rewrite each expression in simpler terms. you may not use negative exponents
32x^3/ 16x^7

The provided in its extended form logarithms ( log₃2/x).  = 2log3 + log x.

The fact that logs represent exponents gives rise to four fundamental properties. The first three are easy to remember: A product's log equals the total of its elements' logs. The log of a quotient is proportional to the distinction between the numerator as well as denominator logs. Power multiplied by that of the logarithmic of the base equals the log of power.

log₃2/x

Applying the property of log  (log a/b = log a +log b)

log₃2/x

log₃2 + log x

Applying the property (logₐᵇ = a log b)

log₃2

2log3

we get substituting the.(log₃2 + log x)

2log3 + log x

The provided in its extended form logarithms ( log₃2/x).  = 2log3 + log x.

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Answer:

Triangular inequality:  Length of third side must be less than the sum of the lengths of the other 2 sides.

x < 18 + 29

x < 47

so Maximum length of third side is 46 units.

Also 29 < 18 + x

x > 11    so minimum length = 12

Difference  = 46-11 = 35

[tex]\huge\text{Hey there!}[/tex]

[tex]\large\text{If we were to find the difference between the two years you have}\\\large\text{provided you would have to go back (almost like you're going}\\\large\text{back in time). You're going to take the highest year (238 B.C.)}\\\large\text{from the lowest year (15 B.C.) and you should have your equation}\\\large\text{and answer if you did what you were told.}[/tex]

[tex]\large\text{Equation: }\rm{238\ B.C. - 15\ B.C.}[/tex]

[tex]\large\text{Get your number line ready because this will make the equation easier to}\\\large\text{solve.}[/tex]

[tex]\large\text{Start at 238 and go back 15 spaces to your 15 to your left.}[/tex]

[tex]\large\text{If you did the right calculation you should be at: 223}[/tex]

[tex]\huge\text{Thus, your answer can be: \boxed{\mathsf{238\ B.C. - 15\ B.C. }}}\huge\checkmark[/tex]

[tex]\large\text{Remember: \textsf{difference} means subtraction/subtract}[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

The exponent property which must be applied first to simplify the expression as given in the task content is; The power of a power property.

It follows from the task content that the exponent property which must be applied first in a bid to simplify the expression be determined.

Since the expression given is;

(4y)³ • (2g)² • y • g

Consequently, to solve the parentheses, the power of a power property must be used first so that we have;

4³•y³ • 2²•g² • y • g

The expression can then be further simplified by using the the product of a power property on like terms so that the simplified form is therefore;

256g³y⁴.

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[tex]100^{\frac{-3}{ 2} }[/tex] can be simplified into 0.001.

Prime factorization is the process of breaking down a number into its prime factors. Multiplying these prime numbers gives back the original number.

Prime factorization of 100 = 5 x 5 x 2 x 2 = [tex]10^{2}[/tex]

According to the law of indices, if a term with a power is raised to a power, then the powers are multiplied together.

i.e.,[tex](x^{m} )^{n} = x^{mn}[/tex]

According to the given condition,

∴ [tex]100^{\frac{-3}{2} }[/tex] = [tex](10^{2})^{\frac{-3}{2} }[/tex]

Applying the law of indices mentioned above,

[tex]100^{\frac{-3}{2} }[/tex] = [tex](10^{2 X}^{\frac{-3}{2} })[/tex]

= [tex]10^{-3}[/tex] = 0.001.

Thus,  [tex]100^{\frac{-3}{2} }[/tex] can be simplified into 0.001.

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Answer:

= 17

Step-by-step explanation:

If f(x)=3x+2, then replacing x=5 we get f(5)=3x5+2=15+2=17

Answer:

the answer to the equations is 17

Step-by-step explanation:

The probability that only one of the counter is white is 6/11.

So we know that there are 11 counters, 5 of them are white, 6 are not white.

