Algebra 2 volume 2 question 60

La ecuación de la fuerza resultante es el vector R = F · cos 234.689° i + F · sin 234.689° j.

Los vectores se caracterizan por tener magnitud y dirección, sea F la magnitud de la fuerza resultante del avión (nótese que la magnitud es un valor no negativo por regla general), cuya fórmula es la siguiente:

R = F · cos θ i + F · sin θ j

Donde:

La dirección del vector se determina mediante la siguiente función trigonométrica inversa:

θ = tan⁻¹ (Fy / Fx)

Donde:

Si sabemos que Fx = - 17 km y Fy = - 24 km, entonces la ecuación de la fuerza resultante es:

θ ≈ 234.689°

R = F · cos 234.689° i + F · sin 234.689° j

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Answer:

x=125    y=130

Step-by-step explanation:

I believe if you add 50+75 you get x

50+75=125

And if you subtract 180 from 50 you get y

180-50= 130

The reason being is because the two numbers inside the triangle add up to the number outside of the triangle "x". Then you would subtract 180 from 50 because that is a supplementary angle meaning it adds up to 180 to get the number on the outside of the triangle "y".

Hope this helped!

Answer:

a = not viable

b = 265

c = 0

good?

Answer: a = not viable b= 265 c = 0

Step-by-step explanation:

The least expensive will be the lowest cost among the cost greater than $13.

i.e $13.5

If the cost of the favors is:

$13.5 < $14 < $15 < $20

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

All of the party favors cost more than $13.

This means,

Cost = x

x > 13

Now,

If the following are the cost of the favors:

$13.5, $14, $15, and $20

The least expensive will be the lowest cost among the cost greater than $13.

i.e $13.5

13.5 < 14 < 15 < 20

Thus,

The least expensive will be the lowest cost among the cost greater than $13.

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Answer:

Your answer is 9x^6*y^2π

Step-by-step explanation:

The formula for a circle is πr^2, with r as the radius.

Since 3x^3*y is the radius, you put that value in to get the equation:

(3x^3*y)^2*π

Once simplified, you get 9x^6*y^2π.

You can simplify further using the value of π, but it depends if the questions wants you to or not, mostly it doesn't.

I hope this was helpful.

The last temperature will be 73.2 degrees Fahrenheit.

The parameter f(m) 15.2m+58 in the straight capability addresses the rate at which the water temperature increments over the long haul. In particular, it addresses the number of degrees Fahrenheit that the water temperature increments for each 1 moment of warming. So assuming the water has been warming for 2 minutes, its temperature will have expanded by 2 * 15.2 = 30.4 degrees Fahrenheit.

Parameter 58 in the linear function addresses the underlying temperature of the water when it begins warming. It is estimated in degrees Fahrenheit. So on the off chance that the water begins at a temperature of 58 degrees Fahrenheit and is warmed for 1 moment, its last temperature will be 15.2 + 58 = 73.2 degrees Fahrenheit.

Subsequently, The last temperature will be 73.2 degrees Fahrenheit.

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The answer is the fourth one: Gary would need 15.2 oz glue and 7.6 oz of glitter to make 4 bottles.

Answer: 108 mph

Step-by-step explanation: 378 divided by 3.5= 108mph

Answer: 108mph

Step-by-step explanation: 378 divided by 3.5= 108mph

15 + 6t >= 63

t >= (63 - 15) / 6

t >= 4.5

t >= 5 (since t must be a whole number of minutes)

So the possible numbers of minutes Kaitlin could add water are 5, 6, 7, 8, ... (any whole number greater than or equal to 5). This can be written as t >= 5.

Answer:

9

Step-by-step explanation:

make them equal to each other

15x = 14x + 9

x = 9

Answer:

y = (-5/6)x - (5/3)

Step-by-step explanation:

The equation of a line in point-slope form is y - y1 = m(x - x1) where (x1,y1) is a point on the line, and m is the slope of the line.

Given that the line passes through the point (6,-8) and has a slope of -5/6, the equation of the line is:

y - (-8) = (-5/6)(x - 6)

y + 8 = (-5/6)x + (-5/6) * 6

y = (-5/6)x - (5/3)

Answer:

(6,-5)

Step-by-step explanation:

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

(y--8)=-5/6(x-6)

6y=-5x+2

Answer:

To find the slope of a line, we can use the formula:

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

where (x1, y1) and (x2, y2) are the coordinates of two points on the line.

Given the points (0,-10) and (-4,-11), we can plug these coordinates into the formula:

slope = (-11 - (-10)) / (-4 - 0) = -1 / -4 = 1/4

So, the slope of the line that passes through the points (0,-10) and (-4,-11) is 1/4.

