the angle of depression of the light to the nearest minute is

The least polynomial that contains the roots - 1 and 3 - i is x³ - 5 · x² + 4 · x + 10.

In this case we need to find a polynomial that contains a set of roots, a real root and a complex root. In accordace to the quadratic formula, the root 3 - i must be accompanied by its conjugate, that is, 3 + i to guarantee that all coefficients of the polynomial are real.

Then, the factor form of the cubic equation is:

f(x) = (x + 1) · (x - 3 + i) · (x - 3 - i)

f(x) = (x + 1) · [x² - (3 - i) · x - (3 + i) · x + (3 - i) · (3 + i)

f(x) = (x + 1) · (x² - 3 · x + i x - 3 · x - i x + 9 - i²)

f(x) = (x +1) · (x² - 6 · x + 10)

f(x) = x³ - 6 · x² + 10 · x + x² - 6 · x + 10

f(x) = x³ - 5 · x² + 4 · x + 10

The least polynomial is x³ - 5 · x² + 4 · x + 10.

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Multiplication is not possible with so similar variables in the denominator, in the given fractions and hence the answer is incorrect.

So, -4y × 1/5y:

Theefore, multiplication is not possible with so similar variables in the denominator, in the given fractions and hence the answer is incorrect.

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Answer:

The missing number is 3.

Step-by-step explanation:

1. For the sake of the equation, let's represent the missing number as y. Then write the equation: 4*7=(4*10)-4*y

2. Follow according to the order of operations, then you should get the result of 28=40-4y

3. Swap -4y and 28 in the equations: 4y=40-28 which goes to 4y=12.

4. Find y by dividing the rest of the equation by 4: y=3

Answer:

Step-by-step explanation:

Let's illustrate the situation in a diagram to understand.

In a right triangle if the altitude drawn divides the hypotenuse into two segments, then the length of the altitude is the geometric mean of the lengths of the two segments.

Therefore,

Hypothesis: It is January and Conclusion: There is snow

The initial clause, or "if," of a conditional statement is the hypothesis. The second, or "then," component of a conditional statement is the conclusion. The theory led to the conclusion.

An if-then statement, also known as a conditional statement, is a set of hypotheses followed by a conclusion. As indicated, this is pq. Read this: if p, then q. If the hypothesis is correct but the conclusion is untrue, a conditional statement is false.

Conditionals are in the form if P, then Q.

P is the hypothesis.

Q is the conclusion.

If It is January, then there is snow.

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The distance between C and D is 17.26 units

What is meant by distance?

Distance is a numerical or qualitative measurement of the distance between two objects or places. Distance can refer to a physical length or an estimate based on other factors in physics or common use (e.g. "two counties over"). Because spatial cognition is a rich source of conceptual metaphors in human thought, the term is frequently used metaphorically to mean a measurement of the amount of difference between two similar objects (such as statistical distance between probability distributions or edit distance between text strings) or a degree of separation (as exemplified by distance between people in a social network). The concept of a metric space is used in mathematics to formalize most such conceptions of measurement, both real and metaphorical.

Distance CD = √{(-9-8)² + (-6+3)²}

                      = √{(-17)² + (-3)²}

                      = √{289 + 9}

                      = √298

                      = 17.26 units

Hence, the distance between C and D is 17.26 units

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Answer: 17.3

Step-by-step explanation:

The expression to show the number of cookies that Cindy receive is 96/8 - c.

An expression is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

In this case, 96 cookies were shared among 8 people and Cindy has c fewer cookies. This will be:

= 96/8 - c

This illustrates the concept of expression.

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Answer:

Explanation:

The diagram representing the two towers is given below:

Answer: x=2

Step-by-step explanation:

1. Distribute

2. Subtract 9 from both sides

3. Simplify

4. Subtract x from both sides

5. Simplify

6. Divide both sides by the same factor

7. Simplify

Based on the information provided about Arthur, we have the following:

In Mathematics, a graph can be defined as a type of chart that is commonly used for the graphical representation of data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis (x-coordinate) and y-axis (y-coordinate).

Distance simply refers to the amount of ground that is covered or travelled by a physical object (body) over a particular period of time and speed, irrespective of the physical object's direction, starting point, or ending point.

In conclusion, the distance covered by a physical object (body) over a particular period of time can be plotted by using a position-time graph as shown in the image attached below.

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Paper towels are being ordered by a restaurant. The data table compares the number of cases to the quantity of paper towel rolls. 1:12 ratio does the proportionality constant appear at in the data table.

Given that,

There is a table.

Paper towels are being ordered by a restaurant. The data table compares the number of cases to the quantity of paper towel rolls.

