If a worker earns 200 for the first 40 hours of work in a week.

The length and width of the rectangle with a perimeter of 378ft are 168ft and 21ft respectively.

The formula used in calculating the perimeter of a rectangle is expressed as;

P = 2( l + w )

Where l is length and w is width.

Given the data in the question;

Let 'x' represent the width of the rectangle.

Plug the given values into perimeter formula and solve for x .

P = 2( l + w )

378 = 2( 8x + x )

378 = 2( 9x )

378 = 18x

18x = 378

x = 378/18

x = 21

Now, we find the length and width of the rectangle.

Width of the rectangle w = x = 21ft

Length of the rectangle l = 8x = 8( 21 ) = 168ft

Therefore, the width of the rectangle is 21ft while its length is 168ft.

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Answer:

Slope, m = 5

Step-by-step explanation:

Picking points on the x-axis and y-axis of the graph;

Point on x-axis (x1, x2) = 2, 4

Points on the y-axis (y1, y2) = 10, 20

To find the slope;

Mathematically, slope is given by the formula;

\( Slope = \frac{Change \; in \; y \; axis}{Change \; in \; x \; axis} \)

\( Slope, m = \frac {y_{2} - y_{1}}{x_{2} - x_{1}} \)

Substituting into the equation, we have;

\( Slope, m = \frac {20 - 10}{4 - 2} \)

\( Slope, m = \frac {10}{2} \)

Slope, m = 5

Answer:

you already know the answer?

Answer:

3

Step-by-step explanation:

Ascending order:

4 ,4 , 4 ,4 ,5, 6 ,7 , 7 ,7

9 data: split in

4 ,4 , 4 ,4   |   5   |   6 ,7 , 7 ,7

4 ,4   |   4 ,4   |   5   |   6 ,7   |   7 ,7

(7+7)/2-(4+4)/2

=7-4

=3

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

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The ordered pair that solves the system of equation is (0, 0).

To solve this system, we can substitute the first equation into the second equation to eliminate y:

x = 2x

Solving for x, we get x = 0.

Substituting x = 0 into the first equation, we get y = 0.

Therefore, the ordered pair that solves the system is (0, 0).

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Answer:

$15.15 x 5 hrs= $75.75

$156.44 - $75.75= $80.69

The answer is $80.69

Answer:

1.false

2.false

3.false

Answer:

All three are false.

Step-by-step explanation:

Let's say a equaled 2 and b equaled 5.

For reference: |2| = 2 |5| = 5

2 > 5 - False

|2| > |5| - False

2 > |5| - False

Hope this helps!!

The phrase "La sexta parte de la diferencia de dos números" in algebraic sentence can be written as \( \frac{x}{6} \) where "x" represents the difference between two numbers.

The quantity \( \frac{x}{6} \) is a fraction that represents one-sixth of the difference between two numbers. In other words, if you have two numbers "a" and "b", and you subtract them to find their difference "a-b", then \( \frac{x}{6} \) would equal \( \frac{(a - b)}{6} \).

The fraction \( \frac{x}{6} \) gives us a portion or a ratio of the difference between the two numbers, and in this case, it's one-sixth of that difference. So, if you want to find what one-sixth of the difference between two numbers is, you can simply divide that difference by 6.

Let's say that the two numbers you want to find the difference between are 15 and 6. To find their difference, we would subtract the smaller number from the larger one:

15 - 6 = 9

So, the difference between these two numbers is 9. To find one-sixth of this difference, we would divide the difference by 6:

\( \frac{9}{6} = 1.5\)

So, one-sixth of the difference between 15 and 6 is 1.5.

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Answer:

1. 332

2. 177

Step-by-step explanation:

In a direct variation, y=9 when x=3. A direct variation equation that shows the relationship between x and y is y=3x

What do you mean by direct variation?

Direct variation is a type of proportionality when one quantity changes right away in reaction to a change in another variable. This implies that if one number rises, the other will follow suit in a comparable manner. Similar to the last illustration, if one quantity decreases, the other quantity also decreases. Direct variation will have a linear relationship with the graph, resulting in a straight line.

Given,

In a direct variation, y=9 when x=3.

