide 45 by 7.

45/7=6.4285

That gives  you  [tex]\frac{45}{7}[/tex] or 6.4285

Hope this helps!

We must first convert the given information into an equivalent fraction. The answer is 56%.

Equivalent fractions have the same value or represent the same portion of a whole even though they may have different numerators and denominators.

To do this, we must multiply both the numerator (14) and denominator (25) by the same number so that the denominator equals 100.

To do this, we must multiply both 14 and 25 by 4.

This gives us 14*4/25*4 = 56/100.

To convert this fraction to a percent, we can simply divide the numerator by the denominator and multiply the result by 100.

Therefore, 56/100 * 100 = 56%.

This result can also be found by setting up a proportion. We can set up the proportion as follows:

14/25 = x/100.

To solve for x, we must multiply both sides by 100. This gives us 14*100/25 = x.

Hence, x = 56. Therefore, 56% of swimmers finished the race in less than 47 minutes.

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The type of variable for,

a. The number of counties in California: Quantitative discrete.

b. The stages of childhood: Qualitative ordinal.

c. In the scenario above, 23 minutes is a statistic, because 28 students is a sample.

d. Between 6 minutes and 8 minutes: Approximately 68% of the athlete's mile times are expected to be between 6 and 8 minutes, according to the empirical rule.

e. Between 4 minutes and 7 minutes: Approximately 68% of the athlete's mile times are expected to be between 4 and 10 minutes, according to the empirical rule.

f. Less than 9 minutes: Approximately 84% of the athlete's mile times are expected to be less than 9 minutes, according to the empirical rule.

In statistics, variables can be categorized into two types: qualitative and quantitative.

Qualitative variables describe characteristics or qualities that cannot be measured numerically, such as gender or hair color.

Quantitative variables, on the other hand, represent numerical values that can be measured or counted.

There are two types of quantitative variables: continuous and discrete. Continuous variables can take any numerical value within a range, such as age or weight.

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The perimeter of the rectangular mural after increasing the dimensions by Hailey is equal to 7826 centimeters.

Measures of rectangular mural are,

length = 890 centimeters

Width = 2891 centimeters

New mural is 66 centimeters longer.

The new dimensions of the  rectangular mural will be,

New  length = 890 cm + 66 cm

                     = 956 cm

New width = 2891 cm + 66 cm

                  = 2957 cm

The perimeter of the new mural can be calculated by adding up the lengths of all four sides,

Perimeter = 2(length + width)

⇒Perimeter = 2(956 cm + 2957 cm)

⇒Perimeter = 2(3913 cm)

⇒ Perimeter = 7826 cm

Therefore, the perimeter of Hailey's new mural will be 7826 centimeters.

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The above question is incomplete , the complete question is:

A rectangular mural measures 890 centimeters by 2891centimeters. Hailey creates a new mural that is 66 centimeters longer. What's is the perimeter of Hailey new mural?

Answer:

below

Step-by-step explanation:

26. yes because a straight line is formed

27. domain - -2 to 2

range -2 to 1

Answer:

Yes, the graph is a linear function.

Domain: x∈[-2, -1.5, -1, -0.5, 0, 0.5, 1, 1.5]

Range: y∈[-1.5, -1, -0.5, 0, 0.5, 1, 1.5, 2]

Step-by-step explanation:

A linear function is an expression that will form a straight line when graphed (or a graph that forms a straight line). These points form a straight line, so the function is linear.

The domain of the function is everything that x can be equal to. We can see here that the ordered points are:

(-2, -1.5), (-1.5, -1), (-1, -0.5), (-0.5, 0), (0, 0.5), (0.5, 1), (1, 1.5), (1.5, 2)

So, the domain of the function is all of the x values of the ordered pairs, or:

x∈[-2, -1.5, -1, -0.5, 0, 0.5, 1, 1.5]

(the symbol next to the x means "belongs to.")

As for the range, it is everything that y can be equal to. Let us look once again at the ordered pairs. The range of the function is equal to the y coordinates of these ordered pairs, or:

Range: y∈[-1.5, -1, -0.5, 0, 0.5, 1, 1.5, 2]

Keep in mind that if the function contains more than one value for x or y, it is listed ONLY ONCE in the domain/range.

The height of the parabolic balloon arch for the prom is 12.25 feet.

