If the limit exists, find its value. 3x + 1 7) lim 11x - 7 If the limit exists, find its value. 1 1 X + 6 6 8) lim X- х X2 +16% +63 9) lim X-9 X + 9 Find the derivative. 12 10) g(t) t-11 11) y = 14% - 1 Find the derivative of the function. 12) y = In (x-7) Find the equation of the tangent line at the given point on the curve. 13) x2 + 3y2 = 13; (1,2)

Step-by-step explanation:

here,

x1=-7

x2=13

y1=-2

y2=-23

so

\(\boxed{\blue{ distance=\sqrt{(y2-y1)^2+(x2-x2)^2} }}\) ⠀

=\(\tt{\sqrt{(-23-(-2))^2+(13-(-7))^2}}\) ⠀

=\(\tt{\sqrt{(-21)^2+(20)^2} }\) ⠀

=\(\tt{\sqrt{ 441+400} }\) ⠀

=\(\tt{\sqrt{841} }\) ⠀

=\(\tt{ 29 }\) ⠀

So,

the distance between (-7, -2) and (13,-23)=29

Answer:

12 1/2

Step-by-step explanation:

Answer:

your answer is 4x

Step-by-step explanation:

15-10 is 5

5 divided by 5 is 1

1 times 2 greater than 2 is 4

4x is your answer

Have a good day

Using the SAS (Side Angle Side) criteria of congruency, both triangles can be proved congruent.

In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -

∠x + ∠y + ∠z = 180°

There are different types of triangles such as -

equilateral triangle , scalene triangle , isosceles triangle etc.

Given is that two sides and the non-included right angle of one right triangle are congruent to the corresponding parts of another right triangle.

In order to prove these two triangles congruent, we can use SAS (Side Angle Side) criteria of congruency.

Therefore, using the SAS (Side Angle Side) criteria of congruency, both triangles can be proved congruent.

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Answer:

We can find the answer by multiplying the percentage (85%) by the value (P78):

85% of P78 = 0.85 * P78

So, the amount that represents 85% of P78 is 0.85 times P78.

If we know the value of P78, we can substitute it into the formula to find the answer. For example, if P78 is 100, then:

85% of P78 = 0.85 * 100 = 85

Therefore, 85% of P78 is 85, if P78 is 100. If the value of P78 is different, the answer will be different.

Answer:

EH is 9 cm

DE is 18 cm

x is

18^2=9^2+b^2

b≈15,588

Answer: Choice B

\((x,y) \to \left(\frac{5}{2}x,\frac{5}{2}y\right)\)

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

Explanation:

When dilating with respect to the origin, any point of the form (x,y) moves to (kx, ky) for some real number k. The k is the scale factor.

Point C is at (-2,2). It moves to C ' (-5,5)

The jump from x = -2 to x = -5 is "times 5/2" since kx = (5/2)*(-2) = -5

The same scale factor is used when going from y = 2 to y = 5.

Both x and y coordinates are multiplied by 5/2 to move from (-2,2) to (-5,5)

Therefore, the dilation rule we use is \((x,y) \to \left(\frac{5}{2}x,\frac{5}{2}y\right)\)

-----------

We could have these steps to confirm

\((x,y) \to \left(\frac{5}{2}x,\frac{5}{2}y\right)\\\\(-2,2) \to \left(\frac{5}{2}*(-2),\frac{5}{2}(2)\right)\\\\(-2,2) \to (-5,5)\\\\\)

a) To calculate the pressure at 12 hours of shut-in:

substitute the given values into the pressure buildup equation and solve for P(t=12).

b) Superposition in time is used in pressure buildup analysis by adding or summing the responses of multiple transient tests to analyze and interpret reservoir behavior and properties.

