Concept Check: Sketch each angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, that are coterminal with the given angle. Give the quadrant of each angle, if applicable.

75°

174°

300°

-61°

-90°

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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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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The sorrect option: y - 4 = 5x - 10, is the equation of the line, in point-slope form.

The slope of the line;

Slope m = 5.

Passing points: (x1, y1) =  (-2, 4).

So, general equation of the line,

y - y1 = m(x - x1)

y - 4 = 5(x + 2)

y - 4 = 5x - 10

Thus, the equation of line, in point-slope form, that has a slope of 5 is found as : y - 4 = 5x - 10.

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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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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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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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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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The interest accumulation on the loan is equals to $526.50.

As a financial term, when an interest is added to the account balance, it is considered accrued. Interest accrues on loans such as a mortgage, savings accounts, student loans, and other investments.

In our calculation, we are using a simple interest because it is only an interest charge that borrowers pay lenders for a loan. It is calculated by using the principal only and does not include compounding interest.

Data

Loan = 4,050

Interest rate = 6.5%

Time = 2 years

To get our Interest, we will use the simple interest formula which is "S.I. = PRT/100". Where P is 4050, r = 6.5%, T= 2 years.

The interest accumulated is computed as follows:

= $4050 * 6.5% * 2 years

= $526.50

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This text describes a scenario where someone has taken out a loan of $4050. The loan has an interest rate of 6.5%, which means that the borrower will have to pay an additional 6.5% of the loan amount as interest. The loan is taken for a period of 2 years, which is the time frame during which the borrower has to repay the loan.

The question being asked is about the interest that will be accumulated on this loan. Interest accumulation refers to the increase in the amount of money that the borrower owes due to the interest that is being charged on the loan.

In this case, we need to calculate the total amount of interest that will be charged over the 2-year period, based on the loan amount and interest rate.

To calculate the interest accumulated on this loan, we can use the following formula:

Interest = Principal * Rate * Time

Where:

- Principal = the amount borrowed (in this case, $4050)

- Rate = the interest rate (in this case, 6.5% or 0.065 as a decimal)

- Time = the length of the loan in years (in this case, 2 years)

Plugging in the values, we get:

Interest = $4050 * 0.065 * 2

Interest = $527.25

So the interest accumulated on this loan is $527.25. This means that the borrower will have to pay back a total of $4577.25 ($4050 + $527.25) over the 2-year period.

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 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.

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:

[tex]54,59,64,69[/tex]

Step-by-step explanation:

[tex]a_{n}=54+5(n-1)=54+5n-5=49+5n \\ \\ a_{1}=49+5(1)=54 \\ \\ a_2=49+5(2)=59 \\ \\ a_3=49+5(3)=64 \\ \\ a_3=49+5(4)=69[/tex]

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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When a polynomial is to be divided by a linear expression and the leading coefficient (first number) must be a 1, synthetic division is used. Any polynomial equation, regardless of degree, can, for instance, be divided by x + 1, but not by x2+1.

Additionally, the binomial must be of degree 1; synthetic division cannot be used to divide by a binomial such as x2 + 1. Here are the steps for performing synthetic division on a polynomial by a binomial.

To get the quotient and the remainder, write down the coefficients and divide them by the linear factor's zero. Q(x) + (R/(x - a)) = (P(x)/(x - a)).

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Using the concept of rates and ratio, it will take approximately 0.12 days to finish 4 bananas

When comparing two or more similar amounts or numbers using the same units, a ratio is utilized. In spoken language, we state the ratio of one quantity "to" the second quantity, and it is frequently written with a colon. For instance, a class has a 3:4 (or 3:4) ratio of boys to girls. When comparing two quantities, for example, some issues may only give you two numbers, but other problems might have more than two. For example, the proportions of the various ingredients used in a recipe.

We can use the concept of ratio or proportions to determine the number of days they will consume 4 banana

4 days = 13 banana

1 day = x banana

Cross multiply both sides and solve for x

x * 4 = 13 * 1

4x = 13

x = 13 / 4

x = 3.25

Now, we can find the number of days it will take to consume 4 banana

1 day = 3.25 banana

x days = 4 banana

Cross multiply both sides and solve for x

4 * 1 = 3.25x

x = 4 / 3.25

x = 0.12 days

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Answer: Your answer is x = 8  for c and m = -12 for b

Step-by-step explanation:

c.

-8x = -64

-8x - 8 these cancel out

-64 - 8

64/8 = 8

x = 8

b.

-8 + m = -20

m - 8 = -20

m - 8 + 8 = -20 + 8 (add the -20 + 8 because the 8's cancel out)

m = -12

Answer:

(n+5)(n-2)

Step-by-step explanation:

n^2+3n-10

(n+5)(n-2)

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°

The value of r when y = 18 is 17.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

Given the equation which is linear having the exponent of the variable equals 1.

10r - 9y = 8

We have to find the value of r when value of y = 18.

Substituting y = 18 in the equation,

10r - (9 × 18) = 8

10r - 162 = 8

10r = 170

r = 170/10

r = 17

Hence when the value of y = 18, then the value of r = 17.

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The equation that represents the relationship between the number of fruit Tyler ate and Han ate is x = y + 34

A linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always results in a straight line.

Also a linear equation can be defined as an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

The number of fruits Tyler ate is represented by x

The number of fruits Han ate is represented by y

Han ate 34 less than tyler, this means that y = x-34

and also making x the subject,

x = y + 34

Therefore the equation that represents the relationship between the number of fruits Tyler ate and Han ate is x = y+34

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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

840 cubes can be placed in the given cuboid.

Now, According to the question:

We know that,

Volume of cuboid = l × b × h

Volume of cuboid = 84cm × 60cm × 36cm

Volume of cuboid = 181,440[tex]cm^3[/tex]

Side of the cube = 6 cm

Volume of the cube = side³

= 6³

= 216 cm³

Required number of cubes = volume of cuboid / volume of the cube

= 181,440/216

= 840

Thus, 840 cubes can be placed in the given cuboid.

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The complete question is this:

A box measure 84cm by 60cm by 36cmthe box is completely filled with identical cube. How many small cubes with side 6 cm can be placed in the given cuboid?

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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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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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)

Around 100 hours will take for both vats to contain the same amount of liquid.

How do you calculate the rate of evaporation of a liquid?

The equation indicates that the evaporation rate,

W = (95+0.425*V)*(Pw-Pa)/Y, where W is the evaporation rate, V is the air velocity at the water surface,  Pw is the saturation vapor pressure at water temperature.

To find out how many hours it will take for both vats to contain the same amount of liquid, we need to compare the rates at which the liquid is evaporating from each vat.

We can set up the following equation:

(35 - x) / 0.25 = (40 - x) / 0.35

where x is the amount of liquid in both vats at the time they reach the same level.

We can then solve for x by multiplying both sides by 0.25 and 0.35 and then subtracting one equation from the other:

35 - x = 40 - x

x = 5

So, both vats will contain 5 liters of liquid at the time they reach the same level.

To find out how many hours it will take to reach this point, we can use the rate of evaporation for either vat.

For Vat A:

35 - 5 = 30 liters

30 liters / 0.25 liters/hour = 120 hours

For Vat B:

40 - 5 = 35 liters

35 liters / 0.35 liters/hour = 100 hours

So, It will take around 100 hours for both vats to contain the same amount of liquid.

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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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