last trigonometry question plz help me for 30 points

When writing a piecewise function from a graph, the domain of each rule is determined by the x-values of the graph.

A piecewise function is a function that is defined by different rules for different ranges of the input (x-values). Each rule corresponds to a different interval of the domain.

To determine the domain of each rule when writing a piecewise function from a graph, you can use the following steps:

Identify the intervals of the x-axis where the graph changes behavior.

Write the domain of the function for each interval.

Write the rule for each interval of the domain.

For example, if a graph has a behavior change at x = 1, x = 3, and x = 5, then the domain of the function can be written as:

f(x) = {

y1, x < 1

y2, 1 ≤ x < 3

y3, 3 ≤ x < 5

y4, x ≥ 5

}

The domain for each rule is the interval of x-values between the changes in behavior. In this example, the first rule applies to x values less than 1, the second rule applies to x values between 1 and 3, the third rule applies to x values between 3 and 5, and the fourth rule applies to x values greater than or equal to 5.

Here, note that when writing a piecewise function, it is important to make sure that there are no gaps or overlaps in the domain of the function and that the x-values where the graph changes behavior are included in the domain of at least one of the rules.

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The percentage increse in value from 5 to 7 is 40 %

A percentage is a ratio or fraction where the full value is always 100. Sam, for instance, would have received 30 out of a possible 100 points if he had received 30% on his arithmetic test. In ratio form, it is expressed as 30:100 and in fraction form as 30/100.

Finding the percentage of a whole in terms of 100 is what percentage calculation refers to. A percentage can be found in one of two ways:

It should be noted that when the denominator is not a factor of 100, the second technique of percentage calculation is not applied. In these situations, we employ the unitary technique.

The initial value is 5

Final value = 7

Increse in value 7-5 = 2

Percentage increse is [tex]\frac{2}{5}* 100 = 40 \ \% \\[/tex]

The percentage increse in value from 5 to 7 is 40 %

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The triangle with sides 25cm, 5cm and 24cm is not a right triangle.

Now, According to the question:

Let us assume that :

ABC is a right triangle,

A = 25cm

B = 5 cm

C = 24 cm

We have to find if the given sides of a triangle form a right triangle.

By using Pythagoras theorem for a right triangle,

[tex]A^2 = B^2+C^2[/tex]

[tex](25)^2 = (5)^2 + (24)^2[/tex]

LHS:[tex](5)^2 + (24)^2[/tex]

= 25 + 576

= 601

RHS:[tex](25)^2[/tex]

= 625

LHS ≠ RHS

Since, the Pythagorean theorem does not apply, the given sides do not form a right triangle.

Therefore, the triangle with sides 25cm, 5cm and 24cm is not a right triangle.

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The discount amount is $3.75 ($25 x 15% = $3.75).

1.Calculate the discount: Regular price x discount percentage = discount amount

2. Plug in the values: $25 x 15% = $3.75

3.The discount amount is $3.75.

The discount amount can be calculated by taking the regular price and multiplying it by the discount percentage. For example, if the regular price is $25, and the discount percentage is 15%, the discount amount can be calculated by multiplying the regular price by the discount percentage ($25 x 15% = $3.75). Therefore, the discount amount is $3.75. This calculation can be used to calculate the discount amount for any given regular price and discount percentage.

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Answer:

Number of soda = 186

Number of hot dog= 62

Step-by-step explanation:

Let us take number of sodas as x and number of hot dogs as y

Then

x + y = 248 [Equation 1]

and

3y = x

Hence,

3y -x = 0 [Equation 2]

By adding [Equation 1 & 2]

(+x -x) 3y + y = 248 + 0

4y = 248

4 4

y = 62

Substitute y= 62 in [Equation 1] to get

x + y = 248

x + 62 = 248

x = 248 - 62

x = 186

The Additive Inverse of 924 is -924

⇒ The number that, when added to 924, will result in a sum of zero is the additive inverse of 924. The formula to solve the issue where x is the additive inverse of 924 is as follows:

924 + x = 0

⇒ When we solve the preceding equation for x, we obtain x = -924. As a result, the answer to the question "What is the additive inverse of 924?" is -924.

