15. The sides of a parallelogram are 100 m each and the length of the longest diagonal is 160 m. Find the area of the parallelogram.
Answers
Answer:
Area of parallelogram = 9600 m²
Step-by-step explanation:
• We can find the measure of angle x using the cos rule:
[tex]160^2 = 100^2 +100^2 -2(100)(100) \cdot cos (x)[/tex]
Make x the subject of the equation:
⇒ [tex]20000 \cdot cos(x) = 100^2 +100^2 - 160^2[/tex]
⇒ [tex]cos(x) = -0.28[/tex]
⇒ [tex]x = cos^{-1} (-0.28)[/tex]
⇒ [tex]x = 106.26 \textdegree[/tex]
• Now we can find the area of one the triangles formed using the formula:
[tex]Area =\frac{1}{2} ab \cdot sin \theta[/tex]
where a and b are two sides of a triangle, and θ is the angle between them (angle x).
Substituting the values:
Area of one triangle = [tex]\frac{1}{2}[/tex] × (100)(100) × sin(106.26°)
= 4800 m²
• Since the parallelogram is formed by two such triangles, we have to double the area of the triangle to find the parallelogram's area:
Area of parallelogram = 2 × 4800
= 9600 m²
Related Questions
Find the x-intercept and and y-intercept algebraically
y = log2 (x + 1) - 3
need work
Answers
Answer:
x intercept is 7 y intercept is -3
Step-by-step explanation:
Write equation out and have y=0
[tex] log_{2}(x - 1) - 3 = 0[/tex]
Add 3 to both sides
[tex] log_{2}(x - 1) = 3[/tex]
Using the log to exponet rule
[tex] (log_{b}(x) = y ) \: equal \: b {}^{y} = x[/tex]
Where b and x are real numbers and b cannot equal 1.
Reorder the equation as a exponet
[tex] log_{2}((x + 1) = 3[/tex]
[tex] {2}^{3} = x + 1[/tex]
Simplify
[tex]8 = x + 1[/tex]
Subtract 1 from both sides
[tex]x = 7[/tex]
So the x intercept is 7
To find y intercept plug 0 in as x
[tex] log_{2}(0 + 1) - 3 = y[/tex]
[tex] log_{2}(1) - 3 = y[/tex]
Add 3 to both sides
[tex] log_{2}(1) = y + 3[/tex]
Rewrite in exponet form
[tex] {2}^{y + 3} = 1[/tex]
Using the zero exponet property, anything to the zero power equal 1 so we must find a value that equal out to zero using the exponet so we'll set up the equation
[tex]y + 3 = 0[/tex]
Subtract 3 from both sides and we get
[tex]y = - 3[/tex]
So the x intercept is 7 and the y intercept is -3
Roberto can lift 103.5 pounds. That is .9 times the amount his friend Vance can lift. Can Vance lift more or less than 103.5 pounds?
Answers
Answer:
Step-by-step explanation:
Vance can lift 0.9×103.5 pounds.
0.9 < 1, so you know that
0.9×103.5 < 103.5
What is the value of 2 (38 –14) + 38 = 9?
Answers
Answer: 2(38−14)+38=?9
86≠9
False
Step-by-step explanation: hope this help
If 5 friends each had one part of a scarf that's 1 and 5/12 yards long what fraction of the scarf could each friend knit
Answers
Answer:
17/60 yards of scarf
Step-by-step explanation:
If 5 friends each had one part of a scarf that's 1 and 5/12 yards long what fraction of the scarf could each friend knit
To solve the above question:
5 friends = 1 5/12 yards
1 friend = x yards
Cross Multiply
5 × x = 1 × 1 5/12 yards
x = 17/12 yards ÷ 5
x = 17/12 yards × 1/5
x = 17/60 yards of scarf
Answer:
its D
Step-by-step explanation:
1x5/12 + 5/12 1 X 5 = 5 SO 1 X 5/12 IS D
CAN SOMEONE ANSWER PLEASEEEEEE I SUCK AT MATH
Answers
Answer:
area = 472 in^2
Step-by-step explanation:
19 x 8 x 3 = 456 in^2 for large rectangle
1/2 x 2 x 8 x 2 = 16 in^2 for triangles
area = 456 + 16 = 472 in^2
The perimeter of a rectangular atrium is 300 yards. The length of the garden is ninety-six yards more than the width. Find the length and the width
Answers
Answer:The perimeter of a rectangular atrium is 27 yards in width and 123 yards in length.
Step-by-step explanation:
Step 1
The perimeter of a rectangular atrium is given as 2( l+b)
The perimeter of a rectangular atrium is 300 yards.
Let the width be represented as x
such that the
The length of the garden which is ninety-six yards more than the width is expressed as x+ 96
and the expression to solve for length and width will now be
Step 2
Perimeter = 2(l+b) = 2l + 2b
300=2( x+96) + 2 x
300= 2x+ 192 + 2x
300= 192+ 4x
300-192=4x
108=4x
x=108/4
x=27
width = 27 yards
length = x+ 96= 27 +96=123 yards
Help a dmb person out
You are renting a Porsche for the day. There is a daily fee of $50 and a charge of $0.50 per mile. Your budget allows a maximum total cost of $100. How many miles can you travel in the car on your budget?
