the cities portland, oregon; tacoma, washington; and seattle, washington, in respective order, lie approximately in a straight line. the distane from portland to tacoma is 120 miles. the distance from portalnd to seattle is 145 miles. find the distance from tacoma to seattle.

The simplified form of the expression (2⁴)⁻¹ is 1/2⁴ (one over two raised to the power of four).

The integers exponents are the exponents that should be an integer. It can be either a positive integer or a negative integer. In this, the positive integer exponents describe how many times the base number should be multiplied by itself.

An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

It is given that the expression is (2⁴)⁻¹

Now,

using the integer exponent properties,

=> (2⁴)⁻¹  

=> (2)⁴* ⁻¹

=> (2)⁻⁴

=> 1/2⁴

Therefore, the answer is 1/2⁴ (one over two raised to the power of four) derived using the properties of integer exponents.

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Polynomials which have (x-4) as a factor are a. x³ - 13x - 12 = 0 and c. x³ + 6x + 5x - 12 = 0.

An algebraic equation having two or more than two terms is called a polynomial.

According to the given question we have determine which of the following polynomials have (x-4) as a factor.

One way is factoring each of these polynomials.

Another way is given x - 4 is a factor,

∴ x - 4 = 0

x = 4 must satisfy the polynomial which has a factor of (x-4).

Now we have to replace x with 4 in each of the given polynomials and if LHS = RHS then (x -4) is a factor.

a. x³ - 13x - 12 = 0

(4)³ - 13(4) - 12 = 0

64 - 52 - 12 = 0

64 - 64 = 0. (LHS = RHS).

b. x³ + 8x² + 19x + 12 = 0

(4)³ + 8(4)² + 19(4) + 12 ≠0

Here you don't need to calculate further because in LHS sum of these terms won't be zero.

c. x³ + 6x + 5x - 12 = 0.

x³ + 11x - 12 = 0.

64 + 44 - 12 ≠ 0.

d. x³ - x² - 10x - 8 = 0.

64 - 16 - 40 - 8 = 0.

64 - 64 = 0, (LHS = RHS).

e. x² - 4

16 - 4 ≠ 0.

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Answer:

26.2

Step-by-step explanation:

7 + (2x3) 5-6 (9/5)

7 + 6*5-6*1.8

7 + 30-10.8

37 - 10.8

26.2

Based on the fact that Raven is trying to decide between two plumbing services, the costs of the service charge are:

The Service cost for Service provider A is:

= 50 x  1.5 + (50 x ((1.75 / 1.5) - 1)

= $83.33

Service cost for Service provider B is:

= Number of hours x Cost per hour

= 60 x 1.75

= $105

The cheaper plumber is Service provider A.

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Volume is equal to [tex]a^{3}[/tex] where an is the width or length of its edges.

The number of cubic units that a cube totally occupies is determined by its volume. The cubic unit of measurement for the volume of a cube includes [tex]centimetres^{3}[/tex], [tex]metres^{3}[/tex], [tex]inches^{3}[/tex], [tex]feet^{3}[/tex], etc.

A solid three-dimensional figure with 6 square faces or sides is known as a cube. The total amount of space a cube takes up is its volume. The cube's square shape means that all of its sides are square, and as a result, all of its edges would be of equal length. As a result, the cube's length, breadth, or height are all equal.

If a cube's length, breadth, and height are equal to "a," then;

Cube volume = a[tex]\times[/tex]a[tex]\times[/tex]a.

Therefore, Volume of cube is [tex]a^{3}[/tex] where a is the length of the edge.

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For the bucket to hold the 10 litres, then it s said to contains 2.64 gallons.

A multi-step procedure encompassing multiplication as well as division by a mathematical factor is known as unit conversion. We can measure weight, length, and temperature in a variety of ways.

Now, per the given question;

The total amount a bucket contains is 10 litres.

Noe, the conversion of litres in gallons is given as;

1 litres = 0.26 gallons.

Thus, 10 litres = 10×0.264

= 2.64 gallons.

Therefore, the bucket will contain 2.64 gallons.

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Answer:

(-2, 32, -21)

Step-by-step explanation:

You just multiply B by 3 and then subtract the corresponding parts. For example -2 -(0*3). and then 14-(-6*3)

Answer:2

Step-by-step explanation:

Answer:

8 nickels and 14 pennies

Step-by-step explanation:

Let p = number of pennies

Let n = number of nickels

p + n = 22             .01p + .05n =.54

Take the second equation and multiple it through by 100 to clear the decimals.

100(.01p + .05n( = .54(100)

p + 5 n = 54  Multiply this through by -1 so that I can add it to the first equation.

