Find the values of the missing sides of the right triangle

So the formula for the nth term of the arithmetic sequence with the third term 7 and the common difference -2 is aₙ = 13 - 2n.

An arithmetic sequence's nth term is represented by the formula:

aₙ = a₁ + (n-1)d

In this case, we are given that the third term is 7, so we can use this information to find a₁:

a₃ = a₁ + (3-1)(-2)

7 = a₁ - 4

a₁ = 11

Now we have a₁ and d, so we can write the formula for the nth term:

aₙ = 11 + (n-1)(-2)

Simplifying this expression, we get:

aₙ = 13 - 2n

So the formula for the nth term of the arithmetic sequence with the third term 7 and the common difference is

-2 is aₙ = 13 - 2n.

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The answer of the given figure is ∠B = 72° and ∠C = 108°

In geometry, corresponding angles are pairs of angles that have the same relative position and the same degree of rotation, in two different geometric figures that are being compared.

More specifically, when two lines are crossed by another line, the angles on one side of the crossing line that are in the same relative position to each other (i.e., they are on the same side of the crossing line and are either both interior angles or both exterior angles), are corresponding angles.

According to question

∠CFE = 72°

In given diagram

DC ║ EF ║ AB and CB is transversal

∴ ∠CFE + ∠BFE = 180° ( Linear pair )

72° + ∠BFE = 180°

∠BFE = 180 - 72

∠BFE = 108°

∵∠DCF = ∠BFE ( Corresponding equal angle )

∠DCF = 108°

∠C = 108°

∠CFE = ∠B (  Corresponding equal angle )

72° = ∠B

∴∠B = 72°

Hence, the ∠B = 72° and ∠C = 108°

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The equation of the circle is represented by [tex]x^{2} + (y-3)^{2} = 16[/tex] with radius of the circle as r = 4.

How to find the equation of the circle?

To find the equation of the circle is

[tex](x-h)^{2} + (y-k)^{2} = r^{2}[/tex]

here h is the x- coordinate of the center of the circle

        k is the y- coordinate of the center of the circle

        r is the radius of the circle

From the given figure,

h = 0

k = 3

r = 4

putting all the values of the above equation

[tex](x-0)^{2} + (y - 3)^{2} = 4^{2}[/tex]

[tex]x^{2} + (y-3)^{2} = 16[/tex]

Therefore the equation of the circle is

[tex]x^{2} + (y-3)^{2} = 16[/tex]

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Step-by-step explanation:

The green triangle :

The angle x is 65°

this is because both the sides are equal so when the other angle is 65° angle x is also 65°

The blue triangle :

The angle x is 25°

this is because both the sides are equal so when the other angle is 25° angle x is also 25°

The red triangle :

The angle x is 45°

this is because both the sides are equal so when the other angle is 45° angle x is also 45°

Therefore , the solution of the given problem of surface area comes out to be scale factor of the dilation is 15.0, rounded to one decimal point.

By calculating how much space would be needed to fully enclose its exterior, its overall size can be calculated. The surrounding region is considered when selecting a comparable product in the rectangular design. The surface area of something determines its overall dimensions. The number of sides connecting a cuboid's four trapezoidal forms determines how much water it can hold.

Here,

By dividing the volume of the dilated figure by the volume of the initial figure, we can determine the scale factor of the dilation:

volume of dilated figure / volume of initial figure is the scale factor.

Scale factor:

=>  25,500/1700 cm3

=> 15 scale factor

The approximate scale factor of the dilation is 15.0, rounded to one decimal point.

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Answer:

if its a circle

Volume - 7.20 cm

Surface area 18.1 cm

Step-by-step explanation:

Volume of a sphere = 4/3 πr^3

4/3 (3.14) 1.2^3

4/3 (3.14) 1.728

4/3 of 5.42592=

7.23456 or 7.20

Surface area of sphere = 4πr²

4(3.14) 1.2^2

4(3.14) 1.44

4 (4.5216) =

18.0864 or 18.1

Thus, the  arc length of DC for the given central angle of circle is found as: 16.74 units.

Arc Length Formula: Assume a circle with radius r. If a circle's arc of length s subtends a central angle theta (measured in radians), the formula is as follows: r X theta = s.

