(x + 1)3 − x (x − 2)2 − 1

When Point Q is on line segment PR, if PQ=x,QR=6, and PR =2x-10, then the length of PR is 18 units

Given,

That point Q is on line segment PR

The length of PQ = x

The length of QR = 6

The length of PR = 2x-10

We know,

Point Q is on line segment PR

So, the length of the PR = Length of PQ + Length of QR

Substitute the values in the equation

2x-10 = x+6

2x-x=6+10

x=14

Substitute the value of x in the equation of the length of line PR

PR= 2x-10

=2×14-10

=28-10

=18 units

Hence, when Point Q is on line segment PR, if PQ=x,QR=6, and PR =2x-10, then the length of PR is 18 units

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By factor decomposition and algebra properties we conclude that the fraction 42 / 49 is equivalent to the fraction 6 / 7.

According to the statement, we have the equation of a fraction and we need to find the expression by simplify the former expression. In this situation we must use factor decomposition and algebra properties to make simplification effective:

42 / 49                           Given

(2 × 3 × 7) / (7 × 7)          Factor decomposition

(2 × 3) / 7 × (7 / 7)           Commutative and associative properties / Multiplication of fractions

6 / 7 × 1                           Definition of division / Existence of the multiplicative inverse

6 / 7                                 Modulative property / Result

By factor decomposition and algebra properties we conclude that the fraction 42 / 49 is equivalent to the fraction 6 / 7.

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The diameter is 18 inches.

It should be noted that the area of a circle is represented by πr². This will be:

πr² = 254.34

(3.14 × r²) = 254.34

3.14r² = 254.34

r² = 254.34/3.14

r² = 81

r = ✓81

r = 9

Therefore the diameter will be:

= 2 × radius

= 2 × 9

= 18

The diameter is 18 inches.

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Answer:

The diameter is 18 inches.

Step-by-step explanation:

Area of a circle formula:

A=πr2 (Area equals pi times radius squared)

254.34/3.14  (3.14 substituted for pi)

=81

square root of 81

=9

9x2

=18

Therefore, the diameter is 18 inches.

Answer:

C. [tex] \frac{ - 15x - 53}{ {x}^{2} + 8x + 15 }≥ 0[/tex]

Step-by-step explanation:

See attached image for explanation

Answer:

5 miles

Step-by-step explanation:

distance = rate times time

distance = (10 miles per hour)( 30 minutes)  30 minutes is equal to 1/2 hour

distance = [tex]\frac{10 miles}{hour}[/tex] [tex](\frac{1 hour}{2} )[/tex]  You can cancel words, like like cancelling numbers  The hours cancel out and you are left with [tex]\frac{10 miles}{2}[/tex]  which is equal to 5 miles.

Answer: 5 miles

Step-by-step explanation:

Jim runs 10 miles per hour, and 30 minutes is half an hour, so divide 10 by 2.

the variable(s) x have a value of 13.

A variable is any property, amount, or number that can be measured or counted. A data item is another name for a variable. Age, sex, business income and expenses, place of birth, capital expenditures, class grades, eye color, and car kind are only a few examples of variables.

A variable is a value that could change based on the details of an experiment or the parameters of a mathematical problem. A variable is typically identified by a single letter. The letters x, y, and z are the universal symbols for variables that are most frequently employed.

According to given value ;

4x+(7x+37)=180

sum of three angle equal to 180

4x+7x+37=180

4x+7x=180-37

11x=143

x=143/11

x=13

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After you depart jblm you will be the closest to mt. rainier after 4 minutes 35.5 seconds

The distance from JBLM to Mt. Rainier is found using the Pythagorean theorem:

 d = √((56 km)² +(40 km)²) = 8√74 km

The bearing from JBLM to Mt. Rainier is ...

 arctan(40/56) ≈ 35.538°  . . . . .  south of east

The heading of the airplane to its destination is ...

 arctan(289/218) ≈ 8.393°  . . . . .  south of east

Then the difference between these angles is ...

8.393° - 35.538° ≈ -27.145°

and the distance to the point of closest approach is ...

 8√74×cos(-27.145°) ≈ 61.238 . . . . km

The relation between time, speed, and distance is ...

 time = distance / speed

Then the time from JBLM to the point of closest approach is ...

 time = (61.238 km)/(800 km/h) ≈ 0.07654819 h ≈ 4.5928 minutes

≈ 4 minutes 35.5 seconds

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Answer:

no

Step-by-step explanation:

i don't think he is correct because it's asking whats the difference between the two

Answer: PLSSSS HELP MEEEE

Step-by-step explanation:

The ratio of the area of the smaller square to the area of the larger square, that have a perimeter ratio of 2:7 is 4:49

According to the given question.

