Simplify each expression. x¹/₂ y⁻¹/₃ / x³/₄ y¹/₂

Answer:

29

Step-by-step explanation:

firat 4 78374748383838

The inverse of the function is x²+8x+13

In mathematics, an inverse function is a arithmetic operator that "reverses" another function: if the function f applied to an input x gives a result of y, then applying its inverse function g to y provides the result x, and contrariwise, i.e., f(x) = y if and only if g = x.

To get the inverse of any function f(x) [ just make sure that it passes the horizontal line test] follow the steps:- Solve for x, i.e separate x in one side and the other terms in the other side, included f(x).-

Swap x and f(x).-

The result is the inverse of the original function .

y=√x+3-4

y+4=√x+3

on squaring with sides we get

y²+16+8y=x+3

y²+8y+13=x

swapping x And y we get y=x²+8x+13

f inverse x =x²+8x+13

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Answer:

[tex]x = 2[/tex]

Step-by-step explanation:

Using the pythagorean theorem in the right triangle:

[tex]1^2 + 2^2 = c^2\\1 + 4 = c^2\\c = \sqrt5[/tex]

Using the pythagorean theorem in the left triangle:

[tex]x^2 + (\sqrt5)^2 = 3^2\\x^2 + 5 = 9\\x^2 = 4\\x = 2[/tex]

The values of x and y that makes quadrilateral ABCD a parallelogram are x = 9 and y = 3

The figure that completes the question is added as an attachment

The opposite sides of a parallelogram are congruent

This means that

5x - 20 = 7x - 38

4y + 11 = 6x - 31

So, we have

5x - 20 = 7x - 38

Collect the like terms

7x - 5x = 38 - 20

Evaluate the like terms

2x = 18

Divide through by 2

x = 9

Substitute x = 9 in 4y + 11 = 6x - 31

So, we have

4y + 11 = 6 x 9 - 31

Evaluate the product

So, we have

4y + 11 = 23

This gives

4y = 12

So, we have

y = 3

Hence, the values of x and y that makes quadrilateral ABCD a parallelogram are x = 9 and y = 3

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The required simplification of rational expression is (4 + x) / (x - 3).

What is a rational number?

Any real number that can be represented in the form of p/q, where q is not equal to 0 is called a rational number. The decimal expansion of rational numbers is terminating and repeating.

Simplifying the rational expression: x² + 2x - 8 / x² - 5x + 6

Given a rational expression,

x² + 2x - 8 / x² - 5x + 6

On simplifying, we get,

For numerator, x² + 2x - 8: (x - 2)(x + 4)

For denominator, x² - 5x + 6: (x - 2)(x - 3)

Now, x² + 2x - 8 / x² - 5x + 6 = (x - 2)(4 + x) / (x - 2)(x - 3)

= (4 + x) / (x - 3)

Restriction is that the denominator, x - 3 should not be 0.

Hence, the required simplification of rational expression is (4 + x) / (x - 3)

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Answer:

0.0068

Step-by-step explanation:

i had this question

Time taken by 3 boys to clean a house is 8 hours.

What is Division method?

Division method is used to distributing a group of things into equal parts.

Now, Time taken by 4 teenagers to clean a house = 6 hours

So, Time taken by 1 boy to clean a house = 4 * 6 = 24 hours

Hence, Time taken by 3 boys to clean a house = 24 ÷ 3

                                                                         = 8 hours.

Therefore, Time taken by 3 boys to clean a house is 8 hours.

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Answer: 8 hours

Step-by-step explanation:

I also do rsm

The least integer greater than each number for log₃38 = 4

All whole numbers and negative numbers are considered integers. This means that if we combine negative numbers with whole numbers, a collection of integers results.

Let y = log₃38

We know, logₐ x = y, only if  [tex]a^{y}[/tex]= x

Therefore, [tex]3^{y}[/tex] = 38

So, we must find an integer y such that [tex]3^{y}[/tex] = 38

[tex]3^{y}[/tex] = 38

(As, 3³ = 27; 3⁴ = 81)

(Since, 3³ = 27 and 3⁴ = 81, the answer will be 3⁴ as 3⁴ > log₃38)

In this case, y = 4 will be the least integer greater than each number to satisfy this equation.

Therefore, the ultimate answer to the equation is log₃38 = 4

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Answer:

Judah's hourly wage is $7/hr.

