Use I=PRT
p=12,000
r=4%
t=3year
find I

The radical expression [tex]\sqrt[5]{x^3}^8.x^4[/tex] simplifies to [tex]x^\frac{44}{5}[/tex].

We know there are two types of radicals one is surds when the number has been raised by such power that it is greater than zero and less than one,

The other type of radicals are indices where a number is raised to such power that is greater than one.

Given, [tex]\sqrt[5]{x^3}^8.x^4[/tex].

= [tex]x^3(^\frac{8}{5}).x^4[/tex].

= [tex]x^\frac{24}{5}.x^4[/tex].

= [tex]x^\frac{24}{5}^{+4}[/tex].

= [tex]x^\frac{24 + 20}{5}[/tex].

= [tex]x^\frac{44}{5}[/tex].

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Answer:1341

Step-by-step explanation:

1342123

Answer:

The rate of change is -2

Step-by-step explanation:

formula we will use: G(x)= [tex]\frac{f(b)-f(a)}{b-a}[/tex]  [-1,2]

g(x)= [tex]x^3[/tex]-5x

g(-1)=[tex]-1^3[/tex]-5(-1)

g(-1)=-1+5

g(-1)=4

g(2)=[tex]2^3[/tex]-5(2)

g(2)=8-10

g(2)=-2

so g(x)= [tex]\frac{(-2)-(4)}{(2)-(-1)}[/tex]

g(x)= [tex]\frac{-6}{3}[/tex]

g(x)=-2

The missing values of the ordered pairs using the given equation are:

x = -1; y = 8

The table is:

x  | y  

-3   8

-1,   2

To find the missing values of an ordered pair that satisfies a given equation, plug n the given value of one of the variables into the equation and solve to find the value of the other variable.

The equation given is y = -3x - 1

Find the missing value of the ordered pair (-3, y) by plugging in x = -3 into the equation given:

y = -3(-3) - 1

y = 8

Find the missing value of the ordered pair (x, 2) by plugging in y = 2 into the equation given:

2 = -3x - 1

2 + 1 = -3x - 1 + 1

3 = -3x

x = 3/-3

x = -1

The ordered pairs are: (-3, 8) and (-1, 2).

Therefore, we would have:

x  | y  

-3   8

-1,   2

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Step-by-step explanation:

your teacher gave you the solution to the real problem of this question : how many cups are in 1 gallon. 16 cups.

and if you remember that a year has 365 days, then the rest is rant simple and straight forward :

8 cups per day

so

365 × 8 = 2920 cups per year.

2920 cups = 2920/16 = 182.5 gallons

therefore, she drinks 182.5 gallons of water per year.

Answer:

Step-by-step explanation:

Answer:$190

Step-by-step explanation:

for an expression is $80+$65+$50=190 per dog to adopt a from the animal shelter.

Answer:

Step-by-step explanation:

457-235= 222

222-125=97

97÷2= 48.5

≈49 pairs of pants and shoes

Two plants will never be of the same height.

Given, the height of an experimental plant after x days can be

represented by the formula 3(4x + 2).

The height of a second plant can be represented by the formula 6(2x + 2).

We have to state that will the two plants ever be of the same height,

Let assume that, the height of two plants be same,

So, 3(4x + 2) = 6(2x + 12)

On simplifying, we get

12x + 6 = 12x + 72

On subtracting 12x from both the sides, we get

12x + 6 - 12x = 12x + 72 - 12x

6 ≠ 72

It is an absurd condition, so we do not have any solution for x.

So, the two plants will never be of the same height.

Hence, two plants will never be of the same height.

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The probability that Pat’s second pick will be a blue marble is the fracion 5/3 considering choosing marbles without replacement.

Probability of an event without replacement simply means once an item is drawn, then we do not replace it back to the sample space before drawing a second item.

For the fact that a red marble was first drawn without replacement with the probability of 55/100, given that there are 55 red marbles and a total of 100 marbles in the Urn.

