A park, in the shape of a quadrilateral ABCD has angle B=900 , AB=9m, BC=40m, CD=15m, DA=28m. How much area does it occupy?
Answers
Given:
In quadrilateral ABCD, angle B=90° , AB=9m, BC=40m, CD=15m, DA=28m.
To find:
The area of the quadrilateral ABCD.
Solution:
In quadrilateral ABCD, draw a diagonal AC.
Using Pythagoras theorem in triangle ABC, we get
[tex]AC^2=AB^2+BC^2[/tex]
[tex]AC^2=9^2+40^2[/tex]
[tex]AC^2=81+1600[/tex]
[tex]AC^2=1681[/tex]
Taking square root on both sides, we get
[tex]AC=\sqrt{1681}[/tex]
[tex]AC=41[/tex]
Area of the triangle ABC is:
[tex]A_1=\dfrac{1}{2}\times base\times height[/tex]
[tex]A_1=\dfrac{1}{2}\times BC\times AB[/tex]
[tex]A_1=\dfrac{1}{2}\times 40\times 9[/tex]
[tex]A_1=180[/tex]
So, the area of the triangle ABC is 180 square m.
According to the Heron's formula, the area of a triangle is
[tex]Area=\sqrt{s(s-a)(s-b)(s-c)}[/tex]
where,
[tex]s=\dfrac{a+b+c}{2}[/tex]
In triangle ACD,
[tex]s=\dfrac{28+15+41}{2}[/tex]
[tex]s=\dfrac{84}{2}[/tex]
[tex]s=42[/tex]
Using Heron's formula, the area of the triangle ACD, we get
[tex]A_2=\sqrt{42(42-28)(42-15)(42-41)}[/tex]
[tex]A_2=\sqrt{42(14)(27)(1)}[/tex]
[tex]A_2=\sqrt{15876}[/tex]
[tex]A_2=126[/tex]
Now, the area of the quadrilateral is the sum of area of the triangle ABC and triangle ACD.
[tex]A=A_1+A_2[/tex]
[tex]A=180+126[/tex]
[tex]A=306[/tex]
Therefore, the area of the quadrilateral ABCD is 306 square meter.
Related Questions
At the end of a snowstorm, Jamal had 18 inches of snow on his lawn. The temperature then increased and the snow began to melt at a constant rate of 2.5 inches per hour. Assuming no more snow was falling, how much snow would Jamal have on his lawn 5 hours after the snow began to melt? How much snow would Jamal have on his lawn after tt hours of snow melting?
Answers
Answer:
Part 1)
5.5 inches.
Part 2)
[tex]y=-2.5t+18[/tex]
Step-by-step explanation:
We can write a linear equation to model the function.
Let y represent the inches of snow and let t represent the number of hours since the end of the snowstorm.
A linear equation is in the form:
[tex]y=mt+b[/tex]
Since there was 18 inches of snow in the beginning, our y-intercept or b is 18.
Since it melts at a constant rate of 2.5 inches per hour, our slope or m is -2.5.
Substitute:
[tex]y=-2.5t+18[/tex]
This equation models how much snow Jamal will have on his lawn after t hours of snow melting.
So, after five hours, t = 5. Substitute and evaluate:
[tex]y=-2.5(5)+18=5.5\text{ inches}[/tex]
After five hours, there will still be 5.5 inches of snow.
What number is missing here?
2, 3, 5, 8, 13. ?
Answers
Answer:
2, 3, 5, 8, 13 missing number is 18.
what is the sum of the rational expressions x-4/2x+3x/2x-1
Answers
Answer:
May the ans will help you.
A city is designing a new trail system that will be
6 1/6 miles long. They plan on placing 49 mileage signs to show the distance. How far apart will each sign be?
Answers
Step-by-step explanation:
the answer is 6.125 and its will be divided by 125
Find two consecutive integers whose sum is 901.
