Given y=(x+2)(2x2+3)3 find the equation of the tangent line to this function when x = 1. First find the point on this function and the slope of the tangent line to this function when x = 1. Next use these to find the equation of the tangent line to this function when x = 1. Finally, put this equation in slope intercept form. All work must be shown!!
Point on function when x = 1 is (1, _____)
Slope of tangent line when x = 1 is _____________
Equation of tangent line in slope intercept form is:
_______________________________________

The ordered pair that is a solution to the equation 2x − 3y = 1 is; (2, 1)

We are given the equation;

2x - 3y = 1

Now, the ordered pair that is a solution simply means the least whole numbers for x and y that will make the equation valid.

Now, since the coefficient before x is bigger than the coefficient before y which is negative, then it means x must be larger than y. Thus, let us try x = 2 and y = 1 to get;

2(2) - 3(1) = 1

This makes the equation valid.

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Answer:

Gradient: 5

y-intercept: (0, 15)

Step-by-step explanation:

The gradient is usually just the same as the slope, so if we write the equation in slope-intercept form, y = 5x+15, the coefficient of x value (5) is the slope. The y-intercept is when x equals 0. Plug that in to get y = 15.

The new price after the price increase of Nu 40 will be Nu 840.

The price of a pant after n Nu 40 price increases will be:

= 800 + 40

= 840

The expected weekly sales as a function of the number of price increases will be:

= n - 1) × 800

= (30 - 1) × 800

= 29 × 800

= 23200

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Using the concept of vertical and horizontal asymptotes, it is found that the function will have a horizontal asymptote at y = 2 and a vertical asymptote at x = 1 for a = -1 and m = 1.

In this problem, the function is:

[tex]f(x) = \frac{2x^m}{x + a}[/tex]

It has a vertical asymptote at x = 1, hence:

x + a = 0

1 + a = 0

a = -1

It has a horizontal asymptote at y = 2, hence:

[tex]\lim_{x \rightarrow \infty} f(x) = 2[/tex]

[tex]\lim_{x \rightarrow \infty} \frac{2x^m}{x + a} = 2[/tex]

[tex]\lim_{x \rightarrow \infty} \frac{2x^m}{x} = 2[/tex]

[tex]2^{m-1} = 2[/tex]

Then, since we want to simplify, the exponents at the numerator and the denominator have to be equal, hence m = 1.

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The correct decision for the statements are

This is further explained below.

Generally, alcohol is a colorless liquid that is volatile and combustible. It is created during the natural fermentation of carbohydrates and is the component that gives wine, beer, spirits, and other beverages their intoxicating properties. Additionally, alcohol is utilized as an industrial solvent and as fuel.

In conclusion, The appropriate response for each of the statements is

Alcohol is a significant factor in the large percentage of students who struggle academically and drop out of college, which is true. It's true that drinking more alcohol brings a drop in GPA. Students who consume more alcohol miss the same number of courses as students who consume less alcohol. This statement is false. Students who drink more spend less time studying, which is true. Students with a grade point average of 2.0 (C) drink on average two times as much alcohol as students with a grade point average of 4.0 (A) (A).

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Answer:

y=6.72x^0.996x

Step-by-step explanation:

Answer:

  44.7 mg

Step-by-step explanation:

The equation for exponential decay can be written in the form ...

  y = a·b^(t/p)

where 'a' is the initial value, 'b' is the decay factor, 'p' is the period over which the decay factor is applicable, and t is time in the same units as p.

Using the above equation, we have ...

  a = initial value = 110 mg

  b = decay factor = 55/110 = 1/2 over time period p=20 hours

Then the equation is ...

  y = 110·(1/2)^(t/20) . . . . amount remaining after t hours

We want the amount remaining after 26 hours. That will be ...

  y = 110·(1/2)^(26/20) ≈ 44.67

About 44.7 milligrams will remain after 26 hours.

Answer:

x=7

Step-by-step explanation:

The angle of a straight line is 180 degrees, so let's just say the other angle to the right of 15x+34 is "a" that means that 15x + 34 + A = 180, and since the sum of interior angles of a triangle is 180 degrees, that means that 29 + A + 12x + 26 = 180, and we can define A using this equation in terms of x.