For the given circle:

Thus,

∠APD + ∠DPC = 180° (angle sum property of triangle)

60 + ∠DPC = 180°

∠DPC = 180° - 60°

∠DPC = 120°

Using the formula for the arc length:

Arc length = Ф/360 * 2*π*r

Arc length DC = 120/360 * 2*3.14*8

Arc length DC = 16.74 units

Thus, the  arc length of DC for the given central angle of circle is found as: 16.74 units.

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Complete question:

In the figure below DB and AC are diameters of circle P. The length of PB is 8 units . What is the arc length of DC.

The figure is attached.

QS is the diameter of circle

A circle is a two-dimensional geometric shape consisting of all points in a plane that are a given distance from a fixed point called the center. It is a closed shape, meaning it has no beginning or end, and every point on its perimeter is equidistant from the center. The distance from the center to any point on the circle is called the radius, and the distance across the circle through the center is called the diameter

In the given circle QS bisects perpendicularly the chord PR in two equal part. so, it must pass through center of circle.

QS is passing through center.

The chord passing through center is called as diameter of circle.

Hence, QS is the diameter of circle.

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Therefore , the solution of the given problem of function comes out to be Oy=-0.5z²+z+4.

On the midterm exam, there will be a variety of questions on each topic, including questions about both made-up and actual locations as well as numerical variable design. a diagram showing the relationships between different elements that cooperate to create the same result. A service is composed of numerous distinctive components that cooperate to create distinctive results for each input.

Here,

We must make use of the data provided in the challenge in order to identify the quadratic function.

=>  f(z) = a(z + 4)(z - 2)

where an is a constant we need to figure out.

We can use the position (-6, -8), which is where the function passes through, to determine the value of a:

=>  -8 = a(-6 + 4)(-6 - 2)

=>  -8 = a(-2)(-8)

=>  -8 = 16a

=>  a = -1/2

Inputting this number of an into the quadratic function equation yields the following results:

=>  f(z) = -1/2(z + 4)(z - 2)

By extending this phrase, we get:

=> f(z) = -1/2(z² - 2z - 8)

Further simplification results in:

=>  f(z) = -0.5z² + z + 4

The quadratic function's corresponding equation is thus:

=>  Oy=-0.5z²+z+4

The following is the appropriate decision from the options provided:

=> Oy=-0.5z²+z+4

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The ratios that would create the same orange color as Maia's ratio of  [tex]2:3[/tex] are  [tex]2[/tex] red to [tex]3[/tex] yellow,  [tex]44[/tex] red to  [tex]66[/tex] yellow, and [tex]28[/tex] red to [tex]42[/tex] yellow.

The ratio of 4 drops of red food coloring to 6 drops of yellow food coloring can be simplified to 2:3 by dividing both numbers by 2. This means that for every 2 drops of red food coloring, Maia used 3 drops of yellow food coloring to create orange icing.

Let's evaluate each of the given ratios:

2 red to 3 yellow: This ratio is equivalent to Maia's ratio of 2:3, so it would create the same orange color.

40 yellow to 100 red: We can simplify this ratio by dividing both numbers by 20, giving us 2 yellow to 5 red. This ratio is not equivalent to Maia's ratio of 2:3, so it would not create the same orange color.

44 red to 66 yellow: We can simplify this ratio by dividing both numbers by 22, giving us 2 red to 3 yellow. This ratio is equivalent to Maia's ratio of 2:3, so it would create the same orange color.

24 red to 26 yellow: We can simplify this ratio by dividing both numbers by 2, giving us 12 red to 13 yellow. This ratio is not equivalent to Maia's ratio of 2:3, so it would not create the same orange color.

28 red to 42 yellow: We can simplify this ratio by dividing both numbers by 14, giving us 2 red to 3 yellow. This ratio is equivalent to Maia's ratio of 2:3, so it would create the same orange color.

Therefore, the ratios that would create the same orange color as Maia's ratio of  [tex]2:3[/tex] are  [tex]2[/tex] red to [tex]3[/tex] yellow,  [tex]44[/tex] red to  [tex]66[/tex] yellow, and [tex]28[/tex] red to [tex]42[/tex] yellow.