Step-by-step explanation:

The cc of each that should be mixed are 73.33 and 146.67

From the question, we have the following parameters that can be used in our computation:

Using x and y as the variables, we have the following equations:

x + y = 220

0.14x + 0.08y = 220 * 10% = 22

So, we have

x + y = 220

0.14x + 0.08y = 22

Make y the subject

y = 220 - x

So, the second equation becomes

0.14x + 0.08(220 - x) = 22

This gives

0.14x - 0.08x + 17.6 = 22

Evaluate the like terms

0.06x = 4.4

This gives

x = 73.33

Recall that

y = 220 - x

So, we have

y = 220 - 73.33

y = 146.67

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Complete question

A pharmacist needs 220cc of a solution with a 10% concentration of medicine. They have one solution with 14% concentration and another solution with 8% concentration. How many cc of each should be mixed? etup an equation and solve.

The expression for the area of a rectangle is A = L * W, where L is the length and W is the width.

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The proportional relationship is option D. The graph of the relationship is given below.

Proportions are defined as the concept where two or more ratios are set to be equal to each other.

A relationship is proportional if y = kx, for some constant k.

Consider the last table.

x −2   1   2   3

y −6   3  6   9

When x = -2, y = -2 × 3 = -6

When x = 1, y = 1 × 3 = 3

When x = 2, y = 2 × 3 = 6

When x = 3, y = 3 × 3 = 9

So this is a proportional relationship with constant of proportionality k = 3.

Hence the table shown in the last option is the proportional relationship.

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The predicted demand of a bobblehead that has price of $6.00 is given as follows:

49.093 units.

The function in the context of this problem is defined as follows:

y = -0.227x + 50.445.

In which:

For a price of $6.00, the predicted demand is obtained with the numeric value at x = 6, replacing the lone instance of x by 6, hence:

y = -0.227(6) + 50.445

y = 49.093 units.

Meaning that the second option is the correct option.

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By using the combination theorem, it can be concluded that the value of m + n = 125

Combination is the number of ways to choose a sample of r elements from a set of n distinct objects where order does not matter and replacements are not allowed.

nCr = n! / (n - r)! r!

Let's denote the number of rectangles as r, and the number of squares as s:

r = ⁹C₂ x ⁹C₂

 = (9! / (9 - 2)! 2!) x (9! / (9 - 2)! 2!)

 = (9! / 7! 2!)   x   (9! / 7! 2!)

 = 36 x 36

 = 1296 rectangles

s = 1² + 2² + 3² + 4² + 5² + 6² + 7² + 8²

  = 1 + 4 + 9 + 16 + 25 + 36 + 49 + 64

  = 204 squares

Then we get the ratio of s : r as follows:

s / r = 204 / 1296

      = 17 / 108

Since m represents the horizontal lines and n represents the vertical lines, then m + n = 17 + 108 = 125.

Thus, it can be concluded that the value of m + n = 125

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Answer:2216 feet

Step-by-step explanation:

Badwater Basin is below sea level, so already we know that the 284 should be a negative number since it is below sea level. Mount McKinley is above sea level, so that number stays as a positive number. Now we can put these two number into an equation to solve, which would be 2,500 + (-284).

Note that the parenthesis are only there so you know that the number is negative, you don't need to solve anything.

Since adding a negative to a positive number is the same as subtraction, we can simplify it to look a little less confusing. You only need to solve 2,500 - 284 , which then equals 2216 ft.

Hope this helps you!

-0.05 is the average rate of change in median age per year from 1930 to 1960.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Given,  a data set that gives the median age of an American man at the time of his first marriage.

Year                             Median age

1910                              25.1

1920                             24.6

1930                             24.3

1940                             24.3

1950                             22.8

1960                             22.8

1970                             23.2

1980                             24.7

1990                             26.1

2000                             26.8

The average rate of change from 1930 to 1960 = (-24.3 + 22.8) / (1960-1930)

The average rate of change from 1930 to 1960 = -0.05

Therefore, the average rate of change in median age per year from 1930 to 1960 is -0.05.

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The zeros of the function f(x)=x²-8x+15 are x = 3 and x = 5. Option A

From the information given, we have that the quadratic equation is given by the function;

f(x)=x²-8x+15

Using the factorization method, we have to multiply the coefficient of x² by the constant 15

Then move further to find the pair factors of 15 that add up to -8

Substitute the value, we get;

x² - 5x - 3x + 15

Pair the expression

(x² -5x) - (3x + 15)

factorize

x(x -5) - 3(x-5)

Then,

x - 3

x = 3

And

x = 5

Hence, the values are 3 and 5

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We must sell 625 loaves of bread to break even.

If it is a solution of equations, fill all the information of your solution into the equations you are working on to ensure that all equations are satisfied by your solution. And then, solve these equations to find the answer to your problem.

Let N be the number of loaves you sell.