Step-by-step explanation:

x=(86+12)/14

x=98/14

x=7

Check the picture below.

Answer:

d'accord est-ce moi ou pas la même chose que j'ai fait

Answer:

29.33333... feet per second

Step-by-step explanation:

20×5280=105600 Because 1 mi=5280ft, you multiply 20 by 5280

105600÷60=1760  You divide 105600 by 60 because there are 60 minutes in an hour

1760 ÷ 60  You divide it by 60 again because there are 60 seconds in a minute

Your answer is 29.33333...

Lin knows that there are 4 quarts in a gallon. To figure out how many gallons are in six quarts, she should divide six by four.

This is further explained below.

Generally,  The unitary method is an approach to problem-solving that involves first determining the value of a single unit and then determining the component values by multiplying the value of the single unit by itself.

6 qs=0.25* 6gallons

6=1.5gallons

In conclusion, in order to calculate how many gallons are in six quarts, she needs to divide six by four.

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Answer:

[tex]\begin{aligned} \textsf{a)} \quad & \textsf{Position function}: \quad s(t) = -16t^2+1362 \\ & \textsf{Velocity function}: \quad v(t) = -32t\end{aligned}[/tex]

[tex]\textsf{b)} \quad \overline{v}=-48\:\: \sf ft/s[/tex]

[tex]\begin{aligned}\textsf{c)} \quad v(1) & = -32\:\: \sf ft/s\\ v(2) & = -64\:\: \sf ft/s\end{aligned}[/tex]

[tex]\textsf{d)} \quad t = 9.226\:\: \sf s \:\: (3\: d.p.)[/tex]

[tex]\textsf{e)} \quad v = -292.242\:\: \sf ft/s \:\: (3\: d.p.)[/tex]

Step-by-step explanation:

Given:

[tex]s(t)=-16t^2+v_0t+s_0[/tex]

If v₀ is the initial velocity, and s₀ is the initial position:

[tex]\implies v_0=0[/tex]

[tex]\implies s_0=1362[/tex]

Therefore:

[tex]\begin{aligned}\textsf{Position function}: \quad s(t) & =-16t^2+0+1362\\ \implies s(t) & = -16t^2+1362 \end{aligned}[/tex]

[tex]\begin{aligned}\textsf{Velocity function}: \quad v(t)&=s\:'(t)\\ \implies v(t) &=-32t\end{aligned}[/tex]

Average velocity is the change in displacement divided by the change in time:

[tex]\overline{v}=\dfrac{s(t_2)-s(t_1)}{t_2-t_1}[/tex]

Given interval: 1 ≤ t ≤ 2

[tex]\implies t_1=1[/tex]

[tex]\implies t_2=2[/tex]

Find the values of s(t) at t = 1 and t = 2:

[tex]\implies s(1)=-16(1)^2+1362=1346[/tex]

[tex]\implies s(2)=-16(2)^2+1362=1298[/tex]

Substitute the values into the formula:

[tex]\overline{v}=\dfrac{s(2)-s(1)}{2-1}=\dfrac{1298-1346}{2-1}=-48\:\: \sf ft/s[/tex]

To find the velocity at t = 1 and t = 2, substitute these values into the velocity function found in part (a):

[tex]\implies v(1)=-32(1)=-32\:\: \sf ft/s[/tex]

[tex]\implies v(2)=-32(2)=-64\:\: \sf ft/s[/tex]

The time required for the coin to reach ground level is when s(t) = 0:

[tex]\begin{aligned}s(t) & = 0\\-16t^2+1362 & = 0\\16t^2 & = 1362\\t^2 & = 85.125\\t & = \sqrt{85.125}\\t & = 9.226\: \sf s\:\:(3\:d.p.)\end{aligned}[/tex]

To find the velocity of the coin at impact with the ground, substitute the found value of t from part (d) into the equation for velocity found in part (a):

[tex]\begin{aligned}v(t) & = -32t\\\implies v(\sqrt{85.125}) & = -32(\sqrt{85.125})\\ v & =-295.242\:\: \sf ft/s\:\:(3\:d.p.)\end{aligned}[/tex]

Note: I have used the non-rounded value of t from part (d) for accuracy.