Formulate an equation based on the conditions stated: y=kx

We put the value of the y and x in this equation

9=k*3

Subtract the coefficient of the variable from both sides of the equation

k= 3

We can write the equation of the function by putting the value of k:  y=3x

Hence the correct answer is y=3x

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Answer:

Yes

Step-by-step explanation:

g(x) = 1/4 x

g(x) = x/4

f(x) = 4x

If you plugin f(x) in g(x) and g(x) into f(x), you should get x:

f(g(x))=

4(g(x)= => plugin g(x) for x in f(x)

4(x/4)=

4*x/4=x √

g(f(x))=

f(x)/4= ==> plugin f(x) for x in g(x)

4x/4 = x√

Hence, f(x) and g(x) are inverse of each other.

To solve for x in the equation 4x3 = -5x - 21, we can follow these steps:

1. Move all the terms containing x to one side of the equation, and move the constant term to the other side. We can do this by adding 5x to both sides and then adding 21 to both sides:

   4x3 + 5x = -21

2. Factor out x from the left-hand side of the equation:

   x(4x2 + 5) = -21

3. Divide both sides by (4x2 + 5):

   x = -21 / (4x2 + 5)

So the solution for x is x = -21 / (4x2 + 5). Note that this is a rational function, which means that the value of x depends on the value of the variable x. This equation has no real solutions because the denominator is always positive, and the numerator is negative.

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Answer: 1) b = 2

2) c = 20

Explanation:

I hope this helped!

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Answer:

3) b = 2.24

4) c = 15.62

Step-by-step explanation:

Pythagorean formula:

a² + b² = c²

3)

a² + b² = c²

2² + b² = 3²

4 + b² = 9

b² = 5

b = 2.24

4)

a² + b² = c²

10² + 12² = c²

100 + 144 = c²

244 = c²

c = 15.62

The maximum home value that can be financed is approximately $35,365.85.

Let's represent the maximum home value that can be financed by H.

If the minimum down payment is 18%, the amount financed is 100% - 18% = 82%.

Therefore, we have:

H × 82% = $29,000

Multiplying both sides by (1/82%), we get:

H = $29,000 / 82%

= $35,365.85

Hence, the maximum home value that can be financed is approximately $35,365.85.

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To answer this question, we need to remember that the sum of the total area of a probability distribution is always 1.

First case: the area to the right of x

Then, if we have that the area to the left of x in a normal distribution is 0.272, the area to the right of x is:

If we sum both areas, we will get 1 as the total area of this probability distribution.

Second case: the area to the left of x

Now, if we have that

Using Monotone Convergence Theorem,  {aₙ} is an increasing sequence that is bounded above by 3, and thus it is convergent

To show that the sequence {aₙ} defined by a₁ = 1 and aₙ₊₁ = 3 - (1/aₙ) is increasing, we need to prove that aₙ < aₙ₊₁ for all n.

Let's first prove that aₙ < 3 for all n by induction:

Base case: For n = 1, a₁ = 1 < 3.

Inductive step: Assume aₙ < 3 for some arbitrary n. Then we have:

aₙ₊₁ = 3 - (1/aₙ) < 3 - (1/3) = 8/3

Since aₙ₊₁ is positive (because aₙ < 3), we can also write:

aₙ₊₁ = 3 - (1/aₙ) > 3 - 1 = 2

Therefore, we have:

2 < aₙ < 3 < aₙ₊₁

This shows that {aₙ} is an increasing sequence that is bounded above by 3, and thus it is convergent by the Monotone Convergence Theorem.

To find the limit of {aₙ}, we can take the limit of both sides of the recursive definition:

limₙ→∞ aₙ₊₁ = limₙ→∞ (3 - (1/aₙ))

Since {aₙ} is convergent, we can replace limₙ→∞ aₙ with a to get:

a = 3 - (1/a)

Multiplying both sides by a, we get:

a² = 3a - 1

This is a quadratic equation that can be solved using the quadratic formula:

a = (3 ± √(3² + 4))/2

a = (3 ± √13)/2

Since aₙ < 3 for all n, we have:

a = (3 - √13)/2

Therefore, the limit of {aₙ} is (3 - √13)/2.