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English please I don't unless

The solution for the given system is x1 = (23/5s - x2)/4s, x2, where s ≠ -360/49 and x2 can be any non-zero

The values of the parameter s

for which the system has a unique solution are s ≠ -45/8. Let's understand how to find the solution and the values of s:

Given equation of the system is,5x1s + 9x2 = -3 ...(1)

5x1 + sx2 = 4 ...(2)

Now, let's solve the given system of equations using the elimination method:

Multiply equation (2) by 5, we get:25x1 + 5sx2 = 20 ...(3)

Now, we'll subtract equation (1) from equation (3) as:

25x1 + 5sx2 = 20- (5x1s + 9x2 = -3)20x1 + 5sx2 = 23 ... (4)

Let's divide equation (4) by 5s, we get:

4x1 + x2/s = 23/5s ... (5)

Multiply equation (2) by 9 and subtract equation (1) from it. We get:40x2 + 9sx2 = 39

Simplifying the above equation, we get:(49s+360)x2 = 39 ... (6)

Now, we have two equations:(5) 4x1 + x2/s = 23/5s(6) (49s+360)

x2 = 39The given system of equations will have a unique solution only if x2 ≠ 0. So, let's consider the value of x2.If x2 ≠ 0, then from equation (6)

we get,49s+360 ≠ 0 or s ≠ -360/49

This means that s ≠ -360/49 is necessary for the given system to have a unique solution.

Now, let's solve the equation (5):4x1 + x2/s = 23/5s

If we multiply both sides of the equation (5)

by s, we get:

4sx1 + x2 = 23/5If x2 ≠ 0, then we can solve this equation for x1 as:

x1 = (23/5s - x2)/4s

Therefore, the solution for the given system is x1 = (23/5s - x2)/4s, x2, where s ≠ -360/49 and x2 can be any non-zero value.

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Answer: 586.20

Step-by-step explanation:

you add the balance on june 5th with the amount withdrawed to get the past balance

Answer: We know that the formula for the circumference of a circle is:

Circumference = 2πr

where r is the radius of the circle.

In this problem, we are given the circumference, which is 5π ft, so we can set up an equation:

5π = 2πr

Dividing both sides by 2π, we get:

r = 5/2 feet

Now that we know the radius, we can use the formula for the area of a circle:

Area = πr^2

Substituting in the value of r that we found, we get:

Area = π(5/2)^2

Area = π(25/4)

Simplifying, we get:

Area = 25π/4

Therefore, the area of the circle is 25π/4 square feet.

Step-by-step explanation:

The translation vector is (5, 5). Now we can find the image of point (-3, -2) under the same translation: (-3+5, -2+5) = (2, 3)

What are coordinates?

A pair of numbers that use the separations between the two reference axes to define the location of a point on a coordinate plane. usually represented by the x- and y-values, respectively, (x, y).

Let's denote the translation vector as (a, b), then the image of point (x, y) under the translation is given by (x+a, y+b).

We know that the image of point (6, -9) under the translation is (11, -4), so we can write:

(6+a, -9+b) = (11, -4)

Solving this system of equations for a and b, we get:

a = 5 and b = 5

Therefore, the translation vector is (5, 5). Now we can find the image of point (-3, -2) under the same translation:

(-3+5, -2+5) = (2, 3)

So the image of point (-3, -2) under the given translation is (2, 3).

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17,600 citizens chose Fish or Snakes.

What is circle graph?

A circle graph, also known as a pie chart, is a type of data visualization used to represent data in a circular format. It is called a pie chart because the graph resembles a pie, which is divided into slices or sectors, where each sector represents a portion of the whole data set. The size of each slice is proportional to the corresponding value it represents in the data set. The circle graph is often used to show relative sizes of different categories or portions of a whole. It is a popular way to display data in business, statistics, and other fields.

According to the given information, the percentage of citizens who chose Fish or Snakes is 12% + 10% = 22%.

It is also given total number of citizens are 80,000.

