Three of the vertices of square ABCD are located at A(0,3), B(4,0), and C(7,4).
Determine the area of square ABCD.​

Answer/Step-by-step explanation:

1. Sin A = opp/hyp

Opp = 3

Hyp = 5

[tex] sin(A) = \frac{3}{5} [/tex] (substitution)

[tex] sin(A) = 0.6 [/tex]

2. Sin B = opp/hyp

Opp = 4

Hyp = 5

[tex] sin(B) = \frac{4}{5} [/tex] (substitution)

[tex] sin(B) = 0.8 [/tex]

3. Cos Q = adjacent/hypotenuse

Adjacent = 12

Hypotenuse = 13

[tex] cos(Q) = \frac{12}{13} [/tex] (substitution)

[tex] cos(Q) = 0.9231 [/tex] (4 decimal places)

4. Cos S = adjacent/hypotenuse

Adjacent = 5

Hypotenuse = 13

[tex] cos(S) = \frac{5}{13} [/tex] (substitution)

[tex] cos(S) = 0.3846 [/tex] (4 decimal places)

9514 1404 393

Answer:

  all are No

Step-by-step explanation:

The given triangle is ΔABE, where AB is the hypotenuse and BE is the long side.

In each of the other triangles listed, The first two letters are not the name of the hypotenuse, so none are similar.

_____

Additional comment

The similar triangles would be ΔADB, ΔEDC, ΔBEC, and ΔBDE.

Answer:

all of them are

Step-by-step explanation:

Answer:

12 meters

Step-by-step explanation:

30 times 40 = 1200

100 cm in a meter

1200/100= 12

Answer:

The answer is C. $16,780

Step-by-step explanation:

Answer:

c, 16,780

Step-by-step explanation:

plato

Answer:

Simplifying

27 + y = 10

Solving

27 + y = 10

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-27' to each side of the equation.

27 + -27 + y = 10 + -27

Combine like terms: 27 + -27 = 0

0 + y = 10 + -27

y = 10 + -27

Combine like terms: 10 + -27 = -17

y = -17

Simplifying

y = -17

Step-by-step explanation:

As per the given ratio comparison, We can say that the Second job generates the most income and that position makes him $5 per hour.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Given, An employee working 40 hours per week earns a salary of $600 per week but gets a second job offer to work 40 hours per week, hourly at $20 an hour.

For the first job, we will calculate the ratio of the employee Salary to the working hours to compare with the salary of the Second job:

Since,

He makes $600 per week for working 40 hours

Thus,

His hourly salary = 600/40

His hourly salary will be $15.

For the second job, it is already mentioned that the employee gets $20 per hour for the same working hours.

therefore, the Second job generates the most income and that position makes him $5 per hour.

Learn more about ratios here:

https://brainly.com/question/13419413

#SPJ6

Answer:

m/6+  n/3  +1/2  

Step-by-step explanation:

The height of the cone in figure 2 is 4.5 centimeters.

Two figures are said to be similar if they have the same shape and the ratio of their corresponding sides are in the same proportion.

From the diagram, the two cone are similar. Let h represent the height of the cone in figure 2, hence:

h/3 = 12/8

h = 4.5 cm

The height of the cone in figure 2 is 4.5 centimeters.

Find out more on Similar figure at: https://brainly.com/question/4014697

Answer:

4.5

Step-by-step explanation:

Answer:

15.6%

Step-by-step explanation:

Since each day there is a 6% chance that Lisa smiles at him then that means that each day there is a 94% chance that Lisa does not smile at him. To find the probability of Milhouse going longer than a month (30 days) without a smile from Lisa we need to multiply this percentage in decimal form for every day of the month. This can be solved easily by putting 94% to the 30th power which would be the same, but first, we need to turn it into a decimal...

94% / 100 = 0.94

[tex]0.94^{30}[/tex] = 0.156

Now we can turn this decimal into a percentage by multiplying by 100

0.156 * 100 = 15.6%

Finally, we can see that the probability that Milhouse goes longer than a month without a smile from Lisa is 15.6%

Using the binomial distribution, it is found that there is a 0.1563 = 15.63% probability that Milhouse goes longer than a month without a smile from Lisa.

For each day, there are only two possible outcomes, either Lisa smiles at him, or she does not. The probability that she smiles at him on day is independent of any other day, hence, the binomial distribution is used to solve this question.

Binomial probability distribution

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

In this problem:

The probability that Milhouse goes longer than a month without a smile from Lisa is the probability of no smiles during 30 days, that is, P(X = 0), hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{30,0}.(0.06)^{0}.(0.94)^{30} = 0.1563[/tex]

0.1563 = 15.63% probability that Milhouse goes longer than a month without a smile from Lisa.

To learn more about the binomial distribution, you can take a look at https://brainly.com/question/24863377

Answer: c

Step-by-step explanation: because 7 squared is 49 and 8 squared is 64

nvm i read the question wrong

Step-by-step explanation:

the person above is correct

Answer:

75.8 is your answer

Step-by-step explanation:

119:157*100 =

(119*100):157 =

11900:157 = 75.8

Answer:

187.301 is 157% of 119.3

Step-by-step explanation:

Answer:

Step-by-step explanation:

Three tenths is 3/10 or 30/100 so if we take three hundreds from this it is 27 over hundred ( 27/100).

