What is the length of side s of the square shown below?

What Is The Length Of Side S Of The Square Shown Below?

Answers

Answer 1

The length of side "s" of the square is 3 units, as it is equal to one of the legs of the 45-45-90 right triangle formed by the diagonal of the square.

To find the length of side "s" of the square shown below, we can use trigonometry, specifically the properties of right triangles and the fact that the diagonal divides the square into two congruent 45-45-90 right triangles.

Given information:

The diagonal of the square measures 6 units.

One of the angles at the top of the square is 45 degrees.

Step 1: Recognize the properties of the 45-45-90 triangle:

Since the diagonal divides the square into two congruent right triangles, and one angle is 45 degrees, we have a 45-45-90 triangle. In such a triangle, the two legs (the sides opposite the 45-degree angles) are congruent, and the hypotenuse (the side opposite the 90-degree angle) is √2 times the length of a leg.

Step 2: Use trigonometric ratios:

Let "x" be the length of one leg of the 45-45-90 triangle, which is also equal to side "s" of the square.

From the properties of the 45-45-90 triangle:

x (leg) = s (side of the square)

Hypotenuse = √2 * leg

Given that the diagonal of the square is 6 units, we can relate the diagonal to the legs:

Diagonal = 2 * leg

6 = 2 * x

Now, solve for x (the length of one leg of the triangle and side "s" of the square):

x = 6 / 2 = 3 units

So, the length of side "s" of the square is 3 units.

Therefore, from the given options the correct one is B.

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Related Questions

Jason empties his piggy bank and counted out exactly $10 in nickels, dimes and quarters. There were twice as many dimes as Nickels. There were twice as many quarters as dimes. How many nickels did they have ?

Answers

Answer:

8 nickels

Step-by-step explanation:

Total Amount of Money owned by Jason=$10

1 nickel =$0.05

1 dime=$0.10

1 quarter =$0.25

Let the number of dimes =dLet the number of nickels =nLet the number of quarters =q

If there were twice as many dimes as Nickels, then:

d=2n

Also, there were twice as many quarters as dimes.

q=2d

Therefore:

0.1d+0.05n+0.25q=100

Substituting d=2n and q=2d into the above relations

0.1(2n)+0.05n+0.25(2d)=10

0.2n+0.05n+0.25(2(2n))=10

0.2n+0.05n+1n=10

1.25n=10

n=8

q=2d=2X16=32

d=2n=2X8=16

Jason had 8 nickels

help me pls ASAP !!

I just need the simplified exponent

Answers

The answer as a whole is256x^8y^7

Answer:

256y^3/x^2

Step-by-step explanation:

Choose the term described.
a string stretched across a doorway
Select the correct answer.
angle
line segment
ray

Answers

a line segment. the string is vertical & the door is vertical. they are both straight.

Choose the correct answer
Distance between 2 airports = 1,450 miles
Average speed of airplane = 350 mph
Travel time by bus after arrival at airport = 20 minutes
Total travel time = ??? hours
The choices are:
A) 4.47
B) 3.56
C) 3.97

Answers

1450 miles / 350 mph = 4.1428 hours
4.1428 hours = 4 hours and 9 minutes
So the total travel time is 4 hours and 47 minutes. So A

Answer:

4.14

Step-by-step explanation:

The generator of a cone forms a 20⁰ angle with the central axis. At what angle could a plane intersect the central axis of the cone to form an ellipse?
10⁰
20⁰
40⁰
90⁰

Answers

Answer:

40

Step-by-step explanation:

It takes Evan 14 minutes to complete a word search.

How many word searches can Evan complete in 98 minutes?

Answers

Answer:

7 word searches

Step-by-step explanation:

To solve this problem, all we have to do is take the total amount of minutes and divide it by the amount of minutes it takes Evan to complete one word search.

98/14 = 7

Evan can complete 7 word searches in 98 minutes.

He can search 7 words.

What is unitary method?