Hence, there will be 99 samples left for the second draw to be made.

The probability that the second pick will be a blue marble = 15/99.

Therefore, the probability that the second pick is a blue marble after the first pick without replacement is the fraction 5/33 reduced to its lowest term from 15/99.

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The order of reasons that best justifies each step of the equation's solution is as follows;

It follows from the task content that the reasons which best justify each step of the solution be identified.

Therefore; Given the equation; -2(x - 5) = 4x; we have;

Ultimately, the reasons which best justifies each of the steps as required are as provided above.

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Answer:  Justification for each step is provided below.

Step-by-step explanation:

Original Equation: -2(x - 5) = 4x

-2x + 10 = 4x  -->  Distributive property - simplify the left side

-2x + 10 + 2x = 4x + 2x  -->  Addition property of Equality - add 2x to both sides

10 = 6x  -->  Simplifying

10/6 = 6x/6   -->   Division Property of Equality - divide each side by 6

5/3 = x   -->  Simplifying

The evaluated expression of (6x+3y) - z² divide by 2x when x = -3, y = 4 and z = -6 is 5.3

An algebraic expression consists of unknown variables, numbers and arithmetic operators.

Therefore, let's evaluate the expression, (6x+3y) - z² divide by 2x when x = -3, y = 4 and z = -6.

To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number.

In other words, to evaluate the expression, we have to substitute the given value of the variable and simplify the expression.

Therefore,

(6x+3y) - z² = (6(-3)+3(4)) - (-6)² = (-18 + 12) - 36 = -32

2x = 2(-3) = -6

Hence,

- 32 / -6 = 5.3

Therefore,

(6x+3y) - z² / 2x when  x = -3, y = 4 and z = -6 is 5.3

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The number of miles (m) between the two cities as represented in the equation given 2[(4m * 3.5) / 400] = 171.5 is 2450 miles

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an ‘equal’ sign. The most basic and simple algebraic equations consist of one or more variables in math.

In the equation given;

2[(4m * 3.5) / 400] = 171.5

Using changing the subject of formula to find the miles travelled;

2[(4m * 3.5) / 400] = 171.5

28m / 400 = 171.5

28m = 400 * 171.5

28m = 68600

m = 68600 / 28

m = 2450

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The linear equation that passes through the two given points is:

y = (-1/4)*x - 2/4

A general linear equation is written as:

y = m*x + b

Where m is the slope and b is the y-intercept.

If the line passes through two points (x₁, y₁) and (x₂, y₂), then the slope of the line is:

m = (y₂ - y₁)/(x₂ - x₁)

Here we know that the line passes through (-1, -1/4) and (1, -3/4)

Then the slope is:

m = (-3/4 + 1/4)/(1 + 1)

m = (-2/4)/2 = -2/8 = -1/4

the line is:

y = (-1/4)*x + b

To find the value of v we can replace the point  (1, -3/4) so we get:

-3/4 = (-1/4)*1 + b

-3/4 + 1/4 = b

-2/4 = b

The linear equation is:

y = (-1/4)*x - 2/4

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A possible perimeter for the rectangular table that was built by Irene is 50 inches.

My thinking was gotten by getting the dimensions and then using the perimeter formula to solve it.

From the information given, it should be noted that the area of the rectangle is given as 114 square inches. A dimension that can give this is 19 inches and 6 inches

The perimeter of a rectangle is calculated as:

= 2(Length + Width)

= 2(19 inches + 6 inches)

= 2(25 inches)

= 2 × 25

= 50 inches

The perimeter is 50 inches.

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Answer:   6

Step-by-step explanation:   You'll need to substitute x for 12 in the expression, which will be 12 - 2 + 2(4) - 12, and using BODMAS/BIDMAS/PEDMAS (or whatever you use), you should get 6 if you did it correctly.

