a phrase that describes a set of real numbers is given. express the phrase as an inequality involving an absolute value. all real numbers x more than 2 units from 0

The expression that is equivalent to the given expression is 3⁶/7¹⁵

From the question, we are to determine the expression that is equivalent to the given expression

The given expression is

[tex]\left(\frac{7^{-3} }{3^{-2} \times 7^{2}} \right)^{3}[/tex]

Simplifying

[tex]\left(\frac{7^{-3} }{3^{-2} \times 7^{2}} \right)^{3}[/tex]

[tex]\left(\frac{7^{-3 \times 3} }{3^{-2 \times 3} \times 7^{2 \times 3}} \right)[/tex]

[tex]\left(\frac{7^{-9} }{3^{-6} \times 7^{6}} \right)[/tex]

= [tex]\left( 7^{-9} \times \frac{1}{3^{-6}} \times \frac{1 }{7^{6}} \right)[/tex]

= [tex]\left( \frac{1}{7^{9} } \times 3^{6} \times \frac{1 }{7^{6}} \right)[/tex]

= [tex]\left(\frac{3^{6} }{7^{9} \times 7^{6}} \right)[/tex]

= [tex]\frac{3^{6} }{7^{9+6}}[/tex]

= [tex]\frac{3^{6} }{7^{15}}[/tex]

Hence, the expression that is equivalent to the given expression is 3⁶/7¹⁵

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Answer:

[tex]8+2z[/tex]

Step-by-step explanation:

[tex]Rule: a\left(b+c\right)=ab+ac\\= 2\left(4+z\right)=2\cdot \:4+2z\\2\cdot \:4+2z\\2\cdot \:4=8\\=8+2z[/tex]

Answer:

Practice with this   https://www.ixl.com/math/grade-8/solve-proportions-word-problems

Step-by-step explanation:

An absolute value inequality that represents all the distances you may be from your house is -14 ≤ x ≤ 14.

Inequality:

Basically, inequality is the relation which makes a non-equal comparison between two numbers or other mathematical expressions.

Given,

You plan on going golfing this weekend with a friend. you can either go to your favorite course which is 14 miles north of your house or to your friends favorite course which is 14 miles south of your house.

Here we need to write an absolute value inequality that represents all the distances you may be from your house.

Consider your house is in the center.

So, both sides you have the Golf course.

So, it can be written as

-14 for north side one and 14 for the south side one.

And let x be the distance between the house and the golf course.

So, it can be written as the inequality,

=> -14 ≤ x ≤ 14.

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The greatest angle in the given triangle is 104 degrees.

Given:

So,

As a result, the second angle has a measurement of 26 degrees.

The first angle's measurement is now 24 degrees greater than the second angle's measurement.

Now,

As a result, the first angle has a measure of 50 degrees.

The third angle is now four times the size of the second angle.

So,

Therefore, the greatest angle in the given triangle is 104 degrees.

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The absolute-value equation to find Jason's max and min speeds is |x| = |55 ± 5| mi/h and the maximum speed is 60 mi/h and the minimum speed is 50 mi/h.

Absolute Value equation:

An absolute value equation in the form | ax + b | has the following properties:

If c < 0 , | a x + b | = c has no solution .

If c = 0 , | a x + b | = c has one solution .

If c > 0 , | a x + b | = c has two solutions .

Given,

Jason is driving his car at 55mi/h he needs to keep his car within 5 mi/h of his current speed.

Here we need to write solve an absolute-value equation to find Jason's max and min speeds.

We know that, the current speed = 55 mi/h

And he want to keep the speeds within 5 mi/h of his current speed.

Let x be the unit that measure the maximum and minimum speed.

So,

The maximum speed.

|x| = 55 + 5 = 60 mi/h

and the minimum speed,

|x| = 55 - 5 = 50 mi/h

So, the absolute value of the equation is,

|x| = |55 ± 5| mi/h

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Answer: y=4

Step-by-step explanation:

If the line is perpendicular to the y - axis and goes through the point (3,4) then it's just y=4

Answer:

=0.0000541

Step-by-step explanation:

[tex]\frac{0.00541}{10^2}[/tex]
[tex]\frac{0.00541}{100}[/tex]
[tex]=0.0000541[/tex]

Answer:0.0000541

Step-by-step explanation:

Firstly, you'll simplify 10².

10²÷0.00541 ---> 100 ÷ 0.00541

Then, you'll divide 100 by 0.00541.

100 ÷ 0.00541 ---> 18484.2883549

Answer:

No

Step-by-step explanation:

like terms are terms which have the same variable , that is

10x and - 5x are like terms, they both have the same variable x

Answer:

-96/7x or 13.714x

Step-by-step explanation:

-4/7+ 2/7x - 14x+4/7

first we do

4/7-4/7 which is zero, so we can cancel those out.

then we do

2/7x-14x ( or you can do -14x+2/7, it’s the same thing

use your calculator to make this easier. if you look you’ll be able to find a fraction button on most

after we do 2/7x-14x , we get -96/7x

if you want it in a fraction just divide and you’ll get -13.714x

The purchase price of a 5-year zero coupon bond will be $768.87.

