What is the reference angle of 255°?​

The value of x° and y° are 26.8° and  86.2°.

What is rounding to tenth?

Look at the hundredth number to round the decimal number to the nearest tenth. If it's more than 5, add one to the tenth value. Remove all the numbers that are present after the tenth place and leave the tenth place value alone if it is less than 5.

The length of sides of the triangle are 8, 6, and 5.

Assume that AB = c = 6, BC = a = 5, and AC = b = 8

m∠A = x° and m∠B = y°.

Cosine law:

c² = a² + b² - 2ab cos C  ....(i)

b² = a² + c² - 2ac cos B  ....(ii)

a² = b² + c² - 2bc cos A  ....(iii)

Putting a = 5, b = 8, c = 6, and A = x° in law (iii)

5² = 8² + 6² - 2×8×6 cos x

25 = 64 + 36 - 84 cos x

84 cos x = 75

cos x = 75/84

x = 26.76°

x = 26.8°  (nearest tenth)

Putting a = 5, b = 8, c = 6, and B = y° in law (ii)

8² = 5² + 6² - 2×5×6 cos y

64 = 25 + 36 - 60 cos y

60 cos y = 4

cos y = 4/60

y =86.177°

y =86.2°

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Answer:

Step-by-step explanation:

[tex]x^{2} -6x[/tex]

Answer:

98 laps

Step-by-step explanation:

(5x 14) + (2 x 14)

70+ 28 =98

Answer: see below

Step-by-step explanation:

The domain of a graph consists of all the input values shown on the x-axis

We want to find the left-most x value and the right-most x value.

-8, 3

since there is a hole at the point where x=3 we will use a paratensesis

D:xE[-8,3)

Divide the base for that period by the appropriate commission rate to determine your commission for that period. Mark earns more money.Since $1680 > $1080, Mark earns more.

This is a pretty straightforward computation based on percentages. Simply take the selling price, multiply it by the commission rate, then divide the result by 100.

Mark: $24/h; 150% OT

Calculate Mark's overtime (OT) pay

Convert OT rate to decimals --> 150% = 1.5

Mark's OT wage is 1.5*$24 = $36

Mark worked for 20h OT. (60h-40h = 20h)

(Regular pay X regular hours worked) + (OT wage X OT hours worked)

= ($24 X 40h) + ($36 X 20h)

= $1680

Joe: 5% commission

Convert 5% to decimals --> 0.05

(Jewelry sold) X (commission rate)

= $21000 X 0.05

= $1050

Since $1680 > $1080, Mark earns more.

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Mode of the distribution 3, 5, 7, 4, 2, 1, 4, 3, 4 is 4.

As per the question the data given is 3, 5, 7, 4, 2, 1, 4, 3, 4.

Now we have to determine the mode of the given distribution.

Mode: A mode is defined as the value that has a higher frequency in a given set of values. It is the value that appears the most number of times.

The simple way to determine the mode is the most repeated data.

The number or the value which is "repeated more number of times compared to the other values".

From the data given:

3 repeated two times.

5 repeated one time.

7 repeated one time.

4 repeated three times.

2 repeated one time.

1 repeated one time.

Therefore the value of mode is 4.

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The value of a,b,c,d, and e is 45, 60, 58, 77, and 135 respectively, required to complete the two-way table.

A two-way table shows the connections between two sets of category data visually. Labels are positioned at the top and left sides of the table, which has rows and columns.

The sums for each row are displayed to the right, while the sums for each column are displayed at the bottom. 

We must create a two-way table based on the issue to ascertain the worth of each letter.

| Pens | Pencils | Total |

| Boys | 30 | 28 | c |

| Girls | a | 32 | d |

| Total | 75 | b | e |

This shows the entries in the body of the table. To find the value of each letter, we need to add and subtract.

Add the entries in the table to get the total and subtract if the total is given and one value is missing.

a= 75-30 = 45

b = 28+32= 60

c= 30+28 = 58

d= 45+32= 77

e= 75+60 = 135

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| Pens | Pencils | Total |

| Boys | 30 | 28 | c |

| Girls | a | 32 | d |

| Total | 75 | b | e |

This shows the entries in the body of the table. To find the value of each letter, we need to add and subtract.