Let's assume that first we take the white one, the probability is equal to the quotient between the number of white counters and the total number of counters, so we have:

p = 5/11

Now for the second one, we don't want to take a white one, so here the probability is equal to the quotient between the number of non-white counters (6) and the total number of counters (now there are 10, because we took one)

q = 6/10

The joint probability is the product of the individual probabilities, this is:

P = p*q

And, also notice that there are 2 permutations:

So we need to add a factor 2.

P = 2*p*q = 2*(5/11)*(6/10) = 6/11

The probability is 6/11

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The option d ,that is , x= 5y is the equation that represents inverse variation between x and y.

1: A mathematical connection between two variables that can be described by an equation in which the sum of their products equals a fixed value.

2: an expression of inverse variation by an equation or function; contrast with direct variation.

In an inverse variation, the inverse percentage establishes the link between two quantities or variables. The inverse relationship between two quantities, x and y, is provided by:

x ∝ 1/y

or

x = k/y

xy = k

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The inequalities and their graphs are;

1)  -x - 5 ≤ -2 is represented by the third graph

2) 6 + x ≤ 3 is represented by the fourth graph

3) x - 4 < -7 is represented by the second graph

4) 2x > -6 is represented by the first graph

1) We are given the inequality;

-x - 5 ≤ -2

Rearranging gives us;

-x ≤ -2 + 5

- x ≤ 3

Divide both sides by -1 to get;

x ≥ -3

The graph must be a closed circle starting at -3 and pointing to the right.

It is the third graph in the link at the end of this answers.

2) We are given the inequality; 6 + x ≤ 3

Rearranging gives;

x ≤ -6 + 3

x ≤ -3

The graph must be a closed circle starting at -3 and pointing to the left. Thus, it is the fourth graph.

3) We are given the inequality; x - 4 < -7

Rearranging gives us;

x < -7 + 4

x < -3

The graph must be an open circle starting at -3 and pointing to the left.

Thus, it is the second graph.

4) We are given the Inequality; 2x > -6

Divide both sides by 2 to get;

x > -6/2

x > -3

It must be a graph with an open circle starting at -3 and then to the right.

Thus, it is the first graph as seen in the attached link

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Answer:

False

True

missing info

missing info

Step-by-step explanation:

2.8mm = 28cm    False since 28 cm = 280 mm

1760 ml < 10 litres     True since 1760 ml = 1.76 l

18g > 0.17    missing units

1.68 = 168cm    missing units

x=0 is an extraneous solution of the equation and x = 8 is not an extraneous solution of the equation.

√(3x+1) - √(x+1) = 2

√(3x+1) = 2 + √(x+1)

Squaring both the sides of the equation

(√(3x+1))² = (2 + √(x+1))²

3x + 1 = (2)² + (√(x+1))² + 2(2) (√(x+1))

3x + 1 = 4 + x + 1 + 4(√(x+1))

3x + 1 = 5 + x + 4(√(x+1))

2x - 4 = 4(√(x+1))

Squaring again on both the side of the equation, we get

(2x - 4)² = (4(√(x+1))²

4x² + 16 - 16x = 16x + 16

4x² - 32x = 0

4x(x - 8) = 0

4x = 0 and x - 8 = 0

x = 0 and 8

Check for Extraneous Solution by keeping value of x in the original equation √(3x+1) - √(x+1) = 2

Let x=0

√(3(0)+1) - √(0+1) = 2

0 ≠ 2

LHS ≠ RHS

x = 0 is an extraneous solution of the equation

Let x=8

√(3(8)+1) - √(8+1) = 2

✓25 - ✓9 = 2

5 - 3 = 2

2 = 2

LHS = RHS

∴ x=8 is not an extraneous solution of the equation.

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Answer:

x=-5nakalimutan ......................

......

