The sum of two numbers is 21. One number is three less that the other. Find the numbers.

Given

A rectangle is placed inside a circle whose diameter is 13unit all corners of it on the circle.

area of the rectangle = 60 square unit

Find the dimensions of the rectangle.

To proof

As given in the question

rectangle is placed inside a circle whose diameter is 13unit .

now by using the diagram given below

the diagonal of the rectangle is equal to the diameter of the circle.

Thus DB = 13 unit

FORMULA

Area of the rectangle = Length × Breadth

area of the rectangle =  60 square unit

let the value of the length be ( Say AB ) = x

put the value in the above equation

we get

60 = x  × Breadth

[tex]Breadth( say AD)= \frac{60}{x}[/tex]

now in ABD

Using the pythagorus theorem

we get

BD²= AB² + AD²

[tex]13^{2} = x^{2}+ (\frac{60}{x}) ^{2}[/tex]

solving the above equation

we get

[tex]169x^{2}= x^{4} + 3600[/tex]

[tex]x^{4} - 169x^{2}+3600 =0[/tex]  

[tex]x^{4} - 144x^{2} -25x^{2} + 3600 =0[/tex]

[tex]x^{2} (x^{2} - 144) - 25 (x^{2} - 144) =0[/tex]

(x² - 25) (x² -144) =0

The roots are

x = -12 ,-5, 5, 12

-12 and -5 are neglected  because of negative terms .

( Length and breadth of recangle cannot be negative )

thus x = 12 and 5

Two case arise

First case

when

Length of rectangle= 12unit

[tex]Breadth = \frac{60}{12}[/tex]

Breadth of rectangle = 5 unit

Second case

Length of rectangle= 5unit

[tex]Breadth = \frac{60}{5}[/tex]

Breadth of rectangle = 12 unit

Hence proved

Final answer:

To find the dimensions of a rectangle inside a circle with a diameter of 13, we use the Pythagorean Theorem and the area of the rectangle. After substituting values and solving, we find the dimensions are 5 units by 12 units.

Explanation:

To find the dimensions of the rectangle that fits inside a circle with a diameter of 13, one must first recognize that the rectangle forms the sides of a right-angled triangle where the diagonal of the rectangle serves as the hypotenuse of the triangle. This hypotenuse, thus, equals the diameter of the circle, which is 13 units.

Since the area of the rectangle is 60 square units, we let the sides of the rectangle be denoted as length (l) and width (w), with the area equation being l×w = 60.

Using the Pythagorean Theorem, we have: l2 + w2 = 132. We also know that lw = 60, which allows us to solve for one variable in terms of the other. Let's solve for w: w = 60/l. Substituting this into the Pythagorean equation gives l2 + (60/l)2 = 169. Solving this quadratic equation will give us the dimensions of the rectangle that can fit within the circle.

After solving, one finds that the dimensions that satisfy both the area and the Pythagorean Theorem are 5 and 12.

Therefore, the dimensions of the rectangle are 5 units by 12 units.

The product of the expressions 3a + 5 and 6a - 2 is 18a² + 24a - 10. The distributive property is used to multiply each term in the first expression by each term in the second.

The product of the two expressions 3a + 5 and 2a + 4a - 2 can be found using the distributive property. First, combine like terms in the second expression to simplify it to 6a - 2. Now, to find the product, multiply each term in the first expression by each term in the simplified second expression:

Multiply 3a by 6a to get 18a².

Multiply 3a by -2 to get -6a.

Multiply 5 by 6a to get 30a.

Multiply 5 by -2 to get -10.

Combining these products gives you the final answer: 18a² + 24a - 10.

Using a system of equations based on the ratio of baskets made by Mr. McDonagh to Ms. Klein (13 to 2) and the information that Mr. McDonagh made 22 more baskets than Ms. Klein, we determine that Ms. Klein made 4 baskets and Mr. McDonagh made 26 baskets.

