Divide x cubed minus 3 x squared minus 10 x + 24 by x minus 2. Step 1 - Fill in the missing number: A vertical line and horizontal line combine to make a L shape. There is one row of entries in the shape including 1, negative 3, negative 10, 24. On the outside to the left of the L shape is k. k = -3 ⇒ 2 Step 2 - Fill in the missing number: A vertical line and horizontal line combine to make a L shape. There is one row of entries in the shape including 1, negative 3, negative 10, 24. On the outside to the left of the L shape is 2 and to the outside below 1 is a. a = 24 ⇒ 1 Step 3 - Fill in the missing numbers: A vertical line and horizontal line combine to make a L shape. There are two rows of entries in the shape. The first row includes 1, negative 3, negative 10, 24. The second row includes blank, b, d, blank. On the outside to the left of the L shape beside row 1 is 2. On the outside below the L shape in the first column is 1 and in the second column is c. b = c = d =

The value of the cosine of the angle of (a - b) will be 0.80.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

It is a function that repeats itself in a particular time interval.

Suppose that sin(a) = 4/6 and cos(b) = 1/5.

Then the value of 'a' is given as,

sin(a) = 4/6

sin(a) = 2/3

a = 41.81°

Then the value of 'b' is given as,

cos(b) = 1/5

b = 78.46°

Then the value of the cosine of the angle of (a - b) will be given as,

⇒ cos(41.81° - 78.46°)

⇒ cos(-36.65°)

⇒ cos 36.65°

⇒ 0.80

The value of the cosine of the angle of (a - b) will be 0.80.

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Answer:

Step-by-step explanation:

Nearest 10000s: 20000

Nearest 1000s  : 21000

Nearest 100     : 21000 This one is very hard. That nine gets bumped up.

Nearest 10        :20970

This one's a special case of a right angled triangle with sides (3, 4, and 5 units)

\(\qquad\displaystyle \tt \dashrightarrow \: 5 \sin \bigg( \frac{ \pi}{3} x \bigg) = 3\)

\(\qquad\displaystyle \tt \dashrightarrow \: \sin \bigg( \frac{ \pi}{3} x \bigg) = \frac{3}{5} \)

Now, check the triangle, sin 37° = 3/5

therefore,

\(\qquad\displaystyle \tt \dashrightarrow \: \sin \bigg( \frac{ \pi}{3} x \bigg) = \sin(37 \degree) \)

[ convert degrees on right side to radians ]

\(\qquad\displaystyle \tt \dashrightarrow \: \sin \bigg( \frac{ \pi}{3} x \bigg) = \sin \bigg(37 \degree \times \frac{ \pi}{180 \degree} \bigg ) \)

There are three more possible values as :

\(\qquad\displaystyle \tt \dashrightarrow \: \sin( \theta) = \sin(\pi - \theta) \)

\(\qquad\displaystyle \tt \dashrightarrow \: sin( \theta) = \sin \bigg( { 2\pi}{} + \theta \bigg) \)

\(\qquad\displaystyle \tt \dashrightarrow \: sin( \theta) = \sin \bigg( \frac{ 3\pi}{} - \theta\bigg) \)

\(\qquad\displaystyle \tt \dashrightarrow \: \frac{ \pi}{3} x = 37 \times \frac{ \pi}{180} \)

\(\qquad\displaystyle \tt \dashrightarrow \: x = 37 \times \frac{ \cancel \pi}{180} \times \frac{3}{ \cancel \pi} \)

\(\qquad\displaystyle \tt \dashrightarrow \: x = \frac{37}{60} \)

or in decimals :

\(\qquad\displaystyle \tt \dashrightarrow \: x = 0.616666... = 0.6167\)

[ 6 repeats at third place after decimal, till four decimal places it would be 0.6167 after rounding off ]

similarly,

\(\qquad\displaystyle \tt \dashrightarrow \: \pi - \frac{ \pi}{3} x = 37 \times \frac{ \pi}{180} \)

