[tex]x+7-4(x+1)=-10[/tex]

Answer:

Vertical asymptote: [tex]x=3[/tex]

Horizontal asymptote: [tex]f(x) =2[/tex]

Domain of f(x) is all real numbers except 3.

Range of f(x) is all real numbers except 2.

Step-by-step explanation:

Given:

Function:

[tex]f (x) = -\dfrac{1 }{ x-3} +2[/tex]

One root, [tex]x = 3.5[/tex]

To find:

Vertical and horizontal asymptote, domain, range and roots of f(x).

Solution:

First of all, let us find the roots of f(x).

Roots of f(x) means the value of x where f(x) = 0

[tex]0= -\dfrac{1 }{ x-3} +2\\\Rightarrow 2= \dfrac{1 }{ x-3}\\\Rightarrow 2x-2 \times 3=1\\\Rightarrow 2x=7\\\Rightarrow x = 3.5[/tex]

One root, [tex]x = 3.5[/tex]

Domain of f(x) i.e. the values that we give as input to the function and there is a value of f(x) defined for it.

For x = 3, the value of f(x) [tex]\rightarrow \infty[/tex]

For all, other values of [tex]x[/tex] , [tex]f(x)[/tex] is defined.

Hence, Domain of f(x) is all real numbers except 3.

Range of f(x) i.e. the values that are possible output of the function.

f(x) = 2 is not possible in this case because something is subtracted from 2. That something is [tex]\frac{1}{x-3}[/tex].

Hence, Range of f(x) is all real numbers except 2.

Vertical Asymptote is the value of x, where value of f(x) [tex]\rightarrow \infty[/tex].

[tex]-\dfrac{1 }{ x-3} +2 \rightarrow \infty[/tex]

It is possible only when

[tex]x-3=0\\\Rightarrow x=3[/tex]

[tex]\therefore[/tex] vertical asymptote: [tex]x=3[/tex]

Horizontal Asymptote is the value of f(x) , where value of x [tex]\rightarrow \infty[/tex].

[tex]x\rightarrow \infty \Rightarrow \dfrac{1 }{ x-3} \rightarrow 0\\\therefore f(x) =-0+2 \\\Rightarrow f(x) =2[/tex]

[tex]\therefore[/tex] Horizontal asymptote: [tex]f(x) =2[/tex]

Please refer to the graph of given function as shown in the attached image.

Answer:

-1.031 m/s or  [tex]\frac{-\sqrt{17} }{4}[/tex]

Step-by-step explanation:

We take the length of the rope from the dock to the bow of the boat as y.

We take x be the horizontal  distance from the dock to the boat.

We know that the rate of change of the rope length is [tex]\frac{dy}{dt}[/tex] = -1 m/s

We need to find the rate of change of the horizontal  distance from the dock to the boat =  [tex]\frac{dx}{dt}[/tex] = ?

for x = 4

Applying Pythagorean Theorem we have

[tex]1^{2} +x^{2} =y^{2}[/tex]    .... equ 1

solving, where x = 4, we have

[tex]1^{2} +4^{2} =y^{2}[/tex]

[tex]y^{2} = 17[/tex]

[tex]y = \sqrt{17}[/tex]

Differentiating equ 1 implicitly with respect to t, we have

[tex]2x\frac{dx}{dt} = 2y\frac{dy}{dt}[/tex]

substituting values of

x = 4

y = [tex]\sqrt{17}[/tex]

[tex]\frac{dy}{dt}[/tex] = -1

into the equation, we get

[tex]2(4)\frac{dx}{dt} = 2(\sqrt{17} )(-1)[/tex]

[tex]\frac{dx}{dt} = \frac{-\sqrt{17} }{4}[/tex] = -1.031 m/s

13 since  i think it's when a single didget number has a 1 at the beginning. i might be wrong thoough

Answer:

26

Step-by-step explanation:

Given that:

At time, t=0, Billy puts 625 into an account paying 6% simple interest

At the end of year 2, George puts 400 into an account paying interest at a force of interest, 1/(6+t), for all t ≥ 2.

If both accounts continue to earn interest indefinitely at the levels given above, the amounts in both accounts will be equal at the end of year n. Calculate n.

