a i. AED and CEB are vertically opposite angles. Write a true statement about the measures (i.e., sizes) of the two angles.​

By using the statements AE = EB, ∠CAB = ∠CBA, and mCB = mCAB, we can prove that triangle ABC is isosceles. The following statements can be used to prove that triangle ABC is isosceles:

AE = EB

∠CAB = ∠CBA

mCB = mCAB

To prove that AE = EB, we can use the fact that an altitude of a triangle bisects the base. This means that AD divides BC into two segments of equal length, BD and CD. Since AE and EB are the projections of AD onto AB and AC respectively, they must also be equal in length.

To prove that ∠CAB = ∠CBA, we can use the fact that the angles opposite equal sides of a triangle are equal. Since AE = EB, we know that ∆AED and ∆CEB are congruent by SSS. This means that ∠AED = ∠CEB, and since ∠AED + ∠CEB = ∠CAB + ∠CBA, we have ∠CAB = ∠CBA.

To prove that mCB = mCAB, we can use the fact that the base angles of an isosceles triangle are equal. Since ∠CAB = ∠CBA, we know that ∆ABC is isosceles, and therefore mCB = mCAB.

For more such questions on triangle

https://brainly.com/question/17335144

#SPJ8

Answer:

12.21 m

Step-by-step explanation:

Remember Pathagorean Theorem states that \(a^{2} + b^{2} = c^{2}\)

Whats important to know is that c is always the hypotenuse, so in this case the unknown.

a = 7

b = 10

c = ?

Plug in these values for the equation above:

\(7^{2} + 10^{2} = c^{2}\)

Simplify:

49 + 100 = \(c^{2}\)

149 = \(c^{2}\)

Cancel out the power by taking the square root of both sides:

\(\sqrt{149} = \sqrt{c^{2}}\)

c = 12.21 m

a) The amount of water in the pool after 2 hours can be calculated using the equation.

Water in pool = 10L/hour × 2 hours = 20L.

b) The pool will be 80L when the equation is satisfied: 80L = 10L/hour × Time.

Solving for Time, we find Time = 8 hours.

c) Part b) is linear.

a) To calculate the amount of water in the pool after 2 hours, we can use the equation:

Water in pool = Water filling rate × Time

Since the pool gets filled up with 10L of water per hour, we can substitute the values:

Water in pool = 10 L/hour × 2 hours = 20L

Therefore, after 2 hours, there will be 20 liters of water in the pool.

b) To determine the number of hours it takes for the pool to reach 80 liters, we can set up the equation:

Water in pool = Water filling rate × Time

We want the water in the pool to be 80 liters, so the equation becomes:

80L = 10 L/hour × Time

Dividing both sides by 10 L/hour, we get:

Time = 80L / 10 L/hour = 8 hours

Therefore, it will take 8 hours for the pool to contain 80 liters of water.

c) Part b) is linear.

The equation Water in pool = Water filling rate × Time represents a linear relationship because the amount of water in the pool increases linearly with respect to time.

Each hour, the pool fills up with a constant rate of 10 liters, leading to a proportional increase in the total volume of water in the pool.

For similar question on amount.

https://brainly.com/question/25720319  

#SPJ8

In a rigid body motion, we have that the angle ABC is still the same, the midpoint of AB is mapped to the midpoint of A'B', and the length of BC is equal the length of B'C'.

So the only option that is not always true is that AB is parallel to A'B'.

So the correct option is (1).

Answer:

30

Step-by-step explanation:

3x10=30

The expected number of cute mugs sold in a day is 1.37 (rounded to two decimal places).

Given day, the probabilities of selling different numbers of coffee mugs are given by:

P(X = 0) = 0.2317719

P(X = 1) = 0.3989423

P(X = 2) = 0.2358207

P(X = 3) = 0.0786496

P(X = 4) = 0.0156251

a. The probability of selling 17 coffee mags in a given day is 0.000032.b.

The probability of selling at least 6 coffee mugs is the sum of the probabilities of selling 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, or 17 coffee mugs.

