Tom’s dad is putting crown molding around the top of all of the walls in Tom’s bedroom.
The dimensions of his bedroom are shown.
11 3/4 & 15 3/4
Each foot of crown molding costs $0.85. What is the total cost of the crown molding?
Enter your answer in the box.

Answer:

a. congruent triangle

b. similar triangle

c. congruent triangle

Step-by-step explanation:

a.

In Δ ABD and ΔCBD

BD=BD reflexive property

∡ABD=∡CBD given

AB=BC given

Δ ABD ≅ ΔCBD by SAS (Side-Angle-Side) axiom.

b.

In ΔABE and ΔDCE

∡ABE=∡ DCE being alternative angle

∡BAE=∡CDE being alternative angle

∡AEB=∡CED

Δ ABE  \(\bold{\sim}\)  ΔCBD by AAA (Angle-Angle-Angle) axiom.

Since, all the corresponding angle are equal. So, it is similar triangle not congruent.

C.

In ΔABC and ΔDEF

∡F=∡C=62° given

∡D=∡B =45° given
FE=BC given

Δ ABC ≅ ΔDEF by Angle-Angle-Side axiom.

Answer:

a)  SAS ≅
    ΔABD ≅ ΔCBD

b)  AA ~
    ΔABE ~ ΔDCE

c)  AAS ≅
    ΔABC ≅ ΔDEF

Step-by-step explanation:

If two sides and the included angle in one triangle are congruent to two sides and the included angle in another triangle, the triangles are congruent.

From inspection of the given diagram:

Therefore, as two sides and the included angle of both triangles are congruent, the triangles are congruent by SAS congruence theorem.

\(\hrulefill\)

If any two angles of a triangle are equal to any two angles of another triangle, then the two triangles are similar to each other.

As line segment AB is parallel to line segment CD:

Therefore, as the corresponding interior angles of the triangles are congruent, according to the Angle-Angle Similarity Theorem, the two triangles are similar to each other:

Note: We cannot say the triangles are congruent, since there is no indication that any of the sides are equal in length on the given diagram.

\(\hrulefill\)

If any two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.

The interior angles of a triangle sum to 180°.

Therefore, angle B of triangle ABC is 45°, and angle D of triangle DEF is 73°. So the interior angles of triangles ABC and DEF are the congruent, which means the triangles are similar.

If the triangles are congruent, we would expect one of their corresponding sides to be equal in length. So AB = DE, or BC = EF, or AC = DF.

From inspection of the triangles, we can see that sides BC and EF are both 13 units in length. Therefore, BC = EF.

Therefore, as two angles and the non-included side of both triangles are congruent, the triangles are congruent by AAS congruence theorem.

The equation in point-slope form of the line is:

O y + 2 = (2/3)(x - 5)

Here, we have,

The equation in point-slope form of a line is given by:

y - y₁ = m(x - x₁)

where (x₁, y₁) represents a point on the line, and m represents the slope.

Given that the slope is 2/3

and the line goes through the point (5, -2),

m = 2/3

and, (x₁, y₁) = (5,-2)

we can substitute these values into the equation:

y - (-2) = (2/3)(x - 5)

Simplifying:

y + 2 = (2/3)(x - 5)

Therefore, the equation in point-slope form of the line is:

O y + 2 = (2/3)(x - 5)

To learn more on Equation 0f Straight-Line click:

brainly.com/question/11116168

#SPJ5

Answer:$4669

Step-by-step explanation:

175x19=3325+5(4)=3345

1300+6(4)=1324

The value of y is 18

Similar triangles have the same corresponding angle measures and proportional side lengths. The angles of the two triangle must be equal and it not necessary they have equal sides.

Therefore the corresponding angles of similar triangles are congruent and the ratio of corresponding sides of similar triangles are equal.