\(\qquad\displaystyle \tt \dashrightarrow \: \pi \bigg(1 - \frac{x}{3} \bigg ) = 37 \times \frac{ \pi}{180} \)

\(\qquad\displaystyle \tt \dashrightarrow \: 1 - \frac{x}{3} = \frac{37}{180} \)

\(\qquad\displaystyle \tt \dashrightarrow \: - \frac{x}{3} = 0.205 - 1\)

\(\qquad\displaystyle \tt \dashrightarrow \: \frac{x}{3} = 0.795\)

\(\qquad\displaystyle \tt \dashrightarrow \: x = 3 \times 0.795\)

\(\qquad\displaystyle \tt \dashrightarrow \: x = 2.385\)

\(\qquad\displaystyle \tt \dashrightarrow \: 2\pi + \frac{ \pi}{3} x = 37 \times \frac{ \pi}{180} \)

\(\qquad\displaystyle \tt \dashrightarrow \: \pi \bigg(2 + \frac{x}{3} \bigg ) = 37 \times \frac{ \pi}{180} \)

\(\qquad\displaystyle \tt \dashrightarrow \: 2 + \frac{x}{3} = \frac{37}{180} \)

\(\qquad\displaystyle \tt \dashrightarrow \: \frac{x}{3} = 0.205 - 2\)

\(\qquad\displaystyle \tt \dashrightarrow \: \frac{x}{3} = - 1.795\)

\(\qquad\displaystyle \tt \dashrightarrow \: x = 3 \times -1 .795\)

\(\qquad\displaystyle \tt \dashrightarrow \: x = -5.385\)

\(\qquad\displaystyle \tt \dashrightarrow \: 3 \pi - \frac{ \pi}{3} x = 37 \times \frac{ \pi}{180} \)

\(\qquad\displaystyle \tt \dashrightarrow \: \pi \bigg(3 - \frac{x}{3} \bigg ) = 37 \times \frac{ \pi}{180} \)

\(\qquad\displaystyle \tt \dashrightarrow \: 3 - \frac{x}{3} = \frac{37}{180} \)

\(\qquad\displaystyle \tt \dashrightarrow \: - \frac{x}{3} = 0.205 - 3\)

\(\qquad\displaystyle \tt \dashrightarrow \: \frac{x}{3} = 2.795\)

\(\qquad\displaystyle \tt \dashrightarrow \: x = 3 \times 2.795\)

\(\qquad\displaystyle \tt \dashrightarrow \: x = 8.385\)

" x can have infinite number of values here with the same result, here are the four values as you requested "

I hope it was helpful ~

Answer:

18 w 6 + 62 w 3 W + 73 w 3 + 24 W 2 + 12 W − 36

Step-by-step explanation:

Answer:

Length = 15ft

Width = 12ft

Step-by-step explanation:

First, re-read the problem until you acknowledge it and can put it into your own words.  

This is what I did:

 Find the area of a rectangle by first finding the length  and the width.  Note that:

L = Length  

W = Width

Find L and W

We will need formula:

P=2L+2W

A=LW

The length of a rectangle is 3 ft longer than its width :

L                             =    3             +         W                 Equation [1]

 "the perimeter of the rectangle is 30 ft"     means

            P                                = 54                           Equation [2]

     P = 54 = 2L + 2W                        

          54 = 2(3+W)  +  2W              

          54 = 6 + 2W   + 2W              

           54 = 6 + 4W                    

           48 + 4w

          12 ft = w

L = 3 + W        

          L = 3 + 12

         L = 15 ft

Area if needed

A = L*W

          A = (12 ft)*(15 ft)

          A = 180 sq ft

Kavinsky

Seth must attend 16 matinees in order to break even. Additionally, Seth will see a benefit from attending his 17th show.

What is linear equation ?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

Ax+By=C is the usual form for two-variable linear equations. When an equation is given in this format, finding both intercepts is rather simple (x and y).

Something that is linear is related to a line. A line is built using all of the linear equations. A non-linear equation is one that cannot be represented by a straight line. It has a variable slope value and resembles a graphed curve.