Answers
Answer:
100 miles
Step-by-step explanation:
WILL MARK AS BRAINLIEST Write a complete Spanish sentence to indicate what the following people
eat/drink each day. Make sure to capitalize the first word of the sentence, end
with a period and include the correct article (el, la, los, las)! If there is more
than one of an item, you need to make that food/beverage plural. Follow the
model.
Answers
Daniel want to know the volume of his cube, he notices the the cube has 1/5 centimeters side length, what is the volume of the cube?
Answers
Answer: 1/125cm³
Step-by-step explanation:
The volume of a cube is gotten by multiplying the side length given by itself thrice.
Since the cube in the question has a side length of 1/5cm, the volume of the cube will be:
= 1/5 × 1/5 × 1/5
= 1/125cm³
Therefore, the volume of the cube is 1/125cm³
Mary drove from her home to the library after she left the library she drove to the park after that she drove home the map shows the past you took how far did Mary Drive?
Answers
Answer:
24 miles
Step-by-step explanation:
Distance formula (d):
D = sqrt[(x2 - x1)^2 + (y2 - y1)^2]
Home to library
(-4, 1) ; (-4, 9)
D1 = sqrt((-4 + 4)^2 + (9 - 1)^2)
D1 = 8
Library to park :
(-4, 9) ; (2, 1)
D1 = sqrt((2 + 4)^2 + (1 - 9)^2)
D3 = 10
Park to home :
(2, 1) ; (-4, 1)
D1 = sqrt((-4 - 2)^2 + (1 - 1)^2)
D2 = 6
Brendan has $65 worth of balloons and flowers delivered to his mother. He pays the bill plus an 8.5% sales tax and an 18% tip on the total cost
including tax. He also pays a $10 delivery fee that is charged after the tax and tip. How much change does he receive it he pays with two $50
bills ? Round to the nearest cent
Answers
Answer:
6.77
Step-by-step explanation:
Answer:
Step-by-step explanation:
A wildlife photographer photographs a crocodile and then paddles against a river current for 6 km. Then, hoping to photograph a hippopotamus, she paddles 15 km across a lake. She paddles across the lake for one hour longer than she paddled up the river. Find the speed of the boat as she paddles the lake if the river current is 2 km/h.
Answers
Answer:
5 or 6
Step-by-step explanation:
So I did it in a different way than shown in rsm classes. I said that the speed was x-2 and x.
then I said the distance was 6 and 15. If the time taken was 1 hour more, then we can come up with this equation:
Since the time is 6/x-2 or 15/x
15/x-6/x-2=1
multiply everything to get a common denominator then cancel it out to get
(15x-30)-6x=x^2-2x
11x-30=x^2
x^2-11x+30=0
(x-5)(x-6) is factored form.
so x=5 or x=6. this means that the speed of the boat is either 5km/h or 6 km/h
help brainliest if right
Answers
Answer:
y = 1x + 7
Step-by-step explanation:
The equation formula for this scenario is y = mx + b
m = slope
b = y-intercept
To find the slope, pick two points. I picked (2,9) and (4,11).
Subtract 11 from 9, you'll get 2.
Subtract 4 from 2, you'll get 2.
2/2 equals 1. The slope (m) = 1
To find the b, y-intercept, plot the points on a graph and see if the linear line across the y-intercept. For this case, the y-intercept is 7.
The equation is: y = 1x + 7
why is 60% greater than 3.75
Answers
if k is the incenter of def find each measure
Answers
Answer:
Step-by-step explanation:
An airplane is flying at a constant speed. The airplane descends 450 meters in 9 seconds. Write the speed of the airplane as an integer.
Answers
Answer: Speed = 50meters/ second
Writing as an integer becomes + 50meters/ second 0R 50meters/ second
Step-by-step explanation:
Speed is given as = Distance / Time
distance covered by Airplane = 450 meters
Time = 9 seconds
Therefore, Speed = 450/ 9 = 50 meters/second
Find the area of the shaded region.