To solve how many baskets each person made, we will set up a ratio and use algebra to find the number of baskets made by Mr. McDonagh and Ms. Klein. We are given that for every 13 baskets Mr. McDonagh made, Ms. Klein made 2. Let's denote the number of baskets Mr. McDonagh made as M and the number of baskets Ms. Klein made as K.

According to the ratio, we can write [tex]\frac{M }{ K} = \frac{13 }{ 2}[/tex]. We also know that Mr. McDonagh made 22 more baskets than Ms. Klein, which can be written as M = K + 22. Now we have a system of equations:

[tex]\frac{M }{ K} = \frac{13 }{ 2}[/tex]

M = K + 22

Substitute M in the first equation with (K + 22):

[tex]\frac{K+22 }{ K} = \frac{13 }{ 2}[/tex]

2(K + 22) = 13K

2K + 44 = 13K

44 = 11K

Divide both sides by 11:

K = 4

Ms. Klein made 4 baskets. Now we can find how many baskets Mr. McDonagh made by substituting K back into one of our original equations:

M = 4 + 22

M = 26

Mr. McDonagh made 26 baskets.

The degree of a complete rotation is 360 degrees.

5/6th of a rotation = 5/6 X 360

that is 300 degrees.

Thus the minute hand moves 300 degrees.

(Sorry, I'm not sure about the radians ;-) )

If the minute hand of a clock moves from 12 to 10 ​o'clock, or five-sixths of a complete revolution, by 300 degrees it​ will move.

When two lines or rays converge at the same point, the measurement between them is called an "Angle."

It is given that, the minute hand of a clock moves from 12 to 10 ​o'clock, or five-sixths of a complete revolution.

The degree of a complete rotation is 360 degrees.

5/6th of a rotation it covers,

= 5/6 × 360

=300 degree

Any given angle must be multiplied by π/180 to be converted from the degree scale to the radian scale.

=300 × π/180

=5.235 radians

As a result 5.235 radians, will move.

Thus, if the minute hand of a clock moves from 12 to 10 ​o'clock, or five-sixths of a complete revolution, by 300 degrees it​ will move.

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Actually neither is greater.

these two numbers are equal to each other.

All because 8.720 has an extra number doesn't mean its greater. Because the number place is 0 is gives no significant value and is therefore the same as 8.72.

The bottom line is...

8.72 = 8.720

*(The Answer)*= C. Dilation

*(Explanation)*= If you search than you will find that translation, rotation, and refection or the one that are ridged, however, dilation is.

Answer:

The correct option is 2. A dilation is NOT rigid motion transformation.

Step-by-step explanation:

Rigid motion transformation : A transformation is called a rigid motion transformation if a point or object is moved, but the size and shape remain the same.

In rotation, the point of figure is rotated about the center of rotation but the size and shape remain the same.

Therefore rotation is a rigid transformation and option 1 is incorrect.

In dilation, the figure is stretched of compressed by the scale factor k along the center of dilation, so the size of figure is either increase of decrease.

Therefore dilation  is not a rigid transformation and option 2 is correct.

In translated, the point of figure is shifted but the size and shape remain the same.

Therefore translation is a rigid transformation and option 3 is incorrect.

In reflection, the point of figure is reflected about the line of reflection but the size and shape remain the same.

Therefore reflection is a rigid transformation and option 4 is incorrect.

Answer:

about 105

Step-by-step explanation:

GameStop's total will be 371.00

Best Buy's total will be 337.90

Best Buy will be the better buy

Your answer is Best Buy

Answer:

The best option for buying the Xbox One is GameStop, as the final price would be of $315.35.

Step-by-step explanation:

GameStop: To obtain the price in GameStop, we must first obtain the 15% discount on the price of 350, and subtract it from the initial price. Then, we must calculate the amount of the tax and add it to the price to obtain the final price.

(350 - (350 x 0.15)) x 1.06 = $315.35

Best Buy: Instead, at Best Buy we simply add the sales price tax.