To find the number of citizens who chose Fish or Snakes, we can first calculate 22% of 80,000,

[tex]22\% \: of \: 80000 \\ = \frac{22}{100} \times 80000 \\ = 0.22 \times 80,000 \\ = 17,600[/tex]

Therefore, 17,600 citizens chose Fish or Snakes.

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that means that the slope for all three points is the same, since all are collinear, hmmm what's the slope of (1 , 2) and (7 , -1)?

[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{-1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-1}-\stackrel{y1}{2}}}{\underset{\textit{\large run}} {\underset{x_2}{7}-\underset{x_1}{1}}} \implies \cfrac{ -3 }{ 6 } \implies - \cfrac{1 }{ 2 }[/tex]

ahaaa!, that means from from (-2 , y) and either of those points is the same slope of -1/2, so

[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{y})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{-1})[/tex]

[tex]\stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-1}-\stackrel{y1}{y}}}{\underset{\textit{\large run}} {\underset{x_2}{7}-\underset{x_1}{(-2)}}} ~~ = ~~\stackrel{\stackrel{\textit{\small slope}}{\downarrow }}{ \cfrac{ -1 }{ 2 }}\implies \cfrac{-1-y}{7+2}=\cfrac{-1}{2}\implies \cfrac{-1-y}{9}=\cfrac{-1}{2} \\\\\\ -2-2y=-9\implies -2y=-7\implies y=\cfrac{-7}{-2}\implies y=\cfrac{7}{2}[/tex]

Answer:

Step-by-step explanation: (-2, y) (1, 2) and (7, -1) wat is the value of y

The ability of a study to detect a difference if one actually exists is called option (d) power

Power in statistics is the probability of correctly rejecting a false null hypothesis. In other words, it is the ability of a statistical test to detect a difference or effect if one actually exists in the population being studied. A study with high power has a low probability of a Type II error (failing to reject a false null hypothesis) and a high probability of correctly detecting a true difference or effect.

Power is affected by several factors, including sample size, effect size, level of significance (alpha), and variability of the data. Researchers often aim for a power of at least 80% to ensure that their study has a reasonable chance of detecting a meaningful effect.

Therefore, the correct option is (d) power

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One large bucket of popcorn costs $6 and one box of candy costs $3.75.

Let's call the cost of one large bucket of popcorn as "p" and the cost of one box of candy as "c". We can set up two equations based on the information given in the problem :

Equation 1: 4p + 5c = 42.75 (first group's purchase)

Equation 2: 3p + 2c = 25.50 (second group's purchase)

We can use any method to solve these equations, such as substitution or elimination.

Let's use the elimination method by multiplying both sides of Equation 1 by 2 and both sides of Equation 2 by -5 to eliminate "c" and get an equation in terms of "p":

8p + 10c = 85.50 (multiplying Equation 1 by 2)

-15p - 10c = -127.50 (multiplying Equation 2 by -5)

Adding the two equations, we get :

-7p = -42

p = 6

Now we can substitute the value of "p" into either Equation 1 or Equation 2 to solve for "c". Let's use Equation 1:

4(6) + 5c = 42.75

24 + 5c = 42.75

5c = 18.75

c = 3.75

Therefore, one large bucket of popcorn costs $6 and one box of candy costs $3.75.

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The for the given volume of 12,500 cubic inches for rectangular prism, the base area will be estimated by equation: A. 12500=50B.

A rectangular prism is one of the more typical shapes for prisms. One definition of a rectangular prism is a prism with rectangle-shaped bases. The other surfaces are also rectangles because the bases are rectangles. These are a rectangular prism's characteristics:

Given:

volume of rectangular prism = 12,500 cubic inches

Height h = 50 inches.

Let the base area be B.

Then,

volume of rectangular prism = B*h

12500 = B*50

12500 = 50B  (required equation)

B = 12500/50

B = 250 unit sq.

Thus, the for the given volume of 12,500 cubic inches for rectangular prism, the base area will be estimated by equation: A. 12500=50B.

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Answer:

A line graph, because it would show the association or relationship between two variables

Step-by-step explanation:

The correlation coefficient between x and f(x) is approximately 0.39. This suggests a weak positive correlation between the cost per seat and the profit the airline makes.