Answers
the answer is :
x+1 and x+2
Answer:
900+1=901
Step-by-step explanation:
Suponga que las calificaciones para el IQ (coeficiente de inteligencia) de una población adulta sigue una distribución aproximadamente normal, con una desviación estándar de 15 . Una muestra aleatoria de 25 adultos procedentes de esa población tiene un IQ medio de 105. Con base en estos datos, ¿es posible concluir que el IQ medio para la población es menor de 100? Utilice un nivel de significación de 0.01
Answers
Answer:
El p-value de lo teste es de 0.0475 > 0.01, o que implica que con base en estos datos, no es posible concluir que el IQ medio para la población es menor de 100.
Step-by-step explanation:
Teste que IQ medio para la población es menor de 100
En la hipótese nula, lo teste es se el IQ medio eres de al menos 100, o sea:
[tex]H_0: \mu \geq 100[/tex]
En la hipótese alternative, lo teste es se el IQ medio es menor de 100, o sea:
[tex]H_1: \mu < 100[/tex]
La estatistica de teste es:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
En que X es el promedio de la muestra, [tex]\mu[/tex] es lo valor testado en la hipótese nula, [tex]\sigma[/tex] es la desviacion estandar y n es lo tamaño de la muestra.
100 testado en la hipótese nula:
Entonces [tex]\mu = 100[/tex]
Desviácion esstándar de 15: Una muestra aleatoria de 25 adultos procedentes de esa población tiene un IQ medio de 105.
Esto significa que [tex]\sigma = 15, n = 25, X = 105[/tex]
Estatisitica de teste:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{105 - 100}{\frac{15}{\sqrt{25}}}[/tex]
[tex]z = 1.67[/tex]
P-value de lo teste e decisión:
El p-value de lo teste es la probabilidad de encontrar una amostra com média abajo de 105, que es 1 subtraído por el p-value de z = 1.67.
En la tabla-z, z = 1.67 tiene un p-value de 0.9525.
1 - 0.9525 = 0.0475
El p-value de lo teste es de 0.0475 > 0.01, o que implica que con base en estos datos, no es posible concluir que el IQ medio para la población es menor de 100.
please helppppppppppppppp
Answers
Answer:
10 units
Step-by-step explanation:
Given that,
The area is modeled by the equation as follows :
[tex]A=-l^2-10l+300[/tex]
Where
l is the linear dimensions of the frame.
Put A = 100
So,
[tex]-l^2-10l+300=100\\\\-l^2-10l+200=0\\\\l=10,-20[/tex]
So, the linear dimension of the frame is equal to 10 units.
Which of these strategies would eliminate a variable in the system of equations?
-7x + 2y = 5
3x - 5y = -5
A. Add the equations
B. Multiply the top equation by 3, multiply the bottom equation by 7, then add the equations.
C. Multiply the top equation by 5, multiply the bottom equation by 2, then add the equations.
Answers
Answer:
Step-by-step explanation:
A
Use the table to approximate AB in the triangle below.
Answers
Answer:
Answer is 6.1 units
Step-by-step explanation:
The measure of length of AB in the triangle ABC is 6.1 units.
What are trigonometric ratios?The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).
In the given triangle ABC, BC=5 and ∠A=55°.
We know that, sinθ= Opposite leg length/Hypotenuse length
Here, sinA=BC/AB
sin55°=5/AB
0.82=5/AB
AB=5/0.82
AB=6.1 units
Therefore, the measure of length of AB in the triangle ABC is 6.1 units.
Learn more about the trigonometric ratios here:
brainly.com/question/25122825.
#SPJ2
Find the angle measurements of the intersections for the two equations f(x) = 4x - 5 and g(x) = 2x^2 - 5.