Answer:

18

Step-by-step explanation:

using bodmas rule by working out brackets first

Answer:

23/5 > (sqrt(18)

Step-by-step explanation:

there are many ways you could go about this,

I subtracted (sqrt(18)) from (23/5) and because the answer i got was greater than 0, 23/5 must be bigger than sqrt18

The point slope equation and slope of some lines are given below

1) For y - 6 = 3(x - 5), slope = 3

2) For  y - 4 = -9(x + 8), slope = -9

3) y - 2 = 5x, slope = 5

4) Point slope equation of line whose slope = -10 and passing through   (1, 4)

   y - 4 = -10(x - 1)

5) Point slope equation of line whose slope = 2 and passing through    (5, -3)

      y  + 3 = 2(x - 5)

6) Point slope equation of line whose slope = [tex]\frac{1}{2}[/tex] and passing through    (-7, -7)

   [tex]y +7 = \frac{1}{2}(x +7)\\[/tex]

What is equation of line in point slope form?

The most general form of equation of line in point slope form is given by [tex]y - y_1 = m(x - x_1)[/tex] , [tex](x_1, y_1)[/tex] is a point on the line

Where m is the slope of the line

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If  [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m = [tex]tan\theta[/tex]

1) y - 6 = 3(x - 5)

  y - 6 = 3x - 15

  y = 3x - 15 + 6

  y = 3x - 9

  Slope = 3

  If x = 0,

  [tex]y = 3 \times 0 -9\\y = -9[/tex]

  (0, -9) is a point on the line

2) y - 4 = -9(x + 8)

   y - 4 = -9x - 72

   y = -9x - 72 + 4

   y = -9x - 68

   Slope  = -9

   If x = 0

   [tex]y = -9 \times 0 -68\\y = -68[/tex]

   (0, -68) is a point on the line

3) y - 2 = 5x

   y = 5x + 2

  Slope = 5

    Putting x = 0

    [tex]y = 5 \times 0 + 2\\y = 2[/tex]

    (0, 2) is a point on the line

4) Slope = - 10

    The line passes through (1, 4)

    Point slope equation

      y - 4 = -10(x - 1)

5) Slope = 2

    The line passes through (5, -3)

     Point slope equation

      y - (-3) = 2(x - 5)

      y + 3 = 2(x - 5)

6) Slope = [tex]\frac{1}{2}[/tex]

      The line passes through (5, -3)

     Point slope equation

       [tex]y - (-7) = \frac{1}{2}(x - (-7))\\y +7 = \frac{1}{2}(x +7)\\[/tex]

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0.8 and 0.80 are equivalent representations of the same value, with the latter including a trailing zero for precision or clarity.

In mathematics, the decimal representation of numbers allows for the use of trailing zeros after the decimal point. When a decimal number has trailing zeros, such as in the case of 0.8 and 0.80, they are considered equivalent because they represent the same value.

The trailing zeros after the decimal point do not change the numerical value of the number. The number 0.8 represents eight tenths, and adding a trailing zero to make it 0.80 does not change its value; it still represents eight tenths. The zero after the decimal point in 0.80 is simply a placeholder, indicating that there are no hundredths or smaller fractional parts.

It is common to use trailing zeros in decimal representations to indicate the precision or accuracy of a measurement. For example, if a measurement is known to be accurate to two decimal places, it is common to represent it as 0.80 rather than 0.8 to indicate the level of precision.

Therefore, mathematically speaking, 0.8 and 0.80 are equivalent representations of the same value, with the latter including a trailing zero for precision or clarity.