The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol ‘%’ is used to symbolize it.

Let x be the price before 5 years.

If it is purchased today and has a face value of $1,000. Then we have

(1 + 0.046)(1 + 0.049)(1 + 0.052)(1 + 0.055)(1 + 0.068) x = 1000

(1.046 × 1.049 × 1.052 × 1.055 × 1.068) x = 1000

1.3 x = 1000

x = $768.87

The purchase price of a 5-year zero coupon bond will be $768.87.

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Answer:

252

Step-by-step explanation:

One way we could think about this problem is by grouping the numbers together into pairs: -103+104 would be a pair, -105+106 would be a pair and et cetera up to the pair -199+200.

As you can see, each of these pairs add to 1 (-103+104=1, -199+200=1 etc.), so to solve this problem we can simply find how many of these pairs there are and multiply the number by 1 since each pair will total to 1.

To find how many pairs there are we need to find the number of numbers between 103 and 200 (incl.) and divide it by 2.

200-103= 97 numbers, adding 1 to count the one we started with gives us 98 numbers between 103 and 200 (incl.).

98/2 = 49 pairs of numbers. Since each pair totals 1, 1x49 is the total sum of all these pairs of numbers.

Now we need to address the other two numbers. The sequence started with 101+102 before we looked at the remaining pairs, so to find the sum, we just need to add together 101+102+49.

101+102+49 = 252

Hope this helped!

In linear equation the solution set of the equations x = 1/2, y = -3.

What in mathematics is a linear equation?

Multiply both sides of the equation by a

coefficient -  2(4x - 3y ) = 11 × 2

                     3 ( 10x + 2y ) = ( - 1 ) × 3

apply multiplicative distribution law

8x - 6y = 11 × 2

3( 10x + 2y ) = (-1) × 3

calculate the first terms

8x - 6y = 22

3( 10x + 2y ) = ( -1) × 3

remove the parentheses

8x - 6y = 22

30x + 6y = -3

add up the two equation

8x - 6y + ( 30x + 6y ) = 22 + ( -3)

remove parentheses  - 8x - 6y + 30x + 6y = 22 -3

cancel the unknown variables - 8x + 30x = 22 -3

combine like terms - 38x = 22 - 3

calculate the sum or difference - 38x = 19

reduce the greatest common factor on both

sides of equation - 2x = 1

divide both sides of the equation by the coefficient of variable - x = 1/2

substitute one unknown quantity into the elimination 8 * 1/2 - 6y = 22

reduce the expression to the lowest term 4-6y = 22

reduce the greatest common factor on both sides of the equation

2 - 3y = 11

Rearrange unknown terms to the left side of the equation - 2 - 3y = 11

calculate the sum or difference  -3y = 9

reduce the greatest common factor on both sides of the equation   -y = 3

divide both sides of the equation by the coefficient of variable   y = -3

the solution set of the equations

x = 1/2

y = -3

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Answer:

So bassiccalyy the answer is 3344/3 because it is not equivalent to 4

[tex]6[/tex][tex]x^{12}[/tex][tex]y^{11}[/tex][tex]z^{19}[/tex][tex]\sqrt{5xyz}[/tex]

How do you define the square root of a number?

In mathematics, a square root of a number x is a number y such that y^2 = x; in other words, a number y whose square (the result of multiplying the number by itself, or y ⋅ y) is x. For example, 4 and −4 are square roots of 16, because 42 = (−4)2 = 16.

[tex]\sqrt{180x^{25 } y^{23} z^{39}[/tex]

[tex]180 = 2*2*3*3*5\\x^{25} = x*x*x........*x 25 times\\y^{23}= y*y*y.........*y 23 times\\ z^{39} = z*z*z........*z 39 times[/tex]

we have

square terms comes out

x is 25 times so we can write x as [tex](x^{12})^{2}[/tex] [tex]*[/tex][tex]x[/tex] therefore [tex]x^{12}[/tex] comes out and only left inside is x

similarly [tex](y^{11})^{2}[/tex] [tex]*y[/tex] therefore [tex]y^{11}[/tex] comes out and only left inside is y

[tex](z^{19})^{2} *z[/tex] therefore [tex]z^{19}[/tex] comes out and left inside is z

then the expression become

[tex]6[/tex][tex]x^{12}[/tex][tex]y^{11}[/tex][tex]z^{19}[/tex][tex]\sqrt{5xyz}[/tex]

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Answer:

x = 4       y = 21

Step-by-step explanation:

16x - 23 = 10x + 1

16x - 10x = 23 + 1

6x = 24

24/6 = x

x = 4

16(4) - 23 = 41

41 + (180 - 62) + y = 180

41 + 118 + y = 180

y = 21

Answer:

He will pay $1,050 interest

Step-by-step explanation:

5% interest is paid every year for 3 years

5% * 3(years) = 15%

7000 * 15% = $1,050

$1,050

The spherical tank with a capacity of 750 gallons has a radius of 2.88ft.