The precise metric used in a correlation analysis to quantify the strength of the linear relationship between two variables is the correlation coefficient.

To calculate the correlation coefficient between x and f(x), we need to calculate several quantities first:

mean of x:

[tex]$\overline{x}[/tex] = {50+35+60+65+70+75+80}{7} = {435}/{7}

= 62.14

mean of f(x):

[tex]$\overline{f(x)}[/tex]= {1,272 + 1,884.5 + 2,322 + 2,584.5 + 2,672 + 2,584.5 + 2,322}/{7}

= 2,112.86

and, standard deviation of x:

[tex]$s_x[/tex]=[tex]\sqrt{\frac{\sum_{i=1}^n (x_i - \overline{x})^2}{n-1}}[/tex]

= [tex]= \sqrt{\frac{(50-62.14)^2 + (35-62.14)^2 + (60-62.14)^2 + (65-62.14)^2 + (70-62.14)^2 + (75-62.14)^2 + (80-62.14)^2}{6}} \\\approx 17.27$[/tex]

and, standard deviation of f(x):

[tex]$s_{f(x)} = \sqrt{\frac{\sum_{i=1}^n (f(x_i) - \overline{f(x)})^2}{n-1}}[/tex]

= (1,272-2,112.86)² + (1,884.5-2,112.86)² + (2,322-2,112.86)² + (2,584.5-2,112.86)² + (2,672-2,112.86)²+  (2,584.5-2,112.86)² + (2,322-2,112.86)²}/ 6

= 385.09

Now, covariance of x and f(x):

[tex]$cov(x,f(x)) = \frac{\sum_{i=1}^n (x_i - \overline{x})(f(x_i) - \overline{f(x)})}{n-1}[/tex]

= {(50-62.14)(1,272-2,112.86) + (35-62.14)(1,884.5-2,112.86) + (60-62.14)(2,322-2,112.86) + (65-62.14)(2,584.5-2,112.86) + (70-62.14)(2,672-2,112.86) + (75-62.14)(2,584.5-2,112.86) + (80-62.14)(2,322-2,112.86)} / 6

= 762.36

Using these values, we can calculate the correlation coefficient:

[tex]$r = \frac{cov(x,f(x))}{s_x s_{f(x)}} = \frac{762.36}{17.27 \cdot 385.09} \approx 0.39$[/tex]

Therefore, the correlation coefficient between x and f(x) is approximately 0.39. This suggests a weak positive correlation between the cost per seat and the profit the airline makes.

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Answer:

f(x) has the greater initial value.

linear;  h(x) = 200x + 1500

Step-by-step explanation:

f(0) = 1000

g(0) = 750

Therefore, f(x) has the greater initial value.

In the third area, the model is linear and the function would be:

h(x) = 200x + 1500

The probability that the individual waits more than 7 minutes is 0.3 or 30%. The probability that the individual waits between 2 and 7 minutes is 0.5 or 50%.

Let X be the waiting time for a particular individual at the bus stop. As per the given information, X follows a continuous uniform distribution with parameters a=0 and b=10 (as the bus arrives every 10 minutes).

The probability that the individual waits more than 7 minutes can be calculated as follows:

P(X > 7) = (b-7)/(b-a) = (10-7)/(10-0) = 3/10 = 0.3

Similarly, the probability that the individual waits between 2 and 7 minutes can be calculated as follows:

P(2 < X < 7) = (7-2)/(10-0) = 5/10 = 0.5

In summary, the probability that the individual waits more than 7 minutes is 0.3 and the probability that the individual waits between 2 and 7 minutes is 0.5. This means that there is a higher chance that the individual waits between 2 and 7 minutes than waiting for more than 7 minutes.

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The probability of tossing heads and then tails, given that the coin already shows heads in the first toss, is 1/2.

Let's first find the sample space of this experiment, which is {HH, HT, TH, TT}. We know that the coin has already shown heads in the first toss, so we can eliminate TT from the sample space. Therefore, the new sample space becomes {HH, HT, TH}.

Out of these three possible outcomes, only one satisfies the given condition of tossing heads and then tails, which is HT. Therefore, the probability of tossing heads and then tails, given that the coin already shows heads in the first toss, is 1/2 (i.e., one favorable outcome out of two possible outcomes).

