Need help solving this equation by rewriting using the laws of exponents!

The range of the function is {0.01, 0.1, 1, 10, 100}. With an increase in the value of the domain, the range of the function is increasing.

What is a function?

A function from a set X to a set Y allocates exactly one element of Y to each element of X. The set X is known as the function's domain, while the set Y is known as the function's codomain.

Given function is

f(x) = 10^x.

Given domain is {-2, -1, 0, 1, 2}.

Now putting x = -2, -1, 0, 1, 2 in the function f(x) = 10^x.

When x = -2:

f(-2) = 10^(-2)

f(-2) = 0.01.

When x = -1:

f(-1) = 10^(-1)

f(-1) = 0.1.

When x = 0:

f(0) = 10^(0)

f(0) = 1.

When x = 1:

f(1) = 10^(1)

f(1) = 10

When x = 2:

f(2) = 10^(2)

f(2) = 100

The range of the function is {0.01, 0.1, 10, 100}

The values of the range increase with the increase of domain.

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The equation and solution of the problem are 3/8-7/8 and 1/2.

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

Given;

The food parrot eats = 3/8pounds

The food cat eats = 7/8pounds

Now, food eaten more by cat =7/8-3/8

=(7-3)/8

=4/8

=1/2

Therefore, the answer to equation will be 1/2.

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The area of the circle with diameter 6.4 is 32.15 square centimeters.

A circle closed plane geometric shape. In technical terms, a circle is a locus of a point moving around a fixed point at a fixed distance away from the point.

Area of a circle is the region occupied by the circle in a two-dimensional plane. It can be determined easily using a formula:

[tex]A = \pi r^2[/tex]

Given that the diameter of the circle is 6.4 centimeters.

The radius of the circle is thus half of the diameter that is 3.2 centimeters.

The area of the circle is given by the formula:

[tex]A = \pi r^2[/tex]

Substitute the value of r = 3.2 in the formula:

[tex]A = (3.14) (3.2)^2\\\\A = 32.15[/tex]

The area of the circle is 32.15 square centimeters.

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Therefore , the solution to the given problem of slope intercept comes out to be  dy/dx = -1/2.

After you are certain if Y = mx + b, the gradient intercept approach can be employed. By using just one particular point on the line and its slope, the direction form is a way to represent an axiom for a line. The slope is defined as such rise across run and is represented first by point form (x,y), and may be calculated using the slope intercept method, y = mx + b. (0, b). By using just one specific statement on the vector and its slope, the direction form is a technique to write a linear model for a line.

Here,

Given : x² +2xy - 2y² +x =2

thus,

To find the gradient at point (-4,1) :

We have to find the dy/dx

so,

=>  2x + 2y + 2xdy/dx -2ydy/dx +1 =0

=> dy/dx (2x-2y) = -(2x+ 2y) -1

=>dy/dx = -(2x+2y) -1 / (2x-2y)

So , at the point (-4,1)

=> dy/dx = -(-8 + 2) -1 / (-8 -2)

=>dy/dx = 5/-10

=>dy/dx = -1/2

Therefore , the solution to the given problem of slope intercept comes out to be  dy/dx = -1/2.

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The solutions are - X = [5 5; 5 -2] is a nonzero element in W and  Y = [1 1; 1 1] is the element in V that is not in W.

A nonzero element X in W can be any linear combination of the given basis vectors:

X = a[5 5; 5 -2] + b[5 -4; -4 1]

Where a and b are nonzero scalars. For example, X = [5 5; 5 -2] is a nonzero element in W.

An element Y in V that is not in W can be any symmetric 2x2 matrix that cannot be written as a linear combination of the given basis vectors. For example, Y = [1 1; 1 1] is not in W as it cannot be written as a linear combination of [5 5; 5 -2] and [5 -4; -4 1].

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The complete question is -

Let V be the vector space of symmetric 2 Times 2 matrices and W be the subspace W = span{[5 5; 5 -2], [5  -4; -4 1]}. Find a nonzero element X in W. Find an element Y in V that is not in W.

The slope of a given line is m=1.5.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The formula to find the slope of a line is slope = (y₂-y₁)/(x₂-x₁).

The coordinate points of a line are (1, -3) and (3, 0).

Substitute, (x₁, y₁) and (x₂, y₂) in m=(y₂-y₁)/(x₂-x₁), we get

m= (0+3)/(3-1)

= 3/2

= 1.5

Therefore, the slope of a given line is m=1.5.