Therefore;

14/21 = 12/y

14y = 21 × 12

14y = 252

divide both sides by 14

y = 252/14

y = 18

Therefore the value of y is 18.

learn more about similar triangles from

https://brainly.com/question/14285697

#SPJ1

========================================================

Explanation:

The ultimate goal is to find the value for lowercase c, or find the length of side c. So we'll use the portion sin(C)/c as part of the law of sines.

We don't know the value of lowercase 'a', so we'll ignore the sin(A)/a portion.

This leaves sin(B)/b

We see that one side is 2 cm long, so this means b = 2. The angle opposite this is 105 degrees, so B = 105.

The angle opposite side c is 15 degrees, so C = 15.

The lowercase letters represent side lengths, while the uppercase letters are angles.

--------------------------

We have enough to apply the law of sines to solve for side c.

sin(B)/b = sin(C)/c

sin(105)/2 = sin(15)/c

c*sin(105) = 2*sin(15) ............. cross multiply

c = 2*sin(15)/sin(105) .............. dividing both sides by sin(105)

c = 0.53589838486224

c = 0.5

Side c is roughly 0.5 cm long.

Make sure your calculator is in degree mode.

9514 1404 393

Answer:

  0.5 cm

Step-by-step explanation:

The Law of Sines tells you ...

  c/sin(C) = b/sin(B)

  c = b·sin(C)/sin(B)

  c = (2 cm)sin(15°)/sin(105°) ≈ (2 cm)(0.2588/0.9659) ≈ 0.5359 cm

  c ≈ 0.5 cm . . . . rounded to tenths

Answer:

D, g(x) = 1/4 x^2

Step-by-step explanation:

You can try plugging in the x and y values into each equation. The answer to this would be D, where if you plug in 2 as the x value, you get 1/4 * 4 which equals 1. This also makes sense because 2x would have a narrower curve while 1/2x would have a wider curve.

Answer:

X is the hypotenuse and using 60°

Cos theta =adjacent/ hypotenuse

where 5 is your adjacent cos 60° is equals to 5/X

X= 5/Cos 60° = 5/0.5 = 10... B

The value of x will be;

⇒ x = 5

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The triangle is shown in figure.

The perpendicular side = 5

The hypotenuse side = x

Now,

Since, We know that;

⇒ sin θ = Perpendicular / Hypotenuse

Put θ = 90°, we get;

⇒ sin 90° = 5 / x

⇒ 1 = 5 / x

⇒ x = 5

Thus, The value of x = 5

Learn more about the triangle visit:

brainly.com/question/17335144

#SPJ2

To obatin the graph of y=(x-8)^2 shifts the graph of y=x^2 8 units right

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

y=(x-8)^2

y = x^2

In the above equations, we can see that

The value of 8 is subtracted from x in y = x^2 to get y = (x - 8)^2

This represents a right translation by 8 units

Hence, the translation is 8 units to the right

Read more about transformation at

https://brainly.com/question/27224272

#SPJ1

Answer: Obtuse angle

Step-by-step explanation:

It's an obtuse angle because it is greater than 90 degrees.

Answer:

Obtuse

Step-by-step explanation:

Obtuse angles has degrees larger than 90, but less than 180. 180 degrees is a straight line, but over 180 degrees is a reflex

Answer:

9 squirrels and 36 birds

Step-by-step explanation:

4x+x=45

5x=45

x=9

4*9=36

The government agency as a monopolist will produce and sell internet connections up to the point where the marginal cost is 1/2. The price will be set at 1, given the perfectly elastic demand function.

In the scenario where a government agency has a monopoly in the provision of internet connections and the inverse demand function is given by p = 1, we can analyze the market equilibrium and the implications for pricing and quantity.

The inverse demand function, p = 1, implies that the market demand for internet connections is perfectly elastic, meaning consumers are willing to purchase any quantity of internet connections at a price of 1. As a monopolist, the government agency has control over the supply of internet connections and can set the price to maximize its profits.

