For the parallelogram ABCD the extensions of the angle bisectors AG and BH intersect at point P. Find the area of the parallelogram, if DG = GH, AB = 39 in, GP = 12 in.

For The Parallelogram ABCD The Extensions Of The Angle Bisectors AG And BH Intersect At Point P. Find

Answers

Answer 1

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)

[tex]cos(\angle GAB) = \dfrac{AP}{AB} = \dfrac{AP}{39} = \dfrac{GP}{GH} =\dfrac{12}{GH}[/tex]

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

[tex]cos(\angle GAB) = \dfrac{AP}{AB} = \dfrac{36}{39}[/tex]

[tex]\angle GAB = cos^{-1} \left (\dfrac{36}{39} \right )[/tex]

∠GAB = 22.62°

[tex]cos(\angle GAB) = \dfrac{36}{39} = \dfrac{12}{GH}[/tex]

[tex]GH = \dfrac{39}{36} \times {12}[/tex]

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

For The Parallelogram ABCD The Extensions Of The Angle Bisectors AG And BH Intersect At Point P. Find
Answer 2

Answer:

360 in2

Step-by-step explanation:

The figure ABCD is a parallelogram, so the side AB is parallel to the side DC, and that means the angle mBAG is equal the angle mHGP.

The angles mHGP and mAGD are vertically opposite angles, so mHGP = mAGD.

The angle mDAG is equal the angle mBAG, so mDAG = mBAG = mHGP = mAGD

The angles mDAG and mAGD are equal, so the triangle DAG is isosceles, that means the side DG is equal the side DA.

In the same way, we can find that the angle mCBH is equal the angle mBHC, so triangle BCH is isosceles, meaning that side BC (which is equal side AD) is equal side CH, so we have that:

DG + GH + HC = AB = 39

GH + GH + GH = 39

GH = 13

in the parallelogram we have the property:

mDAB + mABC = 180°

We have that mGAB = mDAB/2 and mABH = mABC/2, so using this information for the sum of internal angles of triangle APB, we have:

mGAB + mABH + mBPA = 180

mDAB/2 + mABC/2 + mBPA = 180

(180/2) + mBPA = 180

mBPA = 90°

If the triangle APB is a right triangle, we can find the cosine of the angle mHGP:

cos(mHGP) = GP / GH = 12 / 13

Then, we can find the sine of mHGP using:

sin(mHGP)^2 + cos(mHGP)^2 = 1

sin(mHGP)^2 + 144/169 = 1

sin(mHGP)^2 = 25/169

sin(mHGP) = 5/13

If we draw the height of the triangle GPH relative to the side GH, we have:

sin(mHGP) = height / GP

5 / 13 = height / 12

height = 60/13

The triangles GPH and APB are similar (using the case angle-angle), so we can use this relation to find the height 'h2' of the triangle APB:

height / (h2+height) = GH / AB

(60/13) / (h2 + (60/13)) = 13/39 = 1/3

180 / 13 = h2 + (60/13)

h2 = 120/13

Then the area of the parallelogram is:

Area = AB * h2 = 39 * 120/13 = 360 in2


Related Questions

Which strategy may enable you to earn an associate's degree while you are
still in high school?
O A. Taking dual enrollment courses
B. Taking AP courses
C. Enrolling in extracurricular activities
O D. Passing the ACT exam
Help ‼️

Answers

A. dual enrollment courses are college courses you take while in high school, to help earn credits and possibly earn an associates degree.
ap courses don’t give you credits and neither do extracurriculars or the act

The glee club has $90 to spend on pens and pencils. Each pen costs $0.75 and each pencil costs $0.15. Let x represent the number of pens, and let y represent the number of pencils. Part A Select the equation that describes the number of club pens and pencils that the glee club can buy. A. 0.15x + 0.75y = 90 B. 0.75x + 0.15y = 90 C. 0.90(x + y) = 90 Part B What is the greatest number of each type of writing tool that the club can buy? the greatest number of pens =? the greatest number of pencils =?

