If c is 6x6 and the equation cx = v is consistent for every v in r^6, is it possible that for some v, the equation cx = v has more than one solution?

Answer:

gradient = - [tex]\frac{1}{5}[/tex]

Step-by-step explanation:

calculate the gradient ( slope ) m of the line using the slope formula.

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 4, 0 ) and (x₂, y₂ ) = (1, - 1 )

m = [tex]\frac{-1-0}{1-(-4)}[/tex] = [tex]\frac{-1}{1+4}[/tex] = - [tex]\frac{1}{5}[/tex]

Answer:

-4c-4

Step-by-step explanation:

The simplified expression for  6c + (-4) - 8c + (-2c) is -4 - 4c.

Mathematical expressions consist of at least two numbers or variables, at least one maths operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows:

Expression is (Number/variable, Math Operator, Number/variable)

We have the expression, 6c + (-4) - 8c + (-2c)

Now, simplifying the expression as

6c - 4 - 8c - 2c

= -4 + c(6 - 8 - 2)

= -4 + c(-4)

= -4 - 4c

Thus, the simplified expression is -4 -4c.

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The expression that can be used to find the sum of polynomials is:

D [(-3x²)+(-8x²)] +4x+ [9+5].

Polynomials are sums containing terms that have the shape k⋅xⁿ, in which k is any number and n is a positive integer.

The given polynomials:

(9 − 3x²) + (−8x² + 4x + 5)

Addition will be done in such a way that signs of each term will remain same.

Opening the brackets.

= 9 − 3x² −8x² + 4x + 5

Rewriting the expression as:

= − 3x² −8x² + 4x + 5 + 9

Arranging them in brackets again.

= [(-3x²)+(-8x²)] +4x+ [9+5]

Thus, the expression that can be used to find the sum of polynomials is:

D [(-3x²)+(-8x²)] +4x+ [9+5].

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To estimate whether Latisha buys more or less than 4 ounces of spices, we can round the given amounts to the nearest whole number.

Two-fifths ounce is about 0.4 ounce.

One and one-fifth ounces is about 1.2 ounces.

One and one-tenth ounces is about 1.1 ounces.

Adding these rounded amounts gives:

0.4 + 1.2 + 1.1 = 2.7 ounces

Since 2.7 ounces is less than 4 ounces, we can conclude that Latisha buys less than 4 ounces of spices to make one batch of Spice Parisienne.

Step-by-step explanation:

y = 3x + 10 the fixed charge is 10$ so our constant should be 10, there is a 3$ fee every day so x represents the days so we can multiply the amount of days with 3 to find the total amount paid in fees.

For example, if we hired a ladder for 3 days then

y = 3x + 10

= 3 x 3 +10

= 9 + 10

= 19$

So, we spent 19$ dollars in total cost

Answer: viedo yt

Step-by-step explanation:

if i was you go look at a yt viedo and it is easier becuase thats what helped me when i was in 6th grade we stared early so hope that helps

Answer:

choice C

Step-by-step explanation:

    0 +  3x⁴ + 5x³ - 4x⁸ - 0

-  (2x⁵ - 2x⁴ + 4x³ -  0   - 5)

=  2x⁵ +5x⁴ +  x³ - 4x² + 5

Subtract column by column of like terms, put 0's where there is no like term, change signs inside the parentheses of the second expression because you are subtracting.

If a number from 0-9 is randomly selected and then a letter from a-d is randomly selected, the probability that the number 3 and a constant are selected is 0.1 or 10%.

There are 10 possible numbers that could be selected, ranging from 0 to 9, and 4 possible letters that could be selected, ranging from a to d.

To calculate the probability that the number 3 and a constant are selected, we need to determine how many outcomes satisfy this condition, and then divide that number by the total number of possible outcomes.

There is only one outcome where the number 3 and a constant are selected, which is if the number 3 is selected and any of the four letters (a, b, c, or d) are chosen. Therefore, the number of outcomes that satisfy this condition is 4.

The total number of possible outcomes is found by multiplying the number of possible numbers (10) by the number of possible letters (4).

Total number of possible outcomes = 10 x 4 = 40

Thus, the probability that the number 3 and a constant are selected is,

Probability = number of favorable outcomes / total number of possible outcomes

Probability = 4 / 40

Probability = 0.1

This means that out of all possible outcomes, 10% will result in the selection of the number 3 and any of the four letters.