In order to calculate n;

Let K constant to be the value of time for both accounts

At  time, t=0, the value of time K when Billy puts 625 into an account paying 6% simple interest is:

[tex]K = 625 \times (1+ 0.06 K)[/tex]

[tex]K = 625 +37.5 K[/tex]

At year end 2; George  amount of 400 will grow at a force interest, then the value of  [tex]K = 400 \times e^{\int\limits^2_k {\dfrac{1}{6+t}} \, dx }[/tex]

[tex]K =400 \times \dfrac{6+K}{6+2}[/tex]

[tex]K =400 \times \dfrac{6+K}{8}[/tex]

[tex]K =50 \times ({6+K})[/tex]

[tex]K =300+50K[/tex]

Therefore:

If K = K

Then:

625 + 37.5 = 300 +50 K

625-300 = 50 K - 37.5 K

325 = 12.5K

K = 325/12.5

K = 26

the amounts in both accounts  at the end of year n = K = 26

Answer:

x=2 y=4

Step-by-step explanation:

Answer:

500 pounds

Step-by-step explanation:

Let the pressure applied to the leverage bar be represented by p

Let the distance from the object be represented by d.

The pressure applied to a leverage bar varies inversely as the distance from the object.

Written mathematically, we have:

[tex]p \propto \dfrac{1}{d}[/tex]

Introducing the constant of proportionality

[tex]p = \dfrac{k}{d}[/tex]

If 150 pounds is required for a distance of 10 inches from the object

[tex]150 = \dfrac{k}{10}\\\\k=1500[/tex]

Therefore, the relationship between p and d is:

[tex]p = \dfrac{1500}{d}[/tex]

When d=3 Inches

[tex]p = \dfrac{1500}{3}\\\implies p=500$ pounds[/tex]

The pressure applied when the distance is 3 inches is 500 pounds.

Answer:

50

Step-by-step explanation:

50 because of the 100 of 79 to 7

Answer:

y + 4 = 4/3(x - 6).

Step-by-step explanation:

The point-slope formula is shown below. We just need to find the slope.

(-4 - (-8)) / (6 - 3) = (-4 + 8) / 3 = 4 / 3

m = 4/3, y1 = -4, and x1 = 6.

y - (-4) = 4/3(x - 6)

y + 4 = 4/3(x - 6).

Hope this helps!

Answer:

A. y ≤ 1/2x + 2

Step-by-step explanation:

Well look at the graph,

It is a solid line with it shaded down,

meaning it is y ≤,

So we can cross out B. and D.

So the y intercept is 2, we know this because the y intercept is the point on the line that touches the y axis.

now the slope can be found by seeing how far away each points are from each other,

Hence, the answer is A. y ≤ 1/2x + 2

Answer

Step-by-step explanation:

Given,

r = 10

Let's create an equation,

[tex]3r = 10 + 5s[/tex]

plugging the value of r

[tex]3 \times 10 = 10 + 5s[/tex]

Multiply the numbers

[tex]30 = 10 + 5s[/tex]

Move 5s to L.H.S and change its sign

Similarly, Move 30 to R.H.S and change its sign.

[tex] - 5s = 10 - 30[/tex]

Calculate

[tex] - 5s = - 20[/tex]

The difference sign ( - ) should be cancelled on both sides

[tex]5s = 20[/tex]

Divide both sides of the equation by 5

[tex] \frac{5s}{2} = \frac{20}{5} [/tex]

Calculate

[tex]s = 4[/tex]

The value of s is 4.

Hope this helps..

Best regards!!

Answer:

A. 4 (on edgenuity)

Step-by-step explanation:

Answer: B

Step-by-step explanation:

Answer:B

Step-by-step explanation: I took the edge quiz and it was right.

Answer:

B Kim rode 3 more miles per week than Eric rode.

Step-by-step explanation:

In the fourth quadrant, the equation of the unit circle is:

y = -√(1 − x²), 0 ≤ x ≤ 1

The x and y coordinates of the centroid are:

cₓ = (∫ x dA) / A = (∫ xy dx) / A

cᵧ = (∫ y dA) / A = (∫ ½ y² dx) / A

For a quarter circle in the fourth quadrant, A = -π/4.

Solving each integral:

∫₀¹ xy dx

= ∫₀¹ -x √(1 − x²) dx

= ½ ∫₀¹ -2x √(1 − x²) dx

If u = 1 − x², then du = -2x dx.

When x = 0, u = 1.  When x = 1, u = 0.

= ½ ∫₁⁰ √u du

= ½ ∫₁⁰ u^½ du

= ½ (⅔ u^³/₂) |₁⁰

= (⅓ u√u) |₁⁰

= 0 − ⅓

= -⅓

∫₀¹ ½ y² dx

= ½ ∫₀¹ (1 − x²) dx

= ½ (x − ⅓ x³) |₀¹

= ½ [(1 − ⅓) − (0 − 0)]

= ⅓

Therefore, the x and y coordinates of the centroid are:

cₓ = (-⅓) / (-π/4) = 4/(3π)

cᵧ = (⅓) / (-π/4) = -4/(3π)

Answer:

Largest possible length is 21 inches.