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d=r•t ,  formula show a joint variation ,  Option C is the answer.

The variation when a variable is dependent upon two or more variables and varies directly as either of them are taken constant is called Joint Variation.

According to the question , which among the options shows a Joint Variation.

Option 1  d = 50 t

It shows direct variation , as increase in t will directly increase d 50 times * the increase

Option 2 d = 16t²

It also shows direct square variation .

Option 3 d=r•t

In this variation d is dependent on two variables and so it is a joint variation.

Therefore Option C is the answer.

The complete question is ?

Which distance formula or formulas show a joint variation? d=50t, d=16t^2, d=r•t

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Answer:

180

Step-by-step explanation:

Answer:

C) House prices are growing faster now than in the past.

Let's assume that the number of diners at the Italian restaurant is "x" and the number of diners at the Mexican restaurant is "y". Then, we can write the following equations based on the given information:

Italian restaurant:

Donation = $462 + $1 per diner

Donation = $462 + $1x

Mexican restaurant:

Donation = $235 + $2 per diner

Donation = $235 + $2y

Since both restaurants will donate the same total amount, we can set their donations equal to each other:

$462 + $1x = $235 + $2y

Simplifying this equation, we get:

$2y - $1x = $227

We know that the number of diners has to be a whole number, so we can try different values of x and see which one gives us a whole number for y.

For example, if we try x = 200, then we can solve for y:

$2y - $1(200) = $227

$2y = $427

y = 213.5

Since y is not a whole number, we need to try a different value of x. If we try x = 250, then we get:

$2y - $1(250) = $227

$2y = $477

y = 238.5

Again, y is not a whole number, so we try another value of x. If we try x = 300, then we get:

$2y - $1(300) = $227

$2y = $527

y = 263.5

Still not a whole number, so we try x = 350:

$2y - $1(350) = $227

$2y = $577

y = 288.5

Finally, we get a whole number for y, so we have our solution:

Italian restaurant: x = 350 diners, donation = $812

Mexican restaurant: y = 289 diners, donation = $812

Therefore, 350 diners promised to participate and each restaurant would donate $812.

Answer:5.41

0.87 is correct

Step-by-step explanation:

We can solve this quadratic equation in terms of cos(θ) by using the quadratic formula:

cos(θ) = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 6, b = 7, and c = -7. Substituting these values, we get:

cos(θ) = (-7 ± sqrt(7^2 - 4(6)(-7))) / 2(6)

cos(θ) = (-7 ± sqrt(169)) / 12

cos(θ) = (-7 ± 13) / 12

Therefore, we have two possible solutions:

Answer:

4.2

Step-by-step explanation:

0.2^(3)-:0.4*60+3.6-:1.2 = 4.2

Answer:

4.2

Step-by-step explanation:

Answer:

84 miles in 12 hour

Step-by-step explanation:

12/4 = 3

3*28=84

Answer:

84 miles.

Step-by-step explanation:

First, find the rate of miles travel per hour.  It is given that the boat covers 28 miles in 4 hours. Simply divide 28 with 4:

28/4 = 7

The boat covers 7 miles per hour.

Now, multiply 12 hours with 7:

12 hours x 7 miles per hour = 84 miles per 12 hours.

84 miles is your answer.

~

Answer: 5m+4

Step-by-step explanation: you have to distribute. 5*m is 5m 5*1 is 5 then add like terms. 5-1=4

Answer:

1: A

2: B

Step-by-step explanation:

When it doesn't have any y-intercepts or when the y-intercept is 0 then we know it's proportional.

The required number is 800. The solution has been obtained by using arithmetic operations.

What are arithmetic operations?

The four fundamental operations, also referred to as "arithmetic operations," are regarded to explain all real numbers sufficiently. After division, multiplication, addition, and subtraction in mathematics are the operations quotient, product, sum, and difference.

We are given that 12 \(\frac{1}{2}\) % of a number is 100.

Let the number be 'x'.

So, from this we get

⇒ 12 \(\frac{1}{2}\) % of x = 100

⇒ 12.5 % of x = 100

⇒ 0.125 of x = 100

⇒ 0.125 * x = 100                (As of denotes multiplication)

⇒ x = 800

Hence, the required number is 800.

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