Answers

Answer:

Part A -  0.90(x + y) = 90 Part B - Pencils

What is the area of the garden in Plan A? (Type the numeric answer only

Answers

Answer:
9•12=108
108 ft2
The answer is 108 ft

What is the ratio of x to y? (Write it in simplest form)

Answers

Answer:

There is no explanation so I guess 1 to 1?

Step-by-step explanation:

Y = X if that is what the question asks

Maria, an experienced shipping clerk, can fill a certain order in 13 hours. Felipe, a new clerk, needs 15 hours to do
the same job. Working together, how long will it take them to fill the order?

Answers

Answer:

≈ 7 hours

Step-by-step explanation:

Maria can do full job in 13 hours,

she can do 1/13 part of job in one hour

Felipe can do full job in 15 hours,

he can do 1/15 part of job in 1 hour

Together they can do:

1/13 + 1/15= 28/13*15= 28/195 of job in 1 hour

to complete full job they need:

1 ÷ 28/195= 195/28 ≈ 7 hours

Answer:

7 hr 10 min 12 seconds

Step-by-step explanation:

Maria, an experienced shipping clerk, can fill a certain order in 13 hours. Felipe, a new clerk, needs 16 hours to do the same job. Working together, how long will it take them to fill the order?

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

Maria rate = 1/13 job/hr

-----

Felipe rate = 1/16 job/hr

----

Together rate = 1/x job/hr

-------

Equation:

rate + rate = Together rate

1/13 + 1/16 = 1/x

----

16x + 13x = 13*16

------

29x = 13*16

ASAP, pls I need help with these questions ​

Answers

Answer:

a) 2/5 x 900 = 360 hectares

b) 3/5th

c) 3/5 x 900 = 540

540 - 360 = 180

Farmer Richards needs to bring another 180 hectares under cultivation.

help again please thank you

Answers

Answer:

1) False

2) True

3) False

4) True

5) True

6) False

7) True

8) True

Answer:

The electron configuration of an element describes how electrons are distributed in its atomic orbitals. Electron configurations of atoms follow a standard notation in which all electron-containing atomic subshells (with the number of electrons they hold written in superscript) are placed in a sequence. For example, the electron configuration of sodium is 1s22s22p63s1.

Step-by-step explanation:

Find the value of x if A, B, and C are collinear points and B is between A and C. AB=2x,BC=x−2,AC=28

Answers

Answer:

x = 10

Step-by-step explanation:

Data

AB=2xBC=x−2AC=28

Given that A, B, and C are collinear points and B is between A and C, then the addition of the measure of segments AB and BC must be equal to the measure of segment AC, that is:

AB + BC = AC

Replacing with data:

2x + (x - 2) = 28

3x - 2 = 28

3x = 28 + 2

x = 30/3

x = 10

does 4 1/2 times 2 3/4 equal 11 11/48?

Answers

Answer:No

4 1/2 times 2 3/4 does not equals to 11 11/48.

It actually equals to 12 3/8

hope it helps

Good luck on your assignment

Answer:

No,it's wrong

The correct answer is

[tex] = 12 \frac{2}{8} \\ = 12 \frac{1}{4} \\ [/tex]

Step-by-step explanation:

[tex]4 \frac{1}{2} \times 2 \frac{3}{4} \\ \frac{9}{2} \times \frac{11}{4} \\ = \frac{99}{8} \\ = 12 \frac{2}{8} \\ = 12 \frac{1}{4} [/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Select the correct answer.
This pyramid has the same base as the prism, and its height is three times the height of the prism. What is the ratio of the volume of the
pyramid to the volume of the prism?

Answers

Answer:

b

Step-by-step explanation:

If the cosine value is 80*, the secant value to the hundredths degree is: 0.98 0.17 5.76

Answers

Answer:  5.76

Work Shown:

sec(80) = 1/cos(80) = 5.75877048314363 which rounds to 5.76

Make sure your calculator is in degree mode.

0.2 ✕ -0.5 ✕ ( -0.9- -0.7)

Answers

Answer:

0.02

Step-by-step explanation:

[tex]0.2\times -0.5\times (-0.9 - -0.7)= \\\\0.2\times -0.5 \times (-0.2)= \\\\0.02[/tex]

Hope this helps!

