What is the length of the third side?

Answer:

[tex]12w^7 z^6[/tex]

Step-by-step explanation:

[tex]2w^5 z(6w^2 z^5)=(2)(6)w^5 w^2 z^5 z=12w^7 z^6[/tex]

1. -2

2. 9

Also could you mark my answer as brainliest? It helps and doesnt hurt

The down payment for the installment purchase for the $900 refrigerator is $300.

An installment purchase is a method of buying high value assets or goods on credit. A percentage of the total purchase price is paid immediately as a down payment, while the remaining amount is settled by paying periodic installments.

the good to be paid for installment after a down payment of 1/3 of the total amount is a refrigerator which cost $900

1/3 of $900 = 1/3 × $900

1/3 of $900 = $900/3

1/3 of $900 = $300

In conclusion, $300 will be the down payment for the installment purchase of the refrigerator.

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The two numbers which are 14 and -5 give you -70 when multiplied but when added give you 9

An equation is an expression composed of variables and numbers linked together by mathematical operations.

Let x and y represent the unknown numbers

The two numbers give -70 when multiplied, hence:

xy = -70   (1)

The two numbers give 9 when added, hence:

x + y = 9   (2)

x = 9 - y

put x = 9 - y in equation 1:

(9 - y)y = -70

9y - y² = -70

y² - 9y - 70 = 0

y = -5 or 14

when y = -5; x = 9 - (-5) = 14

when y = 14; x = 9 - 14 = -5

The two numbers are 14 and -5

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equation in slope-intercept form of the line that pae through the point (4, 7) and is parallel to the line represented by y = 2x - 5 is ( y - y1 ) = m( x - x1 ) => y - 7 = 2 (x-8) => 2x - y - 1 = 0

A number that specifies a line's direction and slope is known as the slope or slope of a line in mathematics. A line's steepness is determined by its slope. The "gradient overflow" is a mathematical expression for the gradient (the change in y divided by the change in x).

equation is -

y = 2x - 5

since these are parallel to each other,

slope, m= 2

now the equation is -

( y - y1 ) = m( x - x1 )

y - 7 = 2 (x-8)

2x - y - 1 = 0

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Answer: < B is larger than a right angle

Step-by-step explanation:

This equation has no solution

To solve this problem, you will need to use the rules of complex numbers to multiply and simplify the given expressions.

First, let's simplify each of the given expressions:

(a+ib) (3 + 4i ) = a3 + a4i + ib3 + ib4i

= (3a - 4b) + (4a + 3b)i

(2 + i ) (2- i ) = (2*2) + (2(-1))i + (1*2) + (1(-1))i

= (4 - 1) + (2 - 1)i

= 3 + i

Now, we can set the two expressions equal to each other and solve for a and b:

(3a - 4b) + (4a + 3b)i = 3 + i

3a - 4b = 3

4a + 3b = 1

We can solve this system of equations using any method you prefer, such as substitution or elimination. One way to solve this system is to eliminate one of the variables by multiplying the first equation by 4 and the second equation by -3:

12a - 16b = 12

-12a - 9b = -3

This simplifies to:

0 = 9

This equation has no solution, so the original expression cannot be true. This means that a²+b² is not defined in this case.

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Answer: $24

Step-by-step explanation: There were 4 people splitting the bill You, Ben, Carla, and David the bill was 96

divide 96 by four so that  you each pay the same amount

96 divided by 4 is 24 so everyone payed $24

24+24+24+24 equals 96 so it is the correct answer

Answer:

7704 R 2

Step-by-step explanation:

61634/8 = 7704.25

7704.25 = 7704 + 0.25  ==>

In order to find the remainder value, multiply 8 with 0.25:

8 * 0.25 = 2

Hence, the quotient is 7704 and the remainder is 2.

7704 R 2

Answer:

g( [tex]\frac{3}{2}[/tex] ) = - [tex]\frac{35}{4}[/tex]

Step-by-step explanation:

substitute x = [tex]\frac{3}{2}[/tex] into g(x) , that is

g( [tex]\frac{3}{2}[/tex] )

= - 2( [tex]\frac{3}{2}[/tex] )³ - [tex]\frac{4}{3}[/tex] × [tex]\frac{3}{2}[/tex]

= - 2 × [tex]\frac{27}{8}[/tex] - 2

= = - [tex]\frac{27}{4}[/tex] - [tex]\frac{8}{4}[/tex]

= - [tex]\frac{35}{4}[/tex]

Note that the scale and actual area are matched as follows;

To find the area of the scale drawing, you can use the following formula:

Scale Drawing Area = (Actual Area) x (Scale Ratio)²

Let's take the first for example.

We have the Actual Area to be 147; and

Scale Ratio to be 1 inch to 7 feet. That is 1/7

Thus,

Scale Drawing Area = 147 x (1/7)²

Scale Drawing Area = 147 x 0.02040816326  ; thus

Scale Drawing Area = 3

Thus, where you have:

147 square feet is equivalent to 3 square inches when using a scale of 1 inch to 7 feet.

