From the attachment, what is the missing side?

The area of the arrow of the painting is A = 70 units²

Given data ,

Mr. Barth is painting an arrow on the school parking lot.

The coordinates are (-2, 2), (5, 2), (5, 6), (12, 0), (5, -6), (5, -2), (-2, -2)

The area of the arrow would be:

Area of Arrow = Area of Triangle + Area of Rectangle

Let the base of the triangle be = 12 units

Let the height of the triangle is = 7 units

So , area of triangle = 42 units²

Area of rectangle = 7 x 4 = 28 units

Hence , the area of arrow A = 70 units²

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The line integral of the given function f(x, y) along the given curve r(t) is 0.8404.

First, we need to parameterize the curve by substituting x = t³ and y = [tex]t^4[/tex] into the function f(x, y) to get:

f(t) = √([tex]t^4[/tex]/t³) = [tex]t^{1/2}[/tex]

Next, we need to find the derivative of r(t) with respect to t:

r'(t) = 3t²i + 4t³j

Then, we can compute the line integral using the formula:

∫f(r(t))|r'(t)|dt from ½ to 1

Substituting the values, we get:

∫[tex]t^{1/2}[/tex] |3t²i + 4t³j| dt from ½ to 1

= ∫[tex]t^{1/2}[/tex] |t²(3i + 4tj)| dt from ½ to 1

= ∫[tex]t^5[/tex] (9 + 16t²) dt from ½ to 1

This integral is not easy to solve analytically, so we can use numerical methods to find an approximate value. Using a numerical integration method such as Simpson's rule, we get:

≈ 0.8404

Therefore, the line integral of f(x, y) = √y/x along the curve r(t) = t³i + [tex]t^4[/tex]j, ½ ≤ t ≤ 1 is approximately 0.8404.

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The exact values of cosecant, secant, and cotangent ratios of -pi/4 radians is:

[tex]csc=\frac{\pi }{4}=\frac{hypontenuse}{opposite}=\frac{\sqrt{2} }{1}=\sqrt{2}[/tex]

[tex]sec=\frac{\pi }{4}=\frac{hypotenuse}{adjacent}= \frac{\sqrt{2} }{1}=\sqrt{2}[/tex]

[tex]cot=\frac{\pi }{4}=\frac{adjacent}{opposite}=\frac{1}{1}=1[/tex]

[tex]\frac{\pi }{4}[/tex] radians is the same as 90 degrees. So, first draw a right triangle with an angle of [tex]\frac{\pi }{4}[/tex]:

This creates a 45-45-90 triangle, also known as a right isosceles triangle. This is a very special triangle, and we know that both of its legs will be the same length, and the hypotenuse will be the length of one of the legs times √2.

The  three functions are just the inverses of the first three. Cosecant is the inverse of sine, secant is the inverse of cosine, and cotangent is the inverse of tangent.

[tex]csc=\frac{\pi }{4}=\frac{hypontenuse}{opposite}=\frac{\sqrt{2} }{1}=\sqrt{2}[/tex]

[tex]sec=\frac{\pi }{4}=\frac{hypotenuse}{adjacent}= \frac{\sqrt{2} }{1}=\sqrt{2}[/tex]

[tex]cot=\frac{\pi }{4}=\frac{adjacent}{opposite}=\frac{1}{1}=1[/tex]

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Therefore, the percent increase in temperature is approximately 65.44%.

The percent increase in temperature, we need to find the difference between the initial and final temperatures, divide that by the initial temperature, and then multiply by 100 to get a percentage:

Calculate the variation between the initial and end values. Subtract the beginning value from its absolute value. Add 100 to the result.  

Even in a low-emission scenario, the earth is predicted to rise by two degrees Celsius by 2050, suggesting that we might not be able to keep the Paris Agreement. Compared to the average temperature between 1850 and 1900, the global temperature has increased by 1.1°C.

percent increase = ((final temperature - initial temperature) / initial temperature) x 100

In this case:

percent increase = ((1034 - 625) / 625) x 100

percent increase = (409 / 625) x 100

percent increase = 65.44%

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To solve this problem, we can use the formula for probability of an event:

P(event) = (number of favorable outcomes) / (total number of outcomes)

Let's first find the total number of ways to select two fuses from 20:

20 choose 2 = 20! / (2! * (20-2)!) = 190

Now let's find the number of ways to select one defective fuse and one non-defective fuse:

There are 10 defective fuses and 10 non-defective fuses, so we can choose one of each in 10 * 10 = 100 ways.

