Recursive Rules from Word Problems

1) Sally started a new job. After depositing her 1st paycheck into her bank account she had
$225. Every week she was paid the same amount. After her 8th paycheck she had $1275 in her
bank account.

Complete the table

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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Answer:b

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Assuming that the ".." at the end of the number represents it being continuous, then it would be irrational.

0.121121112.. is an irrational number but not rational.

A number system is defined as a system of writing to express numbers.

0.121121112... is rational or irrational is to consider its decimal representation and whether it is a repeating or terminating decimal.

We can see that 0.121121112... is not a terminating decimal because it goes on forever.

Additionally, it is not a repeating decimal because there is no fixed pattern of digits that repeats continuously.

Therefore, we can conclude that 0.121121112... is an irrational number.

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The stars in order from the closest one to the farthest one are:

0.883, 0.886, 0.89, 1.25

so, the answer is A.

What is a sequence?

A sequence is an enumerated collection of objects in which repetitions are allowed. Like a set, it contains members (also called elements, or terms).

To put the given distances in order from the closest one to the farthest one, we need to arrange them in ascending order.

That means we need to start with the smallest value and move toward the largest value.

Looking at the given distances, we see that the smallest value is 0.883, followed by 0.886, then 0.89, and finally 1.25, which is the largest value.

Putting the given distances in ascending order, we get:

0.883, 0.886, 0.89, 1.25

Therefore, the stars in order from the closest one to the farthest one are:

0.883, 0.886, 0.89, 1.25

so, the answer is A.

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Answer:

1191 cm²

Step-by-step explanation:

Area of parallelogram = base X vertical height.

Call the vertical line h.

h/ sin 80  =  7/ sin 10

h = (7 sin 80) / sin 10

= 39.7.

Area of parallelogram = 30 X 39.7

= 1191 cm²

The Area of Parallelogram whose side length is 30 cm is 1,190.952 square cm.

Given:

Side length = 30 cm

Using Trigonometry

tan 80 = P / Base

5.6712 = P / 7

P = 39.6984 cm

Using the formula for Area of parallelogram

= Base x height

= 30 x 39.6984

= 1,190.952 square cm.

Therefore, the area is 1,190.952 square cm.

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Answer:

Step-by-step explanation:

x18y32 x18y ​x6y4 ​x6y32

​

The equation of the line in slope-intercept form is y = (3/5)x + 2. This form allows us to easily identify the slope and y-intercept of the line and to graph it on a coordinate plane.

To write the equation of a line in slope-intercept form, we use the formula:y = mx + b

where:

- y represents the dependent variable (the vertical axis)

- x represents the independent variable (the horizontal axis)

- m represents the slope of the line

- b represents the y-intercept, the point where the line intersects the y-axis.

In this case, we are given the slope as 3/5 and the y-intercept as 2. Plugging these values into the formula, we get:

y = (3/5)x + 2

This equation represents a line with a slope of 3/5, indicating that for every 5 units we move horizontally (along the x-axis), the line moves 3 units vertically (along the y-axis). The y-intercept of 2 tells us that the line intersects the y-axis at the point (0, 2).

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Check the picture below.

\(\sin( \theta )=\cfrac{\stackrel{opposite}{0.5}}{\underset{hypotenuse}{0.64}} \implies \sin^{-1}(~~\sin( \theta )~~) =\sin^{-1}\left( \cfrac{0.5}{0.64} \right) \\\\\\ \theta =\sin^{-1}\left( \cfrac{0.5}{0.64} \right)\implies \theta \approx 51.4^o\)

Make sure your calculator is in Degree mode.

Answer:

5/y-3z

Step-by-step explanation:

Quotient is division

Product is multiplication

please mark brainliest

The equivalent value of the expression is A = 5/y - 3z

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

In an equation, the expressions on either side of the equals sign are called the left-hand side (LHS) and the right-hand side (RHS), respectively. The equals sign (=) indicates that the two expressions have the same value, and that the equation is true for certain values of the variables involved.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. It typically consists mathematical operations, such as addition, subtraction, multiplication, division, and exponentiation.