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Based on the image provided, the actual height of the structure would be 1/975.36.

This refers to a picture or model that is made based on the proportion of an original structure. Most models are smaller than their original.

According to the image, 1 centimeter represents 32 feet of the actual structure, which means there is a 1:32 scale factor, let's calculate then the number of centimeters in total to know the height:

1 foot = 30.48 cm

32 feet = x

x= 30.48 x 32/ 1 = 975.36 cm

Based on this the height can be expressed as  1/975.36.

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A continuous random variable is one that has a range of possible values. In other words, if a random variable adopts a value that fits within a specific range, it is said to be continuous.

Measurements like height, weight, and time are all represented by continuous random variables. A continuous random variable is represented as the area under a density curve. The concept of a continuous random variable, as well as its mean, variance, types, and related examples

P(X < 0.35) = 0.35

P(X = 0.35) = 0 since X is a continuous random variable and the probability of a specific value is 0.

P(0.35 < X < 1.25) = 1.25 - 0.35 = 0.9

P(0.10 < X < 0.20 or 0.6 < X < 0.9) = (0.20 - 0.10) + (0.9 - 0.6) = 0.3

P(X < 0.5 or X > 0.6) = (0.5 - 0) + (1 - 0.6) = 0.9

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The solution to the indices is 50.

Index (indices) is the power or exponent which is raised to a number or a variable. The plural of index is indices. Indices contain constants and variables. The constant is a value which cannot be changed and a variable quantity can be assigned any number or its value can be changed.

Indices are a convenient tool in mathematics to correctly denote the process of taking a power or a root of a number. Taking a power is simply a case of repeated multiplication of a number with itself while taking a root is just equivalent to taking a fractional power of that same number.

8^1/3 / 5^-2

Applying the necessary laws of indices;

= 8^1/3 / 5^-2

= ∛8 / (1/5^2)

= 2 / (1/25)

= 2 x (25/1)

= 50

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The two factors such that their product is the first number and their sum is the second number are 8 and 5.

A factor is defined as the number that divides another number, leaving no remainder.

In other words, if multiplying two numbers gives us a product, then the number we multiply is a factor of the product and divided by the product.

The factors of 40 and 13 such that their product is the first number and their sum is the second number = 8 and 5.

That is, 8×5 = 40

8+5 = 13

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The minimum of the function is at x = -10. The minimum on the interval [-10,6] is -2.67.

What is a function?

A function from a set X to a set Y allocates exactly one element of Y to each element of X. The set X is known as the function's domain, while the set Y is known as the function's codomain.

Given function is f(x) = ³√(x-9)

The graph of the given function increases with the increase of the value of x and decreases with the decrease of the value of x.

Thus the minimum value of f(x)on the interval [-10,6] is at x = -10

Putting x = -10 in the given function.

f(-10) = ³√(-10-9)

f(-10) = ³√(-19)

f(-10) = -2.668

f(-10) = -2.67 (rounded to 2 decimal places).

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Answer:

x = 67°

Step-by-step explanation:

When two parallel lines are cut by a transversal, the pair of angles formed on the interior of the parallel lines but on the opposite sides of the transversal are called alternate interior angles and they are congruent.

          x = 67°

Answer:

a)not quadratic

b)quadratic

c)quadratic

d)not quadratic

a) x=-3

b) maximum is (-3,4)

c)[tex](-3-\sqrt{2},0)[/tex] and[tex](-3+\sqrt{2},0)[/tex]

d)(0,-14)

e) Domain: (-∞,∞), {xIx∈ℝ}

   Range: (-∞,4), {yIy≤4}

Step-by-step explanation:

Hope this helps!

The power series representation for f(x) = arccot(x) is

      [tex]\pi /2- \lim_{n \to \infty} (-1)^n\frac{x^2^n^+^1}{2n+1}[/tex]

The power series ∑aₙxⁿ is an infinite series and looks like a function of x. An easy way to illustrate the idea of a power series representing a function is to use the geometric series as an example.

The power series is a very important kind of infinite series where the terms contain the powers of a variable. A power series is a series of the general form:

∑aₙ(x-x₀)ⁿ=a₀+a₁(x-x₀)+a₂(x-x₀)²+a₃(x-x₀)³+.........

called a power series centered at x₀

where  x is a variable,

x₀ is a real constant, and the

aₙ's are real constants called the coefficients of the series.

