EASY MATH PLS HELP !!!

we have the equation of curve C

Part a

Find out the gradient, where x=3

To find the gradient, take the derivative of the function with respect to x, then substitute the x-coordinate of the point of interest for the x values in the derivative

so

the first derivative is equal to

Evaluate the first derivative for x=3

Part b

we know that the gradient is equal to 1 at point P

so

equate the first derivative to 1

Find out the possible y-coordinate of point P

For x=2

substitute in the given equation of C

For x=-2

To solve the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0, we can use algebraic methods and the unit circle to determine the values of x that satisfy the equation.

1. Start by rearranging the equation to a quadratic form: \(6sin^2(x)\) + 6sin(x) + 1 = 0.

2. Notice that the equation resembles a quadratic equation in terms of sin(x). Let's substitute sin(x) with a variable, such as u: \(6u^2\) + 6u + 1 = 0.

3. Solve this quadratic equation for u. You can use the quadratic formula or factorization methods to find the values of u. The solutions are u = (-3 ± √3) / 6.

4. Since sin(x) = u, substitute back the values of u into sin(x) to obtain the values for sin(x): sin(x) = (-3 ± √3) / 6.

5. To find the values of x, we can use the inverse sine function. Take the inverse sine of both sides: x = arcsin[(-3 ± √3) / 6].

6. The arcsin function has a range of [-π/2, π/2], so the values of x lie within that range. Use a calculator to find the approximate values of x based on the values obtained in step 5.

7. Plot the obtained x-values on the graph to show the solutions of the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0. The graph will illustrate the points where the curve intersects the x-axis.

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Answer:

44

Step-by-step explanation:

* means multiply

put 8 where the x is

6 * 8 - 4

48 - 4

44

Answer:

After buying additional hair bands, Colleen can own a total of 43 hair bands.

Step-by-step explanation:

Solving this problem entails of finding out the total number of hair bands Colleen can own, based on the amount she already owns and how many more she purchases. Start by reading the problem carefully to break down the information provided.

We know that Colleen already owns twenty eight hair bands. This is important to remember to include. The problem also states that she has a total of fifteen dollars and each individual hair band is priced at one dollar.

Because the hair bands are only a dollar, Colleen can purchase an additional fifteen hair bands.

Setting up an equation will help us solve. Here is how we could set up the equation:

(amount of hair bands already owned = 28) + (number hair bands bought = 15) = (total number of hair bands owned = x)

28 + 15 = x

The equation is now in place. Solve by adding both terms. This is how you will reach the answer.

28 + 15 = x

43 = x

This means that Colleen will have 43 hair bands in total, after purchasing fifteen hair bands.

The statements that is true about the similarity of the two triangles the option D

D. ΔMNO and ΔJKL are not similar triangles

Similar triangles are triangles which have proportional corresponding sides

The parameters in the question are;

The length of segment MN = 20

Length of segment NO = 12

Length of segment OM = 25

Measure of angle ∠O = 56°

Length of segment LJ =- 15

Length of segment JK = 12

Length of segment KL = 9

Measure of angle ∠L = 56°

Two triangles are similar if the ratio of two sides on one triangle are proportional to two sides of another triangle, and the included  angle between the two sides are congruent

The included angle between sides ON and MO on triangle MNO is congruent to the included angle between segment LK and JL in triangle JKL

However, the ratio of the sides  LK to ON and JL to MO are;

9/12 ≠ 15/25

Therefore, the triangles are not similar

The correct option is option D

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The relationship between segments AB and CD is that they are perpendicular because they have slopes that are opposite reciprocals of -5 and 1/5.

Option B is the correct answer.

We have,

For segment AB, the equation of the line is y - 4 = -5(x - 1).

By rearranging this equation to the slope-intercept form (y = mx + b),

we get:

y = -5x + 5 + 4

y = -5x + 9

Comparing this with the general equation, we can see that the slope of segment AB is -5.

For segment CD, the equation of the line is y - 4 = 1/5(x - 5).

Again, rearranging to the slope-intercept form, we get:

y = 1/5 x + 1/5 * 5 + 4

y = 1/5 x + 1 + 4

y = 1/5 x + 5

Comparing this with the general equation, we can see that the slope of segment CD is 1/5.