Original Equation:

x+40 = 3.50x

3.50x - x = 40

40 = 2.5X

2.5 X = 40

x = 40/2.5

x = 16

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Answer:

Angle 1 = 51.6°

Angle 2 = 38.4°

Step-by-step explanation:

All complimentary angles add up to 90°.

If two complimentary angles were congruent then their measures would both be 45°.

Since one angle's measure is 6.6° more than the other's measure, it's measure is 6.6° more than 45°

Vice versa for the second angle, its measure will be 6.6° less than 45°

Answer:

y = (-1/8)x + (29/4)

Step-by-step explanation:

(10, 6), (2, 7)

(x₁, y₁)  (x₂, y₂)

       y₂ - y₁         7 - 6             1             -1

m = ------------ = ----------- = ----------- = ---------

       x₂ - x₁          2 - 10         -8              8

y - y₁ = m(x - x₁)

y - 6 = (-1/8)(x - 10)

y - 6 = (-1/8)x + (5/4)

   +6                 +6

-------------------------------

y = (-1/8)x + (29/4)

I hope this helps!

Answer:

 Table B -

Step-by-step explanation:

You want to know which of the four offered tables represents a linear function.

A linear function will have differences in y that have the same ratio to differences in x for all pairs of values in the table.

Table A has x-differences that are 1 between adjacent terms. The y-differences are negative for the first pair of table values, but positive for the last pair (2 -5 vs 5 -2).

Table B has x-differences that are 1 between adjacent terms. The y-differences are -2 between any pair of adjacent terms, so their ratio to x-differences is -2/1 = -2, a constant. Table B represents a linear function.

Table C has x-differences that change from 0 to -3 to +3 while y-differences are constant at +1. The ratios of differences are not constant.

Table D has x-differences of +1, and y-differences that alternate in sign and magnitude.

Only Table B represents a linear function.

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The graph's function g(x) has a single x-intercept, a y intercept, a vertical asymptote, an oblique asymptote, and both.

Asymptotes are points along a line that a curve approaches but never touches. The term "asymptote" refers to the point at which a function's graph converges. Asymptotes are often not necessary when graphing functions.

There are three distinct asymptotes.

Asymptote horizontal (HA) - Given that it is horizontal, its equation has the form y = k. The horizontal asymptote is the point at which the function f(x) tends to zero.

As it is a vertical line, the vertical asymptote's equation has the form x = k. When the denominator of a rational function approaches towards 0, vertical asymptotes are defined.

The equation for the slanting asymptote (also known as the oblique asymptote) is y = mx + b since the line is inclined.

given the information,

Let's write the function as g. (x)

The value of g (x) is right now.

g (x) = ( -4x² + 36) / (x + 3)

We gain by simple.

g (x) = -4x² - 4×9) / (x + 3)

We gain more after additional simplification.

g (x) = -4 (x + 3) (x - 3) / (x + 3)

g (x) = -4x + 12

There is now a vertical asymptote for the function at (0, 12)

There is a horizontal asymptote for the function at (3, 0)

The function is so resolved.

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The complete question is:

G(x)=-4x^2+36/x+3

What key features does f(x), shown in the graph, share

with g(x), shown in the equation? Select three options.

at least one x-intercept

at least one y-intercept

Dan oblique asymptote

O a vertical asymptote

the domain of x

Answer:

Step-by-step explanation:

Answer:

B   D   F

Step-by-step explanation:

Took quiz

Answer:

16

Step-by-step explanation:

Step 1: Write down the function \(f(x)=7x^2+2x+3.\)

Step 2: Write down the limit definition of the derivative:
\(f'(x)= lim_{h0} \frac{f(x+h)=f(x)}{h} .\)

Step 3: Substitute the function \(f(x)\) into the limit definition:
\(f'(x)=lim_{h0} \frac{(7(x+h)^2+2(x+h)+3)-(7x^2+2x+3)}{h}.\)