Answer:

arccos(439/1976)

Step-by-step explanation:

The largest angle is opposite the longest side. So, by the Law of Cosines, if we let this angle be x,

[tex]x=\arccos \left(\frac{7.6^2 + 5.2^2 - 8.2^2}{2(7.6)(5.2)} \right) \\ \\ =\arccos(439/1976)[/tex]

Using the relation between velocity, distance and time, it is found that the average speed of the record winner of the wheelchair division was of 20.04 miles per hour.

"The record for the Boston Marathon’s wheelchair division is 1 hour,

18 minutes, and 27 seconds.

The Boston Marathon is 26.2 miles long. What was the average speed of the record winner of the wheelchair division?"

Velocity is distance divided by time, that is:

v = d/t.

For this problem, we have that:

Hence the velocity is given by:

v = 26.2/1.3075 = 20.04 miles per hour.

The average speed of the record winner of the wheelchair division was of 20.04 miles per hour.

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According to the distributive property:

[tex] \alpha ( \beta + \gamma ) = \alpha \beta + \alpha \gamma [/tex]

So, applying this to our equation:

[tex]7(x + 3y) = 7 \times x + 7 \times 3y \\ 7(x + 3y) = 7x + 21y[/tex]

Answer:

22°, 79° and 79°

Step-by-step explanation:

Let x  be the vertex angle and y each of the congruent angles.

The sum of all angles =180°

So x + y + y = 180

x + 2y = 180 ·········· Equation (1)

Given "The measure of each of the congruent angles of an isosceles triangle is 9 less than 4 times the vertex angle", the equation is

y = 4x - 9

Substitute for y in terms of x in equation 1

⇒ x + 2(4x - 9) = 180

⇒ x + 8x - 18 = 180

⇒ 9x - 18 = 180

⇒ 9x = 180 + 18

⇒ 9x = 198

⇒ x = 198/9 = 22

So vertex angle is 22°

Substituting for x in Equation 1:
22 + 2y = 180
2y = 180 - 22
2y = 158
y = 158/2
y = 79°

So each congruent angle is 79°

The Nethanel's monthly Social Security benefit is :$ 705.88

What makes the household monthly income of $1,800?

The household monthly income of $1,800 comprises the monthly income and social security of Nethanel Stuck and his wife monthly income from social security which is 70% of Nethanel's

total income=$600+x+(70%*x)

total income=$1,800

Nethanel social security=x

wife's monthly income=70%*x=0.70x

1800=600+x+0.70x

1800-600=1.70x

1200=1.70x

x=1200/1.70

x=Nethanel's monthly Social Security benefit=$ 705.88

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If the length of the rectangle given is larger than the width of the rectangle then the inequality which represents given situation is 13x-9 > 4.5x+8

What is an inequality?

Inequality is a kind of equation which compares two mathematical expressions instead of equating them using relations like less than, greater than, less than or equal to, greater than or equal to.

Given that Victoria drew a diagram of her laptop which is in the shape of the rectangle. The dimension are Length 13x-9 and width 4.5x+8

If the length is given greater than width, then this can be represented by  inequality: length > width

i.e. 13x-9 > 4.5x+8

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The complete question is mentioned below :

Victoria drew a diagram of her laptop that she uses at school. It is in the shape of a rectangle. The dimensions are as follows:

Length: 13x - 9 units

Width: 4.5x + 8 units

If the length is greater than the width, which inequality represents this situation?

Answer:

a) 6 hours

b) 12 hours

c) 36 hours

Step-by-step explanation:

let hours taken to mow lawns = x

baby sit hours = 2x

walk dogs hours = 3(2x) = 6x

x+2x+6x = 54

thus, x = 6

Answer: y=3(x+3)^3-1

Step-by-step explanation:

Using proportions and the percentage concept, it is found that:

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using a rule of three, that can be either direct(cross multiplication) or inverse(line multiplication), deriving from proportional relationships. One example of application of proportions is for percentage problems.

This is because a percentage of an amount a divided by a total amount b is given by the following proportion:

P = a/b x 100%.