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Answer:

224 in²

Step-by-step explanation:

The formula for the area of a triangle is 0.5bh, where b is the base and h is the height. Here the base is '4t' and the height is '7t'. Subbing in 4 for t, we get

Base = 4(4) = 16

Height = 7(4) = 28

Subbing this values into our formula for the area of a triangle, and we have:

Area = 0.5(16)(28) = 224 in²

All the coordinates on the line represent the possible quantities in pounds which she can take to prepare the mixture.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is Birdseed that costs ​$0.67 a pound and sunflower seeds that cost ​$0.97 a pound. Angela​ Leinenbachs' pet store wishes to make a 30 pound mixture of birdseed and sunflower seeds that sells for ​$0.79 per pound.

Assume that she used [x] pound and [y] pound of each type. We can write -

0.67x + 0.97y = 0.79 x 30

0.67x + 0.97y = 23.7

Plot the graph of this function. All the coordinates on the line represent the possible quantities in pounds which she can take to prepare the mixture.

Therefore, all the coordinates on the line represent the possible quantities in pounds which she can take to prepare the mixture.

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A circle is a two-dimensional figure with a radius and circumference of 2 x pi x r.

The area of a circle is given as:

Area = πr²

The total sector of a circle is 360°

The area of the sector of 270° is 37.68 square meters.

A circle is a two-dimensional figure with a radius and circumference of 2 x pi x r.

The area of a circle is given as:

Area = πr²

We have,

The radius of the circle = 4 m

The total sector of a circle is 360°

The area of the sector with 270°.

= (270°/360°) x πr²

= 0.75 x πr²

= 0.75 x 3.14 x 4²

= 37.68

= 37.7 square meters

Thus,

The area of the sector of 270° is 37.68 square meters.

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The distance from Kano to Lagos is 1200 km

The problem involves addition of fractions

The fraction required are:

let the distance form kano to Lagos be x

it was discovered that a driver has travelled 3/8 = 3x/8

another driver had travelled 3/10 of that distance = 3x/10

The drivers are still 390 km apart

total distance, x

x = 390 + 3x/8 + 3x/10

x - 3x/8 - 3x/10 = 390

0.325x = 390

x = 390 / 0.325

x = 1200 km

From the driving distance information 1200 km is the distance from Kano to Lagos

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The x- intercept of the equation is (13,0) and y-intercept of the equation is (0,-39/8) when the equation is 3x-8y=39.

Given that,

The equation is 3x-8y=39.

We have to find the x- intercept and y- intercept of the equation.

We know that,

x/a + y/b = 1 is the intercept form of the line's equation. One of the key types of line equations is this one. In this equation, the sign of the intercepts also enables us to determine where the line is in relation to the coordinate axes.

To find the x- intercept of the equation.

We have to take y as 0.

3x-8(0)=39

3x=39

x=39/3

x=13

To find the y- intercept of the equation.

We have to take x as 0.

3(0)-8y=39

-8y=39

x=-39/8

Therefore, The x- intercept of the equation is (13,0) and y-intercept of the equation is (0,-39/8) when the equation is 3x-8y=39.

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The total amount of money Sam paid for his food, tip for the waitress and sales tax at the Texas Roadhouse is $54

Amount of tip = 15% × $45

= 0.15 × 45

= $6.75

Amount of sales tax = 5% × $45

= 0.05 × 45

= $2.25

Total amount Sam spent at the Texas Roadhouse = Sam's bill at the Texas Roadhouse + Amount of tip for the waitress + Amount of sales tax

= $45 + $6.75 + $2.25

= $54

In conclusion, the total amount of money Sam paid at the Texas Roadhouse is $54

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Answer:

Given

Addition property of equality

Division property of equality

Step-by-step explanation:

The first line is given.

Next 2x was added to each side.  The addition property of equality says that for an equation to stay in balance, it you add something to one side of the equation, you have to add that same thing to the other side of the equation.

The same is true for the division property.

Answer:

The profit from selling 275 shirts is 3,995

Step-by-step explanation:

P= R-C

P=14x- (1,780+7x)

since we are producing 275 shirts substitute that for x

P=14(275)-1,780+7(275)

P=3850-1780+1925

P=2070+1925

P=3995