Step 4: Simplify the expression inside the limit:
\(f'(x)=lim_{h0}\frac{7x^2+14xh+7h^2+2x+2h+3-7x^2-2x-3}{h} .\)

Step 5: Combine like terms:
\(f'(x)=lim_{h0} \frac{14xh+7h^2+2h}{h} .\)

Step 6: Factor out an \(h\) from the numerator:
\(f'(x)=lim_{h0} \frac{h(14x+7h+2h}{h} .\)

Step 7: Cancel out the \(h\) in the numerator and denominator:
\(f'(x)=lim_{h0}(14x+7h+2).\)

Step 8: Evaluate the limit as \(h\) approaches 0:
\(f'(x)=14x+2.\)

Step 9: Substitute \(x=1\) into the derivative:
\(f'(1)=14(1)+2=14+2=16.\)

The Slope of the tangent line to the curve \(f(x)=7x^2+2x+3\) at \(x=1\) would be \(16.\)

The assertion is true. Both 7√5 and √2 + 21 are irrational numbers because they cannot be expressed as fractions.

The assertion is true. Both 7√5 and √2 + 21 are irrational numbers.

An irrational number is defined as a number that cannot be expressed as a fraction of two integers and has an infinite non-repeating decimal representation.

In the case of 7√5, the square root of 5 is an irrational number because it cannot be expressed as a fraction. Multiplying it by 7 does not change its irrational nature.

Similarly, √2 is also an irrational number because the square root of 2 cannot be expressed as a fraction. Adding 21 to √2 does not alter its irrationality.

The reason provided, that every integer is a rational number, is not relevant to the given assertion. While it is true that every integer is a rational number because it can be expressed as a fraction (e.g., 3 can be written as 3/1), it does not contradict the fact that 7√5 and √2 + 21 are irrational numbers.

In conclusion, the assertion is valid, and both 7√5 and √2 + 21 are irrational numbers.

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Answer:7719

Step-by-step explanation:

The y-coordinate of -3f(x-1) when x = 0 is -63

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

The table of values

So, we have

-3f(x - 1)

When x = 0, we have

y = -3f(0 - 1)

This gives

y = -3f(-1)

From the table, we have

y = -3 * 21

Evaluate

y = -63

Hence, the y-coordinate is -63

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Answer: 4(4b - 5)(b + 5)

Step-by-step explanation:

All have a common factor of 4

4(4b^2 + 15b - 25)

--------------------------------------------------------------------------------------------------------------

Now you need to find two numbers that:

a) multiply to -100 (the a term * the c term = 4 * -25)

b) add to 15 (the b term)

After a little thinking, we can determine that the two numbers are:

20 and -5

--------------------------------------------------------------------------------------------------------------

Now we can rewrite the middle term as 20b - 5b (notice how it still equals 15b)

4(4b^2 + 20b - 5b - 25)

--------------------------------------------------------------------------------------------------------------

4((4b^2 + 20b) + (-5b - 25))

Group the terms (associative property)

--------------------------------------------------------------------------------------------------------------

Take out a common factor from each

4(4b(b + 5) - 5 (b + 5))

--------------------------------------------------------------------------------------------------------------

Now we can factor by grouping

4(4b - 5)(b + 5)

--------------------------------------------------------------------------------------------------------------

Answer:

The change is of -1.3 percentage points.

Step-by-step explanation:

The humidity is currently 56% and falling at a rate of 4 percentage points per hour.

This means that after n hours the humidity is of:

\(H(n) = 56 - 4n\)

Estimate the change in humidity over the next 20 minutes.

It currently is 56%.

20 minutes is 20/60 = 1/3 of an hours, so:

\(H(\frac{1}{3}) = 56 - 4\frac{1}{3} = 54.7\)

Change:

54.7 - 56 = -1.3

The change is of -1.3 percentage points.

The change in humidity over the next 20 minutes falling at a rate of  4 percentage points per hour is -1.3.