Using these assumptions, we can find the equation of the parabola that the arch follows as x = a(y-k)² + h, where (h,k) is the vertex and a is a constant that determines the shape of the parabola. We can find the value of a by using one of the points that the arch passes through, say (3,0):

3 = a(0-k)² + h h = 3 - a(k²)

Similarly, using the other point that the arch passes through, say (7,0):

7 = a(0-k)² + h h = 7 - a(k²)

Equating the expressions for h, we get:

3 - a(k²) = 7 - a(k²) a = -1/4

Substituting this value of a into one of the equations for h, say h = 7 - a(k²), we get:

h = 7 + 1/4(k²)

So the vertex of the parabola is at (h,k) = (7,0), and the equation of the parabola is x = -1/4(y² - 28y + 49).

To find the height of the arch, we need to find the y-coordinate of the vertex, which is k = 0. So the height of the arch is given by the distance between the vertex and the lowest point of the arch, which is the x-intercept of the parabola. To find the x-intercept, we set y = 0 in the equation of the parabola:

x = -1/4(0² - 28(0) + 49)

x = -1/4(49) = -12.25

However, since we are dealing with a physical object, the height cannot be negative. Therefore, we take the absolute value of the x-intercept, which gives us:

| -12.25 | = 12.25 feet

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Answer:

y = -4

Step-by-step explanation:

13 - y = 17

y = 13 - 17 = -4

Answer:

y = -4

Step-by-step explanation:

Alright so you shift the y to the other side:
13 = 17 + y

Now you shift the 17 to the other side,
y = 13 - 17 = -4

Hence, y = -4

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The only option that represents an independent event is: Option C: "Spinning a Spinner with eight evenly spaced sections, then spinning it again.".

Independent events are defined as those events whose occurrence is not dependent on any other event. For example, if we flip a coin in the air and get the outcome as Head, then again if we flip the coin but this time we get the outcome as Tail. In both cases, the occurrence of both events is independent of each other.

Looking at the given options, the only one that represents an independent event is "Spinning a Spinner with eight evenly spaced sections, then spinning it again.".

This is because each event does not depend on another one of the events being described.

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Sharon's desired percentile rank of 0.78.

To determine the goal Sharon set for herself, we need to understand the relationship between standardized scores and percentile ranks.

In a standardized test, such as Sharon's Statistics final, the standardized score represents how well a student performed relative to the average score of the test-takers.

The percentile rank, on the other hand, indicates the percentage of test-takers that scored below a particular student.

In Sharon's case, she wants her standardized score to be equal to her percentile rank.

Therefore, her goal is to achieve a standardized score of 0.78 (written as a decimal) on her Statistics final.

This means she aims to score better than approximately 78% of her classmates, as indicated by her desired percentile rank of 0.78.

Hence her desired percentile rank of 0.78.

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Answer: 1 is .4

2. is .6

3 is .5

4 is .375

5 is .18

6 is .71

7 is .16

8 is .66 repeating

9 is .91

and 10 is .25

Step-by-step explanation:

to get all these and fractions to decimals in the future just divide the numerator by the denominator in other words the top number by the bottom number

1): 0.4

2): 0.67 or 0.7

3): 0.5

4): 0.37 or 0.4

5): 0.18

6): 0.42 or 0.5

7): 0.17

8): 0.7

9): 0.97 or 1

10): 0.25

The tent occupies 640 cubic feet of space.

Volume is a measurement of the amount of three-dimensional space occupied by an object or substance. It is the measure of the amount of space that an object or substance occupies in three dimensions, typically expressed in cubic units such as cubic meters, cubic centimeters, or cubic feet.

For example, the volume of a cube can be calculated by multiplying its length by its width by its height (or side cubed):

V = l x w x h = [tex]s^3[/tex],

where V is the volume, l is the length, w is the width, h is the height, and s is the length of a side.

Volume is an important measurement in fields such as physics, engineering, architecture, and chemistry, where it is used to calculate quantities such as the amount of fluid that can be held by a container, the amount of material needed to construct a building, or the amount of a substance that can react with another substance in a chemical reaction.

The volume of the tent can be found by calculating the volume of the square pyramid and then adding the volume of the rectangular box formed by the tent's base.