We have,

a) To calculate the pressure in the production well at 12 hours of a shut-in, we can use the equation for pressure transient analysis during shut-in periods, known as the pressure buildup equation:

P(t) = Pi + (Q / (4πKh)) * log((0.14ϕμCt(t + Δt)) / (Bo(ΔP + Δt)))

Where:

P(t) = Pressure at time t

Pi = Initial reservoir pressure

Q = Flow rate

K = Permeability

h = Reservoir thickness

ϕ = Porosity

μ = Viscosity

Ct = Total compressibility

t = Shut-in time (12 hours)

Δt = Time since the start of the flow period

Bo = Oil formation volume factor

ΔP = Pressure drop during the flow period

Given:

Pi = 3100 psi

Q = 200 STB/day

K = 45 md

h = 60 ft

ϕ = 15%

μ = 1.2 cp

Ct = 15x10^-6 psi^-1

Bo = 1.3 bbl/STB

t = 12 hours

Δt = 48 hours

ΔP = Pi - P(t=Δt) = Pi - (Q / (4πKh)) * log((0.14ϕμCt(Δt + Δt)) / (Bo(ΔP + Δt)))

Substituting the given values into the equation:

ΔP = 3100 - (200 / (4π * 45 * 60)) * log((0.14 * 0.15 * 1.2 * 15x\(10^{-6}\) * (48 + 48)) / (1.3 * (3100 - (200 / (4π * 45 * 60)) * log((0.14 * 0.15 * 1.2 * 15 x \(10^{-6}\) * (48 + 48)) / (1.3 * (0 + 48))))))

After evaluating the equation, we can find the pressure in the production well at 12 hours of shut-in.

b) Superposition in time is a principle used in pressure transient analysis to analyze and interpret pressure build-up tests.

It involves adding or superimposing the responses of multiple transient tests to simulate the pressure behavior of a reservoir.

The principle of superposition states that the response of a reservoir to a series of pressure changes is the sum of the individual responses to each change.

Superposition allows us to combine the information obtained from multiple tests and obtain a more comprehensive understanding of the reservoir's behavior and properties.

It is a powerful technique used in reservoir engineering to optimize production strategies and make informed decisions regarding reservoir management.

Thus,

a) To calculate the pressure at 12 hours of shut-in:

substitute the given values into the pressure buildup equation and solve for P(t=12).

b) Superposition in time is used in pressure buildup analysis by adding or summing the responses of multiple transient tests to analyze and interpret reservoir behavior and properties.

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Answer:

Step-by-step explanation:

Given that, There are 16 songs that are put on the next CD.And there are 8.75 more songs.Also, 60% of the songs are removed. Based on the above information, the calculation is as follows:

16+(0.875 x 16)=17.4

17.4(0.60 x 17.4)= 181.656 = 182 :)

Answer:

Yes, store's profit is proportional to number of customers

Step-by-step explanation:

Yes, the profit is proportional to the number of customers.

Profit = Revenue - Cost = (Price x Quantity) -  Cost

Profit = (0 x 20) + (3 x q) - c(20+q) : Where q refers to quantity beyond 20, & c is average cost per unit

Profit = 3q - 20c - cq = (3 - c)q + 20c

As 20c is constant, component of equation has coefficient 'q' which stands for quantity of sales ie number of customers

Answer:

a: 1/6

Step-by-step explanation:

Answer: 16

Step-by-step explanation:

Answer:

oval, triangle

hope it helped you ☺

The cross sections of the cone shown can be circle, oval, parabola and triangle.

Cross section of a figure or shape can be defined as a plane intersecting with the figure. The resulting shape formed in the intersection part is termed as cross section.

Given shape is a cone.

When a cone is intersected vertically, then the cross section formed is triangle.

When the cone is intersected through the straight horizontal line, we get the cross section as circle.

We will get an oval shape when the cone is intersected with the plane with a given slant by not touching the base.

A parabola shape is formed when a slant plane intersects by touching the base

Hence the cross sections of the given cone are circle, oval, parabola and triangle.

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Answer:

Step-by-step explanation:

Begin by dividing by 5

2x + 4 = 3            

Is this written as 2^(x + 4) = 3? I think it is.