The given power series representation is f(x) = arccot(x).

we observe that f '(x)=-1/(1+x²) and find the required series by integrating the power series for -1(1+x²)

arccot(x)=∫-1/(1+x²)dx

⇒∫-(1-x²+x⁴-x⁶+....)dx

⇒C-x+1/3x³-x⁵/5+1/7x⁷-......

To find C we put x=0 and obtain C=arccot(0)=π/2

Therefore,

C=π/2-x+1/3x³-x⁵/5+1/7x⁷-.......

f(x)=π/2- ∑(-1)ⁿₓ x^2n+1/2n+1

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The graph below shows the number of blocks away from home Bentley is 21 minutes after he left his house, until he got back home.

The distance-timed graph is the type of graph that is used to represent the relationship that exists between the distance covered by a moving object and the time take to reach its destination.

The distance covered from house to store= 4 blocks

The time used = 2 minutes

The distance covered from store to the bank = 10 blocks

The time used = 7 minutes

The time used to return home from the bank = 12 minutes

Therefore, Bentley is 21 minutes after he left his house, until he got back home. That is 2+7+12 = 21 minutes.

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The indicated measures:

m∠ABC =  138° and m∠BCD = 52°.

According to the Angle Addition Postulate, an angle's measure is equal to the sum of the measures of any two adjacent angles. The Angle Addition Postulate can be used to determine the measurement of a missing angle or to determine the angle produced by two or more other angles.

Given:

The angle measures:

m∠DAE = 16° and m∠EDC = 64°.

The diagonals of the kite intersect at 90°.

(1).

In ΔAED,

the sum of all the angles of the triangle is 180°.

m∠DAE + m∠ADE + m∠AED = 180°

m∠ADE = 180 - 90 - 16

m∠ADE = 74°

According to the angle addition postulate,

m∠ADE + m∠EDC = m∠ADE

m∠ADE = (74 + 64)°

m∠ADE = 138°

From the property of kites,

m∠ADE = 138° =  m∠ABC.

(2).  m∠EBC =  m∠EDC,

m∠EBC = 64°

In ΔBCD,

the sum of all the angles of the triangle is 180°.

m∠DBC + m∠BCD + m∠CDB = 180°

m∠BCD = 180 - 64 - 64

m∠BCD = 52°

Therefore,  138° =  m∠ABC and m∠BCD = 52°.

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Answer

17y^2  + 6y

Step-by-step explanation:

A journal entry is a format used in accounting to record transactions. The amount we owe someone else that we must get in the future is known as notes receivable.

Notes receivable are claims for which official documents of credit, like promissory notes, are issued as proof of debt. In most cases, the credit instrument has a minimum term of 30 days and imposes an interest payment obligation on the debtor.

Given the following information:

Note receivable $15,000

Rate of interest 9%

Discount rate    12%

Period              2 months

Preparing journal entry to record accrued interest

To prepare the journal entry, we must first calculate the interest. We can compute interest by multiplying the notes receivable, the interest rate, and the period, i.e.

Interest = Notes receivable × Rate of interest × Period

Interest = 15000 × 0.09 × 2/12

Interest = 225

Now we can prepare the journal entry

Date                          Particulars              Debit ($)               Credit($)

February 28, 2016     Interest receivable        250

                                          Interest                                    250

                           To record accrued interest  

Preparing the journal entry to record discounting

To begin preparing the Journal entry, we must first calculate the necessary data.

We can calculate the cash as the difference between Maturity Value and Discount. That is,

Cash = Maturity Value – Discount

The value of Maturity is unknown. We can compute it as the sum of the receivable notes and interest. That is,

Maturity Value = Notes receivable + Interest

Interest =Notes receivable × Rate of interest × Period

= $15,000 × 0.1 × 6/12

= $1,500 × 0.5

= $750

​Maturity Value = Notes receivable + Interest

= $15,000 + $750

=  $15,750

Discount =Maturity Value × Discount rate × Period

= $15,750 × 0.12 ×  4/12

= $1,890 × 0.33

= $630

Finally, we can calculate cash

Cash = Maturity Value – Discount

= $15,750 − $630

= $15,120

Loss on sale = Cash – Notes receivable - Interest

= $15,120 − $15,000 − $250

= $130

Finally, we can prepare our journal entry.