310 x 1.09 = $337.90

Answer:

$99.50

Step-by-step explanation:

Given that only if a minimum balance of 1000 dollars is maintained it will attract high interest.

To enjoy the privilege of high interest, it should be ensured that the balance does not go below 1000 dollars at any point of time.

Keeping the above in mind, we see that

Balance as of now   ..    1053 dollars

Deposit                     ..        44.50 dollars

Balance after deposit  ..   1097.50 dollars

Minimum balance        ..    1000 dollars

Maximum amount

that can be withdrawn   ..  1097.50 -1000 = 97.50 dollars.

one number that could round to 3 100 when rounded is 3 120

The squirrel will collect a total of 252 acorns in the 21 days before the winter storm. This is calculated by multiplying 12 acorns/day by 21 days. Instead of retaliating against a bear, the squirrel should focus on preparing for winter.

If the squirrel collects 12 acorns a day and there are 21 more days until the big winter storm, we can calculate the total number of acorns the squirrel will collect. We do this by multiplying the number of acorns collected per day by the number of days remaining, which gives us:

12 acorns/day × 21 days = 252 acorns

After 21 days, the squirrel will have accumulated 252 acorns more than the original amount she had before the given 21-day period.

Regarding what the squirrel should do to get even with the bear for eating the acorns, it's important to remember that animals in nature often have to deal with challenges like this. The squirrel could focus on collecting more acorns, perhaps finding a better hiding place to store them, to prepare for the winter storm. However, revenge actions, such as retaliating against the bear, are not advisable nor part of natural behaviors in wildlife, and focusing on preparations for winter would be a more practical approach for survival.

10.125 as a percentage is 1012.5%

Answer:

10.125 = 1012.5%

Step-by-step explanation:

[tex]p\%=\dfrac{p}{100}[/tex]

therefore

[tex]a=a\cdot100\%[/tex]

----------------------------------------------

[tex]10.125=10.125\cdot100\%=1012.5\%[/tex]

(2x)(x^2)+(2x)(x)+(2x)(-2)+(3)(x^2)+(3)(x)+(3)(-2)

Simplifying

(2x)(x2) + (2x)(x) + (2x)(-2) + (3)(x2) + (3)(x) + (3)(-2)

Remove parenthesis around (2x)

2x(x2) + (2x)(x) + (2x)(-2) + (3)(x2) + (3)(x) + (3)(-2)

Multiply x * x2

2x3 + (2x)(x) + (2x)(-2) + (3)(x2) + (3)(x) + (3)(-2)

Remove parenthesis around (2x)

2x3 + 2x(x) + (2x)(-2) + (3)(x2) + (3)(x) + (3)(-2)

Multiply x * x

2x3 + 2x2 + (2x)(-2) + (3)(x2) + (3)(x) + (3)(-2)

Remove parenthesis around (2x)

2x3 + 2x2 + 2x(-2) + (3)(x2) + (3)(x) + (3)(-2)

Reorder the terms for easier multiplication:

2x3 + 2x2 + 2 * -2x + (3)(x2) + (3)(x) + (3)(-2)

Multiply 2 * -2

2x3 + 2x2 + -4x + (3)(x2) + (3)(x) + (3)(-2)

Multiply 3 * -2

2x3 + 2x2 + -4x + 3x2 + 3x + -6

Reorder the terms:

-6 + -4x + 3x + 2x2 + 3x2 + 2x3

Combine like terms: -4x + 3x = -1x

-6 + -1x + 2x2 + 3x2 + 2x3

Combine like terms: 2x2 + 3x2 = 5x2

-6 + -1x + 5x2 + 2x3

Answer:

The product is,[tex]-6 + -1x + 5x2 + 2x3[/tex]

explanation:

Simplifying

[tex](2x)(x2) + (2x)(x) + (2x)(-2) + (3)(x2) + (3)(x) + (3)(-2)[/tex]

