(a) Solve the equation 4 cos x + 2 = 3 for 0° < x < 360°.

Answer:

All the sides of the square are equalso the squares are congruent.. Are congruent shapes? Two shapes that are the same size and the same shape are congruent.

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Step-by-step explanation:

Answer:

The nth root theorem is a mathematical principle that states that, for any positive integer, it will have n nth roots!

An nth root of x is equivalent to saying [tex]\sqrt[n]{x}[/tex]. To elaborate, if you want to know how many 2nd roots that 1 has, through this theorem you will know it has 2 of these roots (-1 and 1). This applies for all numbers!

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Answer:

−7+y/3  is the same as that, but simplified.

Answer:

y/3-7

Step-by-step explanation:

The answer is the solved equation of -3+2/3y-4-1/3y.

Subtract 4 from -3 to get -7

= -7+2/3y-1/3y

Combine 2/3y and -1/3y to get 1/3y

-7+1/3, or just y/3-7.

Answer:

[tex]y = 2x - 3[/tex]

Step-by-step explanation:

❗ The way I solved this problem doesn't involve me using point-slope form like the problem tells you to use❗

⭐ Perpendicular lines have a slope that is the opposite reciprocal of the slope of the line it is perpendicular to

⭐What does "opposite reciprocal" mean?

⭐What is slope-intercept form?

We can find the equation of the perpendicular line by:

1. Substituting the slope into the point-slope form equation:

⭐ Perpendicular lines have a slope that is the opposite reciprocal of the slope of the line it is perpendicular to

The slope of the line the perpendicular like is perpendicular to is [tex]\frac{-1}{2}[/tex].

Therefore, the slope of the perpendicular line is [tex]2[/tex]

Substitute the slope into the point-slope form equation.

[tex]y = 2x + b[/tex]

Now, all we have to do is solve for b.

2. Substituting the given coordinate into the point-slope form equation:

We are given the coordinate (6,9).

[tex]y = 2x + b[/tex]

[tex]9 = 2(6) + b[/tex]

[tex]9 = 12 + b[/tex][tex]-3 = b[/tex]

Substitute "b" into the point-slope form equation.

[tex]y = 2x + 3[/tex]

As per the tangent formula, the distance does the laser spot on the wall move if the mirror is rotated by 10 is 2.9m

While we looking into the given question we have identified the following values,

Previous distance = 9.5

And the angle = 30 degrees

Rotated angle = 10 degrees

And the distance is considered as x.

Then as per the tangent formula, it can be written like the following,

=> tan 30/9.5 = tan 10/x

When we apply the tangent value, then we get,

=> 0.5773/9.5 = 0.1763/x

When we perform the cross multiplication, then we get,

=> 0.5773x = 9.5 x 0.1763

=> 0.5773x = 1.6749

Then the value of x is obtained as,

=> x = 1.6749/0.5773

=> x = 2.9012

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Answer:

0.84 m^2

Step-by-step explanation:

Long: 1200 millimeter = 1.2 meter

Wide: 700 millimeters = 0.7 meter

Area of rectangle: L x W

1.2 x 0.7 = 0.84 m^2

( x+2) , ( x-3 ) and ( x+ 5 ) are the roots of the equation .The function's zeros are frequently referred to as the function's roots, solutions, or x-intercepts.

The function's zeros are frequently referred to as the function's roots, solutions, or x-intercepts. These are all used across mathematics and have the same meaning as the zero concept. As a result, when a function y= or f(x)= is supplied, the zeros of the function are function values where y=0 or f(x)=0 f (x) = 0.

here ,

Since the sum of the coefficients is not zero , 1 is not a root

let x = -2

= -8 + 16 + 22 - 30 = 0

= -2 is a factor

dividing [tex]x^{3} + 4x^{2} -11x -30[/tex] by ( x + 2)

quotient = [tex]x^{2} + 2x -15[/tex]

= [tex]x^{2} +5x - 3x -15 =0[/tex]

= x(x + 5) - 3 ( x+ 5 ) =0

= ( x -3 ) ( x + 5 ) =0

other factors are ( x -3 ) and ( x+5 )

So , ( x+2) , ( x-3 ) and ( x+ 5 ) are the roots of the equation .