Answers
Answer:
80
Step-by-step explanation:
multiply 10 by 8
(If it is not right... i apoligize but i don't see a shaded region)
Answer:
80 in
Step-by-step explanation:
To find the area of a rectangle, you have to multiply the length and height of the rectangle. When you do you will get 80 in
Hope this Helped
-2.7F + 0.4F - 11 - 9
How do I solve this, like I understand the first few parts but when I have to combine Like terms I get stuck♀️
Answers
Answer:
-2.3F-20
Step-by-step explanation:
-2.7F + 0.4F - 11 - 9 = -2.3F-20
Answer:
I think when you collect all the like terms the equation comes out to be
Step-by-step explanation:
-2.3F - 20
Johnny is standing on a platform 12 meters high throw ball up velocity 11 meters what time will ball hit the ground after 2 seconds
Answers
Answer:
The ball will hit the ground after 1.54 seconds
Step-by-step explanation:
This is a form of projectile motion in horizontal direction
Thus, time taken to reach the ground
[tex]t = \sqrt{\frac{2*d}{g} }[/tex]
Substituting the given values in above equation, we get -
[tex]t = \sqrt{\frac{2* 12}{10} } \\t = 1.54[/tex]seconds
Which expression is equivalent to |a|≤5 ?
a ≥ –5 or a ≤ 5
a ≥ –5 and a ≤ 5
a ≤ –5 and a ≥ 5
a ≤ –5 or a ≥ 5
Answers
Answer:
I think its the first one but not 100 % sure
Step-by-step explanation:
Answer:
A>= -5 and A<= 5
Step-by-step explanation:
Which of the following is a tautology?
a. Proposition
b. Modus Tollens
c. Argument
d. Affirming the Disjunct
Answers
Answer the photo below thanks
Answers
Answer: C. Never
Similar polygon are never different shapes. They are always the same shape. As usual, read the question carefully before choosing an answer.
Step-by-step explanation: hope this help:)
what do u mean by trigonometry
Answers
Answer:
Step-by-step explanation:
There are six trigonometric ratios, sine, cosine, tangent, cosecant, secant and cotangent. These six trigonometric ratios are abbreviated as sin, cos, tan, csc, sec, cot. These are referred to as ratios since they can be expressed in terms of the sides of a right-angled triangle for a specific angle θ.
Basic Formulas
By using a right-angled triangle as a reference, the trigonometric functions or identities are derived: sin θ = Opposite Side/Hypotenuse. cos θ = Adjacent Side/Hypotenuse. tan θ = Opposite Side/Adjacent Side.
Main Trigonometric Functions
Sine (sin)Cosine (cos)Tangent (tan)Secant (sec)Cosecant (csc)Cotangent (cotBoth depend on distances and angles, but trigonometry uses the measurement of angles while geometry deals with angles only in terms of equality of angles and sums of angles. Actually, it seems like basic calculus is easier than basic trigonometry.
(hope this helps can i plz have brainlist :D hehe)
If the circumference of a circle is 62.8 feet what is the radius of the circle
Answers
Answer: r≈ 9.99ft
Using the formula
C=2 π r
Solving for r
r= C/2π = 62.8/2·π ≈9.99493ft
116 is less than a number, R increased by 35?
Answers
Answer:
R - 116 + 35 is your expression I am pretty sure
HEEEEELP The height of a street light is 50 feet. It casts a 40−foot shadow. At the same time, a man standing next to the street light casts a 5−foot shadow. How tall is the man?
Answers
Answer:
5 foot
Step-by-step explanation:
how to find lateral surface and total surface area of triangular prism
Answers
Answer:
using the formula ...........duh
Answer:
Lateral Surface Area of a Triangular Prism Formula
Finds the total area contained by the three rectangular sides of the prism. You can think of the lateral surface area as the total surface area of the prism minus the two triangular areas at the top and bottom of the prism.
James cut out four parallelograms, the dimensions of which are shown below. Parallelogram 1 length: 12 in. width: 15 in. diagonal: 20 in. Parallelogram 2 length: 16 in. width: 30 in. diagonal: 34 in. Parallelogram 3 length: 20 in. width: 21 in. diagonal: 29 in. Parallelogram 4 length: 18 in. width: 20 in. diagonal: 26 in. James put the parallelograms together so one vertex from each paper exists on a point, as shown in the circle. 4 parallelograms are put together so that one vertex from each paper exists on a point. Which statement explains whether or not the parallelgrams can be put together so each occupies one-quarter of the area of the circle without overlapping any other pieces? Check all that apply.
Answers
Answer:
B. The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 1 do not form right angles.
E. The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 4 do not form right angles.
Step-by-step explanation:
P1: 12^2+15^2=20^2 144+225=400 369=400
P2: 16^2+30^2=34^2 256+900=1156 1156=1156
P3: 20^2+21^2=29^2 400+441=841 841=841
P4: 18^2+20^2=26^2 324+400=676 724=676
So the answers are B and E
Answer:
b and e
Step-by-step explanation:
Si se organizan los niños de mayor a menor de acuerdo con su estatura, ¿cuál es el orden correcto? A. Andrés, Samuel, Laura y Valeria. B. Samuel, Andrés, Valeria y Laura. C. Laura, Valeria, Andrés y Samuel. D. Valeria, Laura, Samuel y Andrés.
Answers
Answer:
A. Andres, Samuel, Laura y Valeria.
Step-by-step explanation:
The height of Andres is greater than all other students. Andres has height of 4.2feet. Samuel is second highest in height and he has height of 4.0 feet. The lowest height student is Valeria who has 3.5 feet height.
pls help me thank you!
Answers
Answer:
D.
If possiable may i have brainlist?