Remove the parentheses (2x)

[tex]2x(x2) + (2x)(x) + (2x)(-2) + (3)(x2) + (3)(x) + (3)(-2)[/tex]

Multiply [tex]x * x2[/tex]

[tex]2x3 + (2x)(x) + (2x)(-2) + (3)(x2) + (3)(x) + (3)(-2)[/tex]

Remove the closing parentheses (2x)

[tex]2x3 + 2x(x) + (2x)(-2) + (3)(x2) + (3)(x) + (3)(-2)[/tex]

Multiply [tex]x * x[/tex]

[tex]2x3 + 2x2 + (2x)(-2) + (3)(x2) + (3)(x) + (3)(-2)[/tex]

Remove all parentheses (2x)

[tex]2x3 + 2x2 + 2x(-2) + (3)(x2) + (3)(x) + (3)(-2)[/tex]

Rearrange the terms to make multiplication easier:

[tex]2x3 + 2x2 + 2 * -2x + (3)(x2) + (3)(x) + (3)(-2)[/tex]

Multiply [tex]2 * -2[/tex]

[tex]2x3 + 2x2 + -4x + (3)(x2) + (3)(x) + (3)(-2)[/tex]

Multiply [tex]3 * -2[/tex]

[tex]2x3 + 2x2 + -4x + 3x2 + 3x + -6[/tex]

Reorder the terms:

[tex]-6 + -4x + 3x + 2x2 + 3x2 + 2x3[/tex]

Combine like terms: -4x + 3x = -1x

[tex]-6 + -1x + 2x2 + 3x2 + 2x3[/tex]

Combine like terms: 2x2 + 3x2 = 5x2

[tex]-6 + -1x + 5x2 + 2x3[/tex]

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 [tex]\sqrt{m^{4} n^{7} }[/tex]

= [tex]\sqrt{m*m*m*m*m*N*N*N*N*N*N*N}[/tex]

Look for groups of 2 (a group of two on the inside, makes one on the outside)

= [tex]m*m*N*N*N\sqrt{N}[/tex]

= [tex]m^{2} n^{3} \sqrt{n}[/tex]

Answer: C

8.58 , 8.508 , 7.5 , 7.058 :]

Answer: 8.58, 8.508, 7.5, 7.058

(1-52/2+5)=(1-26+5)=(-25+5)=-20

continuing:

-20*2*6*6= -40*6*6=-240*6=-1440

result: -1440

C. The square root of 3 is an irrational number. I hope that this helps!

$50 less each week $200 divided by 4

Myra withdraws the same amount of money from her checking account each week.

In 4 weeks, she withdraws a total of $200.

Let she withdraws t amount from her account each week

Then, 4t=$200

t= $ 200/4

i.e. t= $50

So, amount in her account becomes $50 less each week

i.e. If she had $x in her account

then after w weeks amount in her account will be:

x - 50w

The answer is 7.21.

Randy should attach the end of the light string approximately 7.21 feet from the base of the mast using the Pythagorean theorem, as the distance from the base to the end of the string forms the leg of a right-angled triangle with the mast and the string itself.

To solve Randy's problem, we need to use the Pythagorean theorem, which is applicable because we are dealing with a right triangle formed by the mast, the ground, and the string of lights. The mast is one leg of the triangle, and the string of lights is the hypotenuse. We are trying to find the length of the other leg, which is the distance from the base of the mast to the point where the end of the light string will be attached.

The formula for the Pythagorean theorem is:

a² + b² = c²

Where:

In this scenario, a is the mast with a known length of 12 feet, c is the string of lights with a known length of 14 feet, and b is the distance from the base of the mast we need to calculate.

By substituting the known values into the theorem, we have:

12² + b² = 14²

Which simplifies to:

144 + b² = 196

Subtracting 144 from both sides:

b² = 196 - 144

b² = 52

Then, take the square root of both sides:

b = √52

After calculating, we find that:

b ≈ 7.21 feet

So Randy should attach the end of the light string approximately 7.21 feet from the base of the mast to reach the top.