Therefore, the probability of selecting only one defective fuse is:

P(1 defective) = 100 / 190 = 0.5263

So the answer is not one of the options given.

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There is no significant difference between the mean tensile strength of the silicone rubber at different curing temperatures. we should be cautious in interpreting the results of the ANOVA test and consider other factors such as the practical significance of the differences in tensile strength.

(a) To test the hypothesis that curing temperatures affect the tensile strength of the silicone rubber, we can perform an analysis of variance (ANOVA). ANOVA is used to compare the means of two or more groups and determine if there is a significant difference between them.

We can use the following null and alternative hypotheses:

Null Hypothesis (H0): The mean tensile strength of the silicone rubber is the same at all curing temperatures.

Alternative Hypothesis (HA): The mean tensile strength of the silicone rubber is different at least for one curing temperature.

We can use the ANOVA test to determine if there is a significant difference between the means of the groups. The ANOVA table is shown below:

Source | SS | df | MS | F

Between | 0.014 | 2 | 0.007 | 3.06

Within | 0.118 | 18 | 0.007

Total | 0.132 | 20

The F-statistic for the ANOVA is 3.06 and the p-value is 0.068. Since the p-value is greater than 0.05, we fail to reject the null hypothesis. Therefore, we can conclude that there is no significant difference between the mean tensile strength of the silicone rubber at different curing temperatures.

(b) The box plots of the data are shown below:

       +-----+-----+-----+

       |  25 |  40 |  55 |

       +-----+-----+-----+

       |     |     | 2.03|  -

       |     | 2.22|     |  -

       |     |     | 2.07|  -

       | 2.09| 2.14|     |  -

       | 2.10| 2.18|     |  -

       |     |     | 2.03|  -

       | 2.01| 2.11| 2.15|  -

       |     | 2.05|     |  -

       | 2.02| 2.18|     |  -

       +-----+-----+-----+

The box plots do not support the conclusion of the ANOVA test. The box plots show that the median and interquartile range for the tensile strength at 55°C are lower than those at 25°C and 40°C. This suggests that the mean tensile strength at 55°C may be lower than at 25°C and 40°C. However, the ANOVA test failed to reject the null hypothesis of equal means. This discrepancy may be due to the small sample size and the variability of the data. Therefore, we should be cautious in interpreting the results of the ANOVA test and consider other factors such as the practical significance of the differences in tensile strength.

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104 square feet is the total area of the mural.

From the figure, we can say that the total area of the mural can be found by using basic algebra,

So,

The total area of the mural = area of the rectangle +area of the triangle- an area of a smaller triangle.

So, First for a bigger triangle,

the height of the triangle = 5 +2 = 7 ft.

the base of the triangle  = 14 ft.

the area = 1/2*base*height

Thus the area = 49 square feet.

For the rectangle,

Height of the rectangle = 8 ft.

Width of the rectangle  = 10 ft.

Thus the area of the rectangle = width * height

The area of the rectangle = 80 square feet

For the smaller triangle,

the height of the triangle = 5 ft.

the base of the triangle  = 10 ft.

the area = 1/2*base*height

Thus the area = 25 square feet.

Hence,

Total area of the mural = 80 + 49 -25

Therefore, The total area of the mural is 104 square feet

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Based on the given options, the diagram that best represents the activity of a sales clerk manually preparing a sale receipt during a power outage would be option D.

A trapezoid could represent the shape of a receipt, a curved side rectangle could represent the shape of the clerk's desk or the paper she is using, and a circle could represent the shape of a calculator or cash register. Therefore, a trapezoid to a curved side rectangle to a circle could represent the process of the clerk manually calculating and recording the sale amount and inputting it into a calculator or cash register to produce a receipt.

It is important to note that during a power outage, technology-dependent activities such as electronic sales and transactions may be disrupted, and manual methods may have to be used as a backup. This highlights the power of technology in our daily lives and the impact that power outages can have on businesses and individuals.
The question is about selecting the correct diagram that represents the sales clerk manually preparing a sale receipt due to a power outage. Given the options:

a. trapezoid to curvy side rectangle to curved rectangle
b. curved side rectangle to circle to curved rectangle
c. circle to curved side rectangle to curved rectangle
d. trapezoid to curved side rectangle to circle

The appropriate answer for this question cannot be determined based on the provided information. Diagrams typically require visual representation, and the description of the shapes alone is insufficient to convey the activity of preparing a receipt manually. Moreover, the terms "power," "outage," "clerk," "receipt," "trapezoid," "curved," and "curved" don't necessarily correspond to the shapes given in the options.

