Rational exponents; what do i do???

The value of x will be equal to 2.477.

The logarithm is the inverse function of exponentiation in mathematics. That is, the logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised in order to obtain that number x.

The given expression will be solved as follows;-

[tex]5^{x-2}= 8[/tex]

Taking Log on both sides.

[tex]Log_e 5^{x-2}=Log_e8[/tex]

(x-2) Log5 = Log 8

( x-2) = Log8 / Log 5

(x - 2) = Log 8 - Log 5

(x - 2 ) = Log 3

x-2 = 0.477

x  =  2.477

Therefore the value of x will be equal to 2.477.

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Subtraction is a mathematical operation that reflects the removal of things from a collection. The amount by which Rico weighs more than Biscuit is 23.6 kilograms.

Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.

Given Rico weighed 45.7 kilograms, Mocha weighed 15.5 kilograms, and Biscuit weighed 22.1 kilograms. Therefore, the amount by which Rico weighs more than Biscuit is,

Difference = 45.7 kgs - 22.1 kgs = 23.6 kgs

Hence, the amount by which Rico weighs more than Biscuit is 23.6 kilograms.

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Answer: pass 12 fail 12 passes 15 fail1 3

Step-by-step explanation:

pass 12 fail 12

pass 15 fail 13

The speed is the distance covered by an object at a particular time. The speed of the helicopter is equal to 10 kilometer/minute.

The speed is the distance covered by an object at a particular time. Therefore, it is the ratio of distance and time.

[tex]\rm{Speed = \dfrac{Distance}{Time}[/tex]

Given the helicopter travels 30 kilometers in 3 minute. Therefore, the speed of the helicopter is equal to,

Speed = 30 kilometer/ 3minutes = 10 kilometer/minute.

Hence, the speed of the helicopter is equal to 10 kilometer/minute.

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Answer:

6

Step-by-step explanation:

First order them from least to greatest:

1, 3, 6, 7, 9

The median is 6 because it is the middle value.

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Answer:

2

Step-by-step explanation:

The rise is two using the slope formula

rise/run

2/3

2 is the rise

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Answer:

2

Step-by-step explanation:

Remember the rise-run formula

rise ÷ run

The rise is 2, and the run is 3, making this two-over-three.

Usando proporciones, hay que se necessita 8.42 litros de pintura para pintar 1 metro cuadrado de pared.

Una proporción es una fracción de la cantidad total, e puede ser encontrada aplicando una regla de três.

En este problema, se utilizan 9.01 litros de pintura para pintar 1.7 metros cuadrados, por eso, la cantidad relativa a 1 metro cuadrado es dada por:

c = 9.01/1.7 = 8.42 litros.

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Answer:

36960 yards

Step-by-step explanation:

294/14=21

1 gallon is 21 miles

1 mile is 1760 yard

21 miles is 36960 yards

36960 yard is the answer assuming 14 gallons is a full tank of gas

Wealthy Romans relied on servants to run their households.

https://brainly.com/question/16395373

Answer:

The correct answer is Wealthy Romans relied on servants to run their households.

Step-by-step explanation:

I got it right on edge 2022

The regression equation of the data values is y = 2.13x^2 + 0.13x + 6.39

The attached table represents the missing information in the question.

Next, we enter the data values in a graphing technology

Using the graphing technology, we have:

a =2.13; b = 0.13 and c = 6.39

A quadratic regression is represented as:

y = ax^2 + bx + c

So, we have:

y = 2.13x^2 + 0.13x + 6.39

Hence, the regression equation of the data values is y = 2.13x^2 + 0.13x + 6.39

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Based on the function given of y = 2.5x, the true statements are:

The equation y = 2.5x is a proportional relationship because y increases by a certain amount when x increases. That amount is shown by the slope of the line which is 2.5.

For instance, if there is a change of 2 in x, the change in y would be:

= 2.5 × x

= 2.5 x 2

= 5

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Done!

Answer:

[tex]\huge\bold\color{pink}{- Magdonal -}[/tex]

[tex]\blue{\rule{50pt}{999999pt}} \purple{\rule{50pt}{999999pt}} \

\green{\rule{27pt}{999999pt}} \blue{\rule{10pt}{999999pt}} \

[/tex]

The number of acorns that each animal hid is 48

An equation is formed when two algebraic expressions are equated by an equal sign.

It is asked to calculate the number of acorns that each animal hid.

Total number of acorns hid  =  number of acorns hid per tree * number of trees    

Let   T be the number of trees chipmunk used

For chipmunk:    = 3*T

For squirrel:   = 4*(T-4)

 As both the animals hid same number of acorns.

    3T = 4(T-4)      

    3T = 4T - 16      

      16 = T

Therefore the chipmunk hid 16 * 3 = 48 acorns

and the squirrel hid 4(16-4) = 48 acorns.

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Answer: A translation left 3 units and up 6 units

In order to find the translation of a shape in the graph.

Take particular one point from the original shape: (0, 2)

Take particular one point from the translated shape: (-3, 8)

Let the translation be (x, y)

   Original + Translation = Translated Image

This implies the shape has been translated 3 units left and 6 units up.

Answer: 8

Step-by-step explanation:

[tex]\frac{180(n-2)}{n}=135\\180(n-2)=135n\\180n-360=135n\\-360=-45n\\n=\boxed{8}[/tex]

[tex]\huge \boxed{\sf x=2}\\\\\\\displaystyle \sf AC=AB+BC\\\\41=3x-1+14x+8\\\\41=17x+7\\\\Subtracting\ 7\ from\ each\ side \\\\ 41-7=17x+7-7 \\\\ 34=17x\\\\Dividing\ each\ side\ by\ 17 \\\\ \frac{34}{17}=\frac{17x}{17} \\\\ 2=x[/tex]

The dividend per share of common stock is $1.46.