The humidity is currently 56% and falling at a rate of 4 percentage points per hour.

The change is determined by the small about of humidity changes x to x+h, so the output of x+h is the value of f at x plus the approximate change in f, that is

\(\rm f(x+h) =f(x) + f'(x) \times h\)

f(x)= 56%

20 minutes is 20/60 = 1/3 of an hours

So, The change in humidity is

\(f'(x) = 4 \times 1/3\)

f'(x) = 1.3

Here, it is falling at the rate of 4% point per hour so we will take it as negative as -1.3.

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Answer: the answer for #16 is 216

Step-by-step explanation:

1. 75*2=150

2. 33*2=66

3. 150+66=216

Answer:

63

Step-by-step explanation:

450 × 14 ÷ 100 = $63

hope this helps

Answer:

i think is 63

Step-by-step explanation:

Answer:  96 students

=============================================

Work Shown:

(2 vans)/(32 students) = (6 vans)/(x students)

2/32 = 6/x

2x = 32*6

2x = 192

x = 192/2

x = 96 students

----------

Another way to look at it:

2 vans carry 32 students. That must mean each van carries 32/2 = 16 students assuming all vans carry the same amount of people.

So 6 vans would carry 6*16 = 96 students

This excludes the driver for each van.

Answer:

\({ \tt{ \frac{dy}{dx} + 2x + 1 = 2 }} \\ \\ { \tt{ \frac{dy}{dx} = - 2x + 1 }} \\ \\ { \tt{dy = ( - 2x + 1) \: dx}} \\ \\ { \tt{ \int dy = \int( - 2x + 1) \: dx}} \\ \\ { \tt{y = - {x}^{2} + x + c}} \\ \\ { \tt{y = - x(x + 1) + c}}\)

Answer:

\(y=-x^2+x+\text{C}\)

Step-by-step explanation:

Given equation:

\(\dfrac{\text{d}y}{\text{d}x}+2x+1=2\)

\(\text{Isolate $\dfrac{\text{d}y}{\text{d}x}$}:\)

\(\implies \dfrac{\text{d}y}{\text{d}x}+2x+1-2x-1=2-2x-1\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=-2x+1\)

Multiply both sides by dx to get all the terms containing y on the left side, and all the terms containing x on the right side:

\(\implies \text{d}y=(-2x+1)\;\text{d}x\)

Integrate both sides:

\(\implies \displaystyle \int 1\;\text{d}y=\int(-2x+1)\;\text{d}x\)

Fundamental Theorem of Calculus

\(\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))\)

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.

Integrate each term separately:

\(\implies \displaystyle \int 1\;\text{d}y=\int -2x\;\text{d}x+\int 1\;\text{d}x\)

Take the constant outside the integral:

\(\implies \displaystyle \int 1\;\text{d}y=-2\int x\;\text{d}x+\int 1\;\text{d}x\)

Integrate, using the rules given below:

\(\implies y=-2 \cdot \dfrac{1}{1+1}x^{(1+1)}+x+\text{C}\)

\(\implies y=-x^2+x+\text{C}\)

Integration rules:

\(\boxed{\begin{minipage}{4 cm}\underline{Integrating $x^n$}\\\\$\displaystyle \int x^n\:\text{d}x=\dfrac{x^{n+1}}{n+1}+\text{C}$\end{minipage}}\)

\(\boxed{\begin{minipage}{5 cm}\underline{Integrating a constant}\\\\$\displaystyle \int n\:\text{d}x=nx+\text{C}$\\(where $n$ is any constant value)\end{minipage}}\)

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Antonio needs to score at least 111 points in his next game to reach his goal of an average of at least 100 points per game.

What are basic arithmetic operations?

Basic arithmetic operations are fundamental mathematical calculations that involve manipulating numerical values using a set of basic operations.