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A sickness Notification Form is used to inform the SSS loan of your illness or injury.

The sickness benefit, according to SSS President and Chief Executive Officer Aurora C. Ignacio, is a daily cash payment made for each day a member is unable to work as a result of illness or accident.

In order to be eligible for the program, a member must have made at least three monthly contributions in the twelve months prior to the semester of illness or injury, be confined for at least four days in a hospital or at home, have used all of their current company sick days for the current year, and have informed their employer of their illness or injury.

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When two lines are crossed by a transversal, a number of angle pairs are formed. The sum of the measures of these angle pairs can be used to solve for unknown angles in the diagram.

Here are some of the angle pair relationships that hold for two lines crossed by a transversal:

Using these relationships, you can set up equations to solve for unknown angles in the diagram. For example, if you are trying to find the measure of angle A, you might use the fact that corresponding angles are congruent to set up the equation "m<A = m<D". Then, you can use other angle pairs to find the measures of the other angles, and solve the system of equations to find the measure of angle A.

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The number of cans collected in the second week would be 225 cans.

A can of food is a container that holds a prepared food product, such as vegetables, fruits, beans, or soups. Canned foods are shelf-stable, meaning they can be stored for long periods of time without spoiling. They are often used as a convenient and easy-to-store source of food, especially in emergency situations.

To find out how many cans of food were collected in the second week, you need to subtract the number of cans collected in the first week from the total number of cans collected. In this case, the number of cans collected in the second week would be:

410 cans - 185 cans = <<410-185=225>>225 cans.

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A corporate (or credit) spread is the extra interest a lender demands to make up for the extra risk they take on by financing the business.

Companies borrow money from their investors through the use of bonds, which are debt instruments. Better performance and low-risk perceptions for businesses cause bond spreads to narrow. The corporate spread decreases when people have favorable and low-risk impressions about the company issuing the bond since it is the extra interest paid over the interest from US Treasury bonds.

A bond is an IOU that specifies the amount of reward the IOU holder will get upon repayment of the borrowed funds. Basis points are typically used to calculate this interest rate. The matching government bond yield is typically considered for determining spread. The spread decreases as the danger increases.

Basis points are a standard unit of measurement for the corporate spread. These are "hundredths of a percent" more than the interest rate on Treasury bonds. Accordingly, a spread of 100 basis points is equal to 1% more than the yield on government bonds.

Spreads that are getting tighter indicate a company's assessment of risk is getting better. This is because investors have enough faith in the business to invest in it in exchange for reduced spreads. Strong financial statements, improved loan servicing, or a generally stable market impression could all be to blame for this.

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A bond is an IOU that specifies the amount of reward the IOU holder will get upon repayment of the borrowed funds. Basis points are typically used to calculate this interest rate. The matching government bond yield is typically considered for determining spread. The spread decreases as the danger increases.

Basis points are a standard unit of measurement for the corporate spread. These are "hundredths of a percent" more than the interest rate on Treasury bonds. Accordingly, a spread of 100 basis points is equal to 1% more than the yield on government bonds.

Answer:

g(x) = f(x) + 4 → Graph #5

h(x) = f(x + 4) → Graph #6

k(x) = f(x) - 4 → Graph #4

m(x) = f(x - 4) → Graph #3

Step-by-step explanation:

g(x) = f(x) + 4 → Graph #5

⭐ This transformation of f(x) means that to get g(x), you have to shift all of the y-values of f(x) up by 4.

⭐ Graph #5 exhibits this transformation because I took the point (0,1) and shifted it up 4 units to get (0,5). Graph #5 is the only graph that showed point (0,5).

h(x) = f(x + 4) → Graph #6

⭐ This transformation of f(x) means that to get g(x), you have to shift all of the x-values of f(x) by -4.