-p  -5n = -54

p + n = 22   Add these together

    -4n = -32  Divide both sides by -4

n = 8  We have solved for n.  We have 8 nickels.

Plug 8 in for n in the first equation and solve for p.

p + n = 22

p + 8 = 22  Subtract both sides by 8

p  = 14  There are 14 pennies.

Check:

p + n = 22

14 + 8 = 22

22 = 22  Checks

.01p + .05n = .54

.01(14) + .05(8) = .54

.14 + .40 .54

.54 .54 check

Greetings from Brasil...

For rotation, we can use the expression:

Let rotate 180° - specifically for this angle, 180°, either counterclockwise or clockwise

SEN 180 = 0 and COS 180 = - 1

V(X; Y) → V'(- X; - Y)

V(0; - 2) → V'(0; - (- 2))

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The minimum wage per hour = $2

Here we need to find the value of minimum wage per hour in 1975

As is given that the earning minimum wage is $80 for working 40 hours.

40-hour work gives = $80

1-hour work gives = $80/40

                             = $2

Therefore the minimum wage per hour in 1975 is $2

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The total cost of the ski weekend comes out to be $250.

Total expenses for just a given period are the sum of all gross cash expenditures and furthermore any pending subsidiary items like operating expenses, reward fees, interest, & taxes.

Some key features regarding the total cost are-

Now, according to the question;

The cost of all spending are-

$50 for transportation

$50 for lodging

$50 for ski lift tickets

$100 for waiter.

Total cost = transportation cost + lodging cost +  ski lift tickets cost + waiter cost.

Total cost = $50 + $50 + $50 + $100

Total cost = $250.

Therefore, the total spending in the ski weekend are $250.

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Answer:

AC = 8

BC = 10

AH = 4.8

Step-by-step explanation:

A = 1/2(AB)(AC)

24 = 1/2(6)(AC)

AC = (24)(2)/(6) = 8

BC^2 = AB^2 + AC^2 = 6^2 + 8^2 = 36 + 64 = 100

BC = 10

A = 1/2(AH)(BC)

24 = 1/2(AH)(10)

AH = (24)(2)/(10) = 48/10 = 4.8

Answer: ( -2, 4)

Step-by-step explanation:

Except for x = 3, the set of x values for that y will become a real number as per Y=8/x-3 contains all real numbers.

A real number is any number which can be found with in real world. Numbers can be found all around us.

Now according to the question;

In actuality, the expression Y=8/x-3 stops producing a real numerical value for y when the denominator has become zero.

When the denominator is zero, the y value is undefined and thus not a real number.

As a result, if we set;

x - 3 = 0

x = 3

Therefore, except for x = 3, the set of x values for which y is a real number per the Y=8/x-3 includes all real numbers.

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The complete question is-

Y=8/x-3

Identify the set of values x for which y will be a real number

Answer:

40.5

Step-by-step explanation:

It takes approximately 55 mins for the sample to decay to one - fourth of its original amount.

In the given statement is:

λ = 2.5 x 10^-2 [tex]min^{-1}[/tex]is the rate constant of the nucleus

To solve this problem, we use

N(t) = [tex]N_{0}[/tex]e^-λt

and since we are looking for the time it takes to decay the nucleus to one -fourth of its original amount, we set

N(t) = 1/4 [tex]N_{0}[/tex] = 0.25[tex]N_{0}[/tex]

We can substitute this in the decay equation:

0.25[tex]N_{0}[/tex] =[tex]N_{0}[/tex] e^-λt

Cancel the like terms

0.25 = e ^-λt

Take the natural logarithm of both sides:

㏑(0.25) =㏑(e^-λt)

㏑(0.25)= -λt

Solve for the time t:

t = - ㏑(0.25)/λ

Substitute the given rate constant :

t = ㏑(0.25) / 2.5 x 10^-2 [tex]min^{-1}[/tex]

t = -1.3863 /2.5 x 10^-2 [tex]min^{-2}[/tex]

t = 55.452mins

It takes approximately 55 mins for the sample to decay to one - fourth of its original amount.

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Answer:

544 miles

Step-by-step explanation:

160 miles= 5 hours in order to see how much she traveled in 1 hour you need to divide so do 160 divided by 5 = 32 then do 32x17 which would be 544.

I hope it helps you!

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Kaylee would travel 544 miles in 17 hours if she continued at the same rate.

A mathematical number is known as distance measures "how much ground an object has traveled" while moving. Distance is defined as the product of speed and time.

distance = rate × time

We know that Kaylee drove 160 miles in 5 hours, so her rate is:

rate = distance / time = 160 miles / 5 hours = 32 miles/hour

Now we can use this rate to find out how far she would travel in 17 hours:

distance = rate × time

distance = 32 miles/hour × 17 hours

distance = 544 miles

Therefore, Kaylee would travel 544 miles in 17 hours if she continued at the same rate.