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The angle measurement of the triangle would be 9. 59 degrees

The different trigonometric identities are given as;

The ratios of the trigonometric identities are represented as;

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

From the information given, we have;

Opposite side = 1

Hypotenuse side = 6

Using the sine identity, we have;

sin θ = 1/6

Divide the values

sin θ = 0. 1666

Find the inverse of the sine

θ = 9. 59 degrees

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The expected number of heads = 1.5

The correct answer is an option (B)

We know that the formula for the expected value is:

E (x) = ∑ x P ( x )

where P(x) represents the probability of outcome X

and E(x) is the expected value of x

We need to find the expected number of heads.

From the probability distribution table of a 3-coin toss, the expected number of heads would be,

E(H) = 0(1/8) + 1(3/8) + 2(3/8) + 3(1/8)

E(H) = 0 + 3/8 + 6/8 + 3/8

E(H) = 12/8

E(H) = 1.5

The correct answer is an option (B)

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Answer:

Step-by-step explanation:

The circumference of the area of a circle is 4π in² using the formula A = πr², in inches is 4π inches.

The formula for the area of a circle is A = πr², where A is the area and r is the radius. Given that the area is 4π in², we can solve for the radius by taking the square root of both sides:

√(A/π) = √(4π/π) = 2 in

The formula for the circumference of a circle is C = 2πr, where C is the circumference and r is the radius. Substituting the value of r, we get:

C = 2π(2 in) = 4π in

Therefore, the circumference of the circle is 4π inches.

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Answer:

Step-by-step explanation:

1/2*b*h

1/2*4*5

4/2*5

2*5

10

The value of c2 in the notation of the text is 4mk. The units of c2 are Ns/m.
To find the position of the mass after t seconds, we need to solve the differential equation:
m d^2x/dt^2 + c dx/dt + kx = 0
where m is the mass of the spring, c is the damping constant, k is the spring constant, and x is the position of the mass.
We can write the solution to this equation in the general form:
x(t) = G1eat cos( Bt) + ce" sin(St)
where a and B are constants that depend on the initial conditions of the system, and G1 and c are constants determined by those initial conditions.
To find the constants G1 and c, we need to use the initial conditions given in the problem: the spring is stretched 0.5 meters beyond its natural length and then released with zero velocity. This means that x(0) = 0.5 and dx/dt(0) = 0.

Substituting these initial conditions into the general solution, we get:
x(t) = G1e^(-ct/2m) cos( ωt) + c e^(-ct/2m) sin( ωt)
where ω = sqrt(k/m - c^2/4m^2) is the angular frequency of the motion.
To find the constants G1 and c, we differentiate x(t) with respect to time and use the initial condition dx/dt(0) = 0:
dx/dt = -G1c/2m e^(-ct/2m) sin( ωt) + c e^(-ct/2m) cos( ωt)
dx/dt(0) = 0 = c
Therefore, c = 0.
To find G1, we use the initial condition x(0) = 0.5:
x(0) = G1 cos(0) + 0 = G1 = 0.5
Therefore, the position of the mass after t seconds is:
x(t) = 0.5e^(-ct/2m) cos( ωt)
where c = 0 and ω = sqrt(k/m).
Plugging in the given values, we get:
x(t) = 0.5e^(-0t/2*7) cos( sqrt(40/7)t) = 0.5cos(2.226t)
So the position of the mass after t seconds is 0.5cos(2.226t) meters.

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(24 ÷ 3) + x expresses the expression that represents the quotient of 24 and 3 plus x.

The expression refers to a mathematical phrase with two or more numbers or variables with mathematical operations such as addition, subtraction, division, multiplication, exponential, and so on. Examples of expression include 2a + 3p, and 9p.

To convert the given phrase into the expression, we have to start with the first operation which is a division that is represented by the word quotient. Thus we get 24 ÷ 3

Then we add the operation of addition which is represented by the word plus to the existing equation and we get (24 ÷ 3) + x

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The value of the function f(x) =  ( x² + 7 ) / ( x² + 4x - 21 )  for x = 5 is equal to 4/3.