The base of the tent is an 8-ft by 8-ft square, so its area is 8 x 8 = 64 square feet. The height of the pyramid is 3 ft, so its volume is:

V(pyramid) = (1/3) x base area x height

V(pyramid) = (1/3) x 64 x 3

V(pyramid) = 64 cubic feet

The rectangular box formed by the tent's base has dimensions of 8 ft by 8 ft by 9 ft, so its volume is:

V(box) = length x width x height

V(box) = 8 x 8 x 9

V(box) = 576 cubic feet

Therefore, the total volume of space the tent occupies is:

V(total) = V(pyramid) + V(box)

V(total) = 64 + 576

V(total) = 640 cubic feet

So the tent occupies 640 cubic feet of space.

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Based on the definition of the tangent of a circle and the Pythagorean triple of a right triangle, AB is not tangent to circle C in both question 19 and 20.

In geometry, the tangent of a circle is a line that intersects the circle at exactly one point, which is called the point of tangency. This line is perpendicular to the radius of the circle at that point. This means that it forms a right angle at that point.

19. If AB is tangent to circle C, the lengths of the triangle ABC will form a Pythagorean triple. Let's check:

4.8² + 7.2² = 12²

74.88 = 144 [not true} Therefore, AB is not tangent to circle C.

20. Also, we will have the following:

15² + 11.2² = 6.8²

350.44 = 46.24 [not true].

AB is not tangent to circle C.

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The value of x in the Intersecting chords is 15

From the question, we have the following parameters that can be used in our computation:

Intersecting chords

The value of x is then calculated as

x = 1/2(30 - 2x + 30)

So, we have

2x = 30 - 2x + 30

Evaluate the like terms

4x = 60

Divide

x = 15

Hence, the value of x is 15

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Answer:

565.486677646 inches squared

Step-by-step explanation:

Let's recall the formula for the surface area of a cylinder:

[tex]A=2\pi rh+2\pi r^2[/tex]

Where r is the radius and h is the height.

We are given that the radius is 6 inches and the height is 9 inches.

Substitute the values and solve the equation, like so:

[tex]A=2\pi (6)(9)+2\pi (6)^2=\\A=2\pi (54) +2\pi(36)=\\A=108\pi +72\pi =\\A=180\pi[/tex]

Thus, in terms of pi, the surface area is equal to [tex]180\pi[/tex].

180 times pi is equal to approximately 565.486677646 inches squared.

The drive-thru with typically more wait time is Burger Quick, because it has a larger median. The Option A.

The median is a measure of central tendency that represents the middle value of a set of data. In this case, the median wait time at Burger Quick is 15.5 minutes, while the median wait time at Super Fast Food is 12 minutes.

This indicates that, on average, customers at Burger Quick experience a longer wait time compared to customers at Super Fast Food. The larger median at Burger Quick suggests that there may be some longer wait times skewing the data towards the higher end which could be due to various factors such as slower service, or other operational issues at Burger Quick resulting in a longer wait time for customers at their drive-thru.

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Answer:

Eleven below Zero

Step-by-step explanation:

Every number below zero (less than zero) is a negative number.

The area of the intersection of the sphere and the plane in sq cm is 286.46 square centimeters.

The sphere is divided into two equal halves by the plane. The closest point on the plane is 3 cm away from the sphere's center. As a result, a right triangle is formed, with one leg equal to the sphere's radius and the other to the sphere's radius from the plane.

We may calculate the radius of the sphere using the Pythagorean theorem:

r^2 = (20/2)^2 - 3^2

r = sqrt(91) 9.54 cm and r2 = 91

A circle with a radius of 9.54 cm forms the point where the sphere and the plane cross. Its area is therefore: A = r2 A = (9.54)2 A 286.46 sq cm.

The sphere and plane's intersection therefore has a surface area of about 286.46 square centimeters.

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The leg measurement will make a right triangle is 21 cm.

The longest side of a right-angled triangle, i.e. the side opposite the right angle, is called the hypotenuse in geometry.

Pythagorean theorem :

If p be the length of the hypotenuse of a right-angled triangle, q and r be the lengths of the other two sides, then

p² = q² + r²

The lengths of the other two sides of the given right-angled triangle are 20 cm and 21 cm. Put these values in the above theorem to get the desired result.

Now, p² = (20)² + (21)²

= 400 + 441 = 841

i.e. p = √(841) = 29

Therefore the length of the hypotenuse is 29 cm. The right angle traingle is 21 cm.

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