Original equation (sum of interior angles)

A + 29 + 12x + 26 = 180

Combine like terms

A + 12x + 55 = 180

Subtract 12x and 55 from both sides

A = -12x + 125

Original equation (since a line is 180 degrees)

15x + 34 + A = 180

Substitute -12x + 125 as A

15x + 34 + (-12x + 125) = 180

Combine like terms

3x + 159 = 180

Subtract 159 from both sides

3x = 21

Divide both sides by 3

x = 7

Step-by-step explanation:

in a number like 125,734,016

the right most position has the weight 10⁰ = 1

so, 6×1 = 6.

the second right most position has the weight 10¹ = 10.

so, 1×10 = 10

the third right most position has the weight 10² = 100.

so, 0×100 = 0

the 4th right most position has the weight 10³ = 1000.

so, 4×1000 = 4,000

the 5th right most position has the weight 10⁴ = 10000.

so, 3×10000 = 30,000

the 6th right most position has the weight 10⁵ = 100000.

so, 7×100000 = 700,000

the 7th right most position has the weight 10⁶ = 1000000.

so, 5×1000000 = 5,000,000

the 8th right most position has the weight 10⁷ = 10000000

so, 2×10000000 = 20,000,000

and so on.

as we can see, the 2 (the 8th most position from the right or the second position from the left) has the value of 20,000,000.

It is expected the height of the melted wax in this shape is 9.57 inches, this height would make the volume remain constant.

The volume of a sphere can be calculated using the formula V = 4/3 πr³. Let's use this formula to calculate the volume of the spherical ball of wax:

Considering the volume should be the same  (2144.66 cubic inches) and the volume of this shape can be calculated by multiplying the sides, this would be the equation:

This means the height would be 9.57 inches.

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Considering the given tree diagram, there is a 0.5 = 50% probability of an investor choosing either stocks or bonds from portfolio C.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

At each node, the sum of the probabilities is of 1, hence:

0.2 + 0.3 + Z = 1.

Z = 0.5.

There is a 0.5 = 50% probability of an investor choosing either stocks or bonds from portfolio C.

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Answer:

No, they can't

Step-by-step explanation:

According to the Triangle Inequality Theorem, the largest side cannot be greater than the sum of the other two sides.

2+4= 6<7

As you can see from this Equation NOT any two side are greater than the third making this NOT possibly be a tringle.

2+7=9>4

4+7=11>2

The equation of the circle with a center (-5, -6) and a radius of 5 is (x + 5)² + (y + 6)² = 25.

The standard equation for writing the equation of a circle is: (x - h)² + (y - k)² = r².

Given the following:

Center (-5, -6) = (h, k)

Radius = 5 = r

Plug in the values into the formula

(x + 5)² + (y + 6)² = 5²

(x + 5)² + (y + 6)² = 25

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The set  (x1,x2)+(y1,y2)=(x1-x2, y1+y2) is not a vector space.

A set is a vector space if it satisfy all the addition operation axiom and scalar multiplication axiom.

Addition operation:

Commutativity -

(x1, x2) + (y1, y2) equals  (x1 - x2,  y1 + y2) equals  (y1, y2) + (x1, x2)

Associativity -

(x1, x2) plus ((y1, y2) plus (z1, z2)) = (x1, x2) + (z1 + y1, z2 + y2) = (x1+ y1 + z1, x2 + y2 + z2) =

((x1, x2)   + (y1, y2)) + (z1, z2)

Zero element -

(0, 0)  → (x1, x2) + (0, 0) = (x1, x2)

Inverse element -

(x1, x2)  adding (-x1, -x2) = (0, 0)

Scalar multiplication:

Compatibility -

a(b (x, y)) = a(bx, 0) = (abx, 0) = b(ax, 0) = b(a(x, y))

Identity element -

1(x, y) = (x, 0) ≠ (x, y)     [Identity element doesn’t exist for this operation.)

Distributivity law -

a((x1, x2) + (y1, y2)) = a(x1 + y1, x2 + y2) = (a(x1 + y1), 0) = a(x1, x2) + a(y1, y2)

Distributivity law -

(a + b)(x, y) = ((a + b)x, 0) = (ax, 0) + (bx, 0) = a(x, y) + b(x, y)

The scalar multiplication postulate is not fulfilled in this space (this operation does not have the identity element). It is therefore not a vector space.

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Answer:

They can type 825 words in 25 minutes.