The function is equal to,

f(x) =  ( x² + 7 ) / ( x² + 4x - 21 )

find the value of f(x) at x=5 by substituting x=5 into the given function we have,

⇒ f(5) = ( 5² + 7 ) / ( 5² + 4(5) - 21 )

⇒ f(5)  = ( 25 + 7 ) / ( 25 + 20 - 21 )

⇒ f(5)  = 32 / 24

Now reduce the fraction by taking out the common factor of the numerator and the denominator we get,

⇒ f(5)  = ( 8 × 4 ) / ( 8 × 3 )

⇒ f(5)  = 4/3

Therefore, the value of the function f(x) at x=5 is 4/3.

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The given question is incomplete, I answer the question in general according to my knowledge:

Find the value of the function f(x) at x = 5.

f(x) =  ( x² + 7 ) / ( x² + 4x - 21 )

Answer: The answer is 2 and 3 or B and C which ever way you want it.

The reason its 2and3 is because you can see its 60 degree angle.

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The reason its 3 also is because they are all congruent and its the only other right answer that fits.

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Hence, The answer is 2 and 3 or B and C.

Step-by-step explanation: Please give Brainliest.

Hope this helps!!!!

I can answer more questions if you want.

The amount of space within the cylinder not taken up by the tennis balls is 18.9 [tex]inches^3[/tex]

The volume of a tennis ball:

The circumference of the tennis ball is 8 inches.

The tennis ball is the form of sphere whose circumference is given by formula [tex]2\pi r[/tex], where r is the radius.

Thus, if r is the radius then according to condition,

[tex]2\pi r[/tex] = 8 or

r = 8/2[tex]\pi[/tex] inches.

Now, the volume of the sphere of radius r is [tex]\frac{4}{3}\pi r^3[/tex] hence, find the volume of the given tennis ball by substituting r  = 8/2[tex]\pi[/tex] inches in  [tex]\frac{4}{3}\pi r^3[/tex] and simplify:

Volume = [tex]\frac{4}{3}\pi[/tex] × [tex](\frac{8}{2\pi } )^3[/tex]

Volume = 8.65[tex]inches^3[/tex]

Hence the required volume of the tennis ball is 8.65[tex]inches^3[/tex]

The volume of three tennis balls is (3 × 8.65) [tex]inches^3[/tex] = 25.96 [tex]inches^3[/tex]

Find the volume of the cylinder:

The volume of the cylinder with radius r units and height h units is given by [tex]\pi r^2h[/tex] Hence the volume of the given cylinder with radius 1.32 inches , 8.2 height inches is:

[tex]\pi (1.32)^2[/tex] × 8.2

= 3.14 × [tex](1.32)^2[/tex] × 8.2

= 44.86 [tex]inches^3[/tex]

Hence the volume of the cylinder is 44.86 [tex]inches^3[/tex]

Find the amount of space within the cylinder not taken up by the tennis balls.

The required volume can be obtained by subtracting the volume three tennis balls from the volume of the cylinder as follows:

Volume of cylinder - volume of three tennis balls = (44.86 - 25.96) = 18.9 [tex]inches^3[/tex]

Hence, the amount of space within the cylinder not taken up by the tennis balls is 18.9 [tex]inches^3[/tex]

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The area between the two circles in the first quadrant is 18π square units.

To evaluate this integral, we first need to find the polar equations of the two circles.

For the circle [tex]x^2 + y^2 = 144,[/tex] we can convert to polar coordinates using the substitutions x = r cos θ and y = r sin θ, which gives:

[tex]r^2 = x^2 + y^2 = 144[/tex]

r = 12 (since r must be non-negative in polar coordinates)

For the circle [tex]x^2 - 12x + y^2 = 0[/tex], we can complete the square to get:

[tex]x^2 - 12x + 36 + y^2 = 36[/tex]

[tex](x - 6)^2 + y^2 = 6^2[/tex]

Again using the substitutions x = r cos θ and y = r sin θ, we get:

(r cos θ - 6[tex])^2[/tex] + (r sin θ[tex])^2[/tex] = [tex]6^2[/tex]

[tex]r^2 cos^2[/tex] θ - 12r cos θ + 36 +[tex]r^2 sin^2[/tex] θ = 36

r^2 - 12r cos θ = 0

r = 12 cos θ

Now we can set up the integral to find the area between the two circles in the first quadrant. Since we are in the first quadrant, θ ranges from 0 to π/2. We can integrate over r from 0 to 12 cos θ (the radius of the inner circle at the given θ), since the area between the two circles is bounded by these two radii.

