2. Solve the following equations for 0° Sx < 180°.
(i) cosec(x+10°) = 3
(ii) cot(x - 30°) = 0.45 .

Answer:

The vector direction is 83.0° relative to the positive x-axis

Step-by-step explanation:

* Lets explain how to find the direction of a vector

- A vector is a quantity which has both magnitude and direction

- The vector has two components x-component and y-component

- The x-component = v cos Ф , and the y-component = v sin Ф,

  where Ф is the angle between the vector and the positive part

  of the x-axis

- The magnitude of the vector = [tex]\sqrt{x^{2}+y^{2}}[/tex]

- The direction of the vector = [tex]tan^{-1}(\frac{y}{x})[/tex]

* Lets solve the problem

∵ x-component of the vector = 0.15

∵ y-component of the vector = 1.22

- Both x-component and y-component are positive

∴ Ф will be between 0° and 90°

∵ The direction of the vector = [tex]tan^{-1}(\frac{y}{x})[/tex]

∴ The direction of the vector = [tex]tan^{-1}(\frac{1.22}{0.15})[/tex]

∴ The direction of the vector = 83.0°

* The vector direction is 83.0° relative to the positive x-axis

Answer:

1.20 off dog food

Step-by-step explanation:

Inequalities help us to compare two unequal expressions. The coupon that can be doubled is $1.25. The correct option is B.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

Given that the supermarket is advertising double coupons up to $1.25. Therefore, every coupon that has a value less than or equal to $1.25 will be doubled. Therefore, we can write the inequalities as,

x ≤ $1.25

Now, if we look at the given options then the only option that is less than $1.25 is the coupon for dog food.

1.20 < 1.25

Hence, the coupon that can be doubled is $1.25.

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Answer:

The width is 3.3 meters

Step-by-step explanation:

The perimeter of a rectangle is 2L + 2W. L is 4.5.

P = 2L + 2W

15.6 = 4.5 * 2 + 2W

15.6 = 9 + 2W

6.6 = 2W

3.3 = W

Step-by-step explanation:

Given :- y intercept = ( 0 , 5 ) i.e, the line cuts y axis at 5

and , slope of the line ( m ) = 2/9

• Slope intercept form of the equation is

y = mx + c

Where , m is slope of the line

and c is y intercept !!

[tex]y = \frac{2}{9} x + 5 \\ \\ because \: c \: = 5[/tex]

Answer:

Step-by-step explanation:

11² = 11 · 11 = 121 < 136

12² = 12 · 12 = 144 > 136

Answer:

B

In a function, f(x), there are two parts:

x: the input value

f: the output value

Answer:

300 more miles

Step-by-step explanation:

because its easy NO OFFENSE SERIOULSY

Answer:

p=$100

Step-by-step explanation:

Let

y -----> annual revenue

p ----> the charge in dollars for a chair

we know that

The revenue is equal to the number of chairs multiplied by the charge for one chair

so

[tex]y=(600-3p)p[/tex]

[tex]y=600p-3p^2[/tex]

This is the equation of a vertical parabola open downward.

The vertex is a maximum

using a graphing tool

The vertex is the point (100,30,000)

That means

The maximum revenue is y=$30,000

when the carpenter charge $100 for a chair

The revenue is maximum when a fee of $100 is charged per chair.

An equation is an expression used to show the relationship between two or more variables and numbers.

Revenue is the product of the price per item and the total number of items.

Hence:

Revenue (R) = Price * number of item

R = p * 600 - 3o

R = 600p - 3p²

Maximum revenue is at R' = 0:

R' = 600 - 6p

6p = 600

p = 100

The revenue is maximum when a fee of $100 is charged per chair.

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Answer:

A. -1⅕

Step-by-step explanation:

[tex]-4\frac{4}{5}\div 4 = -4,8\div 4 = -1,2 = -1 \frac{1}{5} [/tex]

I am joyous to assist you anytime.

Answer:

4x4x8x2

256

Step-by-step explanation:

the equation to find any slope given two points is (y1-y2)/(x1-x2)

given this equation, the slope of problem 24 would be (6-3)/(-1-4) or (3-6)/(4+1) which is equal to -3/5,

depending on which point you call (x1,y1) and (x2,y2)

calling either of the points 1 or 2 will still result in the same slope

Answer:

The expression for determining the number of distinct subsets for a set with n distinct elements is 2^n (2 raise to the power n).

Step-by-step explanation:

The expression for determining the number of distinct subsets for a set with n distinct elements is 2^n (2 raise to the power n).

If a set has 0 elements then it has 1 subset which is a null set (2^0=1)

if a set has 1 element then it has 2 subsets. One is a null set and the other one would be itself (2^1 = 1).

Like wise if a set has 5 elements then it has 32 subsets (2^5 = 32)

Lets solve an example. We have a set A and we have to find the subsets of set A.

A = {1,2,}

2^n = 2^2 = 4

It means that the number of  all the possible subsets = 4

{0},{1},{2},{1,2}....