Step-by-step explanation:

First, we need to find how many words they can type per minute. To do that, we need to divide 495 by 15.

[tex]495 \div 15 = 33[/tex]

Now, we know how many words per minute, and the question is how many words they can type in 25 minutes. So to find our answer, we need to multiply 33 by 25, since 33 is how many words in one minute.

[tex]33 \times 25=825[/tex]

So now we know our answer: 825 words in 25 minutes.

The x values to make a suitable ordered pair must be a multiple of 5

The function is given as:

y = -2/5x + 2

The slope of the above equation is:

m = -2/5

The above is a fraction with a denominator of 5.

So, the x values to make a suitable ordered pair must also be a multiple of 5

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The probability that battery lasts more than 3 years is [tex]e^{-0.6 }[/tex].

Parameter of Exponential Distribution

It is given that the average lifespan of the car battery = 5 years

⇒ μ = 5

And, we have to find the probability that the car battery lasts more than 3 years.

Now, the relation between the parameter of exponential distribution, λ and average, μ is given as,

1/ λ = μ

⇒ λ = 1/5

Calculating the Probability

The probability for the car battery to lasts more than 3 years is given by P(N>3). Here, N is the lifespan of the car battery.

P(N>3) = 1 - P(N≤3)

P(N>3) = 1-F(4)

Here, F is the exponential distribution  for the lifespan of the car battery.

P(N>3) = 1-(1-e^(-λn))

P(N>3) = [tex]e^{-3/5}[/tex]

Thus, the required probability is,

P(N>3) = [tex]e^{-0.6 }[/tex]

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The value of ML = 3, using the mid-point theorem of triangles.

According to the midpoint theorem, "the line segment of a triangle crossing the midpoints of two sides of the triangle is said to be parallel to its third side and also half the length of the third side."

In the question, we are given that triangle ABC is an equilateral triangle, and L, M, and N are the midpoints of BC, AB, and CA respectively.

Thus, by the midpoint theorem, we can say that:

Assuming AB = BC = AC = x units, we get:

Thus, the triangle LMN is an equilateral triangle.

Thus, MN = ML = NL.

Given MN = 3, we can write the value of ML = 3.

Thus, the value of ML = 3, using the mid-point theorem of triangles.

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The given question is in Spanish. The question in English is:

"Triangle ABC is equilateral and L, M, and N are the midpoints of BC, AB, and CA respectively. If MN = 3, what is the value of ML?"

Answer:

Option D

Step-by-step explanation:

The triangle ABJ is equitorial

So area

Then mBJ is a arc which is 1/6th of circle

Area.

So area of unshaded region

Answer:

[tex]\textsf{d.} \quad r^2\left(\dfrac{\pi}{6}- \dfrac{\sqrt{3}}{4}\right)[/tex]

Step-by-step explanation:

To find the area of the unshaded region, subtract the area of ΔJGB from the area of sector JGB.

The measure of an arc is equal to its corresponding central angle measure.  Therefore, the central angle of sector JGB is 60°.

As the two sides of ΔJGB adjacent the central angle are the radii of the circle (and therefore equal in length), ∠GJB = ∠GBJ.  

Interior angles of a triangle sum to 180°.  Therefore, all interior angles of ΔJGB are 60° which makes it an equilateral triangle.

Area of an equilateral triangle:

[tex]\sf A=\dfrac{\sqrt{3}}{4}a^2 \quad \textsf{(where a is the side length)}[/tex]

As the side length of the given equilateral triangle is the radius (r):

[tex]\implies \sf Area\:of\:triangle=\dfrac{\sqrt{3}}{4}r^2[/tex]

To find the area of the sector, first convert degrees to radians by multiplying the degrees by π/180 :

[tex]\implies 60^{\circ}=60 \times \dfrac{ \pi}{180}=\dfrac{\pi}{3}\:\:\sf radians[/tex]

Area of a sector of a circle

[tex]\textsf{A}=\dfrac12 r^2 \theta \quad \textsf{(where r is the radius and the angle }\theta \textsf{ is in radians)}[/tex]

Substituting the angle in radians, the area of the sector is:

[tex]\implies \sf A=\dfrac{1}{2}r^2\left(\dfrac{\pi}{3}\right)[/tex]

[tex]\implies \sf A=\dfrac{\pi}6}r^2[/tex]

Area of the unshaded region:

[tex]\begin{aligned}\textsf{Area of unshaded region} & =\textsf{Area of sector} - \textsf{Area of triangle}\\\\& = \dfrac{\pi}{6}r^2 - \dfrac{\sqrt{3}}{4}r^2\\\\& = r^2\left(\dfrac{\pi}{6}- \dfrac{\sqrt{3}}{4}\right)\end{aligned}[/tex]

Therefore, the solution is option D.