Multiple answers
63
7 (This is one of the answers already)
20
76
90
Answers
Answer:
76° is the other one
Step-by-step explanation:
nope, no precise calculation here. the option are thankfully enough apart that solving it graphically is just fine. look at the screenshot. the upper intersection is the one with the 7° angle
the lower one is somewhat less than 90° :P
Answer:
76 is the other
Step-by-step explanation:
Simplify: (5x + 3) – (3x – 2)
Answers
Answer: 2x+5
Step-by-step explanation:
(5x + 3) – (3x – 2)
5x+3-3x+2
2x+5
Answer:
[tex]\huge\boxed{\boxed{\underline{\textsf{\textbf{Answer}}}}}[/tex]
╭⋟───────────────
[tex](5x+ 3) - (3x - 2) \\ = 5x + 3 - 3x + 2 \\ = 5x - 3x + 3 + 2 \\ = 2x + 5[/tex]
───────────────⋞╯
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐
Find the hypotenuse, c, of the triangle.
Answers
====================================
Work Shown:
a^2+b^2 = c^2 ... pythagorean theorem
c = sqrt(a^2+b^2)
c = sqrt(4^2+12^2)
c = 12.6491106406736
c = 12.65
Answer:
[tex]4 \sqrt{10} [/tex]Step-by-step explanation:
Given,
Height of the triangle = 4
Base of the triangle = 12
Therefore,
Hypotenuse of the triangle
[tex] {(base)}^{2} + {(height)}^{2} = {(hypotenuse)}^{2} [/tex]
[tex] = > {(12)}^{2} + {(4)}^{2} = {(hypotenuse)}^{2} [/tex]
[tex] = > {(hypotenuse)}^{2} = 144 + 16[/tex]
[tex] = > {(hypotenuse)}^{2} = 160[/tex]
[tex] = > hypotenuse = \sqrt{160} [/tex]
[tex] = > hupotenuse = \sqrt{5 \times 2 \times 2 \times 2 \times 2 \times 2} [/tex]
[tex] = > hypotenuse = 2 \times 2 \sqrt{5 \times 2} [/tex]
[tex] = > hypotenuse = 4 \sqrt{10} \: (ans)[/tex]
cos() =
O A. V
B.
173
2
OC.
OD.
-3
Answers
Answer:
-√3/2
Step-by-step explanation:
Given the expression:
Cos(7π/6)
Conver to degrees
= Cos(7(180)/6)
= cos 210
= -√3/2
Hence the value of cos(7π/6) is -√3/2
Find the equation (in terms of x ) of the line through the points (-2,5) and (3,4)
y=
Answers
Answer:
y = (-1/5)x + 23/5
Step-by-step explanation:
Given:
Two points;
(-2,5) and (3,4)
Find:
Equation of slope
Computation:
y = mx + b
5 = m(-2) + b
5 = -2m + b .......... Eq1
4 = m(3) + b
4 = 3m + b .......... Eq2
Eq2 - Eq1
-1 = 5m
m = -1/5
5 = -2m + b
5 = -2(-1/5) + b
5 = 2/5 + b
b = 23/5
y = mx + b
y = (-1/5)x + 23/5
here we go it riddle time! READY??
whats starts off tall when young and shorter when older
(please dont report we r j trying to have some fun)
Answers
Step by step:
hi will you assit me please? God bless you for helping students
Answers
Pls help this is urgent!!!
Answers
Answer:
1/2
Step-by-step explanation:
numbers taken = 1 to 40
multiples of 2 are = {2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40}
so there are 20 favourable outcomes.
probability = 20/40
=1/2
for multiples of 3
multiples = {3,6,9,12,15,18,21,24,27,30,33,36,39}
there are 13 favourable outcomes
probability = 13/40
since there is no 13/40 the answer should be the probability of multiples of 2 i.e 1/2
Do you think a friend would steal a led light controller after sleeping over cause I cannot find it?
Answers
Answer:
maybe u missplaced it somehow and it also would depend if you trust that person or not. some times that 'friend' can turn out to be fake but i don't mean it about ur friend. for now, u should just ask, there's no harm in that.
Consider the following graph:
What is the limit as it is approaching -1 from the right, what is the limit?