Answer:

0.02

[tex]solution \\ 0.2 \times \: - 0.5 \times ( - 0.9 - ( - 0.7)) \\ = 0.2 \times ( - 0.5) \times ( - 0.9 + 0.7) \\ = 0.2 \times( - 0.5) \times ( - 0.2) \\ = - 0.1 \times ( - 0.2) \\ = 0.02[/tex]

hope this helps..

Good luck on your assignment

Solve for x. answers: A) 4 B) 6 C) 7 D) 5

Answers

Answer:

D) 5

Step-by-step explanation:

The smaller triangle is similar to the big triangle with the big triangle with a scale factor of 1.8.

5x × 1.8 = 45

Divide both sides by 1.8

5x = 25

Divide both sides by 5

x = 5

The answer is 5. Have a good day

Which expression can be used to check the answer to 56+(-14)=n?

Answers

Answer: n = 42

Step-by-step explanation:

56 - 14 = 42

If + and - are right next to each other, the + cancels out.

Answer:

i agree with Thetides5 the answer is n=42

Step-by-step explanation:

plz give me a brainliest i been working so hard to get a brainliest but no one has give me me one so plz can u give me one??? And hope this helps :D

Part A
Choose the inequality and solution to represent the number of cans, c, that Xander must still collect.
A. c + 64 ≤ 120; c ≤ 56
B. c + 120 ≤ 64; c ≤ –56
C. c + 64 ≥ 120; c ≥ 56
D. c + 120 ≥ 64; c ≥ –56

Part B
Choose the graph of the solution on the number line.

Answers

Answer:

Part A: A  

Part B: A

Step-by-step explanation:

1)

the inequality should be less than or equal to, since we need to find how many are left

now, the answer B is wrong, since there can't be negative 56, since Xander collected some cans, though he still must collect a few

thus, the answer is A

2)

A again is correct, since it represents:c ≤ 56

B represents c ≥ 56

C represents c ≤ –56

D represents c ≥ -56

In the spinner below, what is the probability of landing
on 6?
A. 1/4
B. 1/8
C. 1/3
D. 1/6

Answers

Answer:

1/4

Step-by-step explanation:

There are 4 equal sized sections, and 2 sections that are twice the size of the others ( 2*2=4), for a total of 8 sections

The section with a 6 in it is a double size section so it counts as 2 sections

P(6) =number of sections with a 6/ total sections

       =2/8

       =1/4

Answer:

1/4

Step-by-step explanation:

A

If f(x) = 5x + 40, what is f(x) when x = -5?
N
ܩ ܣ
15

Answers

Answer:

15

Step-by-step explanation:

f(x)=5x+40

so f(5)=5(-5)+40

f(5)= -25+40

f(5)=15

Identify the solution to the system of linear equations
Y=-x-2
Y=x-6

Answers

Answer:

(-4, 2)

Step-by-step explanation:

By looking at the graph, the solution to the system of linear equations will always be where they intercept. If they both are the same line it means that there are infinite solutions, and if they don't intercept at all, that means there are no solutions.

PLSS HELP SOON Is the sequence arithmetic? (Yes or no) If yes, please also give its common difference. 14) -2.8, -2.2, -1.6, -1.0

Answers

Answer:

The sequence is an arithmetic sequence.

Common difference = 0.6

Step-by-step explanation:

Given

-2.8, -2.2, -1.6, -1.0

Required

State if it's an arithmetic progression

Also state its common difference

To know if a sequence is arithmetic or not, we simply check for common difference

Common difference is calculated by subtracting a lower term with its immediate higher time;

In other words

[tex]Common difference = T_2 - T_1 = T_3 - T_2 = T_4 - T_3 = ......[/tex]

Where T represent Term and the number represent their positions;

So, from the given above

[tex]T_1 = -2.8\\T_2 = -2.2\\T_3 = -1.6\\T_4 = -1.0[/tex]

Calculating [tex]T_2 - T_1[/tex]

[tex]T2 - T1 = -2.2 - (-2.8)\\T2 - T1 = -2.2 + 2.8\\T2 - T1 = 0.6\\[/tex]

Calculating [tex]T_3 - T_2[/tex]

[tex]T_3 - T_2 = -1.6 - (-2.2)\\T_3 - T_2 = -1.6 + 2.2\\T_3 - T_2 = 0.6[/tex]

Calculating [tex]T_4 - T_3[/tex]

[tex]T_4 - T_3 = -1.0 - (-1.6)\\T_4 - T_3 = -1.0 + 1.6\\T_4 - T_3 = 0.6[/tex]

Notice that all the above workings gave the same result;

This shows that the sequence is an arithmetic sequence.