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given:

Evan 14 minutes to complete a word search

Evan can complete in 98 minutes

=98/14

=7

Hence, Evan can search 7 words in 98 minutes.

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A number cube is rolled three times. What is the probability of rolling a number less than 3 each time?

Answers

Answer:

8/27

Step-by-step explanation:

Final answer:

The probability of rolling a number less than 3 three times in a row on a number cube (or die) is 1/27.

Explanation:

The subject of this question is probability in mathematics. A number cube, often referred to as a die, has six faces numbered 1 through 6. If we are looking for the probability of rolling a number less than 3, we are looking for the probability of rolling a 1 or a 2. Out of six possibilities, two are successful outcomes (1 and 2), so the probability of rolling a number less than 3 in one roll is 2 out of 6, or 1/3.

However, since the number cube is rolled three times, we have to consider this probability for each roll. In probability, when we want to find the likelihood of multiple events all occurring, we multiply the probabilities of each individual event. Therefore, the probability of rolling a number less than 3 three times in a row is (1/3) * (1/3) * (1/3) = 1/27.

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Anouk has two dispensers that can each hold 1.25 liters. She fills them with liquid hand soap from a store that charges $0.19 for every 50 milliliters of soap.


How much does it cost Anouk to fill both of her dispensers with hand soap?


Enter your answer in the box.

Answers

Answer:

$4.75

Step-by-step explanation:

1milliliter = 1mL = 1.0*10^-3L

50mL = 50*10^-3L = 0.05L.

But 0.05L costs $0.19 to refill,

How much will 1.25L cost?

0.05L = 0.19

1.25 = x

X = (1.25*0.19) / 0.05

X = $4.75

It will cost her $4.75 to refill 1.25L of soap

Answer:

$9.5

Step-by-step explanation:

Each dispenser holds 1.25 liters, so we have a total of 1.25*2 = 2.5 liters to be filled.

Each 50 milliliters of soap, that is, 0.05 liters, costs $0.19, so we can solve now using a rule of three:

0.05 liters of soap -> $0.19

2.5 liters of soap -> X

0.05/2.5 = 0.19/X

X = 2.5*0.19/0.05 = $9.5

It will cost $9.5 to fill both dispensers with soap.

What is the measure of angle 1?

A triangle has angles 29 degrees, 65 degrees, and 2. The exterior angle to angle 2 is 1.

Answers

Answer:

86 degrees

Step-by-step explanation:

So what you do is that since a triangle is 180 degrees added together you first subtract 180-29 and then you get 151 and then you subtract 151-65 and that's how I got 86

The measure of angle ∠1 is equivalent to 94°.

What is an angle?

In Euclidean geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

Given is that a triangle has angles 29° and 65°.

We know that -

Exterior angle is equal to Sum of two interior opposite angles.

Mathematically -

∠E = ∠I{1} + ∠I{2}

∠1 = 29° + 65°

∠1 = 94°

Therefore, the measure of angle ∠1 is equivalent to 94°.

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What is 3 divided by 0.05?

Answers

The answer would be 60

3 divided by 0.05 is equal to 60.

Given that we need to find the value of 3 divided by 0.05,

To calculate 3 divided by 0.05, you can use the following formula:

3 ÷ 0.05 = [tex]\frac{3}{0.05}[/tex]

To divide by a decimal number like 0.05, you can multiply both the numerator and denominator by a power of 10 to eliminate the decimal point.

In this case, multiplying by 100 will work:

[tex]3 \div 0.05 = \frac{3}{0.05} \times\frac{100}{100}[/tex]

Now we can perform the division:

[tex]3 \div 0.05 = \frac{3\times 100}{0.05 \times100}[/tex]

Simplifying further:

[tex]3 \div 100 =[/tex] [tex]\frac{300}{5}[/tex]

Finally, performing the division:

300 / 5 = 60

Therefore, 3 divided by 0.05 is equal to 60.

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Find the inequality represented by the graph.

Answers

Answer:

y is less then or equal to 5/2x+5

Step-by-step explanation:

It is plus 5 because the line crosses the y-intercept at 5. And 5/2 because that is the calculated slope between the two places.