To determine the optimal pricing and quantity, the monopolist needs to consider the marginal cost of providing internet connections. In this case, the marginal cost is given as 1/2. The monopolist will aim to maximize its profits by equating marginal cost with marginal revenue.

Since the inverse demand function is p = 1, the revenue received by the monopolist for each unit sold is also 1. Therefore, the marginal revenue is also 1. The monopolist will produce up to the point where marginal cost equals marginal revenue, which in this case is 1/2.

As a result, the monopolist will produce and sell internet connections up to the quantity where the marginal cost is 1/2. The monopolist will set the price at 1 since consumers are willing to pay that price.

For more such question on monopolist. visit :

https://brainly.com/question/28336090

#SPJ8

Answer: It is a difference of two squares, and it factors to (3x-7)(3x+7)

=============================================================

Explanation:

We can write the 9x^2 as (3x)^2 since

(3x)^2 = (3x)*(3x) = (3*3)*(x*x) = 9x^2

The 49 can be written as 7^2 because 7^2 = 7*7 = 49.

This means 9x^2 - 49 is the same as (3x)^2 - 7^2. We have a difference of two squares.

The difference of squares factoring rule is

a^2 - b^2 = (a-b)(a+b)

which we have a = 3x and b = 7 in this case

So,

a^2 - b^2 = (a-b)(a+b)

(3x)^2 - 7^2 = (3x-7)(3x+7)

9x^2 - 49 = (3x-7)(3x+7)

Side note: This is the same as (3x+7)(3x-7). We can multiply two numbers in any order.

The approximate difference in the circumferences of the two circles is: C. 61 cm.

Mathematically, the circumference of a circle can be calculated by using this mathematical expression:

C = 2πr or C = πD

Where:

Substituting the given parameters into the circumference of a circle formula, the circumference of the small circle is;

Circumference of circle, C = πD

Circumference of circle, C = 3.14 × 4.5

Circumference of circle, C = 14.13 cm.

For the larger circle, we have:

Circumference of circle, C = 3.14 × 24

Circumference of circle, C = 75.36 cm.

Difference = 75.36 cm - 14.13 cm.

Difference = 61.23 ≈ 61 cm.

Read more on a circle here: brainly.com/question/6615211

#SPJ1

Answer:

Step-by-step explanation:

Answer:

b cumulative frequency

Step-by-step explanation:

Answer: The function that is represented by the equation y = negative 10 x + 6 has a steeper slope and a greater y-intercept.

Step-by-step explanation: I took the unit test on edge hoped this helped <3

We want to compare the slopes and y-intercepts of two given linear functions.

The comparations that we can make are:

The general linear function in the slope-intercept is:

y = a*x + b

where a is the slope and b is the y-intercept.

Here, the two given lines are:

y = -10*x + 6

(here we can see that the slope is -10 and the y-intercept is 6).

The other line is:

y - 36 = 8*(x - 4)

Writing this in the slope-intercept form we get:

y = 8*x - 8*4 + 36

y = 8*x - 32 + 36

y = 8*x + 4

Then the slope is 8 and the y-intercept is 4.

Then the comparations that we can make are:

If you want to learn more, you can read:

https://brainly.com/question/21835898

Answer: B. Angle ABC is an obtuse angle

Step-by-step explanation:

Answer:

2263.74

Step-by-step explanation:

Answer:

60 *1 2 3 4 do multiply and write the all sum needed

i think i helped you

thank you

Using the binomial distribution, the expected value of the number of points Juan makes when he shoots two free-throw shots is 1.07.

For each shot, there are only two possible outcomes, either Juan makes it, or he misses it. The probability of making a shot is independent of any other shot, hence, the binomial distribution is used to solve this question.

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability, and the expected value is:

\(E(X) = np\)

In this problem:

Then:

\(E(X) = np = 2(0.535) = 1.07\)

A similar problem is given at https://brainly.com/question/24261244

Option D is the correct answer.