The first step is to determine the total value of the dividends that was paid to the preferred stock holders.

Total value = 400,000 x $0.70 = $280,000

The total value of the common stock dividends = $4,300,000 - $280,000 = $4,020,000

Dividend per share = 4,020,000 /  2,750,000 = $1.46

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Answer:

For Questions 1 , 2 and 3 check the attached diagram

4. How many outcomes are in the event "Toss a tails, spin yellow"? 

There is only one outcome ‘TY’ in this event .

5. What is the probability of tossing tails and spinning yellow?

[tex]p\left( TY\right) =\frac{1}{6}[/tex]

Step-by-step explanation:

Diagram

Answer:

h(x) = 1 / 4x

last choice

Step-by-step explanation:

y = 4x becomes x = 4y

we want to solve for y,

divided both sides by 4

x / 4 = 4y / 4

x / 4 = y

Answer:

[tex]h(x) = \dfrac 14 x[/tex]

Step-by-step explanation:

[tex]y = f(x) = 4x\\\\\text{Replace x with y and then solve for y:}\\\\~~~~~x = 4y\\\\\implies y = \dfrac x4\\\\\implies f^{-1}(x) = \dfrac 14x[/tex]

To solve the problem we must know about the Like terms and expressions.

In mathematics, an expression is a set of numbers, variables, and mathematical operations formed according to rules.

Given ;

[tex]3x(x - 12x) + 3x^2 - 2(x - 2)^2[/tex]

To  solve the algebraic expression,

[tex]3x(x - 12x) + 3x^2 - 2(x - 2)^2\\\\3x(x - 12x) + 3x^2 - 2(x^2 - 4x + 4)\\\\3x(x - 12x) + 3x^2 - 2x^2 + 8x - 8\\\\3x^2 - 36x^2 + 3x^2 - 2x^2 + 8x - 8\\\\-33x^2 + x^2 + 8x - 8\\\\\\-32x^2 + 8x - 8\\[/tex]

To solve the problem we must know about the Like terms and expressions.

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Answer:

C

Step-by-step explanation:

[tex]\frac{25!}{(25-3)!} =13800[/tex]

The ball's maximum height is 30.25 feet.

A quadratic equation in math is a second-degree equation of the form ax² + bx + c = 0. Here a, b, are the coefficients, c is the constant term, and x is the variable.

Given:

h= -16t²+36t+10

Differentiate w.r.t. 't',

h' = -32t+36

When h=0, that will be the maximum height

32t= 36

t= 9/8

t= 1.125 sec.

So, The maximum height is

h(1.123)= -16(1.125)² + 36*1.125+10

h(1.125) = 30.25 feet.

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It looks like you might have intended to say the roots are 7 + i and 5 - i, judging by the extra space between 7 and i.

The simplest polynomial with these characteristics would be

[tex]f(x) = (x - (7 + i)) (x - (5 - i))[/tex]

but seeing as each of the options appears to be a quartic polynomial, I suspect f(x) is also supposed to have only real coefficients. In that case, we need to pair up any complex root with its conjugate to "complete" f(x). We end up with

[tex]f(x) = (x - (7 + i)) (x - (7 - i)) (x - (5 - i)) (x - (5 + i))[/tex]

which appears to most closely resemble the third option. Upon expanding, we see f(x) does indeed have real coefficients:

[tex]f(x) = (x^2 - (7^2 - i^2)) (x^2 - (5^2 - i^2)) = (x^2 - 8) (x^2 - 6) = x^4 - 14x^2 + 48[/tex]

Answer:

C on edge 23

Step-by-step explanation:

because i said so

Answer: Given y=3x-3, find y if x=4

              y=3x-3

              x=4

              y=3(4)-3

              y=12-3

              y=9

Step-by-step explanation: hopes this helps

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Answer:

x=5 and y=7

Step-by-step explanation:

Just substitute in y=x+2 into the equation 5x-4y=-3 to get 5x-4(x+2)=-3 which simplifies to x=5. Substitute x into y=x+2 to find y=7

The amount of plywood needed by Trenton = total surface area of the triangular prism-shaped ramp = 21 ft².

Total surface area of a triangular prism = (perimeter of triangular base × length of prism) + 2(area of triangular base) = (s1 + s2 + s3 × L) + 2(1/2 × b ×h).

The amount of plywood needed to cover the ramp = total surface area of the triangular prism-shaped ramp.

We are given the parameters:

Total surface area of the triangular prism-shaped ramp = (s1 + s2 + s3)L + 2(1/2 × b ×h) = (2 + 1.5 + 2.5)3 + 2(1/2 × 2 ×1.5)

= (18) + (3)

Total surface area = 21 ft²

Trenton will need 21 square feet of plywood.

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Using an exponential function, it is found that her total profit for the first ten years is of $422,426.72.

An increasing exponential function is modeled by:

[tex]A(t) = A(0)(1 + r)^t[/tex]

In which:

In this problem, we have that the initial value and the growth rate are given as follows:

A(0) = 31124, r = 0.06.

Hence the profit function is given by:

[tex]P(t) = 31124(1.06)^t[/tex]

Then, the total profit over the first 10 years is given by:

[tex]\int_{0}^{10} P(t) dt[/tex]

[tex]\int_{0}^{10} 31124(1.06)^t dt[/tex]

[tex]\frac{31124}{\ln{1.06}} \times (1.06)^t|_{t = 0}^{t = 10} = 422,426.72[/tex]

Thus, her total profit for the first ten years is of $422,426.72.

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Answer:

11i+4j

Step-by-step explanation:

add the i's together and the j's together.