Therefore, the probability of tossing heads and then tails, given that the coin already shows heads in the first toss, is 1/2, as there is only one favorable outcome out of the two possible outcomes in the new sample space after eliminating TT.

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The probability that the mean of a sample of 45 boards will be between 94.5 inches and 95.1 inches, given that the length of timber cuts are normally distributed with a mean of 95 inches and a standard deviation of 0.52 inches, can be calculated using the Central Limit Theorem. The theorem states that the distribution of sample means will be approximately normally distributed with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

In this case, the population mean (μ) is 95 inches, the population standard deviation (σ) is 0.52 inches, and the sample size (n) is 45. The standard deviation of the sample mean is σ/√n = 0.52/√45 ≈ 0.0775.

To find the probability, we can use the Z-score formula:

Z = (X - μ) / (σ/√n)

For the lower limit of 94.5 inches, the Z-score is:

Z1 = (94.5 - 95) / 0.0775 ≈ -6.45

For the upper limit of 95.1 inches, the Z-score is:

Z2 = (95.1 - 95) / 0.0775 ≈ 1.29

Now, using a Z-table or calculator, find the probability for each Z-score:

P(Z1) ≈ 0 (since it is a very low Z-score)
P(Z2) ≈ 0.9015

The probability that the mean of the sample will be between 94.5 inches and 95.1 inches is the difference between these probabilities:

P(94.5 < X < 95.1) = P(Z2) - P(Z1) = 0.9015 - 0 ≈ 0.9015, or approximately 90.15%.

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Answer:

No solution

Step-by-step explanation:

Solve for x

[tex]|x-13|+18=-4[/tex]

Subtract 18 on both sides

[tex]|x-13|=-22[/tex]

There is no solution to this problem. Absolute value cannot be less then 0.

The equation representing the area of the rectangle with width w is A = w² + 2w.

We have a rectangle with a length that is 2 units longer than the width w. Let's refer to the rectangle's length as L. Then we have:

[tex]L = w + 2[/tex]

The product of a rectangle's length and breadth determines its area A. So, to find an equation representing the area of the rectangle, we need to multiply the length L by the width w. Substituting L with the expression we got from the problem statement, we get:

A = L × w

A = (w + 2) × w

A = w² + 2w

This is the final equation representing the area of the rectangle in terms of its width w

This is a quadratic equation in standard form, where the coefficient of the squared term is 1, the coefficient of the linear term is 2, and the constant term is 0. We can use this equation to find the area of the rectangle for any given width w.

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To prove Triangle ACE is congruent to Triangle BDE using the ASA postulate, we need either ∠A ≅ ∠B or ∠C ≅ ∠D.

To prove two triangle congruent by angle side angle postulate, these triangle must have two sides equal or one angle from these two must be equal and identical to each other.

What are congruent triangle?

Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure. These triangles can be slides, rotated, flipped and turned to be looked identical. If repositioned, they coincide with each other. The symbol of congruence is’ ≅’.

The meaning of congruence in Maths is when two figures are similar to each other based on their shape and size. There are basically four congruence rules that proves if two triangles are congruent.

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The expression for the given statement can be written as (25 + h) / f³.

A sum is the result of adding two or more numbers together. For example, the sum of 2 and 3 is 5, which is obtained by adding 2 and 3. In mathematical notation, we can represent this as:

2 + 3 = 5

The expression for the given statement can be written as:

(25 + h) / f³

where h and f are variables.

If you have specific values for h and f, you can substitute them into the expression and evaluate it. Otherwise, you can leave the expression as it is.

The expression "(25 + h) / f³" represents the result of adding 25 to the value of h, and then dividing the sum by the cube of the value of f.

In general, if you have specific values for h and f, you can substitute them into the expression and evaluate it. If you don't have specific values for h and f, you can leave the expression as it is. This expression is an algebraic expression, which means it contains variables (h and f) and mathematical operations (+, /, and ³).

Note that division is performed before addition, so the sum of 25 and h is first calculated, and then the result is divided by f³.

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