In this exercise we have to have knowledge of sets and subsets to find the value of the unknown, like this:

[tex]2^n = 2^2=4[/tex]

So we have to remember some ideas about sets like:

[tex]2^0=1\\2^1 = 1\\2^5 = 32[/tex]

We have a set A and we have to find the subsets of set A, so that is :

[tex]A = {1,2,}\\2^n = 2^2 = 4\\A= {0},{1},{2},{1,2}....[/tex]

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well, one way to go about it is, to do away with the denominators by using the LCD of all fractions, hmmm let's see, we have denominators of 3,5 and 15, so the LCD will just be 15.

now let's multiply both sides by the LCD of 15 to do away with the denominators,

[tex]\bf \cfrac{2}{3}+\cfrac{3n}{5}=\cfrac{13}{15}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{15}}{15\left( \cfrac{2}{3}+\cfrac{3n}{5} \right)=15\left( \cfrac{13}{15} \right)}\implies 10+9n=13 \\\\\\ 9n=3\implies n=\cfrac{3}{9}\implies n = \cfrac{1}{3}[/tex]

Answer:

[tex]103\ notebooks[/tex]

Step-by-step explanation:

The question in English is

Martha spent $60 to buy the same notebooks if each notebook had cost $2 plus Martha would have bought 80 fewer notebooks for the same $60. How many notebooks did Martha buy?

Let

x -----> the cost of each notebook

n -----> number of notebooks that Marta bought  

we know that

[tex]nx=60[/tex] -----> [tex]n=\frac{60}{x}[/tex] -----> equation A  

[tex](n-80)(x+2)=60\\\\nx+2n-80x-160=60\\\\n(x+2)-80x=220 ---> equation\ B[/tex]

substitute equation A in equation B and solve for x

[tex]\frac{60}{x}(x+2)-80x=220[/tex]

Multiply by x both sides to remove the fraction

[tex]60(x+2)-80x^2=220x[/tex]

[tex]60x+120-80x^2=220x[/tex]

[tex]-80x^2-160x+120=0[/tex]

Using a graphing tool

Solve the quadratic equation

The solution is

x=$0.581

see the attached figure

Find the value of n

[tex]n=\frac{60}{0.581}=103\ notebooks[/tex]

Answer:

D5 is the answer im pretty sure

Step-by-step explanation:

Answer:

The answer is D (5)

Step-by-step explanation:

I just took the test and got it right

Hopefully this helps you

pls mark brainlest

Mrs. Zhang's is 1/10 the size of Mrs. Acquino's.

Since you know Mrs Zhang's, divide the amount she has by the fraction of hers.

48,000 / 1/10

When you divide by a fraction, reverse the fraction and multiply:

48,000 x 10/1 =

48000 x 10 = 480,000 bees.

To estimate Mrs. Aquino's bee population, multiply Mrs. Zhang's bee population, which is 48,000, by 10. Mrs. Acquino has approximately 480,000 bees on her farm.

Since Mrs. Zhang’s bee population is 48,000 and her farm is said to be 1 tenth as large as Mrs. Acquino’s, to find the population of Mrs. Aquino's bees, we need to multiply Mrs. Zhang’s bee population by 10. Performing the calculation:

48,000 × 10 = 480,000

So, Mrs. Aquino's bee farm has approximately 480,000 bees.

Answer:

1/6

Step-by-step explanation:

Let

c-----> the number of cola bottles that Dan picks

s ----> the number of smarties that Dan picks

m ---> the number of marshmallows that Dan picks

we know that

c=3s ----> equation A

m=2s ---> equation B

we know that

To find out the proportion of the bag of sweets that are smarties, divide the number of smarties by the total of sweets

The total of sweets is equal to

(c+s+m)

substitute equation A and equation B in the total of sweets

(3s+s+2s) =6s

Find the proportion

s/6s

Simplify

1/6

The proportion of smarties in Dan's bag of sweets, in its simplest form, is 1/6.

To solve the question about what proportion of the bag of sweets are smarties, let's assume Dan picks x number of smarties. Following the information provided, he picks 3 times as many cola bottles as smarties, which is 3x, and twice as many marshmallows as smarties, which is 2x. The total number of sweets in the bag is the sum of smarties, cola bottles, and marshmallows, which amounts to x + 3x + 2x = 6x. The proportion of smarties in the bag is the number of smarties divided by the total number of sweets, so we get:

Proportion of smarties = Number of smarties / Total number of sweets = x / 6x = 1/6.

The proportion of smarties in the simplest form is 1/6.

Answer:

x-10=6x+3

Step-by-step explanation:

Okay, Is means equals. I used x as the unknown number. 10 less than a number means x-10. Squishing a variable and constant ( x and 6) together means multiplication (Constant always going before the variable) It's three more than six times the number, so it's six times the number plus three.

Hope I helped :)

Answer: It is irrational because it cannot be written as a ratio of two integers. It is not a perfect square

Step-by-step explanation:

Answer:

[tex]27\leq x \leq37[/tex]

Step-by-step explanation:

Let's arrange the numbers from least to greatest:

20, 25, 27, 28, 31, 32, 32, 38, 40, 40, 42, 48

The median is the "middle" number when arranged from least to greatest.