⭐ Graph #6 exhibits this transformation because I took point (0,1) and shifted it left 4 units to get (-4,1). Graph #6 is the only graph that showed point (-4,1).

k(x) = f(x) - 4 → Graph #4

⭐ This transformation of f(x) means that to get g(x), you have to shift all of the y-values of f(x) down by 4.

⭐ Graph #4 exhibits this transformation because I took point (0,1) and shifted it down 4 units to get (0,-3). Graph #4 is the only graph that showed point (0,-3)

m(x) = f(x - 4) → Graph #3

⭐ This transformation of f(x) means that to get to g(x), you have to shift all of the x-values of f(x) right by +4.

⭐ Graph #3 exhibits this transformation because I took point (0,1) and shifted it right 4 units to get (4,1). Graph #3 is the only graph that showed point (4,1).

The quantity or complete absence of the thing being measured is represented by the zero point.

Ex. Because the zero point is set arbitrarily and does not indicate the complete absence of temperature, the Fahrenheit scale is an interval scale.

Zero degrees on either scale is not a "true" zero because it is an arbitrary number. The absence of temperature does not occur at the zero point; It's just a random number on the scale. Other examples of common interval scales include: Age and SAT scores (one is culturally determined).

In addition, on a ratio scale, the distance between two variables is also the same. Furthermore, a proportion scale has a genuine zero point, meaning the worth of zero isn't erratic.

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The best estimate of the solution to the system of equations will be (1, 4). Then the correct option is C.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The system of the equations is given below.

2x + 3y = 12            ...1

4x + 2y = 10           ...2

Divide the equation 2 by 2, then we have

2x + y = 5            ...3

Subtract equation 3 from equation 2, then we have

2x + 3y - 2x - y = 12 - 5

2y = 7

y = 3.5

y ≈ 4

Then the value of 'x' is calculated as,

2x + 3.5 = 5

2x = 1.5

x = 0.75

x ≈ 1

The best gauge of the answer for the arrangement of conditions will be (1, 4). Then, at that point, the right choice is C.

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The value of a if  the lines 5x-ay+26=0 and 3x-y+2=0 intersect on the y-axis is; a = 13

The general form of the equation of a line in slope intercept form is given as;

y = mx + c

where;

m is slope

c is y-intercept

We are given two equations of two lines as;

Line 1; 5x - ay + 26 = 0

Line 2; 3x - y + 2 = 0

Now, since they both intercept each other at the y-axis, it means that at the point of intersection, the value of x will be 0.

Thus, line 2 equation becomes;

3(0) - y + 2 = 0

y = 2

Putting 2 for y in line 1 equation gives;

5(0) - a(2) + 26 = 0

2a = 26

a = 26/2
a = 13

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As there is a common ratio between each term so this is a geometric sequence.

The idea of geometric progression can be used to determine how much money you will have in your account after a particular number of years if you deposit money in a bank that offers a fixed annual rate of interest.

In a geometric progression or series, each term is equal to the one before it times the common factor, which is a fixed non-zero multiplier. The number of terms in a geometric series might be either finite or infinite.

Since in 6 12 and 24 the common ratio r=2. That is if we multiply the previous term by 2 we will get the next term so the given sequence is geometric sequence.

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Answer:

1000

Step-by-step explanation:

answer is 1000 miles per hour

Answer:

232.88

Step-by-step explanation:

I used a calculator on this so it must be correct

Answer:

6,750 pounds

Step-by-step explanation:

3 3/8 tons = ? pounds

there are 2,000 pounds in 1 ton so:

3 3/8 * 2,000 = 6,750 pounds

Answer:

i. (10-y)(100x^2 +10xy + y^2)

ii. See the explanation

Step-by-step explanation:

i. 1000x³-y³ =

10³x³ - y³ =

(10x)³ - y³ =  ==> use formula: x³ - y³ = (x-y)(x^2+yx+y^2)

(10-y)((10x)^2 +10xy + y^2) =

(10-y)(10^2 * x^2 +10xy + y^2) =  ==> simplify

(10-y)(100x^2 +10xy + y^2)

ii. 992/124=

(992-192)/(124-24)=

800/100 = 8

As a result, 8*124=992.

