Find the area of the following figure. Explain how you got your answer.

9514 1404 393

Explanation:

(In order avoid issues with the Brainly censor, we're going to rename point F as point G in this answer. Wherever you see G, you can use F in your own response to this question.)

General Approach

The perpendicular lines tell you these are right triangles. There are a few ways to show right triangles are congruent, one of which is the "HL theorem." It requires you show the hypotenuse and one leg are congruent in the two triangles.

Here, the hypotenuses, DE and AG, are shown as congruent. All that remains is to show one leg is congruent. We have no information about legs BE and CG, but we do have information that will let us show legs AC and DB are congruent.

_____

Proof

1. DE ≅ AG, DC ≅ AB, GC⊥AC, EB⊥DB . . . . given

2. m∠EBD = 90°, m∠GCA = 90° . . . . definition of perpendicular lines

3. CD + CB = DB . . . . segment sum theorem

4. AB + CB = DB . . . . substitution property of equality (CD→AB)

5. AB +CB = AC . . . . segment sum theorem

6. DB = AC . . . . transitive property of equality

7. ΔACG ≅ ΔDBE . . . . HL theorem

Answer:

the slope is -3

Step-by-step explanation:

down 6 and over 2 = -6/2 = -3

Answer:

slope = -3

Step-by-step explanation:

Line pass (1,2) and (3,-4)

slope = difference of y/difference of x

m = (-4 - 2)/(3 - 1) = -6/2 = -3

Answer:

C I think is the answer ok.

Answer:

42

Step-by-step explanation:

The answer is 42 because -3.5 multiplied by -12 is 42

Answer:

-3.5 * -12 = 42

Step-by-step explanation:

Hope this helps

Answer:

18.3824%

Step-by-step explanation:

Sorry, this may be wrong. I am using an old skill, so it may be wrong.

Answer:

D

Step-by-step explanation:

Answer:

A, C, and E

Step-by-step explanation:

just did the assignment on edge 2020 uwu

Answer:

a, e, c or 1, 2, 3

Step-by-step explanation:

just got it right on edge 2021 trust me :)

Answer:

At 116 years and 8 months, the rate would be the same

The solution is not reasonable

Step-by-step explanation:

Given

[tex]m = 220 - a[/tex]

[tex]m = 206 - (0.88 * a)[/tex]

Solving (a): At what age would both rate be equal

To do this, we simply equate both expressions.

[tex]m = m[/tex]

This gives

[tex]220 - a = 206 - (0.88 * a)[/tex]

[tex]220 - a = 206 - 0.88 a[/tex]

Collect Like Terms

[tex]0.88a - a = 206 - 220[/tex]

[tex]-0.12a=-14[/tex]

Divide both sides by -0.12

[tex]\frac{-0.12a}{-0.12} =\frac{-14}{-0.12}[/tex]

[tex]a =\frac{-14}{-0.12}[/tex]

[tex]a =\frac{14}{0.12}[/tex]

Multiply fraction by 100/100

[tex]a = \frac{14*100}{0.12*100}[/tex]

[tex]a = \frac{1400}{12}[/tex]

[tex]a = 116\frac{8}{12}[/tex]

This implies at 116 years and 8 months, the rate would be the same

Is the solution reasonable?

No, it is not reasonable, considering the life expectancy of women to be around 70-72 years old.

116 years old is way too bigger than the life expectancy.

Answer:

The slope is 3, and the y-intercept is -1/2

Answer:

The relation is 1 digit is being added after every number in the pattern.

So, the 7th term can be found like this.

9+4=13   -4th

13+5=18   -5th

18+6=24    -6th

24+7=31      -7th

Answer:

Option A: x+y=136 and x-y=34 is the correct answer.

Step-by-step explanation:

Let,

x and y be the two numbers.

According to given statement,

The sum of two numbers is 136.

x + y = 136     Eqn 1

The difference of two numbers is 34.

x - y = 34      Eqn 2

x+y=136 and x-y=34 is the system of equations that could be used to solve and determine the numbers.

Hence,

Option A: x+y=136 and x-y=34 is the correct answer.

Answer:

Good for him also there is no question

Step-by-step explanation:

Answer: whats the car prices that was in the news paper

Step-by-step explanation:

Answer:

C,D, and E

Step-by-step explanation:

Markup means to raise the price. Multiplying by anything grater than 1 is a markup and since C,D, and E are all multiplying the price of W by greater than one they are all marking up.