Take the log of both sides

log 2^(x + 4) = log(3)

(x + 4) * log(2) = log 3

log 2 = 0.30103

log 3 = 0.47712

(x + 4) = log2 / log3

x + 4 = 0.63093               Add 4 to both sides

x = -3.369                        Rounded to the nearest thousandth

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

If you mean the question exactly as it is written (the 4 is not part of the power)

5(2^x + 4) = 15

2^x + 4 = 3

2^x = 3 - 4

2^x = - 1

This can't be done 2 to any power should be >0.

if x>0 then this will give an ever increasing number

if xK0 then this will give an ever decreasing answer but still greater than 0.

No value will make 2^x go to something minus.

If I have misread this in some way, leave a note and I will get back to you.

Answer: -2.415

Step-by-step explanation: Edge 2022

The amount of RNA transcribed from promoter gene, which can consequently influence the amount of protein made from this gene. So the option c is correct.

A gene's DNA sequence is duplicated during transcription in order to create an RNA molecule.

The primary transcribed enzyme is called RNA polymerase.

RNA polymerase connects to a promoter sequence close to the start of a gene to start transcription (directly or through helper proteins).

A new, complementary RNA molecule is created by RNA polymerase using a template from one of the DNA strands (the template strand).

Termination is the procedure that brings transcription to a conclusion. The RNA sequences that indicate that the transcript is done are what determine when a process is terminated.

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The complete question is:

How frequently RNA polymerase binds to DNA sequence

a. length of RNA transcribed from the gene

b. precise sequence of RNA transcribed from this gene

c. amount of RNA transcribed from promoter gene, which can consequently influence the amount of protein made from this gene

Answer:

$50 and $6

Step-by-step explanation:

(x-6)(250-5x)=0

250x - \(5x^{2}\) - 1500 + 30x = 0

-5x^2 + 280x - 1500 = 0

(divide everything by -5)

x^2 -56x + 300 = 0

(factorise)

(x-50)(x-6)=0

x=50, x=6

4 + 5 = 9

54/9 = 6

4(6) = 24. meaning 24 girls.

5(6) = 30. meaning 30 boys.

The path consists of 4 line segments. Each line segment is the hypotenuse of a different right triangle.

length of line segment AB = \(\sqrt{2^{2}+5^{2} } =\sqrt{29} =5.39cm\)

length of line segment BC = \(\sqrt{3^{2}+4^{2} } =\sqrt{25} =5cm\)

length of line segment CD = \(\sqrt{3^{2}+5^{2} } =\sqrt{34} =5.83cm\)

length of line segment DE \(=\sqrt{2.5^{2}+3^{2} } } =\sqrt{15.25} =3.91cm\)

The total length of the spider's path is about 20.13 cm.

Emma traveled 1127.2 miles from the airport to her house.

The equation to calculate the distance traveled by Emma is:

55 + 3.703 * d = 4242

To solve the equation, we need to subtract 55 from both sides of the equation.

4242 - 55 = 4187

Then, we will divide both sides of the equation by 3.703

4187 / 3.703 = 1127.2

Finally, we can calculate the distance traveled by Emma in miles.

d = 1127.2 miles

Therefore, Emma traveled 1127.2 miles from the airport to her house.

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Emma traveled 10 from the airport to her house.

In this question we have been given that Emma took a taxi from the airport to her house.

She paid a flat fee of $5 plus $3. 70 per mile.

The fare came to $42.

We need to find an equation that can be used to find the correct distance d in miles and then solve it to determine distance.

Let c be the total traveling cost.

So, from given information an equation to calculate the distance traveled by Emma would be,

c = 5 + (3.70)d

The fare came to $42.

c =  $42

Substiting this value in above equation we get,

42 = 5 + 3.70d

We solve this equation for d

42 - 5 = 3.70d

37 = 3.70d

d = 37 / 3.7

d = 10 miles

Therefore, the distance in miles covered by Emma is 10 miles.

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Answer:

The teahcer gave you 4/12 of a bag more than your friend.

Step-by-step explanation:

10/12 ---> 10/12

3/6 ---> 6/12

10/12 - 6/12 = 4/12

The P-value of drawing a random sample of 50 and getting a mean of 100 or less is approximately 0.1726 (17.26%).