How do I justify my answer?

Answers

Your answer would be yes, they would be parallel.

We can justify this using co-interior angles, which state that 2 angles subtended by parallel lines add up to 180°

We can check this with both angles 3x & x, or 2x & 90°.
If AD and BC are parallel, then 3x + x = 180, and since you already found the value of x we can substitute this in:
3(45) + (45) = 180
135 + 45 = 180
180 = 180

So the co-interior angles do add up to 180°, which means that AD and BC are parallel.

I hope this helps! Let me know if you have any questions :)
X is 45 degreesThe lines AD and BC would not be parallel when ABCD is drawn to scale.

a) The value of x as calculated in the image is 45 degrees.

b) For the lines AD and BC to be parallel in a quadrilateral, the opposite angles need to be supplementary (i.e., their sum should be 180 degrees).

In this case, angle A is:

2x = 245 = 90 degrees

and angle D is:

3x = 345 = 135 degrees.

Since 90 + 135 = 225 degrees, which is not equal to 180 degrees, the lines AD and BC would not be parallel when ABCD is drawn to scale.

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the
correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag
the item to the trashcan. Click the trashcan to clear all your answers.

A rectangular prism has dimensions of 2x, 3x, and 5x.

Write an expression for the total surface area of the prism.

Answers

Answer:

46

Step-by-step explanation:

The base and height of a parallelogram must be perpendicular.
True
False

Answers

Answer:

True because no matter what angle or what parallelogram they are equal

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

John and Tyrone each go for a morning jog before work. John's jogging
pace is represented by the equation y=5x, where y is the number of
miles he jogs and x is the number of hours he jogs. Tyrone's pace is
given by the graph. Choose the statement that correctly compares their
unit rates.​

Answers

Final answer:

The question asks to compare the unit rates of two joggers, John and Tyrone. John's unit rate is 5 miles per hour, as indicated by the equation y=5x. Without Tyrone's graph data, a direct comparison cannot be made.

Explanation:

The subject of the question involves comparing unit rates of two joggers, which requires an understanding of linear equations and graph interpretations in mathematics. Based on the given information, John's jogging pace is defined by the linear equation y=5x, where y is the number of miles he jogs and x is the number of hours he jogs. This equation suggests that John's unit rate, or his speed, is 5 miles per hour. However, to compare John's unit rate to Tyrone's, we need additional information about the slope of Tyrone's graph, which represents his speed.

Without the specific graph or a defined equation for Tyrone's pace, we can't make a direct comparison. Typically, the unit rate for a jogger is found by taking the slope of the position vs. time graph, which involves dividing the change in position (the rise) by the change in time (the run). If the slope of Tyrone's graph were provided, we could determine his speed and compare it to John's.

Remember, the unit rate is a measure of how much of something occurs per unit of another thing. In this case, it's the speed at which each jogger moves per hour. If additional data from Tyrone's graph were given, we would look for a constant rate of change or identify two points on the graph to calculate the slope (speed) and thus compare the unit rates of the two joggers.

Mr. Jackson’s monthly salary is revised from $2500 to $2600. What percentage is the salary increased?

Answers

Answer:

.004 %

Step-by-step explanation:

how do I do this pls help It's due in 30 minutes!!!! tanθ=5/12 ​

Answers

Answer:

Step-by-step explanat

Pls mark Brainliest.

Answer:

sin θ = 5/13

cos θ = 12/13

Step-by-step explanation:

We know that tan θ = 5/12 which indicates that the adjacent side relative to θ is 12 and the opposite side relative to θ is 5. The hypotenuse is missing which can be figured out using the Pythagorean Theorem.

a² + b² = c²

c = √(5² + 12²)

c = √(169)

c = 13

The hypotenuse is 13, and we know that the opposite and adjacent sides measure 5 and 12, respectively.

sin θ = opposite/hypotenuse

sin θ = 5/13

cos θ = adjacent/hypotenuse

cos θ = 12/13

Emilia and Sydney went out to dinner. The bill came to $24. They want to leave a 20% tip and split the bill. How much do they each pay?