Now,

The slopes are -5 and 1/5, respectively.

They are perpendicular because they have slopes that are opposite reciprocals of -5 and 1/5.

Therefore,

The relationship between segments AB and CD is that they are perpendicular because they have slopes that are opposite reciprocals of -5 and 1/5.

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The complete question.

Segment AB is on the line y − 4 = −5 (x − 1), and segment CD is on the line y − 4 = 1/5 (x − 5).

Which statement proves the relationship between segments AB and CD?

They are perpendicular because they have slopes that are opposite reciprocals of 5 and −1/5

​They are perpendicular because they have slopes that are opposite reciprocals of -5 and 1/5.

​They are parallel because they have the same slope of 5.

They are parallel because they have the same slope of −1/5.

Set up the partial fraction decomposition for the given function:

\($f(x)=\frac{(b)\sqrt{16x^3+12r^2+10x+2}}{(x^4-4x^2)(x^2+x+1)^2(x^2-3x+2)(x+3x^2+2)}$\)

is: \(=\frac{3}{26}x^2-\frac{21}{13}x+\frac{9}{13}\ln|x+4|-\frac{1}{13}\arctan\frac{x+1}{2}+\frac{5}{39}\ln[(x+1)^2+4]+C\)

The denominator factors completely to:

\(x^4-4x^2=x^2(x^2-4)=x^2(x-\sqrt{2})(x+\sqrt{2})\)

\(x^2+x+1=(x-(\frac{-1+i\sqrt{3}}{2}))(x-(\frac{-1-i\sqrt{3}}{2}))$$\)

\(x^2-3x+2=(x-2)(x-1)\)

\(x+3x^2+2=(x+\frac{3}{2})^2-\frac{1}{4}\)

Therefore,

\(\begin{aligned}\frac{f(x)}{(b)\sqrt{16x^3+12r^2+10x+2}}&=\frac{A}{x}+\frac{B}{x-\sqrt{2}}+\frac{C}{x+\sqrt{2}}+\frac{Dx+E}{x^2+x+1}+\frac{Fx+G}{(x^2+x+1)^2}\\&+\frac{H}{x-2}+\frac{J}{x-1}+\frac{Kx+L}{x+\frac{3}{2}+\frac{1}{2}}+\frac{Nx+M}{(x+\frac{3}{2}+\frac{1}{2})^2}\end{aligned}\)

(a) \($\int\frac{3x^2-3x+1}{(x^2+2x+5)(x+4)}dx$\) is

\($\frac{1}{13}\int\frac{3x^2-3x+1}{x+4}dx-\frac{1}{13}\int\frac{3x^2-3x+1}{x^2+2x+5}dx$\).

\(=\frac{3}{13}\int\frac{x^2-x}{x+4}dx+\frac{1}{13}\int\frac{1}{x+4}dx-\frac{1}{13}\int\frac{3x^2-3x+1}{(x+1)^2+4}dx\)

\(=\frac{3}{13}\int\frac{x^2-x}{x+4}dx+\frac{1}{13}\ln|x+4|-\frac{1}{39}\int\frac{3x-7}{(x+1)^2+4}d(x+1)\)

\(=\frac{3}{13}\int x-4+\frac{16}{x+4}dx+\frac{1}{13}\ln|x+4|-\frac{1}{39}\int\frac{3}{t^2+4}dt-\frac{1}{39}\int\frac{x+5}{(x+1)^2+4}d(x+1)\)

\(=\frac{3}{26}x^2-\frac{21}{13}x+\frac{9}{13}\ln|x+4|-\frac{1}{13}\arctan\frac{x+1}{2}+\frac{5}{39}\ln[(x+1)^2+4]+C\)

where t=x+1 is used. The answer is obtained by partial fraction decomposition and substitution. The value of the constant C is not given.

Conclusion: Partial fraction decomposition is a technique to decompose complex rational functions into simpler rational functions. In this technique, we decompose a complex rational function into simpler fractions whose denominators are linear factors or irreducible quadratic factors. This is the easiest way to solve integrals of rational functions that are complex.

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The partial fraction decomposition for the given function and evaluated the given indefinite integrals.