∴Therefore Additive Inverse of 924 = -924

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The additive inverse of 4 is -4. This means that when 4 is paired with -4, the two numbers cancel each other out and the result is 0.

The additive inverse of a number is the opposite of that number. For example, the additive inverse of 4 is -4. This means that when two numbers are added together and one of them is 4 and the other is -4, the result will be 0. This is because the two numbers cancel each other out. The same is true for any number and its additive inverse. For example, 8 and -8 added together will also result in 0. Additive inverses are an important part of algebra and can be used to solve equations. By understanding the concept of additive inverses, you can easily manipulate equations and solve for unknowns. This is due to the fact that when two numbers are added together and one of them is the additive inverse of the other, the result will always be 0.

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The volume of the cube before it was melted is greater than 49cm^3

The amount of melted liquid left after making the cone is 49 cm^3.

A cone is a three-dimensional shape that has a circular base and a single vertex or point. The amount of liquid remaining after making a cone can be calculated by comparing the volume of the cone to the volume of the cube.

The volume of a cone can be calculated using the formula:

V = (1/3) * pi * r^2 * h

Where V is the volume of the cone, pi is a mathematical constant (approximately 3.14), r is the radius of the circular base, and h is the height of the cone.

However, we don't have information about the radius or height of the cone, we only know the volume of melted liquid left after making the cone is 49 cm^3.

We can use this information to determine the volume of the cube before it was melted and compare it with the volume of the cone.

The volume of a cube can be calculated using the formula:

V = s^3

Where V is the volume of the cube, s is the length of one side of the cube.

Let's call Vc the volume of the cube before it was melted and Vcon the volume of the cone

Vc - Vcon = 49 cm^3

Therefore, the volume of the cube before it was melted is greater than 49cm^3

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The midpoint theorem is used in a variety of mathematical fields, but it is primarily used in geometry and algebra.

In geometry, the midpoint theorem is used to find the midpoint of a line segment, which is the point that is exactly halfway between the two endpoints of the segment. The theorem states that the coordinates of the midpoint of a line segment can be found by averaging the coordinates of the endpoints.

For example, if the endpoints of a line segment have coordinates (x1, y1) and (x2, y2), the coordinates of the midpoint would be ((x1 + x2)/2, (y1 + y2)/2).

In algebra, the midpoint theorem can be used to find the equation of a line when the coordinates of the endpoints of a line segment are known. The equation of a line can be represented in the form of y = mx + b, where m is the slope and b is the y-intercept.

The slope of the line can be found by taking the difference of the y-coordinates of the two endpoints divided by the difference of the x-coordinates of the two endpoints. The y-intercept of the line can be found by using the midpoint of the line segment and the slope of the line.

In Calculus, the midpoint theorem is used in optimization problems. Optimization problems are used to find the maximum or minimum value of a function.

The midpoint theorem is used to find the critical points of the function, which are the points where the function reaches its maximum or minimum value. The critical points are found by taking the derivative of the function and equating it to zero.

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The slope of the given equation [tex]y = -5x^5[/tex] is [tex]-25x^4[/tex].

To find the slope of the equation [tex]y = -5x^5[/tex], you need to take the derivative of the equation with respect to x. The slope of the equation represents the rate of change of y with respect to x, that is how y changes as x changes.

The derivative of [tex]y = -5x^5[/tex] can be calculated using the power rule, which states that if f(x) = [tex]x^n[/tex] then f'(x) = [tex]nx^{(n-1)}[/tex], the slope of the equation is [tex]-55x^4[/tex].

So, the slope of the equation [tex]y = -5x^5[/tex] is [tex]-25x^4[/tex].

Here, note that this equation represents a polynomial function of degree 5, which means that it is a function that has the highest power term of [tex]x^5[/tex]. Also, the slope of a polynomial function is always a polynomial function of one degree lower than the original function.

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A multiple of 10 cannot be equals to a prime number. Multiple of 10 is always equals to a composite number.

As given in the question,

Multiple of a given number 10 are equals to :

10 , 20 , 30, 40, 50, ........, so on.

Prime number are those numbers which have only two factors one and the number itself.