Answers

Answer:

$9.6

Step-by-step explanation:

tip $24×20% = 24×20/100 = 480/100 = $4.8

How much do they each pay ?

($24 - $4.8) : 2 = $19.2 : 2 = $9.6

Consider the function f(x) = 3x2 + 7x + 2.
What is the value of the discriminant?
How many x-intercepts does this function have?
What is the number of zeros for this function?

Answers

Answer:

Step-by-step explanation:

This function I believe has one x intercept which is (-2/13,0)

Answer:

It's 25 , 2 , two real number solutions

Step-by-step explanation:

Just did it



PLEASE I REALLY NEED HELP IT'S DUE TODAY AND I CAN'T DO THIS PLEASE HELP ME!!!

Data from 200 flights were collected. The flights were categorized as domestic or international and late or not late. Is there an association between international flights and a flight being late?


Find the relative frequency of a flight being late among international flights.

Answers

Answer: There is NO correlation between international flights and a flight being late.

Step-by-step explanation:

See attachment for rationale and step by step.

3.24 as a simplified fraction with 4 repeating

Answers

3.24 as a simplified fraction with 4 repeating is 146/45.

What is fraction?

A fraction represents a part of a whole or, more generally, any number of equal parts.

Let x represent the value of the number.

So,

x= 3.2[tex]\bar4[/tex]

Multiplying both side by 10 we get

10x = 32.44...

Subtracting both above equations

10x -x = 32.44..-3.244..

9x= 29.2

x= 29.2/ 9

x= 146/45

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Final answer:

3.24 with the digit 4 repeating can be converted into the simplified fraction ⅔, which is equivalent to 3 ½.

Explanation:

The student is asking how to express the decimal 3.24 with the digit 4 repeating as a simplified fraction. The repeating decimal can be represented as 3.244444... or 3.24 bar.

To convert this repeating decimal to a fraction, we first denote x = 3.24. To eliminate the repeating part, we can multiply x by 100 to shift the decimal two places to the right, getting 100x = 324.44. Then, we subtract the original equation from this new equation (100x - x) to remove the repeating decimal. This results in 99x = 321, which simplifies to x = ⅔ or x = 3 ½ in fraction form. Therefore, 3.24 bar as a simplified fraction is ⅔.

Suppose chocolate costs $17.60 per kilogram. Karega buys 25 grams of chocolate and Samadhi buys 100 grams of chocolate.


How much more did Samadhi pay for her chocolate?



$0.44


$1.32


$2.20


$2.64

Answers

Answer:
$1.32

Explanation:
For 25 grams it costs $0.44 and for 100 grams it costs $1.76 so Samadhi payed $1.32 more than Karega.
Final answer:

Samadhi paid $1.32 more than Karega for her chocolate.

Explanation:

The subject of this question is in Mathematics, specifically it involves unit conversion and arithmetic calculations. We know that chocolate costs $17.60 per kilogram. But Karega and Samadhi are buying chocolate in grams which means we need to convert the cost from kilograms to grams. 1 kilogram is equal to 1000 grams. So, cost of chocolate per gram = $17.60/1000 = $0.0176.

Karega is buying 25 grams of chocolate, so the cost = 25 * $0.0176 = $0.44. Samadhi is buying 100 grams of chocolate, so the cost =$0.0176 * 100 = $1.76. To find out how much more Samadhi paid for her chocolate compared to Karega, we subtract Karega's cost from Samadhi's cost which gives $1.76 - $0.44 = $1.32.

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Katelynn bought a used car and it was 5 years old. She purchased it for 10,250, after two years the Kelly Blue book value for her car is $8,075. Determine how much the car was worth when it was first bought by the original owners and determine what the depreciation rate is. Hint: Remember these are exponential equations of the form y=abx.