P(X ≥ 6)

= P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15) + P(X = 16) + P(X = 17)

= 0.9997231

c. The probability of selling 2 or 17 coffee mugs is:

P(X = 2) + P(X = 17)

= 0.2317719 + 0.000032

= 0.2318049

d. The probability of selling 10 coffee mugs is:

P(X = 10) = 0.0029788e.

The probability of selling at most coffee mugs is:

P(X ≤ k) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

= 0.9609842

f. The expected number of cute mugs sold in a day is given by:

E(X) = Σ x P(X = x)

where x takes the values 0, 1, 2, 3, 4, and their corresponding probabilities.

E(X) = 0 × 0.2317719 + 1 × 0.3989423 + 2 × 0.2358207 + 3 × 0.0786496 + 4 × 0.0156251

= 1.3705172

Therefore, the expected number of cute mugs sold in a day is 1.37 (rounded to two decimal places).

To learn more about number visit;

https://brainly.com/question/3589540

#SPJ11

Answer:

55.5 km

Step-by-step explanation:

speed=distance/time

55.5= 333/6

Answer:

55.5 km per hour

Step-by-step explanation:

The simple formula is D_S-T

D is at the top for Distance

S is down to the left for speed

And T to the right as Time

Its simple so just take

Distance: 333km

Time: 6 hrs

333÷5=55.5/1

Answer:

The second one

Step-by-step explanation:

She started with x dollars and then used 8 dollars to buy a football game ticket, so x-8. Then, she is left with 56 dollars, so x-8=56. Therefore, the second story represents the equation.

Answer:

500

Step-by-step explanation:

I will tell you what 460 is rounded to the nearest hundred and also show you what rules I used to get to the answer.

We did not necessarily round up or down, but to the hundred that is nearest to 460.

500

A) We round the number up to the nearest hundred if the last two digits in the number are 50 or above.

B) We round the number down to the nearest hundred if the last two digits in the number are 49 or below.

C) If the last two digits are 00, then we do not have to do any rounding, because it is already to the hundred.

Answer: 17

Step-by-step explanation:

First, change everything to ascending order.

14, 15, 16, 17, 18, 20, 25

Now, select the middle number, in this case, it is 17.

To find the median of a data set, you must put the numbers in order from least to greatest and find the middle (center) number.

The following data set: 16, 14, 15, 18, 17, 20 and 25 can be organized into the following order: 14, 15, 16, 17, 18, 20, 25.

Now, simply find out the middle number.

17 is the middle number, therefore the median.

The answer is that Point D is Circumcentre and other lengths DE,DF,DG are perpendicular bisectors of sides of triangle ABC

What is Circumcentre?

The point of intersection of Perpendicular bisectors in a triangle is called called Circumcentre.

Solution;

The circumcentre is equidistant from all sides of an triangle when we draw the perpendicular from this point to sides of triangles, the length of all perpendiculars will be same and this is its another property

To learn more about circumcentre click the below link:

https://brainly.com/question/14368399

#SPJ1

Answer:

1 3/4

Step-by-step explanation:

The fractions have unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.

LCD(3/4, 1/1) = 4

Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. This is basically multiplying each fraction by 1.

(34×11)+(11×44)=?

Complete the multiplication and the equation becomes

34+44=?

The two fractions now have like denominators so you can add the numerators.

Then:

3+44=74

This fraction cannot be reduced.

The fraction

74

is the same as

7÷4

Convert to a mixed number using

long division for 7 ÷ 4 = 1R3, so

74=134

Therefore:

34+11=1 3/4

If this helped i'm glad i could help you (´・ω・`)

Answer:

3

Step-by-step explanation:

Total 108 chips were in the both bags.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

10% of chips in the first bag is 6.

To find the total chips in the first bag:

6 = 10 x total number of chips in the first bag / 100

total number of chips in the first bag = 600/10

total number of chips in the first bag  = 60

25% of chips in the second bag is 12.

To find the total chips in the second bag:

12 = 25x total number of chips in the second bag / 100

total number of chips in the second bag = 1200/25

total number of chips in the second bag  = 48

Now, total chips in the both bags = 60 + 48 = 108

Therefore, total 108 chips were in the both bags.