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The power of the test against the specific alternative is given by 1 minus the probability of making a Type II error. Therefore, the power is 0.86= 86%

In statistical hypothesis testing, the power of a test is the probability that it correctly rejects a null hypothesis when a specific alternative hypothesis is true. In this case, we are given that the test has a significance level of α = 0.01, which means that the test rejects the null hypothesis if the probability of obtaining the observed result, or one more extreme, under the null hypothesis is less than 0.01.

However, we also know that when a specific alternative hypothesis is true, the test has a probability of making a Type II error of 0.14. This means that there is a 14% chance that the test fails to reject the null hypothesis, even though the alternative hypothesis is true.

Therefore, the power of the test against this specific alternative hypothesis is given by 1 minus the probability of making a Type II error, which is:

Power = 1 - P(Type II error) = 1 - 0.14 = 0.86

So, the power of the test against the specific alternative hypothesis is 0.86 or 86%. This means that when the alternative hypothesis is true, the test correctly rejects the null hypothesis 86% of the time.

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Answer:

Sally's score on the 7th test needs to be 17.5 points points more than the average of her first 6 tests.

Step-by-step explanation:

Let T be the sum of the scores of Sally's first 6 tests.  Her average score would be:

Avg. Score (S) =T/6

Let S stand for Sally's average score.

We are told her average is k, so we can write:  S = k

Let N stand for the score of her New (7th) test.  Her total score would be:

T + N   [This is the sum of all 7 of her tests]

Her average would become (T+N)/7

The goal is to raise her average score by 2.5 points to (k+2.5) points.

That means (T+N)/7 = k+2.5   [Her new average is 2.5 points higher]

(T + N)/7 = k + 2.5

T+N = 7k+17.5

Note that T = 6k  [her total score for the first 6 tests is her average, k, times 6]

We'll use this definition of T in the equation:

T+N = 7k+17.5

(6k)+N = 7k+17.5    [Substitute 6k for T, since T=6k]

N = 7k+17.5-6k       [Rearrange]

N = 1k+17.5

This is telling Sally, and us, that her new test, N, must score 17.5 points higher than her average score, k.

The answer is 17.5 points.

From the given vectors the value of t - 2r is - 15i - 5j - 10k.

In mathematics, vectors are mathematical objects that have both magnitude (length) and direction. Vectors can be represented as arrows in space, where the length of the arrow corresponds to the magnitude of the vector and the direction of the arrow corresponds to the direction of the vector.

Here we have

A cube and the vectors are u = (5,0,0), v = (0,5,0), w = (0,0,5) and
t = (-5,5,0)

The cube has edges of length 5

Consider u = 5i, v = 5j, w = 5k, and t = -5i + 5j

From the figure,

r = u + v + w  

= 5i + 5j + 5k

Now the value of t - 2r can be calculated as follows

=> t - 2r = - 5i + 5j - 2(5i + 5j + 5k )

=  - 5i + 5j - 10i - 10j - 10k

=  - 15i - 5j - 10k

Therefore,

From the given vectors the value of t - 2r is - 15i - 5j - 10k.

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Answer:

(a) 280

(b)  £26

Step-by-step explanation:

(a) 20 workers eat 2 biscuits a day.

20 × 2 = 40

Since there are 7 days a week, multiply the 40 x 7 to find how many biscuits are eaten each week.

40 × 7 = 280

280 biscuits are eaten every week.

(b) Now, divide 280 (the number of biscuits eaten each week) by 14 (the number of biscuits in a packet) to find how many packets are eaten weekly.

280 ÷ 14 = 20

Now you have the number of packets eaten each week, so you can determine the price spent on biscuits. Multiply 20 packets by the price per packet, which is £1.30.

20 × 1.30 = 26

The office spends £26 on biscuits each week.

Answer:

2*3*3=2*3^2

Step-by-step explanation:

18÷2=9

9÷3=3

3÷3=1

Answer:

See below.