Number 10 itself is not a prime number.

Factors of 10 are equals to :

1, 2, 5, 10

More than two factors.

All the Multiples of 10 cannot be a prime number as they have more than two factors.

Multiple of 10 represents the composite number.

Therefore, multiple of 10 cannot be equals to a prime number they are composite number.

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In y = 10x the value of y is twice the value of x, and in y = x + 10 the value of y is 10 more than the value of x.

What is an Equations?

Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.

y = 10x, we can say that the algebraic equation represents "the value of y is twice the value of x.

Also, for the equation y = x + 10, we can say "the value of y is two more than the value of x.

Hence, In y = 10x the value of y is twice the value of x, and in y = x + 10 the value of y is 10 more than the value of x.

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Julia has lower rate than anna by 0.375 miles/ hour

A rate is a ratio that is used for comparing two different kinds of quantities which have different units. On the other hand, the unit rate illustrates how many units of quantity correspond to the single unit of another quantity. We say that when the denominator in rate is 1, it is called unit rate. In fact, unit rate is said to be the amount of something in each unit or per unit. Let us understand this using some examples:

40 miles/2 hours = 20 miles/hour, Unit rate is 20 miles per hour

160 words/4 minutes = 40 words/minutes, Unit rate is 40 minute per minute

To compare the unit rate of the two riders, we need to determine the number of miles per hour for each of them.

For Anna, the unit rate is 20 miles / 1 1/3 hour = 15 miles/hour.

For Julia, the unit rate is 246 miles / 16 hours = 15.375 miles/hour.

So, Julia has a lower unit rate than Anna by 0.375 miles/hour.

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The dimensions of each side of the square will be 4 centimeters long.

To determine the smallest possible square that can be formed from the tiles without cutting or overlapping them, you will need to find the greatest common divisor (GCD) of the two dimensions of the tile (20 cm and 12 cm).

The GCD represents the largest size of a square that can be formed without cutting or overlapping the tiles.

The GCD of 20 and 12 can be found using the Euclidean algorithm:

Divide 20 by 12. The quotient is 1 and the remainder is 8.

Divide 12 by 8. The quotient is 1 and the remainder is 4.

Divide 8 by 4. The quotient is 2 and the remainder is 0.

Since 4 is the last non-zero remainder, it is the GCD of 20 and 12.

Thus, each side of the square will be 4cm long.

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Answer: For the first 30 hours, Andrew will earn 4 (30) = $120. For each additional hour beyond 30 that Andrew works, he will earn 5 (h - 30). Therefore, the function that gives Andrew's total wages when he works more than 30 hours is

Step-by-step explanation: For the first 30 hours, Andrew will earn 4(30) = $120.  For each additional hour beyond 30 that Andrew works, he will earn 5(h - 30).  Therefore, the function that gives Andrew's total wages when he works more than 30 hours is:

w = 120 + 5(h - 30).

So, if he works 35 hours, he will earn:

120 + 5(35 - 30) = 120 + 5(5) = 120 + 25 = $145.

If he works 42 hours, he will earn:

120 + 5(42 - 30) = 120 + 5(12) = 120 + 60 = $180.

I hope this helps!

When one side and one angle of a right angled triangle are given as 19 and 35°, respectively, the value of b is calculated using trigonometric ratios as 13.03.

Trigonometric ratios are defined as the values of all trigonometric functions based on the right-angled triangle's side ratio. The trigonometric ratios of any acute angle in a right-angled triangle are the ratios of its sides to that angle.

given

one side = 19

angle = 35°

one angle = 90° as right angle triangle

another angle = 35°+ 90° + x = 180°

= 125° + x = 180°

x = 55°

[tex]\frac{a}{sinA} = \frac{b}{sinB}[/tex]

19 / sin55° = b / sin35°

b = 13.03

When one side and one angle of a right angled triangle are given as 19 and 35°, respectively, the value of b is calculated using trigonometric ratios as 13.03.

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Answer:

solutions for these simultaneous equations are x = 6 and y = x = 6, or x = 1 and y = x = 1

Step-by-step explanation:

To solve these simultaneous equations, we need to find the values of x and y that satisfy both equations.