From the image, we have that 3 out of 12 apples are of the Jonagold variety, hence:

3/12 x 100% = 0.25 x 100% = 25%.

Each apple in the image is equivalent to 7 apples, hence:

9 x 7 = 63.

63 apples are not of the Jonagold variety.

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Answer:

168.75 km.

Step-by-step explanation:

Distance = speed * time

               = 75 * 2.25

               = 168.75 km.

The translations for each sentence are listed below:

Herein we find nine sentences that must be translated in terms of algebraic expressions, that is, combinations of constants, variables and operators. Now we proceed to present the result of each case:

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Answer:

I think the answer is 234 miles and 78 gallons.

Step-by-step explanation:

Hope this helped :)

Answer:

You didn't show the problem so ill just make it to where you can answer yourself

Step-by-step explanation:

so if he uses 3 gallons per 21 miles just divide 3 by 21(yes 3 by 21)

So 0.142 is used per mile

So because you don't show how many miles he traveled just take the number of miles he traveled and times it by 0.142

Example: 42 x 0.142 = 5.964 which when rounded is 6

The constant of proportionality for the relationship plotted, on the graph is 25 and the distance in 10 seconds is 250

The graph is the given parameter

On the graph, we have the following point

(x, y) = (2, 50)

The constant of proportionality for the relationship plotted, on the graph is represented with k, and the formula is

k = y/x

This gives

k = 50/2

Evaluate

k = 25

Substitute k = 25 in k = y/x

25 = y/x

When x = 10. we have

25 = y/10

This gives

y = 250

Hence, the constant of proportionality for the relationship plotted, on the graph is 25 and the distance in 10 seconds is 250

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The number of pizza left is 1/12

Nicole and Daniel are splitting a pizza

Nicole gets 1/4 of the pizza

Daniel gets 2/3 of the pizza

let 1 represent the total amount of pizza

1- (1/4 + 2/3)

1- 11/12

= 1/12

Hence 1/12 of the pizza is left from the total amount of pizza

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Answer: The value of p(x) = (-2,6) or p(x) = (-2,0)

Step-by-step explanation:

Given that,

p(x) = x^3-4x^2-8x

p(x) = [tex]x^{3}[/tex] - [tex]4x^{2}[/tex] - 8x

and replace with '0'.

x^3-4x^2-8x = 0

Now, factorizing equation is,

(x+2) ([tex]x^{2}[/tex] - 6x) = 0

(x+2) = 0

x= -2

Therefore, x = -2

and,

([tex]x^{2}[/tex] -6x) = 0

([tex]x^{2}[/tex] -6x+0) = 0

using quadratic formula = - [b ± √[tex]b^{2}[/tex]-4ac] / 2a

substitute the values,

a = 1, b = -6 , c = 0

                          p(x) = - [-6 ± √[tex]-6^{2}[/tex]-4.1.0] / 2.1

                           p(x) = - [-6 ± √36-4.1.0] / 2.1

                            p(x) = - [-6 ± √36-(0)] / 2.1

                             p(x) = - [-6 ± √36] / 2.1

                             p(x) = - [-6 ± 6] / 2

                              p(x) = [6 ± 6] / 2

                             p(x) = 3 ± 3

Therefore, p(x) = 3+3 = 6

                  p(x) = 3-3 = 0

So, that we can say the value of p(x) = (-2,6) or p(x) = (-2,0).

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The equity capital the firm raise from this sale is $15 million.

Equity capital refers to the funds paid into a business by investors in exchange for common or preferred stock. It can be solved by subtracting the total liabilities from the total assets.

Equity Capital = Total Assets – Total Liabilities

If a company sold 1 million shares of common stock at $10 book value, then its total liabilities is $10 million.

If the stock price then rose to $25 per share on the New York stock exchange, then the total assets is $25 million.

Equity Capital = Total Assets – Total Liabilities

Equity Capital = $25 million – $10 million

Equity Capital = $15 million

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