Answers
Answer:
The limit is 0, and the answer is given by option E.
Step-by-step explanation:
Limit to the right:
The limit of a function approacing a value of x to the right is given by the value of the function quite close to the point, looking to the right.
In this question:
Approacing by the right(x quite close, but more than -1, that is, -0.9999...), y tends to 0, so the limit is 0, and the answer is given by option E.
Please help please guys how are you doing
Answers
Answer:
the answer of the the triangle is 6
Answer:
6
Step-by-step explanation:
First row:
8 ÷ 2 = 4. → Square: 4
Second row:
14 - 4 = 10.
[two circles] = 10. So, 10÷2 = 5.
Circle = 5
Third Row:
[triangle] + 5 = 11
11 - 5 = 6
Triangle = 6
Please help meee! I'll make you brainliest or anything you want I swear! I'm desperate
Your neighbor is putting in a small square deck with side length x+4, as pictured below, where x is measured in feet. (x + 4) (x + 4) Part A Write a polymonial in standard form that represents the area of the deck Part B. Write an expression for the cost of the lumber for the top of the deck if the lumber costs $5 per square foot. Part C. If x = 3 feet what will be the cost of lumber for the top of the deck?
Please help meee! I'll make you brainliest or anything you want I swear! I'm desperate
Answers
B: 5(x^2 +8x + 16)
C: $245
Please brainliest!
The function h(x) is a transformation of the square root parent function,
f(x) = V2. What function is h(x)?
Answers
Answer:
[tex]h(x) = \sqrt{x+5}[/tex], option C.
Step-by-step explanation:
The parent function is [tex]f(x) = \sqrt{x}[/tex]
Function h:
Function h is function f shifted left 5 units.
Shifting a function f a units to the left is the same as finding [tex]f(x+a)[/tex]
Thus:
[tex]h(x) = f(x+5) = \sqrt{x+5}[/tex]
The function is [tex]h(x) = \sqrt{x+5}[/tex], and thus, the correct answer is given by option C.
Answer:
c
Step-by-step explanation:
The probability distribution for a random variable x is given in the table X: -5,-3,-2,0,2,3 Probability: .17,.13,.33,.16,.11,.10 Find the probability that X <_-3
Answers
Answer:
0.3 probability that [tex]x \leq -3[/tex]
Step-by-step explanation:
The probability distribution is given in the table.
Probability that x <= -3
The values that are -3 or lower are -3 and -5. So
[tex]P(X \leq -3) = P(X = -3) + P(X = -5)[/tex]
From the table:
[tex]P(X = -3) = 0.13, P(X = -5) = 0.17[/tex]. So
[tex]P(X \leq -3) = P(X = -3) + P(X = -5) = 0.13 + 0.17 = 0.3[/tex]
0.3 probability that [tex]x \leq -3[/tex]
Answer:0.3
Step-by-step explanation:
What is the answer plz?
Answers
Answer:
[tex]1\frac{9}{12}[/tex]
Step-by-step explanation:
Convert any whole numbers to improper fractions
[tex]\frac{9}{4}-\frac{3}{6}[/tex]
Find the LCM of the denominators and use multiplication to change the denominators to the LCM
[tex]\frac{27}{12}-\frac{6}{12}[/tex]
Subtract
[tex]\frac{21}{12}[/tex]
Simplify
[tex]1\frac{3}{4}[/tex]
[tex]1\frac{9}{12}[/tex] can be simplified to [tex]1\frac{3}{4}[/tex] so the answer is [tex]1\frac{9}{12}[/tex]
There are red, blue, and white buttons in a box. The ratio of the
number of red buttons to the number of white buttons is 4:7.
The ratio of the number of blue buttons to the number of red buttons
is 3:2. There are 280 white buttons.
How many buttons are there altogether?