We have to find what ratio does the proportionality constant appear at in the data table.

The table is

Number of cases ordered     |      Number of rolls of paper towels

1                                               |      12

3                                               |      36

5                                               |      60

10                                              |      120

Therefore, 1:12 ratio does the proportionality constant appear at in the data table.

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EXPLANATION:

We are given a circle K with radius KG. Note here that line KJ and line KG are both radii of the circle given.

Also we know that a line tangent to a circle at the point of intersecting with the radius forms a 90-degree angle with the radius.

We can now extract the following triangle from the diagram provided;

We now have a right triangle which we shall solve by use of the Pythagorean theorem;

Where we have c as the longest side (hypotenuse) and then a and b are the two other sides. Substituting into the equation above now gives us;

Subtract 36 from both sides;

Take the square root of both sides;

Rounded to the nearest tenth, the answer is;

ANSWER:

A parabola with focus of (-5, -1) and a directrix of y=7 has the equation of the parabola as: (x + 5)² =  8 (y - 3)

Quadratic equation = parabolic equation, when the directrix is at y direction is of the form:

(x - h)² =  4P (y - k)

OR

standard vertex form, y = a(x - h)² + k     where a = 1/4p

The focus

F (h, k + p) = (-5,-1)

h = -5

k + p = -1

P in this problem, is the midpoint between the focus and the directrix

P = (-1 - 7) / 2 = -4

p = -4

the vertex

v(h, k)

h = -5

k + p = -1, k = 3

v(h, k) = v(-5, 3)

substitution of the values into the equation gives

(x - h)² =  4P (y - k)

(x - -5)² =  4 * 2 (y - 3)

(x + 5)² =  8 (y - 3)

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The greatest number of rows Silvia can plant as per given number of plants and condition is equal to 10.

As given in the question,

Silvia is going to plant 20 tomato plants and 30 bean plants.

Total tomato plants = 20

Total bean plants = 30

If Silvia would like to plant, the plants in rows where each row has the same number of tomato plants and each row has the same number of bean plants.

Then, the greatest number of rows Silvia can plant is equal to greatest common factor of 20 and 30.

20 = 2×2×5

30 = 2×3×5

Greatest common factor of 20 and 30 = 2×5 = 10

Therefore, the greatest number of rows Silvia can plant as per given number of plants and condition is equal to 10.

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The equation of line is 11y + 3x + 37 = 0

What is Equation of Line ?

The equation y = mx + c is the general equation of any straight line where m is the gradient of the line (how steep the line is) and c is the y -intercept (the point in which the line crosses the y -axis).

The given points are, (5, -6) and (-5, -2)

To find slope we have formula ,

m = (y2 - y1 ) / (x2 - x1)

where,

(x1, x2) = (5, -6) and,

(y1, y2) = (-5, -2)

Put the values in given formula of slope,

m = (-2 - (-5) ) / (-6 - 5)

m = (-2 + 5) / (-11)

m = - (3/11)

we get the slope, now to find the equation of line.

We know, the equation of the line with slope intercept is

y = mx + b

Now, for x and y value take any point and put it into this equation and find 'b'

let's take (-5, -2)

-2 = -(3/11) * -5 + b

-2 = 15/11 + b

-2 = (15 + 11b) / 11

-22 = 15 + 11b

-22 - 15 = 11b

-37 = 11b

b = -37/11

We got m = - 3/11 and b = -37/11

Now put these value in equation of line and form the equation

y = mx + b

y = -3/11 x - 37/11

11y = -3x - 37

3x + 11y + 37 = 0

Hence, the equation of line is 11y + 3x + 37 = 0

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slope intercept equation is represented below

Therefore,

In order to calculate the price for each brand, calculate the quotient in between the price for n forks over the number of forks, just as follow:

Brand A:

3.89/72 = 0.05

Brand B:

6.62/96 = 0.07

Hence:

Unit price for brand A:

$0.05

Unit price for brand B:

$0.07

When the mass is 500 grams and the volume is 40 cubic centimeters then density is 12.5 gm per cc.

When the mass is 125 grams and the volume is 1.4 cubic centimeters then density is 89.28 gm per cc.

The amount per unit of length, area, or volume as. a: a substance's mass per unit volume. b: the distribution of an amount (such as mass, electricity, or energy) per unit, typically of space.

D = M/V

a) M = 500 gms

V = 40 cubic cm

D = 500/40

D = 12.5 gm per cc

b) M = 125 gms

V = 1.4 cubic cm

D = 125/1.4

D =89.28 gm per cc

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The equation that represent the relationship between the number of months and the amount remaining on the card is: y = 25 - (2.50x)

a) the independent variable is the: Number of month after the first year

b) the dependent variable is the: Amount remaining on the card

To solve this problem, we have to state the equation using the information of the problem.