Thus, the integral to evaluate is:

∫[θ=0 to π/2] ∫[r=0 to 12 cos θ] r dr dθ

Integrating with respect to r gives:

∫[θ=0 to π/2] [(1/2) r^2] from r = 0 to r = 12 cos θ dθ

= ∫[θ=0 to π/2] (1/2) (12 cos θ)^2 dθ

= ∫[θ=0 to π/2] 72 cos^2 θ dθ

Using the trigonometric identity cos^2 θ = (1 + cos 2θ)/2, we can simplify this to:

∫[θ=0 to π/2] 36 + 36 cos 2θ dθ

= [36θ + (18 sin 2θ)] from θ = 0 to θ = π/2

= 36(π/2) + 18(sin π - sin 0)

= 18π

Therefore, the area between the two circles in the first quadrant is 18π square units.

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If f(x)= - 3(x - m)2 + p Parabola vertical point T(2,5), then m + p is equal to 27.

Since the given parabola is vertical and has a vertex at T(2,5), we know that the equation is of the form f(x) = a(x-2)^2 + 5, where a is a constant.

We also know that f(x) = -3(x-m)^2 + p, which is in the same form as the first equation.

So, we can equate the two equations and get:

a(x-2)^2 + 5 = -3(x-m)^2 + p

Expanding the squares, we get:

a(x^2 - 4x + 4) + 5 = -3(x^2 - 2mx + m^2) + p

Simplifying and collecting like terms, we get:

ax^2 + (-4a + 6m)x + (4a - 3m^2 + p - 5) = 0

Since this equation must hold for all values of x, the coefficients of x^2 and x must be equal to zero.

Therefore, we have:

a = -3    (from the given equation f(x) = -3(x-m)^2 + p)
-4a + 6m = 0    (from the equation above)
-4(-3) + 6m = 0
12 + 6m = 0
m = -2

Substituting m = -2 and a = -3 into the equation above, we get:

4a - 3m^2 + p - 5 = 0

4(-3) - 3(-2)^2 + p - 5 = 0

-12 - 12 + p - 5 = 0

p = 29

Therefore, m + p = -2 + 29 = 27.

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Answer:

6 is the middle point of AD

The value of area of logo is,

A = 139.5 cm²

We have to given that;

The shape of a logo is made up of a triangle, a rectangle, and a parallelogram.

Here, Base of triangle = 9 cm

Height of triangle = 7 cm

Length of rectangle = 9 cm

Width of rectangle = 9 cm

Hence, We get;

The value of area of logo is,

A = (1/2 × 9 × 7) + (3 × 9) + (9 × 9)

A = 31.5 + 27 + 81

A = 139.5 cm²

Thus, The value of area of logo is,

A = 139.5 cm²

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The value of each variable in the circle is:

b = 90°

c = 47°

a = 43°

A circle is a round-shaped figure that has no corners or edges. It can be defined as a closed shape, two-dimensional shape, curved shape.

An angle inscribed in a semicircle is a right angle. Thus,

b = 90°

c = 360 - 133 - 180 (sum of angle in a circle)

c = 47°

a = 180 - 90 - 47  (sum of angle in a triangle)

a = 43°

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a. With 99% confidence, the difference in proportions is between -0.023 and 0.223. b. 99% of the confidence intervals will contain the true population proportion, and about 1% will not contain the true population difference in proportions.

a. To construct a confidence interval for the difference in proportions, we can use the following formula:

CI = (p1 - p2) ± zα/2 * √((p1*(1-p1)/n1) + (p2*(1-p2)/n2))

where:

p1, p2 = proportion of MCC, FSU students who believe they can achieve the American dream

n1, n2 = sample size of MCC, FSU students

zα/2 = critical value from the standard normal distribution for a 99% confidence level, which is 2.576

So,

CI = (0.75 - 0.65) ± 2.576 * √((0.75*(1-0.75)/100) + (0.65*(1-0.65)/100))

CI = 0.10 ± 0.123

CI = (−0.023, 0.223)

Therefore, with 99% confidence, the difference in proportions of MCC and FSU students who believe they can achieve the American dream is between -0.023 and 0.223.

b. Approximately 99% of these confidence intervals will contain the true population proportion of the difference in proportions of MCC students, and FSU students who believe they can achieve the American dream.