Volume refers to the total amount of space an object occupies. It also determines the capacity of the object.

Given the fact that 1 gallon is about 0.1337 ft^3, and the spherical tank has a capacity of 750 gallons, then it's volume or capacity can be converted from gallons to ft^3 by multiplying 750 with 0.1337.

1 gallon = 0.1337 ft^3

750 gallons = 750(0.1337 ft^3)

750 gallons = 100.275 ft^3

To solve for the radius of the spherical tank, use the formula for the volume of sphere given by the formula:

V = 4/3πr^3

where V = 100.275 ft^3

100.275 ft^3 = 4/3πr^3

r^3 = 23.93889288 ft^3

r = 2.882048957ft

Rounding off to the nearest hundredth of a foot:

r = 2.88ft

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Answer:

56247,89

Step-by-step explanation:

The solution to the system of equations is (2.5, -2)

The system of equations is given as:

2x + y = 3

2x - 5y = 15

Subtract the equations to eliminate the variable x

This is represented as

2x - 2x + y - -5y = 3 - 15

Evaluate the like terms in the above equation

So, we have

y + 5y = 3 - 15

Evaluate the like terms in the above equation

So, we have

6y = -12

Divide both sides of the above equation by 6

So, we have

y = -2

Substitute y = -2 in 2x + y = 3

2x - 2 = 3

This gives

2x = 5

Divide by 2

x = 2.5

Hence, the solution to the system of equations is (2.5, -2)

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Approximately 39.26 feet is needed to enclose a circular pond with a diameter of 12. 5 feet.

To fin the circumference:

So,

Therefore, approximately 39.26 feet is needed to enclose a circular pond with a diameter of 12. 5 feet.

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The unit vector is [tex]\left.\pm \frac{1}{\sqrt{17}} \overline{(i}+\overline{4}\right)[/tex].

To find the unit vector:

Differentiate y = x² with respect to x.

We get, dy/dx = 2x.

The slope of a tangent:

[tex]\mathrm{P}(2,4)=\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)_{\mathrm{atP}(2,4)}=2 \times 2=4[/tex]

Tangent P equation is:

y = 4x is the equation of a line passing through the origin O and parallel to the tangent at P.

This line's direction ratios are 1, 4, and 0, and its direction cosines are:

[tex]\pm \frac{1}{\sqrt{1^2+4^2+0^2}}, \pm \frac{4}{\sqrt{1^2+4^2+0^2}}, 0\\\pm \frac{1}{\sqrt{17}}, \pm \frac{4}{\sqrt{17}}, 0[/tex]

The number of unit vectors parallel to the tangent line at P(2,4) is:

[tex]\left.\pm \frac{1}{\sqrt{17}} \overline{(i}+\bar{j}\right)[/tex]

Therefore, the unit vector is [tex]\left.\pm \frac{1}{\sqrt{17}} \overline{(i}+\overline{4}\right)[/tex].

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The correct question is given below:
Find the unit vectors that are parallel to the tangent line to the parabola y=x^2 at the point (2, 4).

The amount of blood that a cylindrical tube hold will be 0.23 cubic dm.

Let r be the radius and h be the height of the cylinder. Then the volume of the cylinder will be

V = π r²h cubic units

A cylindrical tube 14.5 cm high and 4.5 cm in diameter is used to collect blood samples. Then the radius of the cylinder will be

r = d / 2

r = 4.5 / 2

Then the volume of the cylinder will be

V = π r²h

V = 3.14 (4.5 / 2)² × 14.5

V = 3.14 × 20.25 × 14.5 / 4

V = 921.98 / 4

V = 230.5 cubic cm

V = 0.23 cubic dm

The amount of blood that a cylindrical tube hold will be 0.23 cubic dm.

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Answer:

yes hdhdhzbw Ziad uebs U ue susna

The number of students take both AP European History and AP US History is 19 students

A Venn diagram is an illustration of the relationships between and among sets, groups of objects that share something in common.

Let the students take both AP European History and AP US History be x such that;

n(U) = 29 - x + 50 - x

If 60 high school seniors taking AP classes, then n(U) = 60. Substitute to have:

60 = 29 - x + x + 50 - x

60 = 79 - x

-x = 60 - 79

-x =-19

x = 19

Therefore the number of students take both AP European History and AP US History is 19 students

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