Answer:

2

Step-by-step explanation:

6(6) ÷ ( 2 x 9)

= 36 ÷ 18

=2

Tip:

Use BODMAS whenever order of operations question is there

Bracket

Orders (power, roots, indices)

Division

Multiplication

Addition

Subtraction

The statements about the diagram that can be concluded, includes;

The first statement that cannot be concluded is the option;

[tex] \overleftrightarrow{AB}[/tex]

intersects [tex]\overleftrightarrow{CD}[/tex]

[tex] \overleftrightarrow{AB}[/tex] is on plane T, [tex]\overleftrightarrow{CD}[/tex] is on plane S

[tex]\overleftrightarrow{AB}[/tex] is offset from [tex]\overleftrightarrow{CD}[/tex] by [tex] \overline{BC}[/tex]

Therefore;

[tex]\overleftrightarrow{AB}[/tex] cannot intersect [tex]\overleftrightarrow{CD}[/tex]

The second statement that cannot be concluded is the option;

[tex] \overleftrightarrow{HC} \perp \overleftrightarrow{ CD}[/tex]

The angle [tex] \angle {DCH} [/tex] appears more to be obtuse than 90° such that [tex] \overleftrightarrow{HC} [/tex] cannot be [tex] \perp [/tex] to [tex]\overleftrightarrow{ CD}[/tex]

The third statement that cannot be concluded is the option;

[tex] \overleftrightarrow{FA} \perp \overleftrightarrow{ CD}[/tex]

The reason the above statement cannot be concluded is that [tex] \overleftrightarrow{FA} [/tex] and [tex] \overleftrightarrow{ CD}[/tex] are lines that do not intersect.

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Answer:  20

Step-by-step explanation:

Answer: 440-25h = m

Step-by-step explanation:

She makes 25 dollars per hour (25h=m)

If u subtract the amount that the console costs the equation becomes

440-25=m

Im assuming u are in 7th grade math which is what i was in last year so i hope this helps! :)

Answer: The answers are ll and lll.

Answer:

P = a + b + c

Step-by-step explanation:

A triangle has 3 sides. Perimeter is the measurement of the length around a shape. If you add sides A, B, and C, you will get the perimeter. You can also find a missing side by subtracting two known sides of the triangle if you know the perimeter.

Function operations are the rules we use to solve functions. There is a specific way to deal with function addition, multiplication, and division.

x² + 7x + 5 is the domain of all real numbers.

Function operations are the rules we use to solve functions. There is a specific way to deal with function addition, multiplication, and division.

Let the two functions be f and g then f(x) = 7x + 5 and g(x) = x².

we have to calculate (f + g)(x)

Which is equivalent to:

(f + g)(x) = f(x) + g(x)

Taking the two functions and substituting them into this expression, we get,

f(x) + g(x) = (7x + 5) + (x²)

simplifying the above function, we get

f(x) + g(x) = x² + 7x + 5

Therefore, (f + g)(x) = x² + 7x + 5.

We must also determine the domain of the new function. However, because this is a second-order function with no denominators, logarithms, or roots, there are no restrictions on the value of x; thus, the domain is all real numbers.

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Expression written as a single natural logarithm 3 ln x-2 ln 2 x is [tex]ln(x^{} )[/tex] .

 3 ln x-2 ln 2 x is

= [tex]ln x^{3} - lnx^{2}[/tex]

= [tex]ln(x^{3} /x^{2} )[/tex]

=[tex]ln(x^{} )[/tex]

The inverse of an exponential function, the natural log is the logarithm to the base of the number e. Natural logarithms are unique varieties of logarithms that are employed in the treatment of time and growth-related issues.

The distinction between log and ln is that log is expressed in terms of base 10, while ln is expressed in terms of base e. As an illustration, log of base 2 is denoted by log2 and log of base e by loge = ln (natural log).

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Answer:

90

Step-by-step explanation:

Espero que te ayude :)

Answer:

90

Step-by-step explanation:

1800 x 0.05 = 90

Hope this helps :)

Answer:

Therefore (x,y)=(3,7)

Step-by-step explanation:

put the second equation into the first

x+4=3x-2

x-3x=-2-4

-2x=-6

x=3

plug x=3 into the second equation

y=3+4=7

Answer: I got 48

Step-by-step explanation: to find the length of the larger square, 4+2+2=8, 8x10=80, plus the smaller squares on each side equal to (4x2)x2=16, and 80+16=96. 1/2 of 96 is 48

I hope this helps you! (☞ﾟヮﾟ)☞

Answer:

The correct answer is 48.

Step-by-step explanation:

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