There are 12 numbers, so the middle number would be "average" of 6th and 7th terms.

6th term = 32

7th term = 32

Average = (32+32)/2 = 32

Hence, median = 32

Absolute deviation of 5 minutes means 5 minutes less or greater than the median, 32.

So, 32 - 5 = 27  &  32 + 5 = 37

Hence  [tex]27\leq x \leq37[/tex]

To find the inequality range for race times, we must first arrange the times and find the median, which is 32 minutes. The desired race time with an absolute deviation of at most 5 minutes from the median results in the inequality 27 ≤ x ≤ 37.

Explanation:

To solve this problem, we need to arrange the given race times in order and find the median. Once we find the median, we can set up an inequality that represents a race time within 5 minutes more or less than this median time.

First, we arrange the race times in ascending order: 20, 31, 27, 32, 25, 42, 48, 28, 40, 38, 32. After putting them in the proper order (20, 25, 27, 28, 31, 32, 32, 38, 40, 42, 48), we find that the median, which is the middle value, is 32 minutes since there are 11 times, and the 6th time is the median.

Next, we want to have a race time with an absolute deviation of at most 5 minutes from the median (32 minutes). This gives us the inequality 27 ≤ x ≤ 37. So, the time you hope to achieve in the race is between 27 and 37 minutes.

Answer:

Angles B and C are 70 degrees.

Step-by-step explanation:

The sum of three angles of a triangle is 180 degrees.

Of these angle A in triangle ABC is given as 40 degrees.

Another input is that the triangle is isosceles. This means that AB=AC or in other words, angle B and angle C are equal.

Let the angle B or angle C be represented as x degrees.

Representing this in equation format:

A + B + C = 180

=> 40 + x + x = 180

=> 2x = 180 - 40 = 140

=> x = 140/2 = 70

So both the angles B and C are 70 degrees.

If triangle ABC is isosceles, then angles B and C both measure 70°.

We have,

In an isosceles triangle, two angles are congruent (they have the same measure). If angle A is 40°, and triangle ABC is isosceles, then angles B and C must each measure:

B = C = (180° - 40°) / 2

= 140° / 2

= 70°

So, if triangle ABC is isosceles, both angles B and C would measure 70°.

Thus,

If triangle ABC is isosceles, then angles B and C both measure 70°.

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Answer:

A. 35%

Step-by-step explanation:

You can write 42 of 120 as a fraction ---> 42/120

If you simplify you get 7/20.

7/20 can also be written as 35/100, so the percentage would be 35%.

Answer:

A. 35% BRAINLIEST WOULD BE APPRECIATED!

Step-by-step explanation:

Do guess and check. Start with A.

120*0.35=42 ~ that works! check the others to be sure.

120*0.286=34.272 ~ nope!

120*0.042=don't even need to do it, unreasonable.

120*.33=39.6 ~ nope!

Answer:

2748 days

Step-by-step explanation:

687 days * 4 revolves = 2748

2748 earth days.

Expressions included in parentheses, brackets, braces, and fraction bars should be made simpler. Analyze each power. Divide and multiply all numbers from left to right. Make sure to add and subtract all numbers from left to right. last but not least, use any method. BODMAS or PEMDAS.

Given, It takes 687 Earth days for the planet Mars to revolve around the sun once.

Earth days does it take Mars to revolve around the sun four times = 4 *687

Therefore, 2748 Earth days take Mars to revolve around the sun four times.

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Answer:

Less because they are negative

Step-by-step explanation:

The number-2.75 is less than the number -2.5.

A numeral system is a way of writing numbers; it's a way of mathematically notating a collection of numbers by utilizing a consistent set of digits or other symbols. In several numeral systems, the same set of symbols may represent various numbers.

Given numbers are -2.75 and -2.5.

The number -2.75 is less than the number -2.5. For the negative integers the number with a higher magnitude but having a negative sign is lesser than the number with a small magnitude with a negative sign.

Therefore, the number-2.75 is less than the number -2.5.

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Answer:it depends how much he is earning

Answer:

C. Point A is the center of the circle that passes that passes through the points E, F and G and is the center of the circle that passes through the points X, Y and Z.

Step-by-step explanation:

The center of insribed circle into the triangle is the point where the angle bisectors of the triangle meet.

The center of circumsribed circle over the triangle is the point where the perpendicular bisectors of the sides meet.

Line segments ZE, FY and GX are both angle bisectors and perpendicular bisectors of the sides, so the point of intersection of line segments ZE, FY and GX is the center of inscribed circle into the triangle and the center of the circumscribed circle over the triangle. Inscribed circle passes through the points X, Y and Z. Circumscribed circle passes through the points E, F and G. So, point A is the center of the circle that passes that passes through the points E, F and G and is the center of the circle that passes through the points X, Y and Z.

Answer:

c

Step-by-step explanation:

Answer:

8 3/8

Step-by-step explanation:

Answer:

8.375 or  8 3/8