From the graph, we can conclude that,

1. The two lines are continuous lines and not broken lines. So, the inequality sign should be either ≤ or ≥.

2. The points on the lines of the shaded region are also included in the solution.

The only option that matches with the above conditions is option D. So, option D is the correct answer.

Let us verify it.

Now, let us consider a point that is inside the shaded region and also on any one line.

Let us take (0, 2).

Plug in 0 for x and 2 for y in each of the options and check which inequality holds true.

Considering the inequalities,

y ≥ 3x - 2

x + 2y ≤ 4

Solving we get,

2 ≥ 3(0) - 2

2 ≥ -2

x + 2y ≤ 4

0 + 2(2) ≤ 4

4 ≤ 4

Here, both inequalities are correct.

So, option D is the correct answer.

Learn more about inequality click

https://brainly.com/question/20383699

#SPJ1

The complete question is =

Which system of linear inequalities is graphed?

A. y < 3x-2

x + 2y ≥ 4

B. y < 3x - 2

x + 2y > 4

C. y > 3x - 2

x + 2y < 4

D. y ≥ 3x - 2

x + 2y ≤ 4

Exponential growth is a type of growth that occurs when the rate of increase is proportional to the current amount.

To learn more about logarithmic evaluation refer to:

https://brainly.com/question/29168400

#SPJ1

The linear rule for the sequence is f(n) = 7/20 + 3/20(n - 1)

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

35/100,5/10,65/100

In the above sequence, we can see that 15/100 is added to the previous term to get the new term

This means that

First term, a = 35/100

Common difference, d = 15/100

The nth term is then represented as

f(n) = a + (n - 1) * d

Substitute the known values in the above equation, so, we have the following representation

f(n) = 35/100 + 15/100(n - 1)

So, we have

f(n) = 7/20 + 3/20(n - 1)

Hence, the explicit rule is f(n) = 7/20 + 3/20(n - 1)

Read more about sequence at

brainly.com/question/30499691

#SPJ1

Answer:5x + 3

Step-by-step explanation:

5( y + 2/5) = -13

Distribute the 5 by multiplying the 5 by each term inside the set of parentheses:

5y + 2 = -13

Subtract 2 from both sides:

5y = -15

Divide both sides by 5:

Y = 3

The answer is y = 3

Answer:

A. 64

Step-by-step explanation:

alright so first we gotta look at that 148 its on a line so the angle on the other side would be

32 because

180-148=32

now we have 2 sides of a triangle and all triangles = 180 so all we have to do is add then subtract

84+32= 116

180-116 = 64

Answer: A. 64

Step-by-step explanation: Sorry if I'm wrong, I also researched it as well and had this question before.

Answer:

P(B) = 0.20

Step-by-step explanation:

If A and B are events with P(A)=0.5, P(A OR B)=0.54, and P(A AND B)=0.16, find P(B).

Provide your answer below:

We are given two events A and B and the formula for the probability of two events is given as:

P ( A ∪ B) = P(A ) + P( B ) - P( A∩ B)

Where:

P(A)=0.5

P ( A ∪ B) = P(A OR B)=0.54

P( A∩ B) = P(A AND B)=0.16

P(B) = ??

Hence, we have:

0.54 = 0.5 + P(B) - 0.16

Making P(B) subject of the formula

P(B) = 0.54 - 0.5 + 0.16

P(B) = 0.20

The probability that Angela gets to go to the meeting is 2/5 or 0.4.

What is probability?

