The two triangles are similar. What is the value of x? Enter your answer in the box. x =

Answer: Volume = [tex]\frac{20\pi }{3}[/tex]

Step-by-step explanation: The washer method is a method to determine volume of a solid formed by revolving a region created by any 2 functions about an axis. The general formula for the method will be

V = [tex]\pi \int\limits^a_b {(R(x))^{2} - (r(x))^{2}} \, dx[/tex]

For this case, the region generated by the conditions proposed above is shown in the attachment.

Because it is revolting around the y-axis, the formula will be:

[tex]V=\pi \int\limits^a_b {(R(y))^{2} - (r(y))^{2}} \, dy[/tex]

Since it is given points, first find the function for points (3,2) and (1,0):

m = [tex]\frac{2-0}{3-1}[/tex] = 1

[tex]y-y_{0} = m(x-x_{0})[/tex]

y - 0 = 1(x-1)

y = x - 1

As it is rotating around y:

x = y + 1

This is R(y).

r(y) = 1, the lower limit of the region.

The volume will be calculated as:

[tex]V = \pi \int\limits^2_0 {[(y+1)^{2} - 1^{2}]} \, dy[/tex]

[tex]V = \pi \int\limits^2_0 {y^{2}+2y+1 - 1} \, dy[/tex]

[tex]V=\pi \int\limits^2_0 {y^{2}+2y} \, dy[/tex]

[tex]V=\pi(\frac{y^{3}}{3}+y^{2} )[/tex]

[tex]V=\pi (\frac{2^{3}}{3}+2^{2} - 0)[/tex]

[tex]V=\frac{20\pi }{3}[/tex]

The volume of the region bounded by the points is [tex]\frac{20\pi }{3}[/tex].

Answer:

D. [tex]3^3 - 4^2[/tex]

Step-by-step explanation:

Well if Alia gets 4 squared less than Kelly who get 3 cubed it’s natural the expression is 3^3 - 4 ^2

Answer:

Systematic Sampling

Step-by-step explanation:

Systematic sampling is a form of sampling in which the researcher applies probability sampling such that every member of the group is selected at regular intervals or periods. The researcher picks a random starting point and after an interval must have elapsed, another sample member is chosen. This sampling method is similar to that disclosed in the question because it has the key qualities.

For example, an interval is given after the 1000th soda is tested for quality.  This means that the interval for testing can accommodate 1000 sodas after which the first member is tested again. So, this is a Systematic sampling method.

Answer:

Step-by-step explanation:

Given the initial value of X0 = -1, we can determine the solution of the equation x³ + 5x +2 = 0 using the Newton's method. According to newton's approximation formula;

[tex]y = f(x_0) + f'(x_0)(x-x_0)[/tex]

[tex]x_n = x_n_-_1 - \frac{f(x_n_-_1 )}{f'(x_n_-_1 )}[/tex]

If [tex]x_0 = 1\\[/tex]

We will iterate using the formula;

[tex]x_1 = x_0 - \frac{f(x_0 )}{f'(x_0 )}[/tex]

Given f(x) = x³ + 5x +2

f(x0) = f(-1) = (-1)³ + 5(-1) +2

f(-1) = -1 -5 +2

f(-1) = -4

f'(x) = 3x²+5

f'(-1) = 3(-1)²+5

f'(-1) = 8

[tex]x_1 = -1+4/8\\x_1 = -1+0.5\\x_1 = -0.5\\\\x_2 = x_1 - \frac{f(x_1)}{f'(x_1)}\\x_2 = -0.5 - \frac{f(-0.5)}{f'(-0.5)}[/tex]

f(-0.5) = (-0.5)³ + 5(-0.5) +2

f(-0.5) = -0.125-2.5+2

f(-0.5) = -0.625

f'(-0.5) = 3(-0.5)²+5

f'(-0.5) = 3(0.25)+5

f'(-0.5) = 0.75+5

f'(-0.5) = 5.75

[tex]x_2 = -0.5 - \frac{(-0.625)}{5.75}\\x_2 = -0.5 + \frac{(0.625)}{5.75}\\x_2 = -0.5 + 0.1086957\\x_2 = -0.3913[/tex]

The estimated solution is -0.3913 (to 4dp)

Answer:

2-x=-3x-12+6

2-x=-3x-6

8=-3x+x

8=-2x

x=-4

hope it's clear

mark me as brainliest

Answer:

Option B is the correct option.

Step by step explanation

2 - x = -3 ( x + 4) +6

Distribute -3 through the paranthesis

2 - x = - 3x - 12 + 6

Calculate

2 - x = - 3x - 6

Move variable to LHS and change its sign

2 - x + 3x = -6

Move constant to R.H.S and change its sign

- x + 3x = -6 - 2

Collect like terms and simplify

2x = -8

Divide both side by 2

2x/2 = -8/2

Calculate

X = -4

Hope this helps....