Given:

y = x

y = x² - 6

We can substitute the first equation into the second:

x = x² - 6

we can subtract x from both sides to get:

0 = x² - 7x + 6

Then we can factor it:

(x-6)(x-1) = 0

Therefore x = 6 or x = 1

So the solutions for these simultaneous equations are x = 6 and y = x = 6, or x = 1 and y = x = 1

There are two solutions, (6,6) and (1,1)

The solution for f(-3) - 2 in the function when the function f(x) = 4 − (x + 3)⁵ is 2

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

f ( x ) = 4 − ( x + 3 )^5

To make the equation legible, we need to rewrite it

So, we have the following representation

f(x) = 4 − (x + 3)⁵

Also from the question, we have

f(-3) - 2

This means that the value of x is -3, and we calculate f(x) when x = -3

Substitute the known values in the above equation, so, we have the following representation

f(x) - 2 = 4 − (x + 3)⁵ - 2

So, we have the following equation

f(-3) - 2 = 4 − (-3 + 3)⁵ - 2

There are constants to add or subtract to both sides of the equation

However, there is no factor to multiply or divide from both sides of the equation

So, we have the following representation

f(-3) - 2 = 4 − (0)⁵ - 2

Solving further, we have

f(-3) - 2 = 4 - 2

Evaluate the difference

f(-3) - 2 = 2

Hence, the solution is 2

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Complete question

Given that f ( x ) = 4 − ( x + 3 )^5

Find f(-3) - 2

Hint: find f(-3) first and then subtract 2.

Answer: B (-9, -3, 0, 5, 7)

Step-by-step explanation:

Using percentages we know that the savings bond will be worth $787.5 on Greg's 30th birthday.

In mathematics, a quantity or ratio known as A% stands for a percentage of 100.

There are several different ways to depict a dimensionless connection between two numbers, including ratios, fractions, and decimals.

To represent percentages, the symbol "%" is typically written after the number.

So, we know that:

The bond is $350.

The return is 125% when Greg turns 30.

Then, the amount after she turns 30 will be as follows:

350/100 * 125

437.5

Bonds value: 437.5 + 350 = $787.5

Therefore, using percentages we know that the savings bond will be worth $787.5 on Greg's 30th birthday.

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The point of intersection of a triangle's angle bisectors is known as the incentre.

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The value of m in the linear pair with an array is 101°, using supplementary rule.

Two lines converge at a single point to generate a pair of linear angles. If, following the junction of the two lines, the angles are next to one another, they are said to be linear. A linear pair always has an angle total of 180 degrees.

When two lines cross, they generate a linear pair, which is two nearby angles. The numbers 1 and 2 form a linear pair in the figure. The same goes for 2 and 3, 3 and 4, and 1 and 4. In a linear pair, the two angles are always supplementary, which implies that their sum total is 180 degrees.

 79° + m = 180°

          m = 180° - 79°

          m = 101°

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Complete question:

What is the value of m?

79° + m = 180°

Answer:

d) b+b+3c and 2b+3c

Step-by-step explanation:

b+b=2b

2b+3c=2b+3c

The points that the cooking group leader did label are (0,15) and (30,0). Thus, the correct answer is C.

As your first step, find the function that best represents x and y:

Hence, the function is:

The group leader labeled (0,15) on the y-axis, which means that when the number of small jars is 0, the group can use 15 large jars. This means that 15 large jars can hold 240 oz of spaghetti sauce, which is true since:

The group leader also labeled (30,0) on the x-axis, which means that when the number of large jars is 0, the group can use 30 small jars. This means that 30 small jars can hold 240 oz of spaghetti sauce, which is true since:

The function that represents this line is 8x + 16y = 240, where x is the number of small jars and y is the number of large jars. The line passes through (0,15) and (30,0) as the two intercepts.

This question should be written as:

A cooking group made 240 oz of spaghetti sauce to sell at a county fair. The group can pour the sauce into small jars that hold 8 oz and large jars that hold 16 oz. The group leader made a sketch to show the line representing the different combinations of jar sizes the group can use. The x-axis represented the number of small jars and the y-axis represented the number of large jars. The group leader labeled only the intercepts. Which points did the group leader label?