Answers

Answer:

a) rate of depreciation is 11.24%

b) original price of car = $18605.33

Step-by-step explanation:

The formula to apply is;

current price= original price *(1-r)^n where r is the rate of depreciation as a decimal and n is the time period

a) Find the rate of depreciation given that ;

The car was bought at $10,250 when it was 5 years old

After 2 years, the value was $8,075

Apply the formula ;

current price= original price *(1-r)^n

8,075=10,250* (1-r)²

8,075/10250 = (1-r)²

0.78780487804 =(1-r)²

√0.78780487804 =(1-r)

0.88758373016 = 1-r

r=1-0.88758373016

r=0.11241626983 ⇒ 11.24%

b) When the car was first bought, the price was;

Apply the formula;

current price= original price *(1-r)^n

10,250 =original price * (1-0.1124)⁵

10,250=O.P *(0.5509)

10,250/0.5509 = original price

$18605.33= original price

a town has 35,000 registered voters. a random sample of 500 voters finds that 125 of them are in favor of a new dog park. how many are to are likely to vote for the dog park. write a proportion to represent this problem or explain your reasoning.

Answers

Answer:

8750 registered voters

Step-by-step explanation:

Kindly refer to the attached image for explanations

Mark is pitching a tent he ties a rope from a nail to the top of the tent what is the length of the rope between the nail and the top of the tent

6
7
12
14

Answers

i believe that it is 7

What is the name of the relationship between 1 and 4?


Two horizontal parallel lines cut by a diagonal transversal. Angles 1 and 3 are on the left-hand side of the transversal and the interior of the parallel lines. Angles 2 and 4 are on the right-hand side of the transversal and the interior of the parallel lines.

Answers

Answer:

Angles 1 & 4 are alternate interior angles.

The correct name for the relationship between angles 1 and 4 in the given scenario is that they are corresponding angles.

When two parallel lines are cut by a transversal, the following relationships exist between the angles formed:

1. Corresponding angles are equal. These are the angles that are in the same relative position at each intersection where a straight line crosses two others. In this case, angle 1 corresponds to angle 4 because they are both above the parallel lines and on the same side of the transversal.

2. Alternate interior angles are equal. These are the angles that are inside the parallel lines and on opposite sides of the transversal. Angle 3 would be the alternate interior angle to angle 1, not angle 4.

3. Alternate exterior angles are equal. These are the angles that are outside the parallel lines and on opposite sides of the transversal.

4. Consecutive interior angles (also known as same-side interior angles) are supplementary. These are the angles that are on the same side of the transversal and inside the parallel lines.

Since angle 1 and angle 4 are in the same relative position at each intersection (both are above the parallel lines and on the same side of the transversal), they are corresponding angles. Therefore, if the lines are parallel, angle 1 is equal to angle 4.

Trigonometric ratios in rig triangles pls help

Answers

Answer:

c 21 / 29

Step-by-step explanation:

with reference angle α

base (b) = 21

hypotenuse (h) = 29

Now

cos α = b/h

= 21/ 29

Hope it will help you :)

Answer:

The answer is C) 21/29

 The formula for cosine is: adjacent side divided by the hypotenuse (adj/hyp) so 21/29

 Hope it help and good luck!

Step-by-step explanation:

Pleaseee helppp with my online school

Answers

Answer:

it can be a triangle and a rectangle

Step-by-step explanation:

Answer:

triangle and an rectangle

Step-by-step explanation:

What is the minimum value

3.0

0

4.7

2.3
Hurry
Help

Answers

Answer:

3.0 i think

Step-by-step explanation:

Answer:

It would be 0. (Choice B)

Step-by-step explanation:

This is because it is the lowest point on the box and whiskers plot.  

What is the solution of
X-4 +5=2?
O x=-17
O x=13
x = 53
no solution

Answers

The solution of the Equation is x = 1.

What is Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

We have the Equation:

x - 4 + 5 = 2

Now, solving for x we get

x + 1= 2

Now, subtract 1 from both side we get

x+ 1 -1 = 2 - 1

x = 1

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