To learn more about the percentage;

brainly.com/question/24159063

#SPJ5

Answer: pee

Step-by-step explanation:

An ordered pair (x, y) that satisfies the equation 4x - y = 5 is (3, -7).To find an ordered pair (x, y) that satisfies the equation 4x - y = 5, we need to substitute values for x and y and check if the equation holds true.

Let's start by assigning a value to x. Let's choose x = 3. Substituting this value into the equation, we have 4(3) - y = 5, which simplifies to 12 - y = 5. By subtracting 12 from both sides, we get -y = 5 - 12, which further simplifies to -y = -7. To solve for y, we multiply both sides by -1, resulting in y = 7. Therefore, when x = 3 and y = -7, the equation 4x - y = 5 holds true. The ordered pair (3, -7) satisfies the equation 4x - y = 5. This means that if we substitute x = 3 and y = -7 into the equation, the equation will be true. Let's verify this:

4(3) - (-7) = 5

12 + 7 = 5

19 = 5

Since 19 does not equal 5, the equation is not true for the ordered pair (3, -7). Therefore, (3, -7) is not a solution to the equation 4x - y = 5.Apologies for the error in the initial response. Unfortunately, there is no ordered pair that satisfies the equation 4x - y = 5. The equation has no real solution, as there is no combination of x and y that will make the equation true.

Learn more about equation here:- brainly.com/question/29657983

#SPJ11

a. The price of the consol is approximately $133.33.

b. The new price of the consol would be $100. The price of the consol falls by 24.99% and the interest rate rises by 1%.

c. Your holding period return is approximately -49.99%.

a. The price of the consol can be calculated using the formula for the present value of a perpetuity:

Price = Annual Payment / Interest Rate

In this case, the annual payment is $4 and the interest rate is 3%. Substituting these values into the formula:

Price = $4 / 0.03 ≈ $133.33

Therefore, the price of the consol is approximately $133.33.

b. To calculate the new price of the consol if the interest rate rises to 4%, we use the same formula:

New Price = Annual Payment / New Interest Rate

Substituting the values, we get:

New Price = $4 / 0.04 = $100

The percentage change in the price of the consol can be calculated using the formula:

Percentage Change = (New Price - Old Price) / Old Price * 100

Substituting the values, we have:

Percentage Change in Price = ($100 - $133.33) / $133.33 * 100 ≈ -24.99%

The percentage change in the interest rate is simply the difference between the old and new interest rates:

Percentage Change in Interest Rate = (4% - 3%) = 1%

Comparing the two percentages, we can see that the price of the consol falls by approximately 24.99%, while the interest rate rises by 1%.

c. The holding period return can be calculated using the formula:

Holding Period Return = (Ending Value - Initial Value) / Initial Value * 100

The initial value is the purchase price of the consol, which is $133.33, and the ending value is the price of the consol after one year with an interest rate of 6%. Using the formula for the present value of a perpetuity, we can calculate the ending value:

Ending Value = Annual Payment / Interest Rate = $4 / 0.06 = $66.67

Substituting the values into the holding period return formula:

Holding Period Return = ($66.67 - $133.33) / $133.33 * 100 ≈ -49.99%

Therefore, the holding period return is approximately -49.99%.

Learn more about holding period

brainly.com/question/32568151

#SPJ11

The solution of the initial value problem remains finite as t approaches infinity if the eigenvalues of the system are negative or have negative real parts.

The eigenvalues of a system determine the stability of the solution. Negative eigenvalues indicate that the solution will approach a steady state as time goes on. Positive eigenvalues indicate that the solution will diverge, or grow without bound, as time goes on. If the real parts of the eigenvalues are negative, the solution will approach a steady state, but if the real parts of the eigenvalues are positive, the solution will diverge as t approaches infinity.

In order to check for finite solution for a given initial value problem, one needs to evaluate the eigenvalues of the system, and check their real parts. If they are negative, the solution will remain finite, otherwise the solution will diverge as t approaches infinity.