Given data ,

Let the expression be represented as A

Now , the value of A is

A = quotient of 5 and y, decreased by the product of 3 and z

Now , quotient of 5 and y = 5/y

And , product of 3 and z = 3z

So , On simplifying the expression , we get

A = 5/y - 3z

Hence , the equation is A =  5/y - 3z

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Answer:

33

Step-by-step explanation:

2x-7 = 73

2x = 73-7

2x = 66

x = 66÷2

x = 33

Therefore, the value of x is 33

A candidate received the majority of first-place votes but loses hows that A. The statement does not make sense.

It should be noted that plurality voting simply means when each voter is allowed to vote for only one candidate.

In this case, a candidate received the majority of first-place votes will win the election. Here, the majority of the first place votes using the plurality method is the winner.

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Answer:

5

y

−

2.5

z

−

8

Step-by-step explanation:

−

6

z

−

5.5

+

3.5

z

+

5

y

−

2.5

Add  

−

6

z

and  

3.5

z

.

−

2.5

z

−

5.5

+

5

y

−

2.5

Answer:

− 25z+5y−8

Step-by-step explanation:

DIFFERENTIATE W.R.T. Z

−2.5

According to the information, we can infer that the correct expression is (10 * 7) + (2 * 7) (option D).

To find the correct expression we must look at the graph and interpret the information it has. In this case, some tiles are white and others are gray, so they would represent different elements. In this case, the white area is 10 * 7 tiles, so this would be the first part of the expression.

On the other hand, the second part of the expression would be 7 * 2, which represents the length, length and width of the gray area. According to the above, the correct expression would be (10 * 7) + (2 * 7), the first part in parentheses represents the white area and the second part in parentheses represents the gray area.

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An equation for the linear function is f(x) = x - 3.

In Mathematics, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

At data point (-2, -5), a linear function in standard form for this line can be calculated by using the point-slope form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - (-5) = (-1 - (-5))/(4 - (-2))(x - (-2))

y + 5 = (1 + 5)/(4 + 2)(x + 2)

y + 5 = 6/6(x + 2)

y = x + 2 - 5

f(x) = y = x - 3

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Answer:

b

Step-by-step explanation:

34% in decimal is equal to 0.34, which in fraction is equivalent to 34/100.

Therefore we can solve this as

x/83 = 34/100; 28.22.

Answer:

204.4(repeating) degrees

Step-by-step explanation:

The equation to go from F to C, is (F-32)×5/9. So 400-32 is 368.

368×5=1840

Than 1840/9=204.44 degrees. The 4 is repeating at the end.

Answer:

12

Step-by-step explanation:

because the base is 4 and the height is 6

Answer:

Step-by-step explanation:

Formula of area of triangle = 1/2(b*h)

1/2(4*6)

1/2*24

12 units square

Answer:

I think its B but I'm not 100% sure

Answer:

Its 20 buckets.

Step-by-step explanation:

When rolling a standard number cube 72 times, the probability to see a four or a six approximately 24 times.

To conclude the typical number of times a four or a six will appear while moving a standard number 3D square on numerous occasions, we truly need to ponder the probability of moving a four or a six on a single roll.

A number 3D square has six faces, numbered 1 to 6. Out of these six numbers, two are incredible outcomes (four and six). Thus, the probability of moving a four or a six on a singular roll is 2/6 or 1/3.

To find the typical number of occasions, we improve the probability by without a doubt the quantity of fundamentals: (1/3) * 72 = 24.

While moving a standard number block on different occasions, you can expect to see a four or a six generally on different occasions. This is in light of the fact that out of the six possible numbers, two (four and six) are great outcomes, giving a probability of 1/3.

Thus, while moving a standard number block on different occasions, we can expect to see a four or a six generally on various occasions.