Date                        Particulars                   Debit ($)            Credit($)

February 28,2016     Cash                            15,120

                              Loss on sale                      130

                              Notes receivable                                               15,000

                                  Interest                                                  250

                       (To record discounting)  

Thus, Cash & Loss are debited, & Notes Receivable & Interest are credited.

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Answer:

6 and 2

Step-by-step explanation:

50 divided by 8 is 6.25 and since you can't make .25 of a centerpiece he can only make 6 centerpieces

there will be 2 flowers left over because .25 of 8 is 2 (.25 times 8)

Step-by-step explanation:

it us a polynomial with a second degree variable

Answer: 10y

Step-by-step explanation:

4(y-2)+6y+8

4(y-2)=4y-8

4y-8+6y-8

*8's cancel out*

6y+4y=10y

Answer:19

Step-by-step explanation:

I think this is right

In this polygon, all angles are right angles. The area of this polygon = 334 ft²

To calculate the area of a regular polygon, just apply the formula below: Half of a perimeter multiplied by apothem equals area. What it means is as follows: The perimeter is the sum of the lengths of all the sides. A segment known as an apothem joins the midpoint of any perpendicular side to the midpoint of a polygon.

The equation for the area of a regular polygon with n sides is [l2n]/[4tan(180/n)]. where n is the number of sides and l is the length of the sides of the polygon.

To calculate the area of a regular polygon, use the formula Area = (number of sides length of one side apothem)/2.

Given data :

Area of polygon

= Area AGEF + Area BCDG

= 21 x 7 + 17 x 11

= 147 + 187 = 334 ft²

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Answer:334 ft

Step-by-step explanation: i did the test

The length of the hypotenuse is 13 units

From the question, we have the following parameters that can be used in our computation:

Legs = 5 and 12 units

The length of the hypotenuse of the right triangle can then be calculated using

Hypotenuse² = Leg 1² + Leg 2²

Substitute the known values in the above equation, so, we have the following representation

Hypotenuse² = 5² + 12²

So, we have

Hypotenuse² = 169

Take the square roots

Hypotenuse = 13

Hence, the hypotenuse is 13 units

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This event is a binomial experiment because C. there are only two outcomes; the number of trials is fixed; the probability is the same for each trial; the trials are independent of each other.

A binomial experiment is a random experiment with a fixed number of repeated trials with independent outcomes, successes or failures, yes or no, and heads or tails.

In a binomial experiment, the probability of "success" p is the same for each outcome as the chance of "failure" q is the same for each outcome.

The number of free throw shots in this experiment is 20 and they are either missed or scored.

Thus, the fixed number of trials with only two outcomes satisfied as a binomial experiment.

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Answer:

b is 5

I wish you luck in your assignments.

The price of foreign currency in relation to the local currency is referred to as the Nominal Exchange rate. It displays how many units of local money must be renounced in order to obtain one unit of foreign cash.

The amount of local currency required to buy foreign currency is known as the nominal exchange rate. The NEER is a measure of a nation's ability to compete internationally in the foreign exchange (forex) market.

Yes, you can exchange 1 USD for 90 YEN on the foreign exchange market, and vice versa. Nominal currency appreciation is the term used to describe a decline in this measure.

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What is the Nominal Exchange Rate?

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The remaining lemonade in the container after Coach Miller pours g gallons for the players is, (5 - g) gallons.

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

We have to given that;

There are 5 gallons of lemonade in the container.

Now, Initially lemonade available in Container = 5 gallons

Here, Coach Miller pours g gallons for the players.

Hence, Lemonade remaining in Container = (5 - g)  gallons

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When the number of times you roll an odd number increases, the theoretical probability that you roll an even number would decrease.

As the number of times you roll an odd number increases, the theoretical probability that you roll an even number decreases. This is because the probability of rolling an even number is inversely proportional to the number of times you roll an odd number.

If you are rolling a fair die, the probability of rolling an even number is 3/6 or 1/2, and the probability of rolling an odd number is also 3/6 or 1/2.

As the number of times you roll an odd number increases, the number of rolls that are left for an even number decreases, thus the probability of rolling an even number decreases as well.

For example, if you roll the die 10 times and 6 of them are odd numbers, the probability of rolling an even number in the remaining 4 rolls is 4/4 or 1 (100%) because you are guaranteed to roll an even number.

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