Learn more about eigenvalues

brainly.com/question/2289152

#SPJ4

Answer:

Remember the property:

a^-1 = (1/a)^1

and:

(a/b)^n = (a^n)/(b^n)

A table for a function like:

\(\left[\begin{array}{ccc}x&f(x)\\&\\&\\&\\&\end{array}\right]\)

Is just completed as:

\(\left[\begin{array}{ccc}x&f(x)\\x_1&f(x_1)\\x_2&f(x_2)\\x_3&f(x_3)\\x_4&f(x_4)\end{array}\right]\)

So, here we have:

y = f(x) = (1/6)^x

To complete the table, we need to find:

f(-1)

and

f(2)

So let's find these two values:

f(-1) = (1/6)^-1 = (6/1)^1 = 6

and the other value is:

f(2) = (1/6)^2 = 1/36

Then the complete table is:

\(\left[\begin{array}{ccc}x&f(x)\\-2&36\\-1&6\\0&1\\1&1/6\\2&1/36\\1&1/216\end{array}\right]\)

a. To find the first 6 terms of the sequence, we substitute the values of n from 1 to 6 into the given formula:

a1 = ((3(1)+2)!) / ((3(1)-1)!) = (5!) / (2!) = 120 / 2 = 60

a2 = ((3(2)+2)!) / ((3(2)-1)!) = (8!) / (5!) = (8 * 7 * 6 * 5!) / (2 * 1 * 5!) = 8 * 7 * 6 = 336

a3 = ((3(3)+2)!) / ((3(3)-1)!) = (11!) / (8!) = (11 * 10 * 9 * 8!) / (8!) = 11 * 10 * 9 = 990

a4 = ((3(4)+2)!) / ((3(4)-1)!) = (14!) / (11!) = (14 * 13 * 12 * 11!) / (11!) = 14 * 13 * 12 = 2184

a5 = ((3(5)+2)!) / ((3(5)-1)!) = (17!) / (14!) = (17 * 16 * 15 * 14!) / (14!) = 17 * 16 * 15 = 4080

a6 = ((3(6)+2)!) / ((3(6)-1)!) = (20!) / (17!) = (20 * 19 * 18 * 17!) / (17!) = 20 * 19 * 18 = 6840

The first 6 terms of the sequence are: 60, 336, 990, 2184, 4080, 6840.

b. To determine if the sequence is bounded, we need to examine if there exists a number M such that |an| ≤ M for all n. In this case, we can see that the terms of the sequence are factorial expressions, which grow very quickly as n increases. Therefore, the sequence is unbounded.

c. Since the sequence is unbounded, it does not exhibit a specific pattern of increase or decrease. Therefore, we cannot classify it as increasing, decreasing, non-increasing, or non-decreasing.

d. The sequence does not converge because it is unbounded.

e. As the sequence does not converge, there is no specific value that the sequence converges to.

To know more about Formula visit-

brainly.com/question/31062578

#SPJ11

A fraction is a numerical quantity that represents a part of a whole or a collection of objects.

Fractions are represented as two numbers separated by a horizontal or diagonal line, with the number below the line representing the total number of equal parts that make up a whole, and the number above the line representing the number of those parts that are being considered.

Examples of real-world fractions include:

Learn more about ratios here:

https://brainly.com/question/13419413

#SPJ

Answer:

1 (y + x)

(x + y)

The Cartesian equation of the line passing through the point F(1, 8) and perpendicular to the line passing through the points F(1, 8) and (-4, 0) is 8y + 5x = 69.

To find the Cartesian equation of the line passing through the points F(1, 8) and (-4, 0) and is perpendicular to the given line, we follow these steps:

1. Calculate the slope of the given line using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) = (1, 8) and (x2, y2) = (-4, 0).

2. The slope of the line perpendicular to the given line is the negative reciprocal of the slope of the given line.

3.  Use the point-slope form of the equation of a line, y - y1 = m1(x - x1), with the point F(1, 8) to find the equation.