Information about the problem:

Writing the equation according to the information gave, we have:

y = 25 - (2.50x)

Where:

The relationship between the number of months after the first year and the amount remaining on the card is: linear and inverse because when the number of months after the first year increases (x), the amount remaining on the card (y) will decrease.

The "y" variable is the dependent variable, because it will change according to the number of months passed after the first year (x).

The "x" variable is the independent variable, because it doesn't depend on any other value, just the number of months passed after the first year.

An equation is the equality between two algebraic expressions, which have at least one unknown or variable.

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Answer:

6

Step-by-step explanation:

We can round $4.98 up to $5.

Then do $30 / $5 = 6

Go back and check if 6 works:

$4.98 × 6 = $29.88 which is less than $30.

So the answer is 6

The value of x is 85° when a pair of parallel lines intersects another pair of parallel lines.

According to the question,

We have the following information:

A pair of parallel lines intersects another pair of parallel lines.

We have a figure where an angle is given as 85°.

Now, the following theorems would be helpful in finding the value of x:

When a pair of parallel lines is intersected by another line then the sum of two consecutive interior angles is 180°. (1)

When a pair of parallel lines is intersected by another line then the alternate interior angles are equal. (2)

Vertically opposite angles are equal. (3)

(Now, we will refer to these theorems by the number given in the brackets.)

Now, by theorem 3, we have vertically opposite angle as 85°.

Now, its alternate interior angle will also be 85°.

Now, 85° and x° are vertically opposite angles.

So, by theorem 3, we have the value of x as 85°.

Hence, the value of x is 85°.

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Using the properties of equality, the value for m in the equation is: m = pV.

For any given equation, to solve for a variable in the equation, we have to isolate the variable to one side of the equation in order to determine its value. To do this, several properties of equality need to be applied to isolate the variable to one side of the given equation.

Given the equation, p = m/V, we need to isolate the variable m to one side of the equation in order to solve for m.

p = m/V

Multiply both sides of the equation by V

p × V = m/V × V [multiplication property of equality]

Simplify the equation:

pV = m

m = pV

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Answer:

a. 4.2 - 2.8 = 1.4

b. 72.1 - 45.6 = 26.5

c. 82.2 - 41.3 - 29.2 = 11.7

d. 17.1 - 11.7 - 0.8 = 4.6

e. 29.2 - 12.5 - 0.9 = 15.8

f. 21 - 14 = 7

g. 71 - 37 - 18 = 16

h. 50 - 19 - 8 = 23

i. 92 - 57 - 16 = 19

j. 44 - 18 - 9 = 17

The inequality representing d, the total number of days is 76.5d + 24 ≤ 330

From the question, the given parameters are:

Charges per day = $76.50

Charges per mile = $0.06

This means that the equation that represents the total charges for d days is

Total = Charges per day x Number of days + Charges per mile x Number of miles

So, we have

Total = 76.5 x d + 0.06 x m

Where m represents the number of miles

From the question, we have

This means that

m = 400 and Total ≤ 330

So, we have

76.5 x d + 0.06 x 400 ≤ 330

Solve

76.5 x d + 24 ≤ 330

This gives

76.5d + 24 ≤ 330

Hence, the inequality that represents the scenario is 76.5d + 24 ≤ 330

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The given expression is 3 x (5-2)-1

From the options

If Orlando has 5 actions figures.

He decides to give 2 of them to his younger brother, then he will have (5-2) action figures left

His parents were happy with him and tripled what he had left

3 x ( 5 -2 ) action figures.

If he had so many actions figures after that and he gave his brother 1 more action figure then he will have

3 x ( 5-2) - 1 action figures left.

The right answer is therefore option B

pls provide the picture below, because of that its an incomplete answer

The Points are in the form (x,y), and they are A(-3,8) and B(5,-4).

The length between two points is:

In this case:

The correct anser is:

Answer:

17. s = 9

18. x = 8x^(½)

Step-by-step explanation:

s² - 7 = 74?

s² = 74 + 7

s² = 81

√(s²) = √(81)

s = 9

x² - 8x = 0

x² = 0 + 8x

x² = 8x

√(x²) = √(8x)

x = 8x^(½)

OR by factoring

x²−8x=0

x(x−8)=0

x=0 or x−8=0

x=0 or x=8

Answer:

1 answer

Step-by-step explanation:

when the terms are collected

[tex]4k = 0[/tex]

[tex]k = 0[/tex]