Repeat the above process for each of the other categories.

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The system of equations that models the given situation are;

y = 10x + 35

y = 5x + 35

Let x denote the number of years since 2010

Let y denote the total members

The linear equation in slope intercept form is expressed as;

y = mx + b

where;

m is the slope or unit rate

b is the y-intercept or initial value

For the swim team, since  the team increased by an average of 10 members per year, then;

Slope = 10

In 2010, they had 5 members and so; y-intercept = 35

Thus, the equation is; y = 10x + 35

For the chorus team, we can deduce that;

Slope = 5 members per year

In 2010, they had 35 members and so; y-intercept = 35

Thus, the equation is; y = 5x + 35

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Complete question is;

Central High School had five members on their swim team in 2010. Over the next several years, the team increased by an average of 10 members per year. The same school had 35 members in their chorus in 2010. The chorus saw an increase of 5 members per year. Write a system of equations to model this situation, where x represents the number of years since 2010.

Answer:

never

Step-by-step explanation:

because The union of a and b cannot be equal to the intersection of a and b

Answer:

Step-by-step explanation: Jay might run 4 miles in 20 minutes. Step-by-step explanation: If Jay ran on Monday = 1 mile in 5 minutes. On Tuesday = 2 miles in 10 minutes.

The probability of choosing a ball numbered 25 in a lottery game that contains 24 balls numbered 1 through 24 is 0.

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that the event will not occur and 1 indicating that the event will definitely occur.

Since a lottery game contains 24 balls numbered 1 through 24, it does not contain the ball numbered 25. So it can not be chosen at all.

probability = 0

Therefore, the probability of choosing a ball numbered 25 is 0.

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Answer:

|t - 101| ≤ 1.5

Step-by-step explanation:

The correct inequality to determine the range of body temperature for an adult dog is |t - 101| ≤ 1.5. This inequality states that the body temperature t can be as much as 1.5 degrees less than or 1.5 degrees more than 101 degrees Fahrenheit.

The two years that the panthers had the greatest change in their win-loss record is; b. between 2000-2001

A Bar Graph is also called a Bar Chart and is essentially a graphical display of data that makes use of bars of different heights.

The vertical axis is called the y-axis while the horizontal axis is called the x-axis.

Now, from the image attached, we can see that the x-axis represents the years in which the panthers had their win-loss record where the blue bar represents a win record while the purple bar represents the loss record.

Now, looking at the given bar graph, we can see that almost all the years have similar win - loss record except for year 2001 that had a large difference.

Thus, the greatest change came from between year 2000 and 2001.

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Ethan needs 3 more weeks  to pay all the money he owes his mother

Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.

Since Ethan pays his mother $5 a week for his phone bill. At week 12, Ethan still owes $15.

In order to determine how many weeks he needs to pay all the he owes, you need to divide the amount he is owing by the amount he pays per week. That is:

number of weeks = $15/$5 = 3 weeks

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17. (f-g)(x) = ( -x + 2x - 6 ) - ( -x + 5 ) = -2x + 11

18. (fg)(x) = ( -x - 9 )( x + 1 ) = -x² - x - 9

19. (f g)(x) = f(g(x)) = (x + 2x - 6)(-x + 5) = -x² + 6x - 30

20. (g o f)(x) = g(f(x)) = x + 5(x + 2x - 6) = x + 5x + 10x - 30

21. Domain: All real numbers

22. Domain: All real numbers

23. Range: Not given

24. Range: {6}

25. Range: All real numbers

26. Range: Not given

Specifically, it provides the difference, product, and composition of the given functions, as well as the domain and range of certain functions. The problems involve algebraic equations and simplifying expressions.

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Answer:

(8,000/10)=800

Answer:b

Step-by-step explanation:

b

Step-by-step explanation:

In 8 hours temperature different is 20

so average rate is=20/8

2.5

The correct option representing the function is f(t) = 30,303(0.85)t based on the deprivation rate.

Firstly calculating the depreciation rate -

30,303 - x%×30,303 = 25,757

x×303.03 = 30,303 - 25,757

Performing subtraction on Right Hand Side of the equation

x×303.03 = 4546

x = 4546/303.03

Performing division

x = 15%

The formula to be used for function is -

P = Po[tex] {(1+r)}^{t} [/tex], where P is the final value, Po is the original value, r is growth rate and t is time.

P = 30,303 [tex] {(1 - 0.15)}^{t} [/tex]

Performing subtraction on Right Hand Side of the equation

P = 30,303 [tex] {(0.85)}^{t} [/tex]

The value of car after t years is 30,303 [tex] {(0.85)}^{t} [/tex].

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The complete question is-

Jane bought a car for $30,303. The value of the car depreciated at a constant rate per year. The table below shows the value of the car after the first and second years:

Year 1 2

Value (in dollars) 25,757.55 21,893.92

Which function best represents the value of the car after t years?

f(t) = 25,757.55(0.85)t

f(t) = 30,303(0.85)t

f(t) = 30,303 (0.15)t

f(t) = 25,757.55 (0.15)t

The required value of c is c = 1.407 which satisfies the Mean Value Theorem.