4. Rearrange the equation to obtain the Cartesian form, which is in the form Ax + By = C.

Therefore, the Cartesian equation of the line passing through the point F(1, 8) and perpendicular to the line passing through the points F(1, 8) and (-4, 0) is 8y + 5x = 69.

Learn more about Cartesian equation

https://brainly.com/question/32622552

#SPJ11

The Cartesian equation of the line passing through (1, 8) and perpendicular to the line F (1, 8) + (-4, 0), t ∈ R is 8y + 5x = 69.

To find the equation of a line that passes through a given point and is perpendicular to another line, we need to determine the slope of the original line and then use the negative reciprocal of that slope for the perpendicular line.

Let's begin by finding the slope of the line F: (1,8) + (-4,0) using the formula:

\(slope = (y_2 - y_1) / (x_2 - x_1)\)

For the points (-4, 0) and (1, 8):

slope = (8 - 0) / (1 - (-4))

     = 8 / 5

The slope of the line F is 8/5. To find the slope of the perpendicular line, we take the negative reciprocal:

perpendicular slope = -1 / (8/5)

                   = -5/8

Now, we have the slope of the perpendicular line. Since the line passes through the point (1, 8), we can use the point-slope form of the equation:

\(y - y_1 = m(x - x_1)\)

Plugging in the values (x1, y1) = (1, 8) and m = -5/8, we get:

y - 8 = (-5/8)(x - 1)

8(y - 8) = -5(x - 1)

8y - 64 = -5x + 5

8y + 5x = 69

Therefore, the Cartesian equation of the line passing through (1, 8) and perpendicular to the line F (1,8) + (-4,0), t ∈ R is 8y + 5x = 69.

To know more about Cartesian equation, refer here:

https://brainly.com/question/16920021

#SPJ4

Answer:

(n+5) / 4 -7 =___________

Answer:

x = 24

Step-by-step explanation:

if a and b are parallel then

62 and 5x - 2 are same- side interior angles and sum to 180° , that is

5x - 2 + 62 = 180

5x + 60 = 180 ( subtract 60 from both sides )

5x = 120 ( divide both sides by 5 )

x = 24

thus for a to be parallel to b , then x = 24

For the function a(t) = -1/2t + 19, the graph is plotted using the x and y intercepts.

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

To graph the function a(t) = -1/2t + 19, we can follow these steps -

Choose a range of values for t.

Since the function represents the amount of snow remaining after a certain number of hours, we should choose a range that makes sense for the context.

Let's choose t values from 0 to 38, since it's unlikely that there would be much snow left after 38 hours on a warm day.

Substitute each t value into the function to find the corresponding value of a(t).

For example, when t = 0, we have -

a(0) = -1/2(0) + 19 = 19

When t = 10, we have -

a(10) = -1/2(10) + 19 = 14

And so on, for each value of t in our range.

Plot the (t, a(t)) points on a coordinate plane.

For example, the first point is (0, 19), and the second point is (10, 14). Continue plotting points for each value of t.

Draw a smooth curve through the plotted points to represent the function.

The curve should be a straight line with a negative slope, since the function is linear with a negative coefficient on t.

The y-intercept is 19, which means that there is 19 units of snow remaining when t = 0.

The x-intercept can be found by setting a(t) = 0 and solving for t.

0 = -1/2t + 19

1/2t = 19

t = 38

Therefore, the graph for the function is plotted.

To learn more about function from the given link

https://brainly.com/question/2284360

#SPJ1

Answer:

Angle x measures 33.5 degrees.

Step-by-step explanation:

From the given picture, we can note that angle x and the angle of 23 degrees are vertical opposite angles,

Since lines l and m are perperdicular then the angle between then measures 90 degrees, so we have:

\(x+23+x=90\)

By collecting similar terms the equation which represents a relation between these angles is:

\(2x+23=90\)

Now, by subtracting 23 to both sides, we obtain:

\(2x=90-23\\2x=67\)

and by dividing both sides by 2, we get

\(x=\frac{67}{2}\)

\(x=33.5\\\)

Then angle x measures 33.5 degrees.