Answer:

-y^4+4y

Step-by-step explanation:

Answer:

False

Hope my answer helps you pls mark me as brainiest :)

Answer:

Anything??

Step-by-step explanation: (Im joing btw didnt want to offend anyone lol)

x=40

Answer:

YES:  direct variation

Step-by-step explanation:

2x = 3y is equivalent to y = (2/3)x, which has the form of a proportional relationship (direct variation) y = kx.  YES

[tex]\color{plum}m∠ABC = 71° [/tex]

Which means :

m∠ABC = ∠ADC (opposite angles of a parallelogram)

m∠ABC :

= 37° + 34°

= 71°

Thus, the measure of ∠ABC = 71°

Let us find the measures of the other angles as well :

m∠BCD + m∠ADC = 180°

m∠BCD + 71 = 180°

m∠BCD = 180 - 71

m∠BCD = 109°

Thus, the measure of∠BCD = 109°

m∠BCD = ∠BAD (opposite angles of a parallelogram)

m∠BAD = 109°

Thus, the measure of ∠BAD = 109°

Therefore, m∠ABC = 71°

Answer:

Step-by-step explanation:

Given isosceles trapezoid AB = CD

Angles B and C are congruent and angles A and D are congruent.

A and B, as well as C and D sum to 180 as supplementary angles, therefore:

Step-by-step explanation:

hope it's right :)

Answer:

Step-by-step explanation:

66

Answer:

0.8340

Step-by-step explanation:

The aim of this question is to find the probability that the student makes it to the second class prior to when the lecture commences.

Provided that A, B, and C are independent of each other from the full complete question.

Then; we want P(A + C < B)

So A [tex]\sim[/tex] N (2, 1.5)

B [tex]\sim[/tex] N (10, 1)

C [tex]\sim[/tex] N (6, 1)

P(A + C - B < 0)

Since they are normally distributed( i.e. A + C - B)

Then;

E(A + C -B) = E(A) + E(C) - (B)

E(A + C -B) = 2 - 10 + 6

E(A + C -B) =  -2

Var(A+C -B) = Var(A) + Var (B) + Var (C)

Var(A + C -B) = (1.5)² + (1)² + (1)²

Var(A + C -B) = 4.25

The standard deviation = [tex]\sqrt{4.25}[/tex]

The standard deviation = 2.06155

[tex]P(A+C-B) = p \Big (Z < \dfrac{0-(-2)}{2.06155} \Big )[/tex]

[tex]P(A+C-B) = p \Big (Z \le 0.97014 \Big )[/tex]

[tex]\mathbf{P(A+C-B) = 0.8340}[/tex]

Answer:

y = 4x + 3

Step-by-step explanation:

To do this, put the new line into the form y = mx + b where m is the slope and b is the y-intercept.

When two lines are parallel, they have the same slope. Since, the slope of the first line is 4, that means the slope of the second line is also 4.

So far, the equation is y = 4x + b.

Then, since you know (-2, -5) is a solution, x = -2, y = -5 is a solution so you can plug this into the equation.

This would be:

-5 = 4 * -2 + b

-5 = -8 + b

3 = b

This means the equation is y = 4x + 3.

Answer:

Add each side of the rectangle together to get the perimeter.

Step-by-step explanation:

Subscribe to Clutch Gam3r on YT

Answer:

..   ..

..   ..

Step-by-step explanation:

8/2=4

Answer:

The triangle formed is Equilateral triangle.

I have taken Perpendicular = P ( you can say M)

√400 - x²  = OP (OM)

√3 x = AP (AM)

The length of the string of each person = 20√3 m

Step-by-step explanation:

As given , circular park with radius 20m

Let , Ankur sit on boundary point A

       Syed sit on boundary point S

       David sit on boundary point D

As given,

Ankur, Syed and David are sitting at equal distance on its boundary

⇒AS = AD = SD

Let AS = AD = SD = 2x

As the sides are equal

⇒ The triangle formed is Equilateral triangle.

Now,

Draw a perpendicular on the side SD

Let OP be the perpendicular

⇒SP = PD = [tex]\frac{1}{2}[/tex]SD = [tex]\frac{1}{2}. 2x = x[/tex]

So, we get

SP = x , PD = x

Now, Draw the line OS and OA

AS , we can see that ,

ΔOPS and ΔAPS are right angle triangle ,

So , apply Pythagoras theorem to ΔOPS and ΔAPS

In ΔOPS

OS² = OP² + PS²

⇒20² = OP² + x²

⇒400 - x² = OP²

⇒√400 - x²  = OP

Now,

In ΔAPS

AS² = AP² + PS²

⇒(2x)² = AP² + x²

⇒4x² - x² = AP²

⇒√3x²  = AP

⇒√3 x = AP

Now,

We can see that,

AP = AO + OP

⇒√3 x  = 20 + √400 - x²

⇒√3 x  - 20 + = √400 - x²

Squaring both side

⇒(√3 x  - 20 )²= (√400 - x²)²

⇒3x² + 400 - 40√3 x = 400 - x²

⇒3x² + x² =  40√3 x

⇒4x² = 40√3 x

⇒x = 10√3

∴ we get

AS = SD = AD = 2(10√3) = 20√3 m

⇒The length of the string of each person = 20√3 m