The result of each workings above is the common difference

Common difference = 0.6

Can someone please help me

Answers

This Is A Linear Graph Because Quadratic Graphs Are Curved

2. Solve this problem: There will be 460 people at the sport's award banquet. If each table seats 8 people, how many tables are needed?

A. 3,680 tables

B. 57 tables

C. 58 tables

D. 452 tables

Answers

There are 58 tables!

Answer:

C. 58 tables

Step-by-step explanation:

If there are 460 people, and each table seats 8 people, then we divide 460 by 8, giving us 57.5 tables. We cannot have a half of a table, so the answer is 58 tables.

A line is parallel to y = 4x – 2 and
intersects the point (5, -11).
What is the equation of this parallel line?
y = [?]x +
Hint: Use the Point-Slope Form: y - y1 = m(x - X1)
Then write the equation in slope-intercept form.

Answers

Answer:

y=4x-31

Step-by-step explanation:

Ignore the hint. Point slope form makes everything so much harder than it has to be.

Parallel lines always have the same slope, in this case 4.

So our equation is now: y = 4x + b

Let's solve for b by plugging in (5, -11), as it's the only point we know is on the parallel line.

-11 = 4(5) + b

-11-20 = b

b = -31

So plug in b: y = 4x - 31

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

Also rate and tell me if I'm correct :)

Answer:

y = -4x + 15.

Step-by-step explanation:

To find the equation of a line perpendicular to y = -2 and passing through the point (4, -1), we can use the point-slope form of a linear equation.

The given line y = -2 has a constant slope of 0 since there is no variable term involving x. A line perpendicular to it will have an undefined slope.

Using the point-slope form, we have:

y - y₁ = m(x - x₁),

where (x₁, y₁) represents the coordinates of the given point (4, -1), and m represents the slope.

Since the slope is undefined, the equation becomes:

y - (-1) = undefined(x - 4).

Simplifying:

y + 1 = undefined(x - 4).

Now, we can write the equation in slope-intercept form by substituting the slope as -4 (the negative reciprocal of 0):

y + 1 = -4(x - 4).

Expanding the right side:

y + 1 = -4x + 16.

To isolate y, we can subtract 1 from both sides:

y = -4x + 16 - 1.

Combining the constants:

y = -4x + 15.

Therefore, the equation of the perpendicular line is:

y = -4x + 15.

Can someone help me solve this?

Answers

Answer:

x=3,y=-1 or (3,-1) The answer is D

Step-by-step explanation:

Find the x-intercept and y-intercept
from the following linear equation:
6x – 9y = 54
x - intercept ([?], [])
y - intercept ([],[])

Answers

y= (0,-27)
x= (9,0)
That is the answer to this question I’m just hoping more because they won’t let me submit it if it’s under 20 characteristics

Answer:

X=(9,0)

Y=(0,-6)

A truck is bought at the price of $67,000. The price decreases at the rate of .30 every year (t). Which equation matches this exponential model?
Question 3 options:

A)

f(t) = 67(.70)t

B)

f(t) = 70(67,000)t

C)

f(t) = t(.70)67,000

D)

f(t) = 67,000(.70)t

Answers

Answer:

f(t) = $67000(.30)^t          (Must use " ^ " to indicate exponentiation)

Step-by-step explanation:

This is an exponential function:

f(t) = $67000(.30)^t  (Must use " ^ " to indicate exponentiation)

segment if a is a perpendicular bisector of segment BD if the measure of angle frd is represented by the expression 7x + 6 find the value of x​

Answers

Answer:

x = 12

Step-by-step explanation:

If it is a perpendicular bisector, then the intercepting angles are always 90°.