To find out how many points Antonio needs to score in his next game to reach an average of at least 100 points per game, we can use the following formula:

Total points needed = (number of games + 1) × average score goal - total points scored so far

In this case, Antonio has played 5 games, so the number of games he will have played after his next game is 6. His goal is an average of 100 points per game, so his average score goal is 100. The total points he has scored so far is:

105 + 95 + 97 + 82 + 110 = 489

Substituting these values into the formula, we get:

Total points needed = (6) × (100) - 489

Total points needed = 600 - 489

Total points needed = 111

Hence, Antonio needs to score at least 111 points in his next game to reach his goal of an average of at least 100 points per game.

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Answer:

$40 for Mr. Sustar's class, $240 for Dr. Leong's class, $200 for Mrs. Wolbert's class

Step-by-step explanation:

m + 6m + 5m = 480

12m = 480

m = 40, so 6m = 240 and 5m = 200

The algebraic expression for Desmond's height is x + 5.

If we let "x" represent Niki's height in inches, then Desmond's height can be represented by "x + 5", since Desmond is 5 inches taller than Niki.

So the algebraic expression for Desmond's height is x + 5.

Algebraic expressions is consist of variables, numbers, and mathematical operations (such as addition, subtraction, multiplication, and division).

They can contain one or more variables and can be evaluated for different values of the variables.

For example, the expression 3x + 5y - 2z is an algebraic expression that contains three variables (x, y, and z) and three coefficients (3, 5, and -2) that are multiplied by those variables. Algebraic expressions are commonly used in algebra to represent mathematical relationships and solve problems.

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Answer: The answer is D: 7 1/2.

Step-by-step explanation:

Answer:

Step 1 is incorrect because it was mutiplied. Instead, you should divide.

Step-by-step explanation:

The maximum pounds of celery she can buy is  3.25 pounds.

1.5c = o equation 1

1.50o + 1.80c = 8.10 equation 2

Where:

o = pounds of onions

c = pounds of celery

How many pounds of celery can she buy?
Substitute for o in equation 2 using equation 1

1.50(1.50) + 1.80c = 8.10

2.25 + 1.80c = 8.10

1.80 = 8.10 - 2.25

1.80c = 5.85

c = 5.85 / 1.80

c = 3.25 pounds

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According to census the total number of male and female was 88,51,84,692, if number of male was 45,40,34,570 the number of female population is 43,11,50,122.

To find the wide variety of girl population, we will subtract the quantity of male population from the full population.

Total population = 88,51,84,692

Number of male = 45,40,34,570

Number of female = Total population - Number of male

= 88,51,84,692 - 45,40,34,570

= 43,11,50,122

Therefore, the number of female population is 43,11,50,122.

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The expression which shows how many grams of raisins are in the bowl will be

(0.01x) * 150 + (0.01y) * 250

An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.

The expression which shows how many grams of raisins are in the bowl will be:

= (x% × 150) + (y% × 250)

= (0.01x) * 150 + (0.01y) * 250

This equation represents the total grams of raisins in the bowl by multiplying the weight of the Oreana's bag by the percentage of raisins in it, and adding that to the product of the weight of Brandon's bag and the percentage of raisins in it. The "0.01" is used to convert the percentages from x and y to decimal form.

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Answer:

\( x = 27 \)

Step-by-step explanation:

According to congruent chords and arcs theorem, if \( \overline{XY} \cong \overline{ZY} \) then \( \arc{XY} \cong \arc{ZY} \).

This means that \( \arc{XY} = \arc{ZY} = (6x - 20) degrees \)

Thus:

\( \arc{XY} + \arc{ZY} + \arc{ZX} = 360 \) (full circle = 360°)

\( \arc{XY} = (6x - 20) \)

\( \arc{ZY} = (6x - 20) \)

\( \arc{ZX} = 76 \)

Plug in the values into the equation

\( (6x - 20) + (6x - 20) + 76 = 360 \)

\( 6x - 20 + 6x - 20 + 76 = 360 \)

Add like terms

\( 12x + 36 = 360 \)

Subtract 36 on both sides

\( 12x = 360 - 36 \)

\( 12x = 324 \)

Divide both sides by 12

\( x = 27 \)