The correct answer is C.

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The probability of getting no more than 4 calls between eight and nine in the morning is 0.9473

This is a  Poisson distribution problem with a mean of 2.

In a Poisson distribution, the probability that X successes is given by:

P(X = x) = [e^(-λ) ×  λˣ] / x!

where x is the number of successes

e = 2.71828 is the Euler number

λ is the mean

The number of calls received by an office on Monday morning between 8:00 AM and 9:00 AM has a mean of 2 i.e.  λ  = 2

P(X ≤  4) = ([e⁻²× 2⁰]/0!) +  ([e⁻²× 2¹]/1!) +   ([e⁻²× 2²]/2!) +  ([e⁻²× 2³]/3!) +  ([e⁻²× 2⁴]/4!)

P(X ≤  4) = 0.9473

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Answer:

wrong - $32.547

right - $325.47

Step-by-step explanation:

Basically, if the number in the tens place (145) is 5 or higher the nearest would be the next ten or hundred up, if lower than 5 it goes back down.

Rounding cents is basically the same. as rounding Example:

$14.345

(This is not a vaild amount of money because once you reach a hundred cents you have another dollar. So you will move the decimal point over to the left.)

$143.45

More examples:

incorrect - $23.8678

correct - $2386.78

incorrect - $89.264

correct - $892.64

Rounding is something like rounding to the nearest ten or hundred here's an example:

14 to the nearest ten is 10

16 to the nearest ten is 20

284 to the nearest hundred is 300

104 to the nearest hundred is 100

(Hope this helps. Sorry if this confused you further)

The boundary line of the graph of an inequality in two variables is part of the solution when the line is a solid line

A mathematical statement stating the relationship in terms of greater than, larger than or equal to, less than, or less than or equal to between two numbers or algebraic expressions is known as an inequality.

Inequality representation using a solid line and a dotted line

Inequality plots that use the < or > symbols features a dashed line and  this shows the boundary lines are not a part of the solution.

An inequality marked with the symbol "or" such as greater than or equal to or less than or equal to is represented by a solid line boundary line and the region is included in the solution.

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Therefore , the solution of  the given problem of percentage comes out to be percentage of b is 4301%.

In mathematics, a percentage is a number of ratio that is stated as a portion of 100. Also occasionally used are the abbreviations "pct.," "pct," with "pc." To denote it, though, the percent symbol "%" is frequently employed. The % amount has no dimensions. Because percentages contain a numerator of 100, they are effectively fractions. A number should be followed by the % sign (%) to show that it represents a percentage. For instance, someone would receive a 75% grade if you properly solved 75 out of 100 questions on a test. To determine percentages, divide the amount of money by the total, and then multiply the result by 100. The percentage is calculated by multiplying the ratio (value/total) by 100%.

Here,

a =2001/100 * (b+c)

and

b= 87/100*c

thus putting value of b in a

=>a = 2001/100*(87/100*c + c)

=> a= 2001/100 * 187/87 * b

=>a/b = 374187 / 8700 * 100 = 4301%

and

Now percentage of b is 4301%.

Therefore , the solution of  the given problem of percentage comes out to be percentage of b is 4301%.

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So on solving the provided question, we can say that by equation Shayna : [tex];5x + 10y = $175[/tex] and Brenda : [tex]9x + 4y = $147[/tex]; cost =   [tex]$11/ft^2[/tex] of grass, $12/geranium

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

the equation, that will be formed are

Shayna : [tex];5x + 10y = $175[/tex]

Brenda : [tex]9x + 4y = $147[/tex]

[tex]5x + 10y = $175 \\ 5x = $175 - 10y\\(5x/5) = ($175/5) - (10y/5) = > x = $35 - 2y\\9x + 4y = $147 = > 9($35 - 2y) + 4y = $147\\ $315 - 18y + 4y = $147\\$315 - $147 = 18y - 4y \\ $168 = 14y = > y = $12\\ 5x + 10y = $175 = > 5x + 10($12) = $175 = > 5x + $120 = $175 \\5x = $175 - $120 = > 5x = $55 = > x = $11[/tex]

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