∫dx/[(3x²-3x+1)³+1] = -1/6[1/(3x² - 3x + 2)] + 1/6[1/[(3x² - 3x + 2)²]] + 1/2[arctan(6x² - 6x + 1)] + C

∫dx/[(x² + 2x + 5)(x + 4)] = 1/(x + 4) - 2x + 1/(x² + 2x + 5) + C

∫dx/√(2 + 2x + 5) = (1/2) ∫du/√u

The partial fraction decomposition for the given function and evaluated the given indefinite integrals.

The steps to set up the partial fraction decomposition for a given function

f(x) = (b) √ 16x³ +12r² + 10x +2 (x⁴-4x²)(x² + x + 1)²(x²-3x + 2)(x+3x²+2) are given below:

Step 1: Factorise the denominator: x⁴ - 4x² = x²(x² - 4)

= x²(x + 2)(x - 2) (x² + x + 1)²(x² - 3x + 2)(x + 3x² + 2)

Step 2: Determine the degree of the numerator, which is less than the degree of the denominator. In this case, the degree of the numerator is 1. So, the partial fraction decomposition will be of the form

A/x + B/(x² + x + 1) + C/(x² - 3x + 2) + D/(x + 3x² + 2) + E/[(x² + x + 1)²]

Step 3: Multiply the original function f(x) by the denominator, set the numerator of the result equal to the sum of the numerators of the partial fractions, and simplify. Then, equate the coefficients of the resulting polynomial equations in x with each other. Solve the system of equations for the unknown constants. Then, use partial fraction decomposition to break up a rational function into simpler fractions.

Explanation: Given function is f(x) = (b) √ 16x³ +12r² + 10x +2 (x⁴-4x²)(x² + x + 1)²(x²-3x + 2)(x+3x²+2). Partial fraction decomposition is the decomposition of a rational function into simpler fractions. The steps to set up the partial fraction decomposition for a given function f(x) = (b) √ 16x³ +12r² + 10x +2 (x⁴-4x²)(x² + x + 1)²(x²-3x + 2)(x+3x²+2) are as follows:

Step 1: Factorise the denominator: x⁴ - 4x² = x²(x² - 4) = x²(x + 2)(x - 2) (x² + x + 1)²(x² - 3x + 2)(x + 3x² + 2)

Step 2: Determine the degree of the numerator, which is less than the degree of the denominator. In this case, the degree of the numerator is 1. So, the partial fraction decomposition will be of the form A/x + B/(x² + x + 1) + C/(x² - 3x + 2) + D/(x + 3x² + 2) + E/[(x² + x + 1)²]

Step 3: Multiply the original function f(x) by the denominator, set the numerator of the result equal to the sum of the numerators of the partial fractions, and simplify. Then, equate the coefficients of the resulting polynomial equations in x with each other. Solve the system of equations for the unknown constants. Then, use partial fraction decomposition to break up a rational function into simpler fractions.

The answers for the given integrals are as follows:

(a) ∫dx/[(3x²-3x+1)³+1] = 1/3 ∫du/u³

(by substitution, let u = 3x² - 3x + 1)

= -1/6[1/(u² + u + 1)] + 1/6[1/[(u² + u + 1)²]] + 1/2[arctan(2u - 1)] + C

= -1/6[1/(3x² - 3x + 2)] + 1/6[1/[(3x² - 3x + 2)²]] + 1/2[arctan(6x² - 6x + 1)] + C

(b) ∫dx/[(x² + 2x + 5)(x + 4)] = A/(x² + 2x + 5) + B/(x + 4)

= [A(x + 4) + B(x² + 2x + 5)]/[(x² + 2x + 5)(x + 4)]

= [(A + B)x² + (4A + 2B)x + (5B)]/[(x² + 2x + 5)(x + 4)]

= 1/(x + 4) - 2x + 1/(x² + 2x + 5) + C

(d) ∫dx/√(2 + 2x + 5)

= ∫dx/√(7 + 2x) = (1/√2)arcsin((2x + 1)/√7) + C

(e) ∫xdx/(1 + x²) = (1/2)ln(1 + x²) + (1/2)arctan(x) + C(d) ∫dr/[(b) √ 16r³ + 12r² + 10r + 2]

= (1/2) ∫du/√u

(by substitution, let u = 16r³ + 12r² + 10r + 2)

= (1/2) √u + C

= (1/2) √(16r³ + 12r² + 10r + 2) + C.