Answer:

12

Step-by-step explanation:

2 times 2 is 4

4 divided by 2 is 2

2 times 2 is 4

2 times 6 is 12

12 divided by 2 is 6

4 plus 2 plus 6 is 12

The percent of change is 45%.

This can be found, by simply dividing 18, by 40, which would give you 0.45, then multiplying 0.45 by 100, to make it a percentage.

I hope this helps!

f(x) = 2x + 1

To find the inverse, f^-1(x), of the function:

Put the function as an equation:

y = 2x + 1

Then move x to the left and y to the right;

x = 2y + 1

Then solve for y;

y = x/2 - 1/2

f^-1(x) = y

f^-1(x) = x/2 - 1/2

Answer:

its D

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

The correlation coefficients from weakest to strongest negative correlation can be arranged as -0.18, -0.37, -0.52, and -0.82.

The correlation coefficient helps us to know how strong is the relation between two variables. Its value is always between +1 to -1, where, the numerical value shows how strong is the relation between them and, the '+' or '-' sign shows whether the relationship is positive or negative.

Given the correlation coefficients as -0.59 , -0.18 , -0.82 , -0.37. Now, as we know that the number closest to 1 is stronger, while the number closest to 0 is weakest. Therefore, the correlation coefficients from weakest to strongest negative correlation can be arranged as,

-0.18 < -0.37 < -0.59 < -0.82

Hence, the correlation coefficients from weakest to strongest negative correlation can be arranged as -0.18, -0.37, -0.52, and -0.82.

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Answer: (-3,4) and (9,20)

I think these two points will make the answer you have been looking for.

Answer:

Air left in the Tyre after 1 week = 21.36 psi

Explanation:

 Initial psi level = 38 psi

 Psi level after 1 day = 35 psi

 Percentage of remaining of air per day = (35/38)*100 = 92.10%

 Ratio of remaining air per day = 0.921

 Ratio of remaining air after 7 days = 0.921⁷ = 0.562

 Percentage of remaining air after 7 days = 56.21%

 Air left in the Tyre after 1 week = 38*56.21/100 = 21.36 psi

The student's question is about calculating the expected tire pressure at the end of a week, based on a consistent daily percentage decrease from an initial 38 psi to 35 psi. It involves a mathematical analysis using exponential decay, which is a high school level mathematics topic.

The question involves finding the projected tire pressure after a week given an initial pressure of 38 psi that has decreased to 35 psi in one day. The percentage decrease from 38 psi to 35 psi is calculated first, and then this percentage is consistently applied to find the remaining pressure after 7 days using exponential decay since the tire loses the same percentage of air each day.

Step 1: Calculate the percentage decrease.

Initial pressure (yesterday) = 38 psi

Current pressure (today) = 35 psi

Percentage decrease = ((38 - 35) / 38) x 100%

Step 2: Apply this percentage decrease for 7 days using the formula:

Pn = P0 * (1 - percentage decrease)^n

Where:

Pn is the pressure after n days

P0 is the initial pressure

n is the number of days

By calculating P7, we can find the expected pressure at the end of the week.

Step 3: Substitute the known values and calculate the expected pressure after 7 days.

[tex]x+7+14x[/tex]               Take off the parenthesis

[tex]15x+7[/tex]                    Combine Terms

*(Answer)*= [tex]15+7[/tex]

Hope this helps

BangtanBoyScouts

Given equations : Equation A:  4y -3x =16 and

Equation B: -x-8y =3.

We are given a point (-5,0.25) plugging it in first equation

4(0.25) -3(-5) =16

1+15 =16.

16 =16 : Satisfies first equation.

Plugging (-5,0.25) it in second equation.

-(-5)-8(0.25) =3.

5 - 2 = 3.

3=3 : Satisfies first equation.