The Z-score formula is given by,

Z = (X - μ)/(σ/√(n))

X = Sample mean (100)

μ = Population mean (102)

σ = Standard deviation (15)

n = Sample size (50)

Let's calculate the Z-score,

Z = (100 - 102)/(15/√(50))

Z = -2 / (15 / 7.071)

Z = -0.9428

To find the P-value, we need to determine the probability of obtaining a Z-score less than or equal to -0.9428 from the standard normal distribution. We can use a Z-table or a statistical calculator to find this probability.

Looking up the Z-score -0.9428 in a standard normal distribution table, we find that the corresponding cumulative probability is approximately 0.1726. Therefore, the P-value of drawing a random sample of 50 and getting a mean of 100 or less is approximately 0.1726, or 17.26%.

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Answer:

x=6

Step-by-step explanation:

To find x you need to equate X+4 and 3X-8 to give you X+4 = 3X-8 (you can do this as it is an isosceles triangle and both these sides are the same length). you then solve the equation for x which is the length of AC

Answer: -3/16

Step-by-step explanation:

When there is a negative exponent like x^-2 it equals 1/(x^2) the negative puts the number as a fraction so continuing...

-12(x^-2) (y^-2) can be rewritten as

-12 (1/x^2) (1/y^2) now we plug in x = -2 and y = 4

-12 (1/(-2^2) (1/(4^2)); -2^2 = 4 , 4^2 = 16

-12 (1/4) (1/16)

-3 (1/16)

= -3/16

The limit doesn't exist.

The value that a function (or sequence) approaches when the input (or index) gets closer to a particular value is known as a limit. Calculus and mathematical analysis are impossible without limits, which are also required to determine continuity, derivatives, and integrals.

In addition to being closely related to limit and direct limit in category theory, the idea of a limit of a sequence is further generalized to include the concept of a limit of a topological net.

A function's limit is typically expressed in formulas as

\(\lim_{x \to c } F(x) = L\)

It is typically used to assign values to specific functions at locations where none are defined while maintaining consistency with existing values.

\(F(x) = -x+8 ,x\leq 0\)

\(F(x) = 4x+9 , if x > 0\)

\(\lim_{x \to 0^{+} } F(x) = \lim_{n \to 0^{+} } (4x+9) = 9\)

\(\lim_{x \to 0^{-} } F(x) = \lim_{x \to 0^{-} } (-x+8) =8\)

\(\lim_{x \to 0^{+} } F(x) \neq \lim_{x \to 0^{-} } F(x)\)

So limit doesn't exist

For limit to exist

\(\lim_{x \to 0^{+} } F(x) = \lim_{x \to 0^{-} } F(x) = \lim_{x \to 0} f(x)\)

must be satisfied

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Answer:

its c. 1/4

hope it helps;)

Answer:

1/4

Step-by-step explanation:

1. Look at the numbers on the number line (1,0,-1)

2. See where the point falls in between. (0 & 1)

3. Since the point is closer to 0 you can infer that it is 1/4

Answer:

225 Calculators cost $17

Step-by-step explanation:

Since the Function () is Representing the cost, it is logical 17 dollars is the cost, and the 225 is the number of calculators.

Answer:

y = 4x + 13

Step-by-step explanation:

m = 4 at point (-3,1)

y = 4x + b

1 = 4(-3) + b

1 = - 12 + b

b= 13

y = 4x + 13

Answer:

x=a(area of rectangle)

a=x*6

x=a/6

The cost of 11 cans of dog food will be equal to $10.12.

What is unitary method ?

The unitary method is a method in which , you first determine the value of a single unit before determining the value of the required quantity of units.

It is given that the cost of 20 cans of dog food at store B is $18.40.

We need to find cost of 1 can of dog food and that can be calculated by dividing the cost of cans of dog food by total no. of cans.

i.e.,

Cost of 1 can of dog food = $ 18.40 ÷ 20

So ,

The cost of 1 can of dog food will be :

= $0.92

Now , the cost of 11 cans of dog of food will be calculated by multiplying cost of 1 can of food to 11 cans of dog food which will be :

= 11 × $ 0.92

= $10.12

Therefore , the cost of 11 cans of dog food will be equal to $10.12 .

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