Your cost would be,

C = 500 + 0.2N

Your revenue would be,

R = 1. N

Now, find out when is C = R  

⇒500 + 0.2N = N

⇒500  = 0. 8 N

⇒N = 500/0. 8

⇒N = 625

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a) The graph of the parabola opens downwards.

b) The point for axis of symmetry is x = -3.

c) The points of vertex for the parabola is (-3,-3).

d) There is no x-intercept and only one y-intercept, y = - 7.

What is a parabola?

A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves.

The graph of a parabola is given.

a) The parabola is starting from -∞ and is rising and then it is falling downwards towards the +∞.

Therefore, the parabola opens downwards.

b) The vertical line that passes through a parabola's vertex is the axis of symmetry, making the parabola's left and right sides symmetric. This line divides the graph of a quadratic equation into two mirror representations in order to make things simpler.

The parabola is symmetrical about x = -3.

Therefore, the axis of symmetry is x = -3.

c) There is a pivotal point in every parabola. To put it another way, it has a turning point where it either goes from "growing" to "decreasing" or vice versa. The vertex of the parabola is the name given to that pivotal point.

Here, the parabola turns at point (-3,-3).

Therefore, the points of vertex is (-3,-3).

d) The x-intercept is when the graph of parabola crosses the x-axis. In this case the parabola is drawn below the x-axis so there is no x-intercept.

The y-intercept is when the graph of parabola crosses the y-axis. In this case the parabola crosses the y-axis once at y = -7.

Therefore, the y-intercept is y = -7.

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Answer: 342.55

Step-by-step explanation:

689.45 - 346.90 = 342.55

or

346.90 + 342.55 = 689.45

The inequality that describes that Trina must spend at least 45 minutes studying for her test at x ≥ 45 min.

In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. Therefore, inequality emerges from a lack of balance. In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions.

Trina is to spend at least 45 minutes studying for her test which means that she can either spend 45 minutes studying, or more than 45 minutes.

The inequality for this is therefore:

x ≥ 45

Assuming that the minutes she spends studying is x.

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Full question is:

Trina must spend at least 45 minutes studying for her math test. (find the inequality)

0.3 pounds of oranges are left and this can be calculated by following steps :

Convert the 8 2/5 oranges to pounds.

8 2/5 oranges = 8.4 oranges

1 orange = 0.5 pounds

8.4 oranges x 0.5 pounds = 4.2 pounds

Subtract the amount of oranges eaten (4 5/8 pounds) from the total amount of oranges (4.2 pounds).

4.2 pounds - 4 5/8 pounds = 0.3 pounds

Answer: 0.3 pounds of oranges are left.

One of the four operations used in mathematics, along with addition, multiplication, and division, is subtraction. Removal of items from a collection is represented by the operation of subtraction.

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The school need to hire additional teacher to get 1:18 ratio is 20.

The teacher and student ratio in a school is 1:30,

let the number of teachers in a school=x,

then the number of students in school=30x,

total number of students in school=900

So, the number of teachers in school x=900÷30

                                                                x=30.

We want to take ratio of students and teachers =1:18

So, according to this ratio number of students=18x

and the number of required teachers x= 900 ÷ 18

                                                                x=50,

the school required 50 teachers,

Hence, the school need to hired teachers = 50-30=20

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Total cost c as a function of x is $94000 + 11.2x.

A company invests $94,000 for equipment to produce a new product. each unit of the product costs $11.40 and is sold for $17.98.

let x be the number of units produced and sold.

now,

Number of units = x

so,

c(x)= $94000 + 11.2x

Equation

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.

Function

A function relates an input to an output. It is like a machine that has an input and an output. And the output is related somehow to the input.

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Answer:

To solve the equation (4x - 24) + x = 14, we can start by combining like terms on the left side of the equation:

4x - 24 + x = 14

Next we'll add the x terms together and the constants together:

5x - 24 = 14

Then we'll add 24 to both sides to get all the x terms on one side:

5x = 38

Finally we'll divide both sides by 5 to find the value of x:

x = 7.6

So the solution to the equation is x = 7.6

The straight line distance between the northbound and eastbound cars is 5.7 kilometres.

The movement of cars and straight line connecting them forms a right angled triangle. The straight line will be hypotenuse will the eastbound and northbound distance will be perpendicular and base of the triangle. Thus, using Pythagoras theorem to find the distance between the two cars.

Distance between the two cars = ✓4² + 4²

Taking square of the numbers

Distance between the two cars = ✓16 + 16

Performing addition

Distance between the two cars = ✓32

Taking square root

Distance between the two cars = 5.66

Round to nearest tenth = 5.7

Thus, the distance is 5.7 kilometres.

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Answer:

Step-by-step explanation:

Ahh hell nah