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Answer:

Step-by-step explanation:

3 3/4 = 15/4

15/4 divided by 3/4 = 5

The function that Ngozi's salary s(t) in dollars, t years after she starts to work as an interpreter is given by [tex]S = 24000 * (1.035)^t[/tex].

What is a function?

You can use the fact that the raise is done on the previous year's salary.

Let the initial salary be P = $24000

After 1 year, her salary increased by R = 3.5% which, thus,

Total salary = P + increment

Similarly going on, we get

[tex]P_t = P(1+ \frac{R}{100})^t = S[/tex] (we can say)

Putting values of P(value of P) and R(value of R), we get

[tex]S = 24000(1 + 0.035)^t = 24000 *(1.035)^t[/tex]

Thus,

The function that Ngozi's salary s(t) in dollars, t years after she starts to work as an interpreter is given by

[tex]S = 24000 * (1.035)^t[/tex]

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Answer: the second one

Step-by-step explanation:

The inequality that represents buying n notebook with a calculator and a maximum amount of $37 to spend:

37 ≥ 2n + 24

Option D is the correct answer.

It is a statement of an ordered relationship

- greater than,

- greater than or equal to,

- less than,

- less than or equal to between two numbers or algebraic expressions.

We have,

Cost of the calculator = $24

Cost of a notebook = $2

Total amount to spend = $37

Number of notebooks = n

The inequality that represents buying n notebook with a calculator and a maximum amount of $37 to spend:

37 ≥ 24 + 2n

The number of possible notebooks to buy:

37  24 + 2n

37 - 24 ≥ 2n

13 ≥ 2n

13/2 ≥ n

6.5 ≥ n

The number of notebooks can be 6 or fewer.

Thus,

The inequality that represents buying n notebook with a calculator and a maximum amount of $37 to spend:

37 ≥ 2n + 24

Option D is the correct answer.

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The trigonometric function that can be used to find the value of x is 12 / tan ( 25 ) . The correct values of a and b will be 12 and 25 resp . .

Given :

A right angle triangle , one angle = 25 ° and side opposite given angle = 12 units .

Trigonometric Formula for Tan θ

tan θ = perpendicular / base , tan θ = ( sin θ / cos θ ) , tan θ = ( 1 / cot θ ) .

where θ = 25 , perpendicular = 12 , base = x .

Substituting values in above first formula ,

tan 25 = 12 / x

Therefore , x = 12 / tan ( 25 ) .

Hence , a = 12 and b = 25 .

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The value of constant v is 3.75 if y varies directly as x and when

x = 8 and y = 30.

Let v be any constant.

According to the given question.

y varries directly as x.

⇒ y ∝ x

⇒ y = vx                    (beacuse v is constant)

Here, it is give that x = 8 and y = 30.

Thereofre, the value of constant v when y = 30 and x = 8 is given by

y = vx

⇒ 30 = v(8)

⇒ 30/8 = v

⇒ v = 3.75

Hence, the value of constant v is 3.75 if y varies directly as x and when

x = 8 and y = 30.

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Answer:

Step-by-step explanation:

the number is y

you are told

y+0.5y=27

Therefore,

1.5y = 27.

If you divide by 1.5 on both sides, you'll get 18 which is your answer.

18+9=27

The function rule for g(x) is g(x) = -4x

The function is given as

f(x) = 4x

The transformation is given as reflection across the x-axis

The rule of this transformation is

(x, y) = (x, -y)

So, we have

g(x) = -f(x)

This gives

g(x) = -4x

Hence, the function rule for g(x) is g(x) = -4x

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Answer:

slope=y2-y1/x2-x1

=-6-(-6)/9-6

=0/3

any fraction in which numerator is 0 is 0.

Answer:

$8.60

Step-by-step explanation:

Let x = the tip

80 - x = 9(5.85 + 1.25) + 5(1.50)

80 -x = 63.90 + 7.5

80 - x = 71.40  Subtract 80 from both sides

-x = -8.60  Divide both sides by -1

x = 8.60

The measure of the speed during the time is 63. 64 miles per hour

The formula for speed is expressed as;

Speed = distance/ time

Given that;

Let's convert the time in minutes to hour

60 minutes = 1 hour

20 minutes = x hour

cross multiply

x = 20/ 60

x = 0. 33 hours

Substitute the values

Speed = 21/ 0. 33

Speed = 63. 64 miles per hour

Thus, the measure of the speed during the time is 63. 64 miles per hour

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