Good luck on your assignment..

Answer:

[tex]\boxed{11.78}[/tex]

Step-by-step explanation:

From observations, we can note that BC is the hypotenuse.

As the length of hypotenuse is not given, we can only use tangent as our trig function.

tan(θ) = opposite/adjacent

tan(67) = x/5

5 tan(67) = x

11.77926182 = x

x ≈ 11.78

Answer:

np = 81  , nQ = 99

Step-by-step explanation:

Given:

X - B ( n = 180 , P = 0.45 )

Find:

Sampling distribution has an approximate normal distribution

Computation:

nP & nQ ≥ 5

np = n × p

np = 180 × 0.45

np = 81

nQ = n × (1-p)

nQ = 180 × ( 1 - 0.45 )

nQ = 99

[tex]Therefore, sampling\ distribution\ has\ an\ approximately\ normal\ distribution.[/tex]

Answer:

  8 : 1

Step-by-step explanation:

The graph shows a point at the location corresponding to 8 cups of raspberry juice and 1 cup of lemon-lime soda. So the ratio is ...

  raspberry juice : lemon-lime soda = 8 : 1

Answer:

D

Step-by-step explanation:

raspberry : lemon lime soda::8:1

Answer:

The price of one reusable bottle is $8.12

Step-by-steetp explanation:

Ms stone wanted to purchase two reusable bottles but discovered she had only ⅝of the Mone and that ⅝ is equal to $ 10.15.

So the cost of what she wants to purchase will be called x.

Mathematically

⅝ * x = 10.15

X = (10.15*8)/5

X = 81.2/5

X= 16.24

The price of the two bottles is $16.24

So the price if one bottle will be calculated as follows.

2 bottles=$ 16.24

One bottle= $16.24/2

One bottle= $8.12

The price of one reusable bottle is $8.12

Answer:

  B

Step-by-step explanation:

You only need to look at the comparison symbol (≤) to determine the correct graph. It tells you the shading is below the boundary line, and the boundary line is included in the solution region (a solid line).

The shading is below the line because y-values are less than (or equal to) values on the line.

Choice B matches the attached graph.

Answer:

it is graph b

Step-by-step explanation:

Answer:

Lateral Surface Area = 15.072 [tex]mm^2[/tex]

Step-by-step explanation:

Given that:

Base of Cylinder has radius, r = 1.2 mm

Height, h = 2 mm

To find:

Lateral Surface area of cylinder = ?

Solution:

We know that total surface area of a cylinder is given by:

[tex]TSA = 2\pi r^2+2\pi rh[/tex]

Here [tex]2\pi r^2[/tex] is the area of two circular bases of the cylinder and

[tex]2\pi rh[/tex] is the lateral surface area.

Please refer to the attached image for a better understanding of the Lateral and Total Surface Area.

So, LSA = [tex]2\pi rh[/tex]

[tex]\Rightarrow LSA = 2 \times 3.14 \times 1.2 \times 2\\\Rightarrow LSA = 6.28 \times 2.4\\\Rightarrow LSA = 15.072\ mm^2[/tex]

So, the answer is:

Lateral Surface Area of given cylinder = 15.072 [tex]mm^2[/tex]

Answer:

LSA  =   24.1

Step-by-step explanation:

I just did this, I dont know how to upload my work, but It marked it as right and gave me the green check mark. The answer is 24.1

Answer:

D

Step-by-step explanation:

Answer:

  6/(49π) ≈ 0.03898 m/min

Step-by-step explanation:

  V = πr²h . . . . formula for the volume of a cylinder

  dV/dt = πr²·dh/dt . . . . differentiate to find rate of change

Solving for dh/dt and filling in the numbers, we have ...

  dh/dt = (dV/dt)/(πr²) = (6 m³/min)/(π(7 m)²) = 6/(49π) m/min

  dh/dt ≈ 0.03898 m/min

Answer:

a) Fx=-5N  Fy=-5*sqrt(3) N   b) Fx= 5*sqrt(3) N    Fy=-5N

c) Fx=-5*sqrt(2) N    Fy=-5*sqrt(2)   N

Step-by-step explanation:

The arrow's F ( weight) component on axle x  is Fx= F*sinA  and on axle y is

Fy=F*cosA

a) The x component and y component both are opposite directed to axle x and axle y accordingly.  So both components are negative.

So Fx = - 10*sin(30)= -5 N      Fy= -10*cos(30)= -10*sqrt(3)/2= -5*sqrt (3) N

b) Now the x component  is co directed to axle x , and y component is opposite directed to axle y.

