A 45° - 45° - 90° right triangle is inscribed in a circle. If the radius of the circle is given, explain how to find the lengths of the right triangle's legs.

The drawing of rectangle that has diagonal twice as long as its width is attached with this.

The equation for the length of the rectangle is l = [tex]\sqrt{3} x[/tex]

Given,

Width of rectangle, w= x

Diagonal of rectangle, d = 2x

We have to find the equation for length of rectangle.

We know that d² = l² + w²

Here,

(2x)² = l² + x²

4x² = l² + x²

l² = 4x² – x²

l² = 3x²

l = [tex]\sqrt{3}[/tex]x

That is the equation for length of rectangle is l = [tex]\sqrt{3}[/tex]x

Lets take width of rectangle, x = 3

Diagonal of rectangle, d = 2 × 3 = 6

L = [tex]\sqrt{3}[/tex] × 3 = 5.20

Here we proved that the equation is correct.

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The number of hours Aisha worked babysitting and landscaping last week is 7.9 hours and 9.9 hours respectively.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

We have been given that Aisha is working two summer jobs, making $7 per hour babysitting and $8 per hour landscaping

Let the number of hours babysitting would be x

And the number of hours landscaping would be y

Last week Aisha worked 2 more hours babysitting than hours landscaping and earned a total of $134.

y = x + 2

7x + 8y = 134

Substitute the value of y = x + 2 in the equation,

7x + 8(x + 2) = 134

7x + 8x + 16 = 134

15x = 134 - 16

15x = 118

x = 118/15

x = 7.9

Substitute the value of x = 7.9 in the equation y = x + 2 ,

y = 7.9 + 2

y = 9.9

Therefore, the number of hours Aisha worked babysitting and landscaping last week is 7.9 hours and 9.9 hours respectively

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Answer:

(x,y)=(10,8)

Step-by-step explanation:

Let x be hours worked babysitting and y be hours worked landscaping.

We would have our first equation, 7x+8y=134.

Knowing that she worked 2 more hours babysitting than landscaping, we can determine and replace the x variable as: x=y+2

7(y+2)+8y=134

Use the distributive property to multiply 7 by y+2.

7y+14+8y=134

Combine 7y and 8y to get 15y.

15y+14=134

Subtract 14 from both sides.

15y=134−14

Subtract 14 from 134 to get 120.

15y=120

Divide both sides by 15.

y=120/15​

Divide 120 by 15 to get 8.

y=8

and since she worked 2 more hours babysitting, x=10.

Let's replace our values in the original equation:

7x+8y=134

7(10)+8(8)=134.

70+64=134.

Therefore, we can conclude that Aisha worked 10 hours babysitting and 8 hours landscaping last week.

Hope this helped!

Answer

.50x + 6

If you need a step-by-step explanation or just the explanation tell me

Answer:

x+2>1

x>1-2

x>-1

now from the set choose ot the numbers which are greater that -1

we find that x=0,1 and 2

Answer:

{0, 1, 2}.

Step-by-step explanation:

x + 2 > 1

x > 1 - 2

x > -1.

So, the solution set is:

{0, 1, 2}

Answer:-10

Step-by-step explanation:

Answer: 4y^2-25

Step-by-step explanation:

Answer:

$346

Step-by-step explanation:

Babysitting = $250

($10 × 25 hrs)

Neighbour's Chores = $96

($8 x 12 hrs)

Total Earning = $346

($250 + $96)

Answer: 7 81 cents

Step-by-step explanation:

yes

The given series is a geometric series. The sum of its first 6 terms is 728.

To determine whether the series is an arithmetic or geometric one, we need to check how the consecutive terms relate to each other.

If it is an arithmetic series, then:

  a(n) = a(n-1) + d

where d is the common difference.

If it is a geometric series, then:

  a(n) = a(n-1) . r

where r is the common ratio.

The given series is:

     2+6+18+ . . . .

and the number of terms is 6.

In the given series:

a(1) = 2

a(2) = 6

a(3) = 18

Notice that

a(2)/a(1) = 6/2 = 3

a(3)/a(2) = 18/6 = 3

Since the ratio of consecutive terms are constant, then the given series is a geometric series. Furthermore, its ratio, r = 3

Sum formula for the first n term of a geometric series is:

S(n) = a(1) .  (rⁿ -1)/(r -1)

Substitute n = 6, a(1) = 2, and r = 3

S(6) = 2 . (3⁶ - 1)/(3 - 1)

S(6) = 2. 364

      = 728

We can also evaluate the sum directly. Write all the terms until n = 6.

a(4) = 18 . 3 = 54

a(5) = 54 . 3 = 162

a(6) = 162 . 3 = 486

Hence, the series is:

2+6+18+54+162+486 = 728

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34 and 49 is  pair of numbers that are relatively prime.

What is relatively prime example?

What do you mean by relatively prime?

34 and 49 is the pair of numbers that are relatively prime.

The numbers have no common prime factors.