If that is the case then we simply set the expression 7x + 6 equal to 90 and solve for x. We should get 12 as our answer.

Please help me answer these e questions pleasesssss

Answers

Answer:

4) 8^14

7) h^7

10) 29^8 over 10^8

Step-by-step explanation:

If the numbers have the same base, just add their exponents together. So 10 plus 4 is 14.

Same thing for the second problem, since you have the same base, just add the exponents together. 6 plus 1 is 7

The bases are the same so just add the exponents, 7 plus one is 8.

(-2.9)^8

Convert it into a fraction: -(29/10)^8

Raise the fraction to the power (8) and the numerator and denominator to that power: 29^8/10^8

Hope this helps :)

8¹⁴

Step-by-step explanation:

4.) 8¹⁰×8⁴

=8 to the power (10+4)

=8¹⁴

7.) h⁶xh¹

=h to the power (6+1)

=h^7

10.) (-2.9)^1×(-2.9)^7

=(-2.9)^7+1

=(-2.9)^8

If the volume of the planter is 2,560 cubic inches,how tall is the planter

Answers

Answer:

Height of Planter = H = 20 in²

Step-by-step explanation:

As the planter is not given in the question, the question is incomplete.

First, lets complete the question by attaching the diagram related to this question.

(SEE THE ATTACHMENT)

Lets consider the right angled triangle that is formed at the top of the planter, as shown in the diagram attached.

The right angled triangle has a width of 16 inches and a heights of 16 inches as well.

We know that the Area of a triangle can be calculated by following formula:

[tex]A=\frac{1}{2}\cdot(width)\cdot(height)[/tex]

Substitute the values to find Area:

[tex]Area = \frac{1}{2}\cdot16\cdot16\\Area = 128 in^2[/tex]

We also know that the Volume of a triangular prism is given by:

[tex]Volume=(Area)\cdot(Height)[/tex]

Where

Area = Area of the face = 128 in²

Height = Height of the planter = H

Volume = 2560 in³

Substitute the values and solve for H:

[tex]2560=128\cdot{H}\\H=\frac{2560}{128}\\H=20in^2[/tex]

question in attachment

Answers

Answer:

it is C. An = 2(2)^n

Step-by-step explanation:

Answer:it is C. An = 2(2)^n

Step-by-step explanation:

What steps should be taken to calculate the volume of the prism? Select three options.

24 ft

6 ft

oft

ft

Use the formula A = bh to find the area of the base.

Use the formula A= bh to find the area of the base.

Use the formula V=Bn to find the volume of the prism.

Answers

Answer:

the formula is V=BH

Step-by-step explanation:

if the prism is rectangular prism : it has three dimensions then V=length * height * width

V= L*H*W or V= base*H

or V=BH

in your question it does not show V=BH maybe it is misprint

The volume of the prism is V = Bh , where B is the base area and h is the height of the prism

What is the volume of a prism?

A three-dimensional solid object called a prism has two identical ends. It consists of equal cross-sections, flat faces, and identical bases. Without bases, the prism's faces are parallelograms or rectangles.

The volume of a prism is the product of its base area and height

Volume of Prism = B x h

where B = base area of prism

h = height of prism

Given data ,

Identify the shape of the base of the prism: The base of the prism can be any polygon, such as a triangle, rectangle, or hexagon. It is important to identify the shape of the base because the formula for calculating the area of the base will depend on the shape.

Calculate the area of the base: Once the shape of the base has been identified, calculate the area of the base using the appropriate formula. For example, if the base is a rectangle, the area would be calculated as length x width.

Multiply the area of the base by the height of the prism: Once the area of the base has been calculated, multiply it by the height of the prism to get the volume. The height is the perpendicular distance between the two parallel bases of the prism.

Hence , by following these three steps, you can calculate the volume of a prism regardless of its shape, as long as you can identify the shape of the base and calculate its area.

To learn more about volume of prism click :

https://brainly.com/question/11336446

#SPJ7

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