There are a total of 5 people in the club, and they need to pick 2 people to go to the meeting. The number of ways to pick 2 people out of 5 is given by the binomial coefficient:

C(5,2) = 5! / (2! (5-2)!) = 10

This means there are 10 equally likely outcomes, which can be represented by the following probability model:

Outcome            Angela goes to meeting?                 Probability

A,B                                    Yes                                              1/10

A,C                                    Yes                                              1/10

A,D                                    Yes                                              1/10

A,E                                     Yes                                              1/10

B,C                                      No                                              1/10

B,D                                      No                                              1/10

B,E                                       No                                              1/10

C,D                                      No                                               1/10

C,E                                       No                                               1/10

D,E                                       No                                               1/10

The probability that Angela gets to go to the meeting is the sum of the probabilities of the outcomes where Angela goes to the meeting:

P(Angela goes to meeting) = P(A,B) + P(A,C) + P(A,D) + P(A,E)

= 1/10 + 1/10 + 1/10 + 1/10

= 4/10

= 2/5

Therefore, the probability that Angela gets to go to the meeting is 2/5 or 0.4.

To know more about the probability, visit:

https://brainly.com/question/11234923

#SPJ1

Answer:c, the answer is c

Step-by-step explanation:

Answer: 121°

The first to solving this problem is to first find the missing angle in the triangle.

Three angles in a triangle have to add up to 180°

We are given the angles 87° and 34°, so now let's add the two given angles

87° + 34° = 121°

Now let's take 180° and subtract it from 121° to get the missing angle in the triangle

180°-121°=59°

Now we know the missing angle is 59°, we can notice that the angle 59° is also on a straight line and two angles on a straight line must add up to 180°

So let's now subtract 180° from 59°

180°-59°=121°

Answer:

  A)  121°

Step-by-step explanation:

Angle z is an exterior angle of the triangle. Relative to that exterior angle, the two marked angles are referred to as "remote interior angles." The relation between them is ...

  an exterior angle is equal to the sum of the remote interior angles.

In this case, that means ...

  z° = 34° +87° = 121°

b) P(S) = 0.356  , c) P(S') = 0.644  ,d) P(S | R)= 0.078 e) P(R' | S')  = 0.965

is the probability of all cases according to question conditions

what is probability ?

Probability is a measures the likelihood of event occurring. It is expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain.

what is event occurring ?

An event is any outcome or result that can occur in a given situation. It can be a simple outcome, such as flipping a coin and getting heads, or a more complex outcome

In the given question,

a. Here is the tree diagram for the scenario:

        Rain (0.3)

        /      \

    S (0.12)   S' (0.88)

   /     \

No Rain (0.7)  S (0.53)

         \

          S' (0.47)

b. We can use the Law of Total Probability to calculate P(S):

P(S) = P(R) * P(S | R) + P(R') * P(S | R')

    = 0.3 * 0.12 + 0.7 * 0.53

    = 0.356

Therefore, there is a 35.6% chance that Sarina will go to the store on Saturday.

c. P(S') represents the probability that Sarina will not go to the store on Saturday. We can use the complement rule to calculate it:

P(S') = 1 - P(S)

    = 1 - 0.356

    = 0.644

Therefore, there is a 64.4% chance that Sarina will not go to the store on Saturday.

d. P(S | R) represents the probability that Sarina will go to the store on Saturday given that it rains. We can use Bayes' Theorem to calculate it:

P(S | R) = P(R | S) * P(S) / P(R)

        = P(S | R) * P(R) / (P(R | S) * P(S) + P(R | S') * P(S'))

        = 0.12 * 0.3 / (0.12 * 0.3 + 0.53 * 0.7)

        = 0.078

Therefore, there is a 7.8% chance that Sarina will go to the store on Saturday given that it rains.

e. P(R' | S') represents the probability that it doesn't rain given that Sarina doesn't go to the store on Saturday. We can use Bayes' Theorem to calculate it:

P(R' | S') = P(S' | R') * P(R') / P(S')

          = P(S' | R') * P(R') / (P(S | R) * P(R) + P(S' | R') * P(R'))

          = 0.47 * 0.7 / (0.078 * 0.3 + 0.47 * 0.7)

          = 0.965

Therefore, there is a 96.5% chance that it doesn't rain given that Sarina doesn't go to the store on Saturday.

To know more about probability, visit:

https://brainly.com/question/30034780

#SPJ1