And about 1% will not contain the true population difference in proportions. This is because we constructed a 99% confidence interval.

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The domain of rational function f(x) = (x² - 36) / (x - 6) is x ∈ (- ∞, + ∞).

In this question we must determine what function has a domain, that is, the set of all x-values, that comprises all real numbers. According to algebra, polynomic functions have a domain that comprises all real numbers.

Herein we need to determine what rational function is equivalent to a polynomic function. Polynomic functions are expression of the form:

[tex]y = \sum\limits_{i = 0}^{n} c_{i}\cdot x^{i}[/tex]

Where:

Now we check the following expression by algebra properties:

f(x) = (x² - 36) / (x - 6)

f(x) = [(x - 6) · (x + 6)] / (x - 6)

f(x) = x + 6

The rational function f(x) = (x² - 36) / (x - 6) is equivalent to polynomial of grade 1 and, thus, its domain comprises all real numbers.

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Answer:

we find that the incidence rate of asthma in Oklahoma during that year was 454 cases per 100,000 population.

Step-by-step explanation:

The incidence rate of asthma is a measure of the number of new cases of asthma in a given population over a specific period. It is usually expressed per 100,000 population to allow for easier comparison between populations of different sizes. In this case, we are given the number of new cases of asthma and the total population of Oklahoma during the same year.

To calculate the incidence rate, we divide the number of new cases of asthma by the total population, and then multiply by 100,000. Applying this formula, we find that the incidence rate of asthma in Oklahoma during that year was 454 cases per 100,000 population.

This means that for every 100,000 residents of Oklahoma, there were 454 new cases of asthma during that year.

This information can be useful for public health officials and policymakers in identifying areas where more resources may be needed to prevent and manage asthma. It can also help in the evaluation of the effectiveness of interventions aimed at reducing the incidence of asthma.

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Answer: The probability of winning the jackpot is 1/4096, which corresponds to option A

Step-by-step explanation:

To find the probability of winning the jackpot, we need to find the probability of getting a wild symbol on the center line of each of the 4 reels.

Since there are 16 stops on each reel and 2 wild symbols on each reel, the probability of getting a wild symbol on the center line of a single reel is 2/16 or 1/8.

The probability of getting a wild symbol on the center line of all 4 reels is the product of the probabilities for each reel. Thus:

(1/8) * (1/8) * (1/8) * (1/8) = 1/4096

99.8% confidence interval with a margin of error of 0.02, using the estimated proportion of 0.31 from the previous poll.

To find the sample size needed to construct a confidence interval for a proportion with a specified margin of error, we use the following formula:

n = (z^2 * p * q) / E^2

where:

n is the sample size

z is the z-score corresponding to the desired level of confidence (99.8% in this case)

p is the estimated proportion from the previous poll (0.31 in this case)

q = 1 - p

E is the desired margin of error (0.02 in this case)

First, we need to find the value of z for a 99.8% confidence level. Using a standard normal distribution table, we can find that the z-score for a 99.8% confidence level is approximately 2.967.

Substituting the given values into the formula, we have:

n = (2.967^2 * 0.31 * 0.69) / 0.02^2

n = 1202.19

Rounding up to the nearest whole number, we need a sample size of n = 1203 to construct a 99.8% confidence interval with a margin of error of 0.02, using the estimated proportion of 0.31 from the previous poll.

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Answer: 84

Step-by-step explanation:

Sorry if this is wrong.

To find the length of BC in the given right triangle ABC with AC = 48 and DC = 28, we used the Pythagorean theorem twice and simplified the equations to get BC² = 1520. Taking the square root, we got BC = 4√(95).

We are given a right triangle ABC with an altitude BD drawn to hypotenuse AC. We are also given that AC = 48 and DC = 28, and we need to find the length of BC.

To find the length of BC, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides (the legs) is equal to the square of the length of the hypotenuse.

In this case, we have

AB² + BD² = BC² (using the Pythagorean theorem for triangle ABD)

AC² - DC² = BC² (using the Pythagorean theorem for triangle ADC)

Substituting AC = 48 and DC = 28, we get

AB² + BD² = BC²

48² - 28² = BC²

Simplifying, we get

AB² + BD² = BC²

(48 + 28)(48 - 28) = BC²

76 × 20 = BC²

BC² = 1520

Taking the square root of both sides, we get

BC = √(1520) = 4√(95)

Therefore, the length of BC in simplest radical form is 4√(95).

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