Conclusion: Thus, we have set up the partial fraction decomposition for the given function and evaluated the given indefinite integrals.

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Answer: Rebate applied AFTER the discount

Step-by-step explanation:

Because the rebate value stays the same no matter what, but the discount doesn't.

The linear function for this problem is defined as follows:

y = x + 50.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

The graph touches the y-axis at y = 50, hence the intercept b is given as follows:

b = 50.

When x increases by 10, y also increases by 10, hence the slope m is given as follows:

m = 10/10

m = 1.

Hence the function is given as follows:

y = x + 50.

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Answer: 18x+24

Step-by-step explanation:

First, combine there speed

speed = 54 + 63 =117 mph

Distance given = 234 miles

Speed = distance / time

This implies that;

time = distance / speed

=234 / 117

= 2hours

In 2 hours, they will be 234 miles apart

Answer:

5

Step-by-step explanation:

Answer:

\( \boxed{0.76} \: is \: correct.\)

Step-by-step explanation:

\( let \: the \: unknown \: ounce \: be \to \: u_{kn}\\ if \: 1 \: ounce \: is = 23.8 \: grams \\ then \to \: u_{kn} = \frac{18 \: grams \times 1 \: ounce}{23.8 \: grams } \\ u_{kn} = \frac{18}{23.8} (1 \: ounce \:) = 0.756302521 \times 1 \: ounce \\ \boxed{u_{kn} = 0.756302521 \: ounce }\)

♨Rage♨

I recommend the average fan buy season tickets when purchasing seats.

Based on the research, the average local baseball fan plans to attend 67 games during the season. For a fan who is planning to attend this many games, it would be more cost-effective to purchase season tickets rather than individual game tickets.

For fans considering season tickets, here are some recommendations based on the seating section:

Purchasing season tickets rather than individual game tickets is the most cost-effective choice for the average fan who plans to attend 67 games during the season. The best choice of section will depend on the fan's budget and personal preferences.

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Answer:

the distance for 7 minutes is 210m

the distance for 10 minutes is 300m

the distance for 14 minutes is 420m

the distance for 29 minutes is 600m

Step-by-step explanation:

d=30(7)

d=210

d=30(10)

d=300

d=30(14)

d=420

d=30(20)

d=600

Polynomials are closed under the operation of addition, subtraction, and multiplication only. Here's why:

1. Addition: (Closed)

Reason: Say we have two polynomials: (x⁴ + 2x³ - 4) and (3x³ - 2x² + 6x). If we add these two polynomials, (x⁴ + 2x³ - 4) + (3x³ - 2x² + 6x), it will result to x⁴ + 5x³ - 2x² + 6x - 4 which is also a polynomial.

When adding polynomials, the variables and the exponents don't change. This guarantees that the sum of these variables with exponents will always be a polynomial.

2. Subtraction: (Closed)

Reason: Say we have two polynomials: (x⁴ + 2x³ - 4) and (3x³ - 2x² + 6x). If we subtract these two polynomials, (x⁴ + 2x³ - 4) - (3x³ - 2x² + 6x), it will result to x⁴ - x³ + 2x² - 6x - 4 which is also a polynomial.

When subtracting polynomials, the variables, and the exponents don't change. This guarantees that the difference of these variables with exponents will always be a polynomial.

3. Multiplication: (Closed)

Reason: Say we have two polynomials (x + 2) and (x - 4). If we multiply these two polynomials, (x + 2)(x - 4), it will result in x² - 2x - 8, which is also a polynomial.

When multiplying polynomials, the variables do not change but the exponents will be added to each other. In this case, we can guarantee that the new exponents will be positive whole numbers still and this guarantees that the answer will be a polynomial.

4. Division: (Not closed)

Reason: When dividing polynomials, exponents are being subtracted from each other, therefore, we might have a result of a negative exponent. Negative exponents are not allowed in a polynomial. Example, say we have two polynomials (x²) and (x⁴), if we divide (x²) by (x⁴), the resulting value would be:

The resulting value is x to the power of negative 2, and is not a polynomial.