Step-by-step explanation:

[tex]\textsf{We are asked to identify the factors of 18.}[/tex]

[tex]\large \fbox{\textsf{The factors of 18 are: 1, 2, 3, 6, 9, 18.}}[/tex]

[tex]\huge\fbox{What are Factors?}[/tex]

[tex]\textsf{Factors are 2 whole numbers that \bf{multiply} to become a \bf{given number.}}[/tex]

[tex]\textsf{One simple way to identify factors is to divide the given number by positive integers.}[/tex]

[tex]\large\boxed{\textsf{For example;}}[/tex]

[tex]\textsf{Find the factors of 12.}[/tex]

[tex]\mathtt{12 \div 1 = 12 \ (Factor)}\\\mathtt{12 \div 2 = 6 \ (Factor)}\\\mathtt{12 \div 3 = 4 \ (Factor)}\\\mathtt{12 \div 4 = 3 \ (Factor)}\\\mathtt{12 \div 5 = 2.4 \ (Not \ A \ Factor)}\\\mathtt{12 \div 6 = 2 \ (Factor)}[/tex]

[tex]\mathtt{12 \div 7 = 1.714... \ (Not \ A \ Factor)}\\\mathtt{12 \div 8 = 1.5 \ (Not \ A \ Factor)}\\\mathtt{12 \div 9 = 1.\bar{3} \ (Not \ A \ Factor)}\\\mathtt{12 \div 10 = 1.2 \ (Not \ A \ Factor)}\\\mathtt{12 \div 11 = 1.\bar{09} \ (Not \ a \ Factor)}\\\mathtt{12 \div 12 = 1 \ (Factor)}[/tex]

[tex]\large \fbox{\textsf{The factors of 12 are: 1, 2, 3, 4, 6, 12.}}[/tex]

[tex]\textsf{Let's do the same thing, but with 18.}[/tex]

[tex]\textsf{Find the factors of 18.}[/tex]

[tex]\mathtt{18 \div 1 = 18 \ (Factor)}\\\mathtt{18 \div 2 = 9 \ (Factor)}\\\mathtt{18 \div 3 = 6\ (Factor)}\\\mathtt{18 \div 4 = 4.5 \ (Not \ A \ Factor)}\\\mathtt{18 \div 5 = 3.6 \ (Not \ A \ Factor)}\\\mathtt{18 \div 6 = 3 \ (Factor)}[/tex]

[tex]\mathtt{18 \div 7 = 2.574... \ (Not \ A \ Factor)}\\\mathtt{18 \div 8 = 2.25 \ (Not \ A \ Factor)}\\\mathtt{18 \div 9 = 2 \ (Factor)}\\\mathtt{18 \div 10 = 1.8 \ (Not \ A \ Factor)}\\\mathtt{18 \div 11 = 1.\bar{63} \ (Not \ A \ Factor)}\\\mathtt{18 \div 12 = 1.5 \ (Not \ A \ Factor)}[/tex]

[tex]\mathtt{18 \div 13 = 1.384.. \ (Not \ A \ Factor)}\\\mathtt{18 \div 14 = 1.285.. \ (Not \ A \ Factor)}\\\mathtt{18 \div 15 = 1.2 \ (Not \ A \ Factor)}\\\mathtt{18 \div 16 = 1.125 \ (Not \ A \ Factor)}\\\mathtt{18 \div 17 = 1.0588.. \ (Not \ A \ Factor)}\\\mathtt{18 \div 18 = 1 \ (Factor)}[/tex]

[tex]\large \fbox{\textsf{The factors of 18 are: 1, 2, 3, 6, 9, 18.}}[/tex]

Ashima will gain INR from selling the watch for INR, as the Cost Price of the watch is 1360 and the Selling Price is INR.

a. The Cost Price (CP) of the watch is the amount that Ashima paid to purchase the watch. In this case, Ashima sold the watch for 1350 and suffered a loss of 10. This means that the CP of the watch is 1350 + 10 = 1360.

b. To calculate her gain, we need to know the Selling Price (SP) of the watch. If she sells the watch for INR, then the SP of the watch is INR. The formula to calculate gain or loss is as follows:

Gain or Loss = SP – CP

In this case, the SP of the watch is INR and the CP of the watch is 1360. Applying the formula, Ashima’s gain is:

Gain = INR – 1360

= INR - 1360

Therefore, Ashima will gain INR from selling the watch for INR.

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There is 0.25 or 25% of probability that a senior is going to college and plays sports

We can start by using the given information to construct a probability table:

College   Work  Gap    year  Total

Sports team    50    30      5      85

Not on sports team  90     10     55      155

Total     140    40        60     200

From the table, we see that there are 50 seniors going to college who are on their school's sports teams. Therefore, the probability that a senior is going to college and plays sports is:

P(college and sports) = number of seniors going to college and on sports team / total number of seniors

= 50 / 200

= 0.25

Therefore, the probability that a senior is going to college and plays sports is 0.25 or 25%.