Step-by-step explanation:

Given:

Total material available = 60 inches

Length to be 3 more than twice of width.

To find:

Largest possible length = ?

Solution:

As it is rectangular shaped frame.

Let length = [tex]l[/tex] inches and

Width = [tex]w[/tex] inches

As per given condition:

[tex]l = 2w+3[/tex] ..... (1)

Total frame available = 60 inches.

i.e. it will be the perimeter of the rectangle.

Formula for perimeter of rectangle is given as:

[tex]P = 2 \times (Width + Length)[/tex]

Putting the given values and conditions as per equation (1):

[tex]60 = 2 \times (w+ l)\\\Rightarrow 60 = 2 \times (w+ 2w+3)\\\Rightarrow 60 = 2 \times (3w+3)\\\Rightarrow 30 = 3w+3\\\Rightarrow 3w = 27\\\Rightarrow w = 9 \ inch[/tex]

Putting in equation (1):

[tex]l = 2\times 9+3\\\Rightarrow l = 21\ inch[/tex]

So, the answer is:

Largest possible length is 21 inches.

Answer:

The probability is  [tex]P(\= X > x ) = 0.78814[/tex]

Step-by-step explanation:

From the question we are given that

     The population  mean is  [tex]\mu = 149[/tex]

     The standard deviation is  [tex]\sigma = 14[/tex]

     The random number    [tex]x = 147.81[/tex]

      The sample  size is  [tex]n = 88[/tex]

The probability that  the sample mean would be greater than [tex]P(\= X > x ) = P( \frac{ \= x - \mu }{\sigma_{\= x} } > \frac{ x - \mu }{\sigma_{\= x} } )[/tex]

Generally the z- score of this normal distribution is mathematically represented as

       [tex]Z = \frac{ \= x - \mu }{\sigma_{\= x} }[/tex]

Now

        [tex]\sigma_{\= x } = \frac{\sigma }{\sqrt{n} }[/tex]

substituting values

         [tex]\sigma_{\= x } = \frac{14 }{\sqrt{88} }[/tex]

         [tex]\sigma_{\= x } = 1.492[/tex]

Which implies that

         [tex]P(\= X > x ) = P( Z > \frac{ 147.81 - 149 }{ 1.492} )[/tex]

        [tex]P(\= X > x ) = P( Z > -0.80 )[/tex]

Now from the z-table  the  probability is  found to be

        [tex]P(\= X > x ) = 0.78814[/tex]

Answer:

Number:3.75

Equation:7 x-9=3(x+2)

Step-by-step explanation:

Let the number be x.

According to the question,

7 x-9=3(x+2)

7 x-9= 3 x+ 6

7 x- 3 x= 9+6

4 x= 15

x=15/4

x=3.75

If you verify the answer you will get,

11.25=11.25

Thank you!

Answer:

5/12

Step-by-step explanation:

Total number of marbles in the bag

6red+ 4blue + 14 yellow = 24 marbles

Not yellow marbles = 10 marbles

P ( not yellow ) = number of not yellow marbles / total marbles

                          =10/24

                          = 5/12

Answer:

5/12

Step-by-step explanation:

6 red marbles

4 blue marbles

14 yellow marbles

total marbles = 6 + 4 + 14 = 24 marbles

24 - 14 = 10 marbles

10 marbles are not yellow.

P(not yellow) = 10/24 = 5/12

Answer:

15%

Step-by-step explanation:

To calculate the margin of error, we can adopt this formula

Margin of error = critical value* (standard deviation/sqrt of sample size)

Where critical value is 2.33, sd is 0.78 and sample size is150.

Thus, we have:

Margin of error = 2.33*(0.78/√150)

Margin of error = 2.33*(0.78/12.2474)

Margin of error =2.33*0.06369

Margin of error = 0.1484 which is a 15% margin of error

Answer:

23+15i

Step-by-step explanation:

(-3+2i) (-3-7i)

multiply -3 w (-3+2i) and multiply -7i w (-3+2i)

9-6i+21i-14i^2

combine like terms

9+15i-14i^2

i squared is equal to -1 so

9+15i-(14x-1)

9+14+15i

23+15i

hope this helps :)

Answer:

E[x] is larger

Step-by-step explanation:

I think E[x] is larger because the expected number of students on the bus of a randomly chosen student is larger.