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Answer:

D

Step-by-step explanation:

Just did it on T4L

After calling the parents, and explaining them the issue of smashed phone, they travelled at a speed of 2.223 m/s = 8.0028 km/hr

As per the question statement, we are given that we call our parents to explain our issue with having a smashed phone and your parents travel at 20000 meters in 2.5 hours. We are supposed to find out that how fast did the parents rush to get here. Basically we have to find their speed of travelling.

Before solving the question, we must be aware that what is speed.

[tex]speed = \frac{distance}{time}[/tex]

and distance and time should be in SI units.

Given distance = 20,000 meters

Given time = 2.5 hours

[tex]1 hour = 60 min\\2.5 hour = 2.5*60\\2.5 hour = 150 min[/tex]

[tex]1 min = 60 sec\\150 min = 150*60 sec\\150 min= 9000 sec[/tex]

Therefore given time = 9000 sec

Therefore speed = [tex]\frac{distance}{time} = \frac{20000}{9000}[/tex]

Speed= 2.223 m/sec

Hence they travelled at a speed of 2.223 meters per second

2.223 m/s = 8.0028 km/hr

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The required equation is 6x+7=331 and the no. of students traveling on each bus is 54.

A mathematical equation can be defined in a variety of ways. In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. One or more variables are used in the most basic and simple algebraic equations in mathematics.

Given data:

Total no. of students: 331

Number of students on bus = 7

No. of buses = 6

Let the no. of the students on each bus be x.

So according to the given condition,
6x+7=331

6x=331-7

6x=324

x=324/6

x=54

Therefore, the required equation is 6x+7=331 and the no. of students travelling on each bus is 54.

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The rate of interest is 0.26%

Given,

The amount borrowed by Fred to start a new e-commerce business = $13100.

Time of investment = 13 years.

Interest for the money = $3916.90

We have to calculate the rate of interest.

For simple interest, equation is:

P = IRT

Where,

P = Principal amount

R = Rate of interest

I = Interest

T = Time period

Here,

P  = 13100

I = 3916.90

T = 13

Then,

R = P / IT

R = 13100 / (3916.90 × 13)

R = 13100 / 50919.7

R = 0.26%

Therefore, the rate of interest is 0.26%

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If Betsy has a bag with three mint sticks, eight jelly treats, and nine fruit tart chews and she eats one piece every three minutes, the probability her first two pieces will be a fruit tart chew and a jelly treat is 18.9%.

The probability of her first two pieces being a fruit tart chew and a jelly treat can be calculated as follows,

First, we divide the expected outcomes by the total possible outcomes.

Total possible outcomes = 3(mint sticks) + 8(jelly treats) + 9(fruit tart chews) = 20

Hence,

Probability for fruit tart chew: 9 ÷ 20

Probability for jelly treat: 8 ÷ 19 (as one possibility is considered to be fruit tart chew)

The probability of her first two pieces to be fruit tart chew and jelly treat can be determined by multiplying the probability for fruit tart chew with the probability for jelly treat,

Probability = (9/20)(8/19)

Probability = 72/380 = 0.189

Converting into percentage,

Probability = 0.189 × 100 = 18.9%

Hence, the probability that her first two pieces will be a fruit tart chew and a jelly treat is equal to 18.9%.

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Answer:

Here are the answers!

Step-by-step explanation:

When there are two angles on a line that are touching you can subtract what you know from 180° (Ex: 138° and angle 4)

The angles across from each other are the same.

The total of all three angles in a triangle should be 180°

He played 7480 minutes across three years.

The information provided, expressed in minutes per year, is as follows:

The first year is 2181 minutes, the second is 2583 minutes, and the third is 2716 minutes.

Add that now to determine the total amount of time:

The sum of the three years is 7480 minutes (2181 + 2583 + 2716).

The gamer used 7480 minutes throughout the course of three years.

The measurement of continuously occurring events is done in terms of time. In hours, seconds, and minutes, it is measured. The well accepted established formulae can be used to compute it.

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Answer:

[tex]2 \sqrt{45} [/tex]

Answer: (1) y= 2*4-1

(2) y= 2*0-1

Step-by-step explanation:(1) y=8-1

y=7

(2) y=0-1

y= -1

Answer:

4

Step-by-step explanation:

2+2=4

The exact length of the line segments whose endpoints are (10, 1) and (9, -4) is √37

The points are given as (10, 1) and (9, -4)

The exact length of the line segments whose endpoints are (10, 1) and (9, -4) is calculated as

d = √[(x2 - x1)^2 + (y2 - y1)^2]

So, we have

d = √[(10 - 9)^2 + (1 + 5)^2]

Evaluate

d = √37

Hence, the exact length of the line segments whose endpoints are (10, 1) and (9, -4) is √37

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The equation of the line in slope-intercept form is y = (-2)x + (-3)  .

The equation of a line in slope-intercept form can be written as follows,

y = mx + c                                                       equation 1

m in the above equation represents slope of the line and c represents the intercept.

The given equation is 3y + 9 = -6x .