So x component is positive and y components is negative

So Fx = 10*sin(60)= 5*sqrt(3) N       Fy= -10*cos(60)= -10*1/2= -5 N

c)The x component and y component both are opposite directed to axle x and axle y accordingly.  So both components are negative.

So Fx = - 10*sin(45)= -5*sqrt(2)  N    

 Fy= -10*cos(45)= -10*sqrt(2)/2= -5*sqrt (2) N

Answer:

6

Step-by-step explanation:

We want to find the units digit of [tex]2^{4000}[/tex]. Let's first look for a pattern:

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

[tex]2^{2}=4[/tex]

[tex]2^{3}=8[/tex]

[tex]2^{4}=16[/tex]

[tex]2^{5}=32[/tex]

[tex]2^{6}=64[/tex]

[tex]2^{7}=128[/tex]

[tex]2^{8}=256[/tex]

...and so on

Notice the units digits: 2, 4, 8, 6, 2, 4, 8, 6, ... It repeats every four!

This means that for every exponent of 2 that is a multiple of 4 (like 4000 in the problem), the units digit will always be the fourth number in the repeating pattern: 6.

The answer is thus 6.

~ an aesthetics lover

Answer:

4

Step-by-step explanation:

(segment piece) x (segment piece) =   (segment piece) x (segment piece)

JN* NK = LN * NM

3x = 2*6

3x = 12

Divide by 3

3x/3 =12/3

x =4

The 55th term of the 7, 10, 13, 16, ... arithmetic sequence is a(55) = 169.

This is an arithmetic sequence since there is a common difference between each term. In this case , adding 3 to the previous term in the sequence gives the next term.

a(n) = a(1) + d( n- 1)

d = 3

This is the formula of an arithmetic sequence.

an = a(1) + d( n- 1)

Substitute in the values of

a(1) = 7 and

d = 3

a(n) = 7 + 3 ( n- 1)

Simplify each term.

a(n) = 7 + 3n- 3

Subtract 3 from 7.

a(n) =  3n + 4

The nth term = 3n + 4. The formula for the nth term of an arithmetic progression is a(n) = dn + a(1) - d. Therefore in your sequence, the difference d = 3, and the first term a(1) = 7.

Substitute in the value of n to find the nth term.

a(55) = 3 (55) + 4

Multiply 3 by 55 .

a(55) = 165 + 4

Add 165 and 4.

a(55) = 169

Thus , The 55th term in the arithmetic progression of 7, 10, 13, 16,... is a(55) = 169.

To learn more about Aritmetic sequence

https://brainly.com/question/6561461

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Answer:

(A)  (-19,-8)

Step-by-step explanation:

Given that the graph is an inverse variation.

The equation of variation is:

[tex]x=\dfrac{k}{y}[/tex]

Since point (-8, -19) is on the graph

[tex]-8=\dfrac{k}{-19}\\k=152[/tex]

Therefore, the equation connecting x and y is:

[tex]x=\dfrac{152}{y}[/tex]

[tex]\text{When y=-8},x=\dfrac{152}{-8}=-19\\\\\text{When y=19},x=\dfrac{152}{19}=8\\\\\text{When y=8},x=\dfrac{152}{8}=19\\\\\text{When y=-19},x=\dfrac{152}{-19}=-8[/tex]

Therefore, the point that is also on the graph is:

(A)  (-19,-8)

Complete Question:

Find the directional derivative of g(x,y) = [tex]x^2y^5[/tex]at the point (1, 3) in the direction toward the point (3, 1)

Answer:

Directional derivative at point (1,3),  [tex]D_ug(1,3) = \frac{162}{\sqrt{8} }[/tex]

Step-by-step explanation:

Get [tex]g'_x[/tex] and [tex]g'_y[/tex] at the point (1, 3)

g(x,y) = [tex]x^2y^5[/tex]

[tex]g'_x = 2xy^5\\g'_x|(1,3)= 2*1*3^5\\g'_x|(1,3) = 486[/tex]

[tex]g'_y = 5x^2y^4\\g'_y|(1,3)= 5*1^2* 3^4\\g'_y|(1,3)= 405[/tex]

Let P =  (1, 3) and Q = (3, 1)

Find the unit vector of PQ,

[tex]u = \frac{\bar{PQ}}{|\bar{PQ}|} \\\bar{PQ} = (3-1, 1-3) = (2, -2)\\{|\bar{PQ}| = \sqrt{2^2 + (-2)^2}\\[/tex]

[tex]|\bar{PQ}| = \sqrt{8}[/tex]

The unit vector is therefore:

[tex]u = \frac{(2, -2)}{\sqrt{8} } \\u_1 = \frac{2}{\sqrt{8} } \\u_2 = \frac{-2}{\sqrt{8} }[/tex]

The directional derivative of g is given by the equation:

[tex]D_ug(1,3) = g'_x(1,3)u_1 + g'_y(1,3)u_2\\D_ug(1,3) = (486*\frac{2}{\sqrt{8} } ) + (405*\frac{-2}{\sqrt{8} } )\\D_ug(1,3) = (\frac{972}{\sqrt{8} } ) + (\frac{-810}{\sqrt{8} } )\\D_ug(1,3) = \frac{162}{\sqrt{8} }[/tex]

Answer:

x=4200, y=2700

Step-by-step explanation:

let x be first account

y the second

x+y=6900

0.03x+0.08y=342

solve by addition/elimination)

multiply first equation by 0.03

0.03x+0.03y=207  subtract from second

0.03x+0.03y-0.03x-0.08y=207-342

0.05y=135

y=2700, x=4200

Answer/Step-by-step explanation:

*The six raw data values in the second row are for teens are: 14, 15, 15, 15, 16, and 16

*There are 6 raw data values in the 20's represented in the 3rd row. They are: 25, 25, 27, 28, 28, and 28

*There are 3 raw data values in the 30's that are represented in the 4th row. They are: 35, 36, and 36.

*There are 0 raw data values in the 40's represented in the 5th row.

*There are 21 raw data values in the entire data set. They are:

1, 2, 3, 7, 9, 14, 15, 15, 15, 16, 16, 25, 25, 27, 28, 28, 28, 35, 36, 36, and 50.

Answer:

  y

Step-by-step explanation:

The expression

  y = f(x)

tells you that y is the dependent variable, and that it depends on x, the independent variable. The independent variable is always the function argument. Any variable that depends on that is the dependent variable.

Answer:

2

Step-by-step explanation:

5÷2 1/5 = 2

Answer:

2 3/11

Step-by-step explanation:

To find the original number, we need to divide 5 by 2 1/5.

5/ 2 1/5

Convert 2 1/5 to an improper fraction:

11/5

5/ 11/5

When dividing fractions, we can multiply the first number by the reciprocal of the second one to get the answer.

5*5/11

25/11

2 3/11

Answer:

30 m^3

Step-by-step explanation:

Answer:

B. 20m3

Step-by-step explanation:

i dont know if its correct, hope it is tho

Answer:

The value will decrease.

Step-by-step explanation:

Answer:

B) [tex]x^2-3x+15[/tex]

Step-by-step explanation:

[tex]7x^2+6x-9x-6x^2+15=\\7x^2-6x^2+6x-9x+15=\\x^2+6x-9x+15=\\x^2-3x+15[/tex]

A) [tex]x^2+15x+15[/tex]

B) [tex]x^2-3x+15[/tex]

C) [tex]13x^2 + 3x + 15[/tex]

D) [tex]x^4-3x + 15[/tex]

━━━━━━━☆☆━━━━━━━

▹ Answer

B. x² - 3x + 15

▹ Step-by-Step Explanation

7x² + 6x - 9x - 6x² + 15

Collect like terms

x² + 6x - 9x + 15

Subtract

x² - 3x + 15

Final Answer

x² - 3x + 15

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer:

Vertical Line

Step-by-step explanation:

A vertical line is x = [a number]

A horizontal line is y = [a number]

Answer:

vertical line

Step-by-step explanation:

A vertical line is of the form

x =

All the x values are the same and the y value changes

x = -4 is a vertical line

Answer:

given,

AB= 17

AC= 8

angle BCA =90°

as it is a Right angled triangle ,

taking reference angle BAC

we get,h=AB=17

b=AC=8

p=BC=?

now by the Pythagoras theorem we get,

p=

[tex] \sqrt{h { }^{2} - b {}^{2} } [/tex]

so,p=

[tex] \sqrt{17 {}^{2} - 8 {}^{2} } [/tex]

[tex] = \sqrt{225} [/tex]

=15 is the answer....

hope its wht u r searching for....

Answer:

(a) remainder is -40

(b) The remaining zeroes are (x+3) and (x-3)

Step-by-step explanation:

p(x) = x^4 - 2x^3 -7x^2 + 18x – 18

(a) Remainder of P(x) / (x+1) can be found using the remainder theorem, namely

let x + 1 = 0 => x = -1

remainder

= P(-1)

= (-1)^4 - 2(-1)^3 -7(-1)^2 + 18(-1) – 18

= 1 +2 -7-18-18

= -40

remainder is -40

(b)

If one zero is 1-i, then the conjugate 1+i is another zero.

in other words,

(x-1+i) and (x-1-i) are both factors.

whose product = (x^2-2x+2)

Divide p(x) by (x^2-2x+2) gives

p(x) by (x^2-2x+2)

= (x^4 - 2x^3 -7x^2 + 18x – 18) / (x^2-2x+2)

= x^2 -9

= (x+3) * (x-3)

The remaining zeroes are (x+3) and (x-3)