This is because the higher the number of students present in a bus, the higher the probability that a randomly selected student would have been on that bus.

Whereas, for every driver to be chosen, the probability of any bus being chosen is 1/4 irrespective of the number of students in that particular bus

Answer:

viscosity is the state of being thick, sticky, and semifluid in consistency, due to internal friction.

"cooling the fluid raises its viscosity"

a quantity expressing the magnitude of internal friction, as measured by the force per unit area resisting a flow in which parallel layers unit distance apart have unit speed relative to one another.

plural noun: viscosities

"silicone oils can be obtained with different viscosities"

Step-by-step explanation:

The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. hope this helps you :)

Answer:

O An oil's resistance to flow at different temperatures

Step-by-step explanation:

Internal friction of a moving fluid .

Answer:

   (-10, -3)

Step-by-step explanation:

Replacing x with x+1 in a function moves its graph 1 unit to the left. The point that is 1 unit to the left of (-9, -3) is (-10, -3).

Answer:

10

Step-by-step explanation:

To find 20% of 50 you need to times 20 with 50 and divide by 100.

20×50÷100

=10

Answer:

Step-by-step explanation:

Hello!

For the rectangle ABCD

AB= DC= 11

BC= AD= 2

Point E lies halfway between AB and CD

The shaded are forms two triangles, I'll refer to the upper triangle as "Triangle one" and the lower triangle will be "triangle 2"

The area of a triangle is calculated as

[tex]a= \frac{bh}{2}[/tex]

b= base

h= height

Triangle 1

b₁= AB= 11

[tex]h_1= \frac{BC}{2}= \frac{2}{2}= 1[/tex]

[tex]a_1= \frac{b_1h_1}{2}= \frac{11*1}{2}= 5.5[/tex]

Triangle 2

b₂= DC= 11

[tex]h_2= \frac{BC}{2}= \frac{2}{2} = 1[/tex]

[tex]a_2= \frac{b_2h_2}{2}= \frac{11*1}{2}= 5.5[/tex]

Now you add the areas of both triangles to get the area of the shaded region:

a₁ + a₂= 5.5 + 5.5= 11

Since point E is halfway to all sides of the rectangle, even tough it doesn't see so, the shaded area is equal to half the area of the rectangle:

area= bh= DC*AD= 11*2= 22

area/2= 22/12= 11

I hope this helps!

Answer:

10 miles

Step-by-step explanation:

3 mi/1 hr  x (h hours + 2/3 hr) = 5 mi/1 hr  x  h hours

3h + 2 = 5h

2 = 2h

h = 1 hour

3mi/hr  x 1 2/3 hr = 5 miles

5 mi/hr x  1 hr = 5 miles

He hiked 10 miles. (

Answer:

False

Step-by-step explanation:

A tessellation refest to a shape that is repeated over and over again covering a plane without any gaps or overlaps. The statement is false given that regular tessellations use only one polygon. Semi-regular tessellations are created with more than one type of regular polygon.

Answer:

15 pt

Step-by-step explanation:

to convert qt to pt you multiply by 2 so 7 and 1/2 times 2 is 15

Answer:

its a postulate

Step-by-step explanation:

The statement represents a geometric postulate.

A postulate is one of the basic concepts of geography, and indicates an assumption that is accepted as true in the given theory.  

In this way, the main characteristic of the postulate is its general acceptance by the spectrum that studies it, that is, by the totality or vast majority of the scientists who are dedicated to its analysis.

Learn more in https://brainly.com/question/17252827

Answer:

f^-1(x) = x + 5

Step-by-step explanation:

f(x) = x-5

y = x-5

Exchange x and y

x = y-5

Solve for y

x+5 = y-5+5

x+5 =y

The inverse is x+5

Answer:

Hey there!

Pythagorean Theorem:

[tex]a^2+b^2=c^2\\[/tex]

Let 6 be a, and 11 be b.

[tex]6^2+11^2=c^2\\[/tex]

[tex]36+121=c^2\\[/tex]

[tex]157=c^2[/tex]

[tex]\sqrt{157} =c[/tex]

Hope this helps :)

Answer:

[tex]12.529[/tex]

Step-by-step explanation:

[tex] {a}^{2} + {b}^{2} = {c}^{2} \\ {6}^{2} + {11}^{2} = {c}^{2} \\ 36 + 121 = {c}^{2} \\ 157 = {c}^{2} \\ \sqrt{157} = {c}^{2} \\ c = 12.529[/tex]

[tex]hope \: it \: helps \: < 3[/tex]