Simplify them

Answer =11

a= bc-3c-3b/6c

look at the screenshots for steps

Answer:

2x+9

Step-by-step explanation:

-4(-2x-9)

8x+36

2x+9

Hope u got it

If you have any question just ask me

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Answer:

2x + 9

Step-by-step explanation:

-4(-2x-9)

^ first start with distributive property

8x + 36

^ and simplify

2x + 9

and you've got your expression!

let me know if you're confused on anything else

Answer:

y=2x+3

Step-by-step explanation:

The equation of a line is:

\(y=mx+b\) with m being the slope and b being the y-intercept.

The slope is \(\frac{rise}{run}\), where rise is how many units you go up/down from one point to another, and the run is how many units you go left/right from one point to another.

The y-intercept is when x=0, or where the line intercepts the y-axis.

In this case, we can see that the blue line intercepts the y-axis at (0,3), making 3 our y-intercept.

To find the slope, we first have to choose 2 points. Let's choose (0,3) and (1,5).

We can see that to go from (0,3) to (1,5), we have to go up 2 units and go right 1 unit.  This means our slope is 2/1, or 2.

So, we can substitute the y-intercept and slope into our formula:

y=2x+3

Hope this helps! :)

Answer:-1

Step-by-step explanation:

Answer: -6

Step-by-step explanation:

the line pass through (-3,-6)

Answer:

65

Step-by-step explanation:

Since 39 is 60%, 100/60= 1 2/3

39*1 2/3 is 65

Answer:

it is $5 per hour

Answer:

It is c.

Step-by-step explanation:

Divide the amount earned by hours. For example 10/2=5, 20/4=5, 30/6=5 and so on

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Answer:

64?

Step-by-step explanation:

The correct option of the given question is option (c)  fissure.

When coding the phrase "supravesical fissure of urinary bladder," the main term to reference in the index is c. fissure.

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The main term to reference in the index when coding the phrase "supravesical fissure of urinary bladder" is c. fissure.

In medical coding, the index is typically organized alphabetically based on the main terms or significant words within medical terminology. In this case, "fissure" is the main term that represents the specific condition or anatomical feature being coded.

The other terms, such as "urinary," "bladder," and "supravesical," provide additional context but are not the primary focus when searching for the appropriate code in the index.

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Answer:

Surface area of cylinder = 24π

Step-by-step explanation:

Given:

Base diameter = 4 yd

So Radius = 4 / 2 = 2 yd

Height = 4 yd

Find:

Surface area of cylinder

Computation:

Surface area of cylinder = 2πr(h+r)

Surface area of cylinder = 2π(2)(4+2)

Surface area of cylinder = 2π(2)(6)

Surface area of cylinder = 24π

This is the transitive property :)

Answer: The solution is (3, -2)

This means that x = 3 and y = -2 pair up together.

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

Explanation:

The solution is where the two lines cross. Note if we started at the origin (0,0) and moved to the right 3 units, and then down 2 units, we would arrive at the location (3, -2).

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

As a way to check, we can plug x = 3 into each equation. We should get y = -2 as a result for each equation

y = (-5/3)x + 3

y = (-5/3)*3 + 3

y = -5+3

y = -2

The first equation is confirmed. Let's check the second equation

y = (1/3)x - 3

y = (1/3)*3 - 3

y = 1 - 3

y = -2

Both equations have the y value equal -2 when x = 3. Therefore, the overall solution is confirmed.

If the ratio of students who prefer muffins to bagels is 4 to 5. if the number of students surveyed who prefer muffins is 420 then the number of students who prefer bagels is 21

Ratio: In mathematics the quantitative relation between two amounts showing the number of times one value contains or is contained within the other is known as ratio.

Given that,

The ratio of the students who prefer muffins to bagels is 4:5 means 4/5.

Number of students who prefer muffins is 420

Let, the number of students who prefer bagels is x

According to the question,

4a:5a = 420:x

⇒4a/5a = 420/x

⇒4/5 = 420/x

⇒x(4/5) = 420

⇒4x = 420×5

⇒4x = 84

⇒x = 21

Therefore the number of students who prefer bagels is 21

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