Answer:

150(1.28^t). ^ sign is to the power of

Answer:

m∠B = 98°

Step-by-step explanation:

180° - 143° = 37°

61° + 37° = 98°

m∠B = 98°

Answer:

D

Step-by-step explanation:

Answer:

10.33333 or 31/3 or 10 and 1/3 =x

Step-by-step explanation:

-2=3x-23/4

*4    *4

-8=3x-23

+23   +23

31=3x

/3   /3

10.33333 or 31/3 or 10 and 1/3 =x

Answer: The product of x and 5 is 5x

Answer:

209.1 cm2

Step-by-step explanation:

the area of the circle around the rectangle is 113.1 cm2 and the area of the rectangle is 12x8=96cm and 113.1+96=209.1

Answer:

The angle is 30.  It's complement is 60.

Step-by-step explanation:

Complementary angles add up to 90.

x + (5x-90) = 90

6x = 180

x = 30

The measure of the angle is 60 degrees.

Let's denote the angle as "x." The complement of angle x would be 90 degrees minus x.

According to the given information, the angle is 90 less than 5 times its own complement. Mathematically, we can express this as:

x = 5(90 - x) - 90

Now, let's solve this equation to find the value of x:

x = 450 - 5x - 90

x + 5x = 450 - 90

6x = 360

x = 360/6

x = 60

That is the angle.

Learn more about angles at:

https://brainly.com/question/25716982

#SPJ2

Answer:

7644

Step-by-step explanation:

Hope this helps!

Answer:

72%

Step-by-step explanation:

Answer:

seventy two percent

Answer:

[tex]\displaystyle A_{\text{Total}}\approx45.0861\approx45.1[/tex]

Step-by-step explanation:

We can use the trigonometric formula for the area of a triangle:

[tex]\displaystyle A=\frac{1}{2}ab\sin(C)[/tex]

Where a and b are the side lengths, and C is the angle between the two side lengths.

As demonstrated by the line, ABCD is the sum of the areas of two triangles: a right triangle ABD and a scalene triangle CDB.

We will determine the area of each triangle individually and then sum their values.

Right Triangle ABD:

We can use the above area formula if we know the angle between two sides.

Looking at our triangle, we know that ∠ADB is 55 DB is 10.

So, if we can find AD, we can apply the formula.

Notice that AD is the adjacent side to ∠ADB. Also, DB is the hypotenuse.

Since this is a right triangle, we can utilize the trig ratios.

In this case, we will use cosine. Remember that cosine is the ratio of the adjacent side to the hypotenuse.

Therefore:

[tex]\displaystyle \cos(55)=\frac{AD}{10}[/tex]

Solve for AD:

[tex]AD=10\cos(55)[/tex]

Now, we can use the formula. We have:

[tex]\displaystyle A=\frac{1}{2}ab\sin(C)[/tex]

Substituting AD for a, 10 for b, and 55 for C, we get:

[tex]\displaystyle A=\frac{1}{2}(10\cos(55))(10)\sin(55)[/tex]

Simplify. Therefore, the area of the right triangle is:

[tex]A=50\cos(55)\sin(55)[/tex]

We will not evaluate this, as we do not want inaccuracies in our final answer.

Scalene Triangle CDB:

We will use the same tactic as above.

We see that if we can determine CD, we can use our area formula.

First, we can determine ∠C. Since the interior angles sum to 180 in a triangle, this means that:

[tex]\begin{aligned}m \angle C+44+38&=180 \\m\angle C+82&=180 \\ m\angle C&=98\end{aligned}[/tex]

Notice that we know the angle opposite to CD.

And, ∠C is opposite to BD, which measures 10.

Therefore, we can use the Law of Sines to determine CD:

[tex]\displaystyle \frac{\sin(A)}{a}=\frac{\sin(B)}{b}[/tex]

Where A and B are the angles opposite to its respective sides.

So, we can substitute 98 for A, 10 for a, 38 for B, and CD for b. Therefore:

[tex]\displaystyle \frac{\sin(98)}{10}=\frac{\sin(38)}{CD}[/tex]

Solve for CD. Cross-multiply:

[tex]CD\sin(98)=10\sin(38)[/tex]

Divide both sides by sin(98). Hence:

[tex]\displaystyle CD=\frac{10\sin(38)}{\sin(98)}[/tex]

Therefore, we can now use our area formula:

[tex]\displaystyle A=\frac{1}{2}ab\sin(C)[/tex]

We will substitute 10 for a, CD for b, and 44 for C. Hence:

[tex]\displaystyle A=\frac{1}{2}(10)(\frac{10\sin(38)}{\sin(98)})\sin(44)[/tex]

Simplify. So, the area of the scalene triangle is:

[tex]\displaystyle A=\frac{50\sin(38)\sin(44)}{\sin(98)}[/tex]

Therefore, our total area will be given by:

[tex]\displaystyle A_{\text{Total}}=50\cos(55)\sin(55)+\frac{50\sin(38)\sin(44)}{\sin(98)}[/tex]

Approximate. Use a calculator. Thus:

[tex]\displaystyle A_{\text{Total}}\approx45.0861\approx45.1[/tex]