The perimeters of two squares are in the ratio 2 : 7

The perimeter of a square of side x is 4x

The comparative length of the side of each square are 2/4 and 7/4

And, the comparative area are

(2/4)² and (7/4)²

Therefore, the ratios of the areas of the area of the smaller square to the area of the larger square

(2/4)² : (7/4)² = 1/4 : 49/16

⇒ 16×1/4 : 16×49/16

⇒ 4:49

Hence, the ratio of the area of the smaller square to the area of the larger square is 4 : 49

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The bat colony will cover an area of 80,000 square miles in 1.612 hours.

A circle is the collection of all the points together in plane that are equally distant from the a given point known as the circle's center. A circle is represented by the symbol. A radius of a circle is a line segment that connects the center of a circle toward any point on the circle.

Now, as per the given question;

The area covered (A) by the colony, evaluated in square miles, is depicted by the mentioned geometrical formula as the bat colony emerges from a cave & spreads out in a circular pattern:

A = π R²

R = the bat's distance from the cave, calculated in miles.

Furthermore, each bat moves at a constant speed, and distance is depicted by the following kinematic formula:

R = r₀ + rΔt

r₀ = The bat's initial distance from the cave, estimated in miles.

r = Bat speed, estimated in miles per hour.

Δt = Time, expressed in hours.

Substitute the value of R in the formula of area.

A = π (r₀ + rΔt)²

(r₀ + rΔt)² = A/ π

(r₀ + rΔt) = √(A/ π)

rΔt = √(A/ π) - r₀

Δt = (√(A/ π) - r₀)/r

r =  99 miles per hour

The distance between the bat and the cave has now been substituted, and time has been cleared:

A = area of 80,000 square miles

π = 3.14

r₀ = 0 miles per hour

Substituting all the values in the A we calculate the time.

Δt = (√( 80,000/3.14) - 0)/99

On solving;

Δt = 1.612 (approx)

Thus, It will take 1.612 hours for the bat colony to cover an area of 80,000 square miles.

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The complete question is-

The Brazilian free-tailed bat can travel 99 miles per hour. after sunset, a colony of bats emerges from a cave and spreads out in a circular pattern. how long before these bats cover an area of 80,000 square miles? use pi = 3.14.

i think the answer is 3/10

Answer 5795

Step-by-step explanation:

Answer:

A. 6(7 +12)

You need to add the numbers in the parenthisis. Then, multiply 6 with the number.

The number is 5, the equation used is [tex]x^{2}[/tex] - x - 20 = 0

Let x be the number which is between 1 to 10.

From the question we get to know the equation:

(x-3)(x +2) = 14

x(x+2) -3(x+2) =14

[tex]x^{2}[/tex] +2x -3x - 6 =14

[tex]x^{2}[/tex] - x - 6 =14

[tex]x^{2}[/tex] - x - 20 = 0

This is the equation used to solve for Kevin's number.

Now we have to find the value of x.

[tex]x^{2}[/tex] - 5x + 4x -20=0

x(x-5) + 4(x-5) = 0

(x-5)(x+4) = 0

x = 5, -4

Hence we get two values of x which is 5, -4. But we have to find the number between 1 and 10.

Hence from the value of 5 and -4 , the number is 5 which is between 1 and 10 as -4 is not in the range of 1 to 10.

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The complete question is:

a number from 1 to 10. the product of 3 less than this number and 2 more than this number is equal to 14. which equation could be used to solve for kevin's number, x?

a) [tex]x^{2}[/tex]- x - 6 =0

b) [tex]x^{2}[/tex] - x - 20 = 0

c) [tex]x^{2}[/tex]- 6x + 14 =0

d) [tex]x^{2}[/tex] - x + 8 = 0

$23.2

First Multiply 2.12 by ten to get 21.2, and then we multiply 0.20 by ten to get 2 and then we add both to get 23.2

The area of the cover require by Justina to cover the pool is 314 ft²

What is the Area of a circle ?

In geometry, the area enclosed by a circle of radius r is πr². Here the Greek letter π represents the constant ratio of the circumference of any circle to its diameter, approximately equal to 3.14159.