Please help i’m very confused
Answers
Answer:
680
Step-by-step explanation:
Ratio of red to white 4 : 7
Number of white = 280
White + red buttons = x
7x / 11 = 280
7x = 280 * 11
7x = 3080
x = 3080 / 7
x = 440
Number of red buttons 440 - 280 = 160
Number of red bottons ;
Blue + red buttons = x
3 : 2 ; blue : red
3 + 2 = 5 ;
2x / 5 = 160
2x = 160 * 5
2x = 800
x = 800 / 2
x = 400
Number of Blue buttons :
400 - 160 = 240
Total :
White + red + blue
280 + 160 + 240 = 680 buttons
Given the inequalities y < 4 x - 6 and y < X - 6 graphed on the same coordinat
grid, which of the following coordinates gives a true statement?
A. (6,-2)
B. (-4,-2)
C. (-6,-2)
D. None of the above
Answers
Write a recursive formula for the following sequence:10, 5, 0, -5,... *
Answers
Answer:
decrease by 5
Step-by-step explanation:
n= 10
then in sequence,
n= n-5
Graph the Image of AKLM after a translation 1 unit left and 7 units up.
Answers
9514 1404 393
Answer:
see attached
Step-by-step explanation:
Pick a point (such as K, L, or M). Count one grid square to the left and 7 up. That is its new location.
From 1929 through the early 1930s, the prices of consumer goods actually decreased. Economists call this phenomenon deflation. The rate of deflation during this period was about 7% per year, meaning that prices decreased by 7% per year. To get a sense of what this rate would mean in the long run, let's suppose that this rate of deflation persisted over a period of 20 years.
What would be the cost after 20 years of an item that costs $100 initially? (Round your answer to the nearest cent.)
$
Answers
Answer:
23.42
Step-by-step explanation:
If something is decreasing by 7% we can mulitply it by (1-.07) or .93
so our formula is
100(.93)²⁰= 23.42388737
which rounds to 23.42
Using the exponential decline function ; the cost of the item after 20 years would be $23.42
Recall :
[tex] y = A(1 - r)^{t} [/tex] y = final amount A = initial price = $100Rate, r = 7% = 0.07Time, t = 20yearsSubstitute the values into the equation :
[tex] y = 100(1 - 0.07)^{20} [/tex]
[tex] y = 100(0.93)^{20} [/tex]
[tex] y = 100(0.23423887366)[/tex]
y = $23.42
Therefore, the cost of the item after 20 years is $23.42
Learn more : https://brainly.com/question/8317316
A health clinic dietician is planning a meal consisting of three foods whose ingredients are summarized as follows: One Unit ofFood I Food II Food IIIUnits of Protein 10 15 20Units of Carbohydrates 1 2 1Units of Iron 4 8 11Calories 80 120 100The dietician wishes to determine the number of units of each food to use to create a balanced meal containing at least 40 units of protein, 6 units of carbohydrates, and 12 units of iron, and with as few calories as possible. Use solver to find how many units of each food should be used in order to minimize calories.
Answers
Answer:
z (min) = 360 x₁ = x₃ = 0 x₂ = 3
Step-by-step explanation:
Protein Carbohydrates Iron calories
Food 1 (x₁) 10 1 4 80
Food 2 (x₂) 15 2 8 120
Food 3 (x₃) 20 1 11 100
Requirements 40 6 12
From the table we get
Objective Function z :
z = 80*x₁ + 120*x₂ + 100*x₃ to minimize
Subjet to:
Constraint 1. at least 40 U of protein
10*x₁ + 15*x₂ + 20*x₃ ≥ 40
Constraint 2. at least 6 U of carbohydrates
1*x₁ + 2*x₂ + 1*x₃ ≥ 6
Constraint 3. at least 12 U of Iron
4*x₁ + 8*x₂ + 11*x₃ ≥ 12
General constraints:
x₁ ≥ 0 x₂ ≥ 0 x₃ ≥ 0 all integers
With the help of an on-line solver after 6 iterations the optimal solution is:
z (min) = 360 x₁ = x₃ = 0 x₂ = 3