The Mean Value Theorem states that if a function f is continuous on a closed interval [a,b] and differentiable on the open interval (a,b), then there exists a point c in the interval (a,b) such that f'(c) = (f(b) - f(a))/(b-a).

As per the given question, [tex]f(x) = (5x-10)^{2/3}[/tex], a=0, and b=2.

To find the values of c that satisfy the Mean Value Theorem, we need to find the derivative of f(x) and then solve the equation f'(c) = (f(2) - f(0))/(2-0) for c.

The derivative of f(x) is f'(x) = 5 × (2/3) [tex]\dfrac{1}{(5x-10)^{1/3}}[/tex]  = (10/3) × [tex]\dfrac{1}{(5c-10)^{1/3}}[/tex]

Substituting this into the equation above, we get

(10/3) × [tex]\dfrac{1}{(5c-10)^{1/3}}[/tex] =  [tex]\dfrac{0 - 10^{2/3}}{2-0}[/tex]

(10/3) × [tex]\dfrac{1}{(5c-10)^{1/3}}[/tex] = [tex]-\dfrac{10^{2/3}}{2}[/tex]

Solving this equation for c, we find that c =38/27≈ 1.407.

Thus, the value of c that satisfies the Mean Value Theorem is c = 1.407.

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In the given situation there are 144 possible ways for the nine representatives at the table.

We will first determine how many different options there are to seat the delegates of the three nations at the table.

We can arrange the three delegates we have for England in 3! = 6 different ways.

We can arrange the four delegates we have for Germany in 4! = 24 different ways.

We can organize the two representatives we have for France in 2! = 2 different ways.

The total number of arrangements for all nine delegates is obtained by multiplying the number of arrangements for each country's representatives.

6 x 24 x 2 = 288 ways

However, because the table is round, two configurations are deemed identical if they can both be created by rotating one.

To put it another way, the configurations are identical to one another and are not counted individually.

The total number of configurations divided by the number of identical arrangements gives the number of ways to position all nine representatives around the table (also known as rotations).

288 / 2 = 144

The nine representatives can be seated at the table in 144 different ways.

Because 144 is an even number, it should be noted that there are actually twice as many possible methods to solve the problem (144 x 2 = 288), or 540 options.

Therefore, in the given situation there are 144 possible configurations for the nine representatives at the table.

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Complete question:
An international meeting is held between england, Germany, and france. three representatives attend from England, four from germany, and two from france. how many ways can all nine representatives sit around a circular table, if representatives of the same country sit together? (two ways are considered the same if one can be rotated to produce the other.)

Answer:

There were 240/6=<<240/6=40>>40 contestants eliminated in round 1.

There were 240/5=<<240/5=48>>48 contestants eliminated in round 2.

There were 240/3=<<240/3=80>>80 contestants eliminated in round 3.

Altogether, there were 40+48+80=<<40+48+80=168>>168 contestants eliminated.

Therefore, there are 240-168=<<240-168=72>>72 contestants left.

Step-by-step explanation:

Answer:D

Step-by-step explanation: 1/3x-1 = 5

1/3x=6

3(1/3x) = 3(6)

x=18

Each individual outcome of an experiment is called a sample point. So, the right answer is option(b).

The set of all possible outcomes of a random experiment is the sample space , S or the outcome space. An event always associated with a random experiment is a subset of the sample space. Each result in sample space is called a sample point. Also, it is called an element or member of the sample space. For example, there are possible two outcomes for tossing a coin, i.e., the sample space, S = {heads, tails}, or S = {H, T}. If we toss two coins, there are four outcomes : { HH, HT, TH , TT }, where the first letter refers to the outcome of the first tossing and the second to that of the second tossing, each outcome is called a sample point.

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The graphing form of the function is,

⇒ (x - 8)² + (y + 5)² = 9²

And, The center of function = (8, - 5)

The radius of the function is,

⇒ r = 9

A relation between a set of inputs having one output each is called a function.

Given that;

The function is,

⇒ x² + y² - 16x + 10y + 8 = 0

Now,

Since, The function is,

⇒ x² + y² - 16x + 10y + 8 = 0

We can write as;

⇒ x² - 2 × 8 × x + y² + 2 × 5 × y + 8 = 0

⇒ x² - 2×8×x + 64 - 64 + y² + 2×5×y + 25 - 25 + 8 = 0

⇒ (x² - 2×8×x + 64) + (y² + 2×5×y + 25) - 64 - 25 + 8 = 0

⇒ (x - 8)² + (y + 5)² = 81

⇒ (x - 8)² + (y + 5)² = 9²

Thus, The graphing form of the function is,

⇒ (x - 8)² + (y + 5)² = 9²

Clearly, This represent the equation of circle with center (8, - 5) and radius 9.

And, The center of function = (8, - 5)

The radius of the function is,

⇒ r = 9

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