Angles are formed when two or more lines intersect. Angles are majorly measured in degrees.

The required proof is as shown below:

Whenever a transversal passes through two parallel lines, angles are formed which have some similar properties.

             STATEMENTS                                           REASONS

1. AB ║DC                                                          Given.

2. < FDC ≅ < FBA                                              Alternate angle theorem.

3. <AFB  ≅ < DFC                                              Vertical opposite angle rule.

4. DF ≅ BF                                                         Given

5. ΔDFC  ≅ Δ BFA                                            Angle-Angle-Side property

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Answer:

B

Step-by-step explanation:

15% off means 85 % of original price

400 * .85        now increase this price by 25%

400* .85   *  1.25    = $425

The power of the algebraic expression 7xy + 3xy² - x³y² + 4 is  1.

An expression that denotes repeated multiplication of the exact factor exists named a power. The number 5 stands named the base, and the number 2 exists named the exponent. The exponent equals the number of times the base exists utilized as a factor.

Given: 7xy + 3xy² - x³y² + 4

An expression that represents repeated multiplication of the same factor is called a power.

So, the power of the given expression will be 1.

Therefore, the correct answer is 1.

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Henry was 40 feet away from his original starting point. Using Pythagorean's theorem it is calculated.

The theorem says that,

In a right-angled triangle, the sum of squares of the lengths of two arms (opposite and adjacent sides) is equal to the square of the hypotenuse.

I.e, Consider a right-angled triangle ΔABC, where AC is the hypotenuse side of the triangle. So, according to the theory,

AC² = AB² + BC²

It is given that,

Henry walked on a flat field,

9 meters - towards the north

24 feet - towards the east

9 meters + 32 feet - towards the south

This can be shown in the diagram below.

In the diagram, the distance from the starting point is X, and the last point is  S.

To find the distance between these two points, a line is joined as shown in the diagram. Thus, it is formed as a right-angled triangle.

So, according to the Pythagorean theorem,

XS² = (24)² + (32)²

(here 32 feet is the only distance from the assumed point to the endpoint)

⇒ XS² = 1600 = 40²

∴ XS = 40 feet

So, Henry is 40 feet away from the original starting point.

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By using mind ig -,-

Hope Helpful ~

Total number of teams are 10

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation is one that includes a variable, such as x.

As given in the problem,

total number of students in class=30

now professor want to create study teams .

one team consist of 3 members,

lets suppose professor will form n teams

So,

3×n=30

solve this equation to get value of n

n=30÷3

n=10 teams

hence total number of teams are 10 .

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Answer:

a) Perfect square.

b) 9

Step-by-step explanation:

The given numbers are perfect squares.

64 = 8*8

49 = 7*7

36 = 6*6

25 = 5*5

16 = 4*4

So, the next number will be 3 *3 = 9

Answer:

a.) C(x) = 10x + 8,000

Step-by-step explanation:

The fixed cost does not change regardless of the variable. Therefore, it should be attached to no variable. However, the variable cost does depend on the number of alarms and thus should be attached to the variable.

This makes the algebraic expression:

C(x) = 10x + 8,000

Your graph should look very similar to this. Keep in mind that our axis are slightly different. You can plot specific points on your graph by plugging random "x" values into your algebraic expression and finding the subsequent "y" values.

The addition of the polynomials [tex]2x^3+4x-6[/tex] and [tex]3x^3-8x+7[/tex] in the proper location on the grid is [tex]5x^3-4x+1[/tex]

How to find the addition of two polynomials is proper location on the grid ?

Polynomials addition in proper location means add the coefficient of same power of variable

So the addition of polynomials like this

[tex]2x^3+4x-6+3x^3-8x+7[/tex]

[tex]2x^3+3x^3=5x^3\\4x-8x=-4x\\-6+7=1[/tex]

The addition of the polynomials is [tex]2x^3+4x-6+ 3x^3-8x+7=5x^3-4x+1[/tex]

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