(∗− 3x )(∗ +3x) = 16y^2–9x^2<br> Find the * please

For the parallelogram ABCD the extensions of the angle bisectors AG and BH intersect at point P. Find the area of the parallelog

natita [175]

Answer:

The area of a parallelogram is 360 in.²

Step-by-step explanation:

Where DG = GH

GP = 12 in.

AB = 39 in.

∠DAB + ∠ABC = 180° (Adjacent angles of a parallelogram)

Whereby ∠DAB is bisected by AG and ∠ABC is bisected by BH

Therefore, ∠GAB + ∠HBA = 90°

Hence, ∠BPA = 90° (Sum of interior angles of a triangle)

$cos(\angle GAB) = \dfrac{AP}{AB} = \dfrac{AP}{39} = \dfrac{GP}{GH} =\dfrac{12}{GH}$

We note that ∠AGD = ∠GAB (Alternate angles of parallel lines)

∴ ∠AGD = ∠AGD since ∠AGD = ∠GAB (Bisected angle)

Hence AD = DG (Side length of isosceles triangle)

The bisector of ∠ADG is parallel to BH and will bisect AG at point Q

Hence ΔDAQ ≅ ΔDGQ ≅ ΔGPH and AQ = QG = GP

Hence, AP = 3 × GP = 3 × 12 = 36

$cos(\angle GAB) = \dfrac{AP}{AB} = \dfrac{36}{39}$

$\angle GAB = cos^{-1} \left (\dfrac{36}{39} \right )$

∠GAB = 22.62°

$cos(\angle GAB) = \dfrac{36}{39} = \dfrac{12}{GH}$

$GH = \dfrac{39}{36} \times {12}$

GH = 13 in.

∴ AD 13 in.

BP = 39 × sin(22.62°) = 15 in.

GH = √(GP² + HP²)

∠DAB = 2 × 22.62° = 45.24°

The height of the parallelogram = AD × sin(∠DAB) = 13 × sin(45.24°)

The height of the parallelogram = 120/13 = 9.23 in.

The area of a parallelogram = Base × Height = (120/13) × 39 = 360 in.²

7 0

3 years ago

Read 2 more answers

Only the function represented by graph has an inverse function.

Arlecino [84]

Answer:

Only the function represented by graph 2 has an inverse function

Step-by-step explanation:

* Lets explain the inverse of the function

- The Function is a relation between x-coordinates and the y-

coordinates of the order pairs under the condition every

x-coordinate has only one y-coordinate

- Ex: R = {(2 , 3) , (1 , 5) , (-2 , -3)} is a function because every x-

coordinate has only one y-coordinate and R = {(2 , 3) , (-1 , 4) ,

(2 , 5)} not a function because the x-coordinate 2 has two y-

coordinates 3 and 5

- We use the vertical line to test the graph is function or not, if

the vertical line intersects the graph in one point then the

graph is function if intersects it in more than one point then the

graph is not function

- We have two types of function one-to-one function and

many-to-one function

# one-to-one function means every x-coordinate has only 1 y-coordinate

# many-to-one function means some x-coordinates have only 1

y-coordinate

- We find the inverse function by switching x and y, then one-to-

one function has inverse but many-to-one has not inverse

because when we switched x and y it will be one-to-many

means one x-coordinate has many y-coordinates and this is not

a function

- We use the horizontal line to test the graph of the function has

inverse or not, if the horizontal line intersects the graph in one

point then the function of the graph has inverse if it intersects

the graph in more than one point ,then the function of the

graph has no inverse

* Now lets test all the graphs by using the horizontal line

# graph 1

∵ The horizontal line cuts the graph in more than 1 point

∴ The function of graph 1 has no inverse

# graph 2

∵ The horizontal line cuts the graph in just 1 point

∴ The function of graph 2 has inverse

# graph 3

∵ The horizontal line cuts the graph in more than 1 point

∴ The function of graph 3 has no inverse

# graph 4

∵ The horizontal line cuts the graph in more than 1 point

∴ The function of graph 4 has no inverse

* Only the function represented by graph 2 has an inverse function

4 0

3 years ago

Math is hard and suckssssssssssssssss

inessss [21]

Answer:

X=7

Hope it was helpful

Step-by-step explanation:

Good luck ^___^

4 0

2 years ago

Will give brainliest to person who answers first!! And 20 points!!!

UkoKoshka [18]

Concept artist tools programmer their you go <span />

3 0

3 years ago

In measuring the center of the data from a skewed distribution, the median would be preferred over the mean for most purposes be

icang [17]

<span>The median would be preferred over the mean in such scenarios because the median will lessen the impact of the outliers that fall within the "tail" of the skew. Therefore, if a curve is normally distributed, that is to say that data is normally distributed, there will be two tails, each with approximately equal proportions of outliers. Outliers in this case being more extreme numbers, and are based on your determination depending on how you are using the data. If data is skewed there is one tail, and therefore it may be an inaccurate measure of central tendency if you use the mean of the numbers. Thinking of this visually. In positively skewed data where there is a "tail" towards the right and a "peak" towards the left, the median will be placed more in the "peak", whereas the mean will be placed more towards the "tail", making it a poorer measure of central tendency, or the center of the data.</span>

5 0

3 years ago

(∗− 3x )(∗ +3x) = 16y^2–9x^2 Find the * please