To get the equation of the line in slope-intercept form we need to convert the given equation in the format of equation of a straight line i.e., equation1. So, now we will rearrange the given equation as

3y + 9 = -6x

3y = -6x - 9

On dividing both sides of above equation by 3, we will get

y = (-2)x + (-3)                                                 equation 2

On equating equation 1  and equation 2, we will get

Slope of the line = m = -2

Intercept = c = -3

The equation of the line in slope-intercept form is y = (-2)x + (-3)  .      

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The piece of meat has a weight of 1,800g.

So, as the question says allow 30 minutes of cooking to each 450g.

Similarly,

Therefore, the piece of meat has a weight of 1,800g.

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Answer:

1800

Step-by-step-explanation:

The measurement of triangle ΔPQR ≇ ΔXYZ.

So,

To prove: ΔPQR ≅ ΔXYZ

So, we can say that ΔPQR ≇ ΔXYZ.

Therefore, ΔPQR ≇ ΔXYZ.

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Answer:

See explanation

Step-by-step explanation:

2/3 / 5/9=

2/3 * 9/5=      ==> Dividing by a number is basically multiplying by its reciprocal.

(2*9)/(3*5)=

18/15=6/5  ==> The student just switched the numerator and denominator.

Answer:

6/5

Step-by-step explanation:

2/3÷5/9=2/3x9/5=2/1x3/5=6/5

Answer:

yes

yjnujhhhbhhhjhhbhhbhhhjj

The value of x for the quadratic equation is  1.099 or -9.099 .

What is completing the square?

Completing the Square is a method used to solve a quadratic equation by changing the form of the equation so that the left side is a perfect square trinomial .

To solve ax²+bx+c=0 by completing the square:

1.  Transform the equation so that the constant term, c , is alone on the right side.

2.  If a , the leading coefficient (the coefficient of the x² term), is not equal to 1 , divide both sides by a .

3.  Add the square of half the coefficient of the x -term,  to both sides of the equation.

4.  Factor the left side as the square of a binomial.

5.  Take the square root of both sides.  (Remember: (x+q)²=r is equivalent to x+q= ±√ r.)

6.  Solve for x .

According to the question

Quadratic equation by completing the square

x² + 8x = 10  

As we will try to make complete square of left side

for that

we have to add   to both sides of the equation

As

a = 1

2ab = 8

b = 4

x² + 8x + 4² = 10 + 4²

By using the identity (  )

(x + 4)² = 10 + 16

(x + 4)² = 26

x + 4 = ±

x + 4 = ± 5.099  

x = 5.099 - 4

x = 1.099

or

x = -5.099 - 4

x = -9.099

Hence, The value of x for the quadratic equation is  1.099 or -9.099 .

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The area of one of the slices is  54π square inches

The given parameters are

Diameter = 36 inches

Number of slices = 6

The pie represents take the shape of a circle

And the area (A) of a circle using the diameter (d) is

A= π(d/2)^2

Multiply the above area by 1/6 to get the area of a slice of the pie

So, we have

Area = 1/6 * π(d/2)^2

This means that the area of one of the slices is calculated by

Area = 1/6 * π(d/2)^2

Where

d represents the diameter of the pie i.e. d = 36 inches

So, we have

Area = 1/6 * π * (36/2)^2

Evaluate

Area = 54π

Hence, the area of one of the slices is  54π square inches

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A rectangular prism can have a surface area equal to its volume given the dimensions are 9 inches long, 4 inches wide and x inches high, where x is equal to 7.2 inches.

A rectangular prism is a three-dimensional figure with 8 vertices, 12 edges, and 6 rectangular faces.

If the dimensions of a rectangular prism is:

L = 9 inches

W = 4 inches

H = x inches

then the value of its surface area is equal to the value of its volume.

SA = V

2(lw + wh + lh) = lwh

Substitute the values and solve for x.

2(lw + wh + lh) = lwh

2[(9)(4) + 4x + 9x] = (9)(4)x

2(36 + 13x) = 36x

72 + 26x = 36x

10x = 72

x = 7.2 inches

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The value of perimeter of the rectangle is 398, So the length is 177m and breadth is 82m.

The complete length of a rectangle's outside edge is known as its perimeter. The formula P=2l+2w, where l is the rectangle's length and w is its width, determines the perimeter P of a rectangle.

Given the perimeter of the rectangle = 398

perimeter of rectangle = 2 × (L + B)

Length of rectangle = (12x-3)

Breadth of rectangle = (8x+2)

⇒ perimeter of rectangle = 2 × (12x-3 + 8x+2)

⇒ 398 = 2 × (20x - 1)

⇒ 199 = 20x - 1

⇒ x = 200/20

⇒ x = 10

Length = 120 . 10 - 3

Length = 117

Breadth =  8.10+2

Breadth = 82

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Answer:

length = 117

width = 82

Answer: -53

Step-by-step explanation:

-|10-7•5+8•-4+2•2|=

-|10-7•5+8•(-4)+2•2|=

-|10-35+(-32)+4|=

-|-25-32+4|=

-|-25-28|=

-|-53|=

-(53)=-53