Hence, 124 (and 8) is a factor of 992

Answer:

36 feet

Step-by-step explanation:

If one inch in the drawing equals 3 feet, then the 12-inch length of the wing would correspond to 12(3 feet).  This means the final length of the wing will be 36 feet from tip to tip.

The simplest way to get unique number from an array is by putting all numbers of the array into hashmap's key and then print the keySet

an array is a collection of elements or numbers of the same data type.There are more than one way to find unique elements or number from an array:

1.By using hashing

2. By using nested loop

3. By using sorting

4. By putting all the elements in the hashmap's key

But the simplest way to get unique number from an array is the fourth method. And this is done by putting all the number from the array into the hashmap's key, we then print the key set.

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To compare two numbers, a, and b, we can write two inequalities:

a < b when a is less than b

a > b when a is greater than b.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

We may write two inequalities to compare two numbers, a and b:

a < b

a > b

If a is less than b, then the first inequality is true and the second is false. If a is greater than b, then the first inequality is false and the second is true. Otherwise, if a and b are equal, then both inequalities are false.

We can determine which inequality is true by comparing the values of a and b and using the rules of inequality.

For example, if a=3 and b=5, then we can determine that a < b is true and a > b is false because 3 is less than 5.

On the other hand, if a=8 and b=2, then we can determine that a < b is false and a > b is true because 8 is greater than 2.

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Answer:

the way you typed that is kinda confusing but the answer is

[tex]18 - 8q[/tex]

The number of CDs that can be bought are { 5, 4, 3, 2, 1 }.

What is an inequality ?

A relationship between two expressions or values that is not equal to each other is referred to as "inequality" in mathematics. So inequality emerges from an imbalance.

Given, No. of CDs = x

A CD costs $11 and He has total $60.

So, According to the question,

No. of CDs × Cost of each CD ≤ 60

                                         x × 11 ≤ 60

                                         11x ≤ 60

                                          x ≤ 60/11

Since the number of CDs can't be in fraction and The maximum CDs can be bought is 5.

So, The possible No. of CDs that can be purchased are { 5, 4, 3, 2, 1 }

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The division of the whole numbers is not closed under property as the division of whole number is not always a whole number.

A set has the closure property under a particular operation if the result of the operation is always an element in the set.  If a set has the closure property under a particular operation then we say that the set is “closed under the operation.” The closure property of the division tells that the result of the division of two whole numbers is not always a whole number. Whole numbers are not closed under division that is  a ÷ b is not always a whole number.

For example, 5 and 8 are whole numbers, but 5÷8 is not a whole number.

Therefore, closure property does not exist for division of whole numbers.

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I think it could be 1.5 kilometers.

The distance is 1,500 m but you have to convert it so probably 1.5 km.

Answer:

2nd

Step-by-step explanation:

p=17000

r = -0.03

Hn)= p×(1+r)^n

H(n)= 17000(1+-0.03)^n

Pam needs to save $905 per year for seven years to have enough for her first year with the help of her two grandfathers.

Pam needs to save $903 each year to have enough for her first year of college tuition with the help of her two grandfathers.

To calculate this, we first need to add up the total amount of money Pam's two grandfathers are offering to contribute:

Grandfather 1: $6321

Grandfather 2: $6321

Total Contribution: $12642

We then subtract this total contribution from the total cost of tuition for the first year:

Tuition: $6321

Total Contribution: -$12642

Total Amount Needed: $6321

Finally, we divide this total amount needed by the number of years Pam has to save:

Total Amount Needed: $6321

Years: 7

Amount Needed to Save Each Year: $903

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