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Answer:

ava ran the fastest

Step-by-step explanation:

Answer:

Based on the information given, we know that angles 3 and 4 are supplementary (they add up to 180 degrees) and angles 2 and 4 are vertical angles (they are congruent). Therefore, we can write:

m∠4 + m∠3 = 180 (since angles 3 and 4 are supplementary)

m∠4 = m∠2 (since angles 2 and 4 are vertical angles)

Substituting m∠4 = m∠2 into the first equation, we get:

m∠2 + m∠3 = 180

Now we can solve for m∠2 and m∠3:

m∠3 = 43 (given)

m∠2 = 180 - m∠3 = 180 - 43 = 137

Since angles 1 and 2 are also supplementary, we can find m∠1 by subtracting m∠2 from 180:

m∠1 = 180 - m∠2 = 180 - 137 = 43

Therefore, m∠1 = 43 degrees and m∠2 = 137 degrees.

Answer:

The answer would be A.) 4 inches

Step-by-step explanation:

It is A. because if the base of the triangle is 10 inches and one side is 4 then the two sides of the trianlge would be the same they are congruent so if one side of the triangle is 4 then the other side of the triangle is 4.

Hope this helps

Answer:yes

Step-by-step explanation:

Answer:

-8b - 32

Step-by-step explanation:

8(-b-4)

Distribute

8 *(-b) + 8 * (-4)

-8b - 32

Answer:

-8b-32

Step-by-step explanation:

8(-b-4) next it would be -8b-32

1.243 is the measure of the value of x from the given expression

Rational equations are those that contain rational expressions. A rational expression is a fraction with polynomial numerator and denominator. A rational expression, in other terms, is a ratio between two polynomials.

Given the following rational equation

√11 x = √17

We need to determine the measure of the value of x.

Taking the square of both sides we will have:

(√11 x)² = (√17)²

11x² = 17

x² = 17/11

x² = 1.545

Take the square root of both sides

√x² = √1.545
x = 1.243

Hence the measure of the value of x from the given equation is 1.243.

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The value of x that makes the relation a function is 3.

Option A is the correct answer.

We have,

A = (5, 3), (4, 9), (7, 2), (x, 6)

Given the points (5, 3), (4, 9), (7, 2), and (x, 6), we need to ensure that x does not repeat in the relation.

If we substitute the given values of x (3, 4, 5, 7) into the relation, we find:

For x = 3: (3, 6)

For x = 4: (4, 6)

For x = 5: (5, 6)

For x = 7: (7, 6)

Now,

A function can not have the same output for the same input.

So,

(4, 6) and (4, 9) are not possible.

(5, 6) and (5, 3) are not possible.

(7, 6) and (7, 2) are not possible.

And,

(3, 6) is possible

Thus,

The value of x that makes a function is 3.

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Answer:

Therefore, the solution to the equation -x + 3y = 11 is x = -34/11 and y = 29/11.

Step-by-step explanation:

The given equation is:

-x + 3y = 11

To solve this equation by elimination, we need to add or subtract one or both equations to eliminate one of the variables. In this case, we can eliminate the variable x by adding the equation with another equation that has x with the same coefficient, but opposite sign.

Let's suppose we have another equation with x, for example:

2x + 5y = 7

We can eliminate x by multiplying the first equation by 2 and the second equation by 1, so that the coefficients of x are opposite:

-2x + 6y = 22 (multiply the first equation by -2)

2x + 5y = 7 (the second equation)

Now we can add the two equations to eliminate x:

-2x + 2x + 6y + 5y = 22 + 7

Simplifying the equation, we get:

11y = 29

Dividing both sides by 11, we get:

y = 29/11

Now that we know the value of y, we can substitute it back into one of the original equations to find the value of x. Let's use the first equation:

-x + 3y = 11

Substituting y = 29/11, we get:

-x + 3(29/11) = 11

Simplifying the equation, we get:

-x + 87/11 = 11

Subtracting 87/11 from both sides, we get:

-x = 11 - 87/11

Multiplying both sides by -1, we get:

x = 87/11 - 11

Simplifying the equation, we get:

x = (87 - 121)/11

x = -34/11