Add the entries in the table to get the total and subtract if the total is given and one value is missing.

a= 75-30 = 45

b = 28+32= 60

c= 30+28 = 58

d= 45+32= 77

e= 75+60 = 135

All three pairs of corresponding sides are equal. : Two pairs of corresponding sides and the corresponding angles between them are equal. : Two pairs of corresponding angles and the corresponding sides between them are equal.

Congruent Figures :

Those figures which covers each other/one another exactly then they are congruent Figures.

There are 4 ways by which we can prove any 2 triangles as congruent :

If they are having -

Three pairs of side are equal then the triangles are congruent.

If any 2 pairs of angles and 1 side are equal then the triangles are congruent.

If any two pairs of sides and the included angle are equal then the triangles are congruent.

If any right angle triangles are having their hypotenuse and a pair of sides equal then they are congruent.

So, all three pairs of corresponding sides are equal then are congruent to each other.

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The formula of commutative property of addition is a + b = b + a and the formula of commutative property of multiplication is a × b = b ×  a.

The Commutative Property is derived from the word commute, which means to move. It states that the product or sum of two numbers do not change even if the places of numbers are changed or if the numbers move from one place to another.

The commutative property of addition states that a + b = b + a

The commutative property of multiplication states that a × b = b ×  a.

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The value of the sum of the functions f(x) and g(x), (f + g)(x) is 5x³ - 4x.

The outputs for a certain set of inputs can be referred to as a function.

A function's inputs are referred to as its independent variables, while its outputs are referred to as its dependent variables.

Given, f(x) = x³ + 8 and g(x) = 4x³ - 5x - 8.

Let, f(x) = x³ + 0x + 8.

We know, (f + g)(x) = f(x) + g(x).

Therefore, (f + g)(x) = (x³ + 0x + 8) + (4x³ - 5x - 8).

(f + g)(x) = x³ + 4x³ + 0x - 4x + 8 - 8.

(f + g)(x) =  5x³ - 4x.

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The Multiplicative Inverse of the number 6 is "1/6" .

The Inverse (Multiplicative) of the number is the number that when multiplied by the original number gives the product as 1 .

which means the product of the number and its multiplicative inverse is 1 .

the number is given to be 6 .

So , let the multiplicative inverse of 6 be = x .

So , According to Definition of Multiplicative Inverse ,

we can write : x * 6 = 1

dividing both side by "6" .

we get ;

x = 1/6 .

Therefore , the multiplicative inverse is 6 .

The given question is incomplete , the complete question is

What is the Multiplicative Inverse of 6 ?

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The correct answer is 138 students.

x = .24 * 575

x = 138 students

Therefore, the correct answer is 138 students.

The required length of licorice for $1.80 is given as 18 in.

proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.

here,
The price of licorice is proportional to its length. It costs $0.50 to buy 5 in; it is uncertain how much licorice you can get for $1.80.
Let the price be y and the length be x,
according to the quesiton,
y = kx,
put y = 0.50 and x = 5
0.50 = 5k
k = 0.1

Now

y = 0.1 x
for
y = 1.8
1.8 = 0.1x
x = 18

Thus, the length of licorice necessary for $1.80 is specified as 18 in.

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Answer:

Step-by-step explanation:

To find the exact value of x, we need to solve the given equation for x. The equation is:

32^1/25 x 2^x = 8^1/4

To solve this equation, we need to rewrite it in a form that allows us to isolate the variable x. We can start by using the properties of exponents to simplify the left-hand side of the equation. We can use the property that says that raising a number to a fractional power is the same as taking the square root of that number, raised to the power of the denominator of the fraction. So, we can write:

(32^1/25)^2 = (32^1/25)^25/25 = 32^1/25

This simplification allows us to rewrite the left-hand side of the equation as follows:

32^1/25 * 2^x = (32^1/25)^2 * 2^x

Next, we can use the property of exponents that says that the product of two numbers raised to the same power is equal to the product of the numbers, raised to that power. So, we can rewrite the left-hand side of the equation as follows:

(32 * 2)^1/25 * 2^x = (32^1/25)^2 * 2^x

Then, we can use the property of exponents that says that raising a product to a power is the same as raising each factor to that power. So, we can rewrite the left-hand side of the equation as follows:

(32^1/25) * 2^(1/25 + x) = (32^1/25)^2 * 2^x

Finally, we can use the property of exponents that says that the exponent of a power is equal to the product of the exponents of the base and the power. So, we can rewrite the left-hand side of the equation as follows:

(32^1/25) * 2^(1/25 * 25 + 1 * x) = (32^1/25)^2 * 2^x

Since the right-hand side of the equation is already in a form that allows us to isolate the variable x, we can now use the property of exponents that says that raising a number to a power and then taking the square root of that number is the same as

The polynomial function p(x) = 5x³ - 5x² - 10x have zeros of 0, -1 and 2

The zeros of a polynomial p(x) are all the x-values that make the polynomial equal to zero. They are interesting to us for many reasons, one of which is that they tell us about the x-intercepts of the polynomial's graph. We will also see that they are directly related to the factors of the polynomial.

The polynomial function given is

p(x) = 5x³ - 5x² - 10x

The zeros of the function are 0, 2, -1

To test the zeros if they are the roots of the polynomial

p(0) = 5(0)³ - 5(0)² - 10(0)

p(0) = 0

p(2) = 5(2)³ - 5(2)² - 10(2)

p(2) = 0

p(-1) = 5(-1)³ - 5(-1)² - 10(-1)

p(-1) = 0

The zeros are 0, -1, and 2 to the polynomial

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Yes,  All equilateral triangles are similar to each other.

No,  All equilateral triangles are not congruent to each other.

The fact that every angle in an equilateral triangle is equal to 60 degrees is one of its characteristics.

According to the AAA Triangle Similarity Postulate, two triangles are similar  if all of their angles are identical to their corresponding angles in another triangle.

According to the AAA Postulate, all equilateral triangles are similar because their angles are all 60 degrees.

The reason is that although an equilateral triangle's angles are all 60 degrees, their corresponding sides are not necessarily the same .

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199 feet in meters

1 foot = 0.3048 meters

[tex]0.3048(meters)\times199(feet)[/tex]

[tex]=\fbox{60.66}[/tex]

Answer:

40 minutes

Step-by-step explanation:

rate = distance/time = miles/hr

rate = 240 mi/2 hr = 120 mi/hr

time = distance / rate = (80 mi)/(120 mi/hr) = 0.67 hr = 40 minutes

(0.67 hr)(60 min/hr) = 40 minutes

Answer:

the approximate sample proportion is 87%, which means that 13% of the people surveyed do not participate in the city’s recycling program.

The given equation A) 5x -2 + x = x - 4 and B) 5x + x = x - 4 are not equivalent.

The term equation in math refers the mathematical statement that is made up of two expressions connected by an equal sign.

Here we have given that the tow equations are

A) 5x -2 + x = x - 4

B) 5x + x = x - 4

And we need to find if they are equivalent or not.

While we looking into the given question, we have given the following equations,

A) 5x -2 + x = x - 4

B) 5x + x = x - 4

In order to find if they are equivalent or not, we have to simplify each of then then we get,

=> A) 6x - 2 = x - 4

=> A) 6x - 2 - x + 4

=> A = 5x + 2

Now, we have to do the same to simplify the equation (B), then we get

=> B) 6x = x - 4

=>  B = 6x - x + 4

=> B = 5x + 4

Now, we compare the two solved equation,

=> A = B

=> 5x + 2 = 5x + 4

Here the variable part is equal but the constant value is not same.

Therefore, we have identified the the two equation are not equivalent.

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The probability that two red balls are chosen from the vase would be = 1/9

Probability is defined as the concept that proves that an event may occur or not.

The number of red balls = 7

The number of black balls = 2

The number of green balls = 9

The total number of balls in the vase = 18

The probability of getting 2 red balls = 2/18 = 1/9

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The number of real solutions of the system are 2 if y=x²-3, y = -2x +4

An equation system's solution is a collection of values for the variable that concurrently fulfill each equation. Finding all of the possible sets of variable values that make up the system's solutions is necessary to solve an equation system. However, the second equation does not have a solution at (5, 4). There is often only one solution to a system of linear equations, however it is possible for there to be infinite or no solutions (parallel lines) on occasion (same line).