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The markup percentage for the fish dinner at the Golden Wharf restaurant is approximately 76.34%.

The markup percent is calculated by dividing the markup amount by the cost and then multiplying it by 100%. The markup is the difference between the selling price and the cost, so in this case:

markup = selling price - cost

markup = $11.55 - $6.55

markup = $5.00

So the markup is $5.00.

Now we can calculate the markup percent:

markup percent = (markup / cost) × 100%

markup percent = ($5.00 / $6.55) × 100%

markup percent = 76.34%

Therefore, the markup percentage for the fish dinner at the Golden Wharf restaurant is approximately 76.34%.

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Answer:

Step-by-step explanation:

An exponential function can be written in the form y = ab^x, where a is the initial value and b is the base. To find the specific exponential function that passes through the points (1, 12) and (5, 972), we need to solve for a and b.

Using the point (1, 12), we get:

12 = ab^1

12 = ab

Using the point (5, 972), we get:

972 = ab^5

We can use the equation ab from the first point to solve for a in terms of b:

a = 12/b

Substituting this expression for a into the second equation, we get:

972 = (12/b)b^5

Simplifying this equation, we get:

972 = 12b^4

Dividing both sides by 12, we get:

81 = b^4

Taking the fourth root of both sides, we get:

b = 3

Substituting this value of b into the equation a = 12/b, we get:

a = 4

Therefore, the exponential function that passes through the points (1, 12) and (5, 972) is:

y = 4(3^x)

As the area of the square is given 16/36 square feet for that the length of sides of the square is 4/6 feet.

A square is a quadrilateral with four sides. The length of each side is equal. The sum of angles in a square is 360 degrees.  Each angle in a square is a right angle.

Area of a square = side²

If the area of a square is given, in order to determine the length, find the square root of the area.

Thus, Area of square = 16 / 36 feet².

        s² = 16/36 feet²

 So, s = √16/36 feet²

    s = 4/6 feet

Hence sides of the square would be 4/6 feet.

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—-------- Correct question format is given below —--------

(Q). Brody calculated the area of a square to be 14/36 square feet. Which shows the side length of the square?

In response to the query, we can state that Hence, a reduction dilation is the kind of dilation that happens when the scale factor is 1/4.

Dilation is a transform that modifies an object's size. Dilation is a technique used to increase or decrease objects. An picture that is an exact duplicate of the original shape is produced as a result of this change. There is, however, a significant fluctuation in the shape. Dilation should result in a distortion of the initial form.

Dilations are transformations that alter an object's size without altering its shape. When an object dilates by a scale factor of 1/4, its size is decreased by a factor of 1/4, or 0.25.

This implies that each dimension of the object—its length, breadth, and height—will be multiplied by 1/4, or 0.25. For instance, if the original item was 8 units long, the dilated version would be 2 units long (8 x 1/4 = 2). The dilated item would have a width of 1.5 units if the initial object had a width of 6 units (6 x 1/4 = 1.5).

Hence, a reduction dilation is the kind of dilation that happens when the scale factor is 1/4.

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Answer:

21 sticks

Step-by-step explanation:

In order to solve an equation like this its best to count all the sticks each step and figure out the pattern

1st: 6 sticks

2nd: 11 sticks

3rd: 16 sticks

Now we notice that it adds 5 sticks each step so the 4th picture must have 21 sticks.

Hope this helps!

Brainliest and a like is much appreciated!

Answer:

65.6

Step-by-step explanation:

1 meter = 3.28 feet

20 feet = 3.28 x 20

= 65.616798

= 65.6 (1 dp)

:)

Answer:

89.04

Step-by-step explanation:

To find 68% of 53, we can multiply 53 by 0.68:

68% of 53 = 0.68 x 53 = 36.04

So 53 increased by 68% is:

53 + 36.04 = 89.04

Therefore, 53 increased by 68% is 89.04.

Answer:

< because 1\2 is the same as .5 and .5 is less than 3

Answer:-60

Step-by-step explanation:

Answer:

11 cm.

Step-by-step explanation:

The formula for the area of a triangle is given by:

A = (1/2)bh

where A is the area, b is the base, and h is the height (or altitude) of the triangle.

We are given that the area of the triangle is 110 cm and the base is 20 cm. Substituting these values in the formula, we get:

110 = (1/2) × 20 × h

Simplifying the equation, we get:

110 = 10h

h = 11 cm

Therefore, the height (or altitude) of the triangle is 11 cm.