Given,

Diameter, d = 20 ft

radius, r = d/2 = 20/2 = 10 ft

Area of a circle = [tex]\pi[/tex]*r² = 3.14*10*10

= 314 ft²

Therefore, The area of the cover require by Justina to cover the pool is 314 ft².

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The method of factoring

x^(-1/2) (x + 5)(x + 2)

[tex]10x^{-1/2} + 7x^{1/2} + x^{3/2} = x^{-1/2} (10 + 7x + x^{2} )\\ = x^{-1/2} (x + 5)(x + 2)[/tex]

The method of factoring is critical to the simplification of many algebraic expressions and is a useful device in fixing higher diploma equations. In truth, the process of factoring is so crucial that little or no of algebra beyond this point can be done without information it.

In earlier chapters the difference among phrases and factors has been stressed. You should take into account that phrases are introduced or subtracted and elements are expanded. 3 important definitions follow.

terms arise in an indicated sum or difference. elements arise in an indicated product.

An expression is in factored shape only if the entire expression is an indicated product.

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6x-5y=30. Answer Hope it helps

Answer:

See below

Step-by-step explanation:

[tex](5^{4})^{2}[/tex]

[tex]5^{3}[/tex] [tex]5^{5}[/tex]

[tex]5^{1}[/tex] [tex]5^{0}[/tex] [tex]5^{7}[/tex][tex]5^{8}[/tex]

Answer:

10/3 ( width)

Step-by-step explanation:

the length of a rectangle is twice the width if the perimeter is 20 cm find the width

we can solve with an equation

(2x + x) * 2 = 20

3x * 2 = 20

6x = 20

x = 20 : 6

x = 10/3 ( width)

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

check                      Remember PEMDAS

(10/3 * 2 + 10/3) * 2 = 20

(20/3 + 10/3) * 2 = 20

30/3 * 2 = 20

60/3 = 20

20 = 20

the answer is good

The numbers 7 and 14, 28 and 7 have the greatest common factor. The correct options are A and B.

The largest factor of the two numbers which divides both the numbers is called as greatest common factor or GCF. In other words, the greatest common factor is the largest positive number which can be divided into given numbers evenly.

Given the number is 7 the pair of numbers having the greatest common factor is calculated below:-

For pairs 7 and 14. Both the numbers are the multiple of 7 it can be divided by 7. The greatest common factor will be 7 for pairs 7 and 14.

Similarly for pairs 7 and 28. Both the numbers are the multiple of 7 it can be divided by 7. The greatest common factor will be 7 for pairs 7 and 28.

Therefore, the numbers 7 and 14, 28 and 7 have the greatest common factor. The correct options are A and B.

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Answer: B

Step-by-step explanation:

We get the age of Jack is 29 years and the age of Jill is 16 years.

We are given that the sum of Jack's age and Jill's age is 45 years.

Let Jack's age be x.

Let Jill's age be y.

x + y = 45

x = 45 - y

Now, we are also given that jack's age next year will be twice Jill's age last year.

Jack's age next year = x + 1

Jill's age last year = y - 1

ATQ, We get the equation as:

x + 1 = 2( y - 1)

x + 1 = 2 y - 2

x = 2 y - 2 - 1

x = 2 y - 3

We get that:

45 - y = 2 y - 3

2 y + y = 45 + 3

3 y = 48

y = 48 / 3

y = 16 years.

x + y = 45

x + 16 = 45

x = 45 - 16

x = 29 years.

Therefore, we get the age of Jack is 29 years and the age of Jill is 16 years.

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Answer:

he uses 2.33333333333 amount of walnuts in each muffin

Step-by-step explanation:

14 divided by 6 = 2.33333333333

Have a nice day!

Answer: 28 feet

Step-by-step explanation: The ratio of length to width is 2:1. Add the 2 numbers and it will give you 3. Then, divide 84 by 3 and it will give you 28. Times this by 1 (as the ratio of the width is 1). This will give you 28.

The type of correlation not associated with scatterplots is called; an indefinite correlation

Correlation is also called dependence and is defined as any statistical relationship, whether causal or not, between two random variables or bivariate data.

Correlation can only be between -1 and 1 but not outside these values.

The types of correlation that we have to include:

no correlation

positive correlation

negative correlation

Hence the type of correlation not associated with scatterplots is an indefinite correlation

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Complete question is;

Which of the following is not a type of correlation associated with scatterplots?

A. no correlation

B. positive correlation

C. negative correlation

D. indefinite correlation