Given,

y=x²-3 -----(1)

y=-2x +4 -----(2)

Solving equations 1 and 2, we get

x²-3=-2x +4

x²+2x-3-4=0

x²+2x-7=0

We have to solve by using quadratic formula,

x= (-b±√b²-4ac)/2a

x= (-2±√2²-4(1)(-7))/2(1)

x= (-2±√4+28)/2

x= (-2±√32)/2

x= (-2±4√2)/2

x= -1±2√2

x= -1-2√2, -1+2√2

Thus, the system has two solutions.

Therefore, the number of real solutions of the system are 2.

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Given that:  

Angle CBD=6x-40

Angle BFH=4x

From the given diagram, angle CBD=angle BFH ("corresponding angles")

Therefore 6x-40=4x,

                  6x-4x=40,

                   2x=40,

                    x=20

now Angle CBD= 6(20)-40

                          = 80

The variance of 2, 4, 6, 8, 10 is 8.

To calculate the variance of a set of numbers, you first need to calculate the mean of the set. The mean of 2, 4, 6, 8, 10 is 6. Then, for each number in the set, you need to calculate the difference between that number and the mean, and square the result. Finally, you need to sum those squared differences and divide by the number of items in the set.

Here's the calculation:

(2 - 6)^2 + (4 - 6)^2 + (6 - 6)^2 + (8 - 6)^2 + (10 - 6)^2 = (-4)^2 + (-2)^2 + 0^2 + (2)^2 + (4)^2 = 16 + 4 + 0 + 4 + 16 = 40

40 / 5 = 8

So, the variance of 2, 4, 6, 8, 10 is 8.

Variance is a statistical measurement of the variation in numbers within a data set. Variance, in more precise terms, indicates how far apart any number in the set is from both the mean (average) and, consequently, from every other number in the set.

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Therefore, the Z set represents the all integers numbers .

Describe integer.

An integer is a whole number, not a fraction, that can be negative, positive, or zero. The numerals  set of 5, 1, 5, 8, 97, and 3, 043 are a few examples. Non-integer numbers include 1.43, 1 3/4, 3.14, and other numbers.

According to the given question:

The set of integers represented here by Z is..., 2,..., 1, 0, 1, 2,... Q stands for the collection of rational numbers (the set of all possible fractions, including the integers).

The set of real numbers is designated as R. The group of complex numbers is designated as C.

Therefore, the Z set represents the all integers numbers .

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Answer:

Can you make another post showing us a picture of the Geometry book page 599? I may be able to help :-)

On a frictionless horizontal table, the rocket-powered hockey puck moves at an angle of 61.9° above the horizontal in 3 seconds.

The significance of non-zero digits is constant. Between any two significant digits, there can be no zeros. Only the final or trailing zeros in the decimal section are important. Between any two non-zero digits, all zeros are important. Seven significant digits are seen in, for instance, 108.0097. There is never any significance for any zeros that are both to the right and left of the decimal point and a digit that is not zero.

given

Then, using the formula that relates the tangent of angle, vertical component of velocity, and horizontal component of velocity to find the direction in which the puck is moving.

Displacement is the smallest distance between the two points.

The vector representation of velocity is,

s = 1/2at2

= 1 .80 m

The puck moves at an angle 61.9° above the horizontal.

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We calculated standard deviation 4 for the given set of numbers.

In the statistics, standard deviation is an estimation that implies how far each data value apart from the mean value. A high standard deviation indicates that all data are dispersed around the mean. And a low score of standard deviation implies data values are close enough in relation to the mean.

Let, X be the list of data value, X² be the square of the data value.

    X          X²

   2           4

   4           16

  6            36

  8            64

  10         100

  12         144

  14        196

we add all the data value and get ∑X = 56

We add all the squared value and get ∑X² = 560

Standard deviation is calculated by using the formula

SD =

√ [∑X²/N - (∑X/N) ²]

where N is the number of data present N= 7

SD = √[560/7 - (56/7)²]

     = 4

Hence, calculated standard deviation is 4

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The value of k is 9 for quadratic equation 3x²+2kx+27=0 whose roots are real and equal.

A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .

The given equation 3x²+2kx+27=0

Here, a=3,b=2k,c=27

It is given that roots are real and equal.

b²-4ac=0

(2k)²-4(3)(27)=0

4k²-324=0

4k²=324

Divide both sides by 4

k²=81

Take square root on both sides

k=±9

Hence, the value of k is 9 for quadratic equation 3x²+2kx+27=0 whose roots are real and equal.

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