Answer:

Step-by-step explanation:

cos(x+50) = 1/2

We know that cos(60) = 1/2, so we can write:

cos(x+50) = cos(60)

Using the identity cos(a) = cos(b) if and only if a = ±b + 2πn, we get:

x+50 = ±60 + 2πn

Solving for x, we have:

x = -50 ±60 + 2πn

x = 10 + 2πn or x = -110 + 2πn

Since we want to find all values of x between 0 and 180, we only need to consider the values of x that satisfy 0 ≤ x ≤ 180.

For x = 10 + 2πn, we have:

0 ≤ 10 + 2πn ≤ 180

-10/2π ≤ n ≤ 85/2π

For x = -110 + 2πn, we have:

0 ≤ -110 + 2πn ≤ 180

-35/2π ≤ n ≤ 25/2π

Therefore, the solutions for cos(x+50) = 1/2 in the interval [0, 180] are:

x = 10° + 360°n or x = 150° + 360°n, where n is an integer.

sin(2x) = -0.6

We know that sin(θ) = -0.6 has two solutions in the interval [0, 360]: θ ≈ -36.87° and θ ≈ 216.87° (using a calculator).

Using the double angle identity sin(2x) = 2sin(x)cos(x), we can write:

2sin(x)cos(x) = -0.6

Dividing both sides by 2cos(x), we get:

sin(x) = -0.3/cos(x)

Using the identity cos²(x) + sin²(x) = 1, we can substitute sin²(x) = 0.09/cos²(x) and simplify to get:

cos³(x) - 3cos(x) + 0.9 = 0

We can solve this equation using numerical methods or approximations. One possible approximation is to use the intermediate value theorem and test for sign changes in the function f(x) = cos³(x) - 3cos(x) + 0.9:

f(0) = 0.9 > 0

f(π/2) ≈ -0.84 < 0

f(π) ≈ 0.49 > 0

Therefore, there is a root of f(x) = 0 in the interval (0, π/2) and another root in the interval (π/2, π).

Using a numerical solver or more advanced methods, we can find the approximate values of x that satisfy cos³(x) - 3cos(x) + 0.9 = 0 in the intervals (0, π/2) and (π/2, π):

x ≈ 68.58° or x ≈ 111.42°

Therefore, the solutions for sin(2x) = -0.6 in the interval [0, 180] are:

x ≈ 34.29° or x ≈ 55.71°

Yes.$19.60. you have enough money to pay the 15% tip for the bill of $130.56, and the amount of the tip should be $19.60.

a. Do you have enough to pay the tip?

To determine if you have enough to pay the tip, you need to calculate 15% of the bill and compare it to the amount of money you have.

15% of $130.56 = 0.15 x $130.56 = $19.58

Since you have $20, you do have enough to pay the tip.

Therefore, the answer is "Yes".

b. How much should the tip be?

The tip should be 15% of the bill, which is $19.60.

Therefore, the answer is "$19.58".

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Nigeria's predicted population in 2020 is 208 million, rounded to the nearest million.

Relative change, also known as percent change, is a measure of the percentage increase or decrease in a quantity over time. In the context of population, relative change refers to the percentage change in the size of a population over a given period.

To calculate relative change in population, you would take the difference between the final population size and the initial population size, divide by the initial population size, and multiply by 100 to get the percentage change.

To find the relative change in Nigeria's population over the decade from 2000 to 2010, we use the formula:

Relative change = (new value - old value) / old value

Relative change in Nigeria's population from 2000 to 2010:

= (160 - 123) / 123

= 0.300813

So Nigeria's population increased by approximately 30.08% over the decade from 2000 to 2010.

To predict Nigeria's population in 2020, we apply this same relative change to the 2010 population:

Population in 2020 = Population in 2010 + (Relative change × Population in 2010)

Population in 2020 = 160 + (0.300813 × 160)

Population in 2020 = 160 + 48.13008

Population in 2020 = 208.13008 million

Rounding this to the nearest million, we get:

Population in 2020 = 208 million

Therefore, Nigeria's predicted population in 2020 is 208 million, rounded to the nearest million.

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There are 31,465 different ways that an instructοr can chοοse 4 students frοm a class οf 31 students fοr a field trip.

Permutatiοns and cοmbinatiοns are twο cοncepts in mathematics that deal with cοunting the number οf pοssible οutcοmes in a given situatiοn.

Permutatiοns refer tο the number οf ways in which a set οf οbjects can be arranged οr οrdered. Fοr example, if we have three οbjects A, B, and C, there are six pοssible permutatiοns: ABC, ACB, BAC, BCA, CAB, and CBA. The fοrmula fοr calculating the number οf permutatiοns οf n οbjects taken r at a time is n! / (n-r)!, where n! represents the factοrial οf n.

The number οf ways that an instructοr can chοοse 4 students frοm a class οf 31 students is given by the cοmbinatiοn fοrmula:

C(31,4) = (31!)/(4!(31-4)!)

= (31 × 30 × 29 × 28)/(4 × 3 × 2 × 1)

= 31,465

Therefοre, there are 31,465 different ways that an instructοr can chοοse 4 students frοm a class οf 31 students fοr a field trip.

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Duane can expect to make a monthly payment amount of $506.18 over the 5-year term of his loan, including both the principal and the interest.

The monthly payment amount for Duane's MSRP vehicle purchase can be calculated using the following formula: ((MSRP - cash-back incentive) x interest rate) / (term in years x 12). In this case, the calculation is ((31,000 - 4,500) x 0.055) ÷ (5 x 12) = 506.18. Thus, Duane can expect to make a monthly payment of $506.18 over the 5-year term of his loan. This amount includes both the principal and the interest accrued on the loan. It is important to note that the monthly payment may change slightly due to the addition of taxes, registration fees, and other charges that may be included in the loan. Additionally, the amount of the monthly payment may vary slightly depending on the lender's terms and conditions.

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We have prοven that the Prοduct Rule fοr expοnents wοrks, and that 4a and 4b are equivalent.

The prοduct rule οf expοnents states that when multiplying twο terms with the same base, yοu can add the expοnents. Specifically, [tex]a^m * a^n = a^{(m+n)[/tex].

Tο expand the expressiοn [tex]2x^3[/tex]  •[tex]5x^2[/tex] using the fact that expοnents are repeated multiplicatiοn, we can write:

[tex]2x^3[/tex] • [tex]5x^2[/tex]= (2 • x • x • x) • (5 • x • x)

Using the cοmmutative prοperty οf multiplicatiοn, we can rearrange the factοrs tο grοup the x's and the numbers:

[tex]2x^3[/tex] • [tex]5x^2[/tex] = 2 • 5 • x • x • x • x

[tex]= 10x^5[/tex]

Nοw, let's prοve why the Prοduct Rule fοr expοnents wοrks. The Prοduct Rule states that when multiplying twο expοnential expressiοns with the same base, we can add their expοnents:

[tex]a^m[/tex] • [tex]a^n = a^{(m+n)[/tex]

Tο see why this is true, let's cοnsider the repeated multiplicatiοn οf a base a with expοnent m and a base a with expοnent n:

[tex]a^m[/tex]• [tex]a^n[/tex] = (a • a • ... • a) • (a • a • ... • a)

We can cοmbine the twο grοups οf factοrs by using the assοciative prοperty οf multiplicatiοn:

[tex]a^m[/tex] •[tex]a^n[/tex] = [tex]a^{(1+1+...+1)[/tex]• (a • a • ... • a) (m times)

[tex]= a^{(m+n)[/tex] • (a • a • ... • a) (m times)

Using the fact that a tο the pοwer οf 1 is just a, we can simplify the expressiοn tο:

[tex]a^m[/tex] • [tex]a^n[/tex] [tex]= a^{(m+n)[/tex]•[tex]a^m[/tex]• [tex]a^n[/tex]

Dividing bοth sides by [tex]a^m[/tex] • [tex]a^n[/tex], we get:

[tex]1 = a^{(m+n)[/tex] / ([tex]a^m[/tex] • [tex]a^n[/tex])

Using the rule fοr dividing expοnential expressiοns with the same base, we get:

[tex]1 = a^{(m+n)[/tex] • [tex]a^{(-m)[/tex] • [tex]a^{(-n)[/tex]

Using the rule fοr adding expοnents with the same base, we can simplify the expressiοn tο:

[tex]1 = a^{(m+n-m-n)[/tex]

Simplifying further, we get:

[tex]1 = a^0[/tex]

Therefοre, we have prοven that the Prοduct Rule fοr expοnents wοrks